D.2, Auy Cecest, i Kes, Cv, Shece WAHed. May, 177 °7 € SHORE PROTECTION MANUAL VOLUME Il US Army Corps of Engineers Coastal Engineering Research Center DEPARTMENT OF THE ARMY Waterways Experiment Station, Corps of Engineers PO Box 631 Vicksburg, Mississippi 39180 Approved For Public Release; Distribution Unlimited Prepared for DEPARTMENT OF THE ARMY US Army Corps of Engineers Washington, DC 20314 {T EhbLGOO TOEO O ILO 1OHM/18IN OEMCO . dJaque) your 186L of uo! 31 pe SHORE PROTECTION MANUAL VOLUME II (Chapters 6 Through 8; Appendices A Through D) DEPARTMENT OF THE ARMY Waterways Experiment Station, Corps of Engineers COASTAL ENGINEERING RESEARCH CENTER 1984 Fourth Edition For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 (2-part set; sold in sets only) TABLE OF CONTENTS VOLUME I CHAPTER 1. INTRODUCTION TO COASTAL ENGINEERING I—Overview of Coastal Engineering and the SPM, page 1-1; II—The Coastal Area, page 1-2; I]I—The Beach and Nearshore System, page 1-4; 1V—Dynamic Beach Response to the Sea, page 1-9; V—Causes of Shoreline Erosion, page 1-15; VI—Coastal Protection Methods and Navigation Works, page 1-17; VII—Conservation of Sand, page 1-25; Literature Cited, page 1-27 CHAPTER 2. MECHANICS OF WAVE MOTION I—Introduction, page 2-1; II—Wave Mechanics, page 2-1; III—Wave Refraction, page 2-60; IV—Wave Diffraction, page 2-75; V—Wave Reflection, page 2-109; VI—Breaking Waves, 2-129; Literature Cited, page 2-137; Bibliography, page 2-147 CHAPTER 3. WAVE AND WATER LEVEL PREDICTIONS I—Introduction, page 3-1; II—Characteristics of Ocean Waves, page 3-1; III—Wave Field, page 3-19; 1V—Estimation of Surface Winds for Wave Prediction, page 3-27; V—Simplified Methods for Estimating Wave Conditions, page 3-39; VI—Wave Forecasting for Shallow Water, page 3-55; VII—Hurricane Waves, page 3-77; VIII—Water Level Fluctuations, page 3-88; Literature Cited, page 3-130; Bibliography, page 3-140 CHAPTER 4. LITTORAL PROCESSES I—Introduction, page 4-1; II—Littoral Materials, page 4-12; III—Littoral Wave Conditions, page 4-29; IV—Nearshore Currents, page 4-46; V—Littoral Transport, page 4-55; VI—Role of Foredunes in Shore Processes, page 4-108; VII—Sediment Budget, page 4-113; VIII— Engineering Study of Littoral Processes, page 4-133; IX—Tidal Inlets, page 4-148; Literature Cited, page 4-182; Bibliography, page 4-208 CHAPTER 5. PLANNING ANALYSIS I—General, page 5-1; II—Seawalls, Bulkheads, and Revetments, page 5-2; I1I—Protective Beaches, page 5-6; [V—Sand Dunes, page 5-24; V—Sand Bypassing, page 5-26; VI—Groins, page 5-35; VII—Jetties, page 5-56; VIII—Breakwaters, Shore-Connected, page 5-58; [X—Break- waters, Offshore, page 5-61; X—Environmental Considerations, page 5-74; Literature Cited, page 5-75 VOLUME II CHAPTER 6. STRUCTURAL FEATURES I—Introduction, page 6-1; II—Seawalls, Bulkheads, and Revetments, page 6-1; III—Protective Beaches, page 6-14; 1V—Sand Dunes, page 6-37; V—Sand Bypassing, page 6-53; VI—Groins, page 6-76; VII—Jetties, page 6-84; VIII—Breakwaters, Shore-Connected, page 6-88; IX—Break- waters, Offshore, page 6-93; X—Construction Materials and Design Practices, page 6-95; Literature Cited, page 6-99 CHAPTER 7. STRUCTURAL DESIGN: PHYSICAL FACTORS I—Wave Characteristics, page 7-1; 1I—Wave Runup, Overtopping, and Transmission, page 7-16; I1I—Wave Forces, page 7-100; IV—Velocity Forces—Stability of Channel Revetments, page 7-249; V—Impact Forces, page 7-253; VI—Ice Forces, page 7-253; VII—Earth Forces, page 7-256; Literature Cited, page 7-261; Bibliography, page 7-277 CHAPTER 8. ENGINEERING ANALYSIS: CASE STUDY I—Introduction, page 8-1; 1I—Statement of Problem, page 8-1; III—Physical Environment, page 8-1; 1V—Preliminary Design, page 8-46; V—Computation of Potential Longshore Transport, page 8-85; VI—Beachfill Requirements, page 8-90; Literature Cited, page 8-93 APPENDIX A. GLOSSARY, page A-1 APPENDIX B. LIST OF SYMBOLS, page B-1 APPENDIX C. MISCELLANEOUS TABLES AND PLATES, page C-1 APPENDIX D. INDEX, page D-1 Act CHAPTER 6 Structural Features Palm Beach, Florida, 3 October 1964 . “ ’ . : - 9 ra oe? be =a irs), in 4 i ; a oe ; t a Y 7 es, hen > : - ' a] 7 coi es i : : - i = 74 a a ee eS ee a cou 4 ANTS aren i Lat use. mie)" coke epee ae: E11 IV VI \VIELL VIII IX CONTENTS CHAPTER 6 STRUCTURAL FEATURES INTRODUCTION. 6.2 cccccccccccccccccesccceseccsecsscecccccscccscccvcce SEAWALLS, BULKHEADS, AND REVETMENTS...cccccccccccccvccccccccccsccce ompLAy/ PC Sloiekeliotolerokslatelstelatelelotelerololofelclal «late clehelkelelololelaralsieoleleleieleloielelss/eisiellolele)< PMOCleCtTON Ot OEEUCE Ural Mrly PC leteleleleleolelefelelelclelolslelolelelel sich slelolelelolelelereic PROTECTIVE BEACHES... cccscccccccccccccccccccvecccrccccscscscccescese Ig CeoneicallMeraterelciclalelenehetaickelelelelelerelotelclelelelclelorelslotoielelelelelelelelcielatclelcicierelcieleicre ZomE Xs tin lm GOte CtivembeaCheS erereleleleleloleleletolcielolelclclelolelelolelslcliclc/elelelslolels SAND DUNES .cccccccccccccccccccccccccccceccsecccccccscceescscesccece Me OANGMMONCMEMt-elolelonelekelclelelelelollaletolelclalelelcleleleleleteletelelolsielictolslslelolefehelelelelele Ze Dune FOrmation. .cccccccccccccccccccccccccsccccccscecccevcccece 36) Dune Construction Using, Sand Hemline cree. \ce1s1s1e) +) e1)e)ole/e ele) o/0) elelelelele AWeDuUNne sConstLUuctlonmUSINes WepetatdlOMnerereletclelelslelerolelaleiel slelerelsisle/orelelore SVAN) ENIPASSIUNG 5 og ao nocoOD DDD DObDD DDD DODDD DODD OODNOO0D0d000000000000 le Bixed@ Bypassiney Pllamt'sjcjere 10 41016) eves) s!ele)(s)e1sl's).0)e\(6) s\/0)/+)0/1 0s) sc) )e\elele A PlOAtnoMBy passim mE amitsSlereleiclielelelelolelelelevelelcVelelelelelelelclelelslclelelelelelelelels BAdG ttellonaleeBy passin om SCHEME'S|steiele)sielels)e\eleleleVelelelelelel el clelelelelelelelclevelels)e GROMNSrereteretokeioielevercietotelor sve! ollel oelere) sie1s1 olfe)e1 (elle ella" s\ oite)/oliefial olelleVolelere) olelele) set siic: slel's eis) se Ik IY, PC'S iololetalakelelelaleleleielevelelelolclels/isjelelclelelalololeiclelalevelolclelelolelelcvlelelelelele/clelelsleicle 2 SOUAGELON CE IGGoooocod0Go0DobODOOGD ODD DODD DODD DO ODOOOOnDOOOOO Sh DOSAYTNG 6 COS HOOOGO00OHOOOOU DDO BO OUDOD ODDO OOOOUGOODODODDDOO00000 JHMEISUE SlolonelNeKeKolons) cVeolelole! slelelslajlelalelelleleleielictelals) ei olelelclelclelelevelelleyelelslelolelelelerorslelciolote 1S MVD Sionelekalelokevetatelelnierelelelelelclexersiele cielo) clots) clever eletel oleic) (elrcllel sielielievelel ele) cl'eleleVelere) BREAKWATER Sh SHORE=CONNE CIED ors cieieie)s)ellellole)iele)els)e\olel slfelle\el'slelieels/eleve) see) ois’ o\leele lle IBVPESooccosocs00 RA boD0 DDD CONDO ODDO HOODOO ODD UOnDODOODDOOOODOOODS BREAKWATER S pa OBB OHOREstetekeielel oletalclelencleredoierelclensievoisielevelcvelevelerel el cloieley elekevelelcve’e Newey PC Slelevelelolevelelelelersicievelelelevelererercier el cvevoronelelelereerelcl sieve) evelel cleheveveiereverercloncleye ZwocementedWOLtshore sBEeakwalterxSisje sie). cece c/s) s)o/e/elclalelele) ole) eleielelsiclsleie)e CONSTRUCTION MATERIALS AND DESIGN PRACTICES......cccccccccccccccecs Wee CONCEEECIiejerererote cre: cierocieiekovetorerevere eretetevelclelotersvcve ts level aleveteteveteravevere ie ie chete Dee Ste Olli terevetetctercvavotovevevalersiekerctovoleteucva love cite levalera ieee rare oceuaeiie leveigreieaverereleuevere Soe A MYST ay Sight OG CIO CIC COG OO:0I0 CRU OIA CIS.OLIOI 0 CODCOD DIO ICO ICI eR IORICR OG 4 StOMC verercvalokenct sietelelclre:oorevere ener enevenecslevalecnilenaievele lovete:e: sie) eyel eieverevevete aievenetercvete Jo COOUETNAS coccasnDD DD ObORnODDD OUD OOOO DDD ODODDD AO OOD OD AD0000000 OneMiscellancous Weston Pract COSiecle\cleleleleieiele |e eiele) siclelelelelcieleve|eiele)siciels REM RAT URE ps GISTEDcverel ce cVelellelie ololle’s)s}o\ Veleieieloiels/elelcle/elelelelsisleleleleielelele\e)s)se/e\ele/els CONTENTS--Continued TABLES CERC research reports on the geomorphology and sediments of the Inner Continental Shelli jrjcmmtcrticteileis cs + + 0c occ 00000 c 00s clciniosisioinuinia Beach) restoration) projects anmthesUniited States). a. 20-kg by omitting rock on landside Figure 6-4. Rubble-mound seawall. 6-5 SISSY Note: Dimensions and details to be SUS : : : t = YN determined by particular site = ) conditions. =| »|| | Large Riprap Stone Small Stone B Water Level Figure 6-5. Rubble-mound seawall (typical stage placed). Bulkheads are generally either anchored vertical pile walls or gravity walls; i.e., cribs or cellular steel-pile structures. Walls of soldier beams and lagging have also been used at some sites. Three structural types of bulkheads (concrete, steel, and timber) are shown in Figures 6-6, 6-7, and 6-8. Cellular-steel sheet-pile bulkheads are used where rock is near the surface and adequate penetration is impossible for the anchored sheet-pile bulkhead illustrated in Figure 6-7. When vertical or nearly vertical bulkheads are constructed and the water depth at the wall is less than twice the anticipated maximum wave height, the design should provide for riprap armoring at the base to prevent scouring. Excessive scouring can endanger the stability of the wall. The structural types of revetments used for coastal protection in exposed and sheltered areas are illustrated in Figures 6-9 to 6-12. There are two types of revetments: the rigid, cast-in-place concrete type illustrated in Figure 6-9 and the flexible or articulated armor unit type illustrated in Figures 6-10, 6-11, and 6-12. A rigid concrete revetment provides excellent bank protection, but the site must be dewatered during construction so that the concrete can be placed. A flexible structure also provides excellent bank protection and can tolerate minor consolidation or settlement without structural failure. This is true for the quarrystone or riprap revetment and to a lesser extent for the interlocking concrete block revetment. Both the articulated block structure and the quarrystone or riprap structure allow for the relief of hydrostatic uplift pressure generated by wave action. The underlying geotextile filter and gravel or a crushed-stone filter and bedding layer relieve the pressure over the entire foundation area rather than through specially constructed weep holes. Interlocking concrete blocks have been used extensively for shore protec- tion in Europe and are finding applications in the United States, particularly as a form of relatively low-cost shore protection. MTypically, these blocks are square slabs with shiplap-type interlocking joints as shown in Figure 6- ile The joint of the shiplap type provides a mechanical interlock with adjacent blocks. 6-6 Virginia Beach, Virginia (Mar. 1953) 6m Concrete walkway Headwall cast in place Access Stairs Mean Sea Level SECTION A-A So 5 ; : Precast king pile im 5m Figure 6-6. Concrete slab and king-pile bulkhead. 6-7 . en on H nm aa | ce $ . “> 2 es ue ’ Chesapeake Bay, Maryland (1972) Topsoil and Seed 0.5m Min. Elev. 2.7m Elev. 2.7m 0.3m Min. Quarrystone Armor oD y Poured Concrete (Contraction Jt. every 3m) Gravel Blanket 0.3m Thick Existing Beach Over Regraded Bank Elev. 0.0 SL AB Elev. -0.3m Figure 6-10. Quarrystone revetment. 6= 8 Jupiter Island, Florida (1965) (photo, courtesy of Carthage Mills Inc.) 5.2m 13cm to 2.5cm Grovel on Geotextile Filter O.2m Thick Reinf. Concrete Cap 30cm 1.8-to 3.7-metric AGO 35cm ” ton stones —____ - cm ae MSL = 0.0m NG = zl hy re) € Ww Geotextile Filter as For Down a = PLAN VIE os Possible | Prestressed Concrete Pile eal (Sicmy eas -3.4m Sicm 13cm ' Arg —t SECTION A-A rare 30cm Block Shiplap Joint tux SECTION A-A i_O----1— 35 cm Block 13cm 23cm Figure 6-11. Interlocking concrete-block revetment. Cedarhurst, Maryland (1970) Finished Grade 0.3m El. |.2m El. 0.9m Tongue-and-Groove Joint : os ~ = Interlocking Concrete co CS ee They function as a reservoir of sand nourishing beaches during high water and are a levee preventing high water and waves from damaging the backshore areas. They are valuable, nonrigid shore protection structures created naturally by the combined action of sand, wind, and vegetation, often forming a continuous protective system (see Fig. 6-25). Figure 6-25. Foredune system, Padre Island, Texas. 1. Sand Movement. Winds with sufficient velocity to move sand particles deplete the exposed beach by transporting sand in the following three ways. 6-37 (a) Suspension: Small or light grains are lifted into the airstream and are blown appreciable distances. (b) Saltation: Sand particles are carried by the wind in a series of short jumps along the beach surface. (c) Surface Creep: Particles are rolled or bounced along the beach as a result of wind forces or the impact of descending saltating particles. These natural transportation methods effectively sort the original beach material. Smaller particles are removed from the beach and dune area. Medium-sized particles form the foredunes. Larger particles remain on the beach. Although most sand particles move by saltation, surface creep may account for 20 to 25 percent of the moved sand (Bagnold, 1942). 2. Dune Formation. Dune building begins when an obstruction on the beach lowers wind velocity causing sand grains to deposit and accumulate. As the dune builds, it becomes a major obstacle to the landward movement of windblown sand. In this manner, the dune functions to conserve sand in close proximity to the beach system. Foredunes are often created and maintained by the action of the beach grasses, which trap and stabilize sand blown from the beach. Foredunes may be destroyed by the waves and high water levels associated with severe storms or by beachgrass elimination (induced by drought, disease, or overgrazing), which thereby permits local "blowouts." Foredune management has two divisions--stabilization and maintenance of naturally occurring dunes, and the creation and stabilization of protective dunes where they do not already exist. Although dunes can be built by use of structures such as sand fences, another effective procedure is to create a stabilized dune through the use of vegetation. Current dune construction methodology is given by Knutson (1977) and Woodhouse (1978). 3. Dune Construction Using Sand Fencing. Various mechanical methods, such as fencing made of brush or individual pickets driven into the sand, have been used to construct a foredune (McLaughlin and Brown, 1942; Blumenthal, 1965; Jagschitz and Bell, 1966a; Gage, 1970). Relatively inexpensive, readily available slat-type snow fenc- ing (Fig. 6-26) is used almost exclusively in artificial, nonvegetative dune construction. Plastic fabrics have been investigated for use as sand fences (Savage and Woodhouse, 1969). Satisfactory, but short-term, results have been obtained with jute-mesh fabric (Barr, 1966). Field tests of dune building with sand fences under a variety of condi- tions have been conducted at Cape Cod, Massachusetts, Core Banks, North Carolina, and Padre Island, Texas. The following are guidelines and sugges-— tions based on these tests and observations recorded over the years: (a) Fencing with a porosity (ratio of area of open space to total projected area) of about 50 percent should be used (Savage and Woodhouse, 1969). Open and closed areas should be smaller than 5 6-38 - “ . = - - ou. = Figure 6-26. Erecting snow-type sand fencing. centimeters in width. The standard wooden snow fence appears to be the most practical and cost effective. (b) Only straight fence alinement is recommended (see Fig. 6-27). Fence construction with side spurs or a zigzag alinement does not increase the trapping effectiveness enough to be economical (Savage, 1962; Knutson, 1980). Lateral spurs may be useful for short fence runs of less than 150 meters (500 feet) where sand may be lost around the ends (Woodhouse, 1978). (c) Placement of the fence at the proper distance shoreward of the berm crest may be critical. The fence must be far enough back from the berm crest to be away from frequent wave attack. Efforts have been most successful when the selected fence line coincided with the natural vegetation or foredune line prevalent in the area. This distance is usually greater than 60 meters shoreward of the berm crest. (d) The fence should parallel the shoreline. It need not be perpendicular to the prevailing wind direction and will function even if constructed with some angularity to sand-transporting winds. (e) With sand moving on the beach, fencing with 50-percent porosity will usually fill to capacity within 1 year (Savage and Woodhouse, 1969). The dune will be about as high as the fence. The dune slopes will range from about 1 on 4 to 1 on 7, depending on the grain size and wind velocity. (£) Dunes are usually built with sand fencing in one of two ways: (1) By installing a single fence and following it with additional %.. 7 wp Figure 6-27. Snow-type sand fencing filled to capacity, Padre Island, Texas. single-fence lifts as each fence fills (Fig. 6-28); or (2) by installing double-fence rows with the individual fences spaced about 4 times the fence height (4h) apart and following these with succeeding double-row lifts as each fills (Fig. 6-29). Single rows of fencing are usually the most cost-effective, particularly at the lower windspeeds, but double fences may trap sand faster at the higher windspeeds. (g) Dune height is increased most effectively by positioning the succeeding lifts near the crest of an existing dune (see Fig. 6-30). However, under this system, the effective height of succeeding fences decreases and difficulties may arise in supporting the fence nearest the dune crest as the dune becomes higher and steeper. (h) Dune width is increased by installing succeeding lifts parallel to and about 4h away from the existing fence (Fig. 6-31). The dune may be widened either landward or seaward in this way if the dune is unvegetated. (i) Accumulation of sand by fences is not constant and varies widely with the location, the season of the year, and from year to year. Fences may remain empty for months following installation, only to fill within a few days by a single period of high winds. In order to take full advantage of the available sand, fences must be observed regularly, repaired if necessary, and new fences installed as existing fences fill. Usually where appreciable sand is moving, a single, 1.2-meter fence will fill within 1 year. 6-40 (j) The trapping capacity of the initial installation and succeeding lifts of a 1.2-meter-high sand fence averages between 5 and 8 cubic meters per linear meter (2 to 3 cubic yards per linear foot). (k) CERC’s experience has been that an average of 6 man-hours are required to erect 72 meters (235 feet) of wooden, picket-type fence or 56 meters (185 feet) of fabric fence when a six-man crew has materials available at the site and uses a mechanical posthole digger. (1) Junk cars should not be used for dune building. They are more expensive and less effective than fencing (Gage, 1970). Junk cars mar the beauty of a beach and create a safety hazard. Tay a 4 - 40 months 68 months wn *e ca 12 J \g es S ____ Sound A = S Ocean tm Tf 3 = 10 » q *, ‘ie ~ = pe 16 months 2 . 3S s Vis p Le x 0 months & 2 months \ a 6 A 4 -—_——--—— | peerETeTesteareeeeee 2 o Too 120 140 160 ' tt) 220 240 260 L I | | IL | 30 40 50 60 70 80 (m) Distonce from base line Figure 6-28. Sand accumulation by a series of four single-fence lifts, Outer Banks, North Carolina (Savage and Woodhouse, 1969). 6-41 (m) Elevation above MSL Figure 6-29. 52 months 2 27 months Sound 30 40 50 60 70 80 (m) Distance from bose line Sand accumulation by a series of three double-fence lifts, Outer Banks, North Carolina (Savage and Woodhouse, SAND VOLUME m3/lin m of beach (yds3/lin ft of beach) SCHEDULE FENCE ERECTION Time (Months) Cumulative Interval Time (Months) Lift Number 0 0 0 0 | 12 85 (3.4) 85 (3.4) 12 2 24 153 (6.1) 68 (2.7) 24 3 36 26.1 (10.4) 10.8 (4.3) (m) (ft) Elevation above MSL 0 Figure 6-30. Distance from Base Line Sand fence dune with lifts positioned near the crest, Padre Island, Texas. 6-42 SAND VOLUME m3/lin m of beach (yds3/lin ft of beach) SCHEDULE FENCE ERECTION Time (Months) Cumulative Interval Time (Months) Lift Number 0 0 te) 0 | 12 6.0 (2.4) 6.0 (2.4) 12 2 24 16.3 (6.5) 10.3 (4.1) 24 3,4 36 22.9 (9.1) 65 (2.6) (m) (ft) Elevation above MSL Distance from Base Line Figure 6-31. Sand fence dune with lifts positioned parallel to the existing fence, Padre Island, Texas. (m) Fence-built dunes must be stabilized with vegetation or the fence will deteriorate and release the sand (Fig. 6-32). While sand fences ini- tially trap sand at a high rate, established vegetation will trap sand at a rate comparable to multiple lifts of sand fence (Knutson, 1980). The construction of dunes with fence alone is only the first step in a two- step operation. Fences have two initial advantages over planting that often warrant their use before or with planting: (a) Sand fences can be installed during any season and (b) the fence is immediately effective as a sand trap once it is installed. There is no waiting for trapping capacity to develop in comparison with the vegetative method. Consequently, a sand fence is useful to accu- mulate sand before planted vegetation is becoming established. 4. Dune Construction Using Vegetation. a. Plant Selection. Few plant species survive in the harsh beach environment. The plants that thrive along beaches are adapted to conditions that include abrasive and accumulating sand, exposure to full sunlight, high surface temperatures, occasional inundation by saltwater, and drought. The plants that do survive are long-lived, rhizomatous or stoloniferous perennials with extensive root systems, stems capable of rapid upward growth through accumulating sand, and tolerance of salt spray. Although a few plant species 6-43 Figure 6-32. Sand fence deterioration due to exposure and storms. have these essential characteristics, one or more suitable species of beach grasses occur along most of the beaches of the United States. The most frequently used beach grasses are American beachgrass (Ammophtla breviligulata) along the mid- and upper-Atlantic coast and in the Great Lakes region (Jagschitz and Bell, 1966b; Woodhouse and Hanes, 1967; Woodhouse, 1970); European beachgrass (Ammophtla arenaria) along the Pacific Northwest and California coasts (McLaughlin and Brown, 1942; Brown and Hafenrichter, 1948; Kidby and Oliver, 1965; U.S. Department of Agriculture, 1967); sea oats (Uniola panteculata) along the South Atlantic and gulf coasts (Woodhouse, Seneca, and Cooper, 1968; Woodard, et al., 1971); panic grasses (Panicum amarum) and (P. amarulum) along the Atlantic and gulf coasts (Woodhouse, 1970; Woodard, et al., 1971). Table 6-3 is a regional summary of the principal plants used for dune stabilization. b. Harvesting and Processing. The plants should be dug with care so that most roots remain attached to the plants. The clumps should be separated into transplants having the desired number of culms (stems). Plants should be cleaned of most dead vegetation and trimmed to a length of about 50 centi- meters (20 inches) to facilitate mechanical transplanting. Most plants may be stored several weeks if their bases are wrapped with wet burlap, covered with moist sand, or placed in containers with 3 to 5 centimeters of fresh water. Survival of sea oats is reduced if stored more than 3 to 4 days. To reduce weight during transport, the roots and basal nodes may be dipped in clay slurry and the plants bundled and wrapped in 6-44 Table 6-3. Regional adaption of foredune plants. Major species American beachgrass European beachgrass Sea oats Bitter panicum Saltmeadow cordgrass American dunegrass Secondary or regional species Seashore elder Bermuda grass Knot grass or seashore paspalum Ice plant Sand verbena Beach bur Wildrye St. Augustine grass Prairie sandreed Beach morning glory 1 - Dominant planted species. 2 - Part of region only. - Valuable in mixture. - Widely distributed, seldom planted. - Valuable, planting methods undeveloped. Specialized uses. 3 4 5 - Stabilization only. 6 7/ 1 Woodhouse (1978). 6-45 reinforced paper. Plants may be kept longer if refrigerated. Plants dug while dormant (winter) and held in cold storage at 1° to 3° Celsius may be used in late spring plantings. ce. Planting and Fertilization. Transplanting techniques for most species of beach grass are well developed. Transplanting is recommended for areas adjacent to the beach berm and for critical areas, such as sites subject to erosion. Most critical areas require densely spaced transplants to ensure successful stabilization. A mechanical transplanter mounted on a tractor is recommended for flat or moderate slopes (see Fig. 6-33). Steep and irregular slopes must be planted by hand. Table 6-4 provides a tabular summary of planting specifications for beach grasses. Figure 6-33. Mechanical transplanting of American beachgrass. 6-46 and drying winds by mulching or frequent irrigation, applicable to most beach areas. Table 6-4. Planting and fertilization summary by regions. Planting Species Stems per hill Spacing 45 to 60 or 102 - 153 kg/ha N graduated 31 - 51 kg/ha Boe 1/3 let year to none American beachgrass In mixture 102 - 153 kg/ha N 31 - 51 kg/ha 0. Bitter panicum 1/3 lst year to none South Atlantic American beachgrass” 45 to 60 or graduated 102 - 153 kg/ha N 31 - 51 kg/ha Po, 31 - 51 kg/has 1l- to 3-yr intervals 45 to 60 or graduated 102 - 153 kg/ha N 31 - 51 kg/ha Po. 31 - 51 kg/ha l- to 3-yr intervals Bitter panicum Sea oats In mixture 102 - 153 kg/ha N 31 - 51 kg/ha 31 - 51 kg/ha LAO l- to 3-yr intervals Saltmeadow cordgrass 45 to 60 or 102 - 153 kg/ha N 31 - 51 kg/ha graduated 31 - 51 kg/ha “oo. l- to 3-yr intervals Bll 102 kg/ha N According to growth 31 kg/ha Os Bitter panicum Feb. to June 20 to 30 1 60 to 90 or graduated 60 to 90 or graduated Sea oats Jan. to Feb. | 20 to 35 1 102 kg/ha N According to growth 31 kg/ha Dee North Pacific 45 or graduated 45 or graduated European beachgrass 41 - 61 kg/ha N According to growth American beachgrass 41 - 61 kg/ha N According to growth 45 or 41 - 61 kg/ha N According to growth graduated 60 or 41 - 61 kg/ha N According to growth broadcast Great Lakes 45 to 60 or graduated (stabilization only) American beachgrass Feb. to 102 - 153 kg/ha N According to growth 31 ~ 51 kg/ha PO, and K O 2 lWoodhouse (1978). 2 carolina coasts only. 3 garly spring is best when temperatures are below 15° Celsius. 4 Ground should be cool and wet. Seeding is practical only when protection can be provided from eroding seeding. nutrients by increased foliage production. sand-trapping capacity. Rates of fertilizer are provided in Table 6-4. Only American beachgrass should be routinely fertilized the second growing season with 56 kilograms per hectare (50 pounds per acre) of fertilizer (nitrogen) in April and again in September. Other species should be fertilized if overall and is therefore not Beach-grass seeds are not generally available from commercial sources, and must be wild harvested during the fall for spring Where field tested, beach grasses have responded to _ supplemental 6-47 This in turn provides greater growth or survival is poor or if plants do not appear healthy. In general, only areas of poor plant growth will require fertilization. During the third growing season, fertilizer can be applied as required to encourage growth. However, sea oats are not responsive to fertilizer after the second season. The response of beach grasses to slow-release fertilizers has been varied and results are inconclusive (Augustine, et al., 1964; Hawk and Sharp, 1967; Woodhouse and Hanes, 1967). d. Disease and Stress. Beach grasses vary in their tolerance to drought, heat, cold, disease, and parasites. Plantings of a species outside its natural geographic zone are vulnerable during periods of environmental stress. American beachgrass is more susceptible to scale infestation when exposure to sandblasting is reduced. Deteriorating stands of American beachgrass, due to scale infestation (Hrtococcus carolinea), have been identified from New Jersey to North Carolina (Campbell and Fuzy, 1972). South of its natural geographic zone (Nags Head, North Carolina), American beachgrass is susceptible to heat (Seneca and Cooper, 1971), and a fungal infection (Marasius blight) is prevalent (Lucas, et al., 1971). South of Virginia, mixed species plantings are desirable and necessary. The slow natural invasion (6 to 10 years) of sea oats to American beachgrass dunes (Woodhouse, Seneca, and Cooper, 1968) may be hastened by mixed species plantings. Thus, with better vegetation cover, the chance of overtopping during storms is reduced. Sea oats and panic grass occur together throughout much of their natural geographic zone. Mixed plantings of sea oats and beach grass are recommended since they produce a thick cover and more dune profile. e. Planting Width. Plant spacing and sand movement must be considered in determining planting width. When little sand is moved for trapping, and plant spacing is dense, nearly all sand is caught along the seaward side of the planting and a narrow-based dune is formed. If the plant spacing along the seaward side is less dense under similar conditions of sand movement, a wider based dune will be formed. However, the rate of plant growth limits the time in which the less dense plant spacing along the seaward side will be effective. The spacing and pattern should be determined by the charac— teristics of the site and the objective of the planting. Functional planting guidelines for the various geographic regions in the United States are given by Woodhouse (1978). The following example illustrates the interrelationship of the planting width, plant spacing, sand volume, and rate of plant growth. American beach- grass planted on the Outer Banks of North Carolina, at 45 centimeters (18 inches) apart with outer spacing of 60 to 90 centimeters (24 to 36 inches), accumulated sand over a larger part of the width of the planting for the first two seasons. By the end of the second season, the plant cover was so exten- sive along the seaward face of the dune that most sand was being trapped within the first 8 meters (25 feet) of the dune. American beachgrass typically spreads outward by rhizomatous (underground stem) growth, and when planted in a band parallel to the shoreline it will grow seaward while trapping sand. Thus a dune can build toward the beach from the original planting. Seaward movement of the dune crest in North Carolina 6-48 is shown in Figures 6-34 and 6-35. This phenomenon has not occurred with the sea oats plantings at Core Banks, North Carolina (Fig. 6-36), or at Padre Island, Texas (Fig. 6-37). The rate of spread for American beachgrass has averaged about 1 meter per year on the landward side of the dune and 2 meters per year on the seaward slope of the dune as long as sand has been available for trapping (see Figs. 6-34 and 6-35). The rate of spread of sea oats is considerably less, 30 centimeters (1 foot) or less per year. Figure 6-35 shows an experiment to test the feasibility of increasing the dune base by a sand fence in a grass planting. The fence was put in the middle of the 30-meter-wide (100-foot) planting. Some sand was trapped while the American beachgrass began its growth, but afterwards little sand was trapped by this fence. The seaward edge of the dune trapped nearly all the beach sand during onshore winds. The landward edge of the dune trapped the sand transported by offshore winds blowing over the unvegetated area landward of the dune. SAND VOLUME m3/lin m of beach (yds3/lin ft of beach) Time (Months) Cumulative Interval 0 0 0 24 12.8 (5.1) 12.8 (5.1) 5| 22.6 (9.0) 9.8 (3.9) 80 39.1 (15.6) 16.6 (6.6) 5 16 Pen See Cee 4 tof ee 1 a esas a ee ~ ae Ll feniesesates 2 [oS SESE aS 10> | | | ; > re | Gi 2 = 8-| = x [iat Gepune oa | Ss Vy ital eat —jlF _ } } 4 ee ee ope = = seg ea Ss 4b SS I bios | Fae f i | | } Ps ee ese elo SES IE ie p= { + = 4 ob Saas 0 20 40 0 10 20 30 40 50 60 (m) Distance from Bose Line Figure 6-34. American beachgrass dune, Ocracoke Island, North Carolina. 6-49 SAND VOLUME m3/lin m of beach (yds 3/lin ft of beach) Time (Months) Cumulative _—_ Interval 0 0 0 32 11.7 (4.7) I1.7 (4.7) 54 22.8 (9.1) 11.0 (4.4) 80 33.6(13.4) 10.8 (4.3) lin cg TET a a me a 4b 4 3 l2e = - 2 10 a © : 3 ; oe = CF = s= = = 2 a rr | 0 Distance from Base Line Figure 6-35. American beachgrass with sand fence, Core Banks, North Carolina. SAND VOLUME m3/lin m of beach (yds>/lin ft of beach) Time (Months) Cumulative Interval (0) 0 0 22 5.0 (2.0) 5.0 (2.0) 36 7.8 (3.1) 2.8 (1.1) 55 14.0 (5.6) 63 (2.5) 5 ss23 Za ie fSimaes seen aeese l a 253 3 Seale oc cs 5 = a 3 w | 0 Distance from Base Line Figure 6-36. Sea oats dune, Core Banks, North Carolina. 6-50 SAND VOLUME (yds>/lin ft of beach) Time (Months) Cumulative Interval le} (0) (0) 36 296(11.8) 296 (11.8) 96 72.2 (28.8) 42.6 (17.0) Gu/f of Mexico 60-90m Laguna Madre 1,370-1,520m 5 Seaward Edge of Planting A as ge 36 Months ‘ ‘ m~. y} , 4 ‘ U ~ ‘ / (m) w (ft) aN - \ ’ x RZ 96 Months— wae Elevotion above MSL Initial Ground Level | Grass Planted QO Month 0 10 20 30 40 50 60 (m) Distance from Base Line Figure 6-37. Sea oats dune, Padre Island, Texas. Foredune restoration is most likely to succeed when the new dune coincides with the natural vegetation line or foredune line. The initial planting should be a strip 15 meters wide, parallel to the shore, and 15 meters landward of this line. It is essential that part of the strip be planted at a density that will stop sand movement sometime during the first year. If a natural vegetation or foredune line is not evident, restoration should begin at least 75 to 90 meters (250 to 300 feet) inland from the HWL. Where beach recession is occurring, the dune location should be determined from the average erosion rate and the desired dune life. Another 15-meter- wide strip may be added immediately seaward 4 to 5 years later if a base of 30 meters has not been achieved by natural vegetative spread. f. Trapping Capacity. Periodic cross-sectional surveys were made of some plantings to determine the volume of trapped sand and to document the profile of the developing dune. Table 6-5 presents comparisons of annual sand accumulation and dune growth rates. The rates are averaged over a number of profiles under different planting conditions, and should be considered only as an indicator of the dune-building capability. 6-51 Table 6-5. Comparisons of annual sand accumulation and dune growth rates! De Location Species Crest growth Sand Growth accumulation period (m) (ft) (m3/m) (yd3/£t) (yr) ———— EEE Nauset Beach American 0.3 0.9 8.3 3.3 7 Cape Cod, Mass. beachgrass Ocracoke Island, N.C. American 0.2 0.6 8.32 3.32 10 beachgrass Padre Island, Tex. Sea oats and 0.5 to 0.6 1.5 to 2.0 8.3 to 13.0 3.3 to 5.2 5 beachgrass Clatsop Plains, Oreg. European 0.3 0.9 13.8 5-5 30 beachgrass ———_—— ee ee ee 0 05000000000O00—™™" lafter Knutson (1980). 2Three years growth. The European beachgrass annual trapping rate on Clatsop Spit, Oregon, has averaged about 4 cubic meters (5 cubic yards). Although surveys were not taken until nearly 30 years after planting (Kidby and Oliver, 1965), the initial trapping rates must have been greater (see Fig. 6-38). Elevation above MSL ——1a00, 1600. ‘1800 ie} 100 200 300 400 500 600 Distance from Base Line Figure 6-38. European beachgrass dune, Clatsop Spit, Oregon. 6-52 These rates are much less than the rates of vigorous grass plantings. Small plantings of 10 meters square (100 feet square) of American beachgrass that trap sand from all directions have trapped as much as 40 cubic meters per linear meter (16 cubic yards per linear foot) of beach in a period of 15 months on Core Banks, North Carolina (Savage and Woodhouse, 1969). While this figure may exaggerate the volume of sand available for dune construction over a long beach, it does indicate the potential trapping capacity of American beachgrass. Similar data for sea oats or panic grass are not available. How- ever, observations on the rate of dune growth on Padre Island, Texas, follow- ing Hurricane Beulah (September 1967) indicate that the trapping capacity of sea oats and panic grass is greater than the annual rate observed for the planted dunes. . This suggests that dune growth in most areas is limited by the amount of sand transported off the beach rather than by the trapping capacity of the beach grasses. The average annual vertical crest growth, as indicated in Table 6-5, shows some variation over the range of test sites. However, in all cases the dune crest growth has been sufficient to provide substantial storm surge protection to the previously unprotected areas in back of the dune. This was evidenced on North Padre Island during Hurricane Allen in 1980. The storm surge at the location of the experimental dune building site has _ been estimated to be between 2 and 3 meters (8 and 10 feet). Although a substantial part of the dunes had eroded, they still provided protection from flooding in the areas landward of the dune. This area is undeveloped on North Padre Island (National Seashore), but the value of a healthy dune system can be readily appreciated. g- Cost Factors. The survival rate of transplants may be increased by increasing the number of culms per transplant. This increase in survival rate does not offset the increase in cost to harvest multiculm transplants. It is less expensive to reduce plant spacing if factors other than erosion (such as drought) affect the survival rate. Harvesting, processing, and transplanting of sea oats requires 1 man-hour per 130 hills, panic grass requires 1 man-hour per 230 hills. For example, a 15-meter-wide, 1.6-kilometer-long planting of sea oats on 60-centimeter centers requires about 500 man-hours for harvesting, processing, and trans- planting if plants are locally available. Using a mechanical ‘ttransplanter, from 400 to 600 hills can be planted per man-hour. Nursery production of transplants is recommended unless easily harvested wild plants of quality are locally available. Nursery plants are easier to harvest than wild stock. Commercial nurseries are now producing American and European beachgrasses, panic grass, and sea oats. Some States provide additional information through their departments of conservation or natural resources. The Soil Conservation Service routinely compiles a list of commer- cial producers of plants used for soil stabilization. V. SAND BYPASSING The construction of jetties or breakwaters to provide safe navigation conditions at harbor entrances or tidal inlets along sandy coasts usually results in an interruption of the natural longshore transport of sand at the entrance or inlet. The resulting starvation of the downdrift beach can cause 6-53 serious erosion unless measures are taken to transfer or bypass the sand from the updrift side to the downdrift beaches. Several techniques of mechanical sand bypassing have been used where jetties and breakwaters form littoral barriers. The most suitable method is usually determined by the type of littoral barrier and its corresponding impoundment zone. The five types of littoral barriers for which sand transfer systems have been used are illustrated in Figure 6-39. The basic methods of sand bypassing are as follows: fixed bypassing plants, floating bypassing plants, and land-based vehicles or draglines. Descriptions of selected projects illustrating sand bypassing techniques for various combinations of littoral barriers are presented in the following sections. 1. Fixed Bypassing Plants. Fixed bypassing plants have been used at South Lake Inlet, Florida, and Lake Worth Inlet, Florida (both type I inlet improvements, see Fig. 6-39), and at Rudee Inlet, Virginia Beach, Virginia (type V inlet improvement). In the past, in other countries, fixed bypassing plants were used at Salina Cruz, Mexico (U.S. Army Beach Erosion Board, 1951), and Durban, Natal, South Africa (U.S. Army Corps of Engineers, 1956). Both were located at breakwaters on the updrift sides of harbor entrances. The Salina Cruz plant rapidly became land-locked and was abandoned in favor of other methods of channel maintenance (U.S. Army Corps of Engineers, 1952, 1955). The Durban plant bypassed about 153,000 cubic meters (200,000 cubic yards) of sand per year from 1950 to 1954; afterward the amount decreased. Because of insuffi- cient littoral drift reaching the plant, it was removed in 1959. No apparent reduction in maintenance dredging of the harbor entrance channel took place during the 9 years of bypassing operations. Starting in 1960, the material dredged from the channel was pumped to the beach to the north by a pump-out arrangement from the dredge with booster pumps along the beach. a. South Lake Worth Inlet, Florida (Watts, 1953; Jones and Mehta, 1977). South Lake Worth Inlet, about 16 kilometers south of Palm Beach, was opened artificially in 1927 to provide increased flushing of Lake Worth. The dredged channel was stabilized by entrance jetties. The jetties caused erosion of the downdrift beach to the south, and construction of a seawall and groin field failed to stabilize the shoreline. A fixed sand bypassing plant began opera- tion in 1937. The plant consisted of a 20-centimeter (8-inch) suction line, a 15-centimeter (6-inch) centrifugal pump driven by a 48.5-kilowatt (65 horse- power) diesel engine, and about 365 meters of 15-centimeter discharge line that crossed the inlet on a highway bridge and discharged on the beach south of the inlet. The original plant, with a capacity of about 42 cubic meters (55 cubic yards) of sand per hour, pumped an average of 37,000 cubic meters (48,000 cubic yards) of sand per year between 1937 and 1941. This partially restored the beach for more than a kilometer downcoast. During the next 3 years (1942- 45) pumping was discontinued, and the beach south of the inlet severely eroded. The plant resumed operation in 1945, stabilizing the beach. In 1948 the plant was enlarged by installation of a centrifugal pump, a 205-kilowatt (275-horsepower) diesel engine, a 25-centimeter (10-inch) suction line, and ‘[9339mM) pesn useq aaey swaqshs Aeysueij pues yoTuUM (193emMyeVIq JO pus piemei10Yys je suoz 3uy punodmy) Aj3aC 10 1ajeMyPeIq ITAaN Pe Joeuuos-s10yg :A addy 42008 jj1spuaog Auer VO1120S Jom NVIIO 200g s1Updn 19}eMye3Iq Sioyssjo pue AeTuT petjjer Desy ivewer0Ig Y, 42008U044 10N 40 vor20210 y200g JJ14upuaog » GY . aN “III adéy 2 “Ciebuag ~~~ Auer jo be7 ave NvII0 ¥1Q Buruiosy 10u01\d0 Ujs0g vols s0deg dezq pues jetuy ‘“jI addy is0¢suDs1 WN 40 worj20419 NVIIO 42003 4j14p6n 904) puos pabpaig AOJ SAIdTAIeq Te10IITT Jo sadky Bdsy juewpUNOdW] y20eg s)14pdn "(81861 "6€-9 einsTy (teqemyes1q JO pus piemeas je auoz Zutpunoduy) Z97eMxZeVIQ paqzoeuu0d-si0ys :,~y adh Obsy juewe>r0Ig JeTUT petazer yy eddy Desy juewerDIG s20dtu0s) JON 40 vo1N20210 y200g sj1spumog wVvIIO Ayer Oesy juewpUACdW]| y2peg 4s14pdn 6-55 a 20-centimeter discharge line. This plant yielded an average discharge of 75 cubic meters (100 cubic yards) per hour. The remainder of the littoral drift was transported by waves and currents to the offshore zone, the middle ground shoal, and the downdrift shore. In 1967 the north jetty was extended and the bypassing plant was moved seaward (see Fig. 6-40). The current plant consists of a pump, a 300-kilowatt (400-horsepower) diesel engine, and a 30-centimeter-diameter suction line. The estimated discharge is 150 cubic meters (200 cubic yards) of sand per hour. During the period 1968 to 1976, the plant averaged 53,800 cubic meters (70,300 cubic yards) of bypassed material per year. In addition to the fixed plant, a hydraulic pipeline dredge has also been used to bypass sand from the middle-ground shoals. Between 1960 and 1976, the average annual volume of bypassed dredge material was 20,000 cubic meters (26,000 cubic yards). b. Lake Worth Inlet, Florida (Zermuhlen, 1958; Middleton, 1959; Jones and Mehta, 1977). Lake Worth Inlet, located at the northern limit of Palm Beach, was cut in 1918 and stabilized with bulkheads and jetties between 1918 and 1925. The fixed sand-bypassing plant began operation in 1958. The plant (see Fig. 6-41) consists of a 300-kilowatt (400-horsepower) electric motor and pump combination, a 30-centimeter suction line, and twin 25-centimeter discharge lines (added in 1967) which traverse the inlet on the channel bottom. A 240-meter section of the submerged discharge line can be removed during maintenance dredging of the navigation channel. The system was designed to handle 15 percent solids at more than 60 percent efficiency. Design capacity was about 130 cubic meters (170 cubic yards) per hour. The plant can dredge within a 12-meter sector adjacent to the north side of the plant to a depth of -3.7 meters MLW. A complex emergency flushing system, which was never used, was removed in 1971 because of high maintenance costs. The average annual amount of bypassed material between 1958 and 1966 was 57,700 cubic meters (75,500 cubic yards) per year. In 1969 the groin to the north of the plant was removed. The original intent of the groin was to pre- vent the plant from bypassing too much material, which might cause the updrift beaches to recede. However, the effect of the groin was to impede the move- ment of sand toward the pumping area. After removal of the groin, the average annual amount of bypassed material increased to about 99,000 cubic meters (130,000 cubic yards) per year during the period from 1969 to 1976. This estimate, based on an average discharge rate of 150 cubic meters per hour, represents about 60 percent of the estimated annual littoral drift. In addition to the fixed bypassing plant, material dredged during channel maintenance has been placed south of the inlet. In the 3-year period from 1970 to 1973, a total of 227,000 cubic meters (297,000 cubic yards) was bypassed by hydraulic dredge. c. Rudee Inlet, Virginia Beach, Virginia (Richardson, 1977). Rudee Inlet, immediately south and updrift of Virginia Beach, was essentially nonnavigable until 1952 when two short jetties were built and a channel was dredged. The channel immediately began to shoal with littoral material, and erosion occurred on the downdrift beaches. A fixed bypassing plant with a small capacity was installed in 1955 with little effect, and a floating 6-56 ATLANTIC OCEAN Direction of Net Longshore Transport SOUTH LAKE WORTH INLET Pumping Heed i Pipeline Downdrift Updrift ig ~ ei eee © Middle Ground Shoal \ N \ . ES — Highway AIA Sega Ce Sees am _———— a 200 0 200 400m l =] LAKE WORTH 500 0 500 1,000f Intracoastal Waterway Figure 6-40. Fixed bypassing plant, South Lake Worth Inlet, Florida. 6-57 a (Cirea 1968) ATLANTIC OCEAN North Jetty Main Pumping Station South Jetty Ss —— a ———— 100 10} 100 200 300m _————_—_ | 400.0 400. 800 1,200ft LAKE WORTH INLET ——$— — Direction of Net Longshore Transport Discharge Line mA Baap echacss Outfall High Water Shoreline Figure 6-41. Fixed bypassing plant, Lake Worth Inlet, Florida. 6-58 pipeline dredge was added in 1956. The fixed plant was destroyed by a storm in 1962, and the inlet essentially closed, allowing the sand to bypass naturally. In 1968 the inlet was again improved with the construction of a jetty and a breakwater connected to the shore by a sand weir (see Fig. 6-42). The weir jetty impoundment basin was never fully dredged initially, and the 25-centimeter dredge operations were hampered by wave action. From 1968 to 1972, sand bypassing was achieved by dredging material from the channel and back bay and pumping it to the downdrift beaches. In 1972, 76,000 cubic meters (100,000 cubic yards) of sand was removed from the impoundment basin. By 1975, the basin had refilled with littoral material, and bypassing was once again performed as before by the 25-centimeter dredge. Also in’ 1975), an experimental semimobile bypassing system was installed to bypass sand from the weir impoundment basin to the downdrift beach. This system consists of two jet pumps attached by flexible rubber hoses to the steel pipes, which are supported on pilings in the impoundment basin (see Fig. 6-42). The steel pipes are connected to the pumphouse where two centrifugal pumps, having a combined nominal capacity of 115 cubic meters (150 cubic yards) per hour, discharge through a 20-centimeter pipe to the downdrift beaches. The jet pumps are pivoted about the ends of the steel pipes by cables from the shore. This enables the pumps to reach a large area of the impoundment basin. During the first 6 months of operation, 60,400 cubic meters (79,000 cubic yards) of sand was bypassed from the impoundment basin by the jet-pump system, and approximately 23,000 cubic meters (30,000 cubic yards) was bypassed from the channel and impoundment basin by the floating dredge. Once operational procedures were established, the system could be successfully operated by a three-man crew in nearly all wave climates. Since late 1975 the system has been owned and operated by local author- ities who estimate the pumping capacity at 38 cubic meters (50 cubic yards) per hour and the effective pumping time at about 113 hours per month. The U.S. Army Engineer Waterways Experiment Station (WES) estimates the long-term pumping capacity at about 75 cubic meters per hour, assuming both pumps are operating. This estimate is based on the operating times from the first 6 months of operation. Using these two estimates as limits and assuming year- round operation, the system can pump between 51,800 and 103,700 cubic meters (67,800 and 135,600 cubic yards) per year. The estimated yearly littoral drift at Rudee Inlet is between 53,500 and 92,000 cubic meters (70,000 and 120,000 cubic yards). 2. Floating Bypassing Plants. Sand bypassing has been achieved by floating plants at all five types of littoral barriers (Fig. 6-39). Those operations that are discussed and illus- trated in this section are listed below: (a) Type I: Jettied inlet--location at Port Hueneme, California (Fig. 6-43). (b) Type Il: Inlet sand trap--locations at Jupiter Inlet, Florida (Fig. 6-44), and at Sebastian Inlet, Florida (Fig. 6-45). 6-59 Weir Section — OO Net Drift (Feb. 1980) | I ie bleed elie” . | \ (F 1 | fe i: | ; | | Woter Heal Suction Ry | $ yp ess 1 | & 1 4 analy Jet Flexible | § Pump / Hose | | ¥ =] , petal ek: 1000 100 200 300m . ‘ee ——_ —— —_ % Steel Pipe | & | 500 0 500 1,000 ft 0 | =! My % = p SI f ‘ mere: lean ATLANTIC OCEAN Figure 6-42. Fixed bypassing plant, Rudee Inlet, Virginia. 6-60 Accretion Direction ta) a Longshore Transport Phase 2 Dredging Area Primary Feeder Beach Dredge Entry Route Proposed Dredge Entry Route _——— et) PACIFIC OCEAN 500 (o} 500 1,000m ——ES=— == 1,000 0 1,000 3,000 ft Figure 6-43. Sand bypassing, Port Hueneme, California. (c) Type III: Jettied inlet and offshore breakwater--location at Channel Islands Harbor, California (Fig. 6-46). (d) Type IV: Shore-connected breakwater--locations at Santa Barbara, California (Fig. 6-47), and at Fire Island Inlet, New York (Fig. 6-48). (e) Type V: Shore-connected weir breakwater or jetty--locations at Hillsboro Inlet, Florida (Fig. 6-49), Masonboro Inlet, North Carolina (Fig. 6-50), Perdido Pass, Alabama (Fig. 6-51), East Pass, Florida (Fig. 6-52), and at Ponce de Leon Inlet, Florida (Fig. 6-53). Other floating dredge sand-bypassing projects, not illustrated in this section, include the following: (a) Type II: Boca Raton Inlet, Florida (channel dredging). (b) Type III: Ventura Marina, California. (c) Type IV: Oceanside Harbor, California. (d) Type V: Murrells Inlet, South Carolina. a. Port Hueneme, California (Savage, 1957; Herron and Harris, 1967). A unique application of a floating pipeline dredge to a type I littoral barrier was made in 1953 at Port Hueneme, California. Construction of the port and protective jetties in 1940 interrupted the littoral drift, estimated by Herron (1960) to be transported at the rate of 612,000 to 920,000 cubic meters (800,000 to 1,200,000 cubic yards) per year, by impoundment behind the west jetty and also by diverting the sand into the Hueneme Submarine Canyon, where it was permanently lost to the system. The result was severe erosion to the downdrift beaches. In 1953 sand impounded by the updrift jetty was pumped across the harbor 6-61 (Sept. 1974) So Sand Trap ——— SS 100 0 100 200 300 400m — =e 500 0 500 1,000 1,500ft © ATLANTIC OCEAN Figure 6-44. Sand bypassing, Jupiter Inlet, Florida (Jones and Mehta, 1977). 6-62 (photo courtesy of University of Florida, 1976) Sand Trap \ J) ; Spoil Area oo —— 500 (0) 500 1,000 m ATLANTIC OCEAN | 2,000 0 2,000 4,000 ft Figure 6-45. Sand bypassing, Sebastian Inlet, Florida (Jones and Mehta, 1977). 6-63 (Photo was taken just after 2.3 million cubic meters of sand had been dredged from the trap, Sept. 1965.) ri “4 y__ feecer beach 7 area of _ Seawall l£ast Jetty s. Entrance Channel MHW—- Sa i Hueneme -/West Jetty “gm Submarine oe cay (Spee Canyon Direction of Net 4m_.°\ Sand oe CongstoresTragepeuly ies me 7nap \\ Entrance Channel Breakwater | : 08: anor ——— 500 250 0 500 1,000 m By aN — —— a ——| RG 0 Gae 1,000 0 1,000 2,000 3,000 ft Figure 6-46. Sand bypassing, Channel Islands Harbor, California. 6-64 (July 1975) — | Sle Jesse -SANTA BARBARA | Direction of Net Longshore Transport 200 400 600m ss ———— rs ——— | BREAKWATER 500 O 1,000 2,000 ft Ls) CIFIC OCEAN Figure 6-47. Sand bypassing, Santa Barbara, California. 6-65 | | } | | (Sept. 1969) \ \\ 8 e \\ GREAT SOUTH BAY _ 08 BS Gi ee << Deposition Reservoir Channel Democrat Point Fire isiand Stote Park —_—_ Direction of Net Longshore Transport tty 500 500 1,000 m Littoral Reservoir |= = 1,000 0 2,000 4,000 ft AGE AN TUG MOGE AWN. Borrow Area Je Figure 6-48. Sand bypassing, Fire Island Inlet, New York. 6-66 (Sept. 1974) HILLSBORO SHORES Boat Piers Discharge Line A Impounding Area Dredge Dischorge (Rockint aici ©) A reo Oe ve = Timber Be ZL Jetty \ 7 \S Pipeline Dredge { ~ 7 el 7 4 qn \ i : Za 0 \ Hillsboro Lighthouse _———— <0" Sa os 100 0 100 m “\\ ip . \ R Granite Jetty —— ed Y ee —- 500 0 500 ft e Ne Natural Sand <_—__——_—— SPINY Direction of Net ATLANTIC OGEAN Longshore Transport Figure 6-49. Sand bypassing, Hillsboro Inlet, Florida. 6-67 (May 1981) ten Banks Channe/ [?n7e/ 2 ss —— MASONBORO BEACH [ae iy Gs oe) / ve o/ Direction of Net Fa ® Longshore Transport = —_—_ O 200 400m 0 500 1,000 ft ATLANTIC OCEAN / / Sand bypassing, Masonboro Inlet, North Carolina. Figure 6-50. (Apr. 1969) / 3S NWN / We! / y / Direction of Net Longshore Transport COTTON } . BAYOU Sal ny hd 21.8 fir 1S, I c I es.) s = oO ——ESS—S oe 33) @ 100 0 100 200 300m \ \ aa} — —— oo —— N \ ee @ Nea = 300 0 300 600 900ft \ -J é ‘S GULF : EN ; NEN Eost Jetty OF \\ West Jetty NN MEX/CO Sand bypassing, Perdido Pass, Alabama. Figure 6-51. 6-69 (Apr. 1971) n Halifax River 28) Be ae U.S. Coes? Guard Reservation : ai ASI: eee oFeeeyers 50 - eg Si peta Bees Eo.c c Sasi Reh a erty a aes eee me AN pon’ - op 08) (2% iM “en ees Aes i 300 0 300 600 900 m SS | 1,000 te) 1,000 2,000 3,000 ft Figure 6-53. Sand bypassing, Ponce de Leon Inlet, Florida, just south of Daytona Beach. entrance to the downdrift beach through a submerged pipeline. The unique feature of this operation was that the outer strip (or seaward edge) of the impounded fillet was used to protect the dredge from wave action. Land equip- ment excavated a hole in the beach, which was enlarged to permit a large dredge to enter from the open sea. Since it was necessary to close the dredge entrance channel to prevent erosion of the protective strip, water had to be pumped into the dredged lagoon. This problem might have been avoided had the proposed entry route from inside the harbor been used and kept open during phase I dredging (see Fig. 6-43). After completing the phase I dredging (see Fig. 6-43), the floating plant then dredged the protective barrier by making diagonal cuts from the phase I area out to the MLLW line. From August 1953 to June 1954, 1,554,000 cubic meters (2,033,000 cubic yards) of sand was bypassed to downdrift feeder beaches. Subsequent develop- ment updrift at Channel Islands Harbor, discussed below, provided periodic nourishment to the downdrift beaches southeast of Port Hueneme Harbor. b. Channel Islands Harbor, California (Herron and Harris, 1967). This small-craft harbor was constructed in 1960-61 about 1.5 kilometers northwest of the Port Hueneme entrance (see Fig. 6-46). The type III littoral barrier consists of a 700-meter-long (2,300-foot) offshore breakwater, located at the 9-meter-depth contour, and two entrance jetties. The breakwater is a rubble- mound structure with a crest elevation 4.3 meters (14 feet) above MLLW. It traps nearly all the littoral drift, prevents losses of drift into Hueneme Canyon, prevents shoaling of the harbor entrance, and provides protection for a floating dredge. The sand-bypassing dredging operation transfers sand across both the Channel Islands Harbor entrance and the Port Hueneme entrance to the downdrift beaches (U.S. Army Engineer District, Los Angeles, 1957). The general plan is shown in Figure 6-46. In 1960-61 dredging of the sand trap, the entrance channel, and the first phase of harbor development provided 4.6 million cubic meters (6 million cubic yards) of sand. Since the initial dredging, the sand trap has been dredged 10 times between 1963 and 1981, with an average of 1,766,000 cubic meters (2,310,000 cubic yards) of sand being bypassed during each dredging operation. The 22.2 million cubic meters (29 million cubic yards) bypassed since opera- tions began has overcome the severe erosion problem of the beaches downdrift of Port Hueneme. c. Jupiter Inlet, Florida (Jones and Mehta, 1977). The type II sand bypassing method consists of dredging material from shoals or a sand trap located in the protected waters of an inlet or harbor entrance and discharging the spoil onto the downdrift beaches. Jupiter Inlet is an improved natural inlet located in the northern part of Palm Beach County, Florida. Maintenance dredging of the inlet has been performed since the early 1940’s, but bypassed amounts before 1952 are unknown. Between 1952 and 1964 dredging of the inlet produced approximately 367,900 cubic meters (481,200 cubic yards) of sand which was bypassed to the downdrift beaches south of the inlet. Since 1966 most maintenance dredging 6-72 has taken place in the sand trap area (see Fig. 6-44). Between 1966 and 1977 the sand trap was dredged six times for a total of 488,500 cubic meters (639,000 cubic yards), which results in an annual average of about 44,400 cubic meters (58,000 cubic yards) of bypassed sand. d. Sebastian Inlet, Florida (Jones and Mehta, 1977). Sebastian Inlet, 72 kilometers (45 miles) south of Cape Canaveral, is a manmade inlet that was opened in 1948 and subsequently stabilized. The most recent jetty construc- tion occurred in 1970. This inlet differs from most inlets on sandy coasts because the sides of the channel are cut into rock formations. This has limited the inlet cross-sectional area to about half the area that would be expected for the tidal prism being admitted. Consequently, the inlet currents are exceptionally strong and the littoral drift is carried a considerable distance into the inlet. In 1962 a sand trap was excavated in a region where the inlet widens and the currents decrease sufficiently to drop the sediment load (see Fig. 6-45). This initial dredging produced 210,000 cubic meters (274,600 cubic yards) of sand and rock, which was placed along the inlet banks and on the beach south of the inlet. The trap was enlarged to 15 hectares (37 acres) in 1972 when 325,000 cubic meters (425,000 cubic yards) of sand and rock was removed. In 1978 approximately 143,400 cubic meters (187,600 cubic yards) of sand and 75,600 cubic meters (98,900 cubic yards) of rock were excavated, with the sand being bypassed to the downdrift beach. e. Santa Barbara, California. The Santa Barbara sand-bypassing operation was necessitated by the construction of a 850-meter (2,800-foot) breakwater, completed in 1928, to protect the harbor (see Fig. 6-47.) The breakwater resulted in accretion on the updrift side (west) and erosion on the downdrift side (east). Bypassing was started in 1935 by hopper dredges which dumped about 154,400 cubic meters (202,000 cubic yards) of sand in 7 meters of water about 300 meters offshore. Surveys showed that this sand was not moved to the beach. The next bypassing was done in 1938 by a pipeline dredge. A total of 447,000 cubic meters (584,700 cubic yards) of sand was deposited on the feeder beach area, which is shown in Figure 6-47. This feeder beach was successful in reducing erosion downdrift of the harbor, and the operation was continued by periodically placing about 3,421,000 cubic meters (4,475,000 cubic yards) of sand from 1940 to 1952 (Wiegel, 1959). In 1957 the city of Santa Barbara decided not to remove the shoal at the seaward end of the breakwater because it provided additional protection for the inner harbor. A small floating dredge was used to maintain the channel and the area leeward of the shoal, which was occasionally overwashed during storm conditions. Wave and weather conditions limited the dredging operations to 72 percent of the time. In order to reduce the overwashing of the shoal, the city installed a bulkhead wall along 270 meters (880 feet) of the shoal in 1973-74. The top elevation of the wall is 3 meters (10 feet) above MLLW. This caused the littoral drift to move laterally along the shoal until it was deposited adjacent to and into the navigation channel. Since that time an estimated 267,600 cubic meters (350,000 cubic yards) of material per year has been dredged from the end of the bar and the navigation channel. A part of this material is used to maintain the spit, with the remainder being bypassed to the downdrift beaches. f. Hillsboro Inlet, Florida (Hodges, 1955; Jones and Mehta, 1977). Hillsboro Inlet is a natural inlet in Broward County, Florida, about 58 kilometers (36 miles) north of Miami. A unique aspect of the inlet is a natural rock reef that stabilizes the updrift (north) side of the channel (see Fig. 6-49). The rock reef and jetties form what is called a sand spillway. Southward-moving littoral sand is washed across the reef and settles in the sheltered impoundment area where it is dredged and bypassed to the south beaches. A 20-centimeter hydraulic dredge, purchased by the Inlet District in 1959, operates primarily in the impoundment basin, but also maintains the navigation channel. The total quantity of sand bypassed between 1952 and 1965 was 589,570 cubic meters (771,130 cubic yards), averaging 45,350 cubic meters (59,300 cubic yards) per year. The north and south jetties were rebuilt and extended during 1964-65, and the navigation channel was excavated to -3 meters MSL. Between 1965 and 1977 the dredge bypassed 626,000 cubic meters (819,000 cubic yards) of sand for an annual average of 52,170 cubic meters (68,250 cubic yards) per year. This sand-bypassing operation is the origianl wetr jetty, and it forms the basis for the type V bypassing concept. g.- Masonboro Inlet, North Carolina (Magnuson, 1966; Rayner and Magnuson, 1966; U.S. Army Engineer District, Wilmington, 1970.) This inlet is the southern limit of Wrightsville Beach, North Carolina. An improvement to stabilize the inlet and navigation channel and to bypass nearly all the littoral drift was constructed in 1966. This phase of the project included the north jetty and deposition basin. The jetty consisted of an inner section of concrete sheet piles 520 meters (1,700 feet) long, of which 300 meters is the weir section, and a rubble-mound outer section 580 meters (1,900 feet) long. The elevation of the weir section (about midtide level) was established low enough to pass the littoral drift, but high enough to protect the dredging operations in the deposition basin and to control tidal currents in and out of the inlet. The midtide elevation of the weir crest appears to be suitable for this location where the mean tidal range is about 1.2 meters. The basin was dredged to a depth of 4.9 meters (16 feet) MLW, removing 280,600 cubic meters (367,000 cubic yards) of sand. A south jetty, intended to prevent material from entering the channel during periods of longshore transport reversal, was not initially constructed. Without the south jetty, sand that entered the inlet from the south caused a northward migration of the channel into the deposition basin and against the north jetty. Between 1967 and 1979 all dredging operations were involved in channel maintenance. In 1980 the south jetty (see Fig. 6-50) was completed, and 957,000 cubic meters (1,250,000 cubic yards) of material was dredged from the navigation channel and from shoals within the inlet. This material was placed on the beach. It is expected that the south jetty will prevent the navigation chan- nel from migrating into the deposition basin, and that the weir-jetty system will function as originally designed. It is projected that 230,000 cubic meters (300,000 cubic yards) of material will be impounded in the basin each year and hydraulic bypassing will alternate each year between Wrightsville Beach to the north and Masonboro Beach to the south. 6-74 h. Perdido Pass, Alabama. This weir-jetty project was completed in 1969 (see Fig. 6-51). Since the direction of the longshore transport is westward, the east jetty included a weir section 300 meters (984 feet) long at an ele- vation of 15 centimeters (6 inches) above MLW. MThe diurnal tidal range is about 0.4 meter (1.2 feet). A deposition basin was dredged adjacent to the weir and the 3./-meter-deep channel. The scour that occurred along the basin side of the concrete sheet-pile weir was corrected by placing a rock toe on the weir. Nearly all the littoral drift that crosses the weir fills the deposition basin so rapidly that it shoals on the channel. The first redredging of the basin occurred in 1971. During the period from 1972 to 1974, two dredging operations in the basin and the navigation channel produced a total of 596,000 cubic meters (780,000 cubic yards) of sand. Three dredging operations between 1975 and 1979 removed a total of 334,400 cubic meters (437,400 cubic yards) of sand from the channel. In 1980, 175,400 cubic meters (229,400 cubic yards) was dredged from the channel and deposition basin. These figures indicate that approximately 138,000 cubic meters (181,000 cubic yards) of sand is being bypassed each year. In 1979 Hurricane Frederic dislodged three sections of the concrete sheet piling in the weir and cut a channel between the weir and the beach. The discharge from the dredging operations that year was used to close the breach and to fill the beach to the east of the weir. 3. Additional Bypassing Schemes. Several other methods of bypassing sand at littoral barriers have been tested. Land-based vehicles were used in a sand-bypassing operation at Shark River Inlet, New Jersey (Angas, 1960). The project consisted of removing 190,000 cubic meters (250,000 cubic yards) of sand from an area 70 meters (225 feet) south of the south jetty and placing this material along 760 meters (2,500 feet) of the beach on the north side of the inlet. On the south side of the inlet a trestle was built in the borrow area to a point beyond the low- water line allowing trucks access from the highway to a crane with a 2-meter (2.5-yard) bucket. Three shorter trestles were built north of the inlet where the sand was dumped on the beach, allowing wave action to distribute it to the downdrift beaches. This method is limited by the fuel expense and by the requirement for an easy access across the inlet and to the loading and unloading areas. Spltt-hull barges and hopper dredges can be used to bypass dredged mate- rial by placing the spoil just offshore of the downdrift beaches. A test of this method was conducted at New River Inlet, North Carolina, during the summer of 1976 (Schwartz and Musialowski, 1980). A split-hull barge placed 27,000 cubic meters (35,000 cubic yards) of relatively coarse sediment along a 215-meter (705-foot) reach of beach between the 2- and 4-meter-depth (7- and 13- foot) contours. This material formed into bars that reduced in size as they moved shoreward. This final survey, 13 weeks later, indicated a slight accretion at the base of the foreshore and an increased width of the surf zone. The split-hull barge method was also used with commercially available equipment to place 230,000 cubic meters (300,000 cubic yards) at St. Augustine Beach, Florida, in 1979. While this method provides some nourishment and protection to the beach, it is not known how it compares with conventional placement of sand on the 6-75 beach and foreshore. Drawbacks to the use of split-hull barges include the necessity for favorable wind and wave climate during operation and the possi- bility that storms may move the sediment offshore, where it can be lost to the littoral processes. Side-cast dredging has been a successful means of maintaining and improv- ing inlets where shallow depths and wave conditions make operation of a pipe- line or hopper dredges hazardous (Long, 1967). However, the effectiveness of side-cast dredging as a bypassing method is limited by the length of the discharge pipe supporting boom. While it is possible to discharge in the downdrift direction, generally the dredged material is placed too close to the channel to be effectively bypassed. Reversals in the littoral current, and even changes in the tidal flow, can cause the dredged material to move back into the channel. VI. GROINS 1. Types. As described in Chapter 5, Section VI, groins are mainly classified as to permeability, height, and length. Groins built of common construction materials can be made permeable or impermeable and high or low in profile. The materials used are stone, concrete, timber, and steel. Asphalt and sandfilled nylon bags have also been used to a limited extent. Various structural types of groins built with different construction materials are illustrated in Figures 6-54 to 6-59. a. Timber Groins. A common type of timber groin is an impermeable structure composed of sheet piles supported by wales and round piles. Some permeable timber groins have been built by leaving spaces between the sheeting. A typical timber groin is shown in Figure 6-54. The round timber piles forming the primary structural support should be at least 30 centimeters in diameter at the butt. Stringers or wales bolted to the round piles should be at least 20 by 25 centimeters, preferably cut and drilled before being pressure treated with creosote and coal-tar solution. The sheet piles are usually either of the Wakefield, tongue-and-groove, or shiplap type, supported in a vertical position between the wales and secured to the wales with nails. All timbers and piles used for marine construction should be given the maximum recommended pressure treatment of creosote and coal-tar solution. Ayers and Stokes (1976) provide timber structure design guidance. b. Steel Groins. A typical design for a timber-steel sheet-pile groin is shown in Figure 6-55. Steel sheet-pile groins have been constructed with straight-web, arch-web, or Z piles. Some have been made permeable by cutting openings in the piles. The interlock type of joint of steel sheet piles provides a sandtight connection. The selection of the type of sheet piles depends on the earth forces to be resisted. Where the differential loads are small, straight web piles can be used. Where differential loads are great, deep-web Z piles should be used. The timber-steel sheet-pile groins are constructed with horizontal timber or steel wales along the top of the steel sheet piles, and vertical round timber piles or brace piles are bolted to the outside of the wales for added structural support. The round piles may not always be required with the Z pile, but ordinarily are used with the flat or 6-76 Wallops Island, Virginia (1964) Verioble Verlable Veriable =— G.l. bolt Weter Level Dotum Water level datum Timber wale Timber Sheet Piles Ie co aa is Timber sheet E piles NOTE: | Dimensions and details tobe PROFILE VIEW-AA determined by particular site conditions. G1 bolt Clinched nails Clinched noils wae 2«8" 2"x 8° a4 LIT L i KARRHES SHIPLAP TONGUE-AND-GROOVE WAKEFIELD PLAN Figure 6-54. Timber-sheet pile groin. 6=77 New Jersey (Sept. 1962) VARIABLE VARIABLE VARIABLE 61.80LT WATER LEVEL DATUM paren LEVEL STRAIGHT-WEB PILE STEEL SHEET PILES le vaa mnie ARCH-WEB PILE PROFILE SECTION A-A G1 BOLT G1! BOLT Gam 8 TIMBER wALe = SSS SSS PaaS RE SEF ones —SS Ee S: NOTE : Dimensions ond detoils to be determined by particular site TIMBER BLOCK conditions. Z PILE —— ~ wasHers—) PLAN Figure 6-55. Timber-steel sheet-pile groin. 6-78 Newport Beach, California (Mar. 1969) A= eA Steel Cap — Bottom Steel Sheet Piles SECTION A-A Figure 6-56. Cantilever-steel sheet-pile groin. 6-79 Presque Isle, Pennsylvania (Oct. 1965) Shoreline Concrete ,rock,or asphalt cell cap may be used to cover sand-or rock-filled cells Steel sheet piles PLAN Varies Note: Dimensions and details to be determined by particular site conditions. Water level PROFILE Figure 6-57. Cellular-steel sheet-pile groin. 6-80 Doheny Beach State Park, California (Oct. 1965) El. Varies Timber Wale Nut Pile Cap Cast Iron O.G. Washer Steel Plate Slot for Bolt in Pile TIMBER WALE Bolt Existing Bottom Concrete Sheet Piles Pile Lengths Vary Ties (RS, ele Dimensions Vory According to Differential Loading CONCRETE PIEE SECTION Figure 6-58. Prestressed-concrete sheet-pile groin. 6-81 Westhampton Beach, New York (1972) Variable Water Level Datum SRG ~ 1. = Ae’ QO @ PROFILE NOTE: Dimensions and details to be Varies determined by particular site conditions CROSS SECTION Figure 6-59. Rubble-mound groin. 6-82 arch-web sections. The round pile and timbers should be creosoted to the maximum pressure treatment for use in waters with marine borers. Figure 6-56 illustrates the use of a cantilever-steel sheet-pile groin. A groin of this type may be used where the wave attack and earth loads are moderate. In this structure, the sheet piles are the basic structural members; they are restrained at the top by a structural-steel channel welded to the piles. Differential loading after sediments have accumulated on one side is an important consideration for structures of this type. The cellular-steel sheet-pile groin has been used on the Great Lakes where adequate pile penetration cannot be obtained for stability. A cellular- type groin is shown in Figure 6-57. MThis groin is comprised of cells of varying sizes, each consisting of semicircular walls connected by cross dia- phragms. Each cell is filled with sand or aggregate to provide structural stability. Concrete, asphalt, or stone caps are used to retain the fill material. c. Concrete Groins. Previously, the use of concrete in groins was gen- erally limited to permeable-type structures that permitted passage of sand through the structure. Many of these groin designs are discussed by Portland Cement Association (1955) and Berg and Watts (1967). A more recent develop- ment in the use of concrete for groin construction is illustrated in Figure 6-58. This groin is an impermeable, prestressed concrete-pile structure with a cast-in-place concrete cap. At an installation at Masonboro Inlet, North Carolina, a double-timber wale was used as a cap to provide greater flexi- bility. Portland Cement Association (1969) and U.S. Army, Corps of Engineers (1971b) provide guidance on concrete hydraulic structure design. d. Rubble-Mound Groins. Rubble-mound groins are constructed with a core of quarry-run material, including fine material to make them sandtight, and covered with a layer of armor stone. The armor stone should weigh enough to be stable against the design wave. Typical rubble-mound groins are illustrated in Figure 6-59. If permeability of a rubble-mound groin is a problem, the voids between stones in the crest above the core can be filled with concrete or asphalt grout. This seal also increases the stability of the entire structure against wave action. In January 1963 asphalt grout was used to seal a rubble-mound groin at Asbury Park, New Jersey, with apparent success (Asphalt Institute, 1964, 1965, and 1969). e. Asphalt Groins. Experimentation in the United States with asphalt groins began in 1948 at Wrightsville Beach, North Carolina. During the next decade, sand-asphalt groins were built at the following sites: Fernandina Beach, Florida; Ocean City, Maryland (Jachowski, 1959); Nags Head, North Carolina; and Harvey Cedars, Long Beach Island, New Jersey. The behavior of the type of sand-asphalt groin used to date demonstrates definite limitations of their effectiveness. An example of such a structure is a groin extension placed beyond the low-water line which is composed of a 6-83 hot asphalt mixture and tends toward early structural failure of the section seaward of the beach berm crest. Failure results from lack of resistance to normal seasonal variability of the shoreface and consequent undermining of the structure foundation. Modification of the design as to mix, dimensions, and sequence of construction may reveal a different behavior. See Asphalt Insti- tute (1964, 1965, 1969, and 1976) for discussions of the uses of asphalt in hydraulic structures. 2. Selection of Type. After research on a problem area has indicated the use of groins as prac- ticable, the selection of groin type is based on varying factors related to conditions at each location. A thorough investigation of existing foundation materials is essential. Borings or probings should be taken to determine the subsurface conditions for penetration of piles. Where foundations are poor or where little penetration is possible, a gravity-type structure such as a rubble or a cellular-steel sheet-pile groin should be considered. Where penetration is good, a cantilever-type structure made of concrete, timber, or steel-sheet piles should be considered. Availability of materials affects the selection of the most suitable groin type because of costs. Annual maintenance, the period during which protection will be required, and the available funds for initial construction must also be considered. The initial costs of timber and steel sheet-pile groins, in that order, are often less than for other types of construction. Concrete sheet-pile groins are generally more expensive than either timber or steel, but may cost less than a rubble-mound groin. However, concrete and rubble-mound groins require less maintenance and have a longer life than timber or steel sheet-pile groins. 3. Design. The structural design of a groin is explained in a number of Engineer Manuals (EM’s). EM 1110-2-3300 (U.S. Army Corps of Engineers 1966) is a general discussion of the components of a coastal project. A forthcoming EM (U.S. Army Corps of Engineers (in preparation, 1984)) is a comprehensive presentation of the design of coastal groins. The basic soil mechanics involved in calculating the soil forces on retaining walls (and, therefore, sheet-pile groins) are presented in EM 1110-2-2502 (U.S. Army Corps of Engineers 1961). EM 1110-2-2906 (U.S. Army Corps of Engineers 1958) discusses the design of pile structures and foundations that can be used in the design of sheet-pile groins. Wave loading on vertical sheet-pile groins is discussed by Weggel (198la). VIL. JETIIES 1. Types. The principal materials for jetty construction are stone, concrete, steel, and timber. Asphalt has occasionally been used as a binder. Some structural types of jetties are illustrated in Figures 6-60, 6-61, and 6-62. a. Rubble-Mound Jetties. The rubble-mound structure is a mound of stones of different sizes and shapes, either dumped at random or placed in 6-84 ey ¥ a . » Nek ian. a: KR Oe ae Santa Cruz, California (Mar. 1967) SEAWARD SIDE ae CHANNEL SIDE om Concrete Cop 4,3-m B-Stone Concrete Filled El. 4.6m 2 Layers 2 22.4-mt Quadripods re aa El. 1.8-m 3.0m —\5—A-Stone EN MLLW_El.0.0:m Single Row 272.4 22.4-mt Quadripods E1.-2.4m B- Stone Chinked ba Se C- Stone Gore ——s-— Existing Gnound A - Stone Avg. 9.2-mt, Min. 6.1-mt B - Stone 50% > 2,8-mt, Min, 1.8-mt C - Stone 1.8-mt to 0.1m 50% > 224-kg Figure 6-60. Quadripod and rubble-mound jetty. 6-85 Humboldt Bay, California (1972) Existing Concrete Cap 37.7-mt Dolos (2 Layers) . -- 12. Head South Jetty es —- 18m Existing Structure PUA Beat Loyer 9.2 - 12.2-mt Stone (after Magoon and Shimizu, 1971) Figure 6-61. Dolos and rubble-mound jetty. 6-86 Grand Marais Harbor, Michigan (before 1965) Type lI Cells 18-m Dia. Type ICells 14-m Dia. Cover Stone (2.8-mt Min) 1.0-m Dredged. Cell Fill: 20) Material 2020505 Sj Biemeesscce ees ite: fe iaee sea suns Pape cess eeee 2, ; et— Stone Mattress Type S-28 Stee! Sheet Piling Figure 6-62. Cellular-steel sheet-pile jetty. 6-87 courses. Side slopes and armor unit sizes are designed so that the structure will resist the expected wave action. Rubble-mound jetties (see Figs. 6-60 and 6-61), which are used extensively, are adaptable to any water depth and to most foundation conditions. The chief advantages are as follows: structure settling readjusts component stones which increases stability, damage is repairable, and the rubble absorbs rather than reflects wave action. The chief disadvantages are the large quantity of material required, the high initial cost of satisfactory material if not locally available, and the wave energy propagated through the structure if the core is not high and impermeable. Where quarrystone armor units in adequate quantities or size are not economical, concrete armor units are used. Chapter 7, Section III,/7,f dis- cusses the shapes that have been tested and are recommended for considera- tion. Figure 6-60 illustrates the use of quadripod armor units on the rubble- mound jetty at Santa Cruz, California. Figure 6-61 illustrates the use of the more recently developed dolos armor unit where 38- and 39- metric ton (42- and 43- short ton) dolos were used to strengthen the seaward end of the Humboldt Bay, California, jetties against 12-meter breaking waves (Magoon and Shimizu, ISA) b. Sheet-Pile Jetties. Timber, steel, and concrete sheet piles are used for jetty construction where waves are not severe. Steel sheet piles are used for various jetty formations which include the following: a single row of piling with or without pile buttresses; a single row of sheet piles arranged to function as a buttressed wall; double walls of sheet piles, held together with tie rods, with the space between the walls filled with stone or sand (usually separated into compartments by cross walls if sand is used); and cellular-steel sheet-pile structures (see Fig. 6-62), which are modifications of the double-wall type. Cellular-steel sheet-pile structures require little maintenance and are suitable for construction in depths to 12 meters on all types of founda- tions. Steel sheet-pile structures are economical and may be constructed quickly, but are vulnerable to storm damage during construction. If coarse aggregate is used to fill the structure, the life will be longer than with sandfill because holes that corrode through the web have to become large before the coarse aggregate will leach out. Corrosion is the principal disadvantage of steel in seawater. Sand and water action abrade corroded metal near the mudline and leave fresh steel exposed. The life of the piles in this environment may not exceed 10 years. However, if corrosion is not abraded, piles may last more than 35 years. Plastic protective coatings and electrical cathodic protection have effectively extended the life of steel sheet piles. However, new alloy steels are most effective if abrasion does not deteriorate their protective layer. VIII. BREAKWATERS, SHORE-CONNECTED 1. Types. Variations of rubble-mound designs are generally used as breakwaters in exposed locations. In less exposed areas, both cellular-steel and concrete caissons are used. Figures 6-63, 6-64, and 6-65 illustrate structural types of shore-connected breakwaters used for harbor protection. 6-88 Cresent City, California (Apr. 1964) Concrete Cop "BS * Stone Chinked "B" #** Concrete Stone Grout Som * Stone 1.8-2.7-mt €1.47.6 : .om El. 5.5m El. 6.0-m t El. 3.0-m le | 2 Layers 22.4-mt Tetrapods MLLW El. 0.0m 1.8-m D' Stone (Quarry Run) BBO * Stone 1.8-2.8-mt “BA” Stone Min. 6.3-mt, Avg. 10.9-mt “B,' * * Stone 0,5-0.9-mt Ls ek” -~ 0.9-mt Variation to 6.3-mt Max. **"B,” - 0.5-to 0.9-mt Min.; 6.3-mt Max. as Available #** "B" - 0.9-to 6.3-mt or to Suit Depth Conditions at Seaward Toe Figure 6-63. Tetrapod and rubble-mound breakwater. 6-89 Elevation (m) Referred to MLLW Harborside Two Layers 45-mt Tribars Placed Pell-Mell Placed Pell-Mell Figure 6-64. Two Layers 32-mt Tribars Kahului, Maui, Hawaii (1970) Seaside Two Layers 32-mt Tribars A Placed Pell-Mell Concrete Ribs levation (m) Referred to MLLW Distance from Centerline (m) Tribar and rubble-mound breakwater. 6-90 Port Sanilac, Michigan (July 1963) LAKE LAKE SIDE 0.1m Bituminous Cop HURON alee hee ogre ee tal I Steel Sheet Piles Sond and Grove! Fill PORT SANILAC Driven Length Variable Average Penetration | 8m }-—_——. 8. 8 m ——_+| Section A-A LAKESIOE * Entronce Chonne! Steel Sheet Piles Variable Wi re %) Ls-Toe Protection Oriven Length Vorioble Average Penetration 40m Section B-8 50 100m TYPICAL SECTIONS OF BREAKWATER — 2 or | 100 0 100 200300 ft Figure 6-65. Cellular-steel sheet-pile and sheet-pile breakwater. 6-91 a. Rubble-Mound Breakwaters. The rubble-mound breakwaters in Figures 6-63 and 6-64 are adaptable to almost any depth and can be designed to with- stand severe waves. Figure 6-63 illustrates the first use in the United States of tetrapod armor units. The Crescent City, California, breakwater was extended in 1957 using two layers of 22.6-metric ton (25-short ton) tetrapods (Deignan, 1959). In 1965, 31.7- and 45.4-metric ton (35- and 50-short ton) tribars were used to repair the east breakwater at Kahului, Hawaii (Fig. 6-64). b. Stone-Asphalt Breakwaters. In 1964 at Ijmuiden, the entrance to the Port of Amsterdam, The Netherlands, the existing breakwaters were extended to provide better protection and enable passage for larger ships. The southern breakwater was extended 2100 meters (6,890 feet) to project 2540 meters (8,340 feet) into the sea at a depth of about 18 meters. Then rubble breakwaters were constructed in the sea with a core of heavy stone blocks, weighing 300 to 900 kilograms (660 to 2,000 pounds), using the newly developed material at that time, stone asphalt, to protect against wave attack. The stone asphalt contained 60 to 80 percent by weight stones 5 to 50 centimeters in size, and 20 to 40 percent by weight asphaltic-concrete mix with a maximum stone size of 5 centimeters. The stone-asphalt mix was pourable and required no compaction. During construction the stone core was protected with about 1.1 metric tons of stone-asphalt grout per square meter (1 short ton per square yard) of surface area. To accomplish this, the composition was modified to allow some penetration into the surface layer of the stone core. The final protective application was a layer or revetment of stone asphalt about 2 meters thick. The structure side slopes are 1 on 2 above the water and 1 on 1.75 under the water. Because large amounts were dumped at one time, cooling was slow, and successive batches flowed together to form one monolithic armor layer. By the completion of the project in 1967, about 0.9 million metric tons (1 million short tons) of stone asphalt had been used. The requirements for a special mixing plant and special equipment will limit the use of this material to large projects. Im addition, this partic-—- ular project has required regular maintenance to deal with the plastic-flow problems of the stone asphalt caused by solar heating. c. Cellular-Steel Sheet-Pile Breakwaters. These breakwaters are used where storm waves are not too severe. A cellular-steel sheet-pile and steel sheet-pile breakwater installation at Port Sanilac, Michigan, is illustrated in Figure 6-65. Cellular structures provide a vertical wall and adjacent deep water, which is usable for port activities if fendered. Cellular-steel sheet-pile structures require little maintenance and are suitable for construction on various types of sedimentary foundations in depths to 12 meters. Steel sheet-pile structures have advantages of economy and speed of construction, but are vulnerable to storm damage during construc- tion. Retention of cellular fill is absolutely critical to their stability. Corrosion is the principal disadvantage of steel in seawater; however, new corrosion-resistant steel sheet piles have overcome much of this problem. Corrosion in the Great Lakes (freshwater) is not as severe a problem as in the ocean coastal areas. 6-92 d. Concrete-Caisson Breakwaters. Breakwaters of this type are built of reinforced concrete shells that are floated into position, settled on a prepared foundation, filled with stone or sand for stability, and then capped with concrete or stones. These structures may be constructed with or without parapet walls for protection against wave overtopping. In general, concrete caissons have a reinforced concrete bottom, although open-bottom concrete caissons have been used. The open-bottom type is closed with a temporary wooden bottom that is removed after the caisson is placed on the foundation. The stone used to fill the compartments combines with the foundation material to provide additional resistance against horizontal movement. Caissons are generally suitable for depths from about 3 to 10 meters (10 to 35 feet). The foundation, which usually consists of a mat or mound of rub- ble stone, must support the structure and withstand scour (see Ch. 7, Sec. III,8). Where foundation conditions dictate, piles may be used to support the structure. Heavy riprap is usually placed along the base of the caissons to protect against scour, horizontal displacement, or weaving when the caisson is supported on piles. IX. BREAKWATERS, OFFSHORE Offshore breakwaters are usually shore-parallel structures located in water depths between 1.5 and 8 meters (5 and 25 feet). The main functions of breakwaters are to provide harbor protection, act as a littoral barrier, pro- vide shore protection, or provide a combination of the above features. Design considerations and the effects that offshore breakwaters have on the shoreline and on littoral processes are discussed in Chapter 5, Section IX. 1. Types. Offshore breakwaters can usually be classified into one of two types: the rubble-mound breakwater and the cellular-steel sheet-pile breakwater. The most widely used type of offshore breakwater is of rubble-mound construction; however, in some parts of the world breakwaters have been constructed with timber, concrete caissons, and even sunken ships. A variation of offshore breakwater is the floating breakwater. These structures are designed mainly to protect small-craft harbors in relatively sheltered waters; they are not recommended for application on the open coast because they have little energy-dissipating effect on the longer period ocean waves. The most recent summary of the literature dealing with floating break- waters is given by Hales (1981). Some aspects of floating breakwater design are given by Western Canada Hydraulics Laboratories Ltd. (1981). Selection of the type of offshore breakwater for a given location first depends on functional needs and then on the material and construction costs. Determining factors are the depth of water, the wave action, and the avail- ability of material. For open ocean exposure, rubble-mound structures are usually required; for less severe exposure, as in the Great Lakes, the cellular-steel sheet-pile structure may be a more economical choice. Figure 6-66 illustrates the use of a rubble-mound offshore breakwater to trap littoral material, to protect a floating dredge, and to protect the harbor entrance. Probably the most notable offshore breakwater complex in the United 6-93 Lakeview Park, Lorain, Ohio (Apr. 1981) LAKE SIDE Cr SS) BS SDS Ew ee {tse - ae) POOLE ST We 0.4-mt Underlayer 0.9-mt Secondary Stone Bottom Varies -2.4 to-l!0-m Figure 6-66. Segmented rubble-mound offshore breakwaters. 6-94 States is the 13.7-kilometer-long (8.5-mile) Los Angeles-Long Beach breakwater complex built between 1899 and 1949. Other U.S. offshore breakwaters are listed in Table 5-3 of Chapter 5. 2. Segmented Offshore Breakwaters. Depending on the desired function of an offshore breakwater, it is often advantageous to design the structure as a series of short, segmented break- waters rather than as a singular, continuous breakwater. Segmented offshore breakwaters can be used to protect a longer section of shoreline, while allow- ing wave energy to be transmitted through the breakwater gaps. This permits a constant proportion of wave energy to enter the protected region to retard tombolo formation, to aid in continued longshore sediment transport at a desired rate, and to assist in maintaining the environmental quality of the sheltered water. Additionally, the segmented breakwaters can be built at a reasonable and economical water depth while providing storm protection for the shoreline. Figure 6-66 illustrates the structural details of the segmented rubble- mound breakwater at Lakeview Park, Lorain, Ohio, which is on Lake Erie. This project, which was completed in October 1977, consists of three detached rubble-mound breakwaters, each 76 meters long and located in a water depth of -2.5 meters (-8 feet) low water datum (LWD). The breakwaters are spaced 50 meters (160 feet) apart and are placed about 145 meters (475 feet) offshore. They protect 460 meters of shoreline. The longer groin located there was extended to 106 meters (350 feet), and an initial beach fill of 84,100 cubic meters (110,000 cubic yards) was placed. A primary consideration in the design was to avoid the formation of tombolos that would interrupt the longshore sediment transport and ultimately starve the adjacent beaches. Immediately after construction, the project was monitored for 2 years. Findings indicated that the eastern and central breakwaters had trapped littoral material, while the western breakwater had lost material (Walker, Clark, and Pope, 1980). The net project gain was 3800 cubic meters (5,000 cubic yards) of material. Despite exposure to several severe storms from the west during periods of high lake levels, there had been no damage to the breakwaters or groins and no significant erosion had occurred on the lake bottom between the breakwaters. X. CONSTRUCTION MATERIALS AND DESIGN PRACTICES The selection of materials in the structural design of shore protective works depends on the economics and the environmental conditions of the shore area. The criteria that should be applied to commonly used materials are discussed below. 1. Concrete. The proper quality concrete is required for satisfactory performance and durability in a marine environment (see Mather, 1957) and is obtainable with good concrete design and construction practices. The concrete should have low permeability, provided by the water-cement ratio recommended for the exposure conditions; adequate strength; air entrainment, which is a necessity ina 6-95 freezing climate; adequate coverage over reinforcing steel; durable aggregates; and the proper type of portland cement for the exposure conditions (U.S. Army, Corps of Engineers, 197la, 1971b). Experience with the deterioration of concrete in shore structures has provided the following guidelines: (a) Additives used to lower the water-cement ratio and reduce the size of air voids cause concrete to be more durable in saltwater. (b) Coarse and fine aggregates must be selected carefully to ensure that they achieve the desired even gradation when mixed together. (c) Mineral composition of aggregates should be analyzed for possible chemical reaction with the cement and seawater. (d) Maintenance of adequate concrete cover over all reinforcing steel during casting is very important. (e) Smooth form work with rounded corners improves the durability of concrete structures. 2. Steel. Where steel is exposed to weathering and seawater, allowable working stresses must be reduced to account for corrosion and abrasion. Certain steel chemical formulations are available that offer greater corrosion resistance in the splash zone. Additional protection in and above the tidal range is pro- vided by coatings of concrete, corrosion-resistant metals, or organic and inorganic paints (epoxies, vinyls, phenotics, etc.). 3. Timber. Allowable stresses for timber should be those for timbers that are continuously damp or wet. These working stresses are discussed in U.S. Department of Commerce publications dealing with American lumber standards. Experience with the deterioration of timber shore structures (marine use) may be summarized in the following guidelines: (a) Untreated timber piles should not be used unless the piles are protected from exposure to marine-borer attack. (b) The most effective injected preservative for timber exposed in seawater appears to be creosote oil with a high phenolic content. For piles subject to marine-borer attack, a maximum penetration and retention of creosote and coal-tar solutions is recommended. Where borer infestation is severe, dual treatment with creosote and water- borne salt (another type of preservative) is necessary. The American Wood-Preservers Association recommends the use of standard sizes: C-2 (lumber less than 13 centimeters (5 inches) thick); C-3 (piles); and C-18 (timber and lumber, marine use). 6-96 (c) Boring and cutting of piles after treatment should be avoided. Where unavoidable, cut surfaces should receive a field treatment of preservative. (d) Untreated timber piles encased in a Gunite armor and properly sealed at the top will give economical service. 4- Stone. Stone used for protective structures should be sound, durable, and hard. It should be free from laminations, weak cleavages, and undesirable weathering. It should be sound enough not to fracture or disintegrate from air action, seawater, or handling and placing. All stone should be angular quarrystone. For quarrystone armor units, the greatest dimension should be no greater than three times the least dimension to avoid placing slab-shaped stones on the surface of a structure where they would be unstable. All stone should conform to the following test designations: apparent specific gravity, American Society of Testing and Materials (ASTM) C 127, and abrasion, ASTM C 131. In general, it is desirable to use stone with high specific gravity to decrease the volume of material required in the structure. 5. Geotextiles. The proliferation of brands of geotextiles, widely differing in composi- tion, and the expansion of their use into new coastal construction presents selection and specification problems. Geotextiles are used most often as a replacement for all or part of the mineral filter that retains soil behind a revetted surface. However, they also serve as transitions between in situ bottom soil and an overlying structural material where they may provide dual value as reinforcement. The geotextiles for such coastal uses should be evaluated on the basis of their filter performance in conjunction with the retained soil and their physical durability in the expected environment. Two criteria must be met for filter performance. First, the filter must be sized by its equivalent opening of sieve to retain the soil gradation behind it while passing the pore water without a significant rise in head (uplift pressure); it must be selected to ensure this performance, even when subjected to expected tensile stress in fabric. Second, the geotextile and retained soil must be evaluated to assess the danger of fine-sized particles migrating into the fabric, clogging the openings, and reducing permeability. The physical durability of a geotextile is evaluated by its wear resist-— ance, puncture and impact resistance, resistance to ultraviolet damage, flexibility, and tensile strength. The specific durability needs of various coastal applications must be the basis for geotextile selection. 6. Miscellaneous Design Practices. 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ZURMUHLEN, F.H., "The Sand Transfer Plant at Lake Worth Inlet," Proceedings of the Stxth Conference on Coastal Engineering, American Society of Civil Engineers, 1958. 6-106 CHAPTER 7 Structural Design: Physical Factors Praia Bay, Terceira, Azores, 2 March 1970 i Tete Hest: IV VII CONTENTS CHAPTER 7 STRUCTURAL DESIGN: PHYSICAL FACTORS Page WAVE) CHARACTER TS TLCS syeje 0 ole © 90/010 010/00 6610/0 016/6 61601010 eee 6 6 6/0 010010100160 o/e\eie//— IP ePDES TOmm CIES aAtevelels/clelelelslelolere! oleloleleletelelolelolererolaleioleleleleiolelelolsieleleloreler/al ZmeRepLesentat-lonwor. Waves Cond] tilOnsisieleielslelelelelelclolelelelelelelelelelelelelclelel/ = 1 3. Determination of Wave Condi tion's\s\.1c\c \scle!ele)s)0) ojes16 v1e/e | e)elele cleo) —2 A Oelection OL Desien Wave) CondtttlomSlecjcielelelolelelelerelelelelelelerelcleloleisrel/—o WAVE RUNUP, OVERTOPPING, AND TRANSMISSION. ccccccccccccccccccccccosi—10 Wey Wave) RUMUp\s.cie «0101001010101 s) «1 010)0\e10/e/e/e(e/0/0/e/e)0)0]e10/) 01610) 0)0\eleleleolele/lelejeie//— 10 Dom WAVE MOVETE OPP MOieictelclelelelelelolelalelelalololelalelolelololelelclololelelelelclelalsislelolslelei/ 45 Se WAVE MLE ANSM SS ONlorsleielolelelelolelelelolalelelolelelelolelelelolalelerelolelelolelelelelels/ cielo! x“ O)l WAVE EE ORCH Sie teieteieleleleleeols/elle!olels)c/elele) cl eieselelclelelclelelelolelelelclolele/clelelclolajelelclaleleie!/ 1 OO Ie Forces ‘on! PileS <\. <\ccle.c ciel 010 010/010]0 © 00.0 0\0\0\0 lee 0)0\cle\e o/c cleleleleicieis/ 1 OIL 2) Nonbreaking Wave) Forces! on) Wall ls\e\.jic\cleielelelsiclclelelslclcleleie/clelelereleiei/ lO) 3. Breaking Wave Forces on Vertical Walls.....cececcccccceeese/—180 Grom BDLOKEIy WAVE Sle crelolelelelelciele/olele) cles) cloialelelelec/eloleleleleleiele) efeleleleleleloiereleley alta 2 De HEfect (of “Angle of Wave Approdchicicje). ciclsle siclelelsicle eiclelelelsicleleicie— 19S Oe Etfkect of a Nonverticall Wailsly. viele) slele\e clelelelclole)clele/slelalole\e slels/eiel = 200 eo tabiality sor Rubble Structure Siteleielelelslslelelsieleleleleleleleleleleiclelelerelel 22 8. Stability of Rubble Foundations and Toe Protection......../-242 VELOCITY FORCES--STABILITY OF CHANNEL REVETMENTS...cccccccccccccce/—249 IMPACT FORCES. eeeeoeeeeveeeeeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eee 7-253 ICE HORGE Sieyeioheveieiolcloleleleiolcloleistelcielcielelotel eieicioletetelelatclioleverchelsiclersictetetelelcheleieretel/iaa cS. EARTH FORGE Siclersrsiclere eeeeoeveeeoeeeeeeeeeeeeeeeee siohelevetotelelelelovelercleisielciclelslei/i= 20 We Active Forces. eeeoeoevoeveeveeeeeeeveeeeeeeeeeeeeeeeeeeeeeeeevneeeee -/-256 Die Passive Forces. e@eeeoevevoeveeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ed ~/-257 3\5 Cohesive Soils eeeeoevoeoeeaeoeeeeeeeeeeeeeeeeeeeeeeeeeeeveeeeeee -/-260 4 EOELUCLULES EOL siGregular sSeCtlOlierelelelels/sielelolelelelolelelererereleleleievereie— 200 5 Submerged, Matera! <).10\<1cic\clclcisie olele)s\lcje clelelele\slolelelecisieicic sic cielsce/ —200 6. Uplift Forces. eeeoeoeevoeev eevee eeeeeeeeeoeeeeeeeeeeeeeeeee eee ee -/-260 LITERATURE CITED. eeeoevoeaeveeeveeoeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeoeeee -/-261 BEBISMOGRAP HYrorsnckeliolololetoliclolelolelereleleiclele cle leieleleveieleloleteielelereloneleterctelersrerstelalerelelen/ saa vii TABLES Determination jofidestenswavemhedight:s\e cle ole/sle)elelelcleicle elelelelcleloiciciele cee cil 5 Valuesots ra tor sivardousmsopeicharacterd sitlcsSiscicielele clelelelelelelevercic cleleleli= Oe Some considerations of breakwater selection. ..cccccccccccccccccccee/—04 Steady flow drag coefficients for supercritical Reynolds MUM DEMS lelokel elolorerolelelel slotelcielelerersioleteleleretcl cleieiclelelelcvercioicicioleicielcievelerereiorerciereiei loo 1—2 =e CONTENTS TABLES--—CONTINUED Page Experimentally determined values of Cu slolelavelalololelolelelelolele/ololololotstotet mance Example calculation of wave force variation with phase angle...../-153 Comparison of measured and calculated breaker force....eeeeeeeeee/-159 Suggested K values for use in determining armor unit weight.../-206 H as a function of cover-layer damage and type of armor oe D=0 MITA E- coloieier aleve loieve! ofeleleieieleleleln ejelniele clsis\e'o'aleiela\elo{oe\s/siea\slelolevain/ole-aisielelsteletet atemne Types Of AKMOT UNITS. cccccccccceccccccccccvccccccscecccsccescscses slo Concrete armor projects in the United StateS.....cccceseccceeeeee/—226 Weight and size selection dimensions of quarrystone.....seeeeeeee/-230 Layer coefficient and porosity for various armor units........+.../-234 Effects of ice on marine Structures. ccccccccccccccccsccceccsecsel—202 Unit weights and internal friction angles of soils.......s+eeeeee/-258 Coefficients and angles of friction...cccccccccccccccccccsceccves/—L00 FIGURES Definition of breaker PeometTy 110 «« 00/01n cc c\c\clelelele cl clsieleicleleclelslelelelelelelelian” a and §g versus H/et Slolefevolele eleicleleleleleloleleteralelelelelototoreroeleloloisteretiotot-tetiintt Breaker height index ae versus deepwater wave steepness a) H?/gT? dis vevaverevevevesereievereveveresekelevevouelevesonehaletolelelaleterctetorcteteteleleteelelonelererelstololetel inal oO Dimensionless design breaker height versus relative depth at structure Gy'6i'8, 61/6) eyo ev eV SIGN@Ke) exe) veh oHel/eyolsye\eFevevelenexeveloleleletelotetevehetoleheTotelelcketererereret ial CO) , Breaker height index ae ro) versus H Jet sJolelelololehetotelolarototctatetorotoretel leant Logic diagram for evaluation of marine environment...e.eeeeceeeeee/—l7 Definition sketch: wave runup and overtopping...eccccccccccccceee/—18 Wave runup on smooth, impermeable slopes when ae = Q cecccccces—19 Wave runup on smooth, impermeable slopes when d /H~ * 0.45 ...+--/-20 ch (2) Wave runup on smooth, impermeable slopes when d /H~ * 0.80 ...+.-/-21 & 7-24 N22 7-26 27 CONTENTS FIGURES--CONTINUED Page Wave runup on smooth, impermeable slopes when d (/H" 3 200) oooo0c0// ey Wave runup on smooth, impermeable slopes when d /H 360) coosaco/Ze Runup correction for scale CERECESleilevetelolelotelelelololetolelelelcholeicleleletetclelelereielol/ 24 Wave runup on impermeable, vertical wall versus H/T Slee sloeiccees—2) Wave runup on impermeable, quarrystone, 1:1.5 slope versus H* /gT elelavelovolcloioveleiesisiele/c cleteieleieisiclslclcleleveleicteloiolelclelerateietcleietelolerelerslensiciel/ = 20 oO Wave runup on impermeable, stepped, 1:1.5 slope versus He /gT” eee /-27 Wave runup on impermeable seawall versus Ho /gT” cc cccccccccccccee/—29 Wave runup on recurved (Galveston-type) seawall versus We /eT eee/—-29 Wave runup and rundown on graded riprap, 1:2 slope, impermeable base, versus Ho /gT” Cec crccccccccccesccccccccccscs ei —30 Comparison of wave runup on smooth slopes with runup on permeable rubble SWOPE Slejeleichelcleielcleielelcleleloletelelshererelelerelereioicvcleicleleversielersreli= sil Calculation of runup for composite slope: example of a levee cross SECELOM src wis cre c ce 0 oleletereetorctete etelolohebslcietcheleleleis cic cle eielelsiciclesecceetaso Successive approximations to runup on a composite slope: example DEODWEeMlevelel ofejelenelololclelefeletoleloleteleleletolololsisiehetstelctelalelorelcieieleleiele rete ever) Probability of exceedance for relative wave heights or runup WATE Slelolaleleloleleleteleleietcietelolelelelelolersielclelercislclcleterstetclererciclelorercielerelolerereleisieiersienas Ge. Overtopping parameters a and Q (smooth vertical wall on a 1:10 nearshore BLOME) cule nine ter con entre Cooma annie -45 Overtopping parameters a and (smooth 1:1.5 structure slope on a 1:10 nearshore Bilope Vem ieckeree ene ncn seeiiclane ede -46 Overtopping parameters a and Q (smooth 1:3 structure slope on a 1:10 nearshore SiO poco tie ok eee ee eee als esa 47 Overtopping parameters a and Q (smooth 1:6 structure slope on a 1:10 nearshore SVOpe) ee ee Co es cena alede 48 Overtopping parameters a and Q (riprapped 1:1.5 structure sillopemonvay ll Oenearshorel SlOpenicjeicye cielciclelelerelsiclelelelelelers ele) clelololeleleero 49 1=29 7-30 7-41 CONTENTS FIGURES--CONTINUED A Page Overtopping parameters a and Q (stepped 1:1.5 structure slope on a 1:10 nearshore SLOPES os.sdb ve ceis sie vomeene oe nrescsc eee * Overtopping parameters a and Q (curved wall on a 1:10 oO nearshore SIOPE))ferehalolelevelelelelolelsieleleleielclolslelsls/elole|slelelelelsisielelatclalolalelatelereretel/ aol * Overtopping parameters a and Q (curved wall on a 1:25 O nearshore SLOPE) leielololelelolelelerolalelelololelalaleleleletololelololelelelolelelslelolelelolelelsieteteleleti ai * Overtopping parameters a and Q (recurved wall on a 1:10 O nearshore SilOPE) lelelotovelele icicle velerclalelevclele\sieloleleleleleleielololerelslerelevelelclolclelotekersteya=ele) Variations of a with structure slope i) aleleieletelelerelelelcleloteleleleloreletoieniaa en * Variations of qr. between waves conforming to cnoidal theory and waves conforming to linear theory...ccccccccccsccccccccscscscees—ID Q = as and a as functions of relative freeboard and a ....../-60 Wave transmission over submerged and overtopped structures: approximate ranges of d,/eT studied by various AUNVESTLGALOLS .cccccccccccccccccccesccccecccccsccscccccccsccoccsel—O3 Selected wave transmission results for a submerged breakwater...../-65 Wave transmission coefficients for vertical wall and vertical thin-wall breakwaters where 0.0157 < d,/gT” < 0.0793 ......+4+4+7-66 Wave transmission by Overtopping. cccccccccccccccccsccscsccccccccsees—OG Transmitted wave height/incident significant wave height versus relative freeboard for wave transmission by overtopping due to irregular WAVES ole sietsleletel sieleielele (ole eleleieleleleterelelelerevelcreislereneiorelelcielerctatereteleren any Transmitted wave height as a function of the percentage of CEKXCECAATICES oro 0:00:06 01019 :0.6 0:6 0, 0,0:0 (66. 610.6 (0,6, 6:8) 016(6.0.0.416 6.6. 6/010, 6 ele leielelereleleisisicielerotail Hy B Correction factor, CF , to multiply by a for ee Oe Boa5o/e7/ il s Wave transmission by overtopping for a breakwater with no EYEODOATAS b..dis o.6o Sieversicieowwie\¢.eie- oe ee ieie erelaileveleveveie ovevajolel edevevovoterevavelelerelefer/alich Wave runup on breakwaters and riprap....cccccccccccccccccscccsccssi—i) Selected wave transmission results for a subaerial breakwater...../-/6 7-46 7-47 7-52 7-53 7-54 By) 7-56 CONTENTS FIGURES--CONTINUED Page Sample wave transmission and reflection coefficients for a smooth, impermeable breakwater... .cccccccccccccccccccccccccccscces—s/ Monochromatic wave transmission, impermeable rubble-mound breakwater, where n= 13033 alolelel clelcleleleloieteiorelelcvelelclelsicielelelsielelelererel/ (6 8 Monochromatic transmission, impermeable rubble-mound breakwater, where B= 1,133 Srerelevers//ele Glevare al evsvel'e eielelelel oveteteleyeetejereteteleloveieterchereielelel/ 79 8 Influence of structure height on wave transmission for Example Problem 13 dialer cratevevelokevotetel clele: ole coheteevaleirelexctevejevetore etave oheteloleloberc¥elolsveloleteteleric OW Wave transmission through a rubble-mound breakwater...cecsccccccee/—82 Wave transmission past a heavily overtopped breakwater with tribar armor ALIN 'S tavovavedesosen Gu scevetevereteveteicrslecelsielo cioketeveteleteiclaieloreivetevsicletstorerel os Wave transmission and reflection coefficients for a breakwater with a Plat seaward slope in medium-depth water. eooeveeeeeoeeeeee -/-84 Wave transmission and reflection coefficients for a mostly armor breakwater in shallow water. c\<.. << 0101010. 0 see clclejejs/clee oe/e\s/elelee eicle\) =O) Monochromatic wave transmission, permeable rubble-mound breakwater, where h/d, = M033 aiaverdie eo distorctelere eislelelele cles ciovcrolereleie of OO Monochromatic wave transmission, permeable rubble-mound breakwater, where hy dS 135) Sionexejeevelexenedereieleneleisieveveceverolereisversceteiete Ol, Predicted wave transmission coefficients for a rubble-mound breakwater using the computer program MADSEN..-.ccccccccccvcccccee/—88 Ponding for a smooth impermeable breakwater with F = 0......+.+--/-90 Ponding for rubble—mound breakwaters..cceccccccccccccccccccccccccce/—I0 Cumulative curves of relative wave energy with respect to azimuth from the principal wave direction..ccccccccccccccccccces/—Il Change of a maximum directional concentration parameter, S ; : ; max due) to) wave, refraction in’ ‘shallow Watere. cic cclec cic cisicleiscisiciec cos —o 1 Diffraction diagrams of a semi-infinite breakwater for directional random waves of normal incidence....ceccccccccccvcee/—92 Diffraction diagrams of a breakwater gap with B/L = 1.0 for directional random waves of normal incidence....cccccccccccceccee/—9)D U95) 7-64 7-65 CONTENTS FIGURES--CONTINUED Page Diffraction diagrams of a breakwater gap with B/L = 2.0 for directional random waves of normal incidence.....cccccsccccseeeee/—90 Diffraction diagrams of a breakwater gap with B/L = 4.0 for directional random waves of normal incidence....eccccecceceesese/—9/ Diffraction diagrams of a breakwater gap with B/L = 8.0 for directional random waves of normal incidence....ccccceeeeeseeese/—98 Classification of wave force problems by type of wave action and by structure ESY/POiaici cic sicio.c nies! e/je ele, 6.0) sic alolelste wisivivicie siecle ele/ajersieials) slniell aanelm Definition sketch of wave forces on a vertical cylinder.......+.-/—-102 Relative wavelength and pressure factor versus d/gT* slelolelejelele/erelel— LO Ratio of crest elevation above still-water level to wave height../-107 Wavelength correction factor for finite amplitude effects......../-108 Kjm versus relative depth, d/gT2 eicle sisteloleicls ovelelctslajelalcle’evale\elelaloleteteticinles Kpm versus relative depth, d/gT? sletolelele/cvelel oletelelevelolaleroteleialelolelol ovovet Wie Glcs Inertia force moment arm, Sj, versus relative depth, d/gT Ee Mn Nate acted 5 aratareriteta oi AVG 618 et oreialevare ies lSLe exes eiororerexelel el elelerelelelereonerer agile) Drag force moment arm, Sp, , versus relative depth, d/gT?..«++s%allG Breaking wave height and regions of validity of various wave the orslesicaleveistetere aleve elcleveroratelolelelclereleisicleielelelercicieloseleveleleiclerelolexe/elelorolelototor/maalalel| Isolines of @$ versus H/gT2 and d/gt2 Seni! S Os) o6o0cd0d doJ/elily Isolines of $ versus H/gT2 and d/gT2 oo e(W = O.1) ccccccccces lou Isolines of 4 versus H/gT2 and d/gT? Soot =) O55) docoonc00G ela Isolines of 4 versus H/gT2 and d/gt? 500Gt = Woocodssocs67alZ? Isolines of a versus H/gT2 and d/gT2 Soot) & Ws Dloecocdqccog/ellws' Isolines of a versus H/gT2 and d/gT* S60 HS OsDacoddoosbo/el7ys Isolines of a versus H/gT2 and d/ gt? siciel GWe= Oe OD lejercieicleletotelellt2o Isolines of a versus H/gT2 and d/gT2 FOG S NeOodsosocc co /uAs Variation of C/Cp with Keulegan-Carpenter number and H/gT*...7-134 7-85 7-86 CONTENTS FIGURES-—-CONTINUED Page Variation of drag coefficient Cy with Reynolds number R Siatalatetelelatalcictelclclolctcleleloicielcieloleieleiclereleieiclelelelelelolavelerelercichelerelerersicteleleret a-Si e Definition sketch: calculation of wave forces on a group of piles that are structurally connected...ccccccccccccsccccccsceve/—lol Definition sketch: calculation of wave forces on a nonvertical PAC lereiereelele ele cl ele\ cle lole(e olels) eleleccle'e|e oo s\cleleleleleo'e\e)e clelelele clolelelelelsiclelelcioi/—l D0 Definition of terms: nonbreaking wave forceS..ccccecccccccsccce/—l62 Pressure distributions for nonbreaking waveS.cccccccccscccecceee/—l1O3 Nonbreaking waves; yx = 1.0 ccccccccccccccccccccscccccccccccccce/—164 Nonbreaking wave forces; yx = 1.0 ceccccccccccesccccscccccccsccsccce/—1O9 Nonbreaking wave moment; y = 1.0 ccccccccccccccccccsccccscesccce/—1O0 Nonbreaking waves; y = 0.9 cccccccccccccccccccccccccccsesccscccce/—lO/ Nonbreaking wave forces; yx = 029 ceccccccccccccccccccccccccccce/—108 Nonbreaking @wave) moments, =O 9)" c/ccierleicie)ove/ele clelelele|eclcielelc/elee)e o'clel/ 109 Pressure) distribution’ on wall of low height..cec.ccccccccecsiece col—l/4 Force and moment reduction FactoOrs..ccccccccccccccccccccccccccess—l/5 Pressure distribution on wall on rubble foundation.........+22.-/-1/8 Minikin wave pressure diagram. .cccccccccccccccccccccccccccccccce/—1Sl Dimensionless Minikin wave pressure and force..ccccccesseccecces/—185 Dimensionless Minikin wave pressure and fOrce.cccccecceccccvesee/—188 Minikin force reduction factor... ccccccccccccccccccscccccccccccce/—139 Minikin moment reduction for low wall...cceccccccccsccsccccccecce/—190 Wave pressures from broken waves: wall seaward of still-water HNicLtT CVaronevetodateleketel ole Tolel eel evetele: efebeletele)clelersieiererclelelcielefeleleletel el ctelclereteletelelctercie ALO Wave pressures from broken waves: wall landward of still-water NEIM EC iepelelefelelelelolelcleleloteleloleleloleleletclelcichelskelelevelelclercrcielicieclelelelelel siolereteiclelcheterel/ o>) Effect of angle of wave approach: plan VieW...ccceccccccceessee/—-199 7-107 7-108 YONOY) PAV) TN TAO? Younes 7-114 PONS TANG M7) 78 Youle 7-120 Nea TZ 2: T= W238) CONTENTS FIGURES--CONTINUED Page Wall SHAPCSicisle.c.c clelelelsle'c'e oe .e « 010 o's viele eles ele cle e/sielelels clele|clelelvisleielclelelelell mice Views of the tetrapod, quadripod, tribar, and dolos armor UT LESielelare ce cleo cle toie Wiese cloleie wi ele'elelele-aletelere olele-c sleictelelelele'clcie\elelelete\efetetelel aaaean Tetrapod SpecificationS...ercccccccccccececssccsccsccccsscsccsecsee/—218 Quadripod specificationS..cccccccccccscccccccccsccccssccecsessesel—219 Tribar SpeCifLicationS. .cccccccccccccccccccscsescsccsscvesesssece! 22 Dollos specifications cic vc cclsicele cle os ose ecle'vc ciccle sc clvls ole sielsleielelslelali am Toskane specifications. .ccccccccccccccccvccccccscscccsesecesscee! sae Modified cube specifications. .cccccccccccccccccccccccccccccccsee!—sad Hexapod specifications. ..ccccccccccccccccccccccccccscscssscscces/ 224 Rubble-mound section for seaward wave exposure with zero-to- moderate overtopping COonditions...ccccccccccccccccccsecesesese!—22/ Rubble-mound section for wave exposure on both sides with moderate overtopping CONditionS....ecceccccccccccccccceseesees/—228 Logic diagram for preliminary design of rubble structure......../-231 Logic diagram for evaluation of preliminary design......seeeeee+/-232 Stability number N, for rubble foundation and toe PEOCECE LOM s ois cic:e oleic cieivleie «creleicieisia’e s/o o\elele ole'e s cle'eieinie's\clsiele,6/elsieialoreteliieme ans Revetment toe scour aprons for Se€VELe WAVE SCOUT eceeceeeeceeeeee/—248 Definition sketch for Coulomb earth force equation...ececeeeeeee/—259 Active earth force for simple Rankine CcaS€...ecccoceccccccesecee 299 CHAPTER 7 STRUCTURAL DESIGN: PHYSICAL FACTORS I. WAVE CHARACTERISTICS 1. Design Criteria. Coastal structures must be designed to satisfy a number of sometimes conflicting criteria, including structural stability, functional performance, environmental impact, life-cycle cost, and other constraints which add challenge to the designer’s task. Structural stabtlity criteria are most often stated in terms of the extreme conditions which a coastal structure must survive without sustaining significant damage. The conditions usually include wave conditions of some infrequent recurrence interval, say 50 or 100 years, but may also include a seismic event (an earthquake or tsunami), a change in adjacent water depths, or the impact of a large vessel. The extent to which these "survival" criteria may be satisfied must sometimes be compromised for the sake of reducing construction costs. Analysis may prove that the con- sequences of occasional damage are more affordable than the first cost of a structure invulnerable to the effects of extremely rare events. A range of survival criteria should be investigated to determine the optimum final choice. Funettonal performance criteria are stated in terms of the desired effect of the structure on the nearby environment, or in terms of its intended function. For example, the performance criteria for a breakwater intended to protect a harbor in its lee should be stated in terms of the most extreme wave conditions acceptable in the harbor area; the features of the breakwater affecting wave transmission can then be designed to satisfy this criterion. The performance criteria for a groin intended to cause accretion of sand at a certain location will be dissimilar to those for a breakwater. Performance criteria may also require compromise for the sake of first cost, since repairing the consequences of performance limitations could be more afford- able. The high construction cost of most coastal structures requires that risk analysis and life-cycle costing be an integral part of each design effort. 2. Representation of Wave Conditions. Wind-generated waves produce the most powerful forces to which coastal structures are subjected (except for seismic sea waves). Wave characteristics are usually determined for deep water and then analytically propagated shoreward to the structure. Deepwater significant wave height H, and Significant wave period T may be determined if wind speed, wind duration, and fetch length data are available (see Ch. 3, Sec. V). This information, with water level data, is used to perform refraction and shoaling analyses to determine wave conditions at the site. Wave conditions at a structure site at any time depend critically on the water level. Consequently, a design stillwater level (SWL) or range of water levels must be established in determining wave forces on a structure. Struc- tures may be subjected to radically different types of wave action as the water level at the site varies. A given structure might be subjected to 7-1 nonbreaking, breaking, and broken waves during different stages of a tidal cycle. The wave action a structure is subjected to may also vary along its length at a given time. This is true for structures oriented perpendicular to the shoreline such as groins and jetties. The critical section of these structures may be shoreward of the seaward end of the structure, depending on structure crest elevation, tidal range, and bottom profile. Detailed discussion of the effects of astronomical tides and wind- generated surges in establishing water levels is presented in Chapter 3, WAVE AND WATER LEVEL PREDICTIONS. In Chapter 7, it is assumed that the methods of Chapter 3 have been applied to determine design water levels. The wave height usually derived from statistical analysis of synoptic weather charts or other historical data to represent wave conditions in an extreme event is the significant height H,. Assuming a Rayleigh wave height distribution, H. may be further defined in approximate relation to other height parameters of the statistical wave height distribution in deep water: 4/3 or H, = average of highest 1/3 of all waves (an alternate defini- tion of H, sometimes applied is 4 times the standard deviation of the sea surface elevations, often denoted as Hee) m fo) Hyp) = 1-27 H, = average of highest 10 percent of all waves (7-1) aE aioe i H, = average of highest 5 percent of all waves (7=2) H, ~ 1.67 H, = average of highest 1 percent of all waves (7=3) Advances in the theoretical and empirical study of surface waves in recent years have added great emphasis to the analysis of wave energy spectra in estimating wave conditions for design purposes. Representation of wave conditions in an extreme event by wave energy as a function of frequency provides much more information for use in engineering designs. The physical processes which govern the transformation of wave energy are highly sensitive to wave period, and spectral considerations take adequate account of this fact. An important parameter in discussing wave energy spectra is the energy- based wave height parameter Ho » which corresponds to the significant wave height, H. » under most condifions. An equally important parameter is the peak spectral period, T,_ , which is the inverse of the dominant frequency of a wave energy spectrum. ~The peak spectral period, fT, , is comparable to the significant wave period, T, , in many situations. The total energy, E , and the energy in each frequency band, E(w) , are also of importance (see Ch. 3, Sec. I1,3, Energy Spectra of Waves). 3. Determination of Wave Conditions. All wave data applicable to the project site should be evaluated. Visual observation of storm waves, while difficult to confirm, may provide an indica- tion of wave height, period, direction, storm duration, and frequency of occurrence. Instrumentation has been developed for recording wave height, Y=? period, and direction at a point. Wave direction information is usually necessary for design analysis, but may be estimated from directional wind data if physical measurements of wave direction are not available. Visual observa- tions of wave direction during exteme events are important in verifying estimates made from wind data. If reliable visual shore or ship observations of wave direction are not available, hindcast procedures (Ch. 3, Sec. V, SIMPLIFIED METHODS FOR ESTIMATING WAVE CONDITIONS) must be used. Reliable deepwater wave data can be analyzed to provide the necessary shallow-water wave data. (See Ch. 2, Sec. II,3,h, Wave Energy and Power, and Ch. 2, Sec. III, WAVE REFRACTION, and IV, WAVE DIFFRACTION.) 4. Selection of Design Wave Conditions. The choice of design wave conditions for structural stability as well as for functional performance should consider whether the structure is subjected to the attack of nonbreaking, breaking, or broken waves and on the geometrical and porosity characteristics of the structure (Jackson, 1968a). Once wave characteristics have been estimated, the next step is to determine if wave height at the site is controlled by water depth (see Ch. 2, Sec. VI, BREAKING WAVES). The type of wave action experienced by a structure may vary with position along the structure and with water level and time at a given structure section. For this reason, wave conditions should be estimated at various points along a structure and for various water levels. Critical wave conditions that result in maximum forces on structures like groins and jetties may occur at a location other than the seaward end of the structure. This possibility should be considered in choosing design wave and water level conditions. Many analytical procedures currently available to estimate the maximum wave forces on structures or to compute the appropriate weights of primary armor units require the choice of a single design wave height and period to represent the spectrum of wave conditions during an extreme event. The peak spectral period is the best choice in most cases as a design wave period (see Ch. 3, Sec. V, SIMPLIFIED METHODS FOR ESTIMATING WAVE CONDITIONS). The choice of a design wave height should relate to the site conditions, the construction methods and materials to be used, and the reliability of the physical data available. If breaking in shallow water does not limit wave height, a nonbreaking wave condition exists. For nonbreaking waves, the design height is selected from a statistical height distribution. The selected design height depends on whether the structure is defined as rigid, semirigid, or flexible. Asa rule of thumb, the design wave is selected as follows. For rigid structures, such as cantilever steel sheet-pile walls, where a high wave within the wave train might cause failure of the entire structure, the design wave height is normally based on H, . For semtrigid structures, the design wave height is selected from a range of Hig to 4H, - Steel sheet-pile cell structures are semirigid and can absorb wave pounding; therefore, a design wave height of H}g may be used. For flextble structures, such as rubble-mound or riprap structures, the design wave height usually ranges from H,. to the significant wave height H, . H is currently favored for most coastal breakwaters or jetties. Waves higher than the design wave height impinging on flexible structures seldom create serious damage for short durations of extreme wave UGS action. When an individual stone or armor unit is displaced by a high wave, smaller waves of the train may move it to a more stable position on the slope. Damage to rubble-mound structures is usually progressive, and an extended period of destructive wave action is required before a structure ceases to provide protection. It is therefore necessary in selecting a design wave to consider both frequency of occurrence of damaging waves and economics of construction, protection, and maintenance. On the Atlantic and gulf coasts of the United States, hurricanes may provide the design criteria. The frequency of occurrence of the design hurricane at any site may range from once in 20 to once in 100 years. On the North Pacific coast of the United States, the weather pattern is more uniform; severe storms are likely each year. The use Of MH as a design height under these conditions could result in extensive annual damage due to a frequency and duration of waves greater than H in the spectrum. Here, a higher design wave of Hjg or Hy, may be advisable. Selection of a design height between He and Hs is based on the following factors: (a) Degree of structural damage tolerable and associated maintenance and repair costs (risk analysis and life-cycle costing). (b) Availability of construction materials and equipment. (c) Reliability of data used to estimate wave conditions. a. Breaking Waves. Selection of a design wave height should consider whether a structure is subject to attack by breaking waves. It has been commonly assumed that a structure sited at a water depth d, (measured at design water stage) will be subjected to breaking waves if d,< 1.3H where H = design wave height . Study of the breaking process indicates that this assumption is not always valid. The breaking point is defined as the point where foam first appears on the wave crest, where the front face of the wave first becomes vertical, or where the wave crest first begins to curl over the face of the wave (see Ch. 2, Sec. VI, BREAKING WAVES). The breaking point is an intermediate point in the breaking process between the first stages of instability and the area of complete breaking. Therefore, the depth that initiates breaking directly against a structure is actually some distance seaward of the structure and not necessarily the depth at the structure toe. The presence of a structure on a beach also modifies the breaker location and height. Jackson (1968a) has evaluated the effect of rubble structures on the breaking proccess. Additional research is required to fully evaluate the influence of structures. Hedar (1965) suggested that the breaking process extends over a distance equal to half the shallow-water wavelength. This wavelength is based on the depth at this seaward position. On flat slopes, the resultant height of a wave breaking against the structure varies only a small amount with nearshore slope. A slope of 1 on 15 might increase the design breaking wave height by 20 to 80 percent depending on deepwater wavelength or period. Galvin (1968, 1969) indicated a relationship between the distance traveled by a plunging breaker and the wave height at breaking H,. The relationship between the breaker travel distance x and the breaker height Hy depends on the nearshore slope and was expressed by Galvin (1969) as: 7-4 x= tA, = (4.0 -9.25 m)H, (7-4) p where m is the nearshore slope (ratio of vertical to horizontal distance) and 1 = (4.0 - 9.25 m) is the dimensionless plunge distance (see Fig. 7-1). Region where Breaking Starts Xp = Breaker Travel se Distance = THp et ie b 4 / Proposed Structure ( Effect of Structure on Breaking has not been Considered ) Wave Profile at Start of Breaking Wave Profile when Breaking is Nearly Complete Figure 7-1. Definition of breaker geometry. Analysis of experimental data shows that the relationship between depth at breaking d, and breaker height Hp, is more complex than indicated by the equation dp = 1.3 Hp . Consequently, the expression d, = 1.3 h should not be used for design purposes. The dimensionless ratio dp/H,p varies with NMearshore slope m _ and incident wave steepness Hp/gT as indicated in Figure 7-2. Since experimental measurements of dp/Hp exhibit scatter, even when made in laboratory flumes, two sets of curves are presented in Figure =e The curve of a versus Hp/gT represents an upper limit of experimentally observed values. of d /Hy » hence a = (d /By mas : Similarly, 8 is an approximate lower limit of measurements o dp/Hp ; therefore, 8 = (d, /H ree ° Figure 7-2 can be used with Figure 7-3 to determine the water depth in which an incident wave of known period and unrefracted deepwater height will break. kk kk Kk kk kk Ok KOK & & & KEXAMPLE PROBLEM 1 * * * * & & KK KK KK KK GIVEN: A Wave with period T= 10s , and an unrefracted deep-water height of HA = 1.5 meters (4.9 ft) advancing shoreward over a nearshore slope of m = ORO50NC1H20)) Us) 9 z13/ H snszea g pue © °*7Z-/ 21Nn3Ty gif (2261 ‘106B0m 10440) ay 0200 8100 910°0 . : 0100 8000 500) | _l ae ' = ; es [mle T IE + if if [zal if ln lea {in| | Sle & ine = Ua pee t 7 por IESE EE am saiaaeiele feeiaieet i as j \ TA%8 14 ‘ \Wa' NN A \ ¥ = , : h ae ‘ma \ j i, ll 9aS/}}) <— (2998/44) ay ee Siiesritier sae ae SSS Gee SE22R228 S me / ey Am 4 A ee auuers 7c) 7 a aug US SEE ESeEe BOAO See oe Ee SOLOLEL 4 f day, HH EOOERHEE <7h/ AU LTT TT TT tt) — lea a BEanE a etait ea HOE SOLU ===". SESESSESS=S=/— SESS SSSSSee2==55 SUTTON Au Mn CURT ST “ my it Srisst HH? = S aval = (after Goda, 1970a) versus deepwater wave steepness Breaker height index Hy, / HS Dy 2 Hofer - Figure 7-3. FIND: The range of depths where breaking may start. SOLUTION: The breaker height can be found in Figure 7-3. Calculate He gS) 2 = = 0.00153 gT (9.8) (10) 2 and enter the figure to the curve for an m= 0.05 or 1:20 slope. H,/HS is read from the figure Hp a 1.65 Ho Therefore Hy = 1.65(H5)= 1.65 (1.5) = 2.5 m (8.2 ft) H,/eT? may now be computed Hp Das aes i 0.00255 gT (9.8) (10) Entering Figure 7-2 with the computed value of H /g1? the value of a is found to be 1.51 and the value of § fora peach slope of 0.050 is 0.93. Then i pyl (55) i] 3.8 m (12.5 ft) (dy drncize Eat Hy Das} ((255)) S255) im, (7/05) 328) (dy min = 8 Hy Where wave characteristics are not significantly modified by the presence of structures, incident waves generally will break when the depth is slightly greater than (d,) ake As wave-reflection effects of shore structures begin to influence "breaking, depth of breaking increases and the region of breaking moves farther seaward. As illustrated by the example, a structure sited on a 1 on 20 slope under action of the given incident wave (HS = 5) ml C4559) S6t)/s)5 = sllOls)) could be subjected to waves. breaking directly on it, if the depth at the structure toe were between (dy in = Aos\ in (ToS see)) etal Ce Se Sich im CilP~oS) 182) 4 NOTE: Final answers should be rounded to reflect the accuracy of the original given data and assumptions. UMC UME es ates I ee It CH ke se I te oN be to to oF tt bt to to ts fo oF G2 fR to Go o2 ES b. Design Breaker Height. When designing for a breaking wave condition, it is desirable to determine the maximum breaker height to which the structure might reasonably be subjected. The design breaker height H, depends on the depth of water some distance seaward from the structure toe where the wave first begins to break. This depth varies with tidal stage. The design breaker height depends, therefore, on critical design depth at the structure toe, slope on which the structure is built, incident wave steepness, and distance traveled by the wave during breaking. Assuming that the design wave is one that plunges on the structure, design breaker height may be determined from: ie tp p> mt ioe P where d is depth at the structure toe, £8 is the ratio of breaking depth to breaker height d,/H, , m is the nearshore slope, and rc is the dimensionless plunge distance x1 Hp from equation (7-4). P The magnitude of 8 to be used in equation (7-5) cannot be directly known until H is evaluated. To aid in finding , Figure 7-4 has been derived from equations (7-4) and (7-5) using 8 values from Figure 7-2. If maximum design depth at the structure and incident wave period are known, design breaker height can be obtained using Figure 7-4. kk Kk kK Ok k Ok Ok Ok OK OK & & * & EXAMPLE PROBLEM 2 * * * * * * ® KK RK KK KX GIVEN: (a) Design depth structure toe, d, = 255) in (sic s812)) (b) Slope in front of structure is 1 on 20, or m= 0.050 . (c) Range of wave periods to be considered in design T= 6s (minimum) T= 10 s (maximum) FIND: Maximum breaker height against the structure for the maxium and minimum wave periods. SOLUTION: Computations are shown for the 6-second wave; only the final results for the 10-second wave are given. From the given information, compute Eee 0.0071 (T (9.8) (6)? d s 6 s) r & Enter Figure 7-4 with the computed value of d,/gT* and determine value of H, /d, from the curve for a slope of m= 0.050 . d 5, ase 0.0071 ; 3~ = 1.10 (T= 6s) gT s *aanjonays 4e yydep SATILTEI SNsAsA WYZTey 1Seyxee1q usTSep SsseTUOTSUSUTC *y-/ ein8TI alt 1p (2261 ‘1e660m 10440) ? ; : ; 0200 8100 9100 vl00 210'0 010'0 8000 900°0 4000 2000 ebesstostesasandicevastasdlaatactiaatae sgaudadee ootastastogbadentgssantastart geet aula) i 1 saea Tet OOO eooo0! Ere T iE SoOUeBe at en ea ea [ein inGOooee jGBoo! - Tea paseas [a + L r ++ ie or t t al t t i = ‘mie a Tala etal ro l | I a lalate! aL a al jefe] if fe | | i a I ry : aa80 4. 4 : ine BEEooeo! C jalele fatale mB ma felaisietals(eleteiele if aeravadfosssians | sifasistasgatosettacaifassifessitescil Se , 7 See aEae | ae { [itt Peer eee if a i. i — 1 Det ict falajare rH ry iajaiaial SHI SS Lae welt ae a5 Saeeeeeeee L HH | ia ! + ial ror tT a im B eeesgeeesaae HE | EEEEEEEEEEEEEEe ata . in aT rf i] 7 1 ct T if 1) i mt +-+4 at 1 tet —4-- | ia 9d0|8 G10ySsD0N +--+ ‘ai } — i + coh IMS vbiseg ” Al 1a TA | eect oan Het : fatetatatal | tH : : } 4+ i 7-10 Note that H,/d is not identical with H,/d where d, is the depth at breaking and qd. is the depth at the structtire. In geferal, because of nearshore slope, d., < d,, ; therefore H,/d . > H/ ds é For the example, breaker height can now be computed from Ln = 1.10 a = e0) 1(2.5)) = 2.8m C92 LE) CL = 6s) For the 10-second wave, a similar analysis gives ete = 1.27 an = 1627. (2.5) = 362m. C10.5 £E) Cr =1100s) As illustrated by the example problem, longer period waves result in higher design breakers; therefore, the greatest breaker height which could possibly occur against a structure for a given design depth and nearshore slope is found by entering Figure 7-4 with d ,/gT = 0 (infinite period). For the example problem d H BE Sig 2 e124 Ga = 106050) 2 d F518 s H, = 1.41 d= 1.41 (2.5) = 3.5 m (11.6 £t) emma ae, ove)! 1. OK Ae He) He ee KS RK Ke Ke OR KK eee ee Ke eK ee) It is often of interest to know the deepwater wave height associated with the design height obtained from Figure 7-4. Comparison of the design associated deepwater wave height determined from Figure 7-4 with actual deepwater wave statistics characteristic of the site will give some indication of how often the structure could be subjected to breakers as high as the design breaker. Deepwater height may be found in Figure 7-5 and information obtained by a refraction analysis (see Ch. 2, Sec. III, WAVE REFRACTION). Figure 7-5 is based on observations by Iversen (1952a, 1952b), as modified by Goda (1970a), of periodic waves breaking on impermeable, smooth, uniform laboratory slopes. Figure 7-5 is a modified form of Figure 7-3. kkk kK kK kK kK kK Ok Ok Ok Ok Ok & K KEXAMPLE PROBLEM 3 * * * * & KK KKK KK KKK GIVEN: (a) H, = 2.8 m (9.2 ft) (T = 6 s) and Hy = 3.2 m (10.5 ft) (see previous example) (T= 10 s) (b) Assume that refraction analysis of the structure site gives [> (0) Ko Tae 0.85 (T = 6 s) and Kp =) Oe75 (T = 10 s) for a given deepwater direction of wave approach (see Ch. 2, Sec. III, WAVE REFRACTION). 2.8 il i 26h | Sane | i UHL ABREU SLE iN AWB | 2.4 E+ —- H hits | To EHH L awe 2.2 th COT mene ane a . na TH | THAT RRSGG HOGA FRCKL CLV Sana BOA ATT ee tH to tHe | I T i - 7 1.8 Froth 0g 000 o nn Tt tt : ig an is HAQUHL SBOE SSEEe: a aaa ratte PAE ECE CAe ETT 2 ion ~f--- GGG ee t Ti ae m0 HELE tnt + 1.0 Ht th ia Tt | itty so — Li NH BEBE ah | ies] i 0.8 iH tm a i tr | | i t t tT th tae Hi + a A TH TTT t LHRH Ht aL 0.0004 0.0006 = 0.00 0.002 0.003 0.004 0.006 0.01 0.02 0.03 Hp (after Goda, 1970a) gt? Figure 7-5. Breaker height index Hy /H versus H,/et” 5 FIND: The deepwater height H, of the waves resulting in the given breaker heights H, SOLUTION: Calculate H,/gT for each wave condition to be investigated. ee Tas a 0.0079 (T = 6 s) gT (9.8) (6) With the computed value of 4. /gt* enter Figure 7-5 to the curve for a slope of m = 0.05 and determine H,/H* which may be considered an ultimate shoaling coefficient or the shoaling coefficient when breaking occurs. Hp Hp . ie 0.0079 ; Ww gT = 1.16 (T = 6 s) With the value of Hy / 5 thus obtained and with the value of Kp obtained from a refraction analysis, the deepwater wave height resulting in the design breaker may be found with equation (7-6). Hp He = a 7-6 2) K, (i / HS) (7-6) H, is the actual deepwater wave height, where H> is the wave height in deep water if no refraction occurred (H* = unrefracted deepwater height). Where the bathmetry is such that significant wave energy is dissipated by bottom friction as the waves travel from deep water to the structure site, the computed deepwater height should be increased accordingly (see Ch. 3, Sec. VII, HURRICANE WAVES, for a discussion of wave height attenuation by bottom friction). Applying equation (7-6) to the example problem gives H 2.8 b = (85) (1s16) > 278 @ C92 ft) (T = 6 s) A similar analysis for the 10-second wave gives Hp = 2.8 m (9.2 ft) Gi =F10)¥s)) A wave advancing from the direction for which refraction was analyzed, and with a height in deep water greater than the computed H, , will break at a distance greater than Xp feet in front of the structure. Waves with a deepwater height less than the H, computed above could break directly against the structure; however, the corresponding breaker height will be less than the design breaker height determined from Figure 7-4. Mk oe Ke OK KOK Ke OK aK Ok Ok ae Ke OR A OK Ok OR OK OR & & OR OR KF KR KK KR RK KOR KOK KK T—13 c. Nonbreaking Waves. Since statistical hindcast wave data are normally available for deepwater conditions (d > L,/2) or for depth conditions some distance from the shore, refraction analysis is necessary to determine wave characteristics at a nearshore site (see Ch. 2, Sec. III, WAVE REFRACTION). Where the continental shelf is broad and shallow, as in the Gulf of Mexico, it is advisable to allow for a large energy loss due to bottom friction (Savage, 1953), (Bretschneider, 1954a, b) (see Ch. 3, Sec. VII, HURRICANE WAVES). General procedures for developing the height and direction of the design wave by use of refraction diagrams follow: From the site, draw a set of refraction fans for the various waves that might be expected (use wave period increments of no more than 2 seconds) and determine refraction coefficients by the method given in Chapter 2, Section III, WAVE REFRACTION. Tabulate refraction coefficients determined for the selected wave periods and for each deepwater direction of approach. The statistical wave data from synoptic weather charts or other sources may then be reviewed to determine if waves having directions and periods with large refraction coefficients will occur frequently. The deepwater wave height, adjusted by refraction and shoaling coef- ficients, that gives the highest significant wave height at the structure will indicate direction of approach and period of the design wave. The inshore height so determined is the design significant wave height. A typical example of such an analysis is shown in Table 7-l. In this example, although the highest significant deepwater waves approached from directions ranging from W to NW , the refraction study indicated that higher inshore significant waves may be expected from more southerly directions. The accuracy of determining the shallow-water design wave by a refraction analysis is decreased by highly irregular bottom conditions. For irregular bottom topography, field observations including the use of aerial photos or hydraulic model tests may be required to obtain valid refraction information. d. Bathymetry Changes at Structure Site. The effect of a proposed structure on conditions influencing wave climate in its vicinity should also be considered. The presence of a structure might cause significant deepening of the water immediately in front of it. This deepening, resulting from scour during storms may increase the design depth and consequently the design breaker height if a breaking wave condition is assumed for design. If the material removed by scour at the structure is deposited offshore as a bar, it may provide protection to the structure by causing large waves to break farther seaward. Experiments by Russell and Inglis (1953), van Weele (1965), Kadib (1962), and Chesnutt (1971), provide information for estimating changes in depth. A general rule for estimating the scour at the toe of a wall is given in Chapter 5. e. Summary~-Evaluating the Marine Environment. The design process of evaluating wave and water level conditions at a structure site is summarized in Figure 7-6. The path taken through the figure will generally depend on the type, purpose, and location of a proposed structure and on the availability of data. Design depths and wave conditions at a structure can usually be determined concurrently. However, applying these design conditions to structural design requires evaluation of water levels and wave conditions that 7-14 Table 7-1. Determination of design wave heights. 1 2 3 4 5 Combined Refraction Refracted and and Shoaling Shoaled Wave Coefficients! Height (Kp Kg) (m) Significant Deepwater Wave Height (m) 5.0 Direction 1 Refraction coefficient, Kp = Vb,/b at design water level. Shoaling coefficient, Kg, = H/H, at design water level. 2 Adopted as the significant design wave height. NOTES: Columns 1, 2, and 3 are taken from the statistical wave data as determined from synoptic weather charts. Columns 4 is determined from the relative distances between two adjacent orthogonals in deep water and shallow water, and the shoaling coefficient. Column 5 is the product of columns 2 and 4. can reasonably be assumed to occur simultaneously at the site. Where hurri- canes cross the coast, high water levels resulting from storm surge and extreme wave action generated by the storm occur together and usually provide critical design conditions. Design water levels and wave conditions are needed for refraction and diffraction analyses, and these analyses must follow establishment of design water levels and design wave conditions. The frequency of occurrence of adopted design conditions and the frequency of occurrence and duration of a range of reasonable combinations of water level and wave action are required for an adequate economic evaluation any proposed shore protection scheme. II. WAVE RUNUP, OVERTOPPING, AND TRANSMISSION 1. Wave Runup a. Regular (Monochromatic) Waves. The vertical height above the still- water level to which water from an incident wave will run up the face of a structure determines the required structure height if wave overtopping cannot be permitted (see Fig. 7-7 for definitions). Runup depends on structure shape and roughness, water depth at structure toe, bottom slope in front of a structure, and incident wave characteristics. Because of the large number of variables involved, a complete description is not available of the runup phenomenon in terms of all possible ranges of the geometric variables and wave conditions. Numerous laboratory investigations have been conducted, but mostly for runup on smooth, impermeable slopes. Hall and Watts (1953) investigated runup of solitary waves on impermeable slopes; Saville (1956) investigated runup by periodic waves. Dai and Kamel (1969) investigated the runup and rundown of waves on rubble breakwaters. Savage (1958) studied effects of structure roughness and slope permeability. Miller (1968) investigated runup of undular and fully broken waves on three beaches of different roughnesses. LeMehaute (1963) and Freeman and LeMehaute (1964) studied long-period wave runup analytically. Keller et al. (1960), Ho and Meyer (1962), and Shen and Meyer (1963) studied the motion of a fully broken wave and its runup on a sloping beach. Figures 7-8 through 7-13 summarize results for small-scale laboratory tests of runup of regular (monochromatic) waves on smooth impermeable slopes (Saville, 1958a). The curves are in dimensionless form for the relative runup R/ Hz, as a function of deepwater wave steepness and structure slope, where R is the runup height measured (vertically) from the SWL and H- is the unrefracted deepwater wave height (see Figure 7-7 for definitions). Results predicted by Figures 7-8 through 7-12 are probably smaller than the runup on prototype structures because of the inability to scale roughness effects in small-scale laboratory tests. Runup values from Figures 7-8 through 7-12 can be adjusted for scale effects by using Figure 7-13. Runup on impermeable structures having quarrystone slopes and runup on vertical, stepped, curved and Galveston-type recurved seawalls have been studied on laboratory-scale models by Saville (1955, 1956). The results are DETERMINE DESIGN WAVE DETERMINE DESIGN DEPTH AT STRUCTURE Considerations 1) Tidal ranges meon spring 2) Storm surge 3) Voriations of above foctors along structure 1S WAVE DATA AVAILABLE ? DEPTH IN GENERATING AREA AT Shallow WHAT LOCATION ? Goge dato or visual observations SUPPLEMENT DATA BY HINDCASTING Considerations: 1) Synoptic weather chorts 2) Wind doto 3) Fetch doto Offshore NOTE = Greatest depth ot structure will not necessorily produce the most severe design condition! DETERMINE BATHYMETRY AT SITE Existing hydrographic charts or survey dato BATHYMETRY HINOCASTING TO DETERMINE HINOCASTING TO DETERMINE WAVE CLIMATE WAVE CLIMATE Considerations: Considerotions: 1) Synoptic weother 1) Wind data charts 2) Fetch doto 2) Wind dato 3) Hydrography 3) Fetch dato Visual observations or ovailable hindcost data DESIGN DEPTHS SIGNIFICANT WAVE HEIGHT, RANGE OF PERIODS (Hiya. Hisio 1 Hiyio0 ond Spectrum) DETERMINE DESIGN WAVE AT STRUCTURE SITE Refraction doto ovoilable ? (aerial photographs) Refraction analysis Diffraction analysis DESIGN WAVE HEIGHT, DIRECTION AND CONDITION (Breaking, non-breaking or broken ) AT STRUCTURE SITE FREQUENCY ANALYSIS ( Determine frequency of occurrence of design conditions ) Figure 7-6. Logic diagram for evaluation of marine environment. Uy Point of maximum wave runup Design SWL Ho Figure 7-7. Definition sketch: wave runup and overtopping. shown in Figures 7-14 through 7-18. Effects of using graded riprap on the face of an impermeable structure (as opposed to quarrystone of uniform site for which Figure 7-15 was obtained) are presented in Figure 7-19 for a 1 on 2 graded riprap slope. Wave rundown for the same slope is also presented in Figure 7-19. Runup on permeable rubble slopes as a function of structure slope and H/T is compared with runup on smooth slopes in Figure 7-20. Corrections for scale effects, using the curves in Figure 7-13, should be applied to runup values obtained from Figures 7-8 through 7-12 and 7-14 through 7-18. The values of runup obtained from Figure 7-19 and 7-20 are assumed directly applicable to prototype structures without correction for scale effects. As previously discussed, Figures 7-8 through 7-20 provide design curves for smooth and rough slopes, as well as various wall configurations. As noted, there are considerable data on smooth slopes for a wide range of d ,/H values, whereas the rough-slope data are limited to values of d_/H* >3. rf is frequently necessary to determine the wave runup on permeable rubble structures for specific conditions for which model tests have not been conducted, such as breaking waves for d ,/HS < 3. To provide the necessary design guidance, Battjes (1974), Ahrens (1977a), and Stoa (1978) have sug- gested the use of a roughness and porosity correction factor that allows the use of various smooth-slope design curves for application to other structure slope characteristics. This roughness and porosity correction factor, r , is the ratio of runup or relative runup on rough permeable or other nonsmooth slope to the runup or relative runup on a smooth impermeable slope. This is expressed by the following equation: eee eee a ste es sete ee oy S aatses rome 8.0 10.0 oil i i | 12 a 4.0 5.0 6.0 0:3 04 0.5.06 Os (2 (cot @) Slope a/RG = Wave runup on smooth, impermeable slopes when (structures fronted by a 1:10 slope). Figure 7-8. H—N9 Se ee ee Se ee ee ee oe ee ee lie 7.0 fees boa GE ee eee oe ee eee ee aes eof ee ee eee Ee SS Se pops yf EEE eas Sa a eee = 5.0 : eee = propo ee Son ian nee ee ae fae a= eee eS Se Sere ee We ee, Wi ae i] / vif Ley 0.1 0.15 0.2 O33 2045 O5i0'6 SOB RO IED" 2:0 3.0 40 5060 8.0 10.0 Slope (cot @ ) Figure 7-9. Wave runup on smooth, impermeable slopes when d /H* * 0.45 (structures fronted by a 1:10 slope). Beg, Ramee Uf Wa ME a cate | a 0.4 0.5 06 4.0 5.0 6.0 3.0 2.0 1.5 1.0 0.8 Slope (cot @) 0.3 Olid Ore 8.0 10.0 d /H* * 0.80 Wave runup on smooth, impermeable slopes when 2A (structures fronted by a 1:10 slope). Figure 7-10. 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AD Tomaep) Sadots 7:1 ‘deadta papei3 uo umopunaz pue dnuni sae, ' 900°0 vo0O0 £000 z000 §S!1000 100°0 9000°0 iu unaseeaii aE Gees *6I-L eansty vO000 £0000 20 = Ps FH sees He ese Ht esa HH LL ae 1m HH 7-30 7 te fee i iy | ue i ULL, {74 aa: iF LWA ee lig ¢ ea eng iy 4 ar Viv ae it ae aes : = aa 7 af fe 2 RL Pete aay Fria a ia a a i shore i Ha : iH LN Vi f rae se Ai fine alter r raat ae a He ie aa AU e co L cae Li = doeabeeasl SEEREE= $5335 Essseggifl titties! SSe°"= 7-31 0.03 0.015 0.02 0.006 0.008 0.0/ 0.003 0.004 0.0015 0.002 i iat T CO 12] SSS aeea ee is 4 taht St s 93008) Sess: H HH 4 Ei i134 Hy = aot S a: Ea HH i cee PH 2 | + cas on 1 me E os OE GD LO Wa Ol UBS 4: a tH 1 os T ape ead cone eran Oe a 1RaOH eRGRS NGoa A mat as a ot 0.001 Comparison of wave runup on smooth slopes with runup on permeable rubble slopes Figure 7-20. Gl l= >> B50) )) 6 (data for & O Se Ea esp tvs pe) ya a ~ R (smooth slope) — SST. R/H*, (smooth slope) Table 7-2 indicated the range of values of r for various slope character- istics. This roughness and porosity correction factor is also considered applicable, as a first approximation, in the analysis of wave runup on slopes having surface materials with two or more different roughness values, r. Until more detailed guidance is available, it is suggested that the percentage of the total slope length, 2% , subjected to wave runup of each roughness value be used to develop an adjusted roughness correction value. This is expressed by the equation it R r (adjusted) age + _ r,t Dito este (7-8) 1 where & is the total slope length, 2& is the length of slope where the roughness value ro applies, 2 is the length of slope where the roughness value r applies, and so on. ‘This procedure has obvious deficiencies as it does not account for location of the roughness on the structure and the vary- ing interaction of slope roughness characteristics to the depth of water jet running up the structure slope. Table 7-2. Value of r for various slope characteristics (after Battjes, 1974). Smooth, impermeable 42242 222222 J =——=—=— 1.00 Concrete blocks Fitted 0.90 Basalt blocks Fitted 0.85 to 0.90 Gobi blocks Fitted 0.85 to 0.90 GrassnPy he OU ets ge OR dae oe 0.85 to 0.90 One layer of quarrystone Random 0.80 (impermeable foundation) Quarrystone Fitted 0.75 to 0.80 Rounded quarrystone Random 0.60 to 0.65 Three layers of quarrystone Random 0.60 to 0.65 (impermeable foundation) Quarrystone Random 0.50 to 0.55 Concrete armor units Random 0.45 to 0.50 (~ 50 percent void ratio) The use of the figures to estimate wave runup is illustrated by the following example. Usy2 kok kk kK KOR Ok Ok KOK OK & & & KEXAMPLE PROBLEM 4 * *¥ *¥ ®¥ KK KKK KK KKK GIVEN: An impermeable structure has a smooth slope of 1 on 2.5 and is subjected to a design wave, H = 2.0 m (6.6 ft) measured at a gage located in a depth d= 4.5 m (14.8 ft) . Design period is T = 8 sec . Design depth at structure toe at high water is d, = 3.0 m (9.8 ft) . (Assume no change in the refraction coefficient between the structure and the wave gage.) FIND: (a) The height above the SWL to which the structure must be built to prevent overtopping by the design wave. (b) The reduction in required structure height if uniform-sized riprap is placed on the slope. SOLUTION: (a) Since the runup curves are for deepwater height H~ , the shallow-water wave height H = 2.0 m(6.6 ft) must be converted to an equivalent deepwater value. Using the depth where the wave height is measured, calculate O gT 9/58) (8) From Table C-1, Appendix C, for d aa 0.0451 O H ine = 1.041 Therefore fy ee ce a RED O 1.041 1.041 To determine the runup, calculate H On a eee e030 s eT” (9.8) (8)? and using the depth at the structure toe d. =53/50)m (9 Si tb) 133 Che DONO jie oo ile sar 1.58 oO e R Figure 7-10: == = 080) 5 = = 2380 H H O O oe R Interpolated Value: ae hosts} 2 ae 2.5 O d A s R Figure 7-11: aie 2.0 > F 75S) O O Ww I = 25m WSO) R= 458 om CLS.) ft) The scale correction factor k can be found from Figure 7-13. The slope in terms of m= tan 0O is Nags tan 90 = ORB 0.40 The corresponding correction factor for a wave height HS = 1.9 m (6.2 £6) is k = 1.169 Therefore, the corrected runup is R = 1.169 (4.8) = 5.6 m (18.4 ft) (b) Riprap on a slope decreases the maximum runup. Hydraulic model studies for the range of possible slopes have not been conducted; however, Figure 7- 15 can be used with Figures 7-10 and 7-11 to estimate the percent reduction of runup resulting from adding riprap to a 1 on 1.5 slope and to apply that reduction to structures with different slopes. From an analysis similar to the above, the runup, uncorrected for scale effects, on a 1 on 1.5 smooth, impermeable slope is = = 3.04 Oo |smooth From Figure 7-15 (riprap), entering with H¢/gT- = 0.0030 and using the curve for d,/ HS = 1.50 which is closest to the actual value of 7-34 (s:] . = 1.43 H, riprap The reduction in runup is therefore, (R/H’,) riprap a 1.43 = Oey (R/ Hy ) smooth 20) Applying this correction to the runup calculated for the 1 on 2.5 slope in the preceding part of the problem gives > = 0.47 R R-iprap snGoth = 0.47 (5.8) = 2.7 m (8.9 ft) Since the scale-corrected runup (5.8 m) was multiplied by the factor 0.47, the correction for scale effects is included in the 1.7-m runup value. This technique gives a reasonable estimate of runup on riprapped slopes when model test results for the actual structure slope are not available. MEET ee 1) He He. OK Fe He ee RE He RR de Fk de He ok) OR Meats eK de) Fe OK KEK) oe cK Saville (1958a) presented a method for determining runup on composite slopes using experimental results obtained for constant slopes. The method assumes that a composite slope can be replaced with a hypothetical, uniform slope running from the bottom, at the point where the incident wave breaks, up to the point of maximum runup on the structure. Since the point of maximum runup is the answer sought, a method of successive approximations is used. Calculation of runup on a composite slope is illustrated by the following example problem for a smooth-faced levee. The method is equally applicable to any composite slope. The resultant runup for slopes composed of different types of surface roughness may be calculated by using a proportionate part of various surface roughnesses of the composite slope on the hypothetical slope. The composite-slope method should not be used where beach berms are wider than L/4 , where L is the design wavelength for the structure. In the case where a wide berm becomes flooded or the water depth has been increased by wave setup (see Ch. 3, Sec. VIII) such as a reef, the wave runup is based on the water depth on the berm or reef. KKK kK kk kk Rk k Ok Ok & & & & EXAMPLE PROBLEM 5 * * * * & & KK OK KOK Kk RK GIVEN: A smooth-faced levee (cross section shown in Fig. 7-21) is subjected to a design wave having a period T= 8 s-~ and an equivalent deepwater height Ho = 1.5m (4.9 ft) . The depth at the structure toe is d,=1.2m (SLO as ‘i FIND: Using the composite slope method, determine the maximum runup on the levee face by the design wave. 1=35 “uoT}0es SSOID seAeT e& JO oTduexe 02 :edotTs e3tsodwos azoxy dnuni jo VOLIEIMOpPeO alCHL ain3sty aan b'8:| adois wz Noe ae Snore LZZZZZZZZ ce | a meee 8: ese, = Foe ten a - IMS (‘xoiddo | jOuly ) IDUIy) WOO: j-"y W6*9 ado|js pawnssp ySly 403 AV wg | po fecal) gust 8 Nie Swe | 09:1 shee Fite KUT we'b='u be keg | we | adois. oi——-+t- ‘xouddo jsul4 wO'6 wo9 w6 adojs pawnssp 4Siij 40} X= WO'ZD 7-36 SOLUTION: The runup on a 1 on 3 slope (tan 0 = 0.33) is first calculated to determine whether the runup will exceed the berm elevation. Calculate d Bo. lez He Ores e-8 and a 18 = = 0.0024 ae | Oak) Ge From Figure 7-10 for Q g He = 0.8 with cot (O)) = 1/tan’ (6)! = 3.0 and H- — = 0.0024 gt R ace 2.8 O This runup is corrected for scale effects by using Figure 7-13 with tan 0 = 0.33 and H*#= 1.5m (4.9 ft). A correction factor k= 1.15 is obtained, and Ww i 2.8 k He S ete (Gkoilsy) AGUS) R 428 m (C57 £t) which is 3.0 m (9.8 ft) above the berm elevation (see Fig. 7-21). There- fore, the composite-slope method must be used. The breaker depth for the given design wave is first determined with a ae 0.0024 gT calculate H- 2 ad) (eo Enter Figure 7-3 with H2/gT° = 0.0024 , using the curve for the given slope m = 0.050 (1:20) , and ffnd Therefore 1.46 (1.5) Do? TW (Go s2)) & i} calculate ee BT” (9.8) (8)? | 0.0035 Then from Figure 7-2, from the curve for m = 0.05 * Hp 0.95 and dy = 0.95 Hy = 0.95 (2.2) = 2.1 m (6.9 ft) Therefore, the wave will break a distance (2.1-1.2)/0.05 = 18.0 m (59.0 ft) in front of the structure toe. The runup value calculated above is a first approximation of the actual runup and is used to calculate a hypothetical slope that is used to determine the second approximation of the runup. The hypothetical slope is taken from the point of maximum runup on the structure to the bottom at the breaker location (the upper dotted line on Figure 7-22). Then dx = 18.0 + 9.0 + 6.0 + 9.0 = 42.0 m (137.8 ft) and, the change in elevation is Ay = 2.1 + 4.8 = 6.9 m (22.6 ft) therefore Ay TeRC6.S) This slope may now be used with the runup curves (Figs. 7-10 and 7-11) to determine a second approximation of the actual runup. Calculate d,,/H5 using the breaker depth dp d b eet es 1cA0 Tee ES Interpolating between Figures 7-10 and 7-11, for 2 gT gives R= 1.53 O Correcting for scale effects using Figure 7-13 yields Keys O7 and Ro = P5307) 5° 225) m (8.2 ft) A new hypothetical slope as shown in Figure 7-22 can now be calculated using the second runup approximation to determine Ax and Ay . A third approximation for the runup can then be obtained. This procedure is continued until the difference between two successive approximations for the example problem is acceptable, R, = 4.8 m (15.7 ft) R, = 255, 1m (52 388) R, = 1.8 m (5.9) £t) R, S ilo im (Soe see), R, = 1°38 m (5-9) £t) and the steps in the calculations are shown graphically in Figure 7-22. The number of computational steps could have been decreased if a better first guess of the hypothetical slope had been made. Pepper ee Kk) ke) eK ce Kk) Fe OK) KOK: OK KR RE A ROR ak Kk eR KK OK eR ORT K ke b. Irregular Waves. Limited information is presently available on the results of model testing that can be used for predicting the runup of irregular wind-generated waves on various structure slopes. Ahrens (1977a) suggests the following interim approach until more definitive laboratory test results are available. The approach assumes that the runup of individual waves has a Rayleigh distribution of the type associated with wave heights (see Ch. 3, Sec. I1,2, Wave Height Variability). Saville (1962), van Oorschot and d’Angremond (1968), and Battjes (1971; 1974) suggested that wave runup has a Rayleigh distribution and that it is a plausible and probably conservative assumption for runup caused by wind-generated wave conditions. Wave height distribution is expressed by equation (3-7): eae [eG] A where, from equation (3-9), file H,/V 2 ,H= an arbitrary wave height for probability distribution, and n/N = P (cumulative probability) . Thus, if equation (3-7) is rewritten, the wave height and wave runup distribution is given by A al eet (- eT (7-9) ay 7 EL 2 i= 39 \ Limit of runup ona 1:3 slope se a . oe \ oxen NY First approximate | Toe aw Slope to obtain Breaker location * Ae second R 4.8m =R,(Runup ona |:3 slope) SWL B Limit of runup ona 1: 6.1 slope “is Limit of runup on a |:7.6 slope A Second approximate slope Breaker location fee Ol to obtain R3 s “Isis 2.5m=Ro (Runup. on a |:5.7 slope) 2 SW Breaker location Limit of runup ona 1:8.4 slope vi < CLLAP Yh Tae ota Berm Teese Final approximate slope 1.6m=Rq 1.8m COIS 1.8m5R3 | eS SWL . t fm mm» 8.4 ao SL a Note: Final runup calculation will “AQ teen, y indicate minor runup onto SAS Aersvans berm at 1.8m Figure 7-22. Successive approximations to runup on a composite slope: example problem. 7-40 where R is the wave runup associated with a particular probability of exceedance, P , and R, is the wave runup of the significant wave height, nee: Figure 7-23 is a plot of equation (7-9). For illustration, if the 1 percent wave runup (i.e., the runup height exceeded by 1 percent of the runups) is used, then P = 0.01 and equation (7-9) yields A HGIZ)) eau (- Ln gas = 1.517 H, R, 2 This example indicates that the 1 percent wave runup would be about 52 per- cent greater than R, , the runup of the significant wave, Hg, . H(1Z) should not be confused with the term H, which is the average of the highest 1 percent of all waves for a given time period. For the condition of a sloping offshore bottom fronting the structure, a check should be made to determine if a wave height greater than H, breaks on the offshore bottom slope rather than on the structure slope for which the runup, Rg , was determined. Should the larger wave break on the offshore bottom slope, the runup would be expected to be less than that indicated by the ratio Ry/Rs ° The following problem illustrates the use of the irregular wave runup on a rough slope using smooth-slope curves. kok kk kok Ok Ok & & & & & & EXAMPLE PROBLEM 6 * * * * * * * * KK KK KK OK K GIVEN: An impermeable structure with a smooth slope of 1 on 2.5 is subjected to a design significant wave H. = 2.0 m (6.6 ft) and T= 8 s measured in a water depth (d = 4.5 m (14.8 ft) . The design depth at the toe of the structure d, = 5 OnmeGgisc ft) at SW. FIND: (a) The wave runup on the structure from the significant wave Jee and the Ho 1 and Ho 01 waves. (b) The probability of exceedance of the wave height that will begin to overtop the structure with a crest at 7.5 m (24.6 ft) above SWL. SOLUTION: (a) From the example program given in Section II,l,a, Regular Waves, it is found that R= R, = 5.6 m (18.4 ft) . From equation (7-9) or Figure 7-23 La. SO in 0.1\1/2 s s 2 and r ! 6.0 m (19.7 ft) = T-07 R= 2.07 (5.6) Also 7-41 *santea dnunz 10 sqystey aAeM BATIETST 10F aouepesoxe jo ATT TqQeqoid cl et eee = Cll Sura Baa tile ee ieee See ee oo. “EG=1E g0 20 CET EELEPEe Eee UE ain3ty 9°0 G0 100°0 an tl] i EE coo ul lets Ayi1g0Q01d ) d ( 7-42 (jo) e (jo) — i] fo) e (>) — Za fo) e jo) e Se os SS i) I _ e 1S) ho and Ry.o1 = 1.52 R, =) 1. 52iG5\06)) =aSe 5h C27, Inf) 5.6 m and cs = 7.5m and if Figure 7-23 is used for (b) With R, R a) R, 5.6 1.34 then p = 0.028 or 3 percent of the runup exceeds the crest of the structure. Ree te eo Ok ROK OR, KK OR KR OK KK ie RK Oke eK) KK Ae ke eo Kk Ke Ke KX 2. Wave Overtopping. a. Regular (Monochromatic) Waves. It may be too costly to design structures to preclude overtopping by the largest waves of a wave spectrum. If the structure is a levee or dike, the required capacity of pumping facilities to dewater a shoreward area will depend on the rate of wave overtopping and water contributed by local rains and stream inflow. Incident wave height and period are important factors, as are wind speed and direction with respect to the structure axis. The volume rate of wave overtopping depends on structure height, water depth at the structure toe, structure slope, and whether the slope face is smooth, stepped, or riprapped. Saville and Caldwell (1953) and Saville (1955) investigated overtopping rates and runup heights on small-scale laboratory models of structures. Larger scale model tests have also been conducted for Lake Okeechobee levee section (Saville, 1958b). A reanalysis of Saville’s data indicates that the overtopping rate per unit length of structure can be expressed by h-d 0.217 al s x = |p eee 8! Qe (« Q n>) ere ae aes ( R (7-10) Oo Oo in which h - d, <= or R << bao) or equivalently by +h-d Oe Se eee (Ob eae Q= (s OF Hy e a e Rede (7-11) in which where Q is the overtopping rate (volume/unit time) per unit structure length, g is the gravitational acceleration, H“ is the equivalent deepwater wave height, h is the height of the structure crest above the bottom, d is the depth at the structure toe, R is the runup on the structure that would occur if the structure were high enough to prevent overtopping corrected for scale effects (see Sec. II, WAVE RUNUP), and a and Q, : characteristics and structure geometry. Approximate values of a and a as are empirically determined coefficients that depend on incident wave functions of wave steepness HC/gT” and relative height d./ He for various slopes and structure types are given in Figures 7-24 through 7-32. The * numbers beside the indicated points are values of ae and iQ (Q in O parentheses on the figures) that, when used with equation (7-10) or (7-11), predict measured overtopping rates. Equations (7-10) and (7-11) are valid only for 0 = (h=d>) < R_. When (h-d,) = R the overtopping rate is taken as zero. Weggel (1976) suggests a procedure for obtaining approximate values of a and Q, where more exact values are not available. His procedure uses theoretical results for wave overtopping on smooth slopes and gives conserva- tive results; i.e., values of overtopping greater than the overtopping which would be expected to actually occur. It is known that onshore winds increase the overtopping rate at a barrier. The increase depends on wind velocity and direction with respect to the axis of the structure and structure slope and height. As a guide, calculated overtopping rates may be multiplied by a wind correction factor given by h-d a Beets) ; = je => 116) SE We R + 0.1] sin 0 (7-12) where W. is a coefficient depending on windspeed, and O is the structure slope (0 = 90° for Galveston walls) . For onshore windspeeds of 60 mi/hr or greater, Wr = 2.0 should be used. For a windspeed of 30 mi/hr, Wr= 0.5 ; when no onshore winds exist, Wr= 0. Interpolation between values of W given for 60, 30, and O mi/hr will give values of W for intermediate wind speeds. Equation (7-12) is unverified, but is believed to give a reasonable estimate of the effects of onshore winds of significant magnitude. For a windspeed of 30 mi/hr, the correction factor k*~ varies between 1.0 and 1.55, depending on the values of (h-d ,)/R andesinmOn x Values of a and Q larger than those in Figures 7-24 through 7-32 should be used if a more conservative (higher) estimate of overtopping rates is required. Further analysis by Weggel (1975) of data for smooth slopes has shown that for a given slope, the variability of a with incident conditions was relatively small, suggesting that an average a could be used to establish x the Q, value that best fit the data. Figure 7-33 shows values of the average a (a) for four smooth, structure slopes with data obtained at three different scales. An expression for relating a with structure slope (smooth 7-44 (smooth vertical wall ona and Q Qa Overtopping parameters Figure 7-24. * "O 10 nearshore slope). 1 7-45 0.04 f 0.01 0.008 0.006 0.004 0.002 0.001 0.0008 f 0.0001 :1.5 structure (smooth 1 and Q a 10 nearshore slope).? Overtopping parameters slope on a 1 Figure 7-25. 7-46 BREAKING # (0.0110) DENOTES LARGE SCALE TEST CE Te 1TH EE 1 HN ee TT ae i} TUN ee TT ie t HUE Ha ia a Woe HOME Mi EH TT TT TT TA HUE TT TT Hie I CT (0.0150) a qa on A NTT EE WT Be TE HE VO HE 7-47 * 3 structure slope on a 1:10 nearshore (smooth 1 and Qs a Overtopping parameters slope). Figure /-26. *(edots alOYsIeeU OT:] B UO sdoTs 9xANjoONAAS 9:T YIOOUS) 0 pue » siaoqjomeied 3utddoq1eAQ °/7Z-/ eANn3TY os Sb Or s‘¢ oe G2 O@ S| ol sO 00 10000 20000 ¢00 0 9000 8000 100 200 t +00 7-48 HERE EE Riprap roughly 0.9m in diameter SWL Hit ton Cn NG TO OEE Lae 0.001 0.0008 0.0006 0.0004 0.0002 * Figure 7-28. Overtopping parameters a and QQ (riprapped 1:1.5 structure slope on a 1:10 nearshore slope). 7-49 Tt si Ht is ba { mand tH t u (Bo GO i roo T T 0 a cI TCO cy 0.04 1 Ty 1 iB G1 it i in it 1 TT 1 t T tT int i TT i T : =: sss Toh : scassncsz - = = = oa x : as nee roan Somers be sesas eae $ igee Seees Bet s = es eeess est rH F a5 : sega seead ce “po Tht im ual ; mut i a ; Het | ; + H+ t +f ; man a Hote nt tft] 1 t i T T r t H rot me | I t Here rad oe eHttet t Eee t THe 0.02 Sy carayamect grasa ani ant AED HAAGL ARAL AC ; TERED BOOED BEBE 18 BD, i 7m ABO? oo (NG ORD dh du Ded i a0O Bi TH th th 0 GO iat poet | Tope T I cote 1 cote i 108 WEE! al i T 1 | To Toe ia | th iu i i tH 000 000 thi 1 4 O88 1 if | t tnt i | gna! T T f ! tT T | Tit mH Th T TTT | ] thot jit i it } i 4 4 i u| 7 Tht Tritt Tiittihitil T | rH Ty | TT | | | | | i i | WH | | Th COE aaa HON OREO COU URL OEE ATO HOLEU LEE AOU OS UE LG | | | Wy il | 00 | | 0.01 il uh 0.008 0.006 0.004 | al OOo? 0.001 0.0008 0.0006 0.0004 0.0002 x Figure 7-29. Overtopping parameters a and Q (stepped 1:1.5 structure slope on a 1:10 nearshore slope). 7-50 Hae 3.8m 10 9.9m 1.4m to3.9m 3.5 3.0 oO i ei is) ie} ° Ln 3 ic uo) ov > tS 2] 12) Ve 9 So vu =} o 3 ia) Ww co) W vo ge om u ov o OQ ao Leal on Wn G od Y Qa ao os vw Wn wou o 9 sy c Figure 7-30. io 22a NBG pats hg oreal-stone H. a 7 S ee arEtss Brack king KG. HE HH ESSSsee + ! ae =f=tet Tae te os oe oe Seiee iui ll Soee soeee festa be ee eo H jee HH Pe | muti iH ees et ees ; Le opods) HHAEaEeni ieee THM daet a init fg 324.08 = a + beet e tt EERE itt Sooke eSs=s ee gee etl aaa sone LePe EEUU TEDEL EERE Ege ete TEE HH! tat aq nes iia iad a so Ht +t gn aos s = aan setae as uaa dag Bob Cte HEE tt | | TEE | i A aa Hai ul , iM * Figure 7-31. Overtopping parameters a and Qe (curved wall on a 1:25 nearshore slope). 37) 3.0 2.0 1.5 1.0 a) 0 oO oH et is) C ° ce Fa 4 vu Vv > MM =] 1S} Vv wy Vw 9 oS vu q iss) 3 n My v oS) Vv ge om uw oY oo ao eo on Wn i=] ‘fd oO aH ao os Wy Wn wou vo 9 1s f=] Figure 7-32. 1-93 0.14 0.10 ee a mie, F 0.08 a : fe ae 0.04 0.02 SalehOn7 ee SCALE i. a Bin ae a 0.5 0.6 0.7 0.8 0.9 1.0 SIN 4 Figure 7-33. Variation of a with structure slope 0. slopes only), based on this analysis is given by equation (7-13) a = 0.06 - 0.0143 £n (sin 0) (7-13) where © is the structure slope angle from the horizontal. x The variation of & between waves conforming to linear theory and to cnoidal theory was also investigated by Weggel (1976). The findings of this x investigation are illustrated in Figure 7-34. Q is shown as a function of depth at the structure d_ , estimated deepwater wave height Hy » and period T , for both linear and cnoidal theory. Calculation of wave overtopping rates is illustrated by the following example. kK KK kK kk Ok Ok kK Ok O&K & KK ® EXAMPLE PROBLEM 7 * * * * & & & KK KK RK KK GIVEN: An impermeable structure with a smooth slope of 1 on 2.5 is subjected to waves having a deepwater height H* = 1.5 m (4. 2 ft) anda period T= 8 Sie The depth at the structure toe is d. =) 30) m C9osune)) 3 erest elevation is 1.5 m (4.8 ft) above SWL. asics winds of 35 knots are assumed. FIND: Estimate the overtopping rate for the given wave. 0.10 Cnoidol Theory Deepwater Breaking Cutoff 0.001! 0.000! 0.00! 3 0.0! 0.10 Ho/gT (after Weggel, 1976) * Figure 7-34. Variation of Q_ between waves conforming to cnoidal theory and waves conforming to linear theory. SOLUTION: Determine the runup for the given wave and structure. Calculate d Bi So — Tana See fa) HS 158) — = ————; = 0.0024 2 2 Sie eC I 9) 4S) From Figure 7-1l, since ae WT > 2:0 O = 2.9 (uncorrected for scale effect) O Since H* = 1.5 m (4.8 ft) , from Figure 7-13 the runup correction factor ke ais approximately 1.17. Therefore = ]./ (2.9) = 3.4 P35 and R = 3.4 (HD) = (Bo) (hes) = Sigil im (lGa7/ 22) * The values of a and Oy for use in equation (7-10) can be found by interpolation between Figures 7-25 and 7-26. From Figure 7-26, for small- scale data on a 1:3 slope a = 0.09 d- HS * at iri = 2.0 and oD = 0.0024 Oye = 0.033 fo) gT Also from Figure 7-26, for larger scale data a = 0.065 d, HS % at 7 = 2.33 and AEC 0.0028 oF = 0.040 io) gt Note that these values were selected for a point close to the actual values for the problem, since no large-scale data are available exactly at & — ina — 2.0 ) H’ = = 0.0024 gT From Figure 7-25 for small-scale data on a 1 on 1.5 slope a = 0.067 d. He x at 7 leoyand rao 0.0016 Q_ = 0.0135 Oo gT O Large-scale data are not available for a 1 on 1.5 slope. Since larger x values of a and Q give larger estimates of overtopping, interpolation by eye between the data for a 1 on 3 slope and a 1 on 1.5 slope gives approximately a = 0.08 = 0.035 CO QO *+ I From equation (7-10) 7-56 0.217 as [ «9.89 (0.035) 1.5) /2en ees nee ean ages) = 350 1 Oe R 5.1 = 0.294 . The value of =i et tanh ( R To evaluate tanh™'[ (h-d,)/R] find 0.294 in column 4 of either Table C-1 or C-2, Appendix C, and read the value of tanh} [(n-d,)/R ] from column 3. Therefore Canhee COe 294) = 0.311 The exponent is calculated thus: On2170 (Oe31) eo 0.08) 0.84 therefore 0.84 Q = 1.08e — Owe) 2 Oe? ees or 3 5. Ont sort For an onshore wind velocity of 35 mi/hr, the value of interpolation 30 mi/hr We = 0.5 35 mi/hr Wp, = 0.75 60 mi/hr Wp = 2.0 From equation (7-12) where We = 0.75 Bo aa 8 CVn) o De clin BIS O53i7/ We is found by Therefore ee eS I SE OSS (O53) ae Wolby Wosy/ = toil and the corrected overtopping rate is Q k* Q Q (64 ie CORES) OES (5e40£t ener) Cc The total volume of water overtopping the structure is obtained by multiplying Q by the length of the structure and by the duration of the given wave conditions. HEE GE OR OR ee RRR OK kk AK CK ek Oe Ak OK RK RK KR KR RK KR RR Ae b. Irregular Waves. As in the case of runup of irregular waves (see Sec. II,1,b, Irregular Waves), little information is available to accurately predict the average and extreme rate of overtopping caused by wind-generated waves acting on coastal structures. Ahrens (1977b) suggests the following interim approach until more definitive laboratory tests results are available. The approach extends the procedures described in Section II,2,a on wave overtopping by regular (monochromatic) waves by applying the method suggested by Ahrens (1977a) for determining runup of irregular waves. In applying his procedure, note a word of caution: some larger waves in the spectrum may be depth-limited and may break seaward of the structure, tm which case, the rate of overtopping may be overestimated. Irregular wave runup on coastal structures as discussed in Section II,1,b is assumed to have a Rayleigh distribution, and the effect of this assumption is applied to the regular (monochromatic) wave overtopping equation. This equation is expressed as follows: h-d 0.217 -1 8 * ao | ES SS (8 Qf ae , —— tanh @ (7-10) h-d s R & co) where < 1.0 Ox In applying this equation to irregular waves and the resulting runup and overtopping, certain modifications are made and the following equation results: h-d R OG P2I7/ -l s s = * ENS} || 1/2 - tanh ( — % = le ev (oH e a R, R, in which (7-14) hed , R, O= R RR < hae & P where Q, is the overtopping rate associated with RX, » the wave runup with a particular probability of exceedance, P , and R, is the wave runup of the equivalent deepwater significant wave height, (Ho). e The term h-d ./R, will be referred to as the relative freeboard. The relationship between Rp » Rg , and P is given by R 1/2 p 3S (- 3) (7-9) Equation (7-14) provides the rate of overtopping for a particular wave height. In analyzing the rate of overtopping of a structure subjected to irregular waves and the capacity for handling the overtopping water, it is generally more important to determine the extreme (low probability) rate (e.g., Q0.0052 and the average rate Q of overtopping based on a specified design storm wave condition. The extreme rate, assumed to have a probability P of 0.5 percent or 0.005, can be determined by using equation (7-14). The upper group of curves in Figure 7-35 illustrates the relation between the relative free- board, (h-dg)/Rg » and the relative rate of overtopping, % 005/2 » in terms of the empirically determined coefficient, a, where Q _is the overtopping rate for the significant wave height. The average rate Q is determined by first calculating the overtopping rate for all waves in the distribution using equation (7-14). For example, in Figure 7-35, this has been calculated for 199 values of probabilities of exceedance at intervals of P = 0.005 (i-e., Ee 005 0 OLOM OOS eclee's 10995). Noting sthat Rp/Rg is a function of P , solutions will only exist for the previously stated condition that h-dg\ Rg 0O< + She io@) Rs / Rp . and Qp= 0 for other values of P . The average of these overtopping rates is then determined by dividing the summation of the rates by 199 (i.e., the total number of overtopping rates) to obtain Q . The lower group of curves in Figure 7-35 illustrates the relation between the relative freeboard and the relative average rate of overtopping Q/Q in terms of the empirically determined coefficient a. kkk Kk kK KK kK Ok kK KOK OK OK & & EXAMPLE PROBLEM 8 * *& * & KK KK KKK KKK GIVEN: An impermeable structure with a smooth slope of 1 on 2.5 is subjected to waves having a deepwater significant wave height HS = 1.5 m (4.9 ft) and a period T= 8s. The depth at the structure toe is dg = 3.0m (9.8 ft) ; crest elevation is 1.5 m (4.9 ft) above SWL (h-dg=1.5m (4.9 ft)) . Onshore winds of 35 knots are assumed. FIND: (a) Estimate the overtopping rate for the given significant wave. (b) Estimate the extreme overtopping rate Q0.005 ° (c) Estimate the average overtopping rate Q. U-By) SEE SS S=ESe= SSSjS5 Se5: ome ——— cS ee : : TELE | A ee JZ a =) Pealeesal (ana BD RE ee 7 faee TATA NA SS Sr os Soe “HEHE 1.0 h=- ds Rs 29.005 Q Figure 7-35. Ops and Q as functions of relative freeboard and a SOLUTION: (a) The previous example problem in Section II,2,a gives a solution for the overtopping rate of a 1.5-m (4.9-ft) significant wave corrected for the given wind effects as Q= 0.5 nest (b) For the value of a= 0.08 given in the previous example problem, the value of Qo.005 is determined as follows: Rg = 5-1 m (16.7 ft) from previous example problem soe 0.294 Ry al From the upper curves in Figure 7-35, using a = 0.08 and (hd, )/R, = 0.294 29.005 ae Teer 1836 Q Q Sigs) (os) ny ce een (Oe esa 0.005 (c) From the lower set of curves in Figure 7-35, using a= 0.08 and (h-d; )/Ry = 0.294 , 0.515 Clo|l =NOeoL COS) a= Os ap ect @yre2 ee O I The total volume of water overtopping the structure is obtained by multiplying Q by the length of the structure and by the duration of the given wave conditons. Kk Rk KK KKK KR KK KR KK KK KK RK KKK KKK KKK KK KK KKK KK 3. Wave Transmission. ae General. When waves strike a breakwater, wave energy will be either reflected from, dissipated on, or transmitted through or over the structure. The way incident wave energy is partitioned between reflection, dissipation, and transmission depends on incident wave characteristics (period, height, and water depth), breakwater type (rubble or smooth-faced, permeable or imper- meable), and the geometry of the structure (slope, crest elevation relative to SWL, and crest width). Ideally, harbor breakwaters should reflect or dissipate any wave energy approaching the harbor (see Ch. 2, Sec. V, Wave 7-61 Reflection). Transmission of wave energy over or through a breakwater should be minimized to prevent damaging waves and resonance within a harbor. Most information about wave transmission, reflection, and energy dissipation for breakwaters is obtained from physical model studies because these investigations are easy and relatively inexpensive to perform. Only recently, however, have tests been conducted with random waves (for example, Seelig, 1980a) rather than monochromatic waves, which are typical of natural conditions. One of the purposes of this section is to compare monochromatic and irregular wave transmission. Figure 7-36 summarizes some, of the many types of structures and the range of relative depths, d ,/gT » for which model tests have been performed. Some characteristics and considerations to keep in mind when designing breakwaters are shown in Table 7-3. b. Submerged Breakwaters. Submerged breakwaters may have certain attributes as outlined in Table 7-3. However, the major drawback of a submerged breakwater is that a significant amount of wave transmission occurs with the transmission coefficient =e] t ae as i greater than 0.4 for most cases, where H, and He are the incident and transmitted wave heights. One of the advantages of submerged breakwaters is that for a given breakwater freeboard F = h-d, (7-16) water depth, and wave period, the size of the transmission coefficient decreases as the incident wave increases. This indicates that the breakwater is more effective interfering with larger waves, so a submerged breakwater can be used to trigger breaking of high waves. Figure 7-37 shows selected transmission coefficients and transmitted wave heights for a smooth impermeable submerged breakwater with a water depth-to-structure height ratio d/h = 1.07 . Figure 7-38 gives design curves for vertical thin and wide breakwaters (after Goda, 1969). c. Wave Transmission by Overtopping. A subaerial (crest elevation above water level with positive F ) will experience transmission by overtopping any time the runup is larger than freeboard (F/R < 1.0) (Cross and Sollitt, 1971), where R is the runup that would occur if the structure were high enough so that no overtopping occurred. Seelig (1980a) modified the approach of Cross and Sollitt (1971) to show that the transmission by overtopping coefficient can be estimated from Koo = C(1.0 - F/R) C717) s *si10jeSTISeAUT snoTieA Aq petpnys zi3/ P jo sosuei1 ajeutxoidde :seinjzoni4s peddojisao pue pesiouqns 19A0 uoTSsTUSURIZ SAP *g¢-f 2an3Tyq 7aj0M daag 780M [O0U01)1SUOI) 10°0 4J2}0M MO||OYS 1000 4d0|s QUYMVIS J @ 02 a0 Sanjor adojs | $no3nv1139sin () £ (1261) 4410S puo ssos9 (4) (9961) Uosy20¢ puo uospny (H) (9961) vosy2o¢ puo 109 (fr) ss100 0-—— (€961) aiiaos (fT) | | ! Oe ae) (8561) §Sa!4d (1°9) | is l | =a ; (1661) UosisoW puo'syrny ‘uosuyor (y) ® O) (0b61) NOH PuO OH (T'3'D) Ws (ea (Asoay) | —-—-—- ino oy cope ma ee, lb En es MS | (1961) $4294 (9) - @ 0) | (1'r''H'9'3°3 (19eau2g)a'v) [ee MACON Li) eS ieany 3110S shasjya SaneM WopueY 2NeWoIyDOUOW (eQgET) 6119aS | (be61) yar (v) 7-63 Table 7-3. Some considerations of breakwater selection. Tne reas py Pe rome ab Ny High wave transmission (K7>0-4) Low reflection Submerged Low amount of material Does not obstruct view May be a navigation hazard Same Provides habitat for marine life Excellent dissipator of wave energy Low transmission except where runup is extreme Good working platform Low transmission High reflection Low reflection Deserves serious considera- tion if adequate armor material is available Subaerial Occupies little space Structure can be functional even with some failure Failure may be dramatic Provides habitat for marine life Inhibits circulation Allows circulation due to low-steepness waves | << Increasing Structure Height 7-64 SMOOTH IMPERMEABLE 4 3} ge 4 2 0.0001 0.0003 0.001 0.003 1.0 d,/gT? = 0.016 B/h = 0.4 d/h = 1.07 0.9 0.8 0.7 MONOCHROMATIC WAVES 0.6 0.0001 0.0003 0.001 0.003 (after Seelig, 1980a) Figure 7-37. Selected wave transmission results for a submerged breakwater. 7-65 H¢/Hi TEER EEE aaa __. |. MONOCHROMATIC WAVE — | sa ala CONDITIONS Rani He abeeae | Figure 7-38. AFTER GODA, 1969 Wave transmission coefficients for vertical wall and vertical thin-wall breakwaters where 0.0157 Ha. SO (#r)ax = (0.45H_) (0-93) = 0.42H, piemericmaey we eY e e e oke e l ke fe ok oe oe OK OK eck Rk OK ek Kk ok & oe KOR kk kK KK kK KOK OK KO & & & & EXAMPLE PROBLEM 11 * * * * * & & & KK RK RK RK KK H FIND: The percentage of time that (r)p equals or exceeds a value of 0.2 s B for F/R, = (048 etna! ae Oeil SOLUTION: From Figure 7-41, (Hr) 22 (067 He for approximately 6 percent of the time. P PP ns ae ese A a) Raa a OR) ee Ke ae) ee OK KK ke oe eee ek) (x) ok) KR) RK Ke IX CTUTTTATTITTTnmal TTA MM Bane MII 0. : oatth BUNIAQUQANANA AA Sa an il 0 MTT TTT LTT EU OR 0.1 : B/h T/p B i for h > Wail s kk kK kK kK kK kK Ok Ok Ok k Ok & & & EXAMPLE PROBLEM 12 * * * * * & & & KK KK KKK Figure 7-42. Correction factor, CF , to multiply by FIND: Transmitted wave heights for the following conditions for a smooth impermeable breakwater (assume irregular waves): B = 2.0 m (6.56 ft) h = 2.5m (8.2 ft) d, = 2.0 m (6.56 ft) Fo= h-d2 0 oem Chaos Gt) He = 1.0 m~ (3.28 ft) Tp = 10.0 s SOLUTION: Irregular wave runup on a 1:1.5 smooth slope was tested for scale models from Ahrens (198la), who found the relative runup to have the following empirical relation to the dimensionless parameter (H,/eTs): R, He a ee aes er Sse | e197 00nl a H, er” = P op For this example H —S_ = (0.00102 2 gT so P i 1S Ge FZ = 1:38 + 318 (0.00102) - 19700 (0.00102) s Therefore (iz) H Bis at NGS 3/2 ee Ole Ding ae = Sevag ow shiei(a8: = From Figure 7-39 the transmission by overtopping coefficient for F/R, = 0.3 and B/h = 2.0/2.5 = 0.8 is Kio = 0.295 so the transmitted significant wave height would be (Hj), = Hy Kp = 1-0(0.295) = 0.30 m (1.0 ft) kk RK RR KR KKK KKK KKK KKK KKK KR KEKE KEKE KEK KKK KEKE KEK KEKE Note that equation (7-17) gives conservative estimates of for F = 0 with the predicted values of the transmission coefficient corresponding to the case when the magnitude of the incident wave height is very small. Observed transmission coefficients for F = 0 are generally smaller than predicted, with transmission coefficients a weak function of wave steepness as illustrated by the example in Figure 7-43. Wave runup values in equation (7-17) and for use with Figures 7-39, 7-40, 7-41, and 7-42 can be determined from Section II,l1, Wave Runup. Runup for rough impermeable and permeable breakwaters can be estimated from Figure 7-44. The "riprap" curve should be used for highly impermeable rough struc tures and to obtain conservative estimates for breakwaters. The other curves, such as the one from Hudson (1958), are more typical for rubble-mound permeable breakwaters. Note that for wave transmission by overtopping of subaerial breakwaters, the transmission becomes more efficient as the incident wave height increases (all other factors remaining constant) until K reaches a uniform value (Figure 7-45). This is the opposite of the trend observed for a submerged breakwater (Figure 7-37). Figure 7-46 summarizes the transmission and reflection coefficients for a smooth impermeable breakwater, both submerged (d_/h > 1) and subaerial (d/h < 1). Some examples of transmission for rough impermeable breakwaters are shown in Figures 7-47 and 7-48. kkk kk Ok Ok kK Ok Ok kk R & & EXAMPLE PROBLEM 13 * * * ¥ ¥ KK RK RK KK KKK FIND: The wave transmission by overtopping coefficient for a rough impermeable breakwater having the following characteristics: ‘ = 0.57 B = 20m (6256 Ec) h = 3.5)m (lie48 Et) d, = 3.0m (9.84 £t) F=h-d = 0.5m (1.64 ft) H, =il,7im (5258 £t) T STO0 & *pipoqeeiy OU YIM AszeMyYeeIq e AOZ BSutTddoj1eAO Aq UOTSSTUSUeI BABM *EH-/ ein3sty L00°0 S000'0 L000°0 A1IsVAWYsAdWI HLOOWS ie vo = va 404 2+» WawixvW 9100 = 916/‘p ( VHYLOAdS dVMSNOFr ) SAAVM WOGNVY @ \ hg all al cal pa am 9100 = z16/‘p S3AVM DILVWOYHOONOW O 7-74 ee eae CS aa (SC Lae See ee ane 2.05 (AFTER DISKIN, VAJDA, AND AMIR, 1970) Figure 7-58. Ponding for rubble-mound breakwaters. 7-90 Pe (8)(%) Cumulative curves of relative wave energy with respect to Figure 7-59. azimuth from the principal wave direction. 0.02 0.05 0.1 Pe: ae 1.0 S Change of maximum directional concentration parameter, ee 5 Figure 7-60 ° due to wave refraction in shallow water. Height Ratio =---—-———= Period Ratio Smox = 79 +t dn guean t juss cue bes cee is? pot Ht - th caus tt H rasa open sane awees see oe pee See Ht $5 sogeu seeus perssceged Tt eweasast +t: suesueEee rs egesssass Ue re NS A SA peeces 7-92 pateea uae Wave Direction Wave Direction Snax Diffraction diagrams of a semi-infinite breakwater for directional random waves of normal incidence. Figure 7-61. kok k kok k Ok Ok Ok Ok & & & & & EXAMPLE PROBLEM 14 * * * * & KK KK OK RK KK KX GIVEN: A semi-infinite breakwater is sited in 8 meters (26.2 feet) of water. The incident wave spectrum has a significant height of 2 meters (6.56 feet) and a period of maximum energy density of 8 seconds. The waves approach generally perpendicular to the breakwater. FIND: The significant wave height and period of maximum energy density at a point 500 meters (1640 feet) behind and 500 meters in the lee of the breakwater for wave conditions characteristic of wide directional spreading and for narrow directional spreading. SOLUTION: Calculate the deepwater wavelength, L_ , associated with the period of maximum energy density, Tp be I eho agt t= al. 56064) ° P Ly = 99.84 m (327.6 ft) Therefore, d/L, = 8/(99.84) = 0.0801 . Entering Table C-1l with d/L, = 0.0801 yields d/L = 0.1233 . The wavelength at the breakwater tip is, therefore, L d/(0.1233) L 8/ (0.1233) = 64.9) my (21259) Et) The 500-meter (1640-foot) distance, therefore, translates to 500/64.9 = 7.7 wavelengths. From Figure 7-6la, for S§S see eg) (wide directional spreading) for a point 7.7 wavelengths behind the tip and 7.7 wavelengths behind the breakwater, read the diffraction coefficient K~ equals 0.32 and the period ratio equals 0.86 . The significant wave height is, therefore, H. = 0.32(2) = 0.6 m (oul ft) and the transformed period of maximum energy density is 6.9 s T = 0.86(8 5 6(8) From Figure 7-61, for Snax = /2 (marrow spreading), read K* = 0.15 and the period ratio = 0.75 . Therefore, H 5 0.15(2) = 0.3 m (1.0 ft) and W I = 0./75(8) 6.0 s The spectrum with narrow spreading is attenuated more by the breakwater, but no so much as is a monochromatic wave. The monochromatic wave diffraction coefficient is approximately K~ = 0.085 ; hence, the use of the mono- chromatic wave diffraction diagrams will underestimate the diffracted wave height. Ee WC Mert od ON eo oe fo oe ko ots toto ko Eo toed EF eco EP hur to ES ne pd oo ce Diffraction of directional spectra through breakwater gaps of various widths are presented in Figure 7-62 through 7-65. Each figure is for a different gap-width and shows the diffraction pattern for both wide directional spreading (S)., 10) and narrow directional spreading (S,., = 75). Diagrams are given for the area near the gap (0 to 4 gap-widths behind it) and for a wider area (a distance of 20 gap-widths). Each diagram is divided into two parts. The left side gives the period ratio, while the right side gives the diffraction coefficient. Both the period ratio patterns and diffraction coefficient patterns are symmetrical about the center line of the gap. All the diagrams presented are for normal wave incidence; i.e., the center of the directional spreading pattern is along the center line of the breakwater gap. For waves approaching the gap at an angle, the same approxi- mate method as outlined in Chapter 3 can be followed to obtain diffraction patterns. kok kK kk kk Ok Ok Ok OK kK & KX EXAMPLE PROBLEM 15 * * * *¥ & KK KK KK KK KE GIVEN: A wave spectrum at a 300-meter- (984-foot-) wide harbor entrance has a significant wave height of 3 meters (9.8 feet) and a period of maximum energy density of 10 seconds. The water depth at the harbor entrance and inside the harbor is 10 meters (32.8 feet). The waves were generated a large distance from the harbor, and there are no locally generated wind waves. FIND: The significant wave height and period of maximum energy density at a point 1000 meters (3281 feet) behind the harbor entrance along the center line of the gap and at a point 1000 meters off the center line. SOLUTION: Since the waves originate a long distance from the harbor, the amount of directional spreading is probably small; hence, assume Sol Uso Calculate the deepwater wavelength associated with the period of maximum energy density: He stra (a Gino) ° Pp L, = 156 m (512 ft) Therefore d/L, = 10/156 = 0.0641 Entering with d/L, = 0.0641 , yields d/L = 0.1083 . The wavelength at the harbor entrance is, therefore, *aoueprTouT Tewiou JO S@AeM Wopuer TeUOTIOSITP OF O°T = 1/H@ UITM de aoqemyearq e Jo sueaZeTp uoTIOeAZJTG “*Z9-L PANTY sz = **"S NSHM 4 UOI}DA4IG BADM 7 U01}9951G BADM or = *"S NSHM 2 al UOI}I9IIG BADM U014991IG BADM x St abe bs ag | S OL SL te Z = L y L z € SL Clee oes 0 S oL SL € z L 0 | z e 0 0 0 a Ect 7 | v0 Q [al S S L L | H : ir | Pee eels oe Tl “IP qa Al | Ch Ol Ol zZ : ; Is T 1S 1S. OlL= V@ Ol rT 0) i Ol=eus SEI Ol= Va 1S : SL Ol="'S | SL € } £ | 4 JI 4 + + v im [ | : | + 4 | jyb1aH | |poisad | yy619H polled 7-95 *Q0uepToOUT Tew10U JO S@APM WopueT TeUCTIOSITP JOF O°Z = 1/A YITM deB rsjemyYeeI1q B Fo sueiZeTp uoTIoeVAFFIG “°E€9-/ PANSTYy gz = **"S N3SHM 4 uolj9911G aADM 4 UO1}2a41G aADM + of o 9 of | Ol oz o +9 Aa Ba €2 | zZ v 9 SL i a 0 S OL SL € does #4 0 L Z € 0 0 0 , 0 { O@= V9 | =| |_| WS gi = 4s | ; ah 124th OWN | OL S z =e L ri al | O%= 7/@ It letol #1 xeU, g ah 7 g 4 02 eas oT ty Oj! : a Ho} ol Seale yi e ei) pr feo ial | oa sea al o€ : Sl 9 5 cA € | eal alfa sipl aia | "| _f 44012H al poised iit yan | poised Or U0!}9as1G @ADM + oe o 8 o1 | mM oz St (of ARS 0 g OL ° f Ol! Oz= Va +N Ole aes I. i 60 i a as [ [ + 02 oe co > +H 4y610H poisag | [TN [posed | Or 7-96 *aoueprToutT Tewz0U JO S@AEM Wopuer TeUOTIDSATP OF O° = T/A UITM de8 aojemyeoiq e jo sweiAZeTp voTIIeAZITIG *79-/ ein3ty cz = *""S NSHM 4 U01}9a41G @ADM uolj9a41g aADM + 09 oy 8 oz | oz Ov 09 + Zt en cess | y 8 ZI St oO. ™ ¢ 0 S OL fl € Bi eee ih 0 L Z € 0 ) 0 0 | 21 Ov= 7/8 AI T | | Ov= a [ ys o1D al gz = 4s ae] |_| oil | 02 | | moe Viale 4 | $00 I | | | b el ga x ov im Oren o 0 8 Cae : On 4 : | Z 09 St rat € | ] g = G 6p | Q yyb18H | | Bole Wu 18H 5 POllag OE 08 02 9L b ol = **Y"S NSHM ® UO1J9941G BADM UOl}DaIIG aADM x|I 7-97 *Q0UePTOUT Teu1OU JO SdAPM Wopuel TeuOTIOeITP AOFJ O°S = 1/a UITM de azojemyeoiq e Jo sWeAZeTpP uoTIOeATJTIG *C9-/ ANSTY gl = **“S NAHM 4 U01}99J1G aADM uoljoa41q aAom ozt 2 60 bz a1 9 ¢ x SL € c IZA DY HY KOSS + oz os 8 OF | ov 08 ozt = yg St Os 0 S OL 0 lal od : : Op ‘| 4 ep | | | fl Col Al. + 08} t t oB- 78 i) Cl ss vil ozt oT | + | OL iro a O9L 7-98 L = d/(0.1083) L = 10/(0.1083) = 92.34 m (303 ft) The harbor entrance is, therefore, 300/92.3 = 3.25 wavelengths wide; interpolation is required between Figures 7-63 and 7-64 which are for gap- widths of 2 and 4 wavelengths, respectively. From Figure 7-63, using the diagrams for S,., = 75 and noting that 1000 meters equals 5.41 gap-widths (since B/L = 2.0 and, therefore, B = 2(92.34) = 184.7 meters (606 feet) ), the diffraction coefficient 5.41 gap-widths behind the harbor entrance along the center line is found to be 0.48. The period ratio is approximately 1.0. Similarly, from Figure 7-64, the diffraction coefficient 2.71 gap-widths behind the gap is 0./2 and the period ratio is again 1.0. Note that the gap width in Figure 7-64 corresponds to a width of 4 wavelengths, since B/L = 4.0 ; therefore, B = 4(92.34) = 369.4 meters (1212 feet), and 1000 meters translates to 1000/( 369.4) = 2.71 gap widths . The auxiliary scales of y/L and x/L on the figures could also have been used. Interpolating, B/L K* Period Ratio 20 0.48 Nal) 8} G75) 0.63 ite @) 4.0 0.72 1.0 The diffraction coefficient is, therefore, 0.63, and the significant wave height is H, = 0.63(3) = 1.89 m (6.2 ft) There is no change in the period of maximum energy density. For the point 1000 meters off the center line, calculate y/L = 1000/(92.34) = 10.83 wavelengths , and x/L = 1000/(92.34) = 10.83 wavelengths . Using the auxiliary scales in Figure 7-63, read kK” = 0.l1l and a_ period ratio= 0.9 . From Figure 7-63, read K*~ = 0.15 and a period ratio = 0.8 . Interpolating, B/L Ke Period Ratio 2.0 Om 0.9 Bh 5725) 0.135 0.86 4.0 OS 0.8 The significant wave height is, therefore, He = 0.135(3) = 0.4 m (1.3 ft) and the period of maximum energy density is A = 0.86(10) = 8.6 s co fo eo 3 €3 £3 to bd £9 to to tied £9 £2 £2 C2 29 th oS oo toed bod Cou to C2 to ocd to to Lt oto o3 7-99 III. WAVE FORCES The study of wave forces on coastal structures can be classified in two ways: (a) by the type of structure on which the forces act and (b) by the type of wave action against the structure. Fixed coastal structures can generally be classified as one of three types: (a) pile-supported structures such as piers and offshore platforms; (b) wall-type structures such as _ seawalls, bulkheads, revetments, and some breakwaters; and (c) rubble structures such as many groins, revetments, jetties and breakwaters. Individual structures are often combinations of these three types. The types of waves that can act on these structures are nonbreaking, breaking, or broken waves. Figure 7-66 illustrates the subdivision of wave force problems by structure type and by type of wave action and indicates nine types of force determination problems encountered in design. Classification by Type of Wave Action 2 z} NON-BREAKING BREAKING BROKEN Seaward of surf zone In surf zone Shoreward of surf zone P Ww R PILE SUPPORTED RUBBLE Piers, offshore platforms Seawalls, bulkheads, etc. Groins, jetties, etc. Classification by Type of Structure Figure 7-66. Classification of wave force problems by type of wave action and by structure type. Rubble structure design does not require differentiation among all three types of wave action; problem types shown as 1R, 2R, and 3R on the figure need consider only nonbreaking and breaking wave design. Horizontal forces on pile- supported structures resulting from broken waves in the surf zone are usually negligible and are not considered. Determination of breaking and nonbreaking wave forces on piles is presented in Section 1 below, Forces on Piles. Non- breaking, breaking, and broken wave forces on vertical (or nearly vertical) walls are considered in Sections 2, Nonbreaking Wave Forces on Walls, 3, Breaking Wave Forces on Vertical Walls, and 4, Broken Waves. Design of rubble structures is considered in Section 7, Stability of Rubble Structures. NOTE: A careful distinction must be made between the English system use of pounds for weight, meaning force, versus the System International (SI) use of newtons for force. Also, many things measured by their weight (pounds, tons, etc.) in the English system are commonly measured by their mass (kilogram, metric ton, etc.) in countries using the SI system. 7-100 1. Forces on Piles. ae Introduction. Frequent use of pile-supported coastal and offshore structures makes the interaction of waves and piles of significant practical importance. The basic problem is to predict forces on a pile due to the wave- associated flow field. Because wave-induced flows are complex, even in the absence of structures, solution of the complex problem of wave forces on piles relies on empirical coefficients to augment theoretical formulations of the problem. Variables important in determining forces on circular piles subjected to wave action are shown in Figure 7-67. Variables describing nonbreaking, monochromatic waves are the wave height H , water depth d _, and either wave period T , or wavelength L . Water particle velocities and accelerations in wave-induced flows directly cause the forces. For vertical piles, the horizontal fluid velocity u and acceleration du/dt and their variation with distance below the free surface are important. The pile diameter D and a dimension describing pile roughness elements ce are important variables describing the pile. In this discussion, the effect of the pile on the wave- induced flow is assumed negligible. Intuitively, this assumption implies that the pile diameter D must be small with respect to the wavelength L . Significant fluid properties include the fluid density p and the kinematic viscosity v. In dimensionless terms, the important variables can be expressed as follows: = = dimensionless wave steepness gr d — = dimensionless water depth aT” ? = ratio of pile diameter to wavelength (assumed small) ae relative pile roughness and HD , 8 form of the Reynolds’ number Given the orientation of a pile in the flow field, the total wave force acting on the pile can be expressed as a function of these variables. The variation of force with distance along the pile depends on the mechanism by which the forces arise; that is, how the water particle velocities and accelerations cause the forces. The following analysis relates the local force, acting on a section of pile element of length dz , to the local fluid velocity and acceleration that would exist at the center of the pile if the pile were not Pe ae Two dimensionless force coefficients, an inertia or mass coefficient and a drag coefficient C, , are used to establish the wave-force a eee These coefficients are determined by experimental 7-101 ure dz O Figure 7-67. Definition sketch of wave forces on a vertical cylinder. measurements of force, velocity, and acceleration or by measurements of force and water surface profiles, with accelerations and velocities inferred by assuming an appropriate wave theory. The following discussion initially assumes that the force coefficients C and C are known and illustrates the calculation of forces on vertical cylindrical piles subjected to monochromatic waves. A discussion of the selection of C and Cp follows in Section e, Selection of Hydrodynamic Force Coefficients, Cp and Cy - Experimental data are available primarily for the interaction of nonbreaking waves and vertical cylindrical piles. Only general guidelines are given for the calculation of forces on noncircular piles. b. Vertical Cylindrical Piles and Nonbreaking Waves: (Basic Concepts). By analogy to the mechanism by which fluid forces on bodies occur in uni- directional flows, Morison et al. (1950) suggested that the horizontal force per unit length of a vertical cylindrical pile may be expressed by the following (see Fig. 7-67 for definitions): 2 f=£,+£,-¢ uiayen 1 D mM? aap t Sze Pur (7-20) 7-102 f- = inertial force per unit length of pile fp = drag force per unit length of pile p = density of fluid (1025 kilograms per cubic meter for sea water) D = diameter of pile u = horizontal water particle velocity at the axis of the pile (calculated as if the pile were not there) d 2 , F ; = = total horizontal water particle acceleration at the axis of the pile, (calculated as if the pile were not there) Cp = hydrodynamic force coefficient, the "drag" coefficient Cy = hydrodynamic force coefficient, the "inertia" or "mass" coefficient The term f- is of the form obtained from an analysis of force on a body in an accelerated flow of an ideal nonviscous fluid. The term fp is the drag force exerted on a cylinder in a steady flow of a real viscous fluid (Ga is proportional to u and acts in the direction of the velocity u ; for flows that change direction this is expressed by writing u AS. pal (aai| Pv Although these remarks support the soundness of the formulation of the problem as given by equation (7-20), it should be realized that expressing total force by the terms f; and fp ts an assumption justified only if it leads to sufficiently accurate predictions of wave force. From the definitions of u and du/dt , given in equation (7-20) as the values of these quantities at the axis of the pile, it is seen that the influence of the pile on the flow field a short distance away from the pile has been neglected. Based on linear wave theory, MacCamy and Fuchs (1954) analyzed theoretically the problem of waves passing a circular cylinder. Their analysis assumes an ideal nonviscous fluid and leads, therefore, to a force having the form of f; . Their result, however, is valid for all ratios of pile diameter to wavelength, Diy and shows the force to be about proportional to the acceleration du/dt for small values of D/Ly (L, is the Airy approximation of wavelength). Taking their result as indicative of how small the pile should be for equation (7-20) to apply, the restriction is obtained that D2 0.08 (J=21) my Figure 7-68 shows the relative wavelength L/L, and pressure factor K versus d/gT“ for the Airy wave theory. kok k kk kK Ok Ok Ok KO & & & & & EXAMPLE PROBLEM 16 * * * * * *¥ * KX KK KR KK GIVEN: A wave with a period of T= 5s , and a pile with a diameter D = 0.3 Mm Glete in) lid) me C49) ft.) of water. 7103 *(Ax00y. eAem ATTY) im 10 80:0 900 ditt 12360 3355 62332 Ras Soames ce08s sseee SSS SSS = SS Eee pee earn ag es gaa UR TTT eee Hai te tere es -a eS cen EE ti Hy Fbih zus/P SNSI2A 1OJOeJ sAnssoid pue yRSuUEeTIAeM VATIeTSY °gg-/ eANSTYy bO0 £00 ae a Peet ta MUA ELL HL ER 10°0 at i a ae Hn aE ae t t ie iesas Seepe Tot fo na ages sega oe = sages Same espstegs Her eet aly : oe 1 90-5 ‘ 3 » j th pe Wilittg39 egseceeeeeeae 7-104 FIND: Can equation (7-20) be used to find the forces? SOLUTION: ————— 2 eae as = 280) = 39.0 m (128.0 ft) = aoa EC = 0.0061 eT 9.8(5) which, using Figure 7-68, gives A zA = 0.47 oO L, = 0-47 L = 0.47 (39.0) = 18.3 m (60.0 ft) Oo Dee OeSaes i = TGz = 0-016 < 0.05 Since D/L satisfies equation (7-21), force calculations may be based on equation (7-20). kKRKRK KK KKK KKK KKK KKK KKK KR KEK KKK KKK KKK KK KEK KKK The result of the example problem indicates that the restriction expressed by equation (7-21) will seldom be violated for pile force calculations. However, this restriction is important when calculating forces on dolphins, caissons, and similar large structures that may be considered special cases of piles. Two typical problems arise in the use of equation (7-20). (1) Given the water depth d _, the wave height H , and period T , which wave theory should be used to predict the flow field? (2) For a particular wave condition, what are appropriate values of the coefficients C,. and C, ? D M c. Calculation of Forces and Moments. Jt tis assumed in thts sectton that the coefficients Cp and C are known and are constants. (For the selection of C._ and C, see chapter 7, Section III,l,e, Selection of Hydro- dynamic Force Clereieients C and C,.) To use equation (7-20), assume that the velocity and acceleration fields associated with the design wave can be described by Airy wave theory. With the pile at x = 0 , as shown in Figure 7-67, the equations from Chapter 2 for surface elevation (eq. 2-10), hori- zontal velocity (eq. 2-13), and acceleration (eq. 2-15), are — Uf 2nt ‘S n= 5) cos (28) (7-22) 7-105 — H gT cosh [2n (z + d)/L] 2nt . = oT Aa eal es er (7-23) du _ du _ gmH cosh [2m (z + d)))/Aclaee 2-2 re dt ot) 2 cosh [2nd/L] a T (7-24) Introducing these expressions into equation (7-20) gives 2 a 1D mt cosh [2n (z + d)/L] ; a 2m e “5 7 Cy She 2 {t cosh [21d/L] | ae ( Tt ) (7=25) 2 2 1 2 }eT cosh [27 (z + d)/L] 2nt 2nt niet ae en ae D D2 2 cosh [2nd/L] 4L Equations (7-25) and (7-26) show that the two force components vary with elevation on the pile z and with time t . The inertia force f, is maximum for sin (- 2nt/T) = 1, or for t = -— T/4 for Airy wave theory. Since t = 0 corresponds to the wave crest passing the pile, the inertia force attains its maximum value T/4 sec before passage of the wave crest. The maximum value of the drag force component fp coincides with passage of the wave crest when t=0. Variation in magnitude of the maximum inertia force per unit length of pile with elevation along the pile is, from equation (7-25), identical to the variation of particle acceleration with depth. The maximum value is largest at the surface z= 0 and decreases with depth. The same is true for the drag force component fp 3; however, the decrease with depth is more rapid since the attenuation factor, cosh [2n(z + d)/L]/cosh[2nd/L] , is squared. For a quick estimate of the variation of the two force components relative to their respective maxima, the curve labeled K = l/cosh[2nd/L] in Figure 7-68 can be used. The ratio of the force at the bottom to the force at the surface is equal to K for the inertia forces, and to K* for the drag forces. The design wave will usually be too high for Airy theory to provide an accurate description of the flow field. Nonlinear theories in Chapter 2 showed that wavelength and elevation of wave crest above stillwater level depend on wave steepness and the wave height-water depth ratio. The influence of steepness on crest elevation nh and wavelength is presented graphically in Figures 7-69 and 7-70. The use of these figures is illustrated by the following examples. kk kK kk Kk OK KOK Rk & kK K EXAMPLE PROBLEM 17 * * & & * & KK KK KK KK GIVEN: Depth d= 4.5 m (14.8 ft) , wave height H = 3.0 m (9.8 ft ) , and wave period T=10s. FIND: Crest elevation above stillwater level, wavelength, and relative variation of force components along the pile. 7-106 9°0 { == *qy8Tey aABM OJ TEAST I9IEM-TTTIS eAOge UOTIeASTA JSetD Fo OTIEY *69-/ PANSTY aip p v0 20 me) 90°70 00 200 10°0 9000 7000 200 0 100°0 I GO MMH AEHIEES REESE YoYo set EERE | IAAT sua ag ull HHH { | tt a | 9:0 HMAntfooteeeee eee ii HH het : Bea mPa | HUME OB soee erin : ut AS TT it GHe Bae = ey ih 1) DEB ER A L°0 Cy Tr al | | TT Tt | Nt TT A | EEA REECE EEE nn HHL | ti a Hi | THEE tt fafa rc HECHT i TNT *u IE Toot NMED GNOTH NOON NOB OG GBI It | | 4it r TH He } iy JU EW fo 80 VEE AROEE Ht ran ty ih [ [ {| 4 Tt 4 ter fl He i tity i} IT I tt ae Bee wae hago il | | a tt | | Ath Lf | +4 ia ae eat ++ SY 60 tH A THEA ELLEAT [ Hl Ha HH BS HEH EEE CEE EEE fafa ek fas [se] 10°0 200°0 Oe 0! SO 210 rae) me) 900 00 200 7-107 *sqooyjJo epnqt[dwme eqzTUTy AOF AOJVOeF uoTAIeAIOD yRBuseTeAeM °O/-/ esaNn3Ty 216 ( p26] ‘UdaG 42440 ) p 20) gO 10 900 +00 200 100 9000 %00'0 2000 100'0 00'| it a Hn N 4 : a - 1 nin eH G0"! il { b twit tao | t i . MW TOT HEE = =. - -. - Hol 0 HEHE Ge { |_| ss i TH i T a Vv i me it 1 i s1'1— feo 02"! = + MT UT a TH Ge | {| a 2 0! 9°0 v0 20 10 900 00 200 10°0 200°0 0 1 7-108 SOLUTION: Calculate, d a5 stags = 0.0046 2 2 eT 9.8(10) H 320 Beice = 0.0031 2 2 eT 9.8(10) From Figure 7-68, eS nOPAI I Se COSaiy) (3:2) 7 = 63.9 m (209-7 ft) A e (a) e ot es e ‘ From Figure 7-69, 0.85 H = 256 m (8.5 ft) Ne From Figure 7-/0, 1G Nes) 1 1.165 (63.9) = 74.4 m (244.1 ft) and from Figure 7-68, ©. |. mln N N i] i] oO | ~ ja VY ee fp (z fp @ ll | Qo Vv K i jo) YS Note the large increase in Ne above the Airy estimate of H/2 = 1.5 m (4.9 ft) and the relatively small change of drag and inertia forces along the pile. The wave condition approaches that of a long wave or shallow-water wave. RARER KKK KKK KKK KKK KKK KKK KEK KKK KKK KKK KEKE KKK KK kk kk kK kk OK Ok Ok Ok & RK & ® EXAMPLE PROBLEM 18 * * * * * KK * RK RK KK KK GIVEN: Same wave conditions as preceding problem: H = 3.0 m (9.8 ft) and T= 10 s ; however, the depth d = 30.0 m (98.4 ft) . FIND: Crest elevation above stillwater level, wavelength, and the relative variation of force components along the pile. 7-109 SOLUTION: Calculate, d 30.0 2 = I 2 2 gT 9.8 (10) H 3.0 SS ee SS ONE 2. gT 9.8 (10) From Figure 7-68, Et u 0489 =noneS (8) =) 136e8)m (455248 ee) O 27 From Figure 7-69, 0.52 H 0.52(3.0) = 1.6 m (5.1 ft) 2) Il From Figure 7-70, L = 1.01 Ly = 1.01 (138.8) = 140.2 m (459.9 ft) and from Figure 7-68, 2 _ ‘D (2 = -d) K (ean) Note the large decrease in forces with depth. The wave condition approaches that of a deepwater wave. eRe) He) KK KR Re KR IK RRR RIA RG KK Oe: cH RS ee ke rk ky eek ke) ieee For force calculations, an appropriate wave theory should be used to calculate u and du/dt . Skjelbreia, et al. (1960) have prepared tables based on Stokes’ fifth-order wave theory. For a wide variety of given wave conditions (i.e., water depth, wave period, and wave height) these tables may be used to obtain the variation of f- and f with time (values are given for time intervals of 2nt/T = 20°) and position along the pile (values given at intervals of 0.1 d). Similar tables based on Dean’s numerical stream- function theory (Dean, 1965b) are published in Dean (1974). For structural design of a single vertical pile, it is often unnecessary to know in detail the distribution of forces along the pile. Total horizontal 7-110 force (F) acting on the pile and total moment of forces (M) about the mud line z= -d are of primary interest. These may be obtained by integration of equation (7-20). n n =d =d Nn n M= f (z+d) f. dz + i (z + d) 7) dz = M; + Mp (7-28) =d =d In general form these quantities may be written ae Pa = Goeias mae (7-30) De epi) es D aa tS Cis EPS aS (7-32) Dy Dug :PE Deo Di DARED in which Cp and Cy have been assumed constant and where K; , Kp, Sj, and Sp are dimensionless. When using Airy theory (eqs. 7-25 and 7-26), the integration indicated in equations (7-27) and (7-28) may be performed if the upper limit of integration is zero instead of n . This leads to nol 21d ; | Ze a K; =i tanh (24) sin ( 2 ) (7-33) ‘aN 4nd/L Qnt Qnt - EDA e (: * sinh [40d/L] aes) pees (24°) pers (3) Mise) swivel 2nt 2nt =n | cos 7 | cos 7 7-111 1 - cosh [2nd/L] Si = 1 + (ond/L) sinh [2nd/L] i=), an Ute gs ee 1 - cosh [4nd/L] Ls 2D = 2 + 2n (4. (4nd/L) sinh [4nd/L) (7-36) where n=C,/C has been introduced to simplify the expressions. From equations (7=33) and (7-34), the maximum values of the various force and moment components can be written 2 D Fim = Cy e& = H Kim (7-37) . 1 2 Epa = p> eS Dy Xp, (7=38) Mim = Fim d S; (7-39) Mp, = Fon 4 Sp (7-40) where Kjm, and Kp, according to Airy theory are obtained from equations (7-33) and (7-34) taking t = -T/4 and t = 0 , respectively and S; and S are given by equations (7-35) and (7-36) respectively. Equations (7-37) through (7-40) are general. Using Dean’s stream-function theory (Dean, 1974), the graphs = Figures 7-71 through 7-74 have been pre- pared and may be used to obtain Kp) Sams aud . S2) and ; as given in equations (7-35) and eM 52 -36) for Airy theory, are independent of wave phase angle 6 and thus are equal to the maximum values. For stream- function and other finite amplitude theories, §; and Sp depend on phase angle; Figures 7-73 and 7-74 give maximum values, §;,, and - The degree of nonlinearity of a wave can be described by the ratio of wave height to the breaking height, which can be obtained from Figure 7-75 as illustrated by the following example. kok k kk k Kk OK Kk Ok & & & EXAMPLE PROBLEM 19 * * * * * * & kk KK RK KK GIVEN: A design wave H = 3.0 m (9.8 ft) with a period T= 8s ina depth d= 12.0 m (39.4 ft) . FIND: The ratio of wave height to breaking height. SOLUTION: Calculate d 12.0 SSS FS a = Moly z. 2 gT (9.8) (8) TOU? (€261 ‘uDaq 42440) IRGRER AG Loy: bo ee L3/p ‘yqdep eATIeTeA snsi9A IGBAO G 7 & ut >. al baa *TL-L ean3ty IRGEOR2 SO ee Siar, H = eet } T + if TT i + ult IM = + t + i ij | | Wd i Mt ih | | 444} + =i } a eR T AVVO BO | | IR ees eawanm tasted it a 4b IT i it HAT tH { Lyte aU EO eee i ane re SEE EEE TA] HEE 4 i BO UAT ANON an E 4 pUULY Sesh oeeed bette een EE Oe ame a L 1 ODN NY et | OB ITE AD ne LI} a] | | SOB HUNTON) AUR GIGS Mt | if SCOTT {Ofte | fc nt a LAAT Ht NUE inn ORR T ATTA eho HEE te Rn a TOT a t Tt LY] | WW ao MTL 1 00 OH maT HT eeaR 2 {| 1 To HI eta 4} uy | t 1 TH TT | 44d t+44-+ | +44 5 + nt t nin Nag TT [| tbe + | INO UA HEEB faa 1m i 1 | I TU Oe I Y Hh HOON UE COO ti I ti | Ht ita an - mill | - tt Eaaee Anna ae 11 | | a4 O00 000 t INTL LERG ESTE | | i nn aa { Ct cI 7 0 0 OTN INEA NORE Bee TT | i 90am llr" RUORBR ER | H 1 1 7 Tt tt il tet | + i | } iu i aunt qo NOU R0 COA et aii i 10011001 OG ORT IL | WT THT HELE = RIAL van au | £0 Wy 7=113 Eady, Be 255257 250252558 cee eeeee Ee £ ff SESSSS555 SF J555/ S050) JERE fo siestastus fsststl OEE! EA ee rdes aed ce a 558 fa See S55 Eesee ff nae earn aU Beneeenne HEESEreee etd a BEY ae iF ; | J EY sitet MEE) Ses etinneatiit tained Po yA BEEGE/ 2 25/5555 Ei: if aes, [Ty fi AH Pitty a 72 a L_| a SESE SS==S E5558! 2 2EF 2EEEETzz== gEas=2 4 BEEEGGe=? £5 227 Ee CI] HA ff} | | Hi SF gESF SSSSSE555 sesHGesH00(T0N |W af 0b? cessteste=stect | ee aH J [| /| ES a == = COTO H cHiae! a sri! gr Hy, - peed SSEc ie ieze 44 | Hi al guste F255 deasesee ser fsnbcies Seeestir 0 ceeue0ee fi mE Saqsaast =prlaetes BESO ae S08 ia ls SS + . | jets | i fag IE | ! | all +H | | | Leal { | | | | Hosts festeets 7-114 ( after Dean, 1973) Figure 7-72. Kon versus relative depth, d/gt? 5 SEGS5 SSSSESSSSSEEESSSESS= S52 © 2555222222 252222222 =2a=52===22====2==== ESS FEES ft i= =e! 2205555 ssceseee. geeceeoeesosecs se socessa= iE SSS Seisictet SS=SSqSSe 5 SSSe SS SSS SSaa! Spat Stet Ef Fee PELE AG Tate SSS =I = In SSeS - = = i I + cy (after Dean, 1973) 4 Pit TTT mete || | HEHE re : He FEE aE 7-115 d/gt? : Sim » versus relative depth, Inertia force moment arn, Figure 7-73. ©“Io ‘ze quowom a0z03 3eIq *4/-/ ean3Ty 0 z13/P ‘yjdop eat eTeT snsisA (€26| ‘uoag Ja4j0) INGRSae pee pet =o ES t a oo 1 + T =! If Zesae! i. ——} Ss: e252 S2s: see += 41 + = SEEa== \ Pye | =e \ = 7-116 aw gs ale i = 0.040 L 0.500 d d = 0.0155 —S = 0.0792 gt? gt? Shallow water ae Transitional ale| remit” water 0.04 soos (fen en a pon cual Ott] oe ae Ce { ty | iseias fate 0.02 0.002 0.0002 0.0001 0.00008 0.00006 jouaanees oH na te 7 t +t 0.00004 ti Se Seeee aie seer EHH TEEt fH 35 ee HEE HEE Coy Cea rT THe eet Cet oI Cot Tec 0.00003 0.0004 0.001. 0.002 00040006 OO! 0.02 0.04 006 0.1 d gt? (after Le Mehoute, 1969) Figure 7-75. Breaking wave height and regions of validity of various wave theories. 7, Enter Figure 7-75 with d/ gt? = 0.0191 to the curve marked Breaking limit and read, — = 0.014 Therefore, Hy, = 0.014 gT” = 0.014(9.8) (8)7 = 8.8 m (28.9 ft) The ratio of the design wave height to the breaking height is ee ey b 8 H H HK SI RS RI ROR RR CR HO ROK OR KK eR KX, KORK eh ee eee By using equations (7-37) through (7-40) with Figures 7-71 through 7-74, the maximum values of the force and moment components can be found. To estimate the maximum total force F, , Figures 7-76 through 7-79 by Dean (1965a) may be used. The figure to be used is determined by calculating W=—— (7-41) and the maximum force is calculated by 2) Fa = $m WCpH’D (7-42) where ¢$, is the coefficient read from the figures. Similarly, the maximum moment M, can be determined from Figure 7-80 through 7-83, which are also based on Dean’s stream-function theory (Dean, 1965a). The figure to be used is again determined by calculating W using equation (7-41), and the maximum moment about the mud line (z= -d) is found from My = Gm W Cp HY Dd (7-43) where On is the coefficient read from the figures. Calculation of the maximum force and moment on a vertical cylindrical pile is illustrated by the following examples. 7-118 *" (GO°0 =™M) °*° (L3/p pue ~-13/H snsi0n “ JO seuTTosT *9/-/ ean8Ty 216 UDaQ 13440) Th p00 £00 200 100 9000 4000 2000 + (ee Snes pa = eatin 15 Od lf ty ae yi. tpl j) jae ee aa ey ee (0S96| po ¢€0 20 10 800 900 90000 +00 as oP £000°0 Bile «| v0000 1 9000'0 8000°0 100°0 200'0 | £00'0 eee ttt 4000 Ltt 900'0 +—4 800'0 100 200 1 £00 EES 00 7-119 GEO (0. G96] ‘uDag 44j0 ) = Mi) velere 713/P pue 713/H SNSId9A my JO SeuTTOS] °*//-/ 291an3Ty 21 p 10 800 900 ¢0'0 £00 200 100 9000 %000 2000 au ie SEE GE Ge Yee ae tee es gee ee aa e Daa at oat He ee nn | HTT ni | [| Mtg inne gees Uy i aan 7-120 Do (Glo) = ft) 20° z13/P pue 713/H SNns19A my JO SOUTTOSI °8/-/ ean3Ty (0G96] ‘upag 42440) no vo £0 20 10 800 900 +00 £00 200 100 9000 +000 200°0 1000 90000 _+000°0 is SS + ao ae rt tf if Ht + £0000 t peges pees =e ss + v000°0 9000°0 80000 1000 2000 £000 v000 900°0 8000 100 7-121 (OIE Sly), O20 zi3/P pue 713/H snsioA aan JO SeUTTOST °6/-/ eaNn3Ty (06961 ‘uoag 124j0) p pO £0 i i 900 p00 £00 200 9000 i spt izsel tage 8 toes Be ae ee fftas cist —+— =} 8000'0 1000 z200°0 £000 bo00 +—+1-J 900°0 =| 8000 10°0 200 £00 b0'0 7=122 ul 2 (GOO 2 fi) 9° 713/P pue 713/H snsi0A 0 JO SodUTTOST °Qg-/ eaNn3Ty (2 $96] ‘uoag 42440) D v0 £0 20 10 800 900 00 £00 200 100 9000 _ 000 200'0 100° 90000 _+000°0 THE THEA - TE £000°0 v000'0 90000 80000 100°0 2000 £000 ¥00°0 900°0 8000 100 200 £0°0 v00 7-123 > GEO (0G96| ‘uoag 124)0) 10 800 giP p 900 00 £00 200 100 oud) Os EEO! an 2000 —: 0 Ei) Con z13/P pue 713/H snsio9A Wy Jo saeuTTOSIT “*[g-{ ean3Ty cia cetl ieee Bees ubous E eee Seer pues eee ‘= ee eee aS fees treed gees ic fey abe GSES Dimes ea oemiee Ol Gere sfaeet Soy ot. idea 3 Seep BAA aac ee Se eed Eames Bt My wae i Wl : == ii aerate Lt (PEERa OER OD EH ay : fea WUBA EG MAIRERIEEeE aN ai \ a mat {ii 1 FIRiaa C7 ir +t, 4 ray, ir rm y, wes Zr a Su ter- 9." Vag owen ge: for "on optra oe Ge Y ji da beat oe Pts A A ee eS 100°0 htt i 1 Hit 7-124 Oo (G20) = fi) °o° L3/p pue _13/H snsiea mp JO SOUTTOST °*7g-/ 2an3Ty c G (0¢96| ‘uo0ag 4a}j0) Epe £0 oO 800-900 200 £00 200 900'0__000 - 4 ao eee ee ———— Sam van At arerarae pr acveer a VV A, pata ded MT LIT ALLE iad Gee Te NAY oo “iy a an sesh q ft ee 5 is oe « HAE fe pabse reGoa (Get hte , 7-125 SRCORD sa) o (0G961 ‘u0ag 4a4j0) vo £0 2°0 ee 800 900 4 ae ee BEE sagt a eaate a ey Geeeea A op eee pete Ae eee ate ba ie Te eae ERE SR tegehire Sa ee Lie ce cca Se tt mae L i | a oe Scascesee rHetsCeESS ul zi3/P pue 713/H snsio0A ” JO SoUuTTOST ee p boo £00 200 100 9000 4000 2000 te ee "€B-/ eandTy 1000 90000 +%000°0 AA A LL ii ee ee eel ae mae Eg Wy yy ‘ae Ne Lp Ly |. ae a r Pte 7-126 kok k kk kK kK Ok kk Ok Ok Ok * ® EXAMPLE PROBLEM 20 * * ¥ ¥ ¥ ¥ *¥ KKK KK KK GIVEN: A design wave with height H = 3.0 m (9.8 ft) and period T= 10s acts on a vertical circular pile with a diameter D = 0.3 m (1 ft) in depth d= 4.5 m (14.8 ft) . Assume that C, = 2.0 ,, C_= 0.7, and the density of seawater p = 1025.2 kg/m? (1.99 “siugs/£t3) a (Selection of Cu and Cy is discussed in Section III,l,e.) FIND: The maximum total horizontal force and the maximum total moment around the mud line of the pile. SOLUTION: Calculate d 4.5 SS Ss = O50046 2 z gT (9.8) (10) and enter Figure 7-75 to the breaking limit curve and read H = 0.0034 2 gT Therefore, 27 =10200357(928). (10) =033.m (l0e8) ce) H, = 0.0034 gT b and H 3.0 — = ~~ = 0.91 H 38) b From Figures 7-71 and 7-72, using d/gt? = 0.0046 and H = 0.91 HL 5 interpolating between curves H = Hy and H = 3/4 Hy Seen: From equation 7-37: D2 i ee ul ie imo Me im 10 3)? a (2) (GOP 572). (Oot) Saar (3.0) (0.38) = 1619 N (364 1b) and from equation (7-38): 7-127 Pom = (0.7) (0.5) (1025.2) (9.8) (0.3) Ee (0.71) = 6,741 N (1,515 1b) From equation (7-41), compute Interpolation between Figures 7-77 and 7-78 for on is required. Calculate H 3.0 — = ——— = 0.0031 2 2 gT (9.8) (10) and recall that d 2 gT 0.0046 Find the points on Figures. 7-7/7 and 7-78 corresponding to thg computed values of H/gT and d/gT and determine 9 (w= 10,047 N/m or 64 1b/£t?) a Figure 7-77: W= 0.1 ; din = 0.35 Interpolated Value: W = 0.29 ; dm = 0.365 Figure 7-78: W=0.5 ; = 0.38 From equation (7-42), the maximum force is 72 F = Ign D) ®mn % oD = 0.365 (10,047) (0.7) G)- (0.3) = 6,931 N (1,558 1b) al | say ry | = 7,000 N (1,574 1b) To calculate the inertia moment component, enter Figure 7-73 with d — = 0.0046 2 gT and H = 0.91 Hy (interpolate between H = Hp and H = 3/4 Hp) to find Sm = 0.82 Similarly, from Figure 7-74 for the drag moment component, determine S, = 1.01 Dm 1—V28 Therefore from equation (7-39) M. =F. d Sm = 1619 (4.5) (0.82) 5,975 N-m (4,407 ft-lb) and from equation (7-40) S, = 6741 (4.5) (1.01) = 30.6 kN-m (22,600 ft-1b) Mom = Fom d The value of a is found by interpolation, between Figures 7-81 and 7-82 using W = 0.29 us H/gT2 = 0.0031 , and d/gT? = 0.0046 . Dm Figure 7-81: W=0.1 ; Ch 0.33 Interpolated Value W = 0.29 ; oe = 0.34 Figure 7-82: W= 0.5 ; ae 0.35 The maximum total moment about the mud line is found from equation (7-43). ee = a. wC ,H”Dd M = 0.34 (10,047) (0.7) Gyr (0.3) (4.5) = 29.1 kN-m (21,500 ft-1b) The moment arm, measured from the bottom, is the maximum total moment MH divided by the maximum total force E. ; therefore, = _ 29,100 m = Bs = 6030 - AZ mn @l Sis et) If it is assumed that the upper 0.6 m (2 ft) of the bottom material lacks significant strength, or if it is assumed that scour of 0.6 m occurs, the maximum total horizontal force is unchanged, but the lever arm is increased by about 0.6 m . The increased moment can be calculated by increasing the Moment arm by 0.6 m and multiplying by the maximum total force. Thus the maximum moment is estimated to be (m_ ) 0.6 m below mud line = (4.2 + 0.6) F_ = 4.8 (6,931) = 33.3 kN-m (24,500 ft-lb) KK AK KKK KARR KK RK KK RK KK KKK KK KKK KK KKK KK KK KK kok k kk kok Ok & OK & & & & & EXAMPLE PROBLEM 21 * * * * * * & KK OK KK KX GIVEN: A design wave with height H = 3.0 m (9.8 ft) and period T= 10 s acts on a vertical circular pile with a diameter D = 0.3 m (1.0 ft) ina depth d= 30.0 m (98.4 ft) . Assume Cu = 2.0 and Cy =e FIND: The maximum total horizontal force and the moment around the mud line of the pile. T—W29 SOLUTION: The procedure used is identical to that of the preceding problem. Calculate d 30.0 — = ————_= 0.031 2 2 gT (9.8 (10) enter Figure 7-75 to the breaking-limit curve and read H b — = 0.0205 2 gT Therefore Hy = 0.0205 eT? = 0.0205 (9.8) (10) = 20.1 m (65.9 ft) and Bo SAW HL — ORI J Oa IS From Figures 7-71 and 7-72, using d/gt2 = 0.031 and interpolating between H* OQ and H= 1/4 Hy for H= 0.15 Hp > K. = 0.44 um Kon 020 From equation (7-37), 1D aa Cy Pa, SET m(OES)— He = 2 On ClO252))) 19118) ea (3) (0.44) = 1,875 N (422 1b) and from equation (7-38), te 1 2 Fm “py & DHK Dm Dm Fp be2 (05) (1025.2) (9.8) (0.3) (3)2 (0.20) = 3,255 N (732 1b) Compute W from equation (7-41), se aultte a0 Oe GH 1.2 (3) ; 7-130 Interpolation between Figures 7-77 and 7-78 for hs » using =) = 0.031 and =. = 0.0031 , gives gt gT ¢, = Oell From equation (7-42), the maximum total force is _ 2 EF = ¢,0 C) HD F = 0-11 (10,047) (1-2) (3)> (0-3). = 3,581 N (e05) 1p) say E = 3600 N (809 1b) From Figures 7-73 and 7-74, for H = 0.15 Hy A and Spm = 0.69 From equation (7-39), =F. ds. = 1,875 (30.0) (0.57) = 32.1 kN-m (23,700 f£t-1b) and from equation (7-40), Mom = Fon d Som = 3,255 (30.0) (0.69) = 67.4 kN-m (49,700 ft-lb) Interpolation between Figures 7-81 and 7-82 with W-= 0.16 gives a = 0.08 m The maximum total moment about the mud line from equation (/-43) is, M =a w ¢ Dd m m D M_ = 0-08 (10,047) (1.2) (3)7 (0-3) (30.0) = 78.1 kN-m (57,600 ft-1b) If calculations show the pile diameter to be too small, noting that F. is proportional to D and Fy is proportional to D will allow adjustment of the force for a change in pile diameter. For example, for the same wave conditions and a 0.6-m (2-ft) -diameter pile the forces become PoOUSN 2 F, (D= 0.6m) =F, (D= 0.3 m) S98) 1,875 (4) = 7,500 WN (1,686 1b) +m 1m (0.3) Pa _ f 0.6 _ , Foy 7 (D = 0.6 m) =F (D = 0.3 m) S75 = 3,255 (2) = 6,510 N (1,464 1b) and the new values of 6 and a = are m m ¢ = 0.15 m and a = 0.10 m Therefore, from equation (7-42) F 0.6 -m diam. wc HD cE) m m D (F ) 0.6 -m diam. = 0.15 (10,047) (1.2) (3)? (0.6) = 9,766 N (2,195 1b) m and from equation (7-43) (M ) 0.6 -m diam. = a wC H“Dd m m D (@in oeG=m diam. 1 = 06100010, 047) aC 12) 03) 5 1@o.6)m C20 0) = " 195.3 kN-m (144,100 ft-1b) eK RK KR OK KR KR KOR OK KR KR RK RK ce RK OK UR OK OK ROK KR Kick KR OK Ki Kk Re Re d. Transverse Forces Due to Eddy Shedding (Lift Forces). In addition to drag and inertia forces that act in the direction of wave advance, transverse forces may arise. Because they are similar to aerodynamic lift force, transverse forces are often termed 1ift forces, although they do not act vertically but perpendicularly to both wave direction and the pile axis. Transverse forces result from vortex or eddy shedding on the downstream side of a pile: eddies are shed alternately from one side of the pile and then the other, resulting in a laterally oscillating force. Laird et al. (1960) and Laird (1962) studied transverse forces on rigid and flexible oscillating cylinders. In general, lift forces were found to depend on the dynamic response of the structure. For structures with a natural frequency of vibration about twice the wave frequency, a dynamic coupling between the structure motion and fluid motion occurs, resulting in Yousy2 large lift forces. Transverse forces have been observed 4.5 times greater than the drag force. For rigid structures, however, transverse forces equal to the drag force is a reasonable upper limit. This upper limit pertains only to rigid structures; larger lift forces can occur when there is dynamic interaction between waves and the structure (for a discussion see Laird (1962)). The design procedure and discussion that follow pertain only to rigid structures. Chang (1964), in a laboratory investigation, found that eddies are shed at a frequency that is twice the wave frequency. Two eddies were shed after passage of the wave crest (one from each side of the cylinder), and two on the return flow after passage of the trough. The maximum lift force is pro- portional to the square of the horizontal wave-induced velocity in much the same way as the drag force. Consequently, for design estimates of the lift force, equation (7-44) may be used: F_ = Be cos 26 = C ue DEK, cos26 (7-44) where F. iss thers lifts force, Fm is the maximum lift force, @ = (21x/L — 2nt/T) , and Cr. is an empirical lift coefficient analogous to the drag coefficient in equation (7-38). Chang found that Cr. depends on the Keulegan-Carpenter (1956) number u T/D , where u is the maximum macs max horizontal velocity averaged over the depth. When this number is less than 3, no significant eddy shedding occurs and no lift forces arise. As u T/D increases, Cr increases until it is approximately equal to Cy (fom cigta piles only). Bidde (1970, 1971) investigated the ratio of the maximum lift force to the maximum drag force Lee which is nearly equal to C,/Cp alge there is no phase difference between the lift and drag force (this is assumed by equation (7-44)). Figure 7-84 illustrates the dependence of c./C, on OY se T/D . Both Chang and Bidde found little dependence of Cr. on Reynolds number x = ae D/v for the ranges of R, investigated. The range of R, investigated is significantly lower than the range to be anticipated in the field, hence the data presented should be interpreted merely as a guide in estimating Cr, and then Fr . The use of equation (7-44) and Figure 7-84 to estimate lift forces is illustrated by the following example. kk kk kk KOK Ok OK OK OK & & & EXAMPLE PROBLEM 22 * * * * * kK RK Kk kk kK GIVEN: A design wave with height H = 3.0 m (9.8 ft) and period T = 10 133 (0261 02 t *713/H pue Jequnu rzoquedie9j—ueseTney yITM appig 19440) Oat te Jaquny 1sejuedio9 8| 9| vl él Ol Ay/7y yo uotaeTAeA upbajnay aboeaay 8 © "78-2 eansty 20 gO 90 20 7-134 s acts on a vertical circular pile with a diameter D depth d= 4.5 m (14.8 ft) . Assume Cy = 2.0 and Cp 53) mm (QL see)) syn, et 0.7 FIND: The maximum transverse (lift) force acting on the pile and the approximate time variation of the transverse force assuming that Airy theory adequately predicts the velocity field. Also estimate the maximum total force. SOLUTION: Calculate, H 3.0 —_ = ————_ = 0.0031 2 2 gT (9.8) (10) d 4.5 as = = 0.0046 Z gT (9.8) (10) and the average Keulegan-Carpenter number a T/D , using the maximum horizontal velocity at the SWL and at the Fottom to obtain u ° Therefore, from equation (7-23) with z= -d , Heer 1 u = —_—- max}/bottom 2 L A cosh[2n — L A/S (nace ) bottom — 7 Ga (0.90) = 2.0 m/s (6.6 ft/s) where L, is found from Figure 7-68 by entering with d/gT? and reading L/L, = 2nL,/gT ="Qle42 2) Aliso, = l/coshs|(2nd/llteeass the 9K) = vailue! on! Figure 7-68. Then, from equation (7-23) with z = 0 (“nas,) sit 3.0 (9.8) (10) co) SWE a2 65.5 = DoD iis (Wok ie/@)) The average velocity is therefore, rf Tn OU ‘i U mas SWL rons ees SoG ae = Gil m/s (6.9 ft/isd) and the average Keulegan-Carpenter number is Mee ee Die ClO ss aa 0.3 70.0 The computed value of ie T/D is well beyond the range of Figure 7-84, and the lift coefficient should be taken to be equal to the drag coefficient (for a rigid structure). Therefore, Cae — Ch = 0.7 From equation (7-44), Fr, = c, 88 He Kym COS 26= Fr, cos 26 The maximum transverse force F,, occurs when cos 20= 1.0. Therefore, Fry = 047 £402222) (928) (9,3) (3)? (0.71) = 6,741 N (1,515 1b) where Kp, is found as in the preceding examples. For the example problem the maximum transverse force is equal to the drag force. Since the inertia component of force is small (preceding example), an estimate of the maximum force can be obtained by vectorially adding the drag and lift forces. Since the drag and lift forces are equal and perpendicular to each other, the maximum force in this case is simply Emax ~~] Case Sol = 0.707 =—9 535 Nie C2 44a) which occurs about when the crest passes the pile. The time variation of lift force is given by LG 6n/ 4lcosm 210 tO tect ee ee feet tei) MCE ect tee ay Co fd td So Go Kol Go wos! Eee co co fo fF td So £3 to ne oo e. Selection of Hydrodynamic Force Coefficients Cp and Cy - Values of Cy >» Cp and safety factors given in the sections that follow are suggested values only. Selection of Cy » Cp and safety factors for a given design must be dictated by the wave theory used and the purpose of the structure. Values given here are intended for use with the design curves and equations given in preceding sections for preliminary design and for checking design calculations. More accurate calculations require the use of appropriate wave tables such as those of Dean (1974) or Skjelbreia et al. (1960) along with the appropriate Cy and Cp. 7-136 » 24 zequnu sptoussy yyTM a, quotoTyyeoo Beip JO uoTIeTAePA °Cg-/ eINSTY peed (:) g *OWn mi 4y 90! X ¢OIX pOlx Gui EE 8h pA Shi unenea | 7 pevsog 7=137 (1) Factors influencing Cp. The variation of drag coefficient Cp with Reynolds number R for steady flow conditions is shown in Figure 7-85. The Reynolds number is defined by R, =Eo8 (7-45) where u = velocity D = pile diameter v = kinematic viscosity (approximately 1.0 x 107° ft2/sec for sea water) Results of steady-state experiments are indicated by dashed lines (Achenbach, 1968). Taking these results, three ranges of R, exist: (1) Subcritical: Rg Cy (steady flow) Combining this with equation (7-49), the steady-state value of Cp _ should apply to oscillatory motion, provided L is Wh @ Bs Do OD i > 10 (7-50) A or equivalently, L Hy 99 4 (GR) D Lo kk RK Kk KR Kk KK KK KKK KK KK KK KK KK KK KK KKK KK KK KK KK kk kk kk Ok Ok kk kk kK ® EXAMPLE PROBLEM 23 * * * & * & KK RK KK RK KK GIVEN: A design wave with height of H = 3.0 m (9.8 ft) and period T = 10 s ina depth d= 4.5 m (14.8 ft) acts on a pile of diameter D= 0.3m CORO SEED FIND: Is the condition expressed by the inequality of equation (7-51) satisfied? 7-140 SOLUTION: Calculate, d — = 0.0046 2 gT From Figure 7-68: “4 co 0.41 oO Then, Hi SiO) 5) Do Oss. 0 20 T= 8.2 9 Therefore, the inequality is satisfied and the steady-state C) can be used. ema scan se) 19 aaete: iKI Me se te. Fe) See Fe) Fel Hes He Hs Hie, He Ke) Ry KK Ae KK GK Ke) Ke) ok: ce oe ee. Thirriot, et al. (1971) found that the satisfaction of equation (7-51) was necessary only when R,< 4x 10° . For larger Reynolds numbers, they found Cc approximately equal to the steady flow C, , regardless of the value of A/D . It is therefore unlikely that the condition imposed by equation (7-51) will be encountered in design. However, it is important to realize the significance of this parameter when interpreting data of small-scale experiments. The average value of all the C,’s obtained by Keulegan and Carpenter (1956) is (Cp) ees 1.52 . The results plotted in Figure 7-85 @ihirriot et al., 1971) that” account for the influence of A/D show that C * 1.2 is a more representative value for the range of Reynolds numbers co¥ered by the experiments. To obtain experimental values for C for large Reynolds numbers, field experiments are necessary. Such experiments require simultaneous measurement of the surface profile at or near the test pile and the forces acting on the pile. Values of C (and C,) obtained from prototype-scale experiments depend critically on the wave theory used to estimate fluid flow fields from measured surface profiles. kok kk kk k Ok OK KOK Rk & * & EXAMPLE PROBLEM 24 * * * & KK RK kK RK RK KKK GIVEN: When the crest of a wave, with H = 3.0 m (9.8 ft) and T= 10s , passes a pile of D = 0.3 m (0.9 ft) in 4.5 m (14.8 ft) of water, a force F = Pom = 7000 N (1,573 1b) is measured. FIND: The appropriate value of Cy ° SOLUTION: From Figure 7-72 as in the problem of the preceding section, K, = Qoz/il when Hees OR S/, aH te The measured force corresponds to Ba . therefore, rearranging equation (7-38), F Dm Cc = D 2 (1/2)pg DH K Dm 7-141 7,000 C= 073 D 2 (0.5)(1025.2)(9-8)(0.3)(3) (0.71) If Airy theory had been used (H* 0), Figure 7-72 with d/gT2 = 0.0046 would give Kp = 0.23 , and therefore H = 0.87 Hy ofl (c,) ~_—_—____—_—-_ = 0.73 = 2.25 H = 0.87 H, (‘%*) 0.235 Airy (H * 0) D Airy KR KR RE K RR ROR KR KR BK KR KR KIRK KE KR KR K OK ROK KR OR UR CK KH AE kok kk kk kk Kk OK & ROK & EXAMPLE PROBLEM 25 * * * * & * & KK KK KK K GIVEN: Same conditions as the preceding example, but with a wave height H 15.0 m (49.2 ft) , a depth d = 30.0 m (98.4 ft) , and F = Fpm = 130,000 N (295225 .eb) re FIND: The appropriate value of Cp . SOLUTION: From Figure 7-75 Hp = 20.6 m (68 ft) ; then H/Hp = 15.0/20.6 0.73 . Entering Figure 7-72 with d/gT“ = 0.031 , Kp, = 0.38 is found. Therefore, from equation (7-33), Ch = ‘Dr = w/2 pgDH’K,, 130,000 = 0 2 0.5(1025.2)(9.8)(0-3)(15.0) (0.38) If Airy theory had been used, Kp, = 0.17 and ) = nae ji (<¢, H = 0.73 H K ; (0.17) : , (‘“) Airy (H * 0) Some of the difference between the two values of Cp exists because the SWL (instead of the wave crest) was the upper limit of the integration performed to obtain Kp, for Airy theory. The remaining difference occurs because Airy theory is unable to describe accurately the water-particle velocities of finite-amplitude waves. HR OR RK OKC RK RR KK Re KR KR OK RRR eee UX Kees, ee ee 7-142 The two examples show the influence of the wave theory used on the value of Cp determined from a field experiment. Since the determination of wave forces is the inverse problem (i.e., Cp and wave conditions known), tt ts important in force calculations to use a wave theory that is equivalent to the wave theory used to obtain the value of Cp (and Cy). A wave theory that accurately describes the fluid motion should be used in the analysis of experimental data to obtain Cp (and Cy) and in design calculations. Results obtained by several investigators for the variation of Cp with Reynolds number are indicated in Figure 7-85. The solid line is generally conservative and is recommended for design along with Figures 7-7/2 and 7-74 with the Reynolds number defined by equation (7-45). kkk kk kK Ok kK Ok k kk & & & EXAMPLE PROBLEM 26 * * * *¥ * * RK KK KK KKK FIND: Were the values of Cp used in the preceding example problems reasonable? SOLUTION: For the first example with H = 3.0 m (9.8 ft) , T=10s, d= 4.5m (14.8 ft) , and D= 0.3m (1 ft) , from equation (7-47), se ee max dy 7 _ 7 sc@ il i Wax I TOT eOLa Ie Dos in (os) 22e//3)) From equation (7-46) uy D R, Po = VgR— (v = 9.29 x 10 y IES) Ro ae eee) pe Shae 10 9.29 x 107” 5 From Figure 7-85, Cp = 0.7 , which is the value used in the preceding example. For the example with H = 3.0 m (9.8 ft) , T=10s , d = 30.0 m (98.4 fe), and. .Di= 0.3m Gl ft) 5. from equation, (/=47), _ = (3.0) (1) mase (10) (0.89) =) *] 1 m/s: "(36 ft/s) From equation (7-46), R = GEA (0230) 5 3.55 x 10> 9.29 x 10 e 7 7-143 From Figure 7-85, Cp = 0-89 which is less than the value of Cp = 1.2 used in the force calculation. Consequently, the force calculation gave a high force estimate. ek kK KR a OK KOK KR ROK KR RAK ROK OK ORK OK CK OR OK RK OK OR kak eae eee Hallermeier (1976) found that when the parameter ie is approximately equal to 1.0 , the coefficient of drag Cp may significantly increase because of surface effects. Where this is the case, a detailed analysis of forces should be performed, preferably including physical modeling. (Do Factors Influencing Cy, MacCamy and Fuchs (1954) found by theory that for small ratios of pile diameter to wavelength, This is identical to the result obtained for a cylinder in accelerated flow of an ideal or nonviscous fluid (Lamb, 1932). The theoretical prediction of C can only be considered an estimate of this coefficient. The effect of a real viscous fluid, which accounted for the term involving Cp in equation (7-48), will drastically alter the flow pattern around the cylinder and invalidate the analysis leading to Cy = 2.0 . The factors influencing Cy also influence the value of Cy . No quantitative dependence of C on Reynolds number has_ been established, although Bretschneider (1957) indicated a decrease in Cy with increasing R, . However for the range of Reynolds numbers (Re < 3Fsalow) covered by Keulegan and Carpenter (1956), the value of the parameter A/D plays an important role in determining Cy - Ince IVD) «K Il they found CHa ZoO Since for small values of A/D the flow pattern probably deviates only slightly from the pattern assumed in the theoretical develop- ment, the result of Cy = 2.0 seems reasonable. A similar result was obtained by Jen (1968) who found Cy © 2.0 from experiments when A/D < 0.4. For larger A/D values that are closer to actual design conditions, Keulegan and Carpenter found (a) a minimum PANS Lor A/D 2.5) and: (@b)ithat Cy increased from 1.5 to 2.5 for 6 < A/D < 20 . Just as for Cp , Keulegan and Carpenter showed that C was nearly constant over a large part of the wave period, therefore supporting the initial assumption of constant Cy and Cp « Table 7-5 presents values of C reported by various investigators. The importance of considering which wave theory was employed when determining Cp from field experiments is equally important when dealing with Cy ° Based on the information in Table 7-5, the following choice of Cy is recommended for use in conjunction with Figures 7-71 and 7-72: Ge = 220) Gwhen GRa< 92/5 x 10° M e R e 5 5 G S65 oo S——— Pron 25% 10 << R < SF xe iC (7-53) M 5 e Sexe O arte 5 = 1.5 when R, 5) ><) INO) 7-144 with R, defined by equation (7-46). Table 7-5. Experimentally determined values of Cy . * Keulegan and Carpenter (1956) 6) Bretschneider (1957) 1.6) x 10° to) 2/3)x 10° 2.26 to 2.02 Field experiments 3.8 x 10° to 6 x 10° 1.74 to 1.23 | Linear theory Wilson (1965) large (>5 x 10°) 1.53 Field experiment, spectrum Skjelbreia (1960) large (>5 x 10°) 1.02 + 0.53 | Field experiments, Stokes’ fifth-order theory 2x 10° to 2 x 10° Dean and Aagaard (1970) 1.2 to 1.7 Field experiments, Stream-function theory vans (1970) large (>5 x 10°) 1.76 + 1.05 Field experiments, Numerical wave theory or Stokes’ fifth-order theory large (>5 x 10°) Field experiments, Modified spectrum analysis: using Cp = 0.6 and Cy = 1.5, the standard deviation of the calculated peak force was 33 percent Range or mean + standard deviation. The values of (Gy, given in Table 7-5 show that Skjelbreia (1960), Dean and Aagaard (1970), and Evans (1970) used almost the same experimental data, and yet estimated different values of Cy - The same applies to their determination of Cp , but while the recommended choice of Cp from Figure 7- 85 is generally conservative, from equation (7-53) the recommended choice of for R, 5) 26 10) corresponds approximately to the average of the reported values. This possible lack of conservatism, however, is not significant since the inertia force component is generally smaller than the drag force component for design conditions. From equations (7-37) and (7-38) the ratio of maximum inertia force to maximum drag force becomes im _™ MD “im (7-54) 7-145 For example, if Cy =z 2C and a design wave corresponding to H/H, = 0.75 is assumed, the ratio hay may be written (using Figures 7-71 and 7-72) as 2 (shallow-water waves) F. H tm Pm D (7-55) 5-355 (deepwater waves) Since D/H will generally be smaller than unity for a design wave, the inertia-force component will be much smaller than the drag-force component for shallow-water waves and the two force components will be of comparable magni- tude only for deepwater waves. f. Example Problem 27 and Discussion of Choice of a Safety Factor. kok kk kk Ok Ok Ok Ok Ok Ok OK KK EXAMPLE PROBLEM 27 * * * & KK KK KKK KKK GIVEN: A design wave, with height H = 10.0 m (32.8 ft) and period T = 12 s , acts on a pile with diameter D = 1.25 m (4.1 ft) in water of depth d =) 26) mG oer) ie. FIND: The wave force on the pile. SOLUTION: Compute H 10.0 = Sa Fea = 0.0071 eT ((Q5s)) (CZ) and d 26 —_ = —————- = 0.0184 72 2 gT (9.8) (12) From Figure 7-68, for d/gt2 = 0.0184 , L A 5 i 0.76 oO and 2 2 gT (9.8) (12) 0.76 —e o 0.76 = 170.7 m (559.9 ft) 21 20 1 SOG 7/Gy 16 A (a) From Figure 7-69 for d/gT* = 0.0184 , Ss) ce ry = 0.68 7-146 and, therefore, 0.68 H = 0.68 (10.0) = 6.8 m (22.3 ft) Ne say n 7 my (28) 122) e The structure supported by the pile must be 7 m (23 ft) above the still- water line to avoid uplift forces on the superstructure by the given wave. Calculate, from equation (7-21), = 0.0073 < 0.05 Therefore equation (7-20) is valid. From Figure 7-75, H b ——— 0.014 2 gT H H gt 0.0073 i H 0.014 gT From Figures 7-71 through 7-74, Gyr 0e59 From equations (7-46) and (7-47), L u alee Fj = Sane, ORIG) Se4m/sm Gllele ft/s) and u D Max Ge mG. 25)) 6 R = —— = ————_ = 4.57 x 10 e Oe2or = 10) 7-147 From Figure 7-85, Cp = 0.7 and from equation (7-53), with Rg, > 5x 10° ; Cy = 165) Therefore, 2 1D Fim = Cy 98 ZG HK n F. = (1-5) (1025.2) (9.8) 4(1.25)" im : . : 4 (10.0) (0.40) = 74.0 kN (16,700 1b) _ ey 2 Fom = Sp 7 P8DH Ky, Fom 7 (0.7)(0+5)(1025-2)(9.8)(1-25)(10.0)* (0.35) = 153.8 kN (34,600 1b) — — = 6 —s Min = Fim4Sjm = (74,000)(26)(0.59) = 1,135 kN-m (0.837 x 10° £t-1b) Mom = FomdSpm = (153,800)(26)(0.79) = 3,160 kN-m (2.33 x 10° £t-1b) From equation (7-41), Interpolating between Figures 7-77 and 7-78 with H/gT2 = 0.0075 and d/gT? = 0.0183 , bn = 0420 Therefore, from equation (7-42), 2 Fn = dmWCpH’ D F, = (0-20) (10,047) (0.7) (10.0)7 (1.25) = 175.8 kN (39,600 1b) Interpolating between Figures 7-81 and 7-82 gives oS 0.15 Therefore, from equation (7-43), M, = a,WCpH“Dd 7-148 = (0.15)(10,407)(0.7)(10.0) 2(1.25)( 26) = 3,429 kN-m (2.529 x 10° ft-lb) Mn ECM AEA eae AAs) oak, eee KL Ke eee eee ae) Rete ca Ae od: ited ak) se) “Heeese) kak: Before the pile is designed or the foundation analysis is performed, a safety factor is usually applied to calculated forces. It seems pertinent to indicate (Bretschneider, 1965) that the design wave is often a large wave, with little probability of being exceeded during the life of the structure. Also, since the experimentally determined values of Cy and Cp show a large scatter, values of Cy amd Cp could be chosen so that they would rarely be exceeded. Such an approach is quite conservative. For the recommended choice of Cy and Cp when used with the generalized graphs, the results of Dean and Aagaard (1970) show that predicted peak force deviated from measured force by at most + 50 percent. When the destgn wave ts unlikely to occur, it ts recommended that a safety factor of 1.5 be applted to calculated forces and moments and that this nominal force and moment be used as the basis for structural and foundation design for the pile. Some design waves may occur frequently. For example, maximum wave height could be limited by the depth at the structure. Jf the design wave ts likely to occur, a larger safety factor, say greater than 2, may be applied to account for the uncertainty in Cy and Cp. In addition to the safety factor, changes occurring during the expected life of the pile should be considered in design. Such changes as scour at the base of the pile and added pile roughness due to marine growth may be important. For flow conditions corresponding to supercritical Reynolds numbers (Table 7-5), the drag coefficient Cp will increase with increasing roughness. The design procedure presented above is a static procedure; forces are calculated and applied to the structure statically. The dynamic nature of forces from wave action must be considered in the design of some offshore structures. When a structure’s natural frequency of oscillation is such that a significant amount of energy in the wave spectrum is available at that frequency, the dynamics of the structure must be considered. In addition, stress reversals in structural members subjected to wave forces may cause failure by fatigue. If fatigue problems are anticipated, the safety factor should be increased or allowable stresses should be decreased. Evaluation of these considerations is beyond the scope of this manual. Corrosion and fouling of piles also require consideration in design. Corrosion decreases the strength of structural members. Consequently, corrosion rates over the useful life of an offshore structure must be estimated and the size of structural members increased accordingly. Watkins (1969) provides some guidance in the selection of corrosion rates of steel in seawater. Fouling of a structural member by marine growth increases (1) the roughness and effective diameter of the member and (2) forces on the member. Guidance on selecting a drag coefficient Cp can be obtained from Table 7-4. However, the increased diameter must be carried through the entire design procedure to determine forces on a fouled member. 7-149 ge Calculation of Forces and Moments on Groups of Vertical Cylindrical Piles. To find the maximum horizontal force and the moment around the mud line for a group of piles supporting a structure, the approach presented in Section III,l1,b must be generalized. Figure 7-86 shows an example group of piles subjected to wave action. The design wave concept assumes a two- dimensional (long-crested) wave; hence the x-direction is chosen as _ the direction of wave propagation. If a reference pile located at x= 0 is chosen, the x-coordinate of each pile in the group may be determined from xp =—t) (cosna (7-56) n n where the subscript n _ refers to a particular pile and 2& and a are as defined in Figure 7-86. If the distance between any two “adjacent "piles is large enough, the forces on a single pile will be unaffected by the presence of the other piles. The problem is simply one of finding the maximum force on a series of piles. In Section III,l1,b, the force variation in a single vertical pile as a function of time was found. If the design wave is assumed to be a wave of permanent form (i.e., one that does not change form as it propagates), the variation of force at a particular point with time is the same as _ the variation of force with distance at an instant in time. By introducing the phase angle 9 = 2X _ 2nt (7-57) where L is wavelength, the formulas given in Section III,l,c (eqs. (7-25) and (7-26)) for a pile located at x= 0 may be written in general form by introducing © , defined by 2nx/L - 2nt/T in place of -2nt/T . Using tables (Skjelbreia et al., 1960, and Dean, 1974), it is possible to calculate the total horizontal force F(x) and moment around the mud line M(x) as a function of distance from the wave crest x . By choosing the location of the reference pile at a certain position x= x_ relative to the design wave crest the total force, or moment around the mud line, is obtained by summation Ngo F = © F(x +x) (7-58) Total ,=0 Neel M = M a 33) Total ,=0 i =) ¢ ) where N = total number of piles in the group from equation (7-56) *“ i * i} location of reference pile relative to wave crest T= 50 Reference Pile Figure 7-86. Definition sketch: calculation of wave forces on a group of piles that are structurally connected. By repeating this procedure for various choices of x, it is possible to determine the maximum horizontal force and moment around the mud line for the pile group. F_ (8) is an even function, and F ;(6) is an odd function; hence Fy (6) = Fp (- 6) (7-60) and F (8) SS Ee (= 6) (7-61) and calculations need only be done for O=62XmT radians. Equations (/-60) and (7-61) are true for any wave that is symmetric about its crest, and are therefore applicable if the wave tables of Skjelbreia et al. (1960) and Dean (1974) are used. When these tables are used, the wavelength computed from the appropriate finite amplitude theory should be used to transform 96 into distance from the wave crest, x. The procedure is illustrated by the following examples. For simplicity, Airy theory is used and only maximum horizontal force is considered. The same computation procedure is used for calculating maximum moment. T— Si kk kK kK kK KOK kK Ok Ok kk O&K ® EXAMPLE PROBLEM 28 * * * *& ¥ & KK KKK KK KK GIVEN: A design wave with height H = 10.0 m (32.8 ft) and period T= 12 s in a depth d = 26.0 (85.3 ft) acts on a pile with a diameter D = 1.25 m (4.1 ft). (Assume Airy theory to be valid.) FIND: The variation of the total force on the pile as a function of distance from the wave crest. SOLUTION: From an analysis similar to that in Section III,l,e, and From Figures 7-71 and 7-72, using the curve for Airy theory with d 26.0 ark ae ae Vea gT Coe} (ClD)) Kee= 0688) 330K: = 0.20 1m Dm and from equations (7-37) and (7-38), 2 FY = 125° 11025 .-2)) (9.8) wiv (10.0)(0.38) = 70.3 kN (15,800 1b) 4am Ea 0.7 (0.5)(1025.2)(9.8)(1.25)( 10.0)" (0.20) = 87.9 kN (19,800 1b) Combining equations (7-29) and (7-33) gives B= sin 6 t 1m and combining equations (7-30) and (7-34) gives F_=F_ cos @|cos 6 | Dm where The wavelength can be found from Figure 7-68, Leste = 7m A TANS From~ Table 7-6, the maximum force on the example pile occurs when (AE << << 4OM))8 FT = 102 kN (22,930 1b) . Table 7-6. Example calculation of wave force variation with phase angle. =F Dm |cos 8 | cos 6 F (0) = Et F, (kN) Note: 1 Newton (N) = 0.225 pounds of force. 1 kN = 1000 N. 25 £3 23 EP EP C2 9 GF £3 RF B29 Ces Co) ct Coat ce Kt fo Co to cto 63 bo os bo bh Eos be te td td oS kkk kK kK kK kK kK kK kK kk & & & EXAMPLE PROBLEM 29 * * & & & kk Ok kk Ok Ok Ok OK OK GIVEN: Two piles each with a diameter D = 1.25 m (4.1 ft) spaced 30.0 m (98.4 ft) apart are acted on by a design wave having a height H = 10.0 m (G28) £)) and va) period) f= 127s in vaadepthy) di) =) 26) m) (85 £t)i «Lhe direction of wave approach makes an angle of 30° with a line joining the pile centers. FIND: The maximum horizontal force experienced by the pile group and the location of the reference pile with respect to the wave crest (phase angle) when the maximum force occurs. SOLUTION: The variation of total force on a single pile with phase angle 6 was computed from Airy theory for the preceding problem and is given in Table 7-6. Values in Table 7-6 will be used to compute the maximum horizontal force on the two-pile group. Compute the phase difference between the two piles by equation (7-56) x Qe cosa =" 30) Ceos) 30>) n n n ~ i 26.0 m (85.2 ft) T-M53 From the previous example problem, L *® Ly = 171m for d= 26m and T= 8 . x n 12 s . Then, from the expression Lae 27x (ZOO) o, "en tert Tee 0.96 rad or S60 (260) ee ° Coke aa Fi Ga 54.7 Values in Table 7-6 can be shifted by 55 degrees and represent the variation of force on the second pile with the phase angle. The total horizontal force is the sum of the two individual pile forces. The same procedure can be applied for any number of piles. Table 7-6 can be used by offsetting the force values by an amount equal to 55 degrees (preferably by a graphical method). The procedure is also applicable to moment computations. The maximum force is about 183.0 kN when the wave crest is about 8 degrees or [(8° /360°) 171] = 3.5 m (11.5 ft) in front of the reference pile. Because Airy theory does not accurately describe the flow field of finite- amplitude waves, a correction to the computed maximum force as determined above could be applied. This correction factor for structures of minor importance might be taken as the ratio of maximum total force on a single pile for an appropriate finite-amplitude theory to maximum total force on the same pile as computed by Airy theory. For example, the forces on a single pile are (from preceding example problems), Ge) iedieecenpiaeude ee etree = 102 kN (22,930 1b) Therefore, the total force on the two-pile group, corrected for the finite- amplitude design wave, is given by, F i (F) finite-amplitude P Total| 2 piles ([F J Total |2 piles m Airy (corrected for (computed from finite-amplitude Airy theory ) design wave) _ 175.9 ; [Frotat}2 piles 7 T0220 (183.0) = 315.6 kN (71,000 1b) BORK KR ROK KK ROR ROAR ROE CR KR CK IK RR KS RR AK RR Ree eee ee 7-154 This approach is an approximation and should be limited to rough calculations for checking purposes only. The use of tables of ftnite-amplitude wave properties (Skjelbreta et al., 1960 and Dean, 1974) ts recommended for design calculattons. As the distance between piles becomes small relative to the wavelength, maximum forces and moments on pile groups may be conservatively estimated by adding the maximum forces or moments on each pile. The assumption that piles are unaffected by neighboring piles is not valid when distance between piles is less than three times the pile diameter. A few investigations evaluating the effects of nearby piles are summarized by Dean and Harleman (1966). h. Calculation of Forces on a Nonvertical Cylindrical Pile. A single, nonvertical pile subjected to the action of a two-dimensional design wave traveling in the +x direction is shown in Figure 7-67. Since forces are perpendicular to the pile axis, it is reasonable to calculate forces by equation (7-20) using components of velocity and acceleration perpendicular to the pile. Experiments (Bursnall and Loftin, 1951) indicate this approach may not be conservative, since the drag force component depends on resultant velocity rather than on the velocity component perpendicular to the pile axis. To consider these experimental observations, the following procedure is recommended for calculating forces on nonvertical piles. For a given location on the pile (xp , yg , Z im Figure 7-87), the force per unit length of pile is taken as the horizontal force per unit length of a fictitious vertical pile at the same location. kok kk kk kK KOK OK KOK & & & EXAMPLE PROBLEM 30 * * * * & & & KOK KK KK KK GIVEN: A pile with diameter D = 1.25 m (4.1 ft) at an angle of 45 degrees with the horizontal in the x-z plane is acted upon by a design wave with height H = 10.0 m (32.8 ft) and period T= 12s ina depth d = 26 m (85 EE) ° FIND: The maximum force per unit length on the pile 9.0 m (29.5 ft) below the SWL (z = -9.0 Mm). SOLUTION: For simplicity, Airy theory is used. From preceding examples, Cy =yies, Cp= 0.7 , and L=sLy= 171m. From equation (7-25) with sin (-27/T) = 1.0 , 2 » 1D jt cosh [2n(d + z)/L] fim = Cy P& 4 ue 18 cosh [2nd/L] (10.0) —~ (0.8) = 2,718 N/m (186 lb/ft) fo 15 ClO25.2)) C8) 171 AGL PS> im 4 7-155 —EE _——————— wv, - ——_ - ———_ - > XxX LY? m ds : SZ/ ZXy | Note: x,y,and z axes are orthogonal Figure 7-87. Definition sketch: calculation of wave forces on a nonvertical pile. From equation (7-26) with cos (2mt/T) = 1.0 , 2 pg 72, eae cosh [21n(d + z)/L] f = Cc — Dm D2 2 cosh [21d/L] 4L 2 (1025.2)(9.8) 2 G8)? Gh2) 2 if = 0.7 ———————-._ (1.25) (10.0) —————— (0.8) = 3,394 N/m Dm Z 2 4(171) (233) 1b/EE) The maximum force can be assumed to be given by F m fis ££. 4! m Dm Fon where F, and Fp, are given by equations (7-42) and (7-38). Substituting these equations into the above gives C_ HOD 2 sh > 2 H D CA Ceg/2) Kom 7-156 From equation (7-41), Interpolating between Figures 7-77 and 7-78 with H/gT2 = 0.0075 and d/gT2 = 0.0184 , it is found that o = 0.20 « From a preceding problem, m =a = Oea2 b m Enter Figure 7-72 with d/ eT? = 0.0183 and, using the curve labeled 1/2 He » read Kom = 0.35 Therefore, 2 f = a My Dm " XOCD f = 3,394.1 —0.35 7 3,879 N/m (266 1b/ft) say fae 3,900 N/m (267 lb/ft) The maximum horizontal force per unit length at z = -9.0 m (-29.5 ft) on the fictitious vertical pile is f = 3,900 N/m. This is also taken as the maximum force per unit length perpendicular to the actual inclined pile. emmracierac nse) ee Ae ae Ke) ae) Ke ie) de Aes ek) ee) ee de) de) de) KK) es Ke) kK) i. Calculation of Forces and Moments on Cylindrical Piles Due to Breaking Waves. Forces and moments on vertical cylindrical piles due to breaking waves can, in principle, be calculated by a procedure similar to that outlined in Section III,1,b by using the generalized graphs with H = H,. This approach is recommended for waves breaking in deep water (see Ch. 2, Sec. VI, BREAKING WAVES). For waves in shallow water, the inertia force component is small compared to the drag force component. The force on a pile is therefore approxinately 1 2 Fee Ee =e > eee He Kone (7-62) YaNSy/ Figure 7-72, for shallow-water waves with H = Hp , gives Kpm = 0-96 = 1.0; consequently the total force may be written 1 2 rn = Ch oy pg D Hp (7-63) From Figure 7-74, the corresponding lever arm is dpSpp, = dp (1-11) and the moment about the mud line becomes M, = Fy (Lell dp) (7-64) Small-scale experiments (R, = 5 xX 10° by Hall, 1958) indicate that row leGs We ee (7-65) m b and M ms ES Hy (7-66) Comparison of equation (7-63) with equation (7-65) shows that the two equations are identical if Cp = 3.0 . This value of Cp is 2.5 times the value obtained from Figure 7-85 (Cp = 1.2 for Rg = 5 x 104). From Chapter 2, Section VI, since Hp generally is smaller than (leT1) dp, tt=ismeans servative to assume the breaker height approximately equal to the lever arm, 1.ll dp. Thus, the procedure outlined in Section III,1,b of thte chapter may also be used for breaking waves in shallow water. However, Cp should be the value obtained from Figure 7-85 and multiplied by 2.5, Since the Reynolds number generally will be in the supercritical region, where according to Figure 7-85, Cp = 0.7 , it is recommended to calculate breaking wave forces using (Cy) pmeaking = DESeCOMD a= les (7-67) The above recommendation is based on limited information; however, large- scale experiments by Ross (1959) partially support its validity. For shallow-water waves near breaking, the velocity near the crest approaches the celerity of wave propagation. Thus, as a first approximation the horizontal velocity near the breaker crest is Usnest * V8dp * V8Hp (7-68) where Hp is taken approximately equal to dp, _ the depth at breaking. Using 7-158 equation (7-68) for the horizontal velocity, and taking Cp = 1.75 , the force per unit length of pile near the breaker crest becomes i 2 fom Rs Cha pDune ee 0.88 pg DHy (7-69) Table 7-7 is a comparison between the result calculated from equation (/-69) with measurements by Ross (1959) on a 1-foot-diameter pile (Rg = 1.3 x 10 ) 6 Table 7-7. Comparison of measured and calculated breaker force. Breaker Height £m mm (GE) N/m (1b/£f£t) N/m (lb/ft) LCS 57) 3211 9220) 1.16 (3.8) 3648 (250) 1.2 (4.1) 1824 (125) 1.3 (4.2) 2481 (170) Pes C452) 4086 (280) 1.5 (4.9) 3648 (250) —y Values given are force per unit length of pile near breaker crest. Calculated from equation (7-69). Measured by Ross, 1959. bho Based on this comparison, the choice of Cp = 1./5 for Rg>5x 10° appears justified for calculating forces and moments due to breaking waves in shallow water. (a) Calculation of Forces on Noncircular Piles. The basic force equation (eq. 7-20) can be generalized for piles of other than those with a circular cross section, if the following substitutions are made: mate volume per unit length of pile (7=70) where D = width perpendicular to flow direction per unit length of pile 159 Substituting the above quantities for a given noncircular pile cross section, equation (7-20) may be used. The coefficients Kim » e@tc-, depend only on the flow field and are independent of pile cross-section geometry; therefore, the generalized graphs are still valid. However, the hydrodynamic coefficients C and C depend strongly on the cross-section shape of the pile. If values for C and Cy corresponding to the type of pile to be used are available, the procedure is identical to the one presented in previous sections. Keulegan and Carpenter (1956) performed tests on flat plate in oscillating flows. Equation (7-20) in the form applicable for a circular cylinder, with D taken equal to the width of the plate, gave By Gee L405) : A and for Dd? 10 (7-71) Weom< Cy & Boll The fact that C, approaches the value of 1.8 as A/D (eq. 7-50) increases is in good agreement with results obtained under steady flow conditions (Rouse, 1950). The following procedure is proposed for estimating forces on piles having sharp-edged cross sections for which no empirical data are available for values of C€,, and C,. M D (1) The width of the pile measured perpendicular to the flow direction is assumed to be the diameter of an equivalent circular cylindrical pile, D. (2) The procedures outlined in the preceding sections are valid, and the formulas are used as if the pile were of circular cross section with diameter D . (3) The hydrodynamic coefficients are chosen within the range given by equation (7-71); i.e., Cu = 3.5 and Cy 32a o This approach is approximate and should be used with caution. More accurate analyses require empirical determination of Cy and Cp for the pile geometry under consideration. Forces resulting from action of broken waves on piles are much smaller than forces due to breaking waves. When pile-supported structures are constructed in the surf zone, lateral forces from the largest wave breaking on the pile should be used for design (see Sec. 1,2). While breaking-wave forces in the surf zone are great per unit length of pile, the pile length actually subjected to wave action is usually short, hence results in a small total force. Pile design in this region is usually governed primarily by vertical loads acting along the pile axis. 7-160 2. Nonbreaking Wave Forces on Walls. a. General. In an analysis of wave forces on structures, a distinction is made between the action of nonbreaking, breaking, and broken waves (see Sec. 1,2, Selection of Design Wave). Forces due to nonbreaking waves are primarily hydrostatic. Broken and breaking waves exert an additional force due to the dynamic effects of turbulent water and the compression of entrapped air pockets. Dynamic forces may be much greater than hydrostatic forces; therefore, structures located where waves break are designed for greater forces than those exposed only to nonbreaking waves. b. Nonbreaking Waves. Typically, shore structures are located in depths where waves will break against them. However, in protected regions, or where the fetch is limited, and when depth at the structure is greater than about 1.5 times the maximum expected wave height, nonbreaking waves may occur. Sainflou (1928) proposed a method for determining the pressure due to nonbreaking waves. The advantage of his method has been ease of application, since the resulting pressure distribution may be reasonably approximated by a straight line. Experimental observations by Rundgren (1958) have indicated Saniflou’s method overestimates the nonbreaking wave force for steep waves. The higher order theory by Miche (1944), as modified by Rundgren (1958), to consider the wave reflection coefficient of the structure, appears to best fit experimentally measured forces on vertical walls for steep waves, while Sainflou’s theory gives better results for long waves of low steepness. Design curves presented here have been developed from the Miche-Rundgren equations and the Sainflou equations. Ce Miche-Rundgren: Nonbreaking Wave Forces. Wave conditions at a structure and seaward of a structure (when no reflected waves are shown) are depicted in Figure 7-88. The wave height that would exist at the structure if the structure were not present is the incident wave height H - The wave height that actually exists at the structure is the sum of H,- and the height of the wave reflected by the structure H.. The wave reflection coefficient xX equals H /H,- Wave height at the walt Hy is given as lee eC e aO) at Ua) wW Lt f L If reflection is complete and the reflected wave has the same amplitude as the incident wave, then y = 1 and the height of the elapotis or standing wave at the structure will be Do G (See Figure 7-88 for definition of terms associated with a clapotis at a vertical wall.) The height of the clapotis crest above the bottom is given by y =dth Sy Clad) e 2) 2 t where he is the height of the clapotis orbit center above SWL. The height of the clapotis trough above the bottom is given by yeidet ho = ne (7-74) t a) 2 t 7-161 pl of Clapotis Mean Level (Orbit Center i of Clapotis ) / 1+x) jue’ * Incident Wave ( 2 Hj / s / —— pe SS. 7 A (1X), re Ola suey SWL - SS b cin = Yo ) S (((/4739)) Ilr {areush et d Hy = 6 Yt Clapotis d = Depth from Stillwater Level H; = Height of Original Free Wave ( In Water of Depth, d ) x = Wave Reflection Coefficient ho = Height of Clapotis Orbit Center (Mean Water Level at Wall ) Above the Stillwater Level (See Figures 7-90 and 7-93 ) Yo = Depth from Clapotis Crest = d+ho + (>) Hj y; = Depth from Clapotis Trough = d + ho - (14% — ) Hj b = Height of Wall Figure 7-88. Definition of Terms: nonbreaking wave forces. The reflection coefficient, and consequently clapotis height and wave force, depends on the geometry and roughness of the reflecting wall and possibly on wave steepness and the "wave height-to-water depth" ratio. Domzig (1955) and Greslou and Mahe (1954) have shown that the reflection coefficient decreases with both increasing wave steepness and "wave height-to-water depth" ratio. Goda and Abe (1968) indicate that for reflection from smooth vertical walls this effect may be due to measurement techniques and could be only an apparent effect. Until additional research is available, it should be assumed that smooth vertical walls completely reflect incident waves and y= 1. Where wales, tiebacks, or other structural elements increase the surface roughness of the wall by retarding vertical motion of the water, a lower value of yx may be used. A lower value of y also may be assumed when the wall is built on a rubble base or when rubble has been placed seaward of the structure toe. Any value of x less than 0.9 should not be used for design purposes. Pressure distributions of the crest and trough of a clapotis at a vertical wall are shown in Figure 7-89. When the crest is at the wall, pressure 7-162 increases from zero at the free water surface to wd + p,; at the bottom, where pj) is approximated as 1 + A a Bin | SES) aa (HEE) 1 2 cosh (2nd/L) Crest of Clapotis at Wall Trough of Clapotis at Wall ‘a Hydrostatic Pressure Distribution Actual Pressure Distribution Hydrostatic Pressure Distribution Actual Pressure Distribution Figure 7-89. Pressure distributions for nonbreaking waves. When the trough is at the wall, pressure increases from zero at the water surface to wd - p, at the bottom. The approximate magnitude of wave force may be found if the pressure is assumed to increase linearly from the free surface to the bottom when either the crest or trough is at the wall. However, this estimate will be conservative by as much as 50 percent for steep waves near the breaking limit. Figures 7-90 through 7-95 permit a more accurate determination of forces and moments resulting from a nonbreaking wave at a wall. Figures 7-90 and 7-92 show the dimensionless height of the clapotis orbit center above still- water level, dimensionless horizontal force due to the wave, and dimensionless moment about the bottom of the wall (due to the wave) for a reflection coefficient x=1. Figures 7-93 through 7-95 represent identical dimensionless parameters for yy = 0.9 . 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The use of the e figures to determine forces and moments is illustrated in the following example. kk kk kK Ok kk OR OK O&K RK & K EXAMPLE PROBLEM 31 * * *& ¥& ¥ RR KR KKK KKK GIVEN: (a) Smooth-faced vertical wall (y = 1.0). (b) Wave height at the structure if the structure were not there H = 1.5 nn, (Gy ake) )5 (c) Depth at structure d= 3m (10 ft). (d) Range of wave periods to be considered in design T= 6 s_ (minimum) on) L£.= 210) se) Guaximum)ie FIND: The nonbreaking wave force and moments against a vertical wall resulting from the given wave conditions. SOLUTION: Details of the computations are given for only the 6-second wave. From the given information, compute H /d and H ,/gT for the design condition: H, H Di Ibo} t 1.5 — = —=0.5 , — = ——— = 0.0043 (T= 6s) d 3 Z 2 gT 9.81 (6) Enter, Figure 7-90 (because the wall is smooth) with the computed value of Heyer A and determine the value of H_/H. from the curve for H./d = Oly (If the wave characteristics fall outside of the dashed line, the structure will be subjected to breaking or broken waves and the method for calculating breaking wave forces should be used.) Hy h tL — = 0.0043 2 gT i} oO ° fo) oN For (T = 6 s) oO H. Lt Therefore, h, = 0.70 CH; ) = 0.66 (1.5) = 1.00 m (3.3 ft) (Gin (3) 4) 7-170 The height of the free surface above the bottom y , when the wave crest and trough are at the structure, may be determined from equations (7-73) and (7-74) as follows: Fore (42) a (6) fa) 2 o Wf = and m ap licks yy =dt+ h, ( 9} )s ve =eouctn lt OOr+ CD iCl.5)) = 5.50) mise fe) yy = 3+ 1.00 - (1)(1.5) = 2.50 m (8.2 sfie)) (Ge = (6) 3) A similar analysis for the 10-second wave gives y 5.85 m (19.2 ft) c Zeon m (9.4 Le) (T = 6 s) Vt The wall would have to be about 6 meters (20 feet) high if it were not to be overtopped by a 1.5-meter-(5-foot-) high wave having a period of 10 seconds. The horizontal wave forces may be evaluated using Figure 7-91. Entering the figure with the computed value of H;/gT“ , the value of F/wd can be determined from either of two curves of constant H;/d - The upper family of curves (above F/wd* = 9) will give the dimensionless force when phe crest is at the wall: F,/wd ; the lower family of curves (below F/wd* = 0) will give the dimensionless force when the trough is at the wall: F,/wd? . For the example problem, with H,/gT* = 0.0043 and H;/d = 0.50 , ec t 2 2 Therefore, assuming a weight per unit volume of 10 kN/m? (64.0 1b/£t>) for sea water, I = 0.63 (10) (3)2 = 56.7 kN/m (3,890 lb/ft) (T = 6 s) F, = -0.31 (10) (3)? = -27.9 kN/m (-1,900 1b/ft) (T = 6 s) The values found for F and F do not include the force due to the hydrostatic pressure distribution below the still-water level. For instance, if there is also a water depth of 3 meters (10 feet) on the leeward side of the structure in this example and there is no wave action on the leeward side, then the hydrostatic force on the leeward side exactly balances the hydrostatic force on the side exposed to wave action. Thus, in this case, the values found for Fa and F, are actually the net forces acting on the structure. Tal If waves act on both sides of the structure, the maximum net horizontal force will occur when the clapotis crest acts against one side when the trough acts against the other. Hence the maximum horizontal force will be 18 5 with F and F determined for the appropriate wave conditions. Assuming for the example problem that the wave action is identical on both sides of the wall, then n DOH 2 Frog = 0:63 (10) (3) (-0.31)(10)(3) not 7 (0+63 + 0-31) (10) (3)2 = 84.6 kN/m (5,800 1b/ft) say Eee = 85 kN/m (T = 6 s) Some design problems require calculation of the total force including the hydrostatic contribution; e.g. seawalls. In these cases the total force is found by using equation (7-76). For this example, = 2 . F. rotal = 025 (10) (3)° + 56.7 = 101.7 kN/m (7,000 1b/£t) = Veh Pe £ Fe totay = 925 (10) (3)" + (-27.9) = 17.1 kN/m (1,200 1b/ft) The total force acts against the seaward side of the structure, and the resulting net force will be determined by consideration of static loads (e.g-, weight of structure), earth loads (e.g., soil pressure behind a seawall), and any other static or dynamic loading which may occur. The moment about point A at the bottom of the wall (Fig. 7-89) may be determined from Figure 7-92. The procedures are identical to those given for the dimensionless forces, and again the moment caused by the hydrostatic pressure distribution is not included in the design curves. The upper family of curves (above M/wd~ = 0) gives the dimensionless wave moment when the crest is at the wall, while the lower family of curves corresponds to the trough at the wall. Continuing the example problem, from Figure 7-92, with M M e t — = 0.44; —— = -0.123 (I= 60s) 3 3 wd wd Therefore, Te aaron > Rs SE Ce a EE 5 ro) m te (T = 6 s) = dy kN-m /_ lb-ft Ma On 123.510) j(3) 9 33k 2s 00 eee) TAM? M_ and M, , given above, are the total moments acting, when there is still water of depth 3 meters (10 feet) on the leeward side of the structure. The maximum moment at which there is wave action on the leeward side of the structure will be M -M, , with M and M evaluated for the appro- priate wave condition prevail on both sides of the structure. 2 re Souk kN-m Ib=ft re Laan = [0.44 (-0.123)] (10)(3) 152.0 = (34,200 ft ) (T = 6s) The combined moment due to both hydrostatic and wave loading is found using equation (7-77). For this example, 3 _ 10(3) " kN-m lb-ft 5 Ms total 7 et 118-8 = 163-8 S™ (36,800 PH ) (T = 6 s) M - 1063)" 5 233.2) = 11.8 B® (2,650 Leet t total 6 : ee ; ite Figures 7-93, 7-94, and 7-95 are used in a similar manner to determine forces and moments on a structure which has a reflection coefficient of yx = 0.9 e C3 C3 ETE a ee Sec ic Sem ec Pe MC aC, TO, Je, J TP J Se Se ere, ae SO Tek, Ie ht, a a J d. Wall of Low Height. It is often not economically feasible to design a structure to provide a non-overtopping condition by the design wave. Con- sequently, it is necessary to evaluate the force on a structure where the crest of the design clapotis is above the top of the wall, as shown in Figure 7-96. When the overtopping is not too severe, the majority of the incident wave will be reflected and the resulting pressure distribution is as shown in Figure 7-96, with the pressure on the wall being the same as in the non- overtopped case. This truncated distribution results in a force F° which is proportional to F , the total force that would act against the wall if it extended up to the crest of the clapotis (the force determined from Figures 7- 91 or 7-94). The relationship between F° and F is given by where te is a force reduction factor given by 28 (2 -2) when 0.50 <2 < 1.0 he” ripe) y y and (7-79) b a, IAG) when = = 1.0 He y where b and y _ are defined in Figure 7-96. The relationship between tp and b/y is shown in Figure 7-97. UNIS) pea of Clapotis Py Figure 7-96. Pressure distribution on wall of low height. Similarly, the reduced moment about point A is given by M = rM (7-80) where the moment reduction factor r, is given by 2 r= (2) ( =u : henL plOMS Ona ane y y y and (7-81) po YS) when = ilo) “lo The relationship between ln and b/y is also shown in Figure 7-97. Equations (7-78) through (7-81) are valid when either the wave crest or wave trough is at the structure, provided the correct value of y is used. kok kK kok k Ok Ok OK Ok OK & & & & EXAMPLE PROBLEM 32 * * * * & * KOK KOK KOK KK GIVEN: (a) Wall height b = 4.5 m (14.8 ft). (b) Incident wave height alg SS ihe) aa (AGL) ane E (c) Depth at structure toe d= 3m (9.8 ft). (d) Wave period T= 6s (minimum) or 10s (maximum). FIND: The reduced wave force and moment on the given vertical wall. 7-174 Gea Sraticie ireia iat DSHEERrbareaNEaeaN DOOUESBR0RkREE8 j beg a bopete CT bi hl Oly r Bo BSS0SRRRRe“4ooRBoon UES48 nee fe f HEOOCESEReZcloeeso } HBannoonL (1-r¢) and and Tm (i) SUesaaaet Figure 7-97. Force and moment reduction factors. YAS) SOLUTION: From Example Problem 31, vein So 5h0) im CUsoil Ie) (T = 6 s) ues oO) in (So IEe)) Compute b/y for each case b 4.5 Ys 305) (T = 6 s) ba Goes Vp Sit i 1380 > 1-0 Entering Figure 7-97 with the computed value of b/y , determine the values of rf and r, from the appropriate curve. For the wave with T=6s , Be = 0.818 Ye therefore,

i Se = 194 kN/m (13,287 1b/ft) ML = 485 kN-m/m (109,038 ft-lb/ft) (T = 10 s) For the breaker with a period of 6 seconds, the height of the breaker crest above the bottom is d + “b = oS) oF ee | 359) im (Bats) see) s 2 2 The value of b* as defined in Figure 7-102 is 1.9 m (6.2 ft) (i.e., the breaker height H minus the height obtained by subtracting the wall crest elevation from the breaker crest elevation). Calculate 0.679 (T = 6 s) From Figure 7-102, ll (j=) e (oe) 1S) 16 m therefore, from equation (7-91), R* =r R = 0.83 (309) = 256 kN/m (17,540 1b/ft) Cl = 365s) m From Figure 7-103, entering with b/H = 0.679 , Zaye ii beet OnDi/, b hence Bye 0 5258) 5) 0.80 m and from equation (7-93) M7 =R E (4d +a) - aj = 309 [0.83 (2.5 + 0.80) -0.80] m m m & YoU uM = 309 [1.94] = 600 kN-m/m (134,900 ft-1lb/ft) (T = 6 s) A similar analysis for the maximum breaker with a 10-second period gives r 0.79 a = 0.86 m (2.82 ft) Rn 153 kN/m (10,484 lb/ft) kN-m lb-ft 3487 (78,237 ——— ) M* S (T = 10 s) The hydrostatic part of the force and moment can be computed from the hydrostatic pressure distribution shown in Figure 7-99 by assuming the hydrostatic pressure to be zero at H,/2 above SWL and taking only that portion of the area under the pressure Wier cinneton which is below the crest of the wall. RK Ke KK KK UK) OK) KA EK OK oR KK KR OK Ke RK KR ek KR EK OK KOR XP Ree 4. Broken Waves. Shore structures may be located so that even under severe storm and tide conditions waves will break before striking the structure. No studies have yet been made to relate forces of broken waves to various wave parameters, and it is necessary to make simplifying assumptions about the waves to estimate design forces. If more accurate force estimates are required, model tests are necessary. It is assumed that, immediately after breaking, the water mass in a wave moves forward with the velocity of propagation attained before breaking; that is, upon breaking, the water particle motion changes from oscillatory to translatory motion. This turbulent mass of water then moves up to and over the stillwater line dividing the area shoreward of the breakers into two parts, seaward and landward of the stillwater line. For a conservative estimate of wave force, it is assumed that neither wave height nor wave velocity decreases from the breaking point to the stillwater line and that after passing the stillwater line the wave will run up roughly twice its height at breaking, with both velocity and height decreasing to zero at this point. Wave runup can be estimated more accurately from the procedure outlined in Section 1, Wave Runup. Model tests have shown that, for waves breaking at a shore, approximately 78 percent of the breaking wave height Hy is above the stillwater level (Wiegel, 1964). ae Wall Seaward of Stillwater Line. Walls located seaward of the stillwater line are subjected to wave pressures that are partly dynamic and partly hydrostatic (see Figure 7-104). Using the approximate relationship C = Ved for the velocity of wave propagation, C where g is the acceleration of gravity and d, is the 7-192 breaking wave depth, wave pressures on a wall may be approximated in the following manner: The dynamic part of the pressure will be Pn oe (7-94) Figure 7-104. Wave pressures from broken waves: wall seaward of still-water line. where w is the unit weight of water. If the dynamic pressure is uniformly distributed from the still-water level to a height h, above SWL, where h, is given as h, = 0.78H, (7-95) then the dynamic component of the wave force is given as (7-96) and the overturning moment caused by the dynamic force as h c Me tal, + = (7-97) where d is the depth at the structure. & The hydrostatic component will vary from zero at a height h, above SWL to a maximum p, at the wall base. This maximum will be given as, Pa ewe (d) the) (7-98) 7-193 The hydrostatic force component will therefore be 2 W (4, ar ha) nS ar ee C/—95) and the overturning moment will be, 3 (d2eone)) ow (da. ahs) s G s e a a al eam (7-100) The total force on the wall is the sum of the dynamic and hydrostatic components; therefore, ip We ae ike (7-101) and My eae (7-102) b. Wall Shoreward of Still-water Line. For walls landward of the still- water line as shown in Figure 7-105, the velocity v~ of the water mass at the structure at any location between the SWL and the point of maximum wave runup may be approximated by, x x a ee Ape es a vi =C 1 %X = gd), iL X (7-103) and the wave height h~ above the ground surface by Hil h’ =h i —— (7-104) c x 2 where SS distance from the still-water line to the structure x5 = distance from the still-water line to the limit of wave uprush; i.e, x5) = 2H,cot 8 = 2H,/m (note: the actual wave runup as found from the method outlined in Section II,1 could be substituted for the value 2Hp) B = the angle of beach slope m = tan gp An analysis similar to that for structures located seaward of the still-water line gives for the dynamic pressure yy)? . wd), zt Prine 2255 ji ale laa 7-194 h b>» Pm—- Ps Pmt+P, INSERT Assumed locus of wave crest See insert for wave pressure Shoreline Figure 7-105. Wave pressures from broken waves: wall landward of still-water line. The dynamic pressure is assumed to act uniformly over the broken wave height at the structure toe h~ , hence the dynamic component of force is given by wd,h x : Se aes eee (7-106) m m 2 x 2 and the overturning moment by he wd phe x) 4 Me = RD = eh Is an (7-107) 2 The hydrostatic force component is given by ine wh Ph ; R, = 2 SS non i oO = (7-108) and the moment resulting from the hydrostatic force by 7-195 MoeR a =—% [1 -= (7-109) The total forces and moments are the sums of the dynamic and hydrostatic components; therefore, as before, R, = Rn ate R; (7-110) and tase G1) My The pressures, forces, and moments computed by the above procedure will be approximations, since the assumed wave behavior is simplified. Where structures are located landward of the still-water line the preceding equations will not be exact, since the runup criterion was assumed to be a fixed fraction of the breaker height. However, the assumptions should result in a high estimate of the forces and moments. kk kK kk kK Ok k Ok Ok Ok & & & &K EXAMPLE PROBLEM 36 * * * * & & * * KOK KK RK KK GIVEN: The elevation at the toe of a vertical wall is 0.6 m (2 ft) above the mean lower low water (MLLW) datum. Mean higher high water (MHHW) is 1.3 m (4.3 ft) above MLLW, and the beach slope is 1:20. Breaker height is Hp = 3.0 m (9.8 ft), and wave period is T=6s. FIND: (a) The total force and moment if the SWL is at MHHW; i.e., if the wall is seaward of still-water line. (b) The total force and moment if the SWL is at MLLW; i.e., if the wall is landward of still-water line. SOLUTION: (a) The breaking depth d, can be found from Figure 7-2. Calculate, H b 3.0 ——}_ = —————_ = 050085 z 2 eT 9.8 (6) and the beach slope, 2 sel ie m = tan g = 0 0.05 Enter Figure 7-2 with H, /gT? = 0.0085 and, using the curve for m= 0.05 , read d, i Wo IO) "b 7-196 Therefore, d,s 1.10 Hy 1.10 (3.0) S250me ClLOss Le) From equation (7-95) bees 0.78 Hy 0.78" (30)! =e2-5) m Ce? Et) The dynamic force component from equation (7-96) is R= MRO Ee 10,047 (3.3023) = 38.1 kN/m (2,610 1b/ft) and the moment from equation (7-97) is M=R, (ad, +5-]) = 38-1 (0.7 5 29)) = 70,9 SE2 5.009 He 2 2 m fit: ) where d, = 0./ m_ is the depth at the toe of the wall when the SWL is at MHHW. The hydrostatic force and moment are given by equations (7-99) and (7-100): w(d,+h,) 2 R = Se = 40,047 (O.7 + 23)” eS boy kN/m (3,100 lb/ft) (d_+h,) s e Wot ae Boe’ kN-m ft-lb M, = R, a ar onns Ft AD 22 <1 oe ees BO sone a (10,200 it ) The total force and moment are therefore, Reese hy tb Beececcs) wi 45.2 = 83.3 kN/m (5,710 1b/ft) = = Et kN-m ft=I'b MSM te M70 .a5%, 45.2 = 115.7 = 626,000 — ) (b) When the SWL is at MLLW, the structure is landward of the still-water line. The distance from the still-water line to the structure x) is given by the difference in elevation between the SWL and the structure toe divided by the beach slope; hence x = 0.6 IVP 0505 = 12 m (39.4 ft) The limit of wave runup is approximately The dynamic component of force from equation (7-106) is, wdph x 3 3 oe : c ae = _ 10,047 Chee oe 5 = 97.8 KN/m 2 (1,905 lb/ft) and the moment from equation (7-107) is 2 4 _ ihe (| . Bi \ _slosourt03ee) (ous)? /s)_wab Nees gue ekNen Mn Z mG 4 120 oO aa ft-lb (6,500 Fe ) The hydrostatic force and moment from equations (7-108) and (7-109) are, wh? x 2 2 2D aes s By S007 C223) m re ee R, = iL X = 5) ( = = 2155 KN/m (1,475 Ib/£e) and 3 3) wh x 3 Lene Hee \ & AO 047283) D2 q kN=m oes CRs = 6 1 - 350 a Gio ELE Total force and moment are R. = RB, + R = 27.8 + 21.5 = 49.3 kN/m (3,400 1b/ft) kN-m fE=Tb Mle as We 28.8 + 14.9 43.7 = (9,800 —=—) My Rik Kk KR RRR KK KR UROKPR IK ROK ROK OK KX KK KR OK RGR Ke) Xe KEK Kak eee 5. Effect of Angle of Wave Approach. When breaking or broken waves strike the vertical face of a structure such as a groin, bulkhead, seawall, or breakwater at an oblique angle, the dynamic component of the pressure or force will be less than for breaking or broken waves that strike perpendicular to the structure face. The force may be reduced by the equation, Re LR eileen (7-112) where a is the angle between the axis of the structure and the direction of wave advance, R°~ is the reduced dynamic component of force, and R _ is the dynamic force that would occur if the wave hit perpendicular to the struc- ture. The development of equation (7-112) is given in Figure 7-106. Force reduction by equation (7-112) should be applied only to the dynamic wave-force component of breaking or broken waves and should not be applied to the 7-198 Sin @ oy Vertical Wall SS: = —S ™~™~ SS SS — Wave Ray —— Unit Length along Incident Wave Crest R = Dynamic Force Per Unit Length of Wall if Wall were Perpendicular to Direction of Wave Advance Rp= Component of R Normal to Actual Wall. Rn=R sind W = Length Along Wall Affected by a Unit Length of Wave Crest. We Wie os R = Dynamic Force Per Unit Length of Wall R R sind R= ae = ree = R sin? a / sing Ry =tRESINIS: Figure 7-106. Effect of angle of wave approach: plan view. 7-199 hydrostatte component. The reduction ts not applicable to rubble struc- tures. The maximum force does not act along the entire length of a wall simultaneously; consequently, the average force per unit length of wall will be lower. 6. Effect of a Nonvertical Wall. Formulas previously presented for breaking and broken wave forces may be used for structures with nearly vertical faces. If the face is sloped backward as in Figure 7-107a, the horizontal component of the dynamic force due to waves breaking either on or seaward of the wall should be reduced to Re R’sin76 (7-113) where 6 is defined in Figure 7-107. The vertical component of the dynamic wave force may be neglected in stability computations. For design calculations, forces on stepped structures as in Figure 7-10/7b may be computed as if the face were vertical, since the dynamic pressure is about the same as computed for vertical walls. Curved nonreentrant face structures (Fig. 7-107c) and reentrant curved face walls (Fig. 7-107d) may also be considered as vertical. a (b) Stepped Wall (c) Nonreentrant Face Wall (d) Reentrant Face Wall Figure 7-107. Wall shapes. 7-200 kK kK kk Ok kk k Ok kk &k kK EXAMPLE PROBLEM 37. * * * * ¥ ® ® KOK KK KKK GIVEN: A structure in water, de = 253) mi @/.5) £t))) on) a) 1320) nearshore slope, is subjected to breaking waves, Hp, = 2.6 m (8.4 ft) and period T = 6s . The angle of wave approach is, a = 80°, and the wall has a shoreward sloping face of 10 (vertical) on 1 (horizontal). FIND: (a) The reduced total horizontal wave force. (b) The reduced total overturning moment about the toe (Note: neglect the vertical component of the hydrostatic force). SOLUTION: From the methods used in Example Problems 34 and 36 for the given wave conditions, compute Rn = 250 kN/m (17,100 1b/ft) = kN-m ft-lb Mh = 575 = (129,300 FE ) R. = 65 kN/m (4,450 1b/ft) and - kN-m ft-lb M. = 78 = 47,500 ft ) Applying the reduction of equation (7-112) for the angle of wave approach, with Rs =R R* = RT eine a = 250 (sin 80°)? Ree= 250 (0.985)* = 243 kN/m (16,700 1b/ft) Similarly, M* = M tae a = 575 (sin g0°)* M’ = 575 (0.985)7 = 558 ‘won (125,500 te) Applying the reduction for a nonvertical wall, the angle the face of the wall makes with the horizontal is 6 = arctan (10) * 84° Applying equation (7-113), Re R’sin’6 = 243) @simi 4°)" 7-201 R" = 243 (0.995)* = 241 kN/m (16,500 1b/ft) Similarly, for the moment M' = M Bimee = 558 (sin gue)? 558 (0.995)- = 553 ot (124, 200 aoe ) M" The total force and overturning moment are given by the sums of the reduced dynamic components and the unreduced hydrostatic components. Therefore, R, = 241 + 65 = 306 kN/m (21,000 lb/ft) kN-m FES lb t 553 + 78 631 = (141,900 it ) ROR ROK ROKR KR RR KOR KR OR ROR, KR RK OK ROKR KK OK RK KCK KR OR AA M 7. Stability of Rubble Structures. a. General. A rubble structure is composed of several layers of random- shaped and random-placed stones, protected with a cover layer of selected armor units of either quarrystone or specially shaped concrete units. Armor units in the cover layer may be placed in an orderly manner to obtain good wedging or interlocking action between individual units, or they may be placed at random. Present technology does not provide guidance to determine the forces required to displace individual armor units from the cover layer. Armor units may be displaced either over a large area of the cover layer, sliding down the slope en masse, or individual armor units may be lifted and rolled either up or down the slope. Empirical methods have been developed that, if used with care, will give a satisfactory determination of the stability characteristics of these structures when under attack by storm waves. A series of basic decisions must be made in designing a rubble struc- ture. Those decisions are discussed in succeeding sections. b. Design Factors. A primary factor influencing wave conditions at a structure site is the bathymetry in the general vicinity of the structure. Depths will partly determine whether a structure is subjected to breaking, nonbreaking, or broken waves for a particular design wave condition (see Section I, WAVE CHARACTERISTICS). Variation in water depth along the structure axis must also be considered as it affects wave conditions, being more critical where breaking waves occur than where the depth may allow only nonbreaking waves or waves that overtop the structure. When waves impinge on rubble structures, they do the following: (a) Break completely, projecting a jet of water roughly perpendicular to the slope. 7=202 (b) Partially break with a poorly defined jet. (c) Establish an oscillatory motion of the water particles up or down the structure slope, similar to the motion of a clapotis at a vertical wall. The design wave height for a flexible rubble structure should usually be the average of the highest 10 percent of all waves, H as discussed in Section I1,2. Damage from waves higher than the design wave height is progressive, but the displacement of several individual armor units will not necessarily result in the complete loss of protection. A logic diagram for the evaluation of the marine environment presented in Figure 7-6 summarizes the factors involved in selecting the design water depth and wave conditions to be used in the analysis of a rubble structure. The most severe wave condition for design of any part of a rubble-mound structure is usually the combination of predicted water depth and extreme incident wave height and period that produces waves which would break directly on the part of interest. If a structure with two opposing slopes, such as a breakwater or jetty, will not be overtopped, a different design wave condition may be required for each side. The wave action directly striking one side of a structure, such as the harbor side of a breakwater, may be much less severe than that striking the other side. If the structure is porous enough to allow waves to pass through it, more armor units may be dislodged from the sheltered side’s armor layer by waves traveling through the structure than by waves striking the layer directly. In such a case, the design wave for the sheltered side might be the same as for the exposed side, but no dependable analytical method is known for choosing such a design wave condition or for calculating a stable armor weight for it. Leeside armor sizes have been investigated in model tests by Markle (1982). If a breakwater is designed to be overtopped, or if the designer is not sure that it will not be overtopped the crest and perhaps, the leeward side must be designed for breaking wave impact. Lording and Scott (1971) tested an Overtopped rubble-mound structure that was subjected to breaking waves in water levels up to the crest elevation. Maximum damage to the leeside armor units occurred with the still-water level slightly below the crest and with waves breaking as close as two breaker heights from the toe of the structure. This would imply that waves were breaking over the structure and directly on the lee slope rather than on the seaward slope. 7-203 The crest of a structure designed to be submerged, or that might be submerged by hurricane storm surge, will undergo the heaviest wave action when the crest is exposed in the trough of a wave. The highest wave which would expose the crest can be estimated by using Figure 7-69, with the range of depths at the structure d _, the range of wave heights H , and period T , n and the structure height h . Values of a » where ne is the crest elevation above the still-water level, can be found by entering Figure 7-69 with a and “ 5 gT gT which The largest breaking and nonbreaking wave heights for dhe he ne (7-114) can then be used to estimate which wave height requires the heaviest armor. The final design breaking wave height can be determined by entering Figure n 7-69 with values of aa » finding values of ae for breaking conditions, and gT selecting the highest breaking wave which satisfied the equation d=h+H-n, (7-115) A structure that is exposed to a variety of water depths, especially a structure perpendicular to the shore, such as a groin, should have wave conditions investigated for each range of water depths to determine the highest breaking wave to which any part of the structure will be exposed. The outer end of a groin might be exposed only to wave forces on its sides under normal depths, but it might be overtopped and eventually submerged as a storm surge approaches. The shoreward end might normally be exposed to lower breakers, or perhaps only to broken waves. In the case of a high rubble-mound groin (i.e., a varying crest elevation and a sloping beach), the maximum breaking wave height may occur inshore of the seaward end of the groin. c. Hydraulics of Cover Layer Design. Until about 1930, design of rubble structures was based only on experience and general knowledge of site conditions. Empirical formulas that subsequently developed are generally expressed in terms of the stone weight required to withstand design wave conditions. These formulas have been partially substantiated in model studies. They are guides and must be used with experience and engineering judgment. Physical modeling is often a cost-effective measure to determine the final cross-section design for most costly rubble-mound structures. Following work by Iribarren (1938) and Iribarren and Nogales Y Olano (1950), comprehensive investigations were made by Hudson (1953, 1959, 196la, and 1961b) at the U.S. Army Engineer Waterways Experiment Station (WES), and a formula was developed to determine the stability of armor units on rubble structures. The stability formula, based on the results of extensive small- scale model testing and some preliminary verification by large-scale model testing, is 7-204 10 oS SS (7=1'1'6)) 3 K Syee= cot 6 “ ( ) where W = weight in newtons or pounds of an individual armor unit in the primary cover layer. (When the cover layer is two quarrystones in thickness, the stones comprising the primary cover layer can range from about 0.75 W to 1.25 W, with about 50 percent of the individual stones weighing more than W . The gradation should be uniform across the face of the structure, with no pockets of smaller stone. The maximum weight of individual stones depends on the size or shape of the unit. The unit should not be of such a size as to extend an appreciable distance above the average level of the slope) w = unit weight (saturated surface dry) of armor unit in N/m? or lb/ft? Note: Substitution of ae » the mass density of the armor material in kg/m or slugs/ft>, will yield W in units of mass (kilograms or slugs) H = design wave height at the structure site in meters or feet (see Sec. IIE a sis) S = specific gravity of armor unit, relative to the water at the structure » (S =w /w ) r TO By w= unit weight of water: fresh water. = 9,800 N/m? (62.4 1b/£t>) seawater = 10,047 N/m (64.0 lb/ft?) Note: Substitution of lig > 2 ra » where °) is the mass density of water at the Ww structure for (Sr - 1)3 » yields the same result 8 = angle of structure slope measured from horizontal in degrees K, = stability coefficient that varies primarily with the shape of the armor units, roughness of the armor unit surface, sharpness of edges, and degree of interlocking obtained in placement (see Table 7-8). Equation 7-116 is intended for conditions when the crest of the structure is high enough to prevent major overtopping. Also the slope of the cover layer will be partly determined on the basis of stone sizes economically avail- able. Cover layer slopes steeper than 1 on 1.5 are not recommended by the Corps of Engineers. Equation 7-116 determines the weight of an armor unit of nearly uniform size. For a graded riprap armor stone, Hudson and Jackson (1962) have modified the equation to: 7-205 Table 7-8. Suggested Kp Values for use in determining armor unit weight!. No-Damage Criteria and Minor Overtopping 3 Armor Units n Placement Slope Breaking Nonbreaking Breaking Wave Wave Quarrystone Smooth rounded 2 Random Smooth rounded >3 Random Rough angular 1 Random Rough angular 2 Random Rough angular >3 Random Rough angular j 2 Special 3 Parallelepiped 2 Special Tetrapod and 2 Random Quadripod 8.3 9.0 1.5 Tribar 2 Random 9.0 10.0 7.8 8.5 2.0 6.0 6.5 3.0 Dolos 2 Random 2.09 3.0 Modified cube 2 Random 5 Hexapod 2 Random 5 Toskane 2 Random 2 Tribar 1 Uniform Quarrystone (Kpp) Graded angular = Random 1 CAUTION: Those Kp values shown in italics are unsupported by test results and are only provided for preliminary design purposes. Applicable to slopes ranging from 1 on 1.5 to 1 on 5. n is the number of units comprising the thickness of the armor layer. The use of single layer of quarrystone armor units is not recommended for structures subject to breaking waves, and only under special conditions for structures subject to nonbreaking waves. When it is used, the stone should be carefully placed. Until more information is available on the variation of Kp value with slope, the use of Kp should be limited to slopes ranging from 1 on 1.5 to 1 on 3. Some armor units tested on a structure head indicate a Kp-slope dependence. Special placement with long axis of stone placed perpendicular to structure face. Parallelepiped-shaped stone: long slab-like stone with the long dimension about 3 times the shortest dimension (Markle and Davidson, 1979). Refers to no-damage criteria (<5 percent displacement, rocking, etc.); if no rocking (<2 percent) is desired, reduce Kp 50 percent (2Zwamborn and Van Niekerk, 1982). Stability of dolosse on slopes steeper than 1 on 2 should be substantiated by site-specific model tests. 7-206 yee es nt Eo ne hl (7-117) 50 3 K (S = 1) cot 06 RR 1g The symbols are the same as defined for equation (7-116). Ws is the weight of the 50 percent size in the gradation. The maximum weight oe graded rock is 4.0 Woo) 3 the minimum is 0.125 (Wso) « Additional information on riprap gradation for exposure to wave forces is given by Ahrens (1981b). Kpp is a stability coefficient for angular, graded riprap, similar to K, . Values OF K are shown in Table 7-8. These values allow for 5 percent damage (Hudson and Jackson, 1962). Use of graded riprap cover layers is generally more applicable to revet- ments than to breakwaters or jetties. A limitation for the use of graded riprap is that the design wave height should be less than about 1.5 m (5 ft). For waves higher than 1.5 m (5 ft), it is usually more economical to use uniform-size armor units as specified by equation (7-116). Values of Kp and Kpp are obtained from laboratory tests by first determining values of the stability number N. where vi I/S) Je w 1/3) r r or aa) w 5ol/3 ( N (7-118) mets Ww a) The stability number is plotted as a function of cot 6 on log-log paper, and a straight line is fitted as a bottom envelope to the data such that N, = (K, cot 9)! or yee K cot @ RR (7-119) Powers of cot 8 other than 1/3 often give a better fit to the data. N can be used for armor design by replacing Kp, cot 8 in equation (7-116) or Kpp cot 8 in equation (7-117) with N, , where N, is a function of some power of cot 6. d. Selection of Stability Coefficient. The dimensionless stability coefficient Kp in equation (7-116) accounts for all variables other than structure slope, wave height, and the specific gravity of water at the site (i.e., fresh or salt water). These variables include: (1) Shape of armor units (2) Number of units comprising the thickness of armor layer (3) Manner of placing armor units (4) Surface roughness and sharpness of edges of armor units (degree of interlocking of armor units) (5) Type of wave attacking structure (breaking or nonbreaking) 7-207 (6) Part of structure (trunk or head) (7) Angle of incidence of wave attack (8) Model scale (Reynolds number) (9) Distance below still-water level that the armor units extend down the face slope (10) Size and porosity of underlayer material (11) Core height relative to still-water level (12) Crown type (concrete cap or armor units placed over the crown and extending down the back slope) (13) Crown elevation above still-water level relative to wave height (14) Crest width Hudson (1959, 196la, and 1961b), and Hudson and Jackson (1959), Jackson (1968a), Carver and Davidson (1977), Markle and Davidson (1979), Office, Chief of Engineers (1978), and Carver (1980) have conducted numerous laboratory tests with a view to establishing values of K for various conditions of some of the variables. They have found that, for a given geometry of rubble structure, the most important variables listed above with respect to the magnitude of K are those from (1) through (8). The data of Hudson and Jackson comprise the basis for selecting K, , although a number of limita- tions in the application of laboratory results to prototype conditions must be recognized. These limitations are described in the following paragraphs. (1) Laboratory waves were monochromatic and did not reproduce the variable conditions of nature. No simple method of comparing monochromatic and irregular waves is presently available. Laboratory studies by Oeullet (1972) and Rogan (1969) have shown that action of irregular waves on model rubble structures can be modeled by monochromatic waves if the monochromatic wave height corresponds to the significant wave height of the spectrum of the irregular wave train. Other laboratory studies (i.e., Carstens, Traetteberg, and Térum (1966); Brorsen, Burcharth, and Larsen (1974); Feuillet and Sabaton (1980); and Tanimoto, Yagyu, and Goda (1982)) have shown, though, that the damage patterns on model rubble-mound structures with irregular wave action are comparable to model tests with monochromatic waves when the design wave height of the irregular wave train is higher than the significant wave height. As an extreme, the laboratory work of Feuillet and Sabaton (1980) and that of Tanimoto, Yagyu, and Goda (1982) suggest a design wave of H, when comparing monochromatic wave model tests to irregular wave model tests. The validity of this comparison between monochromatic wave testing and irregular wave testing depends on the wave amplitude and phase spectra of the irregular wave train which, in turn, govern the "groupiness" of the wave train; i.e., the tendency of higher waves to occur together. Groupiness in wave trains has been shown by Carstens, Traetteberg, and 7-208 Térum (1966), Johnson, Mansard, and Ploeg (1978), and Burcharth (1979), to account for higher damage in rubble-mound or armor block’ structures. Burcharth (1979) found that grouped wave trains with maximum wave heights equivalent to monochromatic wave heights caused greater damage on dolosse- armored slopes than did monochromatic wave trains. Johnson, Mansard, and Ploeg (1978) found that grouped wave trains of energy density equivalent to that of monochromatic wave trains created greater damage on rubble-mound breakwaters. Goda (1970b) and Andrew and Borgman (1981) have shown by simulation techniques that, for random-phased wave components in a wave spectrum, groupiness is dependent on the width of the spectral peak (the narrower the spectral width, the larger the groupiness in the wave train). On a different tack, Johnson, Mansard, and Ploeg (1978) have shown that the same energy spectrum shape can produce considerably different damage patterns to a rubble-mound breakwater by controlling the phasing of the wave components in the energy spectrum. This approach to generating irregular waves for model testing is not presently attempted in most laboratories. Typically, laboratory model tests assume random phasing of wave spectral components based on the assumption that waves in nature have random phasing. Térum, Mathiesen, and Escutia (1979), Thompson (1981), Andrew and Borgman (1981), and Wilson and Baird (1972) have suggested that nonrandom phasing of waves appears to exist in nature, particularly in shallow water. (2) Preliminary analysis of large-scale tests by Hudson (1975) has indicated that scale effects are relatively unimportant, and can be made negligible by the proper poececton of linear scale to ensure that the Reynolds number is above 3 x 10 in the tests. The Reynolds number is defined in this case as [72 ky 1/3 p = 68H) W_ v W a0) Where v is the kinematic viscosity of the water at the site and kA is the layer coefficient (see Sec. III,/7,g2(2)). (3) The degree of interlocking obtained in the special placement of armor units in the laboratory is unlikely to be duplicated in the prototype. Above the water surface in prototype construction it is possible to place armor units with a high degree of interlocking. Below the water surface the same quality of interlocking can rarely be attained. It is therefore advisable to use data obtained from random placement in the laboratory as a basis for K_ values. (4) Numerous tests have been performed for nonbreaking waves, but only limited test results are available for plunging waves. Values for these conditions were estimated based on breaking wave tests of similar armor units. The ratio between the breaking and nonbreaking wave Kise ator, tetrapods and quadripods on structure trunks, for example, was used to estimate the breaking wave K ’s_ for tribars, modified cubes, and hexapods 7-269 used on trunks. Similar comparisons of test results were used to estimate Kp values for armor units on structure heads. (5) Under similar wave conditions, the head of a rubble structure normally sustains more extensive and frequent damage than the trunk of the structure. Under all wave conditions, a segment of the slope of the rounded head of the structure is usually subject to direct wave attack regardless of wave direction. A wave trough on the lee side coincident with maximum runup on the windward side will create a high static head for flow through the structure. (6) Sufficient information is not available to provide firm guidance on the effect of angle of wave approach on stability of armor units. Quarry- stone armor units are expected to show greater stability when subject to wave attack at angles other than normal incidence. However, an analysis of limited test results by Whillock (1977) indicates that dolos units on a l-on-2 slope become less stable as the angle of wave attack increases from normal incidence (0°) to approximately 45°. Stability increases rapidly again as the angle of wave attack increases beyond 45°, Whillock suggests that structures covered with dolosse should be designed only for the no-damage wave height at normal incidence if the structure is subject to angular wave attack. The stability of any rubble structures subjected to angular wave attack should be confirmed by hydraulic model tests. Based on available data and the discussion above, Table 7-8 presents recommended values for Kp. Because of the limitations discussed, values in the table provide little or no safety factor. The values may allow some rocking of concrete armor units, presenting the risk of breakage. The K,’s for dolosse may be reduced by 50 percent to protect against breakage, as noted in the footnote to Table 7-8. The experience of the field engineer may be utilized to adjust the Kp value indicated in Table 7-8, but deviation to less conservative values is not recommended without supporting model test results. A two-unit armor layer is recommended. If a one-unit armor layer is considered, the Kp values for a single layer should be obtained from Table 7-8. The indicated Kp values are less for a single-stone layer than for a two-stone layer and will require heavier armor stone to ensure stability. More care must be taken in the placement of a single armor layer to ensure that armor units provide an adequate cover for the underlayer and that there is a high degree of interlock with adjacent armor units. These coefficients were derived from large- and small-scale tests that used many various shapes and sizes of both natural and artificial armor units. Values are reasonably definitive and are recommended for use in design of rubble-mound structures, supplemented by physical model test results when possible. The values given in Table 7-8 are indicated as no-damage criteria, but actually consider up to 5 percent damage. Higher values of percent damage to a rubble breakwater have been determined as a function of wave height for several of the armor unit shapes by Jackson (1968b). These values, together with statistical data concerning the frequency of occurrence of waves of different heights, can be used to determine the annual cost of maintenance as a function of the acceptable percent damage without endangering the functional characteristics of the structure. Knowledge of maintenance costs can be used 7-210 to choose a design wave height yielding the optimum combination of first and maintenance costs. A structure designed to resist waves of a moderate storm, but which may suffer damage without complete destruction during a severe storm may have a lower annual cost than one designed to be completely stable for larger waves. Table 7-9 shows the results of damage tests where H/Hp_9 is a function of the percent damage D for various armor units. H is the wave height corresponding to damage D . Hp_g is the design wave height corresponding to O- to 5-percent damage, generally referred to as no-damage condition. Table 7-9. Pie, as a function of cover-layer damage and type of armor unit.! Damage (D) in Percent Quarrystone (smooth) Quarrystone (rough) Tetrapods & Quadripods 1 Breakwater trunk, n = 2, random placed armor units, nonbreaking waves, and minor overtopping conditions. 2 : A Values in ttaltcs are interpolated or extrapolated. 3 CAUTION: Tests did not include possible effects of unit breakage. Waves exceeding the design wave peer eee by more than 10 percent may result in considerably more damage than the values abulated. The percent damage is based on the volume of armor units displaced from the breakwater zone of active armor unit removal for a specific wave height. This zone, as defined by Jackson (1968a), extends from the middle of the breakwater crest down the seaward face to a depth equivalent to one zero- damage wave height Hp_o below the still-water level. Once damage occurred, testing was continued for the specified wave condition until slope equilibrium was established or armor unit displacement ceased. Various recent laboratory tests on dolosse have indicated that once design wave conditions (i.e., zero- damage) are exceeded, damage progresses at a much greater rate than indicated 7201 from tests of other concrete armor units. Note from the table that waves producing greater than 10 percent damage to a dolos structure will produce lesser damage levels to structures covered with other armor units. Concrete units in general will fail more rapidly and catastrophically than quarrystone armor. Caution must be exercised in using the values in Table 7-9 for breaking wave conditions, structure heads, or structures other than breakwaters or jetties. The damage zone is more concentrated around the still-water level on the face of a revetment than on a breakwater (Ahrens, 1975), producing deeper damage to the armor layer for a given volume of armor removed. As a result, damage levels greater than 30 percent signify complete failure of a revetment’s armor. Model studies to determine behavior are recommended whenever possible. The following example illustrates the ways in which Table 7-9 may be used. kok k kk kk Ok Ok OK & OK & & & EXAMPLE PROBLEM 38 * * * * & KK KK RK RK KKK GIVEN: A two-layer quarrystone breakwater designed for nonbreaking waves and minor overtopping from a no-damage design wave Hp = 2-5 m (8.2 ft) and Kp = 4.0. FIND: (a) The wave heights which would cause 5 to 10 percent, 10 to 15 percent, 15 to 20 percent, and 20 to 30 percent damage. The return periods of these different levels of damage and consequent repair costs could also be estimated, given appropriate long-term wave statistics for the site. (b) The design wave height that should be used for calculating armor weight if the breakwater is a temporary or minor structure and 5 to 10 percent damage can be tolerated from 2.5-m waves striking it. (c) The damage to be expected if stone weighing 75 percent of the zero- damage weight is available at substantially less cost or must be used in an emergency for an expedient structure. SOLUTION: (a) From Table 7-9, for rough quarrystone: 7-212 Therefore, for instance, Hp _ ent (os) (l6@&)) S Bor in (Cio) aA) 6 (b) From Table 7-9, for D = 5 to 10 percent H eae O8 Hp_o peers BDO TeleOB Since the H causing 5 to 10 percent damage is 2.5m , = 253 Mm i755) Lt) 4D-0 = 1.08 (c) To determine the damage level, a ratio of wave heights must be calculated. The higher wave height "H" will be the Hpg for the zero- damage weight Wp» - The lower wave height "Hp _j' will be the Hp_g for the available stone weight Way ° Rearranging equation (7-116), W Kp cot 6 V3 H = (S,, -1) Wy from which . 1/3 "oN" D = (0) Hp_o Wav Since Wygy = 0.75 Wp 9 1/3 Ms Wp0 / U5 UU l 1/3 6 (S=35) = 1.10 This corresponds to damage of about 5 to 10 percent if the available stone is used. fo G9 £3 eo to C0 3 £3 £3 tees toe co Cot Cee bey ts oy to bt CY t3 03-03) Co ct te Cet 3 e. Importance of Unit Weight of Armor Units. The basic equation used for design of armor units for rubble structures indicates that the unit weight Wp of quarrystone or concrete is important. Designers should carefully evaluate the advantages of increasing unit weight of concrete armor units to affect savings in the structure cost. Brandtzaeg (1966) cautioned that variations in unit weight should be limited within a range of, say, 18.9 7-213 kilonewtons per cubic meter (120 pounds per cubic foot) to 28.3 kilonewtons per cubic meter (180 pounds per cubic foot). Unit weight of quarrystone available from a particular quarry will likely vary over a narrow range of values. The unit weight of concrete containing normal aggregates is usually between 22.0 kilonewtons per cubic meter (140 pounds per cubic foot) and 24.3 kilonewtons per cubic meter (155 pounds per cubic foot). It can be made higher or lower through use of special heavy or lightweight aggregates that are usually available but are more costly than normal aggregates. The unit weight obtainable from a given set of materials and mixture proportions can be computed from Method CRD-3 of the Handbook for Concrete and Cement published by the U.S. Army Engineer Waterways Experiment Station (1949). The effect of varying the unit weight of concrete is illustrated by the following example problem. kok k kK kK kk kK Ok Ok & OK & & & EXAMPLE PROBLEM 39 * * * * * * KK KOK OK KOK K GIVEN: A 33.5-metric ton (36.8-short ton) concrete armor unit is required for the protection of a rubble-mound structure against a given wave height in salt water (w,, = 10.0 kilonewtons per cubic meter (64 pounds per cubic foot)). This weight was determined using a unit weight of concrete wy, = 22.8 kilonewtons per cubic meter (145 pounds per cubic foot). FIND: Determine the required weight of armor unit for concrete with w = 22.0 kilonewtons per cubic meter (140 pounds per cubic foot) and wr = 26.7 kilonewtons per cubic meter (170 pounds per cubic foot). SOLUTION: Based on equation (7-116), the ratio between the unknown and known armor weight is w 3 Ww — = il oe NO 22.8 3 22.8/(T575 = 1) Thus, for W. = 22.0 kilonewtons per cubic meter 22 <0 3 22.0/(22:2 Fy ! We) 10.9 = B65) oc T0s0e: 39.0 mt (42.9 tons) For bs 26./ Nyame 26.1 [(38-3 - 1)? 5.7 10.9 = 33.5 x 70.9 17s. 5) mee 192) tons) fe Concrete Armor Units. Many different concrete shapes have been developed as armor units for rubble structures. The major advantage of 7-214 concrete armor units is that they usually have a higher stability coefficient value and thus permit the use of steeper structure side slopes or a lighter weight of armor unit. This advantage has particular value when quarrystone of the required size is not available. Table 7-10 lists the concrete armor units that have been cited in literature and shows where and when the unit was developed. One of the earlier nonblock concrete armor units was the tetrapod, developed and patented in 1950 by Neyrpic, Inc., of France. The tetrapod is an unreinforced concrete shape with four truncated conical legs projecting radially from a center point (see Fig. 7-108). Figure 7-109 provides volume, weight, dimensions, number of units per 1000 square feet, and thickness of layers of the tetrapod unit. The quadrtpod (Fig. 7-108) was developed and tested by the United States in 1959; details are shown in Figure 7-110. In 1958, R. Q. Palmer, United States, developed and patented the trtbar. This concrete shape consists of three cylinders connected by three radial arms (see Fig. 7-108). Figure 7-111 provides details on the volume, dimensions, and thickness of layers of tribars. The dolos armor unit, developed in 1963 by E. M. Merrifield, Republic of South Africa (Merrifield and Zwamborn, 1966), is illustrated in Figure 7-108. This concrete unit closely resembles a ship anchor or an "H" with one vertical perpendicular to the other. Detailed dimensions are shown in Figure 7-112. The toskane is similar to the dolos, but the shapes at the ends of the central shank are triangular heads rather than straight flukes. The tri- angular heads are purported to be more resistant to breakage than the dolos flukes. A round hole may be placed through each head to increase porosity. Dimensions are shown in Figure 7-113. As noted in Table 7-8, various other shapes have been tested by the Corps of Engineers. Details of the modified cube and hexapod are shown in Figures 7-114 and 7-115, respectively. As noted, the tetrapod, quadripod, and tribar are patented, but the U.S. patents on these units have expired. Patents on these units may still be in force in other countries, however; payment of royalties to the holder of the patent for the use of such a unit is required. Since other units in Table 7-10 may be patented, in the U.S. or elsewhere, the status of patents should be reviewed before they are used. Unlike quarrystone, concrete armor units have a history of breakage problems. If a unit breaks, its weight is reduced; if enough units break, the stability of an armor layer is reduced. For dolosse, for instance, model tests by Markel and Davidson (1984a) have demonstrated that random breakage of up to 15 percent or up to 5 broken units in a cluster will have little effect on stability. Breakage exceeding these limits may lead to catastrophic failure of the armor layer. 7=215 Table 7-10. Types of armor units!, Development of Unit Reference Name of Unit Country Akmon Netherlands Paape and Walther, 1963 Binnie block England —?2 Hydraulics Research Station, 1980 Bipod Netherlands 1962 Paape and Walther, 1963 Cob England 1969 Anonymous, 1970; Wilkinson and Allsop, 1983 Cube? 4 4 Hudson and Jackson, 1953 Cube (modified)? United States 1959 Jackson, 1968a Dolos? South Africa 1963 Merrifield and Zwamborn, 1966 Dom Mexico 1970 = Gassho block Japan 1967 Personal correspondence, 1971, Prof. S. Nagai, Dean of Faculty of Engineer- ing, Osaka City University, Sugimoto-Cho, Sumiyoshi-Ku, Osaka, Japan Grabbelar South Africa 1957 Personal correspondence, 1971, Mr. P. Grobbelaar, Technical Manager, Fisheries Development Corp. of South Africa, Ltd., Cape Town, Republic of South Africa Hexaleg block Japan _ Giken Kogyo Co., Ltd., undated Hexapod? United States 1959 Jackson, 1968a Hollow square Japan 1960 Personal correspondence, 1971, Prof. S. Nagai (see above); Nagai, 1962. Hollow Tetrahedron Japan 1959 Personal correspondence, 1971, Prof. S. Nagai (see above); Nagai, 1961b; Tanaka et al., 1966 Interlocking H-block United States 1958 U. S. Army Engineer District, Galveston, 1972 Mexapod Mexico 1978 Porraz and Medina, 1978 N-shaped block Japan 1960 Personal correspondence, 1971, Prof. S. Nagai (see above); Nagai, 1962 Pelican stool? United States 1960 Jackson, 1961 Quadripod United States 1959 Jackson, 1968a Rectangular block? A 4 Jackson, 1967 Rentrapod England en Hydraulics Research Station, 1980 Seabee Australia 1978 Brown, 1978 Shed England 1982 Anonymous, 1982; Wilkinson and Allsop, 1983 Stabilopod Romania 1965 Lates and Ulubeanu, 1966 Stabit England 1961 Singh, 1968 Sta-Bar? United States 1966 Personal correspondence, 1971, Mr. R. J. O’Neill, Marine Modules, Inc. Yonkers, N.Y. Sta-Pod? United States 1966 Personal correspondence, 1971, Mr. R. J. O’Neill (see above) Stalk cube Netherlands 1965 Hakkeling, 1971 Svee block Norway 1961 Svee, Traettenberg, and Térum, 1965 Tetrahedron (solid)? 5 5 Jackson, 1968a Tetrahedron (perforated)? United States 1959 Jackson, 1968a Tetrapod France 1950 Danel, Chapus, and Dhaille, 1960; Jackson, 1968 Toskane> South Africa 1966 Personal correspondence, 1971, Mr. P. Grobbelaar (see above) Tribar United States 1958 Jackson, 1968a; Personal correspondence, Mr. Robert Q. Palmer, President, Tribars, Inc., Las Vegas, Nevada Trigon United States 1962 _— Tri-Long United States 1968 Davidson, 1971 Tripod Netherlands 1962 Paape and Walther, 1963 Tripod block England British Transport Docks Board, 1979 1 Modified from Hudson, 1974. 2 Not available. 3 Units have been tested, some extensively, at the U. S. Army Engineer Waterways Experiment Station (WES); not all units were tested in two- layer armor layers. 4 Cubes and rectangular blocks are known to have been used in masonry-type breakwaters since early Roman times and in rubble-mound breakwaters during the last few centuries. The cube was tested at WES as a construction block for breakwaters as early as 1943. 5 Solid tetrahedrons are known to have been used in hydraulic works for many years. This unit was tested at WES in 1959. 7-216 Bottom QUADRIPOD TETRAPOD Elevation Elevation Bottom Bottom DOLOS (DOLOSSE, plural) ~ Elevation Elevation TRIBAR Figure 7-108. 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HOW ‘IVAGIAIGNI dO LHOTA 14 09/81 LHOIGM LIND EVILS OOOUS LEB7H PI LSE ILGeZ OT VIZ WZ EPIL LSBZ OTHE HLL ————— NN: (14 19) SLIN( TVAIAIGNI 40 AW110A T= 22M *suoTqzeoTypToeds oueyso, “ETI-/ 21n3Ty 7G =d eo. = Vx :auayM ((ZZ1-Z) ‘b2 888) ¢/z-A66'0 = ('N) WAYV LINN Y3d (G39V1d WOGNVY ‘SY3AV1 OML) SANVASOL 4O YASWNN H668'0 = (SLINN Z) SSANNOIHL YAAV1 YOWHV yun 40 1YBiay |je4aAO = H HOLEO = G HO9z'0 = 9 HSve'0 = 9 HSZS'0 = V :a4ayM eHes0'0 = (A) LINN HOWYY TIWNGIAIGNI 40 AWNIOA NOILWA3I13 NW 1d 7-222 *suoT}eoTytToeds aqnd peTJIPOW *HTI-/ eansTy lp -d ori> Vy a1aym “NOILWLS LN3WI83SdK3 SAVMY3SLVM 3HL lv O319NGNOD (221-4) (ba as) cyz ALLL = ('(N) V3YV LINN H3d (039V1d WOONYY SH3AV7 OML) S38N9 G31JIGOW JO Y3BWNN S$iS31 T30OW NI G3SN S$38ND A3ISIGOW NO G3SV8 vwivd :31ON Gt? +d wi = Um Jian (1221-2) (BA 995) cy AGBO = ('N) V3 LINN H3d (O30V1d ATWHOJINN SH3AV1OMI) SIAND G3 IW 40 HIAWON WEOL = (WOONVY SLINNZ) SS3NNOIHL B3AV) BOWHY NOILWA313 v6rz0 = 0 vz0s0 = 8 wseeo - 9 agn2 jo ulpim - aay eVt82°0 = (A) LIND HOWNY TWNGIAIGNI 40 3WNIOA zz wz vo'z ze"h eLh zh a zh BO 99°0 zs"0 a zoe ae'z wz es'z 6e'z az 06's ist ut 98'0 (Yar) @) zy ee'y Wy Le"e ost ore se'z gzz 49h ze"s sol 8 ore 9'8 a's vara sie evs 49's ose = ZE"E 97 60'2 v (14) SLINN YOWHY 40 SNOISN3AWIG TOBWAS ZoL4) «= WS'BL SCOOT «SsCSSZ CSTE) =H wLLD «= GO'WZL LOLEL ZA WIE (030V1d WOGONYWHY SYSAV1 OML) 14 OS 000i H3d SLINN YOWHY JO YSBWNN ves coves Ss LW = LZ7°9h ss SBBLC GAUTZZ—SsCEZ =O L®OW'LGSL"BEL © 9Z "RZ (ATWHOSINA G39VId Y3AV1 3NO) 14 OS 000i YHSd SLINN YOWYYW 40 YSBWNN 9z'ai «HLL SsCSS9h ATS GWA CER «= OS4L LGC ve's vz'y (13) Q39¥1d WOONWHY SH3AV71 OML JO SSANNOIHL GBYNSVAW 39WESAY 626 68's v's sek eek 02'9 98s Ts a 3 zz az (14) ATWHOJINN G39V 1d Y3AV1 3NO 4O SSANNDIHL GSYNSV3SW BOVESAV 6z'9 OS OW ALWE |= G'BZCwA'EZ SS HETLLLS*HLC LSS oh as‘ o'z91 is'vy «= oo’se—C(iEWEE = BZ GZ'ZZ_— AL'S LSS GRE ma 98'0 o'9st ear 4 BELe vo'ze OL*92 96°12 zost e9°ol ve's wiz 2o"1 eso ser OO'Ow = OO'SE_—-«OOTCE-—«—«=“iSZ——sC«OZ—s—«sSL—s«C0—s—«iS— «OZ ooh os" vor (SNOL) SLINN YOWHY TVWNOIAIGN! 30 LHOISM 43 99/87 4HOISM 4INn Ev'cS OO'OOS “LS'OZM wITLSE 14°SGZ EZ WIZ GE'ZPL EWIL LS"EZ 6z"vh wee U4 N35) SLINN HOWNY AWNOIAIGN! 40 SWN TOA 7-223 *suoTjeoTytoeds podexey *C{I-{ ean3Ty rele) oii = %s “NOILVLS LN3WIY3dX3 SAVMYILWM 3HL Lv 0319NGNOD $1$31 1300W NI O3SN SCOdv¥xIH NO O3SV@ vivd ©310N (ZZt-Z) D8 A) gp ACT = CN) W3IHV LIN 3d (039V1d WOONVH SHIAV1OML) SUDdYx3H 40 BIAWON ty ec1 > Mn ae NOILWA3 13 ((ZZ0-4) P9998) ge AVEO > (NI V3HWY LIND H3d (039V1d ATWHOSING SUIAVIOML) SUOd¥x 3M 410 5 IAWON V6lt (WOONVY SLINNZ) SS3INNDIHL HIAV) HOWUY vsiZ070 visto= 8 witeo= 9 Lun jo VOHHauNp WRI9A0 oy Pry cV9L10 = (A) LINN BOWHY TYNOIAION! 40 3WNIOA ee so'e 06% cc? ts°z ot? 1oz 6h an c6'0 yar) a ‘ eL'v as'v sev 60” ove sve ore 6c? cyan ows we 2 os's Los zev csv ize zee vee soz sou ss ez 8 ze'vi aim “veh coz perl 69°01 ve'6 bee ov's wee v (14) SLIND YORMY 40 SNOISN3MIO TOSWAS yay Cart es1z 9z'vz 91 ez lowe 6v've zac 99902 ow azE (Q29V1d NOONVWY S¥3AV7 OM1) 14 OS 000) 43d SLINN HOMUY 40 Y3EHNN vc"01 69'11 tot serv 66°91 soz ve'oz zezw 9 @.'rzZi = 60" 86h (ATWYOSINN OFIVId B3IAV1 3NO) 14 OS COOL U3d SLINN HOWEY 40 Y3IBHNN 60°61 9z'e1 vera ze'oh sist yaa) zoz vs'6 £0% a's cry (14) Q29V1d WOONWY SYU3AV7 OML 40 SSINNDIHL CIUNSVIM JOVUIAY o4"or vz"o1 6L'6 £16 os" trae v9 ses v6'e eit ove (14) ATWHOSINA O3DVId Y3AW 3NO 40 SS3NMDIHL O3IUNSV3NW 39VERAY 6z'9v os'ov love 4 virez Er avay ast 64'S ez uh @s'0 oz is'ey 00° & epee 9eue 6z'2z tom view is's zz ue '0 o'est yard) or'“e vote 04'9% ge12 zo"s1 e9'o1 ves viz 4o"t a) S'6¥i 00'0 00's 00°0€ 00'sz 00'0z o's 0001 00's 00°2 00"! os" o'owi (SNOL) SLINN HONEY TWNGIAIGNI 40 LHOISM 43.99/87 4HOISM 4INt Cw'1LS CO'OOS LS'OZM wiLSE IL'SGZ GZ'VIZ 9O'%VL EwIL LSE 6z"¥h wie (14 N35) SLINN YOWNY TWNOIAION! 40 3WNIOA 7-224 Two approaches have been proposed to control breakage. Zwamborn and Van Niekerk, (1981, 1982) surveyed the performance of dolos-armored breakwaters worldwide and concluded that most structures that failed had been under- designed or had experienced construction difficulties. They formulated lower values for the stability coefficients to produce heavier armor units which would be stable against any crack-causing movement such as rocking in place under wave action. Their results are reflected in Table 7-8. Reinforcement of units with steel bar and fibers (Magoon and Shimizer, 1971) has been tried on several structures. Markle and Davidson (1984b) have surveyed the breakage of reinforced and unreinforced armor units on Corps structures and have found field tests to be inconclusive. No proven analytical method is known for predicting what wave conditions will cause breakage or what type or amount of reinforcement will prevent it. Projects using tetrapods, tribars, quadripods, and dolosse in the United States are listed in Table 7-ll. ge Design of Structure Cross~Section. A rubble structure is normally composed of a bedding layer and a core of quarry-run stone covered by one or more layers or larger stone and an exterior layer(s) of large quarrystone or concrete armor units. Typical rubble-mound cross sections are shown in Figures 7-116 and 7-117. Figure 7-116 illustrates cross-section features typical of designs for breakwaters exposed to waves on one side (seaward) and intended to allow minimal wave transmission to the other (leeward) side. Breakwaters of this type are usually designed with crests elevated such that overtopping occurs only in very severe storms with long return periods. Figure 7-117 shows features common to designs where the breakwater may be exposed to substantial wave action from both sides, such as the outer portions of jetties, and where overtopping is allowed to be more frequent. Both figures show both a more complex “idealized" cross section and a "recommended" cross section. The idealized cross section provides more complete use of the range of materials typically available from a quarry, but is more difficult to construct. The recommended cross section takes into account some of the practical problems involved in constructing submerged features. The right-hand column of the table in these figures gives the rock-size gradation of each layer as a percent of the average layer rock size given in the left-hand column. To prevent smaller rocks in an underlayer from being pulled through an overlayer by wave action, the following criterion for filter design (Sowers and Sowers, 1970) may be used to check the rock-size gradations given in Figures 7-116 and 7-117. (cover) < 5 (under) Dis Des where Des (under) is the diameter exceeded by the coarsest 15 percent of the underlayer and Dis (cover) is the diameter exceeded by the coarsest 85 percent of the layer immediately above the underlayer. 7=225 "CQ6l S*PTaA SeTTFAuosyoer ‘39TIISTq JoeuTsuq Away “Ss peczojyuteaun ‘assoTop uoj-OT 07 -9 peodrzosutezun ‘assojzop uoj-zZ peorzojuteiun ‘assoTop u0j-Z peodiojuter ‘assoTop u0oj-9] pediojuteiaun ‘assojTop u0j-Z peorojuteiun ‘assojTop uo 3-9 peorojsuteaun ‘assoyop u0j-TT *peorojyuteiun ‘assoTop uo0j-9 pue ‘paodiojuted ‘assoTop uoj-0¢E 03 -0Z peodiojyuteiun ‘assoTop uoj-g 02 -4 peodrojyuterun ‘assojTop u0j-(F peosojuter ‘saeqtiq uoq-CcE 01 -6T peorosuteiaun ‘sieqytiq uoj-[°/E OF -C*HZ peodlojuteil ‘assoTop uoj-¢€h 02 -Zy peorojzutea *sieqytiq u0j-6T peodsrosuter ‘sieqtiq uojq-¢ 02 -CE pediojuteiaun ‘sieqti} u0oj-/*OT peozosyuteiun ‘spodtipenb u0j-g7z pedzojutTeiun ‘syDOTq 9a3a19U0D U0RI-NNT 93 -0Z pediosyutei ‘sieqy1q u0j-g*/T peorozuteaun ‘spodeijaq u0j-[¢ peodiojyuteiun ‘spodeijez u0j-¢Z peoiosuteaun ‘spodeijzej u0j-¢¢E peoiosyuteaun “suorpeyeijeq u0q-Z] pue Syo0TG 3a3219U0D u07-00T qy3tem pue odé], 1oOW1y *saqeqs peqtug ey ut sqoefoad AzowWIe 9}e19U0D yTeut3stio uoTAeITTFqQeusY uoFIeITTFQeued uoTIeITT FqQeYyoN TeuTst40 Teut3zt3z0 UOTILITTEQeYSY uoTIeITTTqQeyed yTeut3t3z0 uoTIeITTEQeyoN UoTIEIFT EQeUSy Teut3t40 UOT IBITTEQeYUSY UOTIEITFTEQEYSY uoTIeIFTPQeyod Teut3sts0 TeuT3tI0 uoTIeITTTQeuoy UOT IBITTTGeYSY yTeuTsT30 TeUTZTAO TeuTsTI10 woTIBITTFAeYSY adAj, uotzONAWsSUOD JuseujsANy ioe zemMyPeIg 19 enyHeoI1g 4330f£ 19 ]emMyee1g 19 emMyee1g 13 7 emMy4ee1g Jaqyemyee1q 4semM pue 4seg TTemess 1a eMyee1g ia zemMyee1g Jaqemyeaig setaqef yanos pue yII0N Jaqemyeoig ia zemyHee1g 4330¢ Aj30f 4som setiqef yqynos pue y ION JoajemyeeI1g TrTemess JoajzeMyee1g ia zeMyee1g setajzef yqnos pue yI10N *(7L61) Fefys pue urTEX ¢ *q ‘pareMoy eTIeY YITM UoTIeOTUNWMMOD TeUCSied pue (6/61) SUTTTOD pue ‘paoy] ‘xeTUIEZD ‘ *(946T) “SurTIea ¢ *(LL61) SueseTItl 7 *(47861) UospTAeq pue eTHIEW | SpueTS] uTZITA ‘semouy, *3S *310dayy Teuot zeusrequT yoruO *oqiey puelTereTo yoruo *joqieyH pueTeAeToD pen *jaTuy uenbseuey yPFemeH ‘nyeo ‘ioqiey eeuetTeM y PFeMeH ‘tremey ‘Aeg FyXTOYOd yrFeneH “TeMey ‘20q1eH FTTMTTFARN yp FFeMeH ‘fnew ‘10qieH TNTNyey c FFEMEH ‘nyeo ‘q1odafy nTnTouoy y FFTeO *AqTD Juse0seip y FEPMPH ‘yneq ‘roqieH FNTNYyeY *FFTeD ‘uokueg oTqQeTd yj sFtTeo “Aeq IPTOquMH | Z/6I - TL6T pPFemeH “Fnen “20qIeH FNTNYeX 6961 pFFeneH “Ene ‘roqzeH FNTNYEX 9961 *JTTePO *z0q1eH Pinus), £961 teen 2020 ea ueS €961 y ‘3FTeD “hed 3PTOqmMH | €96T - 0961 FReMeH “TeEMeY “TTTATTIAEN 6S61 ee TEP) PORTLET uooU TY LS61 Tz hieo Arte avesker) LS61T Fremey ‘tTneW ‘loqieqH FNTNYyeHX 9c6l z if 8S6I -— O€6T y FFT ‘keg aproquny adAy, 91nq0n145 PUSS CCIE 7-226 Seaward Leeward Crest Width Breakwater Crest Mox. Design SWL < SWL (Minimum) = SWL ( Minimum) -0.5H ~1.5H~ w/200 W/4000 to W/6000 eee W/10 to W/ 300 ed Multilayer Section W/10 to W/15 Rock Size Rock Size Layer Gradation (%) WwW Primary Cover Layer’ 125 to 75 H = Wave Height W/2 and W/15 Secondary Cover Layer? 125 to 75 W = Weight of Individual Armor Unit W/10 and W/300 __ First Underlayer? 130 to 70 r= Average Layer Thickness W/200 Second Underlayer 150 to 50 W/4000-W/6000 Core and Bedding Layer 170 to 30 For concrete armor: ' Sections IL, 7,g, (1), (2) and (6) 2 Section III, 7,g, (7) 3 Section II 7,4, (8) Crest Width Breakwater Crest we, Max. Design SWL aha SWL (Minimum = SWL (Minimum ) =. 5H p> 2 Ome W/10 to W/15 W/200 to W/6000 ~c_,- Recommended Three-layer Section Figure 7-116. Rubble-mound section for seaward wave exposure with zero-to- moderate overtopping conditions. 7-227 Crest Width Breakwater Crest ie al Max. Design SWL SWL (Minimum) 2 SWL ( Minimum) 7.5-m min SE w/200 w/4000 "7, Idealized Multilayer Section Rock Size Rock Size Layer Gradation (%) Ww Primary Cover Layer’ 125 to 75 H = Wave Height W/10 Toe Berm and First Underlayer? 130 to 70 W = Weight of Individual Armor Unit W/200 Second Underlayer 150 to 50 r = Average Layer Thickness W/4000 Core and Bedding Layer 170 to 30 For concrete armor: ‘Sections II, 7,g, (1), (2) and (6) 2Sections II, 7, g, (5) and (8) Mox. Design SWL Ran SWL (Minimum) w/200 to W/4000 —*7) 5 y Recommended Three-layer Section Figure 7-117. Rubble-mound section for wave exposure on both sides with moderate overtopping conditions. 7-228 Stone sizes are given by weight in Figures 7-116 and 7-117 since the armor in the cover layers is selected by weight at the quarry, but the smaller stone sizes are selected by dimension using a sieve or a grizzly. Thomsen, Wohlt, and Harrison (1972) found that the sieve size of stone corresponds approxi- mately to 1.15 1/3 » Where W is the stone weight and W, is the stone ( unit weight, both in the same units of mass or force. As an aid to under- standing the stone sizes referenced in Figures 7-116 and 7-117, Table 7-12 lists weights and approximate dimensions of stones of 25.9 kilonewtons per cubic meter (165 pounds per cubic foot) unit weight. The dimension given for stone weighing several tons is approximately the size the stone appears to visual inspection. Multiples of these dimensions should not be used to determine structure geometry since the stone intermeshes when placed. A logic diagram for the preliminary design of a rubble structure is shown in Figure 7-118. The design can be considered in three phases: (1) structure geometry, (2) evaluation of construction technique, and (3) evaluation of design materials. A logic diagram for evaluation of the preliminary design is shown in Figure 7-119. As part of the design analysis indicated in the logic diagram (Fig. 7- 118), the following structure geometry should be investigated: (1) Crest elevation and width. (2) Concrete cap for rubble-mound structures. (3) Thickness of armor layer and underlayers and number of armor units. (4) Bottom elevation of primary cover layer. (5) Toe berm for cover layer stability. (6) Structure head and lee side cover layer. (7) Secondary cover layer. (8) Underlayers. (9) Bedding layer and filter blanket layer. (10) Scour protection at toe. (11) Toe berm for foundation stability. @b) Crest Elevation and Width. Overtopping of a rubble structure such as a breakwater or jetty usually can be tolerated only if it does not cause damaging waves behind the structure. Whether overtopping will occur depends on the height of the wave runup R. Wave runup depends on wave characteristics, structure slope, porosity, and roughness of the cover layer. 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The selected crest elevation should be the lowest that provides the protection required. Excessive overtopping of a breakwater or jetty can cause choppiness of the water surface behind the structure and can be detrimental to harbor operations, since operations such as mooring of small craft and most types of commercial cargo transfer require calm waters. Overtopping of a rubble seawall or revetment can cause serious erosion behind the structure and flooding of the backshore area. Overtopping of jetties can be tolerated if it does not adversely affect the channel. The width of the crest depends greatly on the degree of allowable overtopping; where there will be no overtopping, crest width is not critical. Little study has been made of crest width of a rubble structure subject to overtopping. Consider as a general guide for overtopping conditions that the minimum crest width should equal the combined widths of three armor units (n = 3). Crest width may be obtained from the following equation. B = nk ei (7-120) A\w r, where B = crest width, m (or ft) n = number of stones (n = 3 is recommended minimum) k, = layer coefficient (Table 7-13) W = mass of armor unit in primary cover layer, kg (or weight in 1b) w= mass density of armor unit, maya (or unit weight in 1b/£t) The crest should be wide enough to accommodate any construction and main- tenance equipment which may be operated from the structure. Figures 7-116 and 7-117 show the armor units of the primary cover layer, sized using equation (7-116), extended over the crest. Armor units of this size are probably stable on the crest for the conditions of minor to no overtopping occurring in the model tests which established the values of Kp in Table 7-8. Such an armor unit size can be used for preliminary design of the cross section of an overtopped or submerged structure, but model tests are strongly recommended to establish the required stable armor weight for the crest of a structure exposed to more than minor overtopping. Concrete armor units placed on the crest of an overtopped structure may be much less stable than the equivalent quarrystone armor chosen using equation (7-116) on a structure with no overtopping. In the absence of an analytical method for calculating armor weight for severely overtopped or submerged structures, especially those armored with concrete units, hydraulic model tests are necessary. Markle and Carver (1977) have tested heavily overtopped and submerged quarrystone-armored structures. 7-233 apm *(MOTSq YZI-Z pue ¢zI-/ °sbe ves) deadti M 243 JO UOTSUSUTp OTqnd 943 SZ Tre ST ssouyoTYy AeAeT poeperzs sy 3eYI auTUIeJep 09 Yooyg ~°deadta OSm ay} JO UOTSUSUTp OTqnNd 9y} 9OTM 39q PTNOYS ssoeuYydTYU AeheT WNUTUTM d3UIZ °(7161 S‘uospny) seqnd petytTpow peoetd ATWAoFTuN Jo AeAeT sUO UO Sjsaq WoIF pezeurqse st AqTSo10g *souo0qs pedtdaetTetT{Teied ay jo uoTSueUTp 3uOT eSeraeAe 2Yy} BOTA] ST SSoUyoOTYR AdKeqT *(8261) r2Aze9 °(1/61) uosptTAeq pue JeAie9 *(81961) “uospny *(€861) TeazeD °(7Z61) uospny CJ GNI Gar Se ny Xe wopury pepeiry auojskrient) L wiostup azeqtal T aueyso] wopuey wopuery wopury wopuey wopuey wopury wopuey S yS0TOd To veo jPod FxeH jPodapend ppodez3eL TAPoFSEPOm) eqn) pedtdetteied) suozsk11ent NIN NUNN NN Net Tetoeds gf wopuey wopuery wopuey % (a) katso204 "x auayor33209 x0er | uaweoera | uf aun omy *sqjtTun Jomze snotiea 10x ARTSOA0d pue JUaeTOTFFIOD ADAPT “ET[-/ PTGeL (sa) aN z (usnoz) suojzshiiend z(usnoz) euoqsfkirend) NN 1 (U00ws ) auo0qsfki1iend 7-234 (2) Concrete Cap for Rubble-Mound Structures. Placed concrete has been added to the cover layer of rubble-mound jetties and breakwaters. Such use ranges from filling the interstices of stones in the cover layer, on the crest, and as far down the slopes as wave action permits, to casting large monolithic blocks of several hundred kilograms. This concrete may serve any of four purposes: (a) to strengthen the crest, (b) to deflect overtopping waves away from impacting directly on the lee side slope, (c) to increase the crest height, and (d) to provide roadway access along the crest for construc tion or maintenance purposes. Massive concrete caps have been used with cover layers of precast concrete armor units to replace armor units of questionable stability on an overtopped crest and to provide a rigid backup to the top rows of armor units on the slopes. To accomplish this dual purpose, the cap can be a slab with a solid or permeable parapet (Czerniak and Collins, 1977; Jensen, 1983; and Fig. 6-64, (see Ch. 6)), a slab over stone grouted to the bottom elevation of the armor layer (Figs. 6-60 and 6-63, or a solid or permeable block (Lillevang, 1977, Markle, 1982, and Fig. 6-65)). Concrete caps with solid vertical or sloped walls reflect waves out through the upper rows of armor units, perhaps causing loss of those units. Solid slabs and blocks can trap air beneath them, creating uplift forces during heavy wave action that may crack or tip the cap (Magoon, Sloan, and Foote, 1974). A permeable cap decreases both of these problems. A parapet can be made permeable, and vertical vents can be placed through the slab or block itself (Mettam, 1976). Lillevang (1977) designed a breakwater crest composed of a vented block cap placed on an unchinked, ungrouted extension of the seaward slope’s under- layer, a permeable base reaching across the crest. Massive concrete caps must be placed after a structure has settled or must be sufficiently flexible to undergo settlement without breaking up (Magoon, Sloan, and Foote, 1974). Ribbed caps are a compromise between the solid block and a covering of concrete armor units. The ribs are large, long, rectangular members of reinforced concrete placed perpendicular to the axis of a structure in a Manner resembling railroad ties. The ribs are connected by reinforced concrete braces, giving the cap the appearance of a railroad track running along the structure crest. This cap serves to brace the upper units on the slopes, yet is permeable in both the horizontal and vertical directions. Ribbed caps have been used on Corps breakwaters at Maalea Harbor (Carver and Markle, 198la), at Kahului (Markle, 1982), on Maui, and at Pohoiki Bay, all in the State of Hawaii. Waves overtopping a concrete cap can damage the leeside armor layer (Magoon, Sloan, and Foote, 1974). The width of the cap and the shape of its lee side can be designed to deflect overtopping waves away from the structure’s lee side (Czerniak and Collins, 1977; Lillevang, 1977; and Jensen, 1983). Ribbed caps help dissipate waves. High parapet walls have been added to caps to deflect overtopping seaward and allow the lowering of the crest of the rubble mound itself. These walls present the same reflection problems described above and complicate the design =—23'5 of a stable cap (Mettam, 1976; Jensen, 1983). Hydraulic model tests by Carver and Davidson (1976; 1983) have investigated the stability of caps with high parapet walls proposed for Corps structures. To evaluate the need for a massive concrete cap to increase structural stability against overtopping, consideration should be given to the cost of including a cap versus the cost of increasing dimensions (a) to prevent overtopping and (b) for construction and maintenance purposes. A massive concrete cap is not necessary for the structural stability of a structure composed of concrete armor units when the difference in elevation between the crest and the limit of wave runup on the projected slope above the structure is less than 15 percent of the total wave runup. For this purpose, an all- rubble structure is preferable, and a concrete cap should be used only if substantial savings would result. Maintenance costs for an adequately designed rubble structure are likely to be lower than for any alternative composite-type structure. The cost of a concrete cap should also be compared to the cost of covering the crest with flexible, permeable concrete armor units, perhaps larger than those used on the slopes, or large quarrystone armor. Bottin, Chatham, and Carver (1976) conducted model tests on an overtopped breakwater with dolos armor on the seaward slope, but with large quarrystone on the crest. The breakwater at Pria, Terceria, Azores, was repaired using large quarrystone instead of a concrete cap on the crest to support the primary tetrapod armor units. Two rows of large armor stones were placed along the shoreward side of the crest to stabilize the top row of tetrapods. An inspection in March 1970 indicated that this placement has performed satisfactorily even though the structure has been subjected to wave overtopping. Hydraulic model tests are recommended to determine the most stable and economical crest designs for major structures. Experience indicates that concrete placed in the voids on the structure slopes has little structural value. By reducing slope roughness and surface porosity, the concrete increases wave runup. The effective life of the concrete is short, because the bond between concrete and stone is quickly broken by structure settlement. Such filling increases maintenance costs. For a roadway, a concrete cap can usually be justified if frequent maintenance of armored slopes is anticipated. A smooth surface is required for wheeled vehicles; tracked equipment can be used on ribbed caps. (3) Thickness of Armor Layer and Underlayers and Number of Armor Units. The thickness of the cover and underlayers and the number of armor units required can be determined from the following formulas: see Ae (7-121) W Pr where r is the average layer thickness in meters (or feet), n is the number of quarrystone or concrete armor units in thickness comprising the cover layer, W is the mass of individual armor units in kilograms (or weight in pounds), and w, is the mass density in kilograms per cubic meter (or unit weight in pounds per cubic foot). The placing density is given by 7-236 N w 2/3 - =nk, (: 2 )(#) (7-122) where N, is the required number of individual armor units for a given surface area, A is surface area, k is the layer coefficient, and P is the average porosity of the cover layer in percent. Values of ky eynl JP - determined experimentally, are presented in Table 7-13. The thickness r of a layer of riprap is either 0.30 m, or one of the following: Wea \l/3 r= 2.0( 3) (7-123) where Ws5g is the weight of the 50 percent size in the gradation, or aes 1/3 E225 (7-124) r where W is the heaviest stone in the gradation, whichever of the three is the greatest. The specified layer thickness should be increased by 50 percent for riprap placed underwater if conditions make placement to design dimensions difficult. The placing density of riprap is calculated as the weight of stone placed per unit area of structure slope, based on the measured weight per unit volume of riprap. The placing density may be estimated as the product of the layer thickness r , the unit weight of the rock w, , and P r (Q =z ioe (4). Bottom Elevation of Primary Cover Layer. The armor units in the cover layer (the weights are obtained by eq. 7-116) should be extended downslope to an elevation below minimum SWL equal to the design wave height H when the structure is in a depth >1.5H , as shown in Figure 7-116. When the structure is in a depth <1.5H , armor units should be extended to the bottom, as shown in Figure 7-117. On revetments located in shallow water, the primary cover layer should be extended seaward of the structure toe on the natural bottom slope as scour protection. The larger values of K for special-placement parallelepiped stone in Table 7-8 can be obtained only if a toe mound is carefully placed to support the quarrystones with their long axes perpendicular to the structure slope (U.S. Army Corps of Engineers, 1979). For dolosse, it is recommended that the bottom rows of units in the primary cover layer be "special placed" on top of the secondary cover layer (Fig. 7-116), the toe berm (Fig. 7-117), or the bot- tom itself, whenever wave conditions and water clarity permit. Site-specific model studies have been performed with the bottom units placed with their vertical flukes away from the slope and the second row of dolosse placed on or overtopping the horizontal flukes of the lower units to assure that the units interlock with the random-placed units farther up the slope (Carver, 1976; 7-237 Bottin, Chatham, and Carver, 1976). The tests indicated that special placement of the bottom dolosse produces better toe stability than random placement. The seaward dolosse in the bottom row should be placed with the bottom of the vertical flukes one-half the length of the units (dimension C in Fig. 7-112) back from the design surface of the primary armor layer to produce the design layer thickness. Model tests to determine the bottom elevation of the primary cover layer and the type of armor placement should be made whenever economically feasible. (5) Toe Berm for Cover Layer Stability. As illustrated in Figure 7-117, structures exposed to breaking waves should have their primary cover layers supported by a quarrystone toe berm. For preliminary design purposes the quarrystone in the toe berm should weigh W/10 , where W is the weight of quarrystone required for the primary cover layer as calculated by equation (7-116) for site conditions. The toe berm stone can be sized in relation to W even if concrete units are used as primary armor. The width of the top of the berm is calculated using equation (7-120), with n = 3. The minimum height of the berm is calculated using equation (7-121), with n=2. Model tests can establish whether the stone size or berm dimensions should be varied for the final design. Tests may show an advantage to adding a toe berm to a structure exposed to nonbreaking waves. The toe berm may be placed before or after the adjacent cover layer. It must be placed first, as a base, when used with special-placement quarrystone or uniform-placement tribars. When placed after the cover layer, the toe berm must be high enough to provide bracing up to at least half the height of the toe armor units. The dimensions recommended above will exceed this requirement. (6) Structure Head and Lee Side Cover Layer. Armoring of the head of a breakwater or jetty should be the same on the lee side slope as on the seaside slope for a distance of about 15 to 45 meters from the structure end. This distance depends on such factors as structure length and crest elevation at the seaward end. Design of the lee side cover layer is based on the extent of wave overtopping, waves and surges acting directly on the lee slope, porosity of the structure, and differential hydrostatic head resulting in uplift forces which tend to dislodge the back slope armor units. If the crest elevation is established to prevent possible overtopping, the weight of armor units and the bottom elevation of the back slope cover layer should theoretically depend on the lesser wave action on the lee side and the porosity of the structure. When minor overtopping is anticipated, the armor weight calculated for the seaward side primary cover layer should be used on the lee side, at least down to the SWL or -0.5 H for preliminary design; however, model testing may be required to establish an armor weight stable under overtopping wave impact. Primary armor on the lee side should be carried to the bottom for breakwaters with heavy overtopping in shallow water (breaking wave conditions), as shown in Figure 7-117. Equation 7-116 cannot be used with values of K listed in Table 7-8 calculate leeside armor weight under overtopping, since the Kp values were established for armor on 7-238 the seaward side and may be incorrect for leeside concrete or quarrystone units (Merrifield, 1977; Lillevang, 1977). The presence of a concrete cap will also affect overtopping forces on the lee side in ways that must be quantified by modeling. When both side slopes receive similar wave action (as with groins or jetties), both sides should be of similar design. (7) Secondary Cover Layer. If the armor units in the primary and secondary cover layers are of the same material, the weight of armor units in the secondary cover layer, between -1.5 H and -2.0 H, should be greater than about one-half the weight of armor units in the primary cover layer. Below -2.0 H, the weight requirements can be reduced to about W/15 for the same slope condition (see Fig. 7-116). If the primary cover layer is of quarrystone, the weights for the secondary quarrystone layers should be ratioed from the weight of quarrystone that would be required for the primary cover layer. The use of a single size of concrete armor for all cover layers- -i.e., upgrading the secondary cover layer to the same size as the primary cover layer--may prove to be economically advantageous when the structure is located in shallow water (Fig. 7-117); in other words, with depth d=1.5H, armor units in the primary cover layer should be extended down the entire slope. The secondary cover layer (Fig. 7-116) from -1.5 H to the bottom should be as thick as or thicker than the primary cover layer. For cover layers of quarrystone, for example, and for the preceding ratios between the armor weight W in the primary cover layer and the quarrystone weight in the secondary cover layers, this means that if n= 2 for the primary cover layer (two quarrystones thick) then n = 2.5 for the secondary cover layer from -H to -2.0 H and n= 5 for that part of the secondary cover layer below =2 0) Vel 6 The interfaces between the secondary cover layers and the primary cover layer are shown at the slope of l-on-1.5 in Figure 7-116. Steeper slopes for the interfaces may contribute to the stability of the cover armor, but material characteristics and site wave conditions during construction may require using a flatter slope than that shown. (8) Underlayers. The first underlayer directly beneath the primary armor units should have a minimum thickness of two quarrystones (m = 2) (see Figs. 7-116 and 7-117). For preliminary design these should weigh about one- tenth the weight of the overlying armor units (W/10) if (a) the cover layer and first underlayer are both quarrystone, or (b) the first underlayer is quarrystone and the cover layer is concrete armor units with a stability coefficient Kp iZ (where Kp is for units on a trunk exposed to nonbreaking waves). When the cover layer is of armor units with SN 5 such as dolosse, toskanes, and tribars (placed uniformly in a single layer), the first underlayer quarrystone weight should be about W/5 or one-fifth the weight of the overlying armor units. The larger size is recommended to increase interlocking between the first underlayer and the armor units of high Kp . Carver and Davidson (1977) and Carver (1980) found, from hydraulic model tests of quarrystone armor units and dolosse placed on a breakwater trunk exposed to nonbreaking waves, that the underlayer stone size could range from W/5 to W/20 , with little effect on stability, runup, or rundown. If the underlayer stone proposed for a given structure is available in weights from W/5 to W/20 , the structure should be model tested with a first underlayer of the available stone before the design is made final. The tests 7-239 will determine whether this economical material will support a stable primary cover layer of the planned armor units when exposed to the site conditions. The second underlayer beneath the primary cover layer and upper secondary cover layer (above -2.0 H) should have a minimum equivalent thickness of two quarrystones; these should weight about one-twentieth the weight of the immediately overlying quarrystones (1/20 x W/10 = W/200 for quarrystone and some concrete primary armor units). The first underlayer beneath the lower secondary cover layer (below -2.0 H), should also have a minimum of two thicknesses of quarrystone (see Fig. 7-116); these should weigh about one-twentieth of the immediately overlying armor unit weight (1/20 x W/15 = W/300 for units of the same material). The second underlayer for the secondary armor below -2.0 H can be as light as W/6,000 , or equal to the core material size. Note in the "recommended" section of Figure 7-116 that when the primary armor is quarrystone and/or concrete units with Kp < 12 , “theiituae underlayer and second (below -2.0 H) quarrystone sizes are W/10 to W/15. If the primary armor is concrete armor units with Kp >» 12° 3) (the ieee underlayer and secondary (below -2.0 H) quarrystone sizes are W/5 and W/10. For a graded riprap cover layer, the minimum requirement for the under- layers, if one or more are necessary, is < 5 (cover) Sars (under) where Dis (cover) is the diameter exceeded by the coarsest 85 percent of the riprap or underlayer on top and Dgs (under) is the diameter exceeded by the coarsest 15 percent of the underlayer or soil below (Ahrens, 1981). For a revetment, if the riprap and the underlying soil satisfy the size criterion, no underlayer is necessary; otherwise, one or more are required. MThe size criterion for riprap is more restrictive than the general filter criterion given at the beginning of Section III,/,g, above, and repeated below. The riprap criterion requires larger stone in the lower layer to prevent the material from washing through the voids in the upper layer as its stones shift under wave action. A more conservative underlayer than that required by the minimum criterion may be constructed of stone with a 50 percent size of about W50/20. This larger stone will produce a more permeable underlayer, perhaps reducing runup, and may increase the interlocking between the cover layer and underlayer; but its gradation must be checked against that of the underlying soil in accordance with the criterion given above. The underlayers should be at least three 50 percent-size stones thick, but not less than 0.23 meter (Ahrens, 1981). The thickness can be calculated using equation (7-123) with a coefficient of 3 rather than 2. Note that, since a revetment is placed directly on the soil or fill of the bank it protects, a single underlayer also functions as a bedding layer or filter blanket. (9) Filter Blanket or Bedding Layer. Foundation conditions for marine structures require thorough evaluation. Wave action against a rubble 7-240 structure, even at depths usually considered unaffected by such action, creates turbulence within both the structure and the underlying soil that may draw the soil into the structure, allowing the rubble itself to sink. Revetments and seawalls placed on sloping beaches and banks must withstand groundwater pressure tending to wash underlying soil through the structure. When large quarrystones are placed directly on a sand foundation at depths where waves and currents act on the bottom (as in the surf zone), the rubble will settle into the sand until it reaches the depth below which the sand will not be disturbed by the currents. Large amounts of rubble may be required to allow for the loss of rubble because of settlement. This settlement, in turn, can provide a stable foundation; but a rubble structure can be protected from excessive settlement resulting from leaching, undermining, or scour, by the use of either a filter blanket or bedding layer. It is advisable to use a filter blanket or bedding layer to protect the foundations of rubble-mound structures from undermining except (a) where depths are greater than about three times the maximum wave height, (b) where the anticipated current velocities are too weak to move the average size of foundation material, or (c) where the foundation is a hard, durable material (such as bedrock). When the rubble structure is founded on cohesionless soil, especially sand, a filter blanket should be provided to prevent differential wave pressures, currents, and groundwater flow from creating a quick condition in the foundation by removing sand through voids of the rubble and thus causing settlement. A filter blanket under a revetment may have to retain the foundation soil while passing large volumes of groundwater. Foundations of coarse gravel may be too heavy and permeable to produce a quick condition, while cohesive foundation material may be too impermeable. A foundation that does not require a filter blanket may require a protective bedding layer. A bedding layer prevents erosion during and after construction by dissipating forces from horizontal wave, tide, and longshore currents. It also acts as a bearing layer that spreads the load of overlying stone (a) on the foundation soil to prevent excessive or differential settlement, and (b) on the filter material to prevent puncture. It interlocks with the overlying stone, increasing structure stability on slopes and near the toe. In many cases a filter blanket is required to hold foundation soil in place but a bedding layer is required to hold the filter in place. Grada- tion requirements of a filter layer depend principally on the size character- istics of the foundation material. If the criterion for filter design (Sowers and Sowers, 1970) is used, D5 (filter) is less than or equal to 5De5 (foundation) the filter material must be less than or equal to 5 times the diameter exceeded by the coarsest 15 percent of the foundation material) to ensure that the pores in the filter are too small to allow passage of the soil. Depending on the weight of the quarrystone in the structure, a geotextile filter may be used (a) instead of a mineral blanket, or (b) with a thinner mineral blanket. Geotextiles are discussed in Chapter 6 and by Moffatt and Nichol, Engineers (1983) and Eckert and Callender (1984), who present detailed requirements for using geotextile filters beneath quarrystone armor in coastal structures. A geotextile, coarse gravel, or crushed stone filter may be (i.e.,. the diameter exceeded by the coarsest 85 percent of 7-241 placed directly over a sand, but silty and clayey soils and some fine sands must be covered by a coarser sand first. A bedding layer may consist of quarry spalls or other crushed stone, of gravel, or of stone-filled gabions. Quarry spalls, ranging in size from 0.45 to 23 kilograms, will generally suffice if placed over a geotextile or coarse gravel (or crushed stone) filter meeting the stated filter design criteria for the foundation soil. Bedding materials must be placed with care on geotextiles to prevent damage to the fabric from the bedding materials, as well as from heavier materials placed above. Filter blanket or bedding layer thickness depends generally on the depth of water in which the material is to be placed and the size of quarrystone used, but should not be less than 0.3 meter to ensure that bottom irregular- ities are completely covered. A filter blanket or bedding layer may be required only beneath the bottom edge of the cover and underlayers if the core material will not settle into or allow erosion of foundation material. Core material that is considerably coarser than the underlying foundation soil may need to be placed on a blanket or layer as protection against scour and settlement. It is also common practice to extend the bedding layer at least 1.5 meters beyond the toe of the cover stone. Details of typical rubble structures are shown in Chapter 6, STRUCTURAL FEATURES. In low rubble-mound structures composed entirely of cover and underlayers, leaving no room for a core, the bedding layer is extended across the full width of the structure. Examples are low and submerged breakwaters intended to control sand transport by dissipating waves (Markle and Carver, 1977) and small breakwaters for harbor protection (Carver and Markle, 1981b). 8. Stability of Rubble Foundations and Toe Protection. Forces of waves on rubble structures have been studied by several investi- gators (see Section 7, above). Brebner and Donnelly (1962) studied stability criteria for random-placed rubble of uniform shape and size used as foundation and toe protection at vertical-faced, composite structures. In their experiments, the shape and size of the rubble units were uniform, that is, subrounded to subangular beach gravel of 2.65 specific gravity. In practice, the rubble foundation and toe protection would be constructed with a core of dumped quarry-run material. The superstructure might consist of concrete or timber cribs founded on the core material or a pair of parallel-tied walls of steel sheet piling driven into the rubble core. Finally, the apron and side slope of the core should be protected from erosion by a cover layer of armor units (see Sec. d and e below). a. Design Wave Heights. For a composite breakwater with a superstructure resting directly on a rubble-mound foundation, structural integrity may depend on the ability of the foundation to resist the erosive scour by the highest waves. Therefore, it is suggested that the selected design wave height H for such structures be based on the following: (1) For critical structures at open exposed sites where failure would be disastrous, and in the absence of reliable wave records, the design wave height H should be the average height of the highest 1 percent of all waves Hy expected during an extreme event, based on the deepwater significant wave height H, corrected for refraction and shoaling. (Early 7-242 breaking might prevent the 1 percent wave from reaching the structure; if so, the maximum wave that could reach the structure should be taken for the design value of H .) (2) For less critical structures, where some risk of exceeding design assumptions is allowable, wave heights between Hig and H, are acceptable. The design wave for rubble toe protection is also between Hyg and H, - b. Stability Number. The stability number (N,) is primarily affected by the depth of the rubble foundation and toe protection below the still-water level dj and by the water depth at the structure site, d, . The relation between the depth ratio d,/d, and Ne is indicated in Figure 7-120. The cube value of the stability number has been used in the figure to facilitate its substitution in equation (7-125). ce. Armor Stone. The equation used to determine the armor stone weight is a form of equation (7-116): W, we We er Tao (7-125) Nepicses — 11) s r where W = mean weight of individual armor unit, newtoms or pounds. Ww, = unit weight of rock (saturated surface dry), newtons per cubic meter or pounds per cubic foot (Note: substitution of pr , the mass density of the armor material in kilograms per cubic meter or slugs per cubic foot, will yield W in units of mass (kilograms or slugs) H = design wave height (i.e., the incident wave height causing no damage to the structure) Sy = specific gravity of rubble or armor stone relative to the water on which the structure is situated (S,, = w/w») Wi, = unit weight of water, fresh water = 9,800 newtons per cubic meter (62.4 pounds per cubic foot), seawater = 10,047 newtons per cubic meter (64.0 pounds per cubic foot). (Note: subsitution of rt - pw ; ; (2 = ) » where pw is the mass density of the water at the structure, for (s,-1)? yields the same result.) Ni; = design stability number for rubble foundations and toe protection (see Fig. 7-120). 7-243 s = a = cares 2=2 = Se a 300 : = = = : SES=== : == 200 SSas t = +f tet - : ++} Rubble i f— f pop . Sea aae it aoe oot eee as Toe Protection T 7 T ! i] | = ct ! ro a tH Man ] 2 100 ——————————— = = = = = — —— s 80 ===> = a ==: iS = = Rubble Toe Protection s 60 ==e { = —— == > ——— = = 4 Es fe = w H? a O S== ——t = : r : = Be SSSSe NE US. SL n” 30 SS SS==' = $s ( r ) = 4 + = : and B=0.4d, ata SI | SELES= SSS=5 Sei it + * + + S| =: + § 2 PEER eet ! Rubble = as Foundation — T | [ : = 410 nee aa ° = 2 : a =Ss 6 = = : == =====—= === == === === ===—===>==5===: Rubble Foundation 55 ————— = —— = -_=SSS= ar See = = ~ == = es re S=S=S5 ==: aS SS ee = s O 0.1 0.2 0.3 0.4 0.5 0.6 On”, 70:8 (After Brebner cond Donnelly, 1962) Depth Ratio 4 dg Figure 7-120. Stability number N, for rubble foundation and toe protection. 7-244 d. Scour Protection. The forces causing loss of foundation soil from beneath a rubble-mound structure are accentuated at the structure toe. Wave pressure differentials and groundwater flow may produce a quick condition at the toe, then currents may carry the suspended soil away. A shallow scour hole may remove support for the cover layers, allowing them to slump down the face, while a deep hole may destabilize the slope of the structure, over- steepening it until bearing failure in the foundation soil allows the whole face to slip. Toe protection in the form of an apron must prevent such damage while remaining in place under wave and current forces and conforming to an uneven bottom that may be changing as erosion occurs. Toe scour is a complex process. The toe apron width and stone size required to prevent it are related to the wave and current intensity; the bottom material; and the slope, roughness, and shape of the structure face. No definitive method for designing toe protection is known, but some general guidelines for planning toe protection are given below. The guidelines will provide only approximate quantities which may require doubling to be conservative, in some cases. A detailed study of scour in the natural bottom and near existing structures should be conducted at a planned site, and model studies should be considered before determining a final design. (1) Minimum Design. Hales (1980) surveyed scour protection practices in the United States and found that the minimum toe apron was an extension of the bedding layer and any accompanying filter blanket measuring 0.6 to 1.0 meter thick and 1.5 meters wide. In the northwest United States, including Alaska, aprons are commonly 1.0 to 1.5 meters thick and 3.0 to 7.5 meters wide. Materials used, for example, were bedding of quarry-run stone up to 0.3 meter in dimension or of gabions 0.3 meter thick; core stone was used if larger than the bedding and required for stability against wave and current forces at the toe. (2) Design for Maximum Scour Force. The maximum scour force occurs where wave downrush on the structure face extends to the toe. Based on Eckert (1983), the minimum toe apron will be inadequate protection against wave scour if the following two conditions hold. The first is the occurrence of water depth at the toe that is less than twice the height of the maximum expected unbroken wave that can exist in that water depth. The maximum unbroken wave is discussed in Chapter 5 and is calculated using the maximum significant wave height Ho, from Figure 3-21, and methods described in Section I of this chapter. Available wave data can be used to determine which calculated wave heights can actually be expected for different water levels at the site. The second condition that precludes the use of a minimum toe apron is a structure wave reflection coefficient , that equals or exceeds 0.25, which is generally true for slopes steeper than about 1 on 3. If the reflection coefficient is lower than the limit, much of the wave force will be dissipated on the structure face and the minimum apron width may be adequate. If the toe apron is exposed above the water, especially if waves break directly on it, the minimum quarrystone weight will be inadequate, whatever the slope. (3) Tested Designs. Movable bed model tests of toe scour protection for a quarrystone-armored jetty with a slope of 1 on 1.25 were performed by Lee (1970; 1972). The tests demonstrated that a layer two stones thick of 7-245 stone weighing about one-thirtieth the weight of primary cover layer armor (W/30) was stable as cover for a core-stone apron in water depths of more than one but less than two wave heights. The width of the tested aprons was four to six of the aprons’ cover layer stones, yand so could be calculated r using equation (7-120) with n= 4to6 and W=+-. 30 Hales (1980) describes jetties, small breakwaters, and revetments with slopes of 1 on 3 or steeper and toes exposed to intense wave action in shallow water that have their aprons protected by a one-stone-thick layer of primary cover layer quarrystone. The aprons were at least three to four cover stones wide; i.e., if equation (7-120) were used, n= 3 to 4 and W= wp. In Hawaii, the sediment beneath the toes of such structures was excavated down to coral; or, if the sand was too deep, the toe apron was placed in a trench 0.6 to 2.0 meters deep. (4) Materials. The quarrystone of the structure underlayers, secondary cover layer, toe mound for cover layer stability, or the primary cover layer itself can be extended over a toe apron as protection, the size of which depends on the water depth, toe apron thickness, and wave height. Eckert (1983) recommended that, in the absence of better guidance, the weight of cover for a submerged toe exposed to waves in shallow water be chosen using the curve in Figure 7-120 for a rubble-mound foundation beneath a vertical structure and equation (7-125) as a guide. The design wave height H to be used in equation (7-125) is the maximum expected unbroken wave that occurs at the structure during an extreme event, and the design water depth is the minimum that occurs with the design wave height. Since scour aprons generally are placed on very flat slopes, quarrystone of the size in an upper secondary cover layer w,/2 probably will be the heaviest required unless the apron is exposed above the water surface during wave action. Quarrystone of primary cover layer size may be extended over the toe apron if the stone will be exposed in the troughs of waves, especially breaking waves. The minimum thickness of cover over the toe apron should be two quarrystones, unless primary cover layer stone is used. (5) Shallow-Water Structures. The width of the apron for shallow- water structures with reflection coefficients equalling or greater than 0.25 can be planned from the structure slope and the expected scour depth. As discussed in Chapter 5, the maximum depth of a scour trough due to wave action below the natural bed is about equal to the maximum expected unbroken wave at the site. To protect the stability of the face, the toe soil must be kept in place beneath a surface defined by an extension of the face surface into the bottom to the maximum depth of scour. This can be accomplished by burying the toe, where construction conditions permit, thereby extending the face into an excavated trench the depth of the expected scour. Where an apron must be placed on the existing bottom or only can be partially buried, its width can be made equal to that of a buried toe; i.e., equal to the product of the expected scour depth and the cotangent of the face slope angle. (6) Current Scour. Toe protection against currents may require smaller protective stone, but wider aprons. Stone size can be estimated from Section IV below. The current velocity used for selecting stone size, the scour depth to be expected, and the resulting toe apron width required can be 7-246 estimated from site hydrography, measured current velocities, and model studies (Hudson et al., 1979). Special attention must be given to sections of the structure where scour is intensified; i.e. to the head, areas of a section change in alinement, bar crossings, the channel sides of jetties, and the downdrift sides of groins. Where waves and currents occur together, Eckert (1983) recommends increasing the cover size by a factor of 1.5. The stone size required for a combination of wave and current scour can be used out to the width calculated for wave scour protection; smaller stone can be used beyond that point for current scour protection. Note that the conservatism of the apron width estimates depends on the accuracy of the methods used to predict the maximum depth of scour. (7) Revetments. Revetments commonly are typically the smallest and most lightly armored of coastal protective structures, yet their failure leads directly to loss of property and can put protected structures in jeopardy. They commonly are constructed above the design water level or in very shallow water where their toes are likely to be exposed to intense wave and current forces during storms. For these reasons, their toes warrant special pro- tection. Based on guidance in EM 1110-2-1614 (U.S. Army Corps of Engineers, 1984), the cover for the toe apron of a revetment exposed to waves in shallow water should be an extension of the lowest cover layer on the revetment slope. Only the cover thickness is varied to increase stability. The toe apron should be buried wherever possible, with the revetment cover layer extended into the bottom for at least the distance of 1 meter or the maximum expected unbroken wave height, whichever is greater. If scour activity is light, the thickness of the cover on the buried toe can be a minimum of two armor stones or 50 percent size stones in a riprap gradation, the same as on the slope. For more intense scour, the cover thickness should be doubled and the extension depth increased by a factor of up to 1.5. For the most severe scour, the buried toe should be extended horizontally an additional distance equal to twice the toe’s depth, that is, 2 to 3 times the design wave height (see Fig. 7-121). If the apron is a berm placed on the existing bottom and the cover is quarrystone armor, the cover thickness may be as little as one stone and the apron width may be three to four stones. A thickness of two stones and a width equal to that of a buried toe is more conservative and recommended for a berm covered by riprap. For the most severe wave scour the thickness should be doubled and a width equal to 3 to 4.5 design wave heights used, as illustrated in Figure 7-121. According to EM 1110-2-1601 (U.S. Army Corps of Engineers, 1970), the width of a toe apron exposed to severe current scour should be five times the thickness of the revetment cover layer, whether the toe is buried or a berm. If a geotextile filter is used beneath the toe apron of a revetment or a structure that passes through the surf zone, such as a groin, the geotextile should not be extended to the outer edge of the apron. It should stop about a meter from the edge to protect it from being undermined. As an alternative, the geotextile may be extended beyond the edge of the apron, folded back over the bedding layer and some of the cover stone, and then buried in cover stone and sand to form a Dutch toe. This additionally stable form of toe is illustrated as an option in Figure 7-121. 2-247 OPTIONAL DUTCH TOE x Ny sani BEDDING 2 LAYER = GEOTEXTILE FILTER 2H TO 3H BURIED TOE APRON 3H TO 4.5H OPTIONAL DUTCH TOE BEDDING LAYER fanO) 20 GEOTEXTILE FILTER BERM TOE APRON Figure 7-121. Revetment toe scour aprons for severe wave scour. If a revetment is overtopped, even by minor splash, the stability can be affected. Overtopping can (a) erode the area above or behind the revetment, negating the structure’s purpose; (b) remove soil supporting the top of the revetment, leading to the unraveling of the structure from the top down; and (c) increase the volume of water in the soil beneath the structure, contribut- ing to drainage problems. The effects of overtopping can be limited by choosing a design height exceeding the expected runup height or by armoring the bank above or behind the revetment with a splash apron. The splash apron 7-248 can be a filter blanket covered by a bedding layer and, if necessary to prevent scour by splash, quarrystone armor or riprap; i.e., an apron similar in design to a toe apron. The apron can also be a pavement of concrete or asphalt which serves to divert overtopping water away from the revetment, decreasing the volume of groundwater beneath the structure. e. Toe Berm for Foundation Stability. Once the geometry and material weights of a structure are known, the structure’s bearing pressure on the underlying soil can be calculated. Structure settlement can be predicted using this information, and the structure’s stability against a slip failure through the underlying soil can be analyzed (Eckert and Callender, 1984). If a bearing failure is considered possible, a quarrystone toe berm sufficiently heavy to prevent slippage can be built within the limit of the slip circle. This berm can be combined with the toe berm supporting the cover layer and the scour apron into one toe construction. If the vertical structure being protected by a toe berm is a cantilevered or anchored sheet-pile bulkhead, the width of the berm B must be sufficient to cover the zone of passive earth support in front of the wall. Eckert and Callender (1984) describe methods of determining the width of this zone. As an approximation, B- should be the greatest of (a) twice the depth of pile penetration, (b) twice the design wave height, or (c) 0.4 d (Eckert, 1983). If the vertical structure is a gravity retaining wall, the width of the zone to be protected can be estimated as the wall height, the design wave height, or 0.4 d, » whichever is greatest. IV. VELOCITY FORCES--STABILITY OF CHANNEL REVETMENTS In the design of channel revetments, the armor stone along the channel slope should be able to withstand anticipated current velocities without being displaced (Cox, 1958; Cambell, 1966). The design armor weight is chosen by calculating the local boundary shear expected to act on a revetment and the shear that a design stone weight can withstand. Since the local boundary shear is a function of the revetment surface roughness, and the roughness is a function of the stone size, a range of stone sizes must be evaluated until a size is found which is stable under the shear it produces. When velocities near the revetment boundaries are availabie from model tests, prototype measurements, or other means, the local boundary shear is Ww 2 w V ge [een (7-126) Paras Die! log. Oy 10 d where g ii local boundary shear V = the velocity at a distance y above the boundary dg = equivalent armor unit diameter; i.e., 7-249 _(6\/3 (w\1/3 4 a, (2) ie (7-127) r w. = armor unit weight for uniform stone = W509 en for riprap The maximum velocity of tidal currents in midchannel through a navigation opening as given by Sverdrup, Johnson, and Fleming (1942) can be approximated by _ 4mAh = 396 (7-128) V where V = maximum velocity at center of opening T = period of tide A = surface area of harbor S = cross section area of openings h = tidal range The current velocity at the sides of the channel is about two-thirds the velocity at midchannel; therefore, the velocity against the revetments at the sides can be approximated by y = = mAh (7-129) If no prototype or model current velocities are available, this velocity can be used as an approximation of V_ and to calculate the local boundary shear. If the channel has a uniform cross section with identical bed and bank armor materials, on a constant bottom slope over a sufficient distance to produce uniform channel flow at normal depth and velocity, velocity can be calculated using the procedures described in Appendix IV of EM 1110-2-1601 (Office, Chief of Engineers, U.S. Army, 1970), or Hydraulic Design Charts available from the U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss.). In tidal channels, different water surface elevations at the ends of the channel are used to find the water surface elevation difference that gives the maximum flow volume and flow velocity. If the conditions described above hold, such that the flow if fully rough and the vertical velocity distribution is logarithmic, the local boundary shear Tp is Ww as 2 = = SNL GELS (7-130) 5.75 log,, tals g Th 7-250 where <| rT average local velocity in the vertical depth at site (V is average over this depth) Q i] If the channel is curved, the computed local boundary shear should be multiplied by a factor appropriate for that cross section (available in EM 1110-2-1601, Office, Chief of Engineers, 1970). If the conditions described above leading to a uniform channel flow at normal depth and velocity do not exist, as they will not for most tidal channels, the local boundary shear computed from the equation above should be increased by a factor of 1.5. If the local boundary shear can be calculated by using the average velocity over depth, it should also be calculated using an estimated velocity at the revetment surface, as described in the two methods above. The calculated local boundary shears can be compared and the most conservative used. Calculate the riprap design shear or armor stone design shear using t = 0.040 (w, = W,? OF G/=131) where t = design shear for the channel bottom if essentially level, and sin-6 M2 e 7e|| al > Se @7=1132)) sin where t = design shear for channel side slopes 6 = angle of side slope with horizontal » = angle of repose of the riprap (normally about 40°) For all graded stone armor (riprap), the gradation should have the following relatins to the computed value for W : 50 min "100 max ~ ? “50 min ere) "100 min ~ * “50 min (7134) Sees =sl5 450 min @/=135)) Wie = 0.5 WSO mar (7-136) (= 2511 Wis max = 9-75 Weo min (7-137) Wis min = Ons Weg min (7-138) If stone is placed above water, the layer thickness is M59 min \I/3 eS Doh rea , or 0.3 m (12 in.) minimum (7-139) r If stone is placed below water, Weg NS r = 3.2 Sapte srs » or 0.5 m (18 in.) minimum (7-140) r to account for inaccuracy in placement. Equations (7-133) through (7-138) are used by choosing a layer thickness for a type of placement, then calculating the dg for Wey min (dg min) and for We max (dg max) « The local boundary shear should be calculated using dg max 3 the design shear should be calculated using dg min « if the design shear matches or exceeds the local boundary shear, the layer thickness and stone sizes are correct. For uniform stone, d is uniform so that the same value is used for calculating the local boundary and design shears. In the special case where the velocity is known within 3 meters of the surface of the revetment, the local boundary shear equation for velocities near the revetment surface can be used with y set equal to dg - This gives sp Sa pct 8 \5.75 log i 30 Setting this equal to the armor stone design shear, and solving the result for V_ gives WW, \1/2 SADEN LA Vasu 5e TE (OROAO)IE, > log, 30 =) —— at!? sin or Wy-W,y\1/2 2 WY v = 5.75 (0.020) !/2 logy, 30 (ey. = j- Sane dee w sin’ 7-252 w_-w .\1/2 Oe Niy th yao Ga |e = ey ag A (7-141) w sin 6 g This is Isbash’s equation for stone embedded in the bottom of a sloped channel modified for stone embedded in a bank with angle 6 to the horizontal (the coefficient 1.20 is Isbash’s constant for embedded stone). From this, the armor stone weight required to withstand the velocity V is as follows: 6 Ww -w 3 Wi = T V en) 6 6 3 a3 ke? 3/2 NGA = (CAs) (", “s) tg: sin’ 0 sin yo we Ww, 3 in26 -3/2 tS 000215 eee) le (7-142) g r ow sin 6 V. IMPACT FORCES Impact forces are an important design consideration for shore structures because of the increased use of thin flood walls and gated structures as part of hurricane protection barriers. High winds of a hurricane propelling small pleasure craft, barges, and floating debris can cause great impact forces on a structure. Large floating ice masses also cause large horizontal impact forces. If site and functional condition require the inclusion of impact forces in the design, other measures should be taken: either the depth of water against the face of the structure should be limited by providing a rubble-mound absorber against the face of the wall, or floating masses should be grounded by building a partially submerged structure seaward of the shore structure that will eliminate the potential hazard and need for impact design consideration. In many areas impact hazards may not occur, but where the potential exists (as for harbor structures), impact forcer should be evaluated from impulse- momentum considerations. VI. ICE FORCES Ice forms are classified by terms that indicate manner of formation or effects produced. Usual classifications include sheet ice, shale, slush, frazil ice, anchor ice, and agglomerate ice (Striegl, 1952; Zumberg and Wilson, 1953; Peyton, 1968). There are many ways ice can affect marine structures. In Alaska and along the Great Lakes, great care must be exercised in predicting the different ways in which ice can exert forces on structures and restrict operations. Most situations in which ice affects marine structures are outlined in Table 7-14. I—253 The amount of expansion of fresh water in cooling from 12.6°C (39°F) to 0° C (32° F) is 0.0132 percent; in changing from water at 0°C (32 F) to ice at 0° C, the amount of expansion is approximately 9.05 percent, or 685 times as great. A change of ice structure to denser form takes place when with a temperature lower than -22°C (-8°F), it is subjected to pressures greater than about 200 kilonewtons per square meter (30,000 pounds per square inch). Excessive pressure, with temperatures above -22° C, causes the ice to melt. With the temperature below -22°C, the change to a denser form at high pressure results in shrinkage which relieves pressure. Thus, the probable maximum pressure that can be produced by water freezing in an enclosed space is approximately 200 kilonewtons per square meter (30,000 pounds per square inch). Designs for dams include allowances for ice pressures of as much as 657,000 to 730,000 newtons per meter (45,000 to 50,000 pounds per linear foot). The crushing strength of ice is about 2,750 kilonewtons per square meter (400 pounds per square inch). Thrust per meter for various thicknesses of ice is about 43,000 kilograms for 0.5 meter, 86,000 kilograms for 1.0 meter, etc. Structures subject to blows from floating ice should be capable of resisting 97,650 to 120,000 kilograms per square meter (10 to 12 tons per square foot, or 139 to 167 pounds per square inch) on the area exposed to the greatest thickness of floating ice. Ice also expands when warmed from temperatures below freezing to a temperature of O°C without melting. Assuming a lake surface free of snow with an average coefficient of expansion of ice between -7°C (20° F) and 0°C equaling 0.0000512 m/m-°C , the total expansion of a sheet of ice a kilometer long for a rise in temperature of 10°C (50°F) would be 0.5 meter. Normally, shore structures are subject to wave forces comparable in magnitude to the maximum probable pressure that might be developed by an ice sheet. As the maximum wave forces and ice thrust cannot occur at the same time, usually no special allowance is made for overturning stability to resist ice thrust. However, where heavy ice, either in the form of a solid ice sheet or floating ice fields may occur, adequate precautions must be taken to ensure that the structure is secure against sliding on its base. Ice breakers may be required in sheltered water where wave action does not require a _ heavy structure. Floating ice fields when driven by a strong wind or current may exert great pressure on structures by piling up on them in large ice packs. This condition must be given special attention in the design of small isolated structures. However, because of the flexibility of an ice field, pressures probably are not as great as those of a solid ice sheet in a confined area. Ice formations at times cause considerable damage on shores in local areas, but their net effects are largely beneficial. Spray from winds and waves freezes on the banks and structures along the shore, covering them with a protective layer of ice. Ice piled on shore by wind and wave action does not, in general, cause serious damage to beaches, bulkheads, or protective riprap, but provides additional protection against severe winter waves. Ice often affects impoundment of littoral drift. Updrift source material is less erodible when frozen, and windrowed ice is a barrier to shoreward-moving wave energy; therefore, the quantity of material reaching an impounding structure 7-254 is reduced. During the winters of 1951-52, it was estimated that ice caused a reduction in rate of impoundment of 40 to 50 percent at the Fort Sheridan, Illinois, groin system. A. C. D. Table 7-14. Effects of ice on marine structures!, Direct Results of Ice Forces on Structures. 1. Horizontal forces. a. Crushing ice failure of laterally moving floating ice sheets. b. Bending ice failure of laterally moving floating ice sheets. c. Impact by large floating ice masses. d. Plucking forces against riprap. 2. Vertical forces. a. Weight at low tide of ice frozen to structural elements. b. Buoyant uplift at high tide of ice masses frozen to structural elements. c. Vertical component of ice sheet bending failure introduced by ice breakers. d. Diaphragm bending forces during water level change of ice sheets frozen to structural elements. e. Forces created because of superstructure icing by ice spray. 3. Second-order effects. a. Motion during thaw of ice frozen to structural elements. b. Expansion of entrapped water within structural elements. c. Jamming of rubble between structural framing members. Indirect Results of Ice Forces on Structures. 1. Impingement of floating ice sheets on moored ships. 2. Impact forces by ships during docking which are larger than might normally be expected. 3. Abrasion and subsequent corrosion of structural elements. Low-Risk but Catastrophic Considerations. 1. Collision by a ship caught in fast-moving, ice-covered waters. 2. Collision by extraordinarily large ice masses of very low probability of occurrence. Operational Considerations. 1. Problems of serving offshore facilities in ice-covered waters. 2. Unusual crane loads. 3. Difficulty in maneuvering work boats in ice-covered waters. 4. Limits of ice cover severity during which ships can be moored to docks. 5. Ship handling characteristics in turning basins and while docking and undocking. 6. The extreme variability of ice conditions from year to year. 7. The necessity of developing an ice operations manual to outline the operational limits for preventing the overstressing of structures. ' After Peyton (1968). 7-255 Some abrasion of timber or concrete structures may be caused, and individual members may be broken or bent by the weight of the ice mass. Piling has been slowly pulled by the repeated lifting effect of ice freezing to the piles, or to attached members such as wales, and then being forced upward by a rise in water stage or wave action. VII. EARTH FORCES Numerous texts on soil mechanics such as those by Anderson (1948), Hough (1957), and Terzaghi and Peck (1967) thoroughly discuss this subject. The forces exerted on a wall by soil backfill depend on the physical character- istics of the soil particles, the degree of soil compaction and saturation, the geometry of the soil mass, the movements of the wall caused by the action of the backfill, and the foundation deformation. In wall design, since pressures and pressure distributions are typically indeterminate because of the factors noted, approximations of their influence must be made. Guidance for problems of this nature should be sought from one of the many texts and manuals dedicated to the subject. The following material is presented as a brief introduction. 1. Active Forces. When a mass of earth is held back by means of a retaining structure, a lateral force is exerted on the structure. If this is not effectively resisted, the earth mass will fail and a portion of it will move sideways and downward. The force exerted by the earth on the wall is called aettve earth force. Retaining walls are generally designed to allow minor rotation about the wall base to develop this active force, which is less than the at-rest force exerted if no rotation occurs. Coulomb developed the following active force equation: 2 , 2 Bis wh” ese [risimuCer =o) (7-143) @ - fsin COitk 6) ei isiniCgit, 6) sin) (Coed) sin (6 - i) where P = active force per unit length, kilonewtons per meter (pounds per G linear foot) of wall w = unit weight of soil, kilonewtons per cubic meter (pounds per linear foot) of wall h = height of wall or height of fill at wall if lower than wall , meters (feet) 8 = angle between horizontal and backslope of wall, degrees. i = angle of backfill surface from horizontal, degrees ¢ = internal angle of friction of the material, degrees 7-256 6 = wall friction angle, degrees These symbols are further defined in Figure 7-122. Equation (7-143) may be reduced to that given by Rankine for the special Rankine conditions where 6 is considered equal to at and @ equal to 90 degrees (vertical wall face). When, additionally, the backfill surface is level (i = 0 degrees), the reduced equation is 2 p. = pan? (45° =) (7-144) Figure 7-123 shows that Ey from equation (7-144) is applied horizontally. Unit weights and internal friction angles for various soils are given in Table 7-15. The resultant force for equation (7-143) is inclined from a line perpendicular to the back of the wall by the angle of wall friction 6 (see Fig. 7-122). Values for 6 can be obtained from Table 7-16, but should not exceed the internal friction angle of the backfill material @ and, for conservatism, should not exceed (3/4) » (Office, Chief of Engineers, 1961). 2. Passive Forces. If the wall resists forces that tend to compress the soil or fill behind it, the earth must have enough internal resistance to transmit these forces. Failure to do this will result in rupture; i.e., a part of the earth will move sideways and upward away from the wall. This resistance of the earth against outside forces is called passive earth force. The general equation for the passive force P is 2 : 2 p = wh ese 6 sin’ (6) + 6) (7=145) 2 | AG Seo) (RCO ee sin (6 - i) It should be noted that Pp is applied below the normal to the structure slope by an angle -6 , whereas the active force is applied above the normal line by an angle +6 (see Fig. 7-122). For the Rankine conditions given in Section 1 above, equation (/-145) reduces to 2 _ wh 2 3 od - F Ses tan (+5 + t) (7-146) Equation (7-146) is satisfactory for use with a sheet-pile structure, assuming a substantially horizontal backfill. U-V5]/ Table 7-15. Unit weights and internal friction angles of soils!. Unit Weight, kg/m? Classification Dry Submerged Min. (loose) Max. (dense) Min. (loose) Max. (dense) Min. (loose) Max. (dense) GRANDULAR MATERIALS 1. Uniform Materials Standard Ottawa SAND 1,474 (92) 1,762 (110) 1,105 (69) Clean, uniform SAND (fine or medium) 1,330 (83) 1,890 (118) 1,169 (73) Uniform, inorganic SILT 1,281 (80) 1,890 (118) 1,169 (73) 2. Well-graded Materials Silty SAND 1,394 (87) | 2,034 (127) 1,265 (79) Clean, fine to coarse SAND 1,362 (85) 2,210 (138) 1,378 (86) Micaceous SAND 1,217 (76) | 1,922 (120) 1,217 (76) Silty SAND and GRAVEL 1,426 (89) | 2,339 (146) 1,474 (92) MIXED SOILS 1. Sandy or silty CLAY 961 (60) | 2,162 (135) 1,362 (65) 2. Skip-graded silty CLAY with stones or rock fragments 1,346 (84) | 2,243 (140) 1,426 (89) 3. Well-graded GRAVEL, SAND, SILT and CLAY mixture 1,602 (100) | 2,371 (148) 1,506 (94) CLAY SOILS 1. CLAY (30 to 50 percent clay sizes) 801 (50) 1,794 (112) 1,137. (71) 2. Colloidal CLAY (-0.002 mm. 50 percent) 208 (13) 1,698 (106) 1,057 (66) ORGANIC SOILS 1. Organic SILT 641 (40) 1.762 (110) 1,105 (69) 2. Organic CLAY (30 to 50 percent clay size) 481 (30) 1,602 (100) 993 (62) Unit Weight, kg/m? Friction Density or Classification Angle ¢ Consistency Equivalent Fluid Coarse SAND or SAND and GRAVEL 45 compact 2,243 (140) 384 (24) 13,135 (820) 38 firm 1,922 (120) 465 (29) 8,169 (510) 32 loose 1,442 (90) 448 (28) 4,645 (290) Medium SAND 40 compact 2,082 (130) 448 (28) 9,611 (600) 34 firm 1,762 (110) 497 (31) 6,247 (390) 30 loose 1,442 (90) 480 (30) 4,325 (270) Fine SAND 34) 5 compact 2,082 (130) 593 (37) 7,368 (460) 30 firm 1,602 (100) 529 (33) 4,805 (300) 28 loose 1,362 (85) 497 (31) 4,485 (280) Fine, silty SAND or sandy SILT 32 compact 2,082 (130) 641 (40) 6,728 (420) 30 firm 1,602 (100) 529 (33) 4,8U5 (300) 28 loose 1,362 (85) 497 (31) 4,485 (280) Fine, uniform SILT 30 compact 2,162 (135) 721 (45) 6,407 (400) 28 firm 1,762 (110) 609 (38) 4,805 (300) 26 loose 1,362 (85) 529 (33) 3,524 (220) CLAY-SILT 20 medium 1,922 (120) 945 (59) 3,924 (245) soft 1,442 (90) 705 (44) 2,931 (183) Silty CLAY 15 medium 1,922 (120) 1,137 (71) 3,268 (204) soft 1,442 (90) 849 (53) 2,451 (153) CLAY 10 medium 1,922 (120) 1,345 (84) 2,723 (170) soft 1,442 (90) 849 (53) 2,451 (153) CLAY 0 medium 1,922 (120) 1,922 (120) 1,922 (120) soft 1,442 (90) 1,442 (90) 1,442 (90) After Hough (1957). 7-258 Figure 7-122. Definition sketch for Coulomb earth force equation. oo oe,’ x Pa ox oe Oe oe xs x R u as o ae | als 7 eee Figure 7-123. Active earth force for simple Rankine case. 7-259 Table 7-16. Coefficients and angles of friction. Surface Coefficient of Angle of Wall Stone — Brick - Concrete Friction, u Friction, 64 On Dry Clay On Wet or Moist Clay On Sand On Gravel NOTE: Angle of friction should be reduced by about 5 degrees if the wall fill will support train or truck traffic; the coefficient uw would then equal the tangent of the new angle 6. 3. Cohesive Soils. Sections 1 and 2 above have briefly dealt with forces in cohesionless soil. A cohesive backfill which reduces the active force may be advan- tageous. However, unless the soil can move continuously to maintain the cohesive resistance, it may relax. Thus, walls should usually be designed for the active force in cohesionless soil. 4. Structures of Irregular Section. Earth force against structures of irregular section such as stepped-stone blocks or those having two or more back batters may be estimated using equations (7-142) and (7-144) by substituting an approximate average wall batter or slope to determine the angle 6. 5. Submerged Material. Forces due to submerged fills may be calculated by substituting the unit weight of the material reduced by buoyancy for the value of w in the preceding equations and then adding to the calculated forces the full hydrostatic force due to the water. Values of unit weight for dry, saturated, and submerged materials are indicated in Table 7-15. 6. Uplift Forces. 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Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1971. de CASTRO, D.E., "Diques de escollera (Design of Rock-Fill Dikes),"' Revista de Obras Publicas, Vol. 80, 1933. DICK, T.M., "On Solid and Permeable Submerged Breakwaters,'"' C.E. Research Report No. 59, Department of Civil Engineering, Queen’s University, Kingston, Ontario, 1968. ERGIN, A., and PORA, S., "Irregular Wave Action on Rubble-Mound Breakwaters," Journal of the Waterways, Harbors and Coastal Engineering Division, ASCE, Vol. 97, No. WW2, Proc. Paper 8114, 1971, pp. 279-293. FRANZIUS, L., "Wirkung und Wirtschaftlichkeit von Rauhdeckwereden im Hinblick auf den Wellenauflauf," Mitteilungen des Franzius-Instituts fur Grund- und Wasserbau der TH Hannover, Heft 25, 1965, pp 149-268 (in German). FUNKE, E.R., and E.P.D. MANSARD, "On the Synthesis of Realistic Sea States," Hydraulics Laboratory Technical Report LTR-HY-66, National Research Council of Canada, 1979. 7-277 GODA, Y., “Numerical Experiments on Wave Statistics with Spectral Simulation," Report of the Port and Harbor Research Institute, Vol. 9, No. 3, 1970. GODA, Y., "The Observed Joint Distribution of Periods and Heights of Sea Waves," Proceedings of the 16th Conference on Coastal Engineering, 1978. GODA, Y., and SUZUKI, Y., “Estimation of Incident and Reflected Waves in Random Wave Experiments," Proceedings of the 15th Coastal Engineering Conference, Vol. 1, Ch. 48, 1976, pp. 828-845. GODA, Y., TAKEDA, H., and MORIYA, Y., "Laboratory Investigation of Wave Transmission over Breakwaters,"' Report of the Port and Harbor Research Institute, No. 13, Apr. 1967. HALL, W.C., and HALL, J.V., "A Model Study of the Effect of Submerged Breakwaters on Wave Action," TM-l, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., May 1940. HENSEN, W., ‘''Modellversuche uber den Wellenauflauf an Seedeichen im Wattengebiet,'’ Mitteilungen der Hannoverschen Versuchsanstalt fur Grundbau und Wasserbau, Franzius-Institut, Hannover, West Germany, 1954. HUDSON, E., et al., "Coastal Hydraulic Models," Coastal Engineering Research Center, SR 5, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., May 1979. HUDSON, R.Y., and JACKSON, R.A., "Design of Tetrapod Cover Layer for a Rubble- Mound Breakwater, Crescent City Harbor, Crescent City, Calif.," Technical Memorandum 2-413, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1955. HUDSON, R.Y., and JACKSON, R.A., "Stability Tests of Proposed Rubble-Mound Breakwaters, Nassau Harbor, Bahamas," Miscellaneous Paper No. 2-799, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., Mar. 1966. IPPEN, A.T., ed., Hstuary and Coastline Hydrodynamics, McGraw-Hill, New York, 1966. IRIBARREN CANVANILLES, R., and NOGALES Y OLANO, C., "Report on Breakwaters," 18th Internattonal Navigation Congress, Ocean Navigation Section, Question 1, Rome, 1953. JACKSON, R.A., "Design of Quadripod Cover Layers for Rubble-Mound Break- waters," Miscellaneous Paper 2-372, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1960. JACKSON, R.A., "Design for Rubble-Mound Breakwater Construction, Tsoying Harbor, Taiwan," Technical Report 2-640, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1964a. JACKSON, R.A., "Designs for Rubble-Mound Breakwaters Repair, Kahului Harbor, Maui, Hawaii," Technical Report 2-644, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1964b. 7-278 JACKSON, R.A., "Stability of Rubble-Mound Breakwaters, Nassau Harbor, Nassau, New Providence, Bahamas," Technical Report 2-697, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1905. JACKSON, R.A., "Designs for Rubble-Mound Breakwater, Noyo Harbor, Calfornia," Miscellaneous Paper 2-841, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., Aug. 1966. JACKSON, R.A, HUDSON, R.Y., and HOUSLEY, J.G., "Designs for Rubble-Mound Breakwater Repairs, Nawiliwili Harbor, Nawiliwili, Hawaii," Miscellaneous Paper No. 2-377, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1960. JEFFREYS, H., "Note on the Offshore Bar Problems and Reflection from a Bar," Wave Report No. 3, Great Britain Ministry of Supply, 1944. JOHNSON, J.W., FUCHS, R.A., and MORISON, J.R., "The Damping Action of Submerged Breakwaters," Transactions of the American Geophystcal Unton, Vol. 32, No. 5, 1951, pp. 704-718. KATO, J., and UEKITA, Y., "On the Wave Damping Effect of Block Mound Breakwater," Transactions of the Japan Soctety of Civil Engineers, Vol. 1, Parte 1969/- KNAJES, R.Ya., "Protective Structures of Breakwater Type, and the Movement of Material on Sandy Shores," Izn., Adkad Nauk, Latv. SSR, 7(36). LAMARRE, P., "Water Wave Transmission by Overtopping of an Impermeable Breakwater," M.S. Thesis, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass., Sept. 1967. LAMBE, T.W., and WHITMAN, R.V., Sotl Mechantcs, Series in Soil Engineering, Wiley, New York, 1969. LeMEHAUTE, B., "Periodical Gravity Wave on a Discontinuity," Journal of the Hydraulics Division, ASCE, Vol. 86, No. HY 9, Part 1, 1960, pp. 11-41. LeMEHAUTE, B., "An Introduction to Hydrodynamics and Water Waves," Report No. ERL 118-POL3-1&2, U.S. Department of Commerce, Environmental Science Services Administration, Washington, D.C., July 1969. NAGAI, S., "Stable Concrete Blocks on Rubble-Mound Breakwaters," Journal, Waterways and Harbors Diviston, American Society of Civil Engineers, Vol. 88, No. WW3, Aug. 1962, pp. 85-115. NAKAMURA, M., SHIRAISHI, H., and SASAKI, Y., "Wave Damping Effect of Submerged Dike," Proceedings of the 10th Conference on Coastal Engineering, ASCE, TSO, WoOlS ey Gre 7/5 NOS po ASL HOI > PALMER, R.Q., "“Breakwaters in the Hawaiian Islands," Proceedings of the Amertcan Soctety of Civtl Engineers, Waterways and Harbors Division, Vol. 86, No. WW2, Paper No. 2507, 1960. 7=279 PECK, R.B., HANSON, W.E., and THORNBURN, T.H., Foundatton Engineering, Wiley, New York, 1967. PRIEST, M.S. "Reduction of Wave Height by Submerged Offshore Structures," Bulletin No. 34, Alabama Polytechnic Institute, Engineering Experiemnt Station, Auburn, Alabama, 1958. REID, R.O., and BRETSCHNEIDER, C.L., "The Design Wave in Deep or Shallow Water, Storm Tide, and Forces on Vertical Piling and Large Submerged Objects," Department of Oceanography, Texas A&M University, College Station, Texas, 1953. ROLLINGS, A.P. “Stability of Crescent City Harbor Breakwater, Crescent City, California," Miscellaneous Paper 2-171, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1956. RYE, H., “Ocean Wave Groups," Report URA-82-18, Marine Technology Center, Trondheim, Norway, Nov. 1981. SAVILLE elon ee Discussioni: Laboratory Investigation of Rubble-Mound Breakwaters by R.Y. Hudson," Journal of the Waterways and Harbors Division, WW3, Vol. 86, 1960, p. 151. SAVILLE, T., Jr., GARCIA, W.J., JR., and LEE, C.E., "Development of Breakwater Design," Proceedings of the 21st International Navigation Congress, Sec. ll, Subject 1, "Breakwaters with Vertical and Sloping Faces," Stockholm, 1965. SAVILLE, T., JR., McCLENDON, E.W., and COCHRAN, L.L., "Freeboard Allowances for Waves on Inland Reservoirs," Journal of the Waterways and Harbors Divtston, ASCE, Vol. 88, No. WW2, May 1962, pp. 93-124. SEELIG, W.N., “A Simplified Method for Determining Vertical Breakwater Crest Elevation Considering the Wave Height Transmitted by Overtopping,'' CDM No. 76-1, Coastal Engineering Research Center, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., May 1976. U.S. ARMY ENGINEER WATERWAYS EXPERIMENT STATION, "Stability of Rubble—Mound Breakwaters," Technical Memorandum No. 2-365, Vicksburg, Miss., 1953. WASSING, F., "Model Investigation on Wave Runup Carried Out in the Netherlands During the Past Twenty Years," Proceedings of the Stxth Conference on Coastal Engineering, ASCE, Council on Wave Research, 1957. WEGGEL, J.R., "The Impact Pressures of Breaking Water Waves,'"' Ph.D. Thesis presented to the University of Illinois, Urbana, Illinois, (unpublished, available through University Microfilms, Ann Arbor, Michigan 1968). WEGGEL, J.R., "Maximum Breaker Height," Journal of the Waterways, Harbors and Coastal Engineering Diviston, ASCE, Vol. 98, No. WW4, Paper 9384, 1972. WEGGEL, J.R., "Maximum Breaker Height for Design," Proceedings of the 13th Conference on Coastal Engineering, Vancouver, B.C., 1973. 7-280 eee eee eS ee ee CHAPTER 8 Engineering Analysis: Case Study ie SS aoe" Redondo-Malaga Cove, California, 23 January 1973 > ¥} I CHAPTER 8 ENGINEERING ANALYSIS: CASE STUDY Page INTRODUCTION clolclelelcleleletcleletclaloleloleloiolercleiciereleteletereleleleliclelclelelelctelclolevelcleleielelelere Ol 1CIL STATEMENT OF PROBIGHMieetelotclelelclchclelclerel ciel clelcicleleletclctelelelelelclerelclcietelelcielolelciclelcrs Os: III PHYSICAL E;]NVASRONMENlistetetetetetciolelotclolclsrcteletelelelerclelelc eleleleletelolelofolelololorcisteletsierels| Osa: IV ile Dis Site DESCHEApitel OMlsiereeofelelelelelelclalclelels/elelclelolslcl slelelelelolcleleleleleleleleleleleleleleree Omi! Water Levels and Currents--Storm Surge and Astronomical Tides..8-/7 a. Design HurricaneS...ccecccccccceccvcccrsccescccccesscccccseG—/ b. Estimate’ of Storm Surges... ccc ccc cc ccclccccccccicc cece ccOrd c. Observed Water Level Data, Breakwater Harbor, Lewes, Delaware svcccceccccccccccicccceccsccccccesecccciccecciecesO— 1) d. Predicted Astonomical Tides...cccccccccccccccccccccccscccccd—l2 ew Desion Water Levels Summarys ciciciclc cielclc cloicleloie clelaieisicle slclelelolelee Oa le Wave ConddeEdion'SisicielerelolelelololelolelelololercietctoreleleleloleleleieleleielclelelclolcleleleielalcheriOsl/e a. Wave Conditions on Bay Side of Island.....cccececvecveceeed-l2 b. Wave Conditions on Ocean Side of isiltandiereteteicteleleleloletelelelelereveleiom ZO) PRELIMINARY WE:SiMGNiojetelevoleteleveleteletetchelodeleleleielcleictercieloiclioielelcielcleloieleleterelolelerelere Oa 4O WG Selection of Design Waves and Water LevelsS...ccccccecsccccces e846 Ae NACETIMLE VE Slotelolelelcleleletelelololelsiele/clelolelelelelelelelelelele) jelelclelelsje clereleleleieio— 40 be. Wave) Conditions on Bay (Side of Tsilandiic cic ciccicisicileicciccecceco—4/, c. Wave Conditions on Ocean Side of Island....ccccccsvesceeeed-4/ Revetment Design: Ocean Side of Island.....ccccccccccccccccced—4/ AeELY PCMOL WAVE WACETON\slclelefelalelelaleleleleleiolele\etel olelelelelelelolelelslelelcisielele(olelOm 47, b. Selection Between Alternative DesignsS....ccccccccccsccecceed—4/ Diffraction Analysis: Diffraction Around Breakwater.........e3-/4 Preliminary Design of Quay Wall Caisson.....cccccccccccccvcceed—/) a. Nonbreaking Wave Forces on Caisson. ccccccccccccccccccccsed—/0 Deeotabilaltys Comput atdlons\sejc\clereleieielelele\eie\c/e/e else lolels)e cle s\slele siecle se O—-OL Cou Calssony Stability Abter! Backbililcimgcrecis o/clele\elelelelelelclelsle\s)sieleliO OF dit) eSoil) Bearing Pressures ole sielelelslsiels\elclelelo/olelelele/eielsielelclejclcleleleisieO=-O) Clots OUMMA'Y fe relete\elole)e\c/leile\elale/eiclolelel clclicle’ ele) sie lc\elelslclc’o/e/elolaleleieielsiclelele)s(eO— OD COMPUTATION OF POTENTIAL LONGSHORE TRANSPORT... cccccccccccccccesesdS) 1k Die Sie Deepwater Wave Angle (a,) occ cece cree cceeccccecesccececseeessb—-GD Calculation of Average F (a) cece ccc ceccrcceecccecceseeeesee sO) Potential Longshore Transport Computed by Energy Flux Method..8-89 CONTENTS (Continued) Page VI BEACHFILL REQUIREMENTS... .cccccccccccccccccccccccccccccccsecsccece sO 1. Material CharacteristicS.....cccccccccccccccccscccccccccccssesG-Gl ae Native Sandls oc sve ers e0e 00101616 ecoeiere &,. eine eleie o(e1c)e 1s ese! oiclevelolefalelelskersisiceene Die Borrow--Source (Neteheisietelelelorsiaielclelelsiolciciololeleleleletsiolelelelelelelelelcletaleteteicment Ce Borrow-—Source Bicievelia ole eveleleevelele\elcieteleie/ovevelelicieieveie cieleletohelereteloreneteomean: 2. Evaluation of Borrow Material. .cccccccccccccccccccccverecvcsce cd Gl Sie Required Volume of BDA ceaehe-o cveveiie. ovale ieveve eve eileloue (slaves etoiereletecovevenelenetenacm oe LITERATURE GIEE Disreroroieielerelolcrelovclolclelelcielerchelelchcishorcloleleloieielelelelolelelelelevolcielotelenaioaory CHAPTER 8 ENGINEERING ANALYSIS: CASE STUDY I. INTRODUCTION This chapter presents as examples of the techniques presented in this manual a series of calculations for the preliminary design of a hypothetical offshore island in the vicinity of Delaware Bay. The problem serves to illustrate the interrelationships among many types of problems encountered in coastal engineering. The text progresses from development of the physical environment through a preliminary design of several elements of the proposed structure. For brevity, the design calculations are incomplete; however, when necessary, the nature of additional work required to complete the design is indicated. It should be pointed out that a project of the scope illustrated here would require extensive model testing to verify and supplement the analysis. The design and analysis of such tests is beyond the scope of this manual. In addition, extensive field investigations at the island site would be required to establish the physical environment. These studies would include a determination of engineering and geological characteristics of local sediments, as well as measurement of waves and currents. The results of these studies would then have to be evaluated before beginning a final design. While actual data for the Delaware Bay site were used when available, specific numbers used in the calculations should not be construed as directly applicable to other design problems in the Delaware Bay area. II. STATEMENT OF PROBLEM A 300-acre artificial offshore island is proposed in the Atlantic Ocean just outside the mouth of Delaware Bay. The following are required: (1) characterization of the physical environment at the proposed island site and (2) a preliminary design for the island. Reference is made throughout this chapter to appropriate sections of the Shore Protection Manual. III. PHYSICAL ENVIRONMENT 1. Site Description. Figures 8-1] through 8-5 present information on the general physical conditions at the proposed island site. Site plans showing the island location, surrounding shorelines, and bathymetry are given. SCALES o 12 3 4N.MI o ai Location Bay oa aos ¥# AS an Figure 8-1. ws Sry ps 13 as M ‘ fo) 8 Location plan, offshore island. eS + : mS NG oy Sant 2% wi | 730 “wa3] 925° ie +40" 2.719 55076 eer OSIVES ~ a ex 8297 P™ (DUMPING. AREA ~ 153 97 764 1150 Chart 1/09 320 : Former USC & GS Chart No . 1000 *pueTst erzoyssjo fuetd 331g °7-g oan3Ty BLZL “ON 14BY4D SO BR OSN Jeud094 —— = a * b Me Pe 4 . o | GNNOBLNO™ INVT DissveL we famegeey adh t ) wo Fo \ 5 5 = JOJDMyDeIgG INOZ © NOLL VeGIS = . ans ODE « » ONNOGN/ = INYT : ® o & esa 6 dig sone ae, LOW gm es F yaeites am! TS, pub|s| pesodoig ,0S,8¢ as Sees UOIJOBIADN uD jj! 4 404 Daisy ebpeiq- ® (g20u 205) ~ WIYY AYYNOLLNW IIA ek a" ei 6E€ ey Fame dommes ane ime ce Perth ine seven bene Romy 8-3 *pueTST y8nozy} uoTjoes pue META eATIOedSIed *€-8 ain3styq pubs, Yohosy; UOl{IaS wolog burpsixz apis u0a20 rs = juauyanay PUOCIS!~ uassio9 j1om honey yyplag o's; 2 y AD) % LI Y, r py a-- i *soTtyoad woq}0q JO UOTIeIOT *+4-8 ain3sty BLZL ‘ON BUD SO B OSN Jeu04 =F Wgdal F aNnogino”™ Inv? INOZ © NO/L VIS a e re 0S, 8€ oF /Q 2/0u 228) . VILY AYYNOILNYIING ww o er 49747 ml thy a‘! Vion sialolees | { g TINN & 1 « 6E 8-5 ELEVATION ABOVE MLW, m ELEVATION BELOW MLW, m PRORIEES PROFILE 2 PROFILE 3 PROFILE 4 CAPE MAY TOWER CAPE MAY TOWER 7 =! .7OP OF WRECK, + CAPE HENLOPEN | TOWER @ PROPOSED ISLAND MLW Figure 8-5. 10 15 DISTANCE, KM Bottom profiles through island site. 20 2. Water Levels and Currents--Storm Surge and Astronomical Tides. The following calculations establish design water levels at the island site using the methods of Chapter 3 and supplemented by data for the Delaware Bay area given in Bretschneider (1959) and U.S. National Weather Service (formerly U.S. Weather Bureau) (1957) . a. Design Hurricanes. For illustrative purposes use hurricanes "A" and "B" given by Bretschneider (1959). Hurricane A Radius to maximum winds = R = 62.04 km (33.5 nmi) Central pressure AP = 55.88 mm Hg (2.2 in. Hg) Forward speed Vr = 27.78 to 46.30 km/hr (15 to 25 knots) (use Vp = 46.30 km/hr) Maximum gradient windspeed (eq. 3-63a) Wi - R(0.31)£] Une = 0-447 [14.5 Ge P,) where for latitude 40 degrees N f = 0.337 1/2 Urar = 0447 [14.5 (55.88) '~ - 62.04(0.31)(0.337)] Unie = 45-55 m/s (163.98 km/hr) Maximum sustained windspeed (eq. 3-62) for Vz = 46.3 km/hr Up = 0.865 Ue ae W655) Vp UR= 0.865 (163.98) + 0.5 (46.3) Up = 165 km/hr Hurricane B R = 62.04 km (33.5 nmi) Vr = 46.30 km/hr (25 knots) Ur = 8-05 km/hr greater than Hurricane A (8.05 km/hr = 2.23 m/s) Calculate AP for Us = (163.98 + 8.05) km/hr Unar = 172.03 km/hr (47.79 m/s) 8-7 PATHS OF STORMS OF TROPICAL QRIGIN DATE LEGEND august 1635 NOT SHOWN augusT 1788 NOT SHOWN SEPTEMBER 1815 NOT SHOWN SEPTEMBER tent SEPTEMBER 1969 NOT SHOWN OCTOBER 1878 «NOT SHOWN aveusT 1079 ° SEPTEMBER co —— avaust 1693 NOT SHOWN OCTOBER 000 SEPTEMBER 1903 NOT SHOWN SEPT.-OCT 1929 august 1933 SEPTEMBER 19308 SEPTEMBER 1944 avousT 1984 SEPTEMBER 1984 OCTOBER 1994 august 1955 avoustT 1986 august i950 auausT i9se SEPTEMBER 1958 SEPTEMBER 1960 FIGURES IN CIRCLES REPRESENT THE POSITION OF THE STORM ON THE DAY OF THE MONTH INDICATED. JAMAICA ho} Significant wave period (eq. 3-40): iy/s) 0.0379 a Hsxk d 3/8 Ux T= ——— = ‘tanh-102833) j= efi (ee & g v2 ea 3/8 UN where ows Uy = adjusted wind stress factor = 0.71 U, (eq. 3-28a) U, = surface windspeed (2) Example Calculation. U = 80 km/hr C2225 miis)) F = 89.3 km (89,300 m) D = 0.01 km (10.37 m) pemOsTe Uses = Oey (22422)2°2? = 32.19 m/s eh _ (9.806) (89,300) 7_ 845.09 2 2 - Uy (32.19) = 0.0981 gd _ (9.806) (10.37) us (32.19) 2 _ 0.283(32.19) [ 3/4] = 5 Ronee ea [990 (0.0981) x (eq. 3-39) 0.00565 (845.09) !/? tanh 3/4 eth [ 90, neglect) NE sts (0) enn 75a ENE i oS} RS D2) E +60.0 ax 30.0 ESE +82.5 eS Uae SE +105.0 Gar 15.0 SSE a hZA7/ 65) a. = 372 Se +150.0 a, = 60-0 SSW sV/265) Gye 82.5 SW +195.0 a, > 90, neglect) 1 The hindcast statistics are available for the Atlantic coast and the Great Lakes. They will be available for the Pacific and gulf coasts at a future date. 2 a. is the angle between the direction of wave approach and a normal to the shoreline. 3 Used for typical refraction calculations given on following pages. 8-26 N .8€ o6& *uOTIBOOT 4 UOTIEIS °C{-g eANSTy (L86L° 1V LS NOSHOO) M,Z ovl Vv v SHALAW LEL = SH WAWIXVA SHSLSW 8'L = SH NVAW SH3LIW 0082 = Hidaa AYOHS OL WY Lz M92 =N,€°Le v NOILVLS NVIIO DILNVILV ff ONWTAY WN =. 3YVMV130 8-27 Table 8-4. Hindcast wave statistics for station 4. Duration (hr) for These Periods Total Direction Duration (deg) 3-4.9s 5-6.9s 7-8.9s 9-10.9s 11-12.9s 13-14.9s 15-16.9s 17-18.9s 19-20.98 21-22.98 30-59 .9 0 - 0.49 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 _76 O- TO 0.49-m WAVE HEIGHT: 30-59 .9 0.50-0.99 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 — 30-59.9 1.00-1.49 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 269 30-59.9 60-89.9 90-119.9 120-149.9 150-179.9 180-209 .9 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 . 30-59.9 2.50-2.99 60-89.9 90-119.9 120-149.9 2 150-179.9 180-209 .9 30-59.9 3.00-3.49 60-89.9 90-119.9 120-149.9 150-179.9 180-209 .9 1 From Corson et al. (1981). Only durations > 1 hr are shown. 8-28 Table 8-4. Hindcast wave statistics for station 4 (continued). D 1 h f£ Direction uration (hr) for These Periods (deg) 3-4.9s 5-6.9s 7-8.9s 9-10.95 11-12.9s 13-14.9s 15-16.9s 17-18.9s 19-20.9s 21-22.9s 30-59.9 3.50-3.99 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 30-59.9 4.00-4.49 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 29 30-59.9 4.50-4.99 60-89.9 90-119.9 5.00-5.49 5.50-5.99 =) 120-149.9 150-179.9 180-209.9 i WNwWNLO 7 un 30-59 .9 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 30-59 .9 60-89.9 90-119.9 120-149.9 150-179.9 180-209 .9 30-59 .9 60-89.9 90-119.9 120-149.9 150-179.9 180-209 .9 Lol nN [oo en ee a) als. wliren Slo wnruse 30-59.9 6.50-6.99 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 2 Only durations > 1 hr are shown. 8-29 Table 8-4. Hindcast wave statistics for station 4 (concluded). Direction (deg) 3-4.9s 5-6.9s 7-8.9s 9-10.9s 11-12.9s 13-14.9s 15-16.9s 17-18.9s 19-20.9s 21-22.9s 30-59 .9 7.00-7 49 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 TOTAL FOR WAVE HEIGHT: 7.50-7.99 8.00-8.49 8.50-8.99 30-59 .9 9.00-9.49 60-89.9 90-119.9 120-149.9 150-179.9 = 180-209 .9 TOTAL FOR WAVE HEIGHT: 30-59 .9 9.50-9.99) 30-59.9 60-89.9 90-119.9 120-149.9 150-179.9 180-209 .9 TOTAL FOR WAVE HEIGHT: 30-59.9 60-89.9 90-119.9 120-149.9 150-179.9 180-209 .9 TOTAL FOR WAVE HEIGHT: 30-59 .9 60-89.9 90-119.9 120-149.9 150-179.9 180-209 .9 TOTAL FOR WAVE HEIGHT: 60-89.9 90-119.9 120-149.9 150-179.9 180-209.9 TOTAL FOR 9.50 TO 9.99-m WAVE HEIGHT: 2 Only durations > 1 hr are shown. 8-30 (L86L°1V 13 NOSHOO) *(UOTIOBITp YORS UT ANDD90 SaAeM BUT JO JUsdIed Jusseadez saTSueTI3 ut SzZequnu ‘fuOoTIO=eITp yore WorzZ BuTAINDD0 AYSTay YUeTeFJIP Jo saaem Jo yuadred aie S3uTI DTAJUSeDUOD UTYIIM SJequNU) soURIQUe Aeg oIeMETEG ay} JJO 4 UOT IeIS JOJ WeiseTp asaeM *OT-g aeaN3tTy 66" 6y- 66° 67° 66° 6y° 66° 66° LHOISH JAAVM Z2-00° c-0S° €-o0°€ £€-OS°€ v¥-GO'¢ v-OS"? by Y3A0 S$3S¥3 CprPrss elo) Shelf. (7 NIGIEELS ES 8-31 10123N.MI ty of Delaware Bay for in vicini shoreline alignment General Figure 8-17. 1Se lys ion ana refract 8-32 (3) Typical Refraction Calculations. Use d= 12.0m at structure. Shoaling Coefficient: , corn 228) 2 | K = re = Sadie (eq. 2-44) SS sinh (ee) equivalently, 4 C, Wi Na eT? W2 Ss 2nC 4mL where H = wave height Hy = deepwater wave height equivalent to observed shallow-water wave if unaffected by refraction and friction L = wavelength C = wave velocity C, = deepwater wave velocity IDS wave period Refraction coefficient and angle: sin a = (5) sin a (eq.2-78b) Note that equation (2-78b) is written between deep water and d = 12.0 m , Since bottom contours and shoreline have been assumed straight and parallel. For straight parallel bottom contours, the expression for the refraction coefficient reduces to — be WY/P je cos a) W/2 R b cos a fe) where b = spacing between wave orthogonals by = deepwater orthogonal spacing 8-33 Recall, 2 LS ca = deepwater wavelength in meters (eq. 2-8a) and = = = tanh (24) (eq. 2-11) O O Typical refraction-shoaling calculations are given in the tabulation below. Calculations for various directions and for a range of periods follow (see Tables 8-5 and 8-6). The following tabulates the results of example calculations for waves between 150 and 179.9 degrees from North (angle between direction of wave approach and normal to the shoreline in deep water = Oe 45 degrees) ; d= 27S Ome 0.4806 | 0.98856] 0.99536 0.9863 0.2136 0.92142; 0.90270 0.8831 0.1201 0.92036} 0.75913 0.8426 0.0769 0.95926] 0.63887 0.8540 0.0534 1.01180] 0.54670 0.8860 0.0392 1.06800] 0.47580 0.9255 0.0300 1.12500] 0.42050 0.9682 0.0237 1.18130] 0.37632 2 1.0118 Column Source of Information (2) From equation (2-8a). (3) 12.0 m divided by column (2). (4) Equation (2-44) or Table C-l, Appendix C. 5) Table C-1, Appendix C: a = tanh (222), O (6) Equation (2-78b) cos a, WZ es acres io (8) Column (4) times column (7). KK, can also be obtained from Plate C-6, Appendix C. Table 8-5. I iGs)) a (deg) Ks Ky We (33) a (deg) Breaker angles and refraction and shoaling coefficients in d = 174 Fike 4 6 8 10 12 14 14.92 13.51 133 oa” 8.13 7.07 6.25 5.59 0.9886 0.9214 0.9204 0.9593 1.012 1.068 Te 1.181 0.9998 0.9967 0.9925 0.9897 0.9878 0.9866 0.9857 0.9852 0.9884. 0.9184 0.9135 0.9493 0.9995 » 1.0537 1.1090 1.21638 16 18 4 44.73 0.9886 Oi, 0.9863 6 39.67 0.9214 0.9584 0.8831 8 10 12 14 16 18 32.47 26.86 22.74 19.66 17.30 15.43 0.9204 0.9593 1.012 1.068 1.125 1.181 0.9155 0.8903 0.8756 0.8670 0.8610 0.8565 0.8426 0.8540 0.8860 0.9255 0.9682 1.012 4 6 8 10 12 14 16 18 74.03 60.67 47.16 38.11 31.88 21330 2396) 2131 0.9886 0.9214 0.9204 0.9593 1.012 1.068 Fe25 1.181 0.9710 0.7271 0.6170) “O-5735, (0.55215 (055398) 0.5322 0.5271 0.9590 0.6699 0.5678 0.5501 0.5586 0.5765 0.5987 0.6227 8-35 Table 8-6. Summary of refraction analyses in d = 12 m (numbers given in table are KcoKp ). Wave Period Direction from N (deg) 30-59 ..9 0.670 0.550 0.559 60-89 .9 0.883 0.854 0.886 90-119.9 0.918 0.949 1.000 120-149.9 0.918 0.949 1.000 150-179.9 0.883 0.854 0.886 180-209 .9 0.670 0.550 0.559 1 Angle between wave orthogonal and normal to the shoreline. Refraction-shoaling coefficients are summarized graphically in Figure 8-18 on the next page. (4) Transformation of Wave Statistics by Refraction and Shoaling. The refraction-shoaling coefficients calculated previously will be used to transform the deepwater wave statistics given in Table 8-4 (see Tables 8-7 and 8-8 and Figure 8-19). The resulting statistics will be only approximations since only the significant wave is considered in the analysis. The actual sea surface is made up of many wave periods or frequencies, each of which results in a different refraction-shoaling coefficient. 8-36 *potzed aAem pue UOTIOPITP eAeM JO UOTIOUNF e& Se JUSTOTJJe0D SuTTeoys—uoTIoeAZOY *QI-g oansTy (S) 1 GOlWad SAVM 8L OL vl Zt OL 8 9 v Tt ‘v0 a hhh mei 44 t tp onan face it i { me ial 4 90 Ui eat mB L ga E ! 80 cae ; oot car geggee! eveetoea °H/H yO T = AySyy ++ a t Bae Besa soog5 maneaubaued| 7 ant Ol + To ~ aeaw Ji ot : raat ff t 7 t t | f Coe : q a a + j } i page at tf Tee 1g : rH + 4 i "pil 8-37 Table 8-7. W260 im 4 Angle from North (deg) Deepwater Height Range (deg) 30-59 .9 180-209.9 30-59.9 5.359 180-209.9 cs 60-89 .9 . 8.476 8.540 8.860 9.255 9.682 10.120 150-179.9 90-119.9 9.184 9.135 9.493 9.995 10.537 11.090 11.638 120-149.9 ql) 30-59.9 6.364 5.394 5.226 5.307 5.477 5.688 5.916 180-209 .9 <9.5 60-89 .9 8.389 8.005 8.113 8.417 8.792 9.198 9.614 150-179.9 90-119.9 8.725 8.678 9.018 9.495 10.010 10.536 11.056 120-149.9 (1) 30-59 .9 6.029 5.110 4.951 5.027 5.189 5.388 5.604 180-209.9 <9.0 60-89.9 7.948 7.583 7.687 7.974 8.330 8.714 9.108 150-179.9 90-119.9 8.266 8.222 8.544 8.996 9.483 9.981 10.474 120-149.9 (1) 30-59.9 5.694 4.826 4.676 4.748 4.900 5.089 5.293 180-209 .9 <8.5 60-89 .9 7.506 7.162 7.259 7.531 7.867 8.230 8.602 150-179.9 90-119.9 7.806 7.765 8.069 8.496 8.956 9.427 9.892 120-149 .9 (1) 60-89.9 7.065 6.741 6.832 7.088 7.404 7-746 8.096 150-179.9 ql) 90-119.9 7.347 7.308 7.594 7.996 8.430 8.872 9.310 120-149.9 Numbers represent transformed wave height. N 75 deg E (in deep water) will be 9.255 meters high Numbers in parentheses represent the number of hours direction. For example, deepwater waves between 9.5 in the one year of hindcast data. Equivalently, the between 5.307 and 5.586 meters for 1 hour. Transformed wave heights: d 6.699! 8.831 significant heights and periods in (s) Wave Period ~ J nN co J ~ v nN 1 5.586 5.765 (1) 4.469 4.612 ey For example, a 10-meter-high deepwater wave with a period of 14 seconds approaching from at the island site (i.e., in a depth of 12.0 meters). waves are below given height and above next lower height for given period and and 10 meters in height with a period of 12 seconds were experienced for 1 hour wave height at the structure site for the given deepwater wave statistics will be 8-38 Table 8-7. 12.0 m Angle from North (deg) ~_ 1) 30-59 .9 180-209.9 60-89.9 165 150-179.9 105 135 90-119.9 120-149.9 ~_ wu = an - > 0 uw uw oo LY ~ > ~N t=) je a fee |e 30-59 .9 180-209.9 7S re) 75 165 60-89 .9 150-179.9 ~ u ~ uu N > wu 1) 105 135 90-119.9 120-149.9 30-59.9 195 180-209 .9 <6.5 45 60-89.9 165 150-179.9 - wu 105 135 90-119.9 120-149.9 - uw 105 90-119.9 120-149.9 1 Numbers represent transformed wave height. N 75 deg E (in deep water) will be 9.255 meters high Numbers in parentheses represent the number of hours direction. For example, deepwater waves between 9.5 in the one year of hindcast data. Equivalently, the between 5.307 and 5.586 meters for 1 hour. Transformed wave heights: d 5.024 2 6.623 6.888 4.689 6.429 4.354 5.740 =~ = - ~ ~ vy uu . ~N un i) (1) (6) 75 45 30-59.9 4.019 3.407 3.301 3.352 3.459 3.592 3.736 195 180-209.9 a) (3) (1) (3) <6.0 45 75 60-89.9 5.299 5.056 5.124 5.316 5.553 5.809 6.072 165 150-179.9 (eb) q) qa) (1) 15 105 90-119.9 5.510 5.481 5.696 5.997 6.322 6.654 6.983 135 120-149.9 (2) @) 75 45 30-59.9 3.684 3.123 3.026 3.072 3.171 3.293 195 189-209.9 (2) (4) (1) (1) (2) (3) <5.5 45 75 60-89 .9 4.857 4.634 4.697 165 150-179.9 q) q) significant heights and periods in (continued). Wave Period (s) i co Lt a (2) (2) 4.259 4.126 4.190 (1) (1) 6.405 6.645 6.941 + - a = a 4.234 4.490 4.670 6.320 7.262 7.590 6.851 7.903 8.318 8.729 3.975 4.036 4.191 4.359 5.898 wn 6.479 6.777 (1) 7.084 ~ i - 6.395 6.645 : ey 3.576 3.631 (1) 5.551 7.376 7.763 8.147 wo ~~ @ a a . . wo i oo oO Nn Nn 3.691 3.747 3.892 4.048 5.477 6.293 6.578 =~ = L 5.938 6.170 6.849 7.209 7.565 a . + io] n For example, a 10-meter-high deepwater wave with a period of 14 seconds approaching from at the island site (i.e., in a depth of 12.0 meters). waves are below given height and above next lower height for given period and and 10 meters in height with a period of 12 seconds were experienced for 1 hour wave height at the structure site for the given deepwater wave statistics will be 8=39 Table 8-7. Transformed wave heights: d = 12.0 m (continued). Angle from North 30-59.9 180-209 .9 60-89 .9 150-179.9 90-119.9 120-149.9 30-59 .9 180-209 .9 60-89 .9 150-179.9 90-119.9 120-149.9 30-59 .9 180-209 .9 60-89 .9 150-179.9 90-119.9 120-149.9 30-59.9 180-209.9 60-89.9 150-179.9 90-119.9 120-149.9 30-59 .9 180-209 .9 60-89 .9 150-179.9 90-119.9 120-149.9 significant heights and periods in Wave Period (s) = NR —_ - a ~ we LL nN nN w os w ~ ry eS . ~ _~ uw ) ~ 7 n + wo = El an ea Numbers represent transformed wave height. For example, a 10-meter-high deepwater wave with a period of 14 seconds approaching from N 75 deg E (in deep water) will be 9.255 meters high Numbers in parentheses represent the number of hours direction. For example, deepwater waves between 9.5 in the one year of hindcast data. Equivalently, the between 5.307 and 5.586 meters for 1 hour. at the island site (i.e., in waves are below given height and 10 meters in height with wave height at the structure 8-40 a depth of 12.0 meters). and above next lower height for given period and a period of 12 seconds were experienced for 1 hour site for the given deepwater wave statistics will be Table 8-7. Transformed wave heights: significant heights and periods in d= 12.0 m (concluded). Deepwater Angle from Wave Period (s) Height North (m) (deg) ~_ uu 30-59 .9 180-209 .9 > we) 60-89 .9 150-179.9 90-119.9 120-149.9 30-59 .9 180-209.9 60-89 ..9 150-179.9 90-119.9 120-149.9 60-89 .9 1.329 150-179.9 (26) 90-119.9 1.499 120-149.9 (9) u = ee e ~“ > ~ = wo a = as fas ]me [oe fee [oe N - > wo av > wn = ~ a av 9 2 4 a (5) 30-59.9 0.559 180-209 .9 60-89 .9 0.886 0.926 150-179.9 (1) 90-119.9 1.000 1.054 120-149.9 (3) 0.279 0.2883 0.299 0.311 (3) 60-89 .9 0.443 0.463 0.484 0.506 150-179.9 (2) 90-119.9 0.527 0.555 0.582 120-149.9 1 Numbers represent transformed wave height. For example, a 10-meter-high deepwater wave with a period of 14 seconds approaching from N 75 deg E (in deep water) will be 9.255 meters high at the island site (i.e., in a depth of 12.0 meters). uu S i Oo ] a u ~ wu > uw n wu _ x PS “N o B a ajo 2 Numbers in parentheses represent the number of hours waves are below given height and above next lower height for given period and direction. For example, deepwater waves between 9.5 and 10 meters in height with a period of 12 seconds were experienced for 1 hour in the one year of hindcast data. Equivalently, the wave height at the structure site for the given deepwater wave statistics will be between 5.307 and 5.586 meters for 1 hour. 8-41 The following tabulations are to be used with Table 8-7. The first lists the number of hours waves of a particular height were present at the structure site. (For example, for waves 7 meters high, with a 12-second period from 75 degrees north (from Table 8-7), wave height at the structure was between 7.088 and 6.645 meters for 1 hour. Therefore, wave height was above 7 meters for 1 x 0.088/(7.088 - 6.645) = 0.199 hour. Wave height between 6 and 7 meters was 1 - 0.199 = 0.801 hour.) The second tabulation sums hours for a given wave height and associated frequency. Note that the total hours of waves less than 3 meters high is given, although the listing for these waves is either incomplete or not given; these totals were obtained by completing the calculations using the data in Table 8-7. Computation of Number of Hours for Wave Groups of the Following Heights at the Structure > 7n 6 to 7m 5 to 6m 4 to 5m 3 to 4m 2 to 3m 0.801 0.948 1.000 1.000 1.000 1.000 0.605 0.395 0.916 1.084 1.357 0.643 0.133 0.867 1.000 1.000 0.871 2.129 1.000 1.000 1.000 3.000 1.000 1.000 3.000 0.690 0.710 1.000 8.000 1.000 3.000 7.000 2.000 1.000 1.000 1.000 1.000 1.000 3.000 1.000 1.000 1.000 6.000 0.671 0.329 1.000 0.053 0.947 3.000 0.466 0.534 0.866 1.134 1.000 0.662 6.338 0.133 0.867 0.866 1.134 0.378 3.622 0.258 0.742 1.518 1.482 0.506 0.494 0.594 0.406 3.794 2.206 11.000 1.265 0.735 4.000 1.000 6.000 13.000 2.000 3.000 10.000 1.000 3.000 3.000 3.000 8-42 Computation of Number of Hours for Wave Groups of the Following Heights at the Structure 6 to 7m 5 to 6m 4 to 5m 3 to 4m 2 to 3m CRUD AWNUONNOK SKU Lome doe G dom & ted.a CSCOWFWUNOFNO Tid Ox Ch Ont On07 5 = . 4.354 11.071 46 .382 146.441 Incomplete Listing Total hours in record = 8766 1 Height (m) Total Hours Frequency 1.199 0.0001372 5.553 0.000634 16.091 0.001836 60.606 0.006914 208.307 0.023763 769.689 0.087804 2278.767 0.259955 8766 1.0000 J Number of hours wave height equalled or exceeded given value. 2 7/.99 hours/8766 hours = 0.000137. 8-43 Table 8-8. Deepwater wave statistics (without consideration of direction).! Significant Wave Cumulative Probability of Height (m) Hours Exceedance Aw 0.00011 0.00023 0.00034 0.00046 0.00091 0.00160 0.00217 0.00308 0.00535 0.00844 0.01358 0.02225 0.03593 0.06046 0.09970 0.14773 0.22325 0.33527 0.44410 1.00000 OF rFNNMWWEHEEUUDAAINNWOAWOWO e Cane” :O:. Gin OF OW NOUWONOMNONONONONONOWNS < < < < < < < < < < < < < < < < < < < 1 Wave statistics are derived from data given in Corson et al. (1981). Curves showing deepwater wave height statistics and transformed statistics are given in Figure 8-19. *SuTTeous pue uoT}OeAZOeA Aq uoTIeMIOFJSUeIA ues00 UT peqeIoues SoAePM JIOF SIYSTSY DBAEM JURDTJTUSTS Jo adUeTAINDD0 jo Aduenberg *61-g o21n8Ty im) t0°0 t0000°0 | TT] 0 I * | | oan TMDL T | 1 T T t T mi | Hit Hi} i] i (} i t | ll if | HAUNT i AAA | it | i Swe} (A i} i [ mt h it i ae t ATT il i i il i IA HA Fa i Ut i - H \ ; Lt i TT ! i eee | | | | Mntnnanae tLe TTT 1 i T Ti 1 T rT rs | ff | } i ANIA Ga alin | tt Il H 1 NH uit 1 at } Nit fl | | ithe i i fh pT ; 1 TTT 00D A A ATA ET mul tt if CTT NT | , 7 rn (papnjoul uoljIe1as HH HHH THUIAMUIHEHECTSOUAOUBUB ; HTT mt UE iI! pue Buyjeoys Jo s19a44a) HOTA ATT | | I tt Aguanbay 1a1eM-Moy/eys azeu/xosddy 9 a rt | x». iI i 1TH ! 1) 1 HITT PTT WI a I | HUT ULSTarLUAL it lf a HH Ti i TTT iL [cjalay) i wii MTT 1 T r f 1 CULL PL ED t thet TTT 1 se rihtht 1 MiHittth ht it H i i oS I] HT iit sit Z Ue HTT | } i S I | | Hil Mitt y WAIL HN Q T t 1 T i aa i wv xy 1 ThtTy i| | | ree | | Ht 8 | | i i] teh, | ] TH T | f | a | 1 Tt it i SP tT : Hot - 1 u 1 s | } | 1 CAC TT il WII | iN | | pitt (S912S1222S HILATHSSASHATTUI t ot ppb st ataiaa QAEM JSeIPUIY WO) ATT TTT iil) Aguanbes, Jazemdeeq ol i TET h | | T | HANA | ana Hl HTT bet fe uit WT T | TTT | i Ui l Hil i i Ne T 1 | t H | III a T Zl l} Loo™ © v o a “aor on 2) nu -oornopn o a -emorno pn ¥ o nu -omorown o nu — 8-45 W ‘LHSISH IV. PRELIMINARY DESIGN 1. Selection of Design Waves and Water Levels. The selection of design conditions is related to the economics of construction and annual maintenance costs to repair structure in the event of extreme wave action. These costs are related to the probability of occurrence of extreme waves and high water levels. There will usually be some design wave height which will minimize the average annual cost (including amortization of first cost). This optimum design wave height will give the most economical design. DESIGN WAVE HEIGHT GIVING fe MOST ECONOMICAL DESIGN | | | i] i] 1 TOTAL AVERAGE ANNUAL COST = 3 Z oO 7 = & REPAIR COSTS DESIGN WAVE HEIGHT Intangible considerations such as the environmental consequences of structural failure or the possibility of loss of life in the event of failure must also enter into the decision of selecting design conditions. These factors are related to the specific purpose of each structure. The following design conditions are assumed for the illustrative purposes of this problem. a. Water Levels (MLW datum). (1) Storm surge (less astonomical tide): use 3.0m. (2) Astronomical tide (use water level exceeded 1 percent of time) ispeelee Dems (3) Wave setup (assumed negligible since structure is in relatively deep water and not at beach). b. Wave Conditions on Bay Side of Island. (1) Use conditions with 100-year recurrence interval: H a 3.59 m au 5 Yok & Ce Wave Conditions on Ocean Side of Island. From hindcast statistics (wave height exceeded 0.1 percent of the time in shallow water), use Note that the reciprocal of an exceedance probability associated with a particular wave according to the present hindcast statistics is not the return period of this wave. For structural design purposes, a statistical analysis of extreme wave events is recommended. 2. Revetment Design: Ocean Side of Island. The ocean side of the island will be protected by a revetment using concrete armor units. ae Type of Wave Action. The depth at the site required to initiate breaking to the 6.0-meter design wave is as follows for a slope in front of the structure where m = zero (see Ch. 7, Sec. 1): or where Hp, is the breaker height and dp, is the water depth at the breaking wave. Since the depth at the structure (d_,* 12.0 m) is greater than the computed breaking depth (7.7 m), the structure will be subjected to non- breaking waves. b. Selection Between Alternative Designs. The choice of one cross section and/or armor unit type over another is primarily an economic design requiring evaluation of the costs of various alternatives. A comparison of several alternatives follows: Type of Armor Unit: Tribars vs Tetrapods StructuresSilopesigal sl. W222 one ands lis3 Concrete Unit Weight: 23.56 N/a Diels kN/m> 5 A570 kN/m> The use of concrete armor units will depend on the availability of suitable quarrystone and on the economics of using concrete as opposed to stone. (1) Preliminary Cross Section (modified from Figure 7-116). CREST ELEVATION VARIES MAX SWL__4.5m PRIMARY COVER LAYER FILL MLW MIN SWL —9.91 m UNDERLAYER SECONDARY “200 6000 Wr (Onn 15 O° ~ Te Wa = WEIGHT OF INDIVIDUAL ARMOR UNIT Wr = WEIGHT OF PRIMARY COVER LAYER IF MADE OF ROCK Ta = COVER LAYER THICKNESS tis THICKNESS OF FIRST UNDERLAYER @ = ANGLE OF STRUCTURE FACE RELATIVE TO HORIZONTAL (2) Crest Elevation. Established by maximum runup. Runup (R) estimate: H, = 6m d= 1665) m T = ? (use point on runup curve giving maximum runup) 7 = 10:2 = 2./5 (use Fig. 7-20) s 1 Crest Elevation : Waves over 6 m will result in some overtopping. 8-48 (3) Armor Unit Size. (a) Primary Cover Layer (see Ch. 7, Sec. III,/7,a). W= (eq. 7-116) where W = mass of armor unit m i} design wave height = 6 m W, = unit weight of concrete 23.56 KN/m> , 25.13 kN/m> , and 26.70 kN/m> cot 8 = structure slope 1.5, 2.0, 2.5, and 3.0 Wp S,, = w, = ratio of pe oa unit weight to unit weight of water Kp = stability coefficient (depends on type of unit, type of wave action, and structure slope) The calculations that follow (Tables 8-9 and 8-10 and Figs. 8-20 through 8-25) are for the structure trunk subjected to nonbreaking wave action. Stability coefficients are obtained from Table 7-8. 8-49 Table -9. Required armor unit weights: structure trunk. Slope Armor Unit Wa" Percent Ga) (cot @ ) Stability (metric tons) Damage for Coefficient, 1% Wave Tetrapod 1 l metric ton = 1000 kg. 2 Represents damage under sustained wave action of waves as high as the l percent wave, not the damage resulting from a few waves in the spectrum having a height H, = 1.67 H, . 3 H) = average height of highest 1 percent of waves for given time period 1.67 H s H) = 1.67 (6) Hy = 10m “ITI-Z pue 60I-Z seanstg worz ‘uin} ut ‘peaTiep e19eM YyoTYM *T7Z-g pue O7Z-g SeANn3Ty wWorly peuTWAIe}ep SaWNTOA |}zeI1DU0D pue sjTuN jo sisquny Zz 9 uTs (OOT) (A®Te 38919 + 16°6) ar 76E°S G7S79 Sly 2) €°92SGS 160°8 0° 8697 L8L°OT GOOeLS 7€8°9 o°7S179 T0Z°8 €°9LSS TS2°OT 0° 8694 899° ET G°€ELlEe podeajay c16°8 G7SV9 769° OT © 9LSS 89° ET 0° 869% 778° LT GT ESLE C7579 €9ILGS 0° 869% G°EeLe LOVES Ca S79 09S°9 €°92GS T0¢°8 0° 86947 7€6° OT SS /AS areqTial (XG 1b 2 AISA) ¢SS°8 €°92SS 769° OT 0° 869% 6SC° FI SSEELE W) o01njz0n14s “nN. §satun (suo} (Ww) 2e1n}0nI13s qtun ( 36 W QOT aed aiowi1y jo dTAjJew) jo Ww QOT aed jow1y jo adj 9}e19U0D FO sUNTOA JAequNN peatnbey Um eoay izehe7] 10WAYy I *yuna} e1njonaAZS Jo AekeT AaAOD AXewTAd :9}3eTDU09 Jo ouwNTOA ‘QT-g eTqeL 8-51 < 2) l= Cc = m v m aD (Ss = + z © z4 OOL Yad SLINN 4O Y3A8SWNN *sieqtiq :ejep BuTAveUT3Uy °O7-g eANSTYy c4/NAZZ=7M 'SNOL OINLIW ‘YVEIYL TVNGIAIGNI 40 LHOISM L te , Ssssasnitossatsti ‘ ae tH tT it 8-52 SNOL DINLIW ‘HVEIYL 40 LHOISM z4 OOL Yad SLINN 4O YASWNN *spodeijeq :ejep 3uTAseuTSUy °{[7-g eANsTy e4/N> ZZ ="m ‘SNOL OINLAW ‘GOdVY¥L3L IWNGIAIGNI 40 LHDISM St ve & (4 4 02 61 dt SL St vt el (as tt Ol 6 8 ZL 9 S v € 4 L 0 8-53 SNOL DINLAW ‘GOdv¥13l 4O LHOISM gL j . sett sesaiitosstiiians PEEEEEEEEEEEEEE HEH Cool BEE oocae s H Gz (6 HHH PEPE aeuem EEE F rch if : i CCH aa ae v aneee cl LH ESS ue if H H H : F eee S s H jaan GL = 9 oe tt o m ite 7 : m : one oo . ¢ HE ce : ool Ag se C : H 5 ; rr | SZL OL i Z| Fe 7 ce sritiae C] a iiss Cy] H E EH Boogo (afetaala vl SL 9L it =k (2) VOLUME OF CONCRETE PER 100m OF STRUCTURE, THOUSANDS OF m? 10) 2 4 6 8 10 12 14 WEIGHT OF TRIBARS, METRIC TONS Figure 8-22. Volume of concrete required per 100 meters of structure as a function of tribar weight, concrete unit weight, and structure slope. 8-54 NUMBER OF ARMOR UNITS REQUIRED PER 100m OF STRUCTURE, THOUSANDS LINE OF CONSTANT STRUCTURE SLOPE ees eee LINE OF CONSTANT CONCRETE DENSITY WEIGHT OF TRIBARS, METRIC TONS Figure 8-23.Number of tribars required per 100 meters of structure as a function of tribar weight, concrete unit weight, and structure slope. 8-55 = an oO = [) oOo 90 80 F —— =LINE OF CONSTANT STRUCTURE SLOPE eeee @= LINE OF CONSTANT CONCRETE DENSITY VOLUME OF CONCRETE PER 100m OF STRUCTURE, HUNDREDS OF m? 4 5 6 7 8 ) 10 11 12 13 14 15 16 17 18 WEIGHT OF TETRAPODS, METRIC TONS Figure 8-24. Volume of concrete required per 100 meters of structure as a function of tetrapod weight, concrete unit weight, and structure slope. 8-56 Seeraze NUR AY on HA rt A PUTA RST TNA TTT LINE OF CONSTANT STRUCTURE SLOPE SONVSNOHL ‘JYNLONYLS 4O WOOL Yad GAYINDAY SGOdVHLaL 40 YSSWNN WEIGHT OF TETRAPODS, KILOTONS Number of tetrapods required per 100 meters of structure as a function of tetrapod weight 2s slope. Figure 8 and structure > concrete unit weight 8-57 (b) Secondary Cover Layer. The weight of the secondary cover layer = a is based on the weight of a primary cover layer made of rock We PRIMARY COVER LAYER UNDERLAYER SECONDARY COVER LAYER We = weight of primary cover layer if it were made of rock W Ta = weight of secondary cover layer w = unit weight of rock = 25.92 eee K_ = 4.0 for stone under nonbreaking wave conditions pee ste tons = ~ aK, S52 1 : cot 6 W R 10 (metric tons) (c) Thickness of Cover Layer. Primary and secondary layers have the same thickness. fe Si) ky A (eq. 7-121) 8-58 where r, = thickness of cover layer (m) n = number of armor units comprising the layer W, = weight of individual armor unit (metric tons) Ciel unit weight of stone material (concrete or quarrystone) ky = layer coefficient of rubble structure (d) Number of Stones Required. where 2/3 w le ip R An ky ( = ais) (ear = Ceqiey 7/—1122)) number of armor units or stones in cover layer Z i] zm i A = area (qu) P = porosity (%) Weight of Armor Layer Thickness (m) When n Individual Stone Unit Weights Below Stones, W (metric tons) | k, and P from Table 7-13. (e) Volume and Weight of Stones in Secondary Cover Layer. Se Sees = ee ee N00) im WHE Slee EMS Number of stones in secondary cover layer: & Wp Ws ee ky 10 w, (Wp in metric tons and w, = unit weight of rock = 25.92 kN/m?) r 10: w 1/3 n Se! = number of layers ky g Wp P 10 we, ars Ue SANs toai enw R Bale 1Onwe\Ghe a ee 7“ Pr _ om Si7/ ie R ky g We A 100]}\ g We ae 6.3 AY , we R g Wp Volume of secondary cover layer: V= r,A Volume of rock in secondary cover layer: VR = 0.63V Weight of Rock: & Wp W= 10 Np or W = 0.63 V Wai Table 8-11. Summary of secondary cover layer characteristics for tribars and tetrapods. A per 100 m Nr Volume of Weight of of structure per Secondary Cover Rock per tri tri ees Satie 100 m Layer Pst 100 m 100 m (m~) Tribar Tetrapod (4) Thickness of Underlayer. Quarrystone ky = 1.00 DS Syl = 3 We = 25.92 kN/m n =2 8-61 Weight of Weight of an Thickness of Number of Stones Weight of Rock Armor Unit, Underlayer Stone,| Underlayer, per 100 m° of per 100 m cf W, (metric W, (metric ie, (Gy) Underlayer, Underlayer il To tons) (metric tons) ° 1.8 1.6 1.4 er 1.0 0.8 0.6 0.4 P =n 37. \ (25.92(10) \?/3 N,=Ank, ( =) fe) = (100)(2)(1.00) (1 a) 25532000) W,8 2/3 he. (25-4) ? W A Weight _ Wy Tun. NO. 100 m The equation for the volume of the first underlayer is as follows: *t ee | pete i ra Toot IN Dosim ie.” 2 sin 0 ies (equation derived from preliminary geometry of cross section on page 8-48) where E = crest elevation (m above MLW) ty = thickness of cover layer (m) 3 ie thickness of first underlayer (m) vy = volume of first underlayer per 100 m of structure Ge) The equation for the volume of the core per 100 m of structure is as follows: 1 ere Ae Vo. == (oO een (1.5 + cot 6) (100) e 7 cos @ 8-62 (equation derived from preliminary geometry of cross section on page 8-48) (5) Volume of First Underlayer. The volume per 100 m of structure (in thousands of m?) is shown in the tabulation below. Armor Unit! size (metric 1 Valid for tribars and tetrapods because V, depends only on 6 and r (ry) is dependent on the armor unit size, but not the type). See Figure 8-26 for a graphic comparison of costs. 8-63 = = MADE IN UB. A. DIETZ3EN CORPORATION VOLUME OF FIRST UNDERLAYER PER 100m OF STRUCTURE, 1000m? NO. 340-20 DIETZGEN GRAPH PAPER 20 X 20 PER INCH 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 WEIGHT OF ARMOR UNIT, METRIC TONS Figure 8-26. Volume of first underlayer per 100 meters of structure as a function of armor unit weight and structure slope. 8-64 (6) Volume of Core: Tribars and Tetrapods. Volume per 100 m of structure (1000 m2) is shown in the following tabulation: Weight of Tribar or Tetrapod 3.0 (metric tons) 95.896 96.583 97.273 98.063 98.956 100.054 101.258 102.773 See Figure 8-27 for a graphic comparison of costs. (7) Cost Analysis: The following cost analysis will be assumed for the illustrative purposes of this problem. Actual costs for particular project would have to be based on the prevailing costs in the project area. Costs will vary with location, time, and the availability of suitable materials. Unit costs of concrete are shown in the tabulation below. W Cost 8-65 White pane HA i L Hy EH pierdipredted tt eWOO0L “AYNLONYLS 4O WOOL Y3d 3HOD 4O AWNTIOA WEIGHT OF ARMOR UNIT, METRIC TONS Volume of core per 100 meters of structure as a function of armor unit weight and structure slope. 2 ke Figure 8 8-66 (a) Cost of Casting, Handling, and Placing MTribars and Tetrapods. Cost per unit is as follows: cot = 1.5 and 2.0 cot = 2.5 and 3.0 Weight of Weight of Armor Unit Armor Unit Cost per Cost per Metric Cost per Cost per Cost per Metric Cost per (tons) (metric tons)]| Ton ($) Ton ($) Unit ($) Ton (S$) Ton ($) Unit (S$) 38.28 40.63 43.17 45.50 47.03 46.67 48.13 74.38 The tabulated costs are graphically presented in Figure 8-28. (b) Rock costs. In place, when WS 25.92 N/a ; Weight Cost per Cost per (metric tons) Ton (S$) Metric Ton ($) 1.36 to 1.81 2 1 WoeNk Te) Wass 1 0.45 to 0.91 up to 0.5 up to 0.45 Quarry run Quarry run 8-67 WEIGHT OF ARMOR UNIT, METRIC TONS 1.81 3.63 5.44 7.26 9.07 10.89 12.70 14.51 1000 900 800 at : 700 —& : : : ++ 600 HE tf. a e sangeet = iauuaes! reer E Z fe 3s seesepuseubasssbst oa ra COT 6 = 2,5 AND 3.0 Rett ee a 500 B 3 at 400 : 300 gestirntii 200 ssaasas: posse at s 100 FS Esesaaal +r t oni { (0) f on 2 4 6 8 10 12 14 16 WEIGHT OF ARMOR UNIT, TONS Costs of casting, handling, and placing concrete armor units as Figure 8-28. a function of unit weight and structure slope. 8-68 (c) Total Cost per 100 Meters of Structure. The following tabulation sums revetment cost by weight of tribar unit: Weight of Wp Concrete Cost Handling Costs First Secondary Armor Unit 3 cot 6 per 100 m of per 100 m of UREEPNES AS Cover Payer Core (metric tons) (kN/m~) Structure Structure Cost Cost Cost 1793.62 3223.25 2215.17 3872.63 2503.35 4480.93 2768.60 4950.87 468.28 1822.10 3182.87 535.52 2245.33 3833.85 589.98 2533.01 4417.97 642.47 2798.43 4832.34 1846.66 3276.15 2269.27 3899.62 2557.31 4486.95 1Ai1 costs are in thousands of dollars per 100 m of structure; all the intermediate steps of cost calculation are not included. For a graphic cost comparison, see Figure 8-29. 8-69 5.0 COT 86 =3.0 Ge s ; S063 a0 a rH a masses ous = Be: + 3. : sobs a1 82% 1 + inpud akganamoan shens ce Ht pezepecee! ag eSes Ser ams oaas ot + z ot Hort + Ee T + : t ae tits poanasas ec! Haft we +t ap poeapooan : +H Tr e = et : + Fosscecesbessseee ; eu beees pensuzess 45 COT 0 = 25 : eee: d 7 rH t Tt Et ae Ho suggesecat a pabes cosgucessent oni Goes sscusses 2 pae ee Sega are =a spacubs! COST PER 100m OF STRUCTURE, MILLIONS OF DOLLARS eae LINE. OF CONSTANT STRUCTURE “SLOPE So LINE OF CONE I CONCRETE DENSITY Tepes 1 2 3 4 5 6 7 8 9 10 WEIGHT OF TRIBAR, METRIC TONS 14 15 Figure 8-29. Total cost of 100 meters of structure as a function of tribar weight, concrete unit weight, and structure slope. 8-70 The tabulation below sums cost of revetment by tetrapod unit: Weight of Concrete Cost Handling Costs First Secondary Armor Unit per 100 m of per 100 m of Waele Nese Cover yer Core (metric tons) (N/m?) Structure Structure Cost Cost Cost 592.18 315.57 1767.91 3340.29 804.53 290.66 2189.02 4042.73 1096.23 322.06 2475.43 4730.95 1255.45 351.20 2740.39 5240.78 666.15 1798.25 3376.42 857.59 2219.77 4054.45 1114.31 2508.26 4700.89 1234.99 2773.49 5167.15 714.04 1823.48 3472.78 850.83 2246.74 4166.36 1089.53 2534.34 4803.88 1181.62 2799.95 5252.82 aq costs are in thousands of dollars per 100 m of structure. Note that total cost given here does not include royalty costs for using tetrapods. For a graphic cost comparison, see Figure 8-30. 8-71 COST PER 100m OF STRUCTURE, MILLIONS OF DOLLARS 3.3 Gat sone fae rs a caged bos a4 Beas 3 dose fons Usoada eee 5 10 15 20 WEIGHT OF TETRAPOD, METRIC TONS Figure 8-30. Total cost of 100 meters of structure as a function of tetrapod weight, concrete unit weight, and structure slope. 8-72 (d) Selection of Armor Unit, Concrete Density, and Structure Slope Based on First Cost (Construction Cost). The preceding analysis is considered the first cost of the structure. To complete the analysis, average annual maintenance and repair costs should be established for each alternative and for a range of design wave heights. Maintenance and repair costs may modify the conditions established here as the most economical based on first cost. 1. Type of unit: tribar 2. Weight of unit: 11.5 metric tons 3. Structure slope: cot 6 = 1.5 4, Unit weight of concrete: 24.87 kN/m? 5. Cost per 100 meter of structure: $3,180,000 Stability Check Wy, 3 UL oe an a ai 3 Kp (s, = 1) cot 6 g Kp = 10.0 Wp, = 24.87 eninee Goes (s) <= ios) Wi 72 0S = ees H=6m ae (24.87) (6)? 10.0 (2.47 -1)7(1.5)(9.806) W = 11.5 metric tons 6. Volume of concrete per 100 m: 5/794 m? 7. Number of armor units per 100 m: 1288 8. Thickness of armor layer: 3.37 m 9. Volume of first underlayer per 100 m: 5988 mn? 10. Thickness of first underlayer: 1.52 m ll. Weight of underlayer stone: 1.15 metric tons 12. Volume of core per 100 m: 66,000 mn 13. Weight of core stone: 0.00192 - 0.0575 metric tons (ClheQ2 tao 57/65) 1) 14. Volume of secondary cover layer per 100 m: 1271 mn? 15. Thickness of secondary cover layer: 3.3/7 m 16. Weight of secondary cover layer stone: 2.421 metric tons 3. Diffraction Analysis: Diffraction Around Breakwater. For the purposes of this problem, establish the required breakwater length so that the maximum wave height in the harbor is 1 meter when the incident wave height is 6 meters (1 percent wave for H, = 3.59 m ) and the period T = 7.78 s . Assume waves generated in Delaware Bay. DIRECTION OF WAVE APPROACH BREAKWATER ISLAND 200m 8 B gt” 2 2 Lo = a = oS sey SS WG (Ho 7B) S O54? an Depth at breakwater d= 16.50 m Depth in basin d= 31.74 m di. Slee ge = GSU 0.33817 O From Appendix C, Table C-l, d= Tt 0.34506 Therefore, i, = 91.98 m5 say 9) = 92) m The 200-m distance, therefore, translates to ys 200 2S yn 2 At 200 meters, the wave height should be 1 meter. Hy = K,(6) 1 = K,(6) Lore 0.167 From Figure 7-61 x om 8 x = (8) (92) x = 736m say 750 m required breakwater length = 750m. 4. Preliminary Design of Quay Wall Caisson. Since the quay will be protected by breakwaters after construction is complete, the caisson will experience extreme wave action only during construction. For illustrative purposes the following conditions will be used to evaluate the stability of the caisson against wave action. It should be noted that these conditions have a low probability of occurrence during construction. he Si5 5) Gi Hy = 6.0 m ite = Toi dil! 20) ale d d= 13.5 m Note that the bearing area for the quay wall acting on the foundation soil may be reduced by toe scour under the edge or by local bearing capacity failures near the toe when the foundation pressure there exceeds the soil’s bearing capacity. Further information on this problem may be found in Eckert and Callender, 1984 (in press) or in most geotechnical textbooks. probability of extreme surge during construction is assumed negligible. 8-75 Le=? | ELEVATION 85m | Ba 6.4: BAY SIDE SWL ELEVATION 1.5m SEAWARD SIDE VOIDS VOIDS PROTEIED i (FILLED (FILLED NO WAVE os WITH WITH ACTION iT) mS ELEVATION -12.0m COMPACT SANDY BOTTOM For preliminary design, assume 75 percent voids filled with seawater and unit weight of water w, = 10.05 kN/m> : a. Nonbreaking Wave Forces on Caisson (see Ch. 7, Sec. III,2). (1) Incident Wave Height: H; =6m. (2) Wave Period: 1 =I Ouse (3) Structure Reflection Coefficient: yxy =1.0. @) Depth: ide =) 135) mi s H- —.; = a = 0.0101 eT’ (9.806)(7.78) H- Ce 6 a ie 3 0.444 (5) Height of Orbit Center Above SWL (see Fig. 7-90). h O — = 0.37 By h, = 0.40 (H,) = 0.37(6) = 2.22 m (6) Height of Wave Crest Above Bottom (see Fig. 7-88). Ik ae = + + ‘ Ye os % 2 a = Papel ye. = jlsjo5) 4b Dev cs ( 5) ) co = PDilo/? ye m Wave will overtop caisson by 1.2 meters; therefore assume structure is not 100 percent reflective. Use 0.9 and recalculate hy C h = = 0.36 (see Fig. 7-93) t i Sessa hy Wace, (Sy) = Salta an Oo 4 \ yapasieesuty2.or aes) (By = DNB Gp) Dimensionless Force (Wave Crest at Structure) (see Fig. 1=94)i Kor H. - He lon — og = TL = = 7375 = 0-444 , and x = 0.9 gT (9.806)(7.78) 8 ‘ E 2 kN = = 0.33, F, = 0.33 (10.05) (13.5)° = 604.48 “~ (force due to wave) wd & Hydrostatic force is not included. (8) Hydrostatic Force. 2 2 p ewd> © (C1005) NUS25e a oie i an D (9) Total Force. F, = 604.43 + 915.81 = 1520.24 = (10) Force Reduction Due to Low Height. b = 12.0 + 8.5 = 20.50 m You=" 270500 m 8-77 ib. — 20.50 i PM 3X5) = 0.9597 From Figure 7-97, ae = 0.998 F, = 0-998 (1520.24) = 1517.20 “ (11) Net Horizontal Force (Due to Presence of Waves). F = 1517.20 — 915.81 = 601.39 EN net m (12) Dimensionless Moment (Wave Crest at Structure) (see Figure 1=9>e HoT H 5 1 % eo 0.0101 , = = 0.444 , and X = 0.9 gT s M pias 0.24 3 M, = 0.24 w d.~= 0.24 (10.05) G@ises) ML oeso an es (3 m (13) Hydrostatic Moment. 3 3 eg? AOS SES) ee os = 6 6 (14) Total Moment. M, = 4121.1 + 5934.4 = 10,055.5 ae (15) Moment Reduction for Low Height. From Figure 7-97 with = = 0.9597 e ee: 0.996 M = 0.996 (10,005.5) = 10,015.3 “X—# (16) Net Overturning Moment About Bottom (Due to Presence of Waves). M = 10s015.3°="41 lees 589407 net m b. Stability Computations. (1) Overturning. R= REACTION FORCE By Bo (a) Weight per Unit Length of Structure. Concrete, w,, = 23.56 kN/m? (25 percent of area) Water in voids , wi 10.05 EN fame (75 percent of area) Height = 20.5 m Equation for weight/unit length: W = 20.5 L, 160.525) @23/556)) +-7.(0)..75)\(10505))5 W (b) Uplift per Unit Length of Structure (see Equation 7-75 275.26 L e and Figure 7-89). 8-79 = 1.5606 (7.78)* = 94.470 m L, = a 1923 f= FP = 0.1429 (6) c= Ube) == Gals ml (ees Heb Cab) cosh -S = 1.687 LORS ClO 05)NC6) 2 i === aa = ee) Ie =w,, d (hydrostatic pressure) ~ ht I (10.05) (13.5) = 135.68 N/a EQ Equations for uplift forces/unit length: P, Lg (33.957) (1,) By Bae os <2 ae ee 16.979 L, wo I ue) i) [5a i] 135.68 L, (2) Summation of Vertical Forces. i Bot BD pW SR, = 0 16.979 L, + 135.68 L, - 275.26 L, + R) = 0 Ry= 122.601 L, kN/m (3) Summation of Moments About A. 2 1 1 1 ui 8 (S)te + By (5) = W(S)t, + (5h. + Mot = 0 Bee 1) 2 \ee2 L\e2 F 16.979 () lL, + 135.68 G) |e 275.26 5 L, + 1225601 G) L, + 5894.2 0 12 = 5894-2 c 17.604 Eee 18.298 m This is the width required to prevent negative soil bearing pressure under caisson (reaction within middle. third). Assume L, = ifej65) tm 6 1 Ry) = vertical component of reaction R. 8-80 (4) Sliding. Coefficient of friction (see Table 7-16) for concrete on sand Mes 0.40 Vertical Forces for L, = 18.5 m W = 275.26 L, = 5092.31 kN/m -314.11 kN/m wo I SOG) My c ow i] -135.68 Lg = -2510.08 kN/m 5092.31 — 314.11 — 2510.08 = 2268.12 kN/m DE; (5) Horizontal Force to Initiate Sliding. Fy = ug Fy = 0.40 (2268.12) = 907.25 kN/m Since the actual net horizontal force is only 601.39 kN/m , the caisson will not slide. ce. Caisson Stability after Backfilling. (1) Assumptions: (a) No wave action (protected by breakwater). (b) Voids filled with dry sand. (c) Minimum water level at -0.91 MLW. (d) Surcharge of 0.6 meter on fill (dry sand). OVERTURNING SEAWARD MINIMUM SWL =-0.91m “SN. SATURATED FILL (SAND) = = ELEVATION = -12.0m FORCE it VOIDS FILLED -y.;}. WITH DRY sgt. UPLIFT ae : S . R i B 8-81 (2) Earth Pressure Diagrams. (2) EARTH PRESSURE DIAGRAMS 1 2 3 7.9 7.9 NOTE: ¢=25 TAN2(45°-@/2) = 0.406 0 -0.91 -0.91 -12.0 =F : SURCHARGE SUBMERGED SUBMERGED DRAINED (0.6)(18.85)kN/m3 SAND SAND SAND = 11.31 kN/m2 10.21 kN/m3 10.21 kN/m3 18.85 kN/m3 Diagram Force sme as Arm Moment Number CENia) (KN - m/m) (0.406) (0.6) (18 .85)(19.9) ee = O.05 909.21 91.378 (0.406)(10.21)(11.09)2 ae eo a = 254.909 10.05 (11.09) 2 2286.66 = 618.015 (18.85(8.81)- 0.406 + 8.81(18.85)(11.09) . 8316.07 = 1044.732 8-82 (3) Total Horizontal Earth Force. F, = 2009.034 kN/m E (4) Total Overturning Moment. Mp = 12455.10 kN - n/m (5) Moment Arm. _ B _ 12455.10 _ F, 2009.034 (6) Weight/Unit Length. Voids filled with dry sand: We= 1. (12 + 7.9 + 0.6) {(23.56)(0.25) + (18.85)(0.75)} = 410.56 Lo a (7) Uplift Force. Piva wd = 10.05 (11.09) = 111.45 kN/m* B = 111.45 L, kN/m (8) Hydrostatic Force (Seaward Side). 2 2 Fy e va _ 10.05 (11.0e) = 618.02 = (moment arm = a = 3.70 m above bottom) (9) Summation of Vertical Forces. 111.45 L, =f R, - 410.56 L. = 0 Ry = 299.11 L, (10) Summation of Moments About A. WL L L Cc c Coe a A SU) iy Nig SB ae 410.561 2 Will =AS 299.11 2a 5) L, + 618.02 (3.70) apoE L, 12455.10 or, L, = 0 49.85 i = 10168.426 I Ry = vertical component of reaction R. 8-83 L = 203.98 C L = 14.28 mn c R, = 299.11 (14.28) = 4271.3 kN Required width of caisson = L, = 14.28 meters. e d. Soil Bearing Pressure. TRIANGULAR PRESSURE DISTRIBUTION, AREA UNDER PRESSURE DISTRIBUTION = Ry Ry = VERTICAL COMPONENT OF REACTION R Ro P max o: v 2 DR 2 op. p23) — 2 Pee i, SER a 598.22 kN/m (1) Sliding. Summation of horizontal forces: Fam Epa kae eo Ri = 2009 .034 - 618.02 Ry = 1391.014 kN/m Vertical forces: R, = 4271.3 kN/m 1 Factor of safety against sliding should be 2: hence Fy > 2 Ry for safe design. Caisson should be widened. 8-84 Ry = horizontal component of reaction R. Coefficient of friction: u = 0.40 (2) Horizontal Force to Initiate Sliding. H v Fy = 0.40 (4271.3) = 1708.52 kN/m 2 Fy > Ry Caisson will not slide. ee Summary. The preceding calculations illustrate the types of calculations required to determine the stability of the proposed quay wall. Many additional loading conditions also require investigation, as do the foundation and soil conditions. Field investigations to determine soil conditions are required, in addition to hydraulic model studies to determine wave effects on the proposed island. V. COMPUTATION OF POTENTIAL LONGSHORE TRANSPORT (see Ch. 4, Sec. V) Using the hindcast deepwater wave data from Table 8-4, the net and gross potential sand transport rates will be estimated for the beaches south of Ocean City, Maryland (see Fig. 8-31). Assume refraction is by straight, parallel bottom contours. Azimuth of shoreline = 20 degrees 1. Deepwater Wave Angle (a) - The angle the wave crest makes with the shoreline (equal to the angle the wave ray makes with normal to shoreline) is shown in the following tabulation: Direction of Approach Deepwater Angle from North (degrees) ay (degrees) 65 35) southward 5 25 5f northward 85 8-85 MATIONS (For complete lat of Symbol and Abbreviations, see C&G S Chart Me 1) Js (Legh are whata unions otherwise indicated ) F hued SL ahert-long OBSC obscured Rot rowing Fi Mashng Occ eccvting WHIS. whine SEC sector DELAWARE eck An ahernavng DIA diaphone mm mnuien Ge grove 1 Qh mterrupted quick Mi navixal miles nee seconds ww whae Wome Blech Or orange Swear Rive G green Y yellow UNITED STATES — EAST COAST CAPE MAY TO CAPE HATTERAS As ar «gil Scale 1:416,944 at Lat. 37°00 = F See Chapter 2 Coast Pilots 2 and 3 for Reter navigation regulations in this area to section number shown will: area designat (For offshore navigation only) s 7 a Mercator Projection } , Region of Interest Y ATLANTIC OCEAN NON DANGEROUS WRECKS 1219 ang 1222 t8 of charts chs shown on cha Figure 8-31. Local shoreline alignment in vicinity of Ocean City, Maryland. 8-86 Table 8-12. Deepwater Wave Statistics (summary of data in Table 8-4). Duration for These oS Wave — eS of Shoreline = 20°) Total a) r=) ROO HOO) COPIES ON SN OU ONES E PS) OL GIS] SITS OE) cD uMNeINe elite egtat emi edreMoluesipenele ments ace Pirie ntierrue CAO en UU Deu Ue oo Dp Doesc5 a) rr tttereFows RR Ree nN Fwounwo bob tm te eww 2. Calculation of Average F (a,)> Equations (4-54) and (4-55) will be used to calculate the potential longshore sand transport rates. Since the wave angle a in both equations represents a 30-degree sector of wave directions, equation (4-55) is averaged over the 30-degree range for more accurate representation; i-.e., a 2 F (a) = - ie (cos ant sin 2a da Pal 4 9/4 = + Str) (cos ale - cos (a,) / | where Aa = A — a) = n/6 and =the) + or = sign is determined by the direction of transport. Special care should be exercised when 0°< a < 15 and 75°< a < 90°. Further discussion on the method of averaging is given in Chapter 4, Section V,3,d. The results of calculation are shown in the following tablulation and also in Figure 8-32. 0.222 or — 0.058 0.708 0.780 ‘06 108 *10j090S 02 aei8ep-0€ 105 (°x) J o8e12ay °7E-8 (53a) ° ‘3T9NV 3AVM H3LVMd330 \09 |0S Ov 10}35 ean3sty Ol, 31VY LYOdSNVUL GNVS SHOHSONOT IWILN3LOd ) 4 0. ( 8-88 3. Potential Longshore Transport Computed by Ener Flux Method. 15.399 —66.265 -114.890 -99.603 -38.758 -108.149 —48 .842 -20.708 -30.203 -631.200 -1,036.277 -316.947 x F (a,) in n?/year where f = numbers of hours of a Ti caees) Bej=) 2-03" iW se Beas specific wave (Table 8-12) divided by 8,766. Negative values represent northward transport. 8-89 With a shoreline azimuth of 20 degrees, 3 (,) south = (296-9 + 781.4 + 109.6) x 10° = 1.89 x 10° m/year ( ( Q 3 Q ( (28.6 + 631.2 + 1036.3 + 316.9) x 10 = 2.01 x 10° m?/yedr 2) north — £ | - 6 23 2) ee () Sa (%) Be us 0.12 x 10 m /year (north) Q, ) gross = (Cnjzeren ii @,) south 10° m/year Note that the computed values are suspect since the net longshore transport is northward which is contrary to the field observations at the adjacent areas (Table 4-6). Except for the net transport rate, the computed values appear larger than those measured at various east coast locations. One of the possible factors that contribute to this discrepancy is the wave data used in the analysis. It is noted that hindcast wave data is for deep water at a location approximately 240 kilometers east of the shoreline of interest. Furthermore, energy dissipation due to bottom and/or internal friction is not considered in the analysis. Consequently, higher energy flux is implied in the sand transport computation. Since the hindcast wave statistics are available at an offshore location! approximately 10 kilometers off the shoreline of interest, analysis of longshore sand transport should be based on this new data rather than on the deepwater data listed in Table 8-4. By using the procedure shown in the preceding calculations, the potential sand transport rates below are obtained. = iloily? ss 10° mf year = 0.66 x 10° ae sect: = 510,000 ae Saee (south) = 1.83 x 10° ae Joon VI. BEACH FILL REQUIREMENTS (SEE Wig Sq Seq 105 3))) A beach fill is proposed for the beach south of Ocean City, Maryland. Determine the volume of borrow material required to widen the beach 20 meters over a distance of 1.0 kilometers. Borrow material is available from two sources. 1 Station No. 32 (Corson et al., 1982). 8-90 1. Material Characteristics. a. Native Sand. dg, = 2.51 » (0.1756 mm) (see table C-5). $16 = 1-37 o (0.3869 mm) Mean diameter (see eq. 5-2): rp Os are 1G on 2 i 25 ae Mn Awe 1.94 » (0.2606 mm) Standard deviation (see eq. 5-1): Mae Atan Wi iue on 2 ~ Zod oo iesy/ oon = 5 0.570 » (0.6736 mm) b. Borrow--Source A. day, = 2.61 » (0.1638 mm) $6 = 1-00 (0.500 mm) Mean diameter (see eq. 5-2): — ZA SOs Myq = «1681 (0.285 mm) Peo 00): Shy ai Ones 0.805 » (0.572 mm) c. Borrow--Source B. bg, = 3.47 » (0.0902 mm) $16 = 0.90 » (0.5359 mm) Mean diameter (see eq. 5-1): Be eaiete 0.90 0 Mop Sag aw es 2.19 » (0.219 mm) _ Soll Wolo) oun See fF 1.29 » (0.4090 mm) 2. Evaluation of Borrow Materials (see Fig. 5-3). M —- M (Aig! UsBieewUs94 2 2 aae Oo 0.57 i on "oA _ 0.805 es SOF 1 412 (oj 0.57 gon 8-91 From Figure 5-3, quadrant 2, (Source A) R, (overfill ratio) = 1.10 Lj See Sie OSLO = ——————_ = 0.439 Co} ORS gon oj B 1.29 20) eee 226 fo} 0.57 gn From Figure 5-3, quadrant l, (Source B) R, (overfill ratio) = 1.55 Conclusion: use material from Source A. 3. Required Volume of Fill. Rule of thumb: 2.5 cubic meters of native material per meter (1 cubic yard per foot) of beach width or 8.23 cubic meters per square meter of beach. 3 8.23 m 1000 m 5) (1.00 km) x ag aaa m Volume of native sand = 1.65 x 10° me Volume of native sand 20.00 m Volume from Source A = 1.10 (1.65 x 10°) = 1.81 x 10° mT LITERATURE CITED BRETSCHNEIDER, C.L., "Hurricane Surge Predictions for Delaware Bay and River," Beach Erosion Board, Miscellaneous Paper No. 4-59, 1959. CALDWELL, J.M., "Coastal Processes and Beach Erosion," Coastal Engineering Research Center, R1-67, 1967. CORSON, W.D., et al., "Atlantic Coast Hindcast, Deepwater, Significant Wave Information,'' WIS Report 2, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., Jan. 1981. CORSON, W.D. et. al., “Atlantic Coast Hindcast Phase II, Significant Wave Information," WIS Report 6, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., Mar. 1982. ECKERT, J., and CALLENDER, G.W., "Geotechnical Engineering in the Coastal Zone," Instruction Report in preparation, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1984 (in press). HARRIS, D.L., "Tides and Tidal Datums in the United States," SR 7, Coastal Engineering Research Center, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., Feb. 1981. JENSEN, R.E., “Atlantic Coast Hindcast, Shallow-Water Significant Wave Information," WIS Report 9, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., Jan. 1983. KOMAR, P.D., "The Longshore Transport of Sand on Beaches," Unpublished Ph.D. Thesis, University of California, San Diego, 1969. NATIONAL OCEAN SERVICE (USC&GS), "Tide Tables" (available each year). NATIONAL OCEAN SERVICE (USC&GS), "Tidal Current Tables" (available for each year). NATIONAL OCEAN SERVICE (USC&GS), "Tidal Current Charts--Delaware Bay and River," 1948 and 1960. NATIONAL WEATHER SERVICE (U.S. Weather Bureau), "Winds Over Chesapeake Bay for Hurricane of September 14, 1944, Transposed and Adjusted for Filling," Weather Bureau Memorandum HUR 7-26, 1957. SAVILLE, T., Jr., "North Atlantic Coast Wave Statistics Hindcast by Bretschneider Revised Sverdrup-Munk Method,'"' Beach Erosion Board, TM 55, 1954. THOM, H.C.S., "Distributions of Extreme Winds in the United States," "Proceedings of the Structural Diviston, ASCE, ST 4, No. 2433, 1960. U.S. ARMY ENGINEER DISTRICT, BALTIMORE, "Atlantic Coast of Maryland and Assateague Island, Virginia--Draft Survey Report on Beach Erosion Control and Hurricane Protection," 1970. 8-93 U.S. ARMY ENGINEER DISTRICT, PHILADELPHIA, "Beach Erosion Control Report on Cooperative Study of Delaware Coast, Kitts Hummock to Fenwick Island," 1956. U.S. ARMY ENGINEER DISTRICT, PHILADELPHIA, "Beach Erosion Control and Hurricane Protection Along the Delaware Coast," 1966. U.S. ARMY ENGINEER DISTRICT, PHILADELPHIA, "Detailed Project Report, Small Beach Erosion Control Project, Lewes, Delaware," 1970. 8-94 APPENDIX A Glossary of Terms Newport Cove, Maine, 12 September 1958 The glossary that follows was compiled and reviewed by the staff of the Coastal Engineering Research Center. Although the terms came from many sources, the following publications were of particular value: American Geological Institute (1957) Glossary of Geology and Related Sctences with Supplement, 2d Edition American Geological Institute (1960) Dticttonary of Geological Terms, 2nd Edition American Meteorological Society (1959) Glossary of Meteorology Johnson, D.W. (1919) Shore Process and Shoreline Development, John Wiley and Sons, Inc., New York U.S. Army Coastal Engineering Research Center (1966) Shore Protection, Planning and Design, Technical Report No. 4, 3d Edition U.S. Coast and Geodetic Survey (1949) Tide and Current Glossary, Special Publication No. 228, Revised (1949) Edition U.S. Navy Oceanographic Office (1966) Glossary of Oceanographic Terms, Special Publication (SP-35), 2d Edition Wiegel, R.L. (1953) Waves, Tides, Currents and Beaches: Glossary of Terms and List of Standard Symbols. Council on Wave Research, The Engineering Foundation, University of California GLOSSARY OF TERMS ACCRETION. May be either NATURAL or ARTIFICIAL. Natural accretion is the buildup of land, solely by the action of the forces of nature, on a BEACH by deposition of water- or airborne material. Artificial accretion is a similar buildup of land by reason of an act of man, such as the accretion formed by a groin, breakwater, or beach fill deposited by mechanical means. Also AGGRADATION. ADVANCE (of a beach). (1) A continuing seaward movement of the shoreline. (2) A net seaward movement of the shoreline over a specified time. Also PROGRESSION. AGE, WAVE. The ratio of wave velocity to wind velocity (in wave forecasting theory). AGGRADATION. See ACCRETION. ALLUVIUM. Soil (sand, mud, or similar detrital material) deposited by streams, or the deposits formed. ALONGSHORE. Parallel to and near the shoreline; LONGSHORE. A-1 AMPLITUDE, WAVE. (1) The magnitude of the displacement of a wave from a mean value. An ocean wave has an amplitude equal to the vertical distance from still-water level to wave crest. For a sinusoidal wave, the amplitude is one-half the wave height. (2) The semirange of a constituent tide. ANTIDUNES. BED FORMS that occur in trains and are in phase with, and strongly interact with, gravity water-surface waves. ANTINODE. See LOOP. ARMOR UNIT. A relatively large quarrystone or concrete shape that is selected to fit specified geometric characteristics and density. It is usually of nearly uniform size and usually large enough to require individual placement. In normal cases it is used as primary wave protection and is placed in thicknesses of at least two units. ARTIFICIAL NOURISHMENT. The process of replenishing a beach with material (usually sand) obtained from another location. ATOLL. A ring-shaped coral reef, often carrying low sand islands, enclosing a lagoon. ATTENUATION. (1) A lessening of the amplitude of a wave with distance from the origin. (2) The decrease of water-particle motion with increasing depth. Particle motion resulting from surface oscillatory waves attenuates rapidly with depth, and practically disappears at a depth equal to a surface wavelength. AWASH. Situated so that the top is intermittently washed by waves or tidal action. Condition of being exposed or just bare at any stage of the tide between high water and chart datum. BACKBEACH. See BACKSHORE. BACKRUSH. The seaward return of the water following the uprush of the waves. For any given tide stage the point of farthest return seaward of the backrush is known as the LIMIT of BACKRUSH or LIMIT BACKWASH. (See Figure A-2.) BACKSHORE. That zone of the shore or beach lying between the foreshore and the coastline comprising the BERM or BERMS and acted upon by waves only during severe storms, especially when combined with exceptionally high water. Also BACKBEACH. (See Figure A-1.) BACKWASH. (1) See BACKRUSH. (2) Water or waves thrown back by an obstruction such as a ship, breakwater, or cliff. BANK. (1) The rising ground bordering a lake, river, or sea; or of a river or channel, for which it is designated as right or left as the observer is facing downstream. (2) An elevation of the sea floor or large area, located on a continental (or island) shelf and over which the depth is relatively shallow but sufficient for safe surface navigation; a group of shoals. (3) In its secondary sense, used only with a qualifying word such as “sandbank" or "gravelbank," a shallow area consisting of shifting forms of silt, sand, mud, and gravel. BAR. A submerged or emerged embankment of sand, gravel, or other unconsoli- dated material built on the sea floor in shallow water by waves and currents. (See Figures A-2 and A-9.) See BAYMOUTH BAR, CUSPATE BAR. BARRIER BEACH. A bar essentially parallel to the shore, the crest of which is above normal high water level. (See Figure A-9.) Also called OFFSHORE BARRIER and BARRIER ISLAND. BARRIER LAGOON. A bay roughly parallel to the coast and separated from the open ocean by barrier islands. Also, the body of water encircled by coral islands and reefs, in which case it may be called an atoll lagoon. BARRIER REEF. A coral reef parallel to and separated from the coast by a lagoon that is too deep for coral growth. Generally, barrier reefs follow the coasts for long distances and are cut through at irregular intervals by channels or passes. BASIN, BOAT. A naturally or artificially enclosed or nearly enclosed harbor area for small craft. BATHYMETRY. The measurement of depths of water in oceans, seas, and lakes; also information derived from such measurements. BAY. A recess in the shore or an inlet of a sea between two capes or head- lands, not so large as a gulf but larger than a cove. (See Figure A-9.) See also BIGHT, EMBAYMENT. BAYMOUTH BAR. A bar extending partly or entirely across the mouth of a bay (see Figure A-9). BAYOU. A minor sluggish waterway or estuarial creek, tributary to, or connecting, other streams or bodies of water, whose course is usually through lowlands or swamps. Sometimes called SLOUGH. BEACH. The zone of unconsolidated material that extends landward from the low water line to the place where there is marked change in material or physiographic form, or to the line of permanent vegetation (usually the effective limit of storm waves). The seaward limit of a beach-~-unless otherwise specified--is the mean low water line. A beach includes FORE- SHORE and BACKSHORE. See also SHORE. (See Figure A-1.) BEACH ACCRETION. See ACCRETION. BEACH BERM. A nearly horizontal part of the beach or backshore formed by the deposit of material by wave action. Some beaches have no berms, others have one or several. (See Figure A-l.) BEACH CUSP. See CUSP. BEACH EROSION. The carrying away of beach materials by wave action, tidal currents, littoral currents, or wind. A-3 BEACH FACE. The section of the beach normally exposed to the action of the wave uprush. The FORESHORE of a BEACH. (Not synonymous with SHORE- FACE.) (See Figure A-2.) BEACH FILL. Material placed on a beach to renourish eroding shores. BEACH RIDGE. See RIDGE, BEACH. BEACH SCARP. See SCARP, BEACH. BEACH WIDTH. The horizontal dimension of the beach measured normal to the shoreline. BED FORMS. Any deviation from a flat bed that is readily detectable by eye and higher than the largest sediment size present in the parent bed material; generated on the bed of an alluvial channel by the flow. BEDLOAD. See LOAD. BENCH. (1) A level or gently sloping erosion plane inclined seaward. (2) A nearly horizontal area at about the level of maximum high water on the sea side of a dike. BENCH MARK. A permanently fixed point of known elevation. A primary bench mark is one close to a tide station to which the tide staff and tidal datum originally are referenced. BERM, BEACH. See BEACH BERM. BERM CREST. The seaward limit of a berm. Also called BERM EDGE. (See Figure A-1.) BIGHT. A bend in a coastline forming an open bay. A bay formed by such a bend. (See Figure A-8.) BLOWN SANDS. See EOLIAN SANDS. BLUFF. A high, steep bank or cliff. BOLD COAST. A prominent landmass that rises steeply from the sea. BORE. A very rapid rise of the tide in which the advancing water presents an abrupt front of considerable height. In shallow estuaries where the range of tide is large, the high water is propagated inward faster than the low water because of the greater depth at high water. If the high water over- takes the low water, an abrupt front is presented, with the high-water crest finally falling forward as the tide continues to advance. Also EAGER. BOTTOM. The ground or bed under any body of water; the bottom of the sea. (See Figure A-1.) A-4 BOTTOM (nature of). The composition or character of the bed of an ocean or other body of water (e.g., clay, coral, gravel, mud, ooze, pebbles, rock, shell, shingle, hard, or soft). BOULDER. A rounded rock more than 10 inches in diameter; larger than a cobblestone. See SOIL CLASSIFICATION. BREAKER. A wave breaking on a shore, over a reef, etc. Breakers may be classified into four types (see Figure A-4): SPILLING--bubbles and turbulent water spill down front face of wave. The upper 25 percent of the front face may become vertical before breaking. Breaking generally occurs over quite a distance. PLUNGING--crest curls over air pocket; breaking is usually with a crash. Smooth splash-up usually follows. COLLAPSING--breaking occurs over lower half of wave, with minimal air pocket and usually no splash-up. Bubbles and foam present. (See Figure 2-77). SURGING--wave peaks up, but bottom rushes forward from under wave, and wave slides up beach face with little or no bubble production. Water surface remains almost plane except where ripples may be produced on the beachface during runback. BREAKER DEPTH. The still-water depth at the point where a wave breaks. Also called BREAKING DEPTH. (See Figure A-2). BREAKWATER. A structure protecting a shore area, harbor, anchorage, or basin from waves. BULKHEAD. A structure or partition to retain or prevent sliding of the land. A secondary purpose is to protect the upland against damage from wave action. BUOY. A float; especially a floating object moored to the bottom to mark a channel, anchor, shoal, rock, etc. BUOYANCY. The resultant of upward forces, exerted by the water on a submerged or floating body, equal to the weight of the water displaced by this body. BYPASSING, SAND. Hydraulic or mechanical movement of sand from the accreting updrift side to the eroding downdrift side of an inlet or harbor entrance. The hydraulic movement may include natural movement as well as movement caused by man. CANAL. An artificial watercourse cut through a land area for such uses as navigation and irrigation. CANYON. A relatively narrow, deep depression with steep slopes, the bottom of which grades continuously downward. May be underwater (submarine) or on land (subaerial). A=5 CAPE. A relatively extensive land area jutting seaward from a continent or large island which prominently marks a change in, or interrupts notably, the coastal trend; a prominent feature. CAPILLARY WAVE. A wave whose velocity of propagation is controlled primarily by the surface tension of the liquid in which the wave is traveling. Water waves of length less than about 1 inch are considered capillary waves. Waves longer than 1 inch and shorter than 2 inches are in an indeterminate zone between CAPILLARY and GRAVITY WAVES. See RIPPLE. CAUSEWAY. A raised road across wet or marshy ground, or across water. CAUSTIC. In refraction of waves, the name given to the curve to which adjacent orthogonals of waves refracted by a bottom whose contour lines are curved, are tangents. The occurrence of a caustic always marks a region of crossed orthogonals and high wave convergence. CAY. See KEY. CELERITY. Wave speed. CENTRAL PRESSURE INDEX (CPI). The estimated minimum barometric pressure in the eye (approximate center) of a particular hurricane. The CPI is considered the most stable index to intensity of hurricane wind velocities in the periphery of the storm; the highest wind speeds are associated with storms having the lowest CPI. CHANNEL. (1) A natural or artificial waterway of perceptible extent which either periodically or continuously contains moving water, or which forms a connecting link between two bodies of water. (2) The part of a body of water deep enough to be used for navigation through an area otherwise too shallow for navigation. (3) A large strait, as the English Channel. (4) The deepest part of a stream, bay, or strait through which the main volume or current of water flows. CHARACTERISTIC WAVE HEIGHT. See SIGNIFICANT WAVE HEIGHT. CHART DATUM. The plane or level to which soundings (or elevations) or tide heights are referenced (usually LOW WATER DATUM). The surface is called a tidal datum when referred to a certain phase of tide. To provide a safety factor for navigation, some level lower than MEAN SEA LEVEL is generally selected for hydrographic charts, such as MEAN LOW WATER or MEAN LOWER LOW WATER. See DATUM PLANE. CHOP. The short-crested waves that may spring up quickly in a moderate breeze, and which break easily at the crest. Also WIND CHOP. CLAPOTIS. The French equivalent for a type of STANDING WAVE. In American usage it is usually associated with the standing wave phenomenon caused by the reflection of a nonbreaking wave train from a structure with a face that is vertical or nearly vertical. Full clapotis is one with 100 percent reflection of the incident wave; partial clapotis is one with less than 100 percent reflection. A-6 CLAY. See SOIL CLASSIFICATION. CLIFF. A high, steep face of rock; a precipice. See also SEA CLIFF. CNOIDAL WAVE. A type of wave in shallow water (i.e., where the depth of water is less than 1/8 to 1/10 the wavelength). The surface profile is expressed in terms of the Jacobian elliptic function cn u; hence the term cnoidal. COAST. A strip of land of indefinite width (may be several kilometers) that extends from the shoreline inland to the first major change in terrain features. (See Figure A-l.) COASTAL AREA. The land and sea area bordering the shoreline. (See Figure A-1.) COASTAL PLAIN. The plain composed of horizontal or gently sloping strata of clastic materials fronting the coast, and generally representing a strip of sea bottom that has emerged from the sea in recent geologic time. COASTLINE. (1) Technically, the line that forms the boundary between the COAST and the SHORE. (2) Commonly, the line that forms the boundary between the land and the water. COBBLE (COBBLESTONE). See SOIL CLASSIFICATION. COMBER. (1) A deepwater wave whose crest is pushed forward by a strong wind; much larger than a whitecap. (2) A long-period breaker. CONTINENTAL SHELF. The zone bordering a continent and extending from the low water line to the depth (usually about 180 meters) where there is a marked or rather steep descent toward a greater depth. CONTOUR. A line on a map or chart representing points of equal elevation with relation to a DATUM. It is called an ISOBATH when connecting points of equal depth below a datum. Also called DEPTH CONTOUR. CONTROLLING DEPTH. The least depth in the navigable parts of a waterway, governing the maximum draft of vessels that can enter. CONVERGENCE. (1) In refraction phenomena, the decreasing of the distance between orthogonals in the direction of wave travel. Denotes an area of increasing wave height and energy concentration. (2) In wind-setup phenomena, the increase in setup observed over that which would occur in an equivalent rectangular basin of uniform depth, caused by changes in planform or depth; also the decrease in basin width or depth causing such increase in setup. CORAL. (1) (Biology) Marine coelenterates (Madreporaria), solitary or colonial, which form a hard external covering of calcium compounds or other materials. The corals which form large reefs are limited to warn, shallow waters, while those forming solitary, minute growths may be found in colder waters to great depths. (2) (Geology) The concretion of coral polyps, composed almost wholly of calcium carbonate, forming reefs and tree-like and globular masses. May also include calcareous algae and other organisms producing calcareous secretions, such as bryozoans and hydrozoans. CORE. A vertical cylindrical sample of the bottom sediments from which the nature and stratification of the bottom may be determined. COVE. A small, sheltered recess in a coast, often inside a larger embayment. (See Figure A-8.) CREST LENGTH, WAVE. The length of a wave along its crest. Sometimes called CREST WIDTH. CREST OF BERM. The seaward limit of a berm. Also called BERM EDGE. (See Figure A-1.) CREST OF WAVE. (1) the highest part of a wave. (2) That part of the wave above still-water level. (See Figure A-3.) CREST WIDTH, WAVE. See CREST LENGTH, WAVE. CURRENT. A flow of water. CURRENT, COASTAL. One of the offshore currents flowing generally parallel to the shoreline in the deeper water beyond and near the surf zone; these are not related genetically to waves and resulting surf, but may be related to tides, winds, or distribution of mass. CURRENT, DRIFT. A broad, shallow, slow-moving ocean or lake current. Opposite of CURRENT, STREAM. CURRENT, EBB. The tidal current away from shore or down a tidal stream. Usually associated with the decrease in the height of the tide. CURRENT, EDDY. See EDDY. CURRENT, FEEDER. Any of the parts of the NEARSHORE CURRENT SYSTEM that flow parallel to shore before converging and forming the neck of the RIP CURRENT. CURRENT, FLOOD. The tidal current toward shore or up a tidal stream. Usually associated with the increase in the height of the tide. CURRENT, INSHORE. See INSHORE CURRENT. CURRENT, LITTORAL. Any current in the littoral zone caused primarily by wave action; e.g., LONGSHORE CURRENT, RIP CURRENT. See also CURRENT, NEAR- SHORE. CURRENT, LONGSHORE. The littoral current in the breaker zone moving essentially parallel to the shore, usually generated by waves breaking at an angle to the shoreline. CURRENT, NEARSHORE. A current in the NEARSHORE ZONE. (See Figure A-1.) CURRENT, OFFSHORE. See OFFSHORE CURRENT. CURRENT, PERIODIC. See CURRENT, TIDAL. CURRENT, PERMANENT. See PERMANENT CURRENT. CURRENT, RIP. See RIP CURRENT. CURRENT, STREAM. A narrow, deep, and swift ocean current, as the Gulf Stream. CURRENT, DRIFT. CURRENT SYSTEM, NEARSHORE. See NEARSHORE CURRENT SYSTEM. CURRENT, TIDAL. The alternating horizontal movement of water associated with the rise and fall of the tide caused by the astronomical tide-producing forces. Also CURRENT, PERIODIC. See also CURRENT, FLOOD and CURRENT, EBB. CUSP. One of a series of low mounds of beach material separated by crescent- shaped troughs spaced at more or less regular intervals along the beach face. Also BEACH CUSP. (See Figure A-7.) CUSPATE BAR. A crescent-shaped bar uniting with the shore at each end. It may be formed by a single spit growing from shore and then turning back to again meet the shore, or by two spits growing from the shore and uniting to form a bar of sharply cuspate form. (See Figure A-9.) CUSPATE SPIT. The spit that forms in the lee of a shoal or offshore feature (breakwater, island, rock outcrop) by waves that are refracted and/or diffracted around the offshore feature. It may be eventually grown into a TOMBOLO linking the feature to the mainland. See TOMBOLO. CYCLOIDAL WAVE. A steep, symmetrical wave whose crest forms an angle of 120 degrees and whose form is that of a cycloid. A trochoidal wave of maximum steepness. See also TROCHOIDAL WAVE. DATUM, CHART. See CHART DATUM. A-9 DATUM, PLANE. water surface elevations are referred. is called a TIDAL DATUM when defined by a certain phase of the tide. The horizontal plane to which soundings, ground elevations, or Also REFERENCE PLANE. The plane The following datums are ordinarily used on hydrographic charts: MEAN LOW WATER--Atlantic coast (U. S.), MEAN LOWER LOW WATER--Pacific coast (U. MEAN LOW WATER SPRINGS--United Kingdon, LOW WATER DATUM--Great Lakes (U. S. and Argentina, Sweden, and Norway. Sere Germany, Italy, Brazil, and Chile. Canada). LOWEST LOW WATER SPRINGS--Portugal. LOW WATER INDIAN SPRINGS--India and Japan (See INDIAN TIDE PLANE). LOWEST LOW WATER--France, Spain, and Greece. A common datum used on topographic maps is based on MEAN SEA LEVEL. See also BENCH MARK. DEBRIS LINE. A line near the limit of storm wave uprush marking the landward limit of debris deposits. DECAY DISTANCE. (FETCH). The distance waves travel after leaving the generating area DECAY OF WAVES. The change waves undergo after they leave a generating area (FETCH) and pass through a calm, or region of lighter winds. In the process of decay, the significant wave height decreases and the signi- ficant wavelength increases. DEEP WATER. bottom. considered deep water. Water so deep that surface waves are little affected by the ocean Generally, water deeper than one-half the surface wavelength is Compare SHALLOW WATER. DEFLATION. The removal of loose material from a beach or other land surface by wind action. DELTA. An alluvial deposit, roughly triangular or digitate in shape, formed at a river mouth. DEPTH. The vertical distance from a specified tidal datum to the sea floor. DEPTH OF BREAKING. The still-water where the wave breaks. Also BREAKER DEPTH. depth at the point (See Figure A-2.) DEPTH CONTOUR. See CONTOUR. DEPTH, CONTROLLING. See CONTROLLING DEPTH. DEPTH FACTOR. See SHOALING COEFFICIENT. DERRICK STONE. See STONE, DERRICK. DESIGN HURRICANE. See HYPOTHETICAL HURRICANE. A-10 DIFFRACTION (of water waves). The phenomenon by which energy is transmitted laterally along a wave crest. When a part of a train of waves is inter- rupted by a barrier, such as a breakwater, the effect of diffraction is manifested by propagation of waves into the sheltered region within the barrier’s geometric shadow. DIKE (DYKE). A wall or mound built around a low-lying area to prevent flooding. DIURNAL. Having a period or cycle of approximately one TIDAL DAY. DIURNAL TIDE. A tide with one high water and one low water in a tidal day. (See Figure A-10.) DIVERGENCE. (1) In refraction phenomena, the increasing of distance between orthogonals in the direction of wave travel. Denotes an area of decreasing wave height and energy concentration. (2) In wind-setup phenomena, the decrease in setup observed under that which would occur in an equivalent rectangular basin of uniform depth, caused by changes in planform or depth. Also the increase in basin width or depth causing such decrease in setup. DOLPHIN. A cluster of piles. DOWNCOAST. In United States usage, the coastal direction generally trending toward the south. DOWNDRIFT. The direction of predominant movement of littoral materials. DRIFT (noun). (1) Sometimes used as a short form for LITTORAL DRIFT. (2) The speed at which a current runs. (3) Floating material deposited on a beach (driftwood). (4) A deposit of a continental ice sheet; e.g., a drumlin. DRIFT CURRENT. A broad, shallow, slow-moving ocean or lake current. DUNES. (1) Ridges or mounds of loose, wind-blown material, usually sand. (See Figure A-7.) (2) BED FORMS smaller than bars but larger than ripples that are out of phase with any water-surface gravity waves associated with them. DURATION. In wave forecasting, the length of time the wind blows in nearly the same direction over the FETCH (generating area). DURATION, MINIMUM. The time necessary for steady-state wave conditions to develop for a given wind velocity over a given fetch length. EAGER. See BORE. EBB CURRENT. The tidal current away from shore or down a tidal stream; usually associated with the decrease in height of the tide. EBB TIDE. The period of tide between high water and the succeeding low water; a falling tide. (See Figure A-10.) AI ECHO SOUNDER. An electronic instrument used to determine the depth oi water by measuring the time interval between the emission of a sonic or ultrasonic signal and the return of its echo from the bottom. EDDY. A circular movement of water formed on the side of a main current. Eddies may be created at points where the main stream passes projecting obstructions or where two adjacent currents flow counter to each other. Also EDDY CURRENT. EDDY CURRENT. See EDDY. EDGE WAVE. An ocean wave parallel to a coast, with crests normal to the shoreline. An edge wave may be STANDING or PROGRESSIVE. Its height diminishes rapidly seaward and is negligible at a distance of one wavelength offshore. EMBANKMENT. An artificial bank such as a mound or dike, generally built to hold back water or to carry a roadway. EMBAYED. Formed into a bay or bays, as an embayed shore. EMBAYMENT. An indentation in the shoreline forming an open bay. ENERGY COEFFICIENT. The ratio of the energy in a wave per unit crest length transmitted forward with the wave at a point in shallow water to the energy in a wave per unit crest length transmitted forward with the wave in deep water. On refraction diagrams this is equal to the ratio of the distance between a pair of orthogonals at a selected shallow-water point to the distance between the same pair of orthogonals in deep water. Also the square of the REFRACTION COEFFICIENT. ENTRANCE. The avenue of access or opening to a navigable channel. EOLIAN SANDS. Sediments of sand size or smaller which have been transported by winds. They may be recognized in marine deposits off desert coasts by the greater angularity of the grains compared with waterborne particles. EROSION. The wearing away of land by the action of natural forces. On a beach, the carrying away of beach material by wave action, tidal currents, littoral currents, or by deflation. ESCARPMENT. A more or less continuous line of cliffs or steep slopes facing in one general direction which are caused by erosion or faulting. Also SCARP. (See Figure A-1l.) ESTUARY. (1) The part of a river that is affected by tides. (2) The region near a river mouth in which the fresh water of the river mixes with the salt water of the sea. EYE. In meteorology, usually the "eye of the storm" (hurricane); the roughly circular area of comparatively light winds and fair weather found at the center of a severe tropical cyclone. A~12 FAIRWAY. The parts of a waterway that are open and unobstructed for naviga- tion. The main traveled part of a waterway; a marine thoroughfare. FATHOM. A unit of measurement used for soundings equal to 1.83 meters (6 feet). FATHOMETER. The copyrighted trademark for a type of echo sounder. FEEDER BEACH. An artificially widened beach serving to nourish downdrift beaches by natural littoral currents or forces. FEEDER CURRENT. See CURRENT, FEEDER. FEELING BOTTOM. The initial action of a deepwater wave, in reponse to the bottom, upon. running into shoal water. FETCH. The area in which SEAS are generated by a wind having a fairly constant direction and speed. Sometimes used synonymously with FETCH LENGTH. Also GENERATING AREA. FETCH LENGTH. The horizontal distance (in the direction of the wind) over which a wind generates SEAS or creates a WIND SETUP. FIRTH. A narrow arm of the sea; also, the opening of a river into the sea. FIORD (FJORD). A narrow, deep, steep-walled inlet of the sea, usually formed by entrance of the sea into a deep glacial trough. FLOOD CURRENT. The tidal current toward shore or up a tidal stream, usually associated with the increase in the height of the tide. FLOOD TIDE. The period of tide between low water and the succeeding high water; a rising tide. (See Figure A-10.) FOAM LINE. The front of a wave as it advances shoreward, after it has broken. (See Figure A-4.) FOLLOWING WIND. Generally, the same as a tailwind; in wave forecasting, wind blowing in the direction of ocean-wave advance. FOREDUNE. The front dune immediately behind the backshore. FORERUNNER. Low, long-period ocean SWELL which commonly precedes the main swell from a distant storm, especially a tropical cyclone. FORESHORE. The part of the shore, lying between the crest of the seaward berm (or upper limit of wave wash at high tide) and the ordinary low-water mark, that is ordinarily traversed by the uprush and backrush of the waves as the tides rise and fall. See BEACH FACE. (See Figure A-l.) FORWARD SPEED (hurricane). Rate of movement (propagation) of the hurricane eye in meters per second, knots, or miles per hour. A-13 FREEBOARD. The additional height of a structure above design high water level to prevent overflow. Also, at a given time, the vertical distance between the water level and the top of the structure. On a ship, the distance from the waterline to main deck or gunwale. FRINGING REEF. A coral reef attached directly to an insular or continental shore. FRONT OF THE FETCH. In wave forecasting, the end of the generating area toward which the wind is blowing. FROUDE NUMBER. The dimensionless ratio of the inertial force to the force of gravity for a given fluid flow. It may be given as Fr = V /Lg where V is a characteristic velocity, L is a characteristic length, and g _ the acceleration of gravity--or as the square root of this number. FULL. See RIDGE, BEACH. GENERATING AREA. In wave forecasting, the continuous area of water surface over which the wind blows in nearly a constant direction. Sometimes used synonymously with FETCH LENGTH. Also FETCH. GENERATION OF WAVES. (1) The creation of waves by natural or mechanical means. (2) The creation and growth of waves caused by a wind blowing over a water surface for a certain period of time. The area involved is called the GENERATING AREA or FETCH. GEOMETRIC MEAN DIAMETER. The diameter equivalent of the arithmetic mean of the logarithmic frequency distribution. In the analysis of beach sands, it is taken as that grain diameter determined graphically by the inter- section of a straight line through selected boundary sizes, (generally points on the distribution curve where 16 and 84 percent of the sample is coarser by weight) and a vertical line through the median diameter of the sample. GEOMETRIC SHADOW. In wave diffraction theory, the area outlined by drawing straight lines paralleling the direction of wave approach through the extremities of a protective structure. It differs from the actual protected area to the extent that the diffraction and refraction effects modify the wave pattern. GEOMORPHOLOGY. That branch of both physiography and geology which deals with the form of the Earth, the general configuration of its surface, and the changes that take place in the evolution of landform. GRADIENT (GRADE). See SLOPE. With reference to winds or currents, the rate of increase or decrease in speed, usually in the vertical; or the curve that represents this rate. GRAVEL. See SOIL CLASSIFICATION. GRAVITY WAVE. A wave whose velocity of propagation is controlled primarily by gravity. Water waves more than 2 inches long are considered gravity waves. Waves longer than 1] inch and shorter than 2 inches are in an indeterminate zone between CAPILLARY and GRAVITY WAVES. See RIPPLE. A-14 GROIN (British, GROYNE). A shore protection structure built (usually perpendicular to the shoreline) to trap littoral drift or retard erosion of the shore. GROIN SYSTEM. A series of groins acting together to protect a section of beach. Commonly called a groin field. GROUND SWELL. A long high ocean swell; also, this swell as it rises to prominent height in shallow water. GROUND WATER. Subsurface water occupying the zone of saturation. Ina strict sense, the term is applied only to water below the WATER TABLE. GROUP VELOCITY. The velocity of a wave group. In deep water, it is equal to one-half the velocity of the individual waves within the group. GULF. A large embayment in a coast; the entrance is generally wider than the length. GUT. (1) A narrow passage such as a strait or inlet. (2) A channel in otherwise shallower water, generally formed by water in motion. HALF-TIDE LEVEL. MEAN TIDE LEVEL. HARBOR (British, HARBOUR). Any protected water area affording a place of safety for vessels. See also PORT. HARBOR OSCILLATION (HARBOR SURGING). The nontidal vertical water movement in a harbor or bay. Usually the vertical motions are low; but when oscilla- tions are excited by a tsunami or storm surge, they may be quite large. Variable winds, air oscillations, or surf beat also may cause oscilla- tions. See SEICHE. HEADLAND (HEAD). A high, steep-faced promontory extending into the sea. HEAD OF RIP. The part of a rip current that has widened out seaward of the breakers. See also CURRENT, RIP; CURRENT, FEEDER; and NECK (RIP). HEIGHT OF WAVE. See WAVE HEIGHT. HIGH TIDE, HIGH WATER (HW). The maximum elevation reached by each rising tide. See TIDE. (See Figure A-10.) HIGH WATER. See HIGH TIDE. HIGH WATER LINE. In strictness, the intersection of the plane of mean high water with the shore. The shoreline delineated on the nautical charts of the National Ocean Service is an approximation of the high water line. For specific occurrences, the highest elevation on the shore reached during a storm or rising tide, including meteorological effects. HIGH WATER OF ORDINARY SPRING TIDES (HWOST). A tidal datum appearing in some British publications, based on high water of ordinary spring tides. A-15 HIGHER HIGH WATER (HHW). The higher of the two high waters of any tidal day. The single high water occurring daily during periods when the tide is diurnal is considered to be a higher high water. (See Figure A-10.) HIGHER LOW WATER (HLW). The higher of two low waters of any tidal day. (See Figure A-10.) HINDCASTING, WAVE. The use of historic synoptic wind charts to calculate characteristics of waves that probably occurred at some past time. HOOK. A spit or narrow cape of sand or gravel which turns landward at the outer end. HURRICANE. An intense tropical cyclone in which winds tend to spiral inward toward a core of low pressure, with maximum surface wind velocities that equal or exceed 33.5 meters per second (75 mph or 65 knots) for several minutes or longer at some points. TROPICAL STORM is the term applied if maximum winds are less than 33.5 meters per second. HURRICANE PATH or TRACK. Line of movement (propagation) of the eye through an area. HURRICANE STAGE HYDROGRAPH. A continuous graph representing water level stages that would be recorded in a gage well located at a specified point of interest during the passage of a particular hurricane, assuming that effects of relatively short-period waves are eliminated from the record by damping features of the gage well. Unless specifically excluded and separately accounted for, hurricane surge hydrographs are assumed to include effects of astronomical tides, barometric pressure differences, and all other factors that influence water level stages within a properly designed gage well located at a specified point. HURRICANE SURGE HYDROGRAPH. A continuous graph representing the difference between the hurricane stage hydrograph and the water stage hydrograph that would have prevailed at the same point and time if the hurricane had not occurred. HURRICANE WIND PATTERN or ISOVEL PATTERN. An actual or graphical representa- tion of near-surface wind velocities covering the entire area of a hurricane at a particular instant. Isovels are lines connecting points of simultaneous equal wind velocities, usually referenced 9 meters (30 feet) above the surface, in meters per second, knots, or meters per hour; wind directions at various points are indicated by arrows or deflection angles on the isovel charts. Isovel charts are usually prepared at each hour during a hurricane, but for each half hour during critical periods. HYDRAULICALLY EQUIVALENT GRAINS. Sedimentary particles that settle at the same rate under the same conditions. HYDROGRAPHY. (1) A configuration of an underwater surface including its relief, bottom materials, coastal structures, etc. (2) The description and study of seas, lakes, rivers, and other waters. A-16 HYPOTHETICAL HURRICANE ("'HYPOHURRICANE"). A representation of a hurricane, with specified characteristics, that is assumed to occur in a particular study area, following a specified path and timing sequence. TRANSPOSED--A hypohurricane based on the storm transposition principle, assumed to have wind patterns and other characteristics basically com- parable to a specified hurricane of record, but transposed to follow a new path to serve as a basis for computing a hurricane surge hydrograph that would be expected at a selected point. Moderate adjustments in timing or rate of forward movement may also be made, if these are compatible with meteorological considerations and study objectives. HYPOHURRICANE BASED ON GENERALIZED PARAMETERS--Hypohurricane estimates based on various logical combinations of hurricane characteristics used in estimating hurricane surge magnitudes corresponding to a range of prob- abilities and potentialities. The STANDARD PROJECT HURRICANE is most commonly used for this purpose, but estimates corresponding to more severe or less severe assumptions are important in some project investigations. STANDARD PROJECT HURRICANE (SPH)--A hypothetical hurricane intended to represent the most severe combination of hurricane parameters that is reasonably characteristte of a specified region, excluding extremely rare combinations. It is further assumed that the SPH would approach a given project site from such direction, and at such rate of movement, to produce the highest HURRICANE SURGE HYDROGRAPH, considering pertinent hydraulic characteristics of the area. Based on this concept, and on extensive meteorological studies and probability analyses, a tabulation of "Standard Project Hurricane Index Characteristics" mutually agreed upon by repre- sentatives of the U. S. Weather Service and the Corps of Engineers, is available. PROBABLE MAXIMUM HURRICANE--A hypohurricane that might result from the most severe combination of hurricane parameters that is considered reasonably possible in the region involved, if the hurricane should approach the point under study along a critical path and at optimum rate of movement. This estimate is substantially more severe than the SPH criteria. DESIGN HURRICANE--A representation of a hurricane with specified charac- teristics that would produce HURRICANE SURGE HYDROGRAPHS and coincident wave effects at various key locations along a proposed project aline- ment. It governs the project design after economics and other factors have been duly considered. The design hurricane may be more or less severe than the SPH, depending on economics, risk, and _ local considerations. IMPERMEABLE GROIN. A groin through which sand cannot pass. INDIAN SPRING LOW WATER. The approximate level of the mean of lower low waters at spring tides, used principally in the Indian Ocean and along the east coast of Asia. Also INDIAN TIDE PLANE. INDIAN TIDE PLANE. The datum of INDIAN SPRING LOW WATER. A-17 INLET. (1) A short, narrow waterway connecting a bay, lagoon, or similar body of water with a large parent body of water. (2) An arm of the sea (or other body of water) that is long compared to its width and may extend a considerable distance inland. See also TIDAL INLET. INLET GORGE. Generally, the deepest region of an inlet channel. INSHORE (ZONE). In beach terminology, the zone of variable width extending from the low water line through the breaker zone. Also SHOREFACE. (See Figure A-1.) INSHORE CURRENT. Any current in or landward of the breaker zone. INSULAR SHELF. The zone surrounding an island extending from the low water line to the depth (usually about 183 meters (100 fathoms)) where there is a marked or rather steep descent toward the great depths. INTERNAL WAVES. Waves that occur within a fluid whose density changes with depth, either abruptly at a sharp surface of discontinuity (an interface), or gradually. Their amplitude is greatest at the density discontinuity or, in the case of a gradual density change, somewhere in the interior of the fluid and not at the free upper surface where the surface waves have their maximum amplitude. IRROTATIONAL WAVE. A wave with fluid particles that do not revolve around an axis through their centers, although the particles themselves may travel in circular or nearly circular orbits. Irrotational waves may be PROGRESSIVE, STANDING, OSCILLATORY, or TRANSLATORY. For example, the Airy, Stokes, cnoidal, and solitary wave theories describe irrotational waves. Compare TROCHOIDAL WAVE. ISOBATH. A contour line connecting points of equal water depths on a chart. ISOVEL PATTERN. See HURRICANE WIND PATTERN. ISTHMUS. A narrow strip of land, bordered on both sides by water, that connects two larger bodies of land. JET. To place (a pile, slab, or pipe) in the ground by means of a jet of water acting at the lower end. JETTY. (1) (United States usage) On open seacoasts, a structure extending into a body of water, which is designed to prevent shoaling of a channel by littoral materials and to direct and confine the stream or tidal flow. Jetties are built at the mouths of rivers or tidal inlets to help deepen and stabilize a channel. (2) (British usage) WHARF or PIER. See TRAINING WALL. KEY. A low, insular bank of sand, coral, etc., as one of the islets off the southern coast of Florida. Also CAY. KINETIC ENERGY (OF WAVES). In a progressive oscillatory wave, a summation of the energy of motion of the particles within the wave. A-18 KNOLL. A submerged elevation of rounded shape rising less than 1000 meters from the ocean floor and of limited extent across the summit. Compare SEAMOUNT. KNOT. The unit of speed used in navigation equal to 1 nautical mile (6,076.115 feet or 1,852 meters) per hour. LAGGING. See TIDES, DAILY RETARDATION OF. LAGOON. A shallow body of water, like a pond or lake, usually connected to the sea. (See Figures A-8 and A-9.) LAND BREEZE. A light wind blowing from the land to the sea, caused by unequal cooling of land and water masses. LAND-SEA BREEZE. The combination of a land breeze and a sea breeze as a diurnal phenomenon. LANDLOCKED. Enclosed, or nearly enclosed, by land--thus protected from the sea, as a bay or a harbor. LANDMARK. A conspicuous object, natural or artificial, located near or on land, which aids in fixing the position of an observer. LEAD LINE. A line, wire, or cord used in sounding. It is weighted at one end with a plummet (sounding lead). Also SOUNDING LINE. LEE. (1) Shelter, or the part or side sheltered or turned away from the wind or waves. (2) (Chiefly nautical) The quarter or region toward which the wind blows. LEEWARD. The direction toward which the wind is blowing; the direction toward which waves are traveling. LENGTH OF WAVE. The horizontal distance between similar points on two successive waves measured perpendicularly to the crest. (See Figure A-3.) LEVEE. A dike or embankment to protect land from inundation. LIMIT OF BACKRUSH (LIMIT OF BACKWASH). See BACKRUSH, BACKWASH. LITTORAL. Of or pertaining to a shore, especially of the sea. LITTORAL CURRENT. See CURRENT, LITTORAL. LITTORAL DEPOSITS. Deposits of littoral drift. LITTORAL DRIFT. The sedimentary matertal moved in the littoral zone under the influence of waves and currents. LITTORAL TRANSPORT. The movement of littoral drift in the littoral zone by waves and currents. Includes movement parallel (longshore transport) and perpendicular (on-offshore transport) to the shore. A-19 LITTORAL TRANSPORT RATE. Rate of transport of sedimentary material parallel or perpendicular to the shore in the littoral zone. Usually expressed in cubic meters (cubic yards) per year. Commonly synonymous with LONGSHORE TRANSPORT RATE. LITTORAL ZONE. In beach terminology, an indefinite zone extending seaward from the shoreline to just beyond the breaker zone. LOAD. The quantity of sediment transported by a current. It includes the suspended load of small particles and the bedload of large particles that move along the bottom. LONGSHORE. Parallel to and near the shoreline; ALONGSHORE. LONGSHORE BAR. A bar running roughly parallel to the shoreline. LONGSHORE CURRENT. See CURRENT, LONGSHORE. LONGSHORE TRANSPORT RATE. Rate of transport of sedimentary material parallel to the shore. Usually expressed in cubic meters (cubic yards) per year. Commonly synonymous with LITTORAL TRANSPORT RATE. LOOP. That part of a STANDING WAVE where the vertical motion is greatest and the horizontal velocities are least. Loops (sometimes called ANTINODES) are associated with CLAPOTIS and with SEICHE action resulting from wave reflections. Compare NODE. LOW TIDE (LOW WATER, LW). The minimum elevation reached by each falling tide. See TIDE. (See Figure A-10.) LOW WATER DATUM. An approximation to the plane of mean low water that has been adopted as a standard reference plane. See also DATUM, PLANE and CHART DATUM. LOW WATER LINE. The intersection of any standard low tide datum plane with the shore. LOW WATER OF ORDINARY SPRING TIDES (LWOST). A tidal datum appearing in some British publications, based on low water of ordinary spring tides. LOWER HIGH WATER (LHW). The lower of the two high waters of any tidal day. (See Figure A-10.) LOWER LOW WATER (LLW). The lower of the two low waters of any tidal day. The single low water occurring daily during periods when the tide is diurnal is considered to be a lower low water. (See Figure A-10.) MANGROVE. A tropical tree with interlacing prop roots, confined to low-lying brackish areas. MARIGRAM. A graphic record of the rise and fall of the tide. MARSH. An area of soft, wet, or periodically inundated land, generally tree- less and usually characterized by grasses and other low growth. A-20 MARSH, SALT. A marsh periodically flooded by salt water. MASS TRANSPORT. The net transfer of water by wave action in the direction of wave travel. See also ORBIT. MEAN DIAMETER, GEOMETRIC. See GEOMETRIC MEAN DIAMETER. MEAN HIGH WATER (MHW). The average height of the high waters over a 19-year period. For shorter periods of observations, corrections are applied to eliminate known variations and reduce the results to the equivalent of a mean 19-year value. All high water heights are included in the average where the type of tide is either semidiurnal or mixed. Only the higher high water heights are included in the average where the type of tide is diurnal. So determined, mean high water in the latter case is the same as mean higher high water. MEAN HIGH WATER SPRINGS. The average height of the high waters occurring at the time of spring tide. Frequently abbreviated to HIGH WATER SPRINGS. MEAN HIGHER HIGH WATER (MHHW). The average height of the higher high waters over a 19-year period. For shorter periods of observation, corrections are applied to eliminate known variations and reduce the result to the equivalent of a mean 19-year value. MEAN LOW WATER (MLW). The average height of the low waters over a 19-year period. For shorter periods of observations, corrections are applied to eliminate known variations and reduce the results to the equivalent of a mean 19-year value. All low water heights are included in the average where the type of tide is either semidiurnal or mixed. Only lower low water heights are included in the average where the type of tide is diurnal. So determined, mean low water in the latter case is the same as mean lower low water. MEAN LOW WATER SPRINGS. The average height of low waters occurring at the time of the spring tides. It is usually derived by taking a plane depressed below the half-tide level by an amount equal to one-half the spring range of tide, necessary corrections being applied to reduce the result to a mean value. This plane is used to a considerable extent for hydrographic work outside of the United States and is the plane of reference for the Pacific approaches to the Panama Canal. Frequently abbreviated to LOW WATER SPRINGS. MEAN LOWER LOW WATER (MLLW). The average height of the lower low waters over a 19-year period. For shorter periods of observations, corrections are applied to eliminate known variations and reduce the results to the equivalent of a mean 19-year value. Frequently abbreviated to LOWER LOW WATER. MEAN SEA LEVEL. The average height of the surface of the sea for all stages of the tide over a 19-year period, usually determined from hourly height readings. Not necessarily equal to MEAN TIDE LEVEL. MEAN TIDE LEVEL. A plane midway between MEAN HIGH WATER and MEAN LOW WATER. Not necessarily equal to MEAN SEA LEVEL. Also HALF-TIDE LEVEL. A-21 MEDIAN DIAMETER. The diameter which marks the division of a given sand sample into two equal parts by weight, one part containing all grains larger than that diameter and the other part containing all grains smaller. MEGARIPPLE. See SAND WAVE. MIDDLE-GROUND SHOAL. A shoal formed by ebb and flood tides in the middle of the channel of the lagoon or estuary end of an inlet. MINIMUM DURATION. See DURATION, MINIMUM. MINIMUM FETCH. The least distance in which steady-state wave conditions will develop for a wind of given speed blowing a given duration of time. MIXED TIDE. A type of tide in which the presence of a diurnal wave is conspicuous by a large inequality in either the high or low water heights, with two high waters and two low waters usually occurring each tidal day. In strictness, all tides are mixed, but the name is usually applied without definite limits to the tide intermediate to those predominantly semidiurnal and those predominantly diurnal. (See Figure A-10.) MOLE. In coastal terminology, a massive land-connected, solid-fill structure of earth (generally revetted), masonry, or large stone, which may serve as a breakwater or pier. MONOCHROMATIC WAVES. A series of waves generated in a laboratory; each wave has the same length and period. MONOLITHIC. Like a single stone or block. In coastal structures, the type of construction in which the structure’s component parts are bound together to act as one. MUD. A fluid-to-plastic mixture of finely divided particles of solid material and water. NAUTICAL MILE. The length of a minute of arc, 1/21,600 of an average great circle of the Earth. Generally one minute of latitude is considered equal to one nautical mile. The accepted United States value as of 1 July 1959 is 1,852 meters (6,076.115 feet), approximately 1.15 times as long as the U.S. statute mile of 5,280 feet. Also geographical mile. NEAP TIDE. A tide occurring near the time of quadrature of the moon with the sun. The neap tidal range is usually 10 to 30 percent less than the mean tidal range. NEARSHORE (zone). In beach terminology an indefinite zone extending seaward from the shoreline well beyond the breaker zone. It defines the area of NEARSHORE CURRENTS. (See Figure A-1.) NEARSHORE CIRCULATION. The ocean circulation pattern composed of the CURRENTS, NEARSHORE and CURRENTS, COASTAL. See CURRENT. Ba 22 NEARSHORE CURRENT SYSTEM. The current system caused primarily by wave action in and near the breaker zone, and which consists of four parts: the shoreward mass transport of water; longshore currents; seaward return flow, including rip currents; and the longshore movement of the expanding heads of rip currents. (See Figure A-7.) See also NEARSHORE CIRCULATION. NECK. (1) The narrow band of water flowing seaward through the surf. Also RIP. (2) The narrow strip of land connecting a peninsula with the mainland. NIP. The cut made by waves in a shoreline of emergence. NODAL ZONE. An area in which the predominant direction of the LONGSHORE TRANSPORT changes. NODE. That part of a STANDING WAVE where the vertical motion is least and the horizontal velocities are greatest. Nodes are associated with CLAPOTIS and with SEICHE action resulting from wave reflections. Compare LOOP. NOURISHMENT. The process of replenishing a beach. It may be brought about naturally by longshore transport, or artificially by the deposition of dredged materials. OCEANOGRAPHY. The study of the sea, embracing and indicating all knowledge pertaining to the sea’s physical boundaries, the chemistry and physics of seawater, and marine biology. OFFSHORE. (1) In beach terminology, the comparatively flat zone of variable width, extending from the breaker zone to the seaward edge of the Continental Shelf. (2) A direction seaward from the shore. (See Figure A-1.) OFFSHORE BARRIER. See BARRIER BEACH. OFFSHORE CURRENT. (1) Any current in the offshore zone. (2) Any current flowing away from shore. OFFSHORE WIND. A wind blowing seaward from the land in the coastal area. ONSHORE. A direction landward from the sea. ONSHORE WIND. A wind blowing landward from the sea in the coastal area. OPPOSING WIND. In wave forecasting, a wind blowing in a direction opposite to the ocean-wave advance; generally, a headwind. ORBIT. In water waves, the path of a water particle affected by the wave motion. In deepwater waves the orbit is nearly circular, and in shallow- water waves the orbit is nearly elliptical. In general, the orbits are slightly open in the direction of wave motion, giving rise to MASS TRANSPORT. (See Figure A-3.) A-23 ORBITAL CURRENT. The flow of water accompanying the orbital movement of the water particles in a wave. Not to be confused with wave-generated LITTORAL CURRENTS. (See Figure A-3.) ORTHOGONAL. On a wave-refraction diagram, a line drawn perpendicularly to the wave crests. WAVE RAY. (See Figure A-6.) OSCILLATION. (1) A periodic motion backward and forward. (2) Vibration or variance above and below a mean value. OSCILLATORY WAVE. A wave in which each individual particle oscillates about a point with little or no permanent change in mean position. The term is commonly applied to progressive oscillatory waves in which only the form advances, the individual particles moving in closed or nearly closed orbits. Compare WAVE OF TRANSLATION. See also ORBIT. OUTFALL. A structure extending into a body of water for the purpose of discharging sewage, storm runoff, or cooling water. OVERTOPPING. Passing of water over the top of a structure as a result of wave runup or surge action. OVERWASH. That portion of the uprush that carries over the crest of a berm or of a structure. PARAPET. A low wall built along the edge of a structure such as a seawall or quay. PARTICLE VELOCITY. The velocity induced by wave motion with which a specific water particle moves within a wave. PASS. In hydrographic usage, a navigable channel through a bar, reef, or shoal, or between closely adjacent islands. PEBBLES. See SOIL CLASSIFICATION. PENINSULA. An elongated body of land nearly surrounded by water and connected to a larger body of land. PERCHED BEACH. A beach or fillet of sand retained above the otherwise normal profile level by a submerged dike. PERCOLATION. The process by which water flows through the interstices of a sediment. Specifically, in wave phenomena, the process by which wave action forces water through the interstices of the bottom sediment and which tends to reduce wave heights. PERIODIC CURRENT. A current caused by the tide-producing forces of the moon and the sun; a part of the same general movement of the sea that is manifested in the vertical rise and fall of the tides. See also CURRENT, FLOOD and CURRENT, EBB. A-24 PERMANENT CURRENT. A current that runs continuously, independent of the tides and temporary causes. Permanent currents include the freshwater discharge of a river and the currents that form the general circulatory systems of the oceans. PERMEABLE GROIN. A groin with openings large enough to permit passage of appreciable quantities of LITTORAL DRIFT. PETROGRAPHY. The systematic description and classification of rocks. PHASE. In surface wave motion, a point in the period to which the wave motion has advanced with respect to a given initial reference point. PHASE INEQUALITY. Variations in the tides or tidal currents associated with changes in the phase of the Moon in relation to the Sun. PHASE VELOCITY. Propagation velocity of an individual wave as opposed to the velocity of a wave group. PHI GRADE SCALE. A logarithmic transformation of the Wentworth grade scale for size classifications of sediment grains based on the negative logarithm to the base 2 of the particle diameter: 9% = -logod - See SOIL CLASSIFICATION. PIER. A structure, usually of open construction, extending out into the water from the shore, to serve as a landing place, recreational facility, etc., rather than to afford coastal protection. In the Great Lakes, a term sometimes improperly applied to jetties. PILE. A long, heavy timber or section of concrete or metal to be driven or jetted into the earth or seabed to serve as a support or protection. PILE, SHEET. A pile with a generally slender flat cross section to be driven into the ground or seabed and meshed or interlocked with like members to form a diaphragm, wall, or bulkhead. PILING. A group of piles. PLAIN, COASTAL. See COASTAL PLAIN. PLANFORM. The outline or shape of a body of water as determined by the still- water line. PLATEAU. A land area (usually extensive) having a relatively level surface raised sharply above adjacent land on at least one side; table land. A similar undersea feature. PLUNGE POINT. (1) For a plunging wave, the point at which the wave curls over and falls. (2) The final breaking point of the waves just before they rush up on the beach. (See Figure A-1.) PLUNGING BREAKER. See BREAKER. A=25 POCKET BEACH. A beach, usually small, in a coastal reentrant or between two littoral barriers. POINT. The extreme end of a cape; the outer end of any land area protruding into the water, usually less prominent than a cape. PORT. A place where vessels may discharge or receive cargo; it may be the entire harbor including its approaches and anchorages, or only the commercial part of a harbor where the quays, wharves, facilities for transfer of cargo, docks, and repair shops are situated. POTENTIAL ENERGY OF WAVES. In a progressive oscillatory wave, the energy resulting from the elevation or depression of the water surface from the undisturbed level. PRISM. See TIDAL PRISM. PROBABLE MAXIMUM WATER LEVEL. A hypothetical water level (exclusive of wave runup from normal wind-generated waves) that might result from the most severe combination of hydrometeorological, geoseismic, and other geo- physical factors and that is considered reasonably possible in the region involved, with each of these factors considered as affecting the locality in a maximum manner. This level represents the physical response of a body of water to maximum applied phenomena such as hurricanes, moving squall lines, other cyclonic meteorological events, tsunamis, and astronomical tide combined with maximum probable ambient hydrological conditions such as wave setup, rainfall, runoff, and river flow. It is a water level with virtually no risk of being exceeded. PROFILE, BEACH. The intersection of the ground surface with a vertical plane; may extend from the top of the dune line to the seaward limit of sand movement. (See Figure A-1.) PROGRESSION (of a beach). See ADVANCE. PROGRESSIVE WAVE. A wave that moves relative to a fixed coordinate system in a fluid. The direction in which it moves is termed the direction of wave propagation. PROMONTORY. A high point of land projecting into a body of water; a HEADLAND. PROPAGATION OF WAVES. The transmission of waves through water. PROTOTYPE. In laboratory usage, the full-scale structure, concept, or phenomenon used as a basis for constructing a scale model or copy. QUARRYSTONE. Any stone processed from a quarry. QUAY (Pronounced KEY). A stretch of paved bank, or a solid artificial landing place parallel to the navigable waterway, for use in loading and unloading vessels. A-26 QUICKSAND. Loose, yielding, wet sand which offers no support to heavy objects. The upward flow of the water has a velocity that eliminates contact pressures between the sand grains and causes the sand-water mass to behave like a fluid. RADIUS OF MAXIMUM WINDS. Distance from the eye of a hurricane, where surface and wind velocities are zero, to the place where surface windspeeds are maximum. RAY, WAVE. See ORTHOGONAL. RECESSION (of a beach). (1) A continuing landward movement of the shore- line. (2) A net landward movement of the shoreline over a _ specified time. Also RETROGRESSION. REEF. An offshore consolidated rock hazard to navigation, with a least depth of about 20 meters (10 fathoms) or less. REEF, ATOLL. See ATOLL. REEF, BARRIER. See BARRIER REEF. REEF, FRINGING. See FRINGING REEF. REEF, SAND. BAR. REFERENCE PLANE. See DATUM PLANE. REFERENCE STATION. A place for which tidal constants have previously been determined and which is used as a standard for the comparison of simultaneous observations at a second station. Also, a station for which independent daily predictions are given in the tide or current tables from which corresponding predictions are obtained for other stations by means of differences or factors. REFLECTED WAVE. That part of an incident wave that is returned seaward when a wave impinges on a steep beach, barrier, or other reflecting surface. REFRACTION (of water waves). (1) The process by which the direction of a wave moving in shallow water at an angle to the contours is changed: the part of the wave advancing in shallower water moves more slowly than that part still advancing in deeper water, causing the wave crest to bend toward alinement with the underwater contours. (2) The bending of wave crests by currents. (See Figure A-5.) REFRACTION COEFFICIENT. The square root of the ratio of the distance between adjacent orthogonals in deep water to their distance apart in shallow water at a selected point. When multiplied by the SHOALING FACTOR and a factor for friction and percolation, this becomes the WAVE HEIGHT COEFFICIENT or the ratio of the refracted wave height at any point to the deepwater wave height. Also, the square root of the ENERGY COEFFICIENT. A-27 REFRACTION DIAGRAM. A drawing showing positions of wave crests and/or orthogonals in a given area for a specific deepwater wave period and direction. (See Figure A-6.) RESONANCE. The phenomenon of amplification of a free wave or oscillation of a system by a forced wave or oscillation of exactly equal period. The forced wave may arise from an impressed force upon the system or from a boundary condition. RETARDATION. The amount of time by which corresponding tidal phases grow later day by day (about 50 minutes). RETROGRESSION (of a beach). (1) A continuing landward movement of the shore- line. (2) A net landward movement of the shoreline over a specified time. Also RECESSION. REVETMENT. A facing of stone, concrete, etc., built to protect a scarp, embankment, or shore structure against erosion by wave action or currents. REYNOLDS NUMBER. The dimensionless ratio of the inertial force to the viscous force in fluid motion, where L is a characteristic length, v the kinematic viscosity, and V a characteristic velocity. The Reynolds number is of importance in the theory of hydrodynamic stability and the origin of turbulence. RIA. A long, narrow inlet, with depth gradually diminishing inward. RIDGE, BEACH. A nearly continuous mound of beach material that has been shaped by wave or other action. Ridges may occur singly or as a series of approximately parallel deposits. British usage, FULL. (See Figure A-/7.) RILL MARKS. Tiny drainage channels in a beach caused by the flow seaward of water left in the sands of the upper part of the beach after the retreat of the tide or after the dying down of storm waves. RIP. A body of water made rough by waves meeting an opposing current, particularly a tidal current; often found where tidal currents are converging and sinking. RIP CURRENT. A strong surface current flowing seaward from the shore. It usually appears as a visible band of agitated water and is the return movement of water piled up on the shore by incoming waves and wind. With the seaward movement concentrated in a limited band its velocity is somewhat accentuated. A rip consists of three parts: the FEEDER CURRENTS flowing parallel to the shore inside the breakers; the NECK, where the feeder currents converge and flow through the breakers in a narrow band or "rip"; and the HEAD, where the current widens and slackens outside the breaker line. A rip current is often miscalled a rip tide. Also RIP SURF. See NEARSHORE CURRENT SYSTEM. (See Figure A-/.) A-28 RIP SURF. See RIP CURRENT. RIPARIAN. Pertaining to the banks of a body of water. RIPARIAN RIGHTS. The rights of a person owning land containing or bordering on a watercourse or other body of water in or to its banks, bed, or waters. RIPPLE. (1) The ruffling of the surface of water; hence, a little curling wave or undulation. (2) A wave less than 0.05 meter (2 inches) long controlled to a significant degree by both surface tension and gravity. See CAPILLARY WAVE and GRAVITY WAVE. RIPPLES (bed forms). Small bed forms with wavelengths less than 0.3 meter (1 foot) and heights less than 0.03 meter (0.1 foot). RIPRAP. A protective layer or facing of quarrystone, usually well graded within wide size limit, randomly placed to prevent erosion, scour, or sloughing of an embankment of bluff; also the stone so used. The quarrystone is placed in a layer at least twice the thickness of the 50 percent size, or 1.25 times the thickness of the largest size stone in the gradation. ROLLER. An indefinite term, sometimes considered to denote one of a series of long-crested, large waves which roll in on a shore, as after a storm. RUBBLE. (1) Loose angular waterworn stones along a _ beach. (2) Rough, irregular fragments of broken rock. RUBBLE-MOUND STRUCTURE. A mound of random-shaped and random-placed stones protected with a cover layer of selected stones or specially shaped concrete armor units. (Armor units in a primary cover layer may be placed in an orderly manner or dumped at random.) RUNNEL. A corrugation or trough formed in the foreshore or in the bottom just offshore by waves or tidal currents. RUNUP. The rush of water up a structure or beach on the breaking of a wave. Also UPRUSH, SWASH. The amount of runup is the vertical height above still-water level to which the rush of water reaches. SALTATION. That method of sand movement in a fluid in which individual particles leave the bed by bounding nearly vertically and, because the motion of the fluid is not strong or turbulent enough to retain them in suspension, return to the bed at some distance downstream. The travel path of the particles is a series of hops and bounds. SALT MARSH. A marsh periodically flooded by salt water. SAND. See SOIL CLASSIFICATION. SANDBAR. (1) See BAR. (2) In a river, a ridge of sand built up to or near the surface by river currents. A-29 SAND BYPASSING. See BYPASSING, SAND. SAND REEF. BAR. SAND WAVE. A large wavelike sediment feature composed of sand in very shallow water. Wavelength may reach 100 meters; amplitude is about 0.5 meter. Also MEGARIPPLE. SCARP. See ESCARPMENT. SCARP, BEACH. An almost vertical slope along the beach caused by erosion by wave action. It may vary in height from a few centimeters to a meter or so, depending on wave action and the nature and composition of the beach. (See Figure A-1.) SCOUR. Removal of underwater material by waves and currents, especially at the base or toe of a shore structure. SEA BREEZE. A light wind blowing from the sea toward the land caused by unequal heating of land and water masses. SEA CHANGE. (1) A change wrought by the sea. (2) A marked transformation. SEA CLIFF. A cliff situated at the seaward edge of the coast. SEA LEVEL. See MEAN SEA LEVEL. SEAMOUNT. An elevation rising more than 1000 meters above the ocean floor, and of limited extent across the summit. Compare KNOLL. SEA PUSS. A dangerous longshore current; a rip current caused by return flow; loosely, the submerged channel or inlet through a bar caused by those currents. SEAS. Waves caused by wind at the place and time of observation. SEASHORE. The SHORE of a sea or ocean. SEA STATE. Description of the sea surface with regard to wave action. Also called state of sea. SEAWALL. A structure separating land and water areas, primarily designed to prevent erosion and other damage due to wave action. See also BULKHEAD. SEICHE. (1) A standing wave oscillation of an enclosed waterbody that continues, pendulum fashion, after the cessation of the originating force, which may have been either seismic or atmospheric. (2) An oscillation of a fluid body in response to a disturbing force having the same frequency as the natural frequency of the fluid system. Tides are now considered to be seiches induced primarily by the periodic forces caused by the Sun and Moon. (3) In the Great Lakes area, any sudden rise in the water of a harbor or a lake whether or not it is oscillatory (although inaccurate in a strict sense, this usage is well established in the Great Lakes area). A-30 SEISMIC SEA WAVE. See TSUNAMI. SEMIDIURNAL TIDE. A tide with two high and two low waters in a tidal day with comparatively little diurnal inequality. (See Figure A-10.) SET OF CURRENT. The direction toward which a current flows. SETUP, WAVE. Superelevation of the water surface over normal surge elevation due to onshore mass transport of the water by wave action alone. SETUP, WIND. See WIND SETUP. SHALLOW WATER. (1) Commonly, water of such a depth that surface waves are noticeably affected by bottom topography. It is customary to consider water of depths less than one-half the surface wavelength as _ shallow water. See TRANSITIONAL ZONE and DEEP WATER. @)) More) strictly) in hydrodynamics with regard to progressive gravity waves, water in which the depth is less than 1/25 the wavelength; also called VERY SHALLOW WATER. SHEET PILE. See PILE, SHEET. SHELF, CONTINENTAL. See CONTINENTAL SHELF. SHELF, INSULAR. See INSULAR SHELF. SHINGLE. (1) Loosely and commonly, any beach material coarser than ordinary gravel, especially any having flat or flattish pebbles. (2) Strictly and accurately, beach material of smooth, well-rounded pebbles that are roughly the same size. The spaces between pebbles are not filled with finer materials. Shingle often gives out a musical sound when stepped on. SHOAL (noun). A detached elevation of the sea bottom, comprised of any material except rock or coral, which may endanger surface navigation. SHOAL (verb). (1) To become shallow gradually. (2) To cause to become shallow. (3) To proceed from a greater to a lesser depth of water. SHOALING COEFFICIENT. The ratio of the height of a wave in water of any depth to its height in deep water with the effects of refraction, friction, and percolation eliminated. Sometimes SHOALING FACTOR or DEPTH FACTOR. See also ENERGY COEFFICIENT and REFRACTION COEFFICIENT. SHOALING FACTOR. See SHOALING COEFFICIENT. SHORE. The narrow strip of land in immediate contact with the sea, including the zone between high and low water lines. A shore of unconsolidated material is usually called a BEACH. (See Figure A-1.) SHOREFACE. The narrow zone seaward from the low tide SHORELINE, covered by water, over which the beach sands and gravels actively oscillate with changing wave conditions. See INSHORE (ZONE). See Figure A-l. A-31 SHORELINE. The intersection of a specified plane of water with the shore or beach (e.g., the high water shoreline would be the intersection of the plane of mean high water with the shore or beach). The line delineating the shoreline on National Ocean Service nautical charts and surveys approximates the mean high water line. SIGNIFICANT WAVE. A statistical term relating to the one-third highest waves of a given wave group and defined by the average of their heights and periods. The composition of the higher waves depends upon the extent to which the lower waves are considered. Experience indicates that a careful observer who attempts to establish the character of the higher waves will record values which approximately fit the definition of the significant wave. SIGNIFICANT WAVE HEIGHT. The average height of the one-third highest waves of a given wave group. Note that the composition of the highest waves depends upon the extent to which the lower waves are considered. In wave record analysis, the average height of the highest one-third of a selected number of waves, this number being determined by dividing the time of record by the significant period. Also CHARACTERISTIC WAVE HEIGHT. SIGNIFICANT WAVE PERIOD. An arbitrary period generally taken as the period of the one-third highest waves within a given group. Note that the composition of the highest waves depends upon the extent to which the lower waves are considered. In wave record analysis, this is determined as the average period of the most frequently recurring of the larger well- defined waves in the record under study. SILT. See SOIL CLASSIFICATION. SINUSOIDAL WAVE. An oscillatory wave having the form of a sinusoid. SLACK TIDE (SLACK WATER). The state of a tidal current when its velocity is near zero, especially the moment when a reversing current changes direction and its velocity is zero. Sometimes considered the intermediate period between ebb and flood currents during which the velocity of the currents is less than 0.05 meter per second (0.1 knot). See STAND OF TIDE. SLIP. A berthing space between two piers. SLOPE. The degree of inclination to the horizontal. Usually expressed as a ratio, such as 1:25 or 1 on 25, indicating 1 unit vertical rise in 25 units of horizontal distance; or in a decimal fraction (0.04); degrees (2° 18’); or percent (4 percent). SLOUGH. See BAYOU. SOIL CLASSIFICATION (size). An arbitrary division of a continuous scale of grain sizes such that each scale unit or grade may serve as a convenient class interval for conducting the analysis or for expressing the results of an analysis. There are many classifications used; the two most ofen used are shown graphically in Table A-l. A-32 SOLITARY WAVE. A wave consisting of a single elevation (above the original water surface), whose height is not necessarily small compared to the depth, and neither followed nor preceded by another elevation or depression of the water surfaces. SORTING COEFFICIENT. A coefficient used in describing the distribution of grain sizes in a sample of unconsolidated material. It is defined as §S = Q1/Q3 » where Qy is the diameter (in millimeters) which has 75 percent of the cumulative size-frequency (by weight) distribution smaller than itself and 25 percent larger than itself, and Q, is that diameter having 25 percent smaller and 75 percent larger than itself. SOUND (noun). (1) A wide waterway between the mainland and an island, or a wide waterway connecting two sea areas. See also STRAIT. (2) IN relatively long arm of the sea or ocean forming a channel between an island and a mainland or connecting two larger bodies, as a sea and the ocean, or two parts of the same body; usually wider and more extensive than a strait. SOUND (verb). To measure the depth of the water. SOUNDING. A measured depth of water. On hydrographic charts the soundings are adjusted to a specific plane of reference (SOUNDING DATUM). SOUNDING DATUM. The plane to which soundings are referred. See also CHART DATUM. SOUNDING LINE. A line, wire, or cord used in sounding, which is weighted at one end with a plummet (sounding lead). Also LEAD LINE. SPILLING BREAKER. See BREAKER. SPIT. A small point of land or a narrow shoal projecting into a body of water from the shore. (See Figure A-9.) SPIT, CUSPATE. See CUSPATE SPIT. SPRING TIDE. A tide that occurs at or near the time of new or full moon (SYZYGY) and which rises highest and falls lowest from the mean sea level. STAND OF TIDE. A interval at high or low water when there is no sensible change in the height of the tide. The water level is stationary at high and low water for only an instant, but the change in level near these times is so slow that it is not usually perceptible. See SLACK TIDE. STANDARD PROJECT HURRICANE. See HYPOTHETICAL HURRICANE. A-33 STANDING WAVE. A type of wave in which the surface of the water oscillates vertically between fixed points, called nodes, without progression. The points of maximum vertical rise and fall are called antinodes or loops. At the nodes, the underlying water particles exhibit no vertical motion, but maximum horizontal motion. At the antinodes, the underlying water particles have no horizontal motion, but maximum vertical motion. They may be the result of two equal progressive wave trains traveling through each other in opposite directions. Sometimes called CLAPOTIS or STATIONARY WAVE. STATIONARY WAVE. A wave of essentially stable form which does not move with respect to a selected reference point; a fixed swelling. Sometimes called STANDING WAVE. STILL-WATER LEVEL. The elevation that the surface of the water would assume if all wave action were absent. STOCKPILE. Sand piled on a beach foreshore to nourish downdrift beaches by natural littoral currents or forces. See FEEDER BEACH. STONE, DERRICK. Stone heavy enough to require handling individual pieces by mechanical means, generally weighing 900 kilograms (1 ton) and up. STORM SURGE. A rise above normal water level on the open coast due to the action of wind stress on the water surface. Storm surge resulting from a hurricane also includes that rise in level due to atmospheric pressure reduction as well as that due to wind stress. See WIND SETUP. STORM TIDE. See STORM SURGE. STRAIT. A relatively narrow waterway between two larger bodies of water. See also SOUND. STREAM. (1) A course of water flowing along a bed in the Earth. (2) A current in the sea formed by wind action, water density differences, etc.; e.g.- the Gulf Stream. See also CURRENT, STREAM. SURF. The wave activity in the area between the shoreline and the outermost limit of breakers. SURF BEAT. Irregular oscillations of the nearshore water level with periods on the order of several minutes. SURF ZONE. The area between the outermost breaker and the limit of wave uprush. (See Figures A-2 and A-5.) SURGE. (1) The name applied to wave motion with a period intermediate between that of the ordinary wind wave and that of the tide, say from 1/2 to 60 minutes. It is low height; usually less than 0.9 meter (0.3 foot). See also SEICHE. (2) In fluid flow, long interval variations in velocity and pressure, not necessarily periodic, perhaps even transient in nature. (3) see STORM SURGE. SURGING BREAKER. See BREAKER. A-34 SUSPENDED LOAD. (1) The material moving in suspension in a fluid, kept up by the upward components of the turbulent currents or by colloidal suspension. (2) The material collected in or computed from samples collected with a SUSPENDED LOAD SAMPLER. Where it is necessary to distinguish between the two meanings given above, the first one may be called the "true suspended load." SUSPENDED LOAD SAMPLER. A sampler which attempts to secure a sample of the water with its sediment load without separating the sediment from the water. SWALE. The depression between two beach ridges. SWASH. The rush of water up onto the beach face following the breaking of a wave. Also UPRUSH, RUNUP. (See Figure A-2.) SWASH CHANNEL. (1) On the open shore, a channel cut by flowing water in its return to the present body (e.g., a rip channel). (2) A secondary channel passing through or shoreward of an inlet or river bar. (See Figure A-9.) SWASH MARK. The thin wavy line of fine sand, mica scales, bits of seaweed, etc., left by the uprush when it recedes from its upward limit of movement on the beach face. SWELL. Wind-generated waves that have traveled out of their generating area. Swell characteristically exhibits a more regular and longer period and has flatter crests than waves within their fetch (SEAS). SYNOPTIC CHART. A chart showing the distribution of meteorological conditions over a given area at a given time. Popularly called a weather map. SYZYGY. The two points in the Moon’s orbit when the Moon is in conjunction or opposition to the Sun relative to the Earth; time of new or full Moon in the cycle of phases. TERRACE. A horizontal or nearly horizontal natural or artificial topographic feature interrupting a steeper slope, sometimes occurring in a series. THALWEG. In hydraulics, the line joining the deepest points of an inlet or stream channel. TIDAL CURRENT. See CURRENT, TIDAL. TIDAL DATUM. See CHART DATUM and DATUM PLANE. TIDAL DAY. The time of the rotation of the Earth with respect to the Moon, or the interval between two successive upper transits of the Moon over the meridian of a place, approximately 24.84 solar hours (24 hours and 50 minutes) or 1.035 times the mean solar day. (See Figure A-10.) Also called lunar day. TIDAL FLATS. Marshy or muddy land areas which are covered and uncovered by the rise and fall of the tide. A=-35 TIDAL INLET. (1) A natural inlet maintained by tidal flow. (2) Loosely, any inlet in which the tide ebbs and flows. Also TIDAL OUTLET. TIDAL PERIOD. The interval of time between two consecutive, like phases of the tide. (See Figure A-10.) TIDAL POOL. A pool of water remaining on a beach or reef after recession of the tide. TIDAL PRISM. The total amount of water that flows into a harbor or estuary or out again with movement of the tide, excluding any freshwater flow. TIDAL RANGE. The difference in height between consecutive high and low (or higher high and lower low) waters. (See Figure A-10.) TIDAL RISE. The height of tide as referred to the datum of a chart. (See Figure A-10.) TIDAL WAVE. (1) The wave motion of the tides. (2) In popular usage, any unusually high and destructive water level along a shore. It usually refers to STORM SURGE or TSUNAMI. TIDE. The periodic rising and falling of the water that results from gravitational attraction of the Moon and Sun and other astronomical bodies acting upon the rotating Earth. Although the accompanying horizontal movement of the water resulting from the same cause is also sometimes called the tide, it is preferable to designate the latter as TIDAL CURRENT, reserving the name TIDE for the vertical movement. TIDE, DAILY RETARDATION OF. The amount of time by which corresponding tides grow later day by day (about 50 minutes). Also LAGGING. TIDE, DIURNAL. A tide with one high water and one low water in a day. (See Figure A-10.) TIDE, EBB. See EBB TIDE. TIDE, FLOOD. See FLOOD TIDE. TIDE, MIXED. See MIXED TIDE. TIDE, NEAP. See NEAP TIDE. TIDE, SEMIDIURNAL. See SEMIDIURNAL TIDE. TIDE, SLACK. See SLACK TIDE. TIDE, SPRING. See SPRING TIDE. TIDE STATION. A place at which tide observations are being taken. It is called a primary tide station when continuous observations are to be taken over a number of years to obtain basic tidal data for the locality. A secondary tide station is one operated over a short period of time to obtain data for a specific purpose. A-36 TIDE, STORM. See STORM SURGE. TOMBOLO. A bar or spit that connects or "ties" an island to the mainland or to another island. See CUSPATE SPIT. (See Figure A-9.) TOPOGRAPHY. The configuration of a surface, including its relief and the positions of its streams, roads, building, etc. TRAINING WALL. A wall or jetty to direct current flow. TRANSITIONAL ZONE (TRANSITIONAL WATER). In regard to progressive gravity waves, water whose depth is less than 1/2 but more than 1/25 the wavelength. Often called SHALLOW WATER. TRANSLATORY WAVE. See WAVE OF TRANSLATION. TRANSPOSED HURRICANE. See HYPOTHETICAL HURRICANE. TROCHOIDAL WAVE. A theoretical, progressive oscillatory wave first proposed by Gerstner in 1802 to describe the surface profile and particle orbits of finite amplitude, nonsinusoidal waves. The wave form is that of a prolate cycloid or trochoid, and the fluid particle motion is rotational as opposed to the usual irrotational particle motion for waves generated by normal forces. Compare IRROTATIONAL WAVE TROPICAL CYCLONE. See HURRICANE TROPICAL STORM. A tropical cyclone with maximum winds less than 34 meters per second (75 mile per hour). Compare HURRICANE. TROUGH OF WAVE. The lowest part of a waveform between successive crests. Also, that part of a wave below still-water level. (See Figure A-3.) TSUNAMI. A long-period wave caused by an underwater disturbance such as a volcanic eruption or earthquake. Also SEISMIC SEA WAVE. Commonly miscalled "tidal wave." TYPHOON. See HURRICANE. UNDERTOW. A seaward current near the bottom on a sloping inshore zone. It is caused by the return, under the action of gravity, of the water carried up on the shore by waves. Often a misnomer for RIP CURRENT. UNDERWATER GRADIENT. The slope of the sea bottom. See also SLOPE. UNDULATION. A continuously propagated motion to and fro, in any fluid or elastic medium, with no permanent translation of the particles themselves. UPCOAST. In United States usage, the coastal direction generally trending toward the north. UPDRIFT. The direction opposite that of the predominant movement of littoral materials. A-37 UPLIFT. The upward water pressure on the base of a structure or pavement. UPRUSH. The rush of water up onto the beach following the breaking of a wave. Also SWASH, RUNUP. (See Figure A-2.) VALLEY, SEA. A submarine depression of broad valley form without the steep side slopes which characterize a canyon. VALLEY, SUBMARINE. A prolongation of a land valley into or across a continental or insular shelf, which generally gives evidence of having been formed by stream erosion. VARIABILITY OF WAVES. (1) The variation of heights and periods between individual waves within a WAVE TRAIN. (Wave trains are not composed of waves of equal height and period, but rather of heights and periods which vary in a statistical manner.) (2) The variation in direction of propagation of waves leaving the generating area. (3) The variation in height along the crest, usually called "variation along the wave." VERY SHALLOW WATER. See SHALLOW WATER. VELOCITY OF WAVES. The speed at which an individual wave advances. See WAVE CELERITY. VISCOSITY (or internal friction). That molecular property of a fluid that enables it to support tangential stresses for a finite time and thus to resist deformation. WATERLINE. A juncture of land and sea. This line migrates, changing with the tide or other fluctuation in the water level. Where waves are present on the beach, this line is also known as the limit of backrush. (Approximately, the intersection of the land with the still-water level.) WAVE. A ridge, deformation, or undulation of the surface of a liquid. WAVE AGE. The ratio of wave speed to wind speed. WAVE, CAPILLARY. See CAPILLARY WAVE. WAVE CELERITY. Wave speed. WAVE CREST. See CREST OF WAVE. WAVE CREST LENGTH. See CREST LENGTH, WAVE. WAVE, CYCLOIDAL. See CYCLOIDAL WAVE. WAVE DECAY. See DECAY OF WAVES. WAVE DIRECTION. The direction from which a wave approaches. WAVE FORECASTING. The theoretical determination of future wave character- istics, usually from observed or predicted meteorological phenomena. A-38 WAVE GENERATION. See GENERATION OF WAVES. WAVE, GRAVITY. See GRAVITY WAVE. WAVE GROUP. A series of waves in which the wave direction, wavelength, and wave height vary only slightly. See also GROUP VELOCITY. WAVE HEIGHT. The vertical distance between a crest and the preceding trough. See also SIGNIFICANT WAVE HEIGHT. (See Figure A-3.) WAVE HEIGHT COEFFICIENT. The ratio of the wave height at a selected point to the deepwater wave height. The REFRACTOPM COEFFICIENT multiplied by the shoaling factor. WAVE HINDCASTING. See HINDCASTING, WAVE. WAVE, IRROTATIONAL. See IRROTATIONAL WAVE. WAVE, MONOCHROMATIC. See MONOCHROMATIC WAVES. WAVE, OSCILLATORY. See OSCILLATORY WAVE. WAVE PERIOD. The time for a wave crest to traverse a distance equal to one wavelength. The time for two successive wave crests to pass a fixed point. See also SIGNIFICANT WAVE PERIOD. WAVE, PROGRESSIVE. See PROGRESSIVE WAVE. WAVE PROPAGATION. The transmission of waves through water. WAVE RAY. See ORTHOGONAL. WAVE, REFLECTED. That part of an incident wave that is returned seaward when a wave impinges on a steep beach, barrier, or other reflecting surface. WAVE REFRACTION. See REFRACTION (of water waves). WAVE SETUP. See SETUP, WAVE. WAVE, SINUSOIDAL. An oscillatory wave having the form of a sinusoid. WAVE, SOLITARY. See SOLITARY WAVE. WAVE SPECTRUM. In ocean wave studies, a graph, table, or mathematical equation showing the distribution of wave energy as a function of wave frequency. The spectrum may be based on observations or theoretical considerations. Several forms of graphical display are widely used. WAVE, STANDING. See STANDING WAVE. WAVE STEEPNESS. The ratio of the wave height to the wavelength. WAVE TRAIN. A series of waves from the same direction. A-39 WAVE OF TRANSLATION. A wave in which the water particles are permanently displaced to a significant degree in the direction of wave travel. Distinguished from an OSCILLATORY WAVE. WAVE, TROCHOIDAL. See TROCHOIDAL WAVE. WAVE TROUGH. The lowest part of a wave form between successive crests. Also that part of a wave below still-water level. WAVE VARIABILITY. See VARIABILITY OF WAVES. WAVE VELOCITY. The speed at which an individual wave advances. WAVE, WIND. See WIND WAVES. WAVELENGTH. The horizontal distance between similar points on two successive waves measured perpendicular to the crest. (See Figure A-3.) WAVES, INTERNAL. See INTERNAL WAVES. WEIR JETTY. An updrift jetty with a low section or weir over which littoral drift moves into a predredged deposition basin which is dredged periodically. WHARF. A structure built on the shore of a harbor, river, or canal, so that vessels may lie alongside to receive and discharge cargo and passengers. WHITECAP. On the crest of a wave, the white froth caused by wind. WIND CHOP. See CHOP. WIND, FOLLOWING. See FOLLOWING WIND. WIND, OFFSHORE. A wind blowing seaward from the land in a coastal area. WIND, ONSHORE. A wind blowing landward from the sea in a coastal area. WIND, OPPOSING. See OPPOSING WIND. WIND SETUP. On reservoirs and smaller bodies of water (1) the vertical rise in the still-water level on the leeward side of a body of water caused by wind stresses on the surface of the water; (2) the difference in still- water levels on the windward and the leeward sides of a body of water caused by wind stresses on the surface of the water. STORM SURGE (usually reserved for use on the ocean and large bodies of water). (See Figure A-11.) WIND TIDE. See WIND SETUP, STORM SURGE. WIND WAVES. (1) Waves being formed and built up by the wind. (2) Loosely, any wave generated by wind. WINDWARD. The direction from which the wind is blowing. A-40 Table A-l. Grain size scales (soil classification ). Unified Soils |astm! mm | Phi Wentworth Classification | Mesh | Size | Value] Classification _ an J sounner COBBLE St CEL LTO COBBLE COARSE aa SeRUEL EL eo ee MMS SESE Yl pe smves| CME LEE Saeed PEBBLE SES Loni value (¢) = logy x diameter (mm). A-41 Coastal area Nearshore zone (defines area of nearshore currents Beoch or shore Inshore or Shorefoce Offshore Backshore (extends through breaker zone) Beac Breakers Ordinary low water Bottom Figure A-l. Beach profile-related terms. Surf or Breoker zone -| Waves peak up but do not break on this bor at high tide Re-formed Outer line Waves flatten oscillatory of breakers again wave Limit of uprush Still-water | level Outer bor Deep bor (Inner bar, low tide) (Outer bar, low tide) Figure A-2. Schematic diagram of waves in the breaker zone. A-42 Direction of Wave Travel can L= Wavelength Wave Crest we H = Wave Height ees, Length | Region Wave Trough Still-water Level Trough Length Region d= Depth Ocean Bottom — Direction of Wave Travel Orbit Diameter (Hg) Still-water Level Direction of orbital movement of water particles in different parts of a deep- water wave. Small motion of water below Lo/, 2 Direction of Wave Travel Lc.) ee Beach grass shows the direction of movement of water particles under various parts of a shallow-water wave. (Wiegel,1953) Figure A-3. Wave characteristics and direction of water particle movement. A-43 BREAKING POINT SKETCH SHOWING THE GENERAL CHARACTER OF SPILLING BREAKERS BREAKING BEACH IS USUALLY STEEP SKETCH SHOWING THE GENERAL CHARACTER PLUNGING BREAKER OF PLUNGING BREAKERS FOAM LINE FOAM LINE = FOOM LINE BEACH IS USUALLY VERY STEEP SKETCH SHOWING THE GENERAL CHARACTER SURGING BREAKER OF SURGING BREAKERS Both photographs and diagrams of the three types of breakers are presented above. The sketches consist of a series of profiles of the wave form as if appears before breaking, during breaking and after breaking. The numbers opposite the profile lines indicate the relative times of occurences. (Wiegel,1953) Figure A-4. Breaker types. A-44 ZONE SURF NARROW SURF ZONE SSS NE Ss < . > ee if HIGH WAVES ON POINT Pt Pinos, California Waves moving over a submarine ridge concentrate to give large wove heights on a point a ve WIDE SURF ZONE \ POINT ty NARROW SURF ZONE WIDE SURF ZONE Halfmoon Bay, California Purisima Pt., California Note the increasing width of the surf zone with increasing degree Refraction of waves around a headiand produces low waves and of exposure to the south a narrow surf zone where bending is greatest (Wiegel, 1953) Figure A-5. Refraction of waves. A-45 LOW WAVES IN COVE HIGH WAVES ON POINT z— DIVERGENCE OF y. ORTHOCOMAL S F. PRODUCES Low WAVES 1 THIS AREA “ARENA COVE CONVERGENCE OF ORTHOGONALS PRODUCES WIGM WAVES Im THIS area 12-SECOND PERIOD ——-OCEPTH CONTOURS, Im FaTHOoms SCALES 1000 FT WAVE FRONTS , / za / 300m (Wiegel, 1953) Figure A-6. Refraction diagram. A-46 =e LONGSHORE aa aeed GET NFEEDER CURRENT~ CURRENT SHORELINE CURRENT OFFSHORE CURRENT INSHORE Nearshore Current System (after Wiegel 1953) Figure A-7. Beach features. A-47 ( Wiegel,1953) Figure A-8. Shoreline features. A-48 Baymouth Bar Cuspote Bor Swash Chonnel Katama Bay “6 tishore bor » 5 Oo rr ‘ie wee Od, Wig, “eb \ = SB = “errs, ott . peceertee . Barrier Beach Double Tombolo (Johnson 1919). Bar and beach forms. Figure A-9. A-49 DEPTH, M DEPTH, M DEPTH, M Tidal Day |+- Tidal Period Lower Low Water Tidal Range MIXED Figure A-10. Types of tides. A-50 O-Datum 12 hours 0) 12 hours 12 hours Higher Low Water (Wiegel, 1953) Water surfoce with eost wind Water surface with west wind Wind setup Wind setup A | (Definition |) (Definition 2) | | | Wind Tide, m | Woter level the Lake bottom ws 5) et Pe Nodal line LAKE ERIE TOLEDO Figure A-ll. Wind setup. A-51 APPENDIX B List of Symbols Dam Neck, Virginia, 20 August Area @ Constant = 7500 @ Major ellipse semiaxis of wave particle motion (eq. 2-22) @ Amplitude of particle motion Surface area of bay (eq. 4-65) Cross-sectional area of inlet channel (eq. 4-64) Individual cross-sectional areas of n_ sections of an inlet channel (eq. 4-69) Waveform amplitude @ Breaking wave dynamic moment reduction factor for low wall @ Breaker height parameter (eq. 2-93) Volume of solids divided by total volume Wave amplitude of bay response to ocean tide (eq. 4-64) Amplitude of aes wave in series Tidal amplitude (eq. 4-70) Wave amplitude of ocean tide (eq. 4-64) Breakwater gap width @Minor ellipse semiaxis of wave particle movement (eq. 2-23) @Rubble structure crest width @Rubble crest width in front of wall @Buoyancy index @Inlet channel width @Berm width Hydrostatic uplift forces Effective breakwater gap width Spacing between wave orthogonals @ Breaker height parameter (eq. 2-94) @Structure crest width (Fig. 7-47) @Height of overtopped wall, sea floor to wall crest (eq. 7-79; Fig. 7-96) @Height of rubble base alone (Fig. 7-98) @Amplitude of offshore bar Overtopped wall height above wave trough (Fig. 7-102) Length of shoreline considered as line source for littoral zone sediment (eq. 4-58) Orthogonal spacing, deep water (Continued) Bl Example Units EE ft English mi Symbol Definition $< Wave celerity; phase velocity @ Volumetric particle concentra- tion (eq. 4-10) @ Empirical overtopping coeffi- cient (eq. 7-18) Wave speed at breaking Friction factor (eq. 4-51) Drag coefficient Group velocity Lift coefficient Mass or inertia coefficient Deepwater wave velocity Jacobian elliptical cosine function Total water depth, including surge @ Depth one wavelength in front of wall (eq. 7-85) @ Duration of an observation @ Decay distance @Pile diameter @Percent damage to rubble struc- ture (Table 7-9) @aArea perpendicular to flow direction per unit length of pile @Quarrystone diameter Water depth (bed to SWL) @Grain diameter @Undisturbed water depth Depth of water at breaking wave Water depth at seaward limit to extreme surf-related effects Equivalent stone diameter Water depth at seaward limit to sand agitation by the median annual wave condition (eq. 4-28) @Water depth at seaward edge of structure Water depth at toe of structure @Sphere diameter (eq. 4-6) Depth below SWL of rubble foun- dation crest (Fig. 7-120) Size of 50th percentile of sedi- ment sample (deo = M4) Total energy in one wavelength per unit crest width @ Crest elevation of structure above MLW or other datum plane (Continued) B2 Example Units Dimension Metric English fe ft Units consistent with units of gravita- tional acceleration and viscosity in equation (4-6) N-m/m crest width ft ft-lb/ft crest width ft Definition Dimension Total average wave energy per unit surface area; specific energy; energy density Average wave energy per unit water surface area for several waves Total average wave energy per unit surface area in deep water Kinetic energy in one wavelength per unit crest width Complete elliptic integral of second kind Deepwater wave energy Potential energy in one wave- length per unit crest width Continuous energy spectrum (eq. 3-17) Energy density in the gee compo- nent of the energy spectrum (eq. 3-18) Fetch length @ Total horizontal force acting about mud line on pile at a given instant @ Nonbreaking, nonovertopping wave force on wall extending the full water depth @ Freeboard (Reduced) force on overtopped wall which extends full water depth (eq. 7-78) (Reduced) force on wall resting on rubble foundation (eq. 7-82) Adjusted fetch length Total horizontal force per unit length of wall from nonbreaking wave crest Total horizontal drag force on a pile at a given instant Maximum value of Fy for a given wave Effective fetch length due to limited width @ Total horizontal earth force Effective fetch length on an unrestricted body of water Horizontal forces on quay wall caisson to initiate sliding (Continued) B3 of crest of crest Example Units English ft-1b/£t? ft-1b/£t ft-1b/ft? ft-lb/ft of crest width ft-lb/ft of crest width ft-lb/ft of crest width £t? ft-1b/£t? ft 1b lb/ft ft lb/ft lb/ft ft lb/ft 1b 1b ft 1b ft 1b of wall of wall of wall of wall 8 Definition SS Hydrostatic force on seaward side of quay wall caisson after backfilling Total horizontal inertial force on a pile at a given instant Maximum value of Fi for given wave Lift force (lateral force on pile from flow velocity) Maximum lift force for given wave Minimum fetch length Dimensionless fall time parameter (eq. 4-29) Total horizontal force per unit length of wall subjected to nonbreaking wave length Total force on pile group Vertical forces on quay wall caisson to initiate sliding Direction term (eq. 4-55) Coriolis parameter @ Wave frequency @Horizontal force per unit length of pile @ Decimal frequency (eq. 4-53) @Darcy-Weisbach resistance coefficient (eq. 4-67) Horizontal drag force per unit length of vertical pile Bottom friction factor Bottom friction factor at seaward edge of segment Horizontal inertial force per unit length of vertical pile Maximum force per unit length of pile @ Frequency of wind sea spectral peak (eq. 3-32) Fractional growth factor of equivalent initial wave Dimensionless parameter for determining beach accretion or erosion Gravitational acceleration Subscript for: @ Group @ Gage @Gross Dimension Metric (Continued) B4 Example Units English lb/ft lb/ft of wall 1b => = Wave height @ Design wave height--wave height for which structure is de- signed; maximum wave height causing no damage or damage within specified limits @High-pressure area on weather maps Average wave height; H = 0.886 H rms Arbitrary wave height for prob- ability distributions Wave height at breaking (breaker height) Significant wave height, end of decay distance Zero-damage wave height Equivalent wave height at end of fetch Wave height at end of fetch Gage wave height Incident wave height @ Initial wave height Equivalent initial wave height Height of pes wave in a series Maximum stable wave height Maximum wave height for specified period of time Significant wave height (energy based); 4 times the standard deviation of the sea surface elevation Most probable a highest wave Deepwater significant wave height Deepwater wave height equivalent to observed shallow-water wave if unaffected by refraction and friction Reflected wave height Root-mean-square wave height Significant wave height (statis- tically based); H, 3 average height of highest éBe-third of waves for a specified time period Maximum significant wave height Mean significant wave height (eq. 4-13) (Continued) B5 Example Units ft ft in. of mercury, mbar ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft ft Example Units Symbol Definition Dimension English Arbitrary significant wave height for probability distributions (eq. 4-12) ft Approximate minimum significant wave height from a distribution of significant heights (eq. 4-12) ft H = Ss min Average height of highest 5 per- cent of all waves for a given time ft Median annual significant wave height (eq. 4-26) ft Significant wave height, breaker value ft Significant wave height, deep- water value ft h Range of tide ft @ Height of retaining wall ft @ Height of backfill at wall if lower than wall Le @ Structure height, toe to crest ft @Vertical distance from dune base or berm crest to depth of seaward limit of signifi- cant longshore transport (Fig. 4-44) ft @ Mean channel water depth (eq. 4-70) ft h' Broken wave height above ground surface at structure toe landward of SWL ft h Height of broken wave above SWL ft h Height of clapotis orbit center above SWL ft Submerged weight of longshore transport lb/yr i Angle of backfill surface from horizontal (eq. 7-143) deg Subscript dummy variable rhe K Pressure response factor at bottom (eq. 2-31) aS @ Constant for Rankin vortex model of hurricane wind field -] (eq. 3-55) s @ Dimensionless coefficient pro- portional to immersed weight transport rate I, and longshore energy flux factor Pos = K' Diffraction coefficient nes Armor unit stability coefficient (eq. 7-116) c= @ Dimensionless factor for cal- culation of total drag force on pile at a given phase (eq. 7-30) == (Continued) B6 k en ex k' Definition Maximum value of Kp for given wave Wave height reduction factor from friction; friction factor (Fig. 3-38) Wave height reduction factor where Ky = 0.01 Wave height reduction factor where Ky # 0.01 Dimensionless factor for calcu- lation of total inertial force on pile at a given phase (eq. 7-29) Maximum value of K; for a given wave Complete elliptic integral of the first kind Refraction coefficient Stability coefficient for smooth, relatively rounded, graded riprap armor units (eq. 7-117) Shoaling coefficient (eq. 2-44) Wave transmission coefficient (eq. 7-15) Wave transmission-by-overtopping coefficient (eq. 7-17) Wave transmission-through-the- breakwater coefficient (eq. 7-19) Pressure response factor at any depth z (eq. 2-29) Friction coefficient for tribu- tary inflow (eq. 4-65) Frequency coefficient for tribu- tary inflow (eq. 4-66) Wave number (27/L) @ Modulus of elliptic integrals @kKip: a unit of force; 1 kip = 4448.222 N (1000 1b) @ Runup correction factor (Fig. 7-13) Entrance loss coefficient for inlet channel (eq. 4-67) Exit loss coefficient for inlet channel (eq. 4-67) Wind correction factor for over- topping rates (eq. 7-12) Source (or sink) fraction of gross longshore transport rate (eq. 4-59) Dimension SS (Continued) B7 Example Units English Example’ Units Definition Dimension English Layer coefficient of rubble structure -- L Wavelength £E @ Low pressure on weather map in. of mercury, mbar @ Length of inlet channel (eq. 4-66) ft Ly Wavelength in given depth ac- cording to linear (Airy) theory; Ly may differ from L (eq. 7-21) Tae Ly Wavelength at breaking ft @ Length to farthest point of channel (eq. 4-68) ft L. Width of caisson ft Ly Wavelength in water depth D (eq. 7-85) ft Ly Wavelength in water depth dq. (eq. 7-88) fe L, Deepwater wavelength ft Ll, Effective inlet channel length (eq. 4-69) ft 2 Structure slope length ft @ Length of an offshore bar or other underwater feature ft aa Enclosed basin length (eqs. 2-81 and 3-68) ft Xp, Length of rectangular basin open at one end (eqs. 2-85 and 3-70) ft Qo Distance from reference pile to fee pile of pile group (eq. 7-56; Fig. 7-86) ft ot Subscript for longshore transport to left as viewed from beach =O M Total wave moment about mud line on pile (eq. 7-28) ft-lb @ Nonbreaking wave moment about toe of wall extending full depth of water ft-lb/ft of wall @Variable of solitary wave theory, function of H/d (eq. 2-67) == @Mean diameter of sediment sample a M' Moment about toe of wall over- topped by nonbreaking wave ft-lb/ft of wall MK Moment about bottom (mud line) for wall on a rubble foundation (eq. 7-83) ft-lb/ft of wall Mp Moment about base of wall on rubble foundation (eq. 7-84) ft-lb/ft of wall M Total moment about toe of wall per unit length from nonbreaking wave crest ft-lb/ft of wall (Continued) B8 Definition Total drag moment acting on pile about mud line (eq. 7-32) Maximum value of Mp (eq. 7-40) Median diameter of sediment sample Median diameter of sediment sample in phi units Total overturning moment Total inertial moment acting on pile about mud line (eq. 7-31) Maximum value of My for a given wave (eq. 7-39) Maximum total moment on pile about mud line (eq. 7-43) @ Maximum overturning moment about toe of wall from dynamic component of wave pressure (breaking or broken waves) (eq. 7-87) Reduced moment about toe for low wall (eq. 7-80) Reduced maximum moment against wall from breaking wave of height greater than wall (eq. 7-93) Hydrostatic moment against wall from breaking or broken waves Total moment about toe of wall per unit length from nonbreaking wave trough (Ch. 7) @Total moment about toe of wall per unit length from breaking or broken wave crest Total moment on pile group about mud line Momentum transport quantity per unit width (eq. 3-77) Momentum transport quantity per unit width (eq. 3-77) Mean diameter of sediment sample in phi units Net overturning moment about wall bottom due to presence of waves Mean diameter (phi units) of borrow material (eq. 5-3) Mean diameter (phi units) of native (beach) material (eq. 5-3) Coefficient determined by equa- tion (4-20) Beach slope (Continued) B9 N-m/m of wall kN-m/m of wall N-m/m of wall N-m/m of wall N-m/m of wall N-m/m of wall kN-m/m m(rise)/m(run) Example Units English phi ft-1b/ft ft-lb ft-1b ft-lb ft-lb/ft ft-lb/ft ft-lb/ft ft-lb/ft ft-lb/ft ft-lb/ft ft-lb ft/s? £t2/s2 phi ft-lb/ft phi phi of of of of wall wall wall wall wall wall ft(rise)/ft(run) Symbol rol Example Units Correction factor in determina- tion of n (eta) from subsurface pressure (eq. 2-32) @ Variable in solitary wave theory (eq. 2-67) @ Total number of items Number of armor units or stones in cover layer Required number of individual armor units (eq. 7-122) Design stability number for rubble foundations and toe pro- tection (eq. 7-118) Number of layers of armor units in rubble structure protective cover @ Number of armor units across rubble structure crest @ Ratio of group velocity to individual wave velocity @ Number of seiche nodes along closed rectangular basin axis @ Degrees latitude (isobar spacing--not location) @A number @ Manning resistance coefficient Number of seiche nodes along rec- tangular basin open at one end, excluding node at opening Subscript referencing a partic- ular pile in a pile group @ Subscript for net longshore transport rate Deepwater ratio of group velocity to individual wave velocity Subscript for deepwater condition Average porosity of rubble struc- ture cover layer (eq. 7-122) @ Probability @Tidal prism; a @ Precipitation rate Central hurricane pressure Wave power; average energy flux transmitted across a plane perpendicular to wave advance N-m/s-m Active earth force (eq. 7-143) N/m of wall Longshore component of wave energy flux (eq. 4-36) N-m/s-m Breaker line approximation of P (eq. 4-37) z (Continued) B10 deg in./hr in. of mercury, mbar ft-lb/s-ft lb/ft of wall ft-lb/s-ft ft-1lb/s-ft Symbol Definition ee Surf zone approximation of Po (eq. 4-39) Deepwater P Passive earth force (eq. 7-145) Gage pressure; pressure at any distance below fluid surface relative to surface @ Atmospheric pressure at point located distance r from hurri- cane storm center @ Precipitation rate @ Percentage of exceedance (Fig. 7-41) Total or absolute subsurface pressure--includes dynamic, static, and atmospheric pressures (eq. 2-26) Atmospheric pressure (eq. 2-26) Maximum dynamic pressure by breaking and broken waves on vertical wall (eq. 7-85) Maximum soil bearing pressure beneath quay wall caisson after backfilling Pressure at outskirts or periph- ery of storm Central pressure of storm; CPI Maximum broken wave hydrostatic pressure against wall (eq. 7-98) Nonbreaking wave pressure differ- ence from still-water hydrostatic pressure as clapotis crest or trough passes (eq. 7-75) Hydrostatic pressure Overtopping rate Average overtopping rate for irregular waves (spectra) Gross longshore transport rate Point source for littoral zone sediment budget Point sink for littoral zone sediment budget Line source total contribution to littoral zone sediment budget Line sink total deduction from littoral zone sediment budget Dimension LF/TL LF/TL F/L (Continued) Bll Example Units Metric English N-m/s-m ft-lb/s-ft N-m/s-m ft-lb/s-ft N/m of wall lb/ft of wall N/m? lb/ft? 2 : mmHg, N/m in. of mercury, mbar mm/hr in/hr percent N/m? lb/ft” N/m? 1b/£t? N/m? 1b/£t? 2 KN/m lb/ft 2 N/m lb/ft mmHg , N/m? in. of mercury, mbar N/m? 1b/£t? N/m? 1b/£t? kN/m? 1b/£t? m?/s-m £t?/s-ft m?/s-m £t?/s-ft m?/yr ya?/yr m?/yx yd>/yr m?/yr ya?/yr m>/yr yd? /yr m?/yr yd°/yr R" ——————S Empirically determined coeffi- cient depending on incident wave characteristics and structure geometry used for figuring over- topping rate (eq. 7-10) Longshore transport rate (Q, = Q) Amounts of littoral drift trans- ported to the left (eq. 4-31) Net longshore transport rate Empirically determined overtop- ping coefficient (eq. 7-10) Overtopping rate associated with R» wave runup with a particular probability of exceedance (eq. 7-14) Amounts of littoral drift trans- ported to the right (eq. 4-31) Longshore transport rate computed from deepwater data (eq. 4-53) Line source per unit length in littoral zone sediment budget Line sink per unit in littoral zone sediment budget Wave runup @ Dynamic component of breaking or broken wave force per unit length of wall if wall is per- pendicular to direction of wave advance (eq. 7-112) @Radial distance from storm (hurricane) center to region of maximum winds (or to region of maximum waves) (eq. 3-55) @Distance along bottom contours, as used in refraction problems (R/J method) @Hydraulic radius (eq. 4-67) @ Reaction force Reduced dynamic component of force per unit wall length from a breaking or broken wave strik- ing a structure at an oblique angle (eq. 7-112) Reduced horizontal dynamic com- ponent of force per unit wall length from a breaking or broken wave striking a nonvertical struc- ture face (eq. 7-113) Ratio of artificial beach nour- ishment: ratio of volume re- quired for placement to volume retained on beach after equilib- rium (Fig. 5-3) Reynolds number Ratio of artificial beach nourish- ment (eq. 5-4) (Continued) B12 N/m of wall N/m of wall N/m of wall Example Units English lb/ft of wall lb/ft of wall lb/ft of wall ai Definition Ratio of windspeed to wind stress factor (Fig. 3-19) Horizontal component of reaction force Fractional reduction at the sea- ward edge of the fetch segment (eq. 3-51) Periodic beach nourishment-to- erosion ratio (eq. 5-3) Ratio of overwater to overland windspeed as a function of over- land windspeed (Fig. 3-15) Maximum dynamic component of breaking or broken wave on wall (eq. 7-86) Reduced maximum dynamic component on wall of height lower than wave crest (eq. 7-91) Component of R normal to actual wall (Fig. 7-106) Hydrostatic component of breaking or broken wave on wall (eq. 7-89) @Wave runup of significant wave Amplification ratio (eq. 3-27) Total breaking or broken wave force on wall per unit wall length (includes dynamic and hydrostatic components) (eq. 7-89) Vertical component of reaction force Individual hydraulic radii of n sections of an inlet channel (eq. 4-69) Total rubble layer thickness @ Radial distance from storm (hurricane) center to any specified point in storm system @ Roughness and porosity correc- tion factor (eq. 7-7) @ Average armor layer thichness (eq. 7-121) @ Moment arm Armor }ayer thickness (rubble structure) Reduction factor for force on wall of height lower than clapotis crest (eq. 7-78) Reduction factor for moment on wall of height lower than clapotic crest (eq. 7-80) @ Reduction factor for maximum dynamic component of force when breaking wave height is higher than wall height (eq. 7-81) F/L F/L F/L (Continued) B13 Dimension N/m N/m N/m of of of of of Metric ——————— wall wall wall wall wall Example Units lb/ft lb/ft lb/ft ft ft English of of of of of wall wall wall wall wall Symbol Definition ————— Subscript for longshore transport to right as viewed from beach Thickness of first underlayer of rubble structure Channel opening cross-sectional area (eq. 7-128) @Surge; height resulting from storm surge of free surface above or below the undisturbed water level datum (eq. 3-77); also called wind setup Wave setup between breaker zone and shore (eq. 3-73) Astronomical tide component of total storm surge Setdown at breaking zone (eq. 3-72) Dimensionless moment arm of total drag force on pile at a given phase angle (eq. 7-32) Maximum value of Sp Dimensionless moment arm of total inertial force on pile at a given wave phase angle Maximum value of S; Maximum directional concentration parameter for a wave spectrum Specific gravity of armor unit (w/w) Net wave setup at shore (eq. 3-73) Subscript for significant wave Wave period @Astronomic tidal period @ Temperature Fundamental period of wave oscil- lation (eq. 2-83) Period of the peak wave spectrum Natural, free-oscillating period of seiche in closed basin with n nodes (excluding node at opening) Free oscillation period in basin open at one end with n' nodes (excluding node at opening) (eq. 3-70) Peak spectral period; inverse of the dominant frequency of a wave energy spectrum Significant wave period Annual average significant wave period (eq. 4-28) Dimension (Continued) B14 Example Units ft ft ft LG hr English Example Units Symbol Definition Dimension English _————— 15 Period of fundamental mode of seiche in rectangular basin open at one end hr Fundamental and maximum period z of seiches in closed basin hr c Time s, min, hr s, min, hr t, Time a tidal wave will take to propagate to a given point hr hr U Windspeed knots, mi/hr @x component (perpendicular to shore) of volume transport per 3 unit width mi /hr-mi U, Wind-stress factor (eq. 3-28) mi/hr Uy Fastest-mile windspeed mi/hr Ue Geostrophic windspeed (eq. 3-30) knots, mi/hr U Gradient windspeed (eq. 3-57) knots, mi/hr UL Windspeed over land mi/hr Ws Maximum gradient windspeed (eq. 3-61) knots, mi/hr UR Maximum sustained gradient wind- speed (eq. 3-60) knots, mi/hr @Ursell parameter (eq. 2-45) -- Uy (2) Convection term to be added vec- torially to wind velocity at each location r to correct for storm motion (eq. 3-58) == UP Surface windspeed mi/hr UL Duration-averaged windspeed mi/hr UL Windspeed over water knots, mi/hr U, Friction velocity (eq. 3-25) knots, mi/hr U(z) Mass transport velocity at depth z for a water particle subject to wave motion mean drift velocity (eq. 2-55) ft/s u Horizontal (x) normal-to-the- shoreline component of local fluid velocity (water particle velocity); current velocity (eq. 2-13) ft/s @ Maximum water velocity at en- trance to inlet channel (eq. 4-70) ft/s uy Particle velocity under a break- ing wave ft/s EEE Horizontal velocity near the breaker crest ft/s Ux Maximum horizontal water particle velocity ft/s u Maximum horizontal water particle max velocity averaged over depth ft/s (Continued) B15 max (-d) Maximum bottom velocity (eq. 4-18) m/s Velocity @ Maximum velocity of tidal cur- rents in midchannel (eq. 7-128) @ Volume transport parallel to shore (y component) (eq. 3-77) @A volume (eq. 2-65) m/s, km/hr m/s 3 m,/s-m m /m of crest width @ Instantaneous average velocity of tidal current in inlet (Fig. 4-74) @Volume of secondary cover layer of revetment Average local channel velocity in the vertical Volume of sand stored in ebb- tidal delta (eq. 4-71) Volume of core in a rubble structure Storm center velocity Fall velocity of particles in water column Fall velocity of a sphere Fall velocity of a concentrated suspension of spheres Average longshore current due to breaking waves (eq. 4-51) Maximum velocity during a tidal cycle (eq. 4-64) Dimensionless maximum channel velocity during tidal cycle (eq. 4-64) Volume of rock in secondary cover layer of revetment Horizontal (y) component of local fluid velocity (water particle velocity) (eq. 3-79) @ Longshore current velocity @Fluid kinematic viscosity Velocity of broken wave water Mass at structure located land- ward of SWL (eq. 7-103) (Continued) B16 Example Units English ft/s knots, mi/hr, ft/s ft/s mi 3/hr-mi ft’ /ft of crest width ft/s knots, mi/hr ft/s ft/s ft/s ft/s ft/s —x if is the newton, which is equal to l kg-m/s*. Example Units Metric English Definition Dimension Weight (or mass) of individual armor units in primary cover layer; weight (or mass) of indi- vidual units, any layer @ Fetch width of channel or other restricted body of water (Ch. 3) @ Windspeed @ Maximum sustained windspeed (Chew) @ Parameter used in pile force and moment calculations (eq. 7-41) @Length of vertical wall af- fected by unit width of wave crest (W = 1/sin a) @Width of surf zone (eq. 4-51) Weight of individual armor unit Weight of available quarrystone Zero-damage quarrystone weight Windspeed coefficient (eq. 7-12) Heaviest stone in the gradation of a layer of riprap (eq. 7-124) Weight of primary cover layer made of rock x component of windspeed (eq. 3-77) y component of windspeed (eq. 3-78) Weight of 50 percent size of armor riprap gradation (eq. 7-117) Unit weight (or mass density) @Vertical (z) component of local fluid velocity or current velocity Unit weight (or mass density). of armor (rock or concrete) unit (saturated surface dry) (eq. 7-116) Unit weight (or mass density)! of water Coordinate axis in direction of wave propagation relative to wave crest @ Coordinate axis along basin major axis @ Coordinate axis perpendicular to and positive toward shore @A distance Subscript for x-coordinate (Continued) can be converted to kilograms (mass) by multiplying by 9.80665. B17 1b nmi, mi knots, mi/hr knots, mi/hr 1b knots, mi/hr knots, mi/hr 1b Nn (or kg/m) 1b/ft? knots, mi/hr N/m? (or kg/m>) 1b/ft? N/m? (or kg/m?) 1b/ft? 2 Note: the SI unit of weight (meaning force, or mass accelerated at the standard free-fall rate of 9.80665 m/s’ ) When computing armor unit weights for practical purposes, newtons (Alpha) Metric Location in pile group of =e pile relative to wave crest (eq. 7-56) Plunging breaker travel distance (eq. 7-4) Location in pile group of refer- ence pile relative to wave crest (eq. 7-58) Coordinate axis: horizontal, parallel to shore, positive to left when facing shore @Coordinate axis: vertical, origin at seabed Vertical distance from seabed to wave crest (eq. 2-60) Vertical distance from seabed to water surface (eq. 2-59) Vertical distance from seabed to wave trough (eq. 2-59) Elevation Coordinate axis: vertical, origin at SWL, positive upwards Surface roughness (eq. 3-25) Subscript referring to z-axis Angle between axis of structure and direction of wave advance (eq. 7-112) @Angle between wave crest and bottom contour @Angle between wave crest and shore (eq. 2-78) @ Upper limit of observed 4 /H, (Fig. 7-2) @Empirically determined over- topping coefficient @Hurricane movement coefficient (eq. 3-60) @Constant for wave spectrum prediction (eq. 3-31) @Factor for reducing fetch length (eq. 3-45) Wave reflection factors Angle between breaking wave crest and shoreline Coefficient in determination of maximum total moment on pile (eq. 7-43) Angle, relative to reference pile, that mee pile of pile group makes with direction of wave travel (eq.7-56) Angle between deepwater wave crest and shoreline (eq. 2-78) (Continued) B18 Example Units deg deg deg deg deg deg ft ft ft English Symbol B (Beta) r (Gamma ) A (Delta) 6 B (Epsilon) (Zeta) n (Eta) n (envelope) Definition Factor for increasing fetch length (eq. 3-47) Local fluid particle acceleration in x-direction (eq. 2-15) Local fluid particle acceleration in z-direction (eq. 2-16) Skewness of sediment sample using phi size measures (eq. 4-5) Lower limit of observed d,/H @ Empirically determined over- topping coefficient @Depth-to-height ratio of breaking waves in shallow water (eq. 4-21) @Constant for wave spectrum predictions Horizontal mixing coefficient in surf zone (eq. 4-21) perpendic- ular to the shoreline Specific gravity of a fluid (eq. 4-6) @Ratio between left and right longshore transport rates (eq. 4-31) Specific gravity of a solid (eq. 4-6) Change; algebraic difference Wall friction angle (eq. 7-143) Characteristic length describing pile roughness elements (Ch. 7) @Phase lag for bay high water with respect to sea high water Vertical particle displacement caused by wave passage (eq. 2-18) @Astronomical tide potential in head of water (eq. 3-77) Displacement of water surface relative to SWL by passage of wave (eq. 2-10) Envelope waveform of two or more superimposed wave trains (eq. 2-34) Water surface displacement by incident wave (Ch. 2) Wave crest elevation above SWL (Ch. 7) Water surface displacement by reflected wave (Ch. 2) Departure of water surface from its average position as a func- tion of time (eq. 3-11) Dimension (Continued) B19 Metric ES EE! deg Example Units English Non 288 min, hr ft ft ft ft ft ft ft ft Example Units Symbol Definition Dimension Metric English 6 Wave phase angle (Ch. 2) rad (Theta) @ Angle of wind measured counter- clockwise from x axis at shore deg @Angle of structure face rela- tive to horizontal (eq. 7-113; Fig. 7-107) deg @Angle of backslope of retaining wall (eq. 7-142) deg @Angle of side slope with the horizontal in direction of flow deg y Coefficient of friction (soil) 25 (Mu) Kinematic viscosity (Ch. 7) £t2/s (Nu) Atmospheric pressure deficit in (Xi) head of water (eq. 3-77) ft @ Horizontal particle displace- ment from wave passage (eq. 2-17) EE @Surf similarity parameter (eq. 2-86) = 1 Constant = 3.14159 = (Pi) p Mass density = et Ib=s-/£er (Rho) @Mass density of water! Df (eq. 4-35) lb-s’/m Cae kg-s’/m ) Pp, Mass density of mara! N-s/m* (or b=n7/fee p Mass density of fresh water = 3\t ye (1000 kg/m) lb-s*/ft F aarii pel! p, Mass density of armor material lb-s'/ft : : t 275.4 Pp. Mass density of sediment lb-s’ /ft Pp, Mass density of water (salt water = 10.31 x 10° kg/m; fresh water 3\f Zest = 1000 kg/m ) Ib-s5/ft fo] Standard deviation z=] (Sigma) @ Wave frequency, 2n/T oy Annual standard deviation of sig- nificant wave height (eq. 4-26) -— % Sediment-size standard deviation in phi units phi (Continued) 2 tote: the SI unit of weight (meaning force, or mass accelerated at the standard free-fall rate of 9.80665 m/s’) is the newton, which is equal to 1 kg-m/s?. When computing armor unit weights for practical purposes, newtons can be converted to kilograms (mass) by multiplying by 9.80665. B20 Symbol %oa “oB? “od Definition Dimension Metric Standard deviation of artificial beach nourishment borrow material in phi units Standard deviation of native beach material in phi units Bottom shear for an approximately level bottom (eq. 7-131) Design shear for channel side slope (eq. 7-132) Local boundary shear (eq. 7-126) x and y components of surface wind stress x and y components of surface wind stress Velocity potential @Angle between wave direction and plane across which energy is being transmitted (Ch. 2) @Angle of incident wave to gap in breakwater @ Latitude of location @Grain size units ( = -log.d 2 (mm) ) @ Internal angle of friction of earthfill or other material @Angle of riprap repose (eq. 7-132) Phase of the oes wave at time t = 0 (eq. 3-11) Coefficient for calculation of maximum total force on piles (eq. 7-42) Particle size in phi units of the xn percentile in sediment sample Wave reflection coefficient (eqs. 2-27, 7-72) Effects of stability of air column on wind velocity (eq. 3-25) Wave angular frequency @Earth angular frequency Frequency of the gas wave at time t = 0 (eq. 3-11) B21 Example Units phi phi deg deg deg phi deg deg deg phi rad/s rad/s English 1b/£t? 1b/£t 1b/£t? 1b/£t? lb/ft? ft-/s rad/s, rad/bhr APPENDIX C Miscellaneous Tables and Plates Cape Florida State Park, Florida, 28 July 1970 MISCELLANEOUS TABLES AND PLATES LIST OF PLATES Page Illustration of various functions of d/LycecccccccccecceeeceeeeeeeeeC“2 Relationship between wave period, length, and depth....eececcceeeeeeC-3l Relationship between wave period, length, and depth for waves of shorter period and wavelength. cccccccccccccccccccccccccccccccesel—I2 Relationship between wave period, velocity, and depth.......e+e+eeee+eC—33 Relationship between wave energy, wavelength, and wave height......C-34 Change in wave direction and height due to refraction on slopes with straight, parallel depth contours including shoaling..........C-35 LISTS OF TABLES Functions of d/L for even increments of 8 Pe ce) Bunctlonsmotud/smeror even! ancrementsmotud!/lictersletoheleleleicicheteleteletctstelcleleters! Gale) Deepwater wavelength (Lo) and velocitiy (Cy) as a LUN ONO LWAVe EPe LllOd aie elelelelelelelelelelolcleletelalefevele) clelelelelolelslelelslelelololoielerclelsi c=) Conversion factors: English to metric (SI) units of measurement...C-36 Phi-millimeter conversion talbilleicveretetcletevetarctolovercreicielcielicieleleieieieicioletelcrcierenero G40) Values of slope angle © and cot © for various slopes.....+eeee-C-45 ~ irr .e2a8 EER = 0.04 0.06 an! egos ees HEPES Eg GEELg eee 7 HiEse 0.1 Ht ban ws apne nae! q eae epee ttt bd Uf t a OGa PSLE2 BBN Bm (NEES ED + 4 ei Belen ieeds Roe teh Ct a Ean HE + ttt 4 la I ean + t wt t e He i HEE Ho A cage ee eeaeertaeue SHER cau nega ess RSS Tr] SAS] $9882 SSSSS Mees eyes: SSSsasssae esse Sazes: BESess H 99 To ae pag) WNW d L oO after Wiegel, R.L., “Oscillatory Waves,” U.S. Army, Beach Erosion Board, Bulletin, Special Issue No. 1, July 1948. pide Lo Illustration of various functions of Plate C-l. 99| GUIDE FOR USE OF TABLES C-1 AND C-2 = ratio of the depth of water at any specific location to the wavelength in deep water = ratio of the depth of water at any specific location to the wavelength at that same location = ratio of the wave height in shallow water to what its wave height would have been in deep water if unaffected by refraction 1 1 ss ; saa = Ki X cr = K,(shoaling coefficient ) C fo) = a pressure response factor used in connection with underwater pressure instruments, where Ha oP) _ cosh [2ra/,, (1 + 2! 4)] eles (d + 2)/,] iG =— = — = Te) : 5 cosh (2nd/, ) cosh (20d); where P is the pressure fluctuation at a depth z measured negatively below still water, P is the surface pressure fluctuation, d is the depth of water from still-water level to the ocean bottom, L_ is the wavelength in any particular depth of water, and H is the corresponding variation of head at a depth z. The values of K_ shown in the tables are for the instrument placed on the bottom using the equation when z=-—d 1 values tabulated in column 8 2md/ cosh L the fraction of wave energy that travels forward with the waveform: i.e., with the wave velocity C rather than the group velocity C, 1 4nd/ @ = i = 2 wat Amd jy Gc Q n is also the ratio of group velocity C, to wave velocity C = ratio of group velocity to deepwater wave velocity where Cc-3 a& C M = an energy coefficient defined as Table C-l. Functions of d/L for even increments of d/L, (from 0.0001 to 1.000). a/L a/L 217 d/L TANH SINH COSH H/H' K Lird/L SINK COSH on (0 M M0 amd/L 2md/L 2td/L = umd/L &ma/L “eo te) () 0) Co) to) 1 cS OM 0) ) i 1 (o) oc .000100 .003990 .02507 .02506 .02507 1.0003 4.67 .9997 .0501h .05016 1.001 .9998 .02506 7,855 2000200 .005643 .03546 .03544 .03547 1.0006 3.757 .9994 .07091 .07097 1.003 .9996 .035L3 3,928 -000300 .006912 04343 .04340 .O43KL 1.0009 3.395 .9991 .08686 .08697 1.004 .9994 .04336 2,620 -00000 .007982 .05015 .05011 .05018 1.0013 3.160 .9987 .1003 .1005 1.005 .9992 .05007 1,965 -000500 .008925 .05608 .05602 .05611 1.0016 2.989 .9984 .1122 .112u 1.006 .9990 .0559% 1,572 2000600 .009778 .061LL .06136 .06148 1.0019 2.856 .9981 .1229 .1232 1.008 .9988 .06128 1,311 2000700 .01056 .06637 .06627 .06642 1.0022 2.749 .9978 .1327 .1331 1.009 .9985 .06617 1,12 000800 .01129 .07096 .0708h .07102 1.0025 2.659 .9975 .1Wl9 .1h2h 1.010 .9983 .07072 933.5 2000900 .01198 .07527 .07513 .07534 1.0028 2.582 .9972 .1505 .1511 1.011 .9981 .07499 874.3 2001000 .01263 .07935 .07918 .07943 1.0032 2.515 .9969 .1587 .159k 1.013 .9979 .07902 787.0 2001100 .01325 .08323 .08304 .08333 1.0035 2.456 .9965 .1665 .1672 1.01L .9977 .08285 715.6 -001200 .0138h .08694 .08672 .08705 1.0038 2.LOolh .9962 .1739 «1718 1.015 .9975 .08651 656.1 2001300 .01LL0 .09050 .09026 .09063 1.0041 2.357 .9959 .1810 .1820 1.016 .9973 .09001 605.8 -001,00 .01L95 .09393 .09365 .09L07 1.004 2.314 .9956 .1879 .1890 1.018 .9971 .09338 562.6 2001500 .015h8 .09723 .09693 .09739 1.0047 2.275 .9953 1945 .1957 1.019 .9969 .09663 525 -001600 .01598 .100, .1001 .1006 1.0051 2.239 .9949 .2009 .2022 1.020 .9967 .09977 193 -001700 .01648 .1035 .1032 .1037 1.0054 2.205 .9946 .2071 .2086 1.022 .9965 .1028 63 -001800 .01696 .1066 .1062 .1068 1.0057 2.17) .9943 «2131 .2147 1.023 .9962 .1058 438 2001900 .017h3 .1095 .1091 .1097 1.0060 2.145 .9940 .2190 .2207 1.02, .9960 .1087 415 2002000 .01788 .1123 1119 .1125 1.0063 2.119 .9937 .22h7 .2266 1.025 .9958 .1114 394 002100 .01832 .1251 .11L6 .1154 1.0066 2.09, .993L .2303 .2323 1.027 .9956 .11h1 376 2002200 .01876 .1178 .1173 .21281 1.0069 2.070 .9931 .2357 .2379 1.028 .9954 .1161 359 -002300 .01918 .1205 .1199 .1208 1.0073 2.047 .9928 .2b10 2433 1.029 .9952 .1193 343 200200 .01959 .1231 .1225 .123h 1.0076 2.025 .9925 .2h62 .2h87 1.031 .9950 .1219 329 2002500 .02000 .1257 .1250 .1260 1.0079 2.005 .9922 .2513 .2540 1.032 .99LB .1243 316 2002600 .020)0 .1282 .1275 .1285 1.0082 1.986 9919 .2563 .2592 1.033 .9946 .1268 30h 2002700 .02079 .1306 = 41299 = «1310 1.0085 1.967 -9916 .2612 22642 = 1.03L = .99UL «21292 2.292 2002800 .02117 = .1330 = .1323 0 «1334 =-1.0089 1.950 9912 .2661 .2692 1.036 .99L2 .1315 282 002900 .02155 .1354 .13L6 .1358 1.0092 1.933 .9909 .2708 .27L1 1.037 .9939 .1338 272 2003000 .02192 .1377 1369 1382 1.0095 1.917 .9906 .2755 .2790 1.038 .9937 .1360 263 2003100 .02228 .1400 .1391 1405 1.0098 1.902 .9903 .2800 .2837 1.0L0 .9935 .1382 255 2003200 .02264 .1423 .1413 11427 1.0101 1.887 .9900 .2845 .288h 1.041 .9933 .1L0h 2u7 2003300 .02300 .1yhb5 11435 .1bu9 1.010 1.873 .9897 .2890 .2930 1.042 .9931 .1425 2h0 .003L00 .02335 .1L67 .1h56 .1h72 1.0108 1.860 .9893 .293L .2976 1.043 .9929 .1Uh6 233 2003500 .02369 .1488 .1h77 .1494 1.0111 1.847 .9890 .2977 .3021 1.0L5 .9927 .1466 226 2003600 .024,03 .1510 .1h98 .1515 1.0114 1.834 .9887 .3020 .3065 1.046 .9925 .1487 220 2003700 .02436 .1531 .1519 .1537 1.0117 1.622 .988L .3061 .3109 1.047 .9923 .1507 21b -003800 .02h69 .1551 .1539 .1558 1.0121 1.810 .9881 .3103 .3153 1.0h9 .9921 .1527 208 2003900 .02502 .1572 .1559 .1579 1.0124 1.799 .9878 31h .3196 1.050 .9919 .1546 203 e00h000 .0253h 1592 .1579 .1599 1.0127 1.788 .9875 .318L .3238 1.051 .9917 .1565 196 eO00h100 .02566 .1612 .1598 .1619 1.0130 1.777 .9872 .322h .3280 1.052 .9915 .158h 193 +004200 .02597 41632 1617 = «1639 1.0133 1.767 .9869 .3263 =. 3322 1.05L .9912 .1602 189 200L300 .02628 .1651 .1636 .1659 1.0137 1.756 .9865 .3302 .3362 1.055 .9910 .1621 184 -OOWLOO .02659 .1671 .1655 .1678 1.0140 1.746 9862 .3341 .3403 1.056 .9908 .16L0 180 200500 .02689 .1690 .167h .1698 1.01L3 1.737 .9859 .3380 34h 1.058 .9906 .1658 176 2004600 .02719 .1708 .1692 .1717 1.01LK6 1.727 .9856 .3417 .3183 1.059 .990: .1676 172 200h700 .027h9 .1727 1710 «9.1736 )=1 01K S—-1.718 9.9853 .3LSu =o 3523 1.060 .9902 .1693 169 e00L800 .02778 .1745 .1728 ) 3=26175L «= 1.0153 1.709 + .98K9 3491 =. 3562 1.062 .9900 .1711 165 -004900 .02807 .1764 .17hK6 .1773 1.0156 1.701 .9846 .3527 .3601 1.063 .9898 .1728 162 -005000 .02836 .1782 .1764 .1791 1.0159 1.692 .9843 23564 .36h0 1.06, .9896 .17h6 159 2005100 .0286L .1800 .1781 .1809 1.0162 1.684 .9840 .3599 .3678 1.066 .989k .1762 156 2005200 .02893 .1818 .1798 .1827 1.0166 1.676 .9837 .3635 3715 1.067 .9892 .1779 153 2005300 .02921 .1835 .1815 .1845 1.0169 1.669 .9834 .3670 .3753 1.068 .9889 .1795 150 2005400 .02948 .1852 .1832 .1863 1.0172 1.662 .9831 .3705 .3790 1.069 .9887 .1811 1h7 2005500 .02976 .1870 .1848 .1880 1.0175 1.654 .9828 .3739 .3827 1.071 .9885 .1827 1h5 -005$00 .03003 .1887 .1865 .1898 1.0178 1.647 .9825 .377L .386L 1.072 .9883 .18L3 1h2 2005700 .03030 .190h .1881 .1915 1.0182 1.640 .9822 .3808 .3900 1.073 .9881 .1859 10 2005800 .03057 .1921 .1897 .1932 1.0185 1.633 .9818 .3841 .3937 1.075 .9879 .187h 137 2005990 .03083 .1937 .1913 .1949 1.0188 1.626 .9815 .3875 3972 1.076 .9877 .1890 135 ¥Also: bs/ag, C/Coy L/Le d/L, 2006000 2006100 -006200 2006300 -00600 2006500 - 006600 - 006700 ~006800 ~006900 .007000 -007100 -007200 -907300 -0071,00 -007500 ~007600 -007700 2007800 -007900 -008000 -008100 2008200 2008 300 - 008,00 ~008500 - 008600 2008700 008800 -008900 009000 009100 009200 + 009300 009400 2009500 -009600 -009700 009800 - 009900 -01000 -01100 -C1200 -01300 -01400 01500 «01600 -01700 -01800 01900 202000 02100 02200 202300 -0200 02500 02600 -02700 02800 02900 d/L 03110 203136 03162 203188 203213 .03238 20326 -03289 03313 03338 -03362 03387 203411 203435 -03459 ~034,82 203506 203529 203552 2035/6 03598 03621 036L4 +03666 03689 203711 203733 203755 203777 203799 .03821 203842 0386), 03885 03906 203928 203949 -03970 03990 -O4011 -04032 04233 0426 204612 204791 20496) 205132 205296 205455 05611 -05763 205912 ~06057 -06200 206340 064,78 06613 -067L7 06878 07007 Table C-l. SINH 2rd/L 21967 1983 «2000 22016 -2033 +209 +2065 2081 2097 2113 2128 21h 2160 2175 +2190 22205 22221 22236 22251 22265 +2280 ©2295 +2310 + 232k +2338 «2353 2367 «2381 22396 «2410 2242) 24,38 22452 © 2h65 +2507 2520 257 2560 2691 +2817 2938 3056 23170 23281 COSH 277 d/L 1.0192 1.0195 1.0198 1.0201 1.0205 1.0208 1.0211 1.021h 1.0217 1.0221 1,022) 1.0227 1.0231 1.023h 1.0237 1.0240 1.0244 1.02h7 1.0250 1.0253 1.0257 1.0260 1.0263 1.0266 1.0270 1.0273 1.0276 1.0280 1.0283 1.0286 1.0290 1.0293 1.0296 1.0299 1.0303 1.0306 1.0309 1.0313 1.0316 1.0319 1.0322 1.0356 1.0389 1.0423 1.0456 1.0490 1.052) 1.0559 1.0593 1.0628 1.0663 1.0698 1.0733 1.0768 1.080), 1.0840 1.0876 1.0912 1.0949 1.0985 H/H' 1.620 1.614 1,607 1.601 u 0595 1.589 1.583 1.578 1.572 1.567 1.561 1.556 1.551 1.546 1.5h1 1.536 1.531 1.526 1.521 1.517 1.512 1.508 1.503 1.499 1.495 1.491 1.487 1.482 1.478 1.L7L 1.471 1.467 1.463 1.459 1.456 1.452 1.448 1.445 1.442 1.438 1.435 1.403 1.375 1.350 1.327 1.307 1.288 1.271 1.255 1.240 1.226 1.213 1.201 1.189 1.178 1.168 1.159 1.150 1.141 1.133 Continued. K Lard/L - 3908 239L1 23973 «4006 1,038 24970 -4101 2133 4164 +225 4256 286 +4316 +4346 4375 +4406 435 ehL6L L493 24522 oh551 04579 4607 4636 66), e691 04719 4 7L7 04774 4801 4828 24855 4882 4909 4936 4962 4.988 501K, . 5040 «5066 05319 25562 25795 6020 26238 26450 26655 6856 27051 27612 27791 ©1967 ~8140 .8310 8478 28643 38805 COSH 47 a/L 1.077 1.079 1.080 1.081 1.083 1,084 1.085 1.087 1.088 1.089 1.091 1.092 1.093 1.095 1.096 1.097 1.099 1.100 1.101 1.103 1.104 1.105 1.107 1.108 1.109 ales bbl 1,112 1.113 1.115 1.116 1.118 1.119 1.120 1.122 1.123 1.124 1.126 1.127 1.128 1,130 1.131 1.1L5 1.159 1.173 1.187 1.201 1.215 1.230 1.2bh 1.259 1.27) 1.289 1.304 1.319 1.335 1.350 1.366 1.381 1.397 1.413 d/u, 203000 203200 203300 203,00 03500 03600 03700 03800 03900 a/L 207135 207260 207385 207507 207630 -077L8 -07867 -0798), 208100 208215 -08329 208L)2 208553 208661, -0877h 208883 208991 209098 209205 209311 209L16 209520 209623 209726 209829 209930 -1003 21013 21023 21033 21043 21053 21063 21082 21092 21101 ellli 21120 21130 01139 e119 21158 21168 21177 21186 21195 21205 21214 21223 21232 212h1 21251 21259 21268 01277 21286 21295 21304 21313 27 d/L TANH SINH COSH and/L 2m7d/L 2m7d/L e483 4205 .463h 1.1022 4562 4269 =6u721-—S 1.1059 4640 4333 4808 1.1096 04717) =o. 395 89K = 1.1133 e794 = =uh57 =. L980) s-1.1171 -4868 .4517 .5064 1.1209 e493 eh57T SUNT. WeLau7, e5017 -olK635 65230) +=1.1285 25090 «=eh69LS w5312)=—-1.132h 25162 =o 7K7)S 539K =: 11362 25233. = es 802.— ss «w5L75 = 1161 OL 2530, 4857 25556 1.14h0 25374 «=eb911l = 5637) = 11:79 Sukh 4964 5717 1.1518 25513-65015. «05796 =: 1.21558 25581 =. 5066 = 65876) 1.1599 2564965116 = 65954 = 121639 25717 = 65166 = 66033: 11.1679 Ash opps qabbl Slay) 25850 86.5263 = «6189S: 11,1760 25916 =65310 = «6267S: 1.21802 25981 =o 5357) 0S 3K Ss 1183 e60L6 .5403 6421 1.188) 26111 =. 5UN9 = 66499 1.1926 26176 «=.5U9h §=— 66575 1.1968 26239 = 65538 «= «66652 s«1.2011 26303. 65582. 66729: 11.2053 26366 «=. 5626-~—S «66805 =: 1.2096 06428 8.5668 .6880 1.2138 6491 .5711 866956 =: 1.2181 26553 5753.6 7033 122225 06616 «9.5794 «=e 710—s—s«12270 26678 = 5834 = 071870 122315 06739 «= 5874 7256 = 1.2355 26799 591 So 7335) 1202 26860 45954 =e TH11 01 27 26920 .5993. e786 201.292 6981 .6031 .7561 1.2537 »1037 6069 .7633 1.2580 27099 .6106 .77hl 1.2628 e7157 = eh =o 7783s 1 2672 e7219 «= «66181 2S «7863S: 1.2721 et2t? 6217 67937 1.2767 27336 «=6.6252,—S «6801S 1.2813 -7395 6289 .8086 1.2861 27453 26324 8162 1.2908 e7511 ©=.6359 = «8237 Ss: 1.2956 27569 6392 .8312 1.300k 27625 6427 8386 1.3051 -7683 .6460 .8462 1.3100 e774. = 66493 «8538 = 139 07799 = «6526 = B61, 1.3198 °7854 .6558 .8687 1.32h6 e7911 .6590 .8762 1.3295 07967 = 66622, «8837 = 12335 8026 .6655 .8915 1.3397 -8080 .6685 .8989 1.3L4L6 28137 =.6716 =. 906, 39S: 1.3197 6193 .6747 =.91K2 = 358 -8250 .6778 .9218 1.3600 Table C-l. H/H' = K Oo) 1.125 .9073 1.118 9042 1.111 9012 1.10, 8982 1.098 8952 1.092 .8921 1.086 .8891 1.080 .8861 1.075 -8831 1.069 6801 1.064 8771 1.059 87L1 1.055 8711 1.050 8688 1.046 +8652 1.042 8621 1.038 8592 1.034 8562 1.030 8532 1.026 8503 1.023 .8473 1.019 .8LL4 1.016 8415 1.013 .8385 1.010 .8356 1.007 8326 1.00) .8297 1.001 .8267 09985 8239 29958 8209 29932 8180 29907 8150 29883 8121 -9860 -8093 ©9837 8063 ©9815 8035 29793 «8005 29772 7977 29752 67948 29732 «7919 -9713 +7890 -9694 »7861 -9676 7833 9658 7804 e941 27775 962 2777 29607 7719 29591 7690 29576» 7662 29562 2 763k 29548 «7605 09534 67577 29520 »75L9 29506 »7522 29493» 749L 9481 .7h6L 969 «7437 29457 27409 2945 7381 ©9433-7353 C-7 Continued. 4d/L SINH wr d/L .8966 1,022 712k = 1 OL 29280 1.067 -9434 1.090 -9588 1.113 09137 ~©=—«s We 135 9886 1.158 1.003 1.180 1.018 1.203 1.032 1.226 1.047 1.2h8 106k) Leer 1.075 1.294 1.089 1.317 1.103 1.340 VeL16) 1.363 11300 S386 1.143 1.409 Paas7) e433 1.170 1.456 1.183 1.479 1.196 1.503 1.209 1.526 1.222 1.550 15235, 57h 1.248 1.598 1.261 1.622 1.273 1.6L6 1.286 1.670 1.298 1.695 seas roe alarAlg) Nnses}) alah 1.336 1.770 1.348 1.795 1.360 1.819 1.372 1.845 1.384 1.870 1.396 1.896 1.408 1.921 1.420 1.948 1.432 1.97h 1.4hk 2.000 1.455 2.025 1.467 2.053 1.479 2.080 1.490 2.107 1.502 2.135 1.514 2.162 1.525 2.189 1.537 2.217 1.548 2.245 1.560 2.27h 1.571 2.303 1.583 2.331 1.59h 2.360 1.605 2.389 1.616 2.18 1.628 2.448 1.639 2.478 1.650 2.508 COSH LTa/L 1.430 1.446 1.462 1.479 1.496 1.513 1.530 1.547 1.564 1.582 1.600 1.617 1.636 1.654 1.672 1.691 1.709 1.728 1.77 1.766 1.786 1.805 1.825 1.8h5 1.865 1.885 1.906 1.926 1.947 1.968 1.989 2.011 2.033 2.055 2.076 2.098 2.121 21h 2.166 2.189 2.213 2.236 2.260 2.28 2.308 2.332 2.357 2.382 2.407 2.432 2.458 2.484 2.511 2.537 22563 2.590 2.617 2.6L 2.672 2.700 21 da/L 8306 -8363 -8420 «8474 ~8528 8583 -8639 B69), -B7L9 8803 8858 8913 «8967 9023 9076 2 9130 918 29239 09293 +9343 . 94,00 9456 9508 9563 29616 -9670 29720 29175 29827 -9882 29936 29989 1,00) 1.010 1.015 1.020 1.025 1.030 1.036 1.041 1.016 1.052 1.057 1.062 1.068 1.073 1.078 1.084 1.089 1.094 1.099 1.105 1.110 1.115 1.120 1.125 1.131 1.136 1.141 1.1h6 Table C-l. SINH * 277 a/L 29295 +9372 29459 29525 -9600 9677 29755 9832 9908 29985 1.006 1,014 1,022 1.030 1.037 1.0L5 1.053 1.061 1.069 1.076 1.085 1.093 1.101 1.109 lousy, 1.125 1.133 1.141 1.149 1.157 1.165 1.174 1.182 1.190 1.198 1.207 1.215 1,223 1.231 1,.2L0 1.28 1.257 1.265 1.273 1.282 1.291 1.300 1.308 1.317 1.326 1.33h 1.343 we352 1.360 1.369 1.378 1.388 1.397 1.L05 1.415 COSH 21 d/L 1.3653 1.3706 1.3759 1.3810 1.3862 1.3917 1.3970 1.4023 1.4077 1.4131 1.4187 1.422 1.4297 1.4354 1.4h10 1.Lh65 1.4523 1.4580 1.4638 1.692 1.4752 1.481 1.4871 1.44932 1.4990 1.5051 1.5108 1.5171 1.5230 1.5293 1.5356 1.5418 1.5479 1.556 1.5605 1.567 K H/H) 9422 -732h ae 296 .9401 - 7268 9391 -72k1 .9381 ° 721u 69371 °° 7186 73362 «7158 29353 7131 .93uy «7104 "9338 °7076 69327. 10L9 mae 7022 .9311 2699L 930, +6967 69297 +6940 .9290 26913 9282 +6886 Continued. Ld/L_ SINH tt d/L 1.661 2.538 1.672 2.568 1.68, 2.599 1.695 2.630 1.706 2.662 1.717 2.693 1.728 2.726 1.739 2.757 1.750 2.790 1.761 2.822 1.772 2.855 1.783 2.888 1.793 2.922 1.805 2.956 1.615 2.990 1.826 3.024 1.837 3.059 1.848 3.094 1.858 3.128 1.869 3.164 1.880 3.201 1.891 3.237 1.902 3.274 1.913 3.312 1.923 3.348 1.934 3.385 1.94h 3.423 1.955 3.462 1.966 3.501 1.977 3.540 1.987 3.579 1.998 3.620 2.008 3.659 2.019 3.699 2,030 3.7L0 2.0L1 3.782 2.051 3.824 2.061 3.865 2.072 3.907 2.082 3.950 2.093 3.992 2.10h 4.036 2.114 4.080 2.125 4.125 2.135 b.169 2.1U6 4.217 2.15 h.262 2.167 4.309 2.177 =4.355 2.188 4.02 2.198 4.50 2.209 h.h98 2.219 =.5h6 2.230 4.595 2.2h0 .6hh 2.251 4.695 2.261 4.76 2.272 4.798 2.282 4.847 2.293 4.901 2m a/L 1.152 1.157 1.162 1.167 1.173 1.178 1.183 1.188 1.19b 1.199 1.20) 1.209 1.215 1.220 1.225 1.230 1.235 1.2h0 1.26 1.251 1.257 1.262 1.267 1.272 1.277 1.282 1.288 1.293 1.298 1.30h 1.309 1.314 1.320 1.325 1.330 1.335 1.341 1.346 1.351 1.356 1.362 1.367 1.372 1.377 1.383 1.388 1.393 1.399 1.404 1.409 1.41h 1.420 1.425 1.430 1.436 1.441 1.46 1.451 1.457 1.462 Table C-l. SINH 27 a/L 1.424 1.433 1.442 1.51 1.460 1.469 COSH 277 d/L 1.70 1.7b7 1.755 1.762 1.770 1.777 1.785 1.793 1.801 1.809 1.817 1.625 1.833 1.841 1.849 1.857 1.865 1.873 1,882 1.890 1.899 1.907 1.915 1.924 1.933 1.9h1 1.951 1.959 1.968 1.977 1.986 1.995 2.004 2.013 2.022 2.032 2.0h1 2.051 2.060 2.070 2.079 2.089 2.099 2.108 2.118 2.128 2.138 2.148 2.158 2.169 2.178 2.189 2.199 2.210 2.220 26231: 2.22 2.252 2.263 2.27h H/H! ° ©9133 ©9133 29132 -9132 9132 «9131 29130 29129 -9130 ©9130 29130 «9130 «9130 29130 -9130 -91L31 29132 «9132 29133 29133 9134 29135 +9136 29137 +9138 ©9139 Continued. kt a/L 2.303 2.314 2.324 2.335 2.345 2.356 2.366 2.377 2.387 2.398 2.108 2.419 2.429 2.4h0 2.450 2.461 2.471 2.482 2.492 2.503 2.513 2.523 2.534 2.54 2.555 2.565 2.576 2.586 2.597 2.607 2.618 2.629 2.639 2.650 2.660 2.671 2.681 2.692 2.702 2.712 2.723 2.73h 2.744 2.755 2.765 2.776 2.787 2.797 2.808 2.819 2.829 2.8L0 2.850 2.861 2.872 2.882 2.893 2.903 2.914 2.925 d/L, 22100 -2110 22120 22130 -2140 22150 ~2160 22170 -2180 -2190 -2200 22210 22220 22230 »22h0 -2250 -2260 +2270 22280 22290 22300 22310 2320 22330 22340 - 2350 «2360 +2370 - 2380 -2390 +200 22410 220 -2h30 ~2h0 2150 2460 -24,70 ~24,80 «2490 ~2500 -2510 22520 22530 +250 2550 -2560 +2570 .2580 -2590 -2600 -2610 -2620 «2630 -2640 +2650 «2660 +2670 +2680 -2690 27 a/L 1.468 1.473 1.479 1.48) 1.489 1.49h 1.500 1.506 alAGi il 1.516 1.521 1.526 1.532 1.537 1.542 1.58 1.553 1.559 1.56 1.569 oT 1.580 1.585 1.591 1.596 1.602 1.607 1.612 1.618 1.623 1.629 1.634 1.640 1.645 1.650 1.656 1.661 1.667 1.672 1.678 1.683 1.689 1.694 1.700 1.705 1.711 1.716 1.722 1.727 1.732 1.738 1.7h4 1.7h9 1.755 1.760 1.766 1.771 1.776 1.782 1.788 TANH 27 da/L 8991 29001 29011 29021 ©9031 29041 29051 ©9061 29070 29079 9088 9097 +9107 +9116 29125 913k, 29143 +9152 9161 9170 9178 +9186 919k 9203 +9211 ©9219 ©9227 +9235 92h3 ©9251 29259 9267 «9275 9282 9289 ©9296 9304, 29311 9318 9325 «9332 +9339 .93L6 +9353 ~9360 9367 9374 9381 -9388 -9394 +9400 9406 -9h12 9418 9425 9431 9437 94h3 -9LL9 -9455 SINH 277 a/L 2.055 2.066 2.079 2.091 2.103 2.115 2.128 2.12 2.154 2.166 2.178 2.192 2.20) 2.218 2.230 2.2hh 2.257 2.271 2.28) 2.297 2.311 2.325 2.338 2.352 2.366 2.380 2.393 2.408 2.422 2.1436 2.450 2.46 2.480 2.494 2.508 2.523 2.538 2.553 2.568 2.583 2.599 2.614 2.629 2.645 2.660 2.676 2.691 2.707 2.723 2.739 2.755 2.772 2.788 2.80), 2.820 2.837 2.853 2.870 2.886 2.90 Table COSH 277 a/L 2.285 2.295 2.307 2.318 2.329 2.3h0 2.351 2.364 2.375 2.386 2.397 2.409 2.421 2.433 2.hhh 2.457 2.469 2.481 2.493 2.506 2.518 2.531 2.5h3 2.556 2.569 2.581 2.594 2.607 2.620 2.634 2.67 2.660 2.674 2.687 2.700 2.714 2.728 2.7h2 2.755 2.770 2.784 2.798 2.813 2.828 2.842 2.856 2.871 2.886 2.901 2.916 2.931 2.946 2.962 2.977 2.992 3.008 3.023 3.039 3.055 3.071 C-1. H/H? 29205 -9207 29210 69213 -9215 -9218 29221 29223 29226 29228 9231 +9234, +9236 ©9239 -92h2 925 9218 29251 925k 9258 9261 926k, 29267 ©9270 9273 9276 29279 29282 29285 -9288 9291 9294 9298 +9301 ©9307 +9310 9314 9317 29320 ©9323 ©9327 ©9330 ©9333 ©9336 -93h0 9343 -93L6 939 ©9353 9356 9360 9363 +9367 29370 9373 9377 9380 9383 9386 c-10 Continued k77a/L 2.936 2.946 2.957 2.967 2.978 2.989 2.999 3.010 3.021 3.031 3.0h2 3.052 3.063 3.074 3.085 3.095 3.106 Selly, 3.128 3.138 3.1h9 3.160 3.171 3.182 3.192 3.203 3.214 3.225 3.236 3.27 32257 3.268 3.279 3.290 a/L, ~2700 +2710 +2720 -2730 -27L0 -2750 -2760 22770 2780 +2790 » 2800 .2810 ~ 2820 - 2830 «2840 -2850 2860 ', 2870 ~ 2880 » 2890 +2900 «2910 -2920 22930 22940 22950 22960 22970 +2980 22990 «3000 23010 » 3020 3030 +300 +3050 «3060 3070 +3080 +3090 «3100 «3110 .3120 «3130 -3140 3150 +3160 -3170 23180 +3190 +3200 +3210 .3220 3230 -32h0 -3250 -3260 -3270 ~ 3280 -3290 27 a/L 1.793 1.799 1.80h 1.810 1.815 1.821 1.826 1.832 1,837 1.843 1.89 1.854 ‘1.860 1.866 1.871 1.877 1.882 1.688 1.893 1.899 1.905 1.910 1.916 1.922 1.927 1.933 1.938 1.9hh 1.950 1.955 1.961 1.967 1.972 1.978 1.98h 1.989 1.995 2.001 2.007 2.012 2.018 2.023 2.029 2.035 2.041 2.06 2.052 2.058 2.063 2.069 2.075 2.081 2.086 2.092 2.098 2.104 2.110 2.115 2.121 2.127 Table C-l. SINH 27a/L 2.921 2.938 2.956 2.973 2.990 3.008 3.025 3.043 3.061 3.079 3.097 3.115 3.133 3.152 Syl 3.190 3.209 3.228 3.2h6 3.264 3.28), 3.303 3.323 3.3h3 3.362 3.382 3.402 3.22 3.42 3.462 3.483 3.503 3.524, 3-545 3.566 3.587 3.609 3.630 3.651 3.673 3.694 3.716 3.738 3.760 3.782 3.805 3.828 3.851 3.873 3.896 3.919 3.943 3.966 3-990 4.01 4.038 4.061 4.085 4.110 4.135 COSH 27 d/L 3.088 3.104 3.120 3.136 3.153 3.170 3.186 3.203 3.220 3.237 3.254 3.272 3.289 3.307 3.325 3.343 3.361 3.379 3.396 3.414 3.433 3.451 3.471 3.490 3.508 3.527 3.546 3.565 3.585 3.60 3.62 3.643 3.663 3.683 3.703 3.72h 3.745 3.765 3.786 3.806 3.827 3.848 H/H! (Gil Continued wad/L 3.587 3.598 3.610 SINH i7a/L 18.0h 18.2) 18.6 18.65 18.86 19.07 19.28 19.49 19.71 19.93 20.16 20.39 20.62 20.85 21.09 21.33 21.57 21.82 22.05 22.30 22.54 22.81 23.07 23.33 23.60 23.86 24.12 24.40 24.68 24.96 25.2h 25.53 25.82 26.12 26.42 26.72 27.02 27.33 27.65 27.96 28.28 28.60 28.93 29.27 29.60 29.9 30.29 30.64 30.99 31.35 31.71 32.97 32.U4 32.83 33.20 33.60 33.97 34.37 34.77 35.18 COSH 47 d/L 18.07 18.27 18.49 18.67 18.89 19.10 19.30 19.51 19.7b 19.96 20.18 20.41 20.6) 20.87 21.11 21.35 21.59 21.84 22.07 22.32 22.57 22.83 23.09 23.35 23.62 23.88 24.15 24.42 2h.70 2.98 25.26 25.55 25.83 26.14 26.4 26.7h 27.04 27.35 27.66 27.98 28.30 28.62 28.95 29.28 29.62 29.96 30.31 30.65 31.00 31.37 31.72 32.08 32.46 32.8h 33.22 33.61 33.99 34.38 34.79 35.19 2m a/L 2.133 2.138 21k 2.150 2.156 2.161 2.167 2.173 2.179 2.185 2.190 2.196 2.202 2.208 2.214 2.220 2.225 2.231 2.237 2.23 2.29 2.255 2.260 2.266 2.272 2.278 2.284 2.290 2.296 2.301 2.307 2.313 2.319 2.325 2.331 2.337 2.32 2.348 2.354 2.360 2.366 2.372 2.378 2.384 2.390 2.396 2.402 2.408 2.13 2.119 2.425 2.431 2.4437 2.443 2.hh9 2.455 2.461 2.467 2.473 2.479 Table C-l. SINK 27 a/L 4.159 4.18), COSH 2m a/L 4.277 301 326 4.350 4.375 4.399 42h 4.450 L474 4.500 4.525 4.550 4.576 4.602 4.630 4.656 4.682 1 H/H! Continued. h7rda/L SINH 7d/L 35.58 35.99 36.42 36.84 37.25 37.70 COSH 47rda/L n 27 d/L 2.485 2.491 2.497 2.503 2.509 Zeke) 2.521 2.527 2.532 2.538 2.5h4h 2.550 2.556 2.562 2.568 2.575 2.581 2.586 2.592 2.598 2.60 2.610 2.616 2.623 2.629 2.635 2.641 2.647 2.653 2.659 2.665 2.671 2.677 2.683 2.689 2.695 2.701 2.707 2.713 2.719 2.725 2.731 2.737 2.7h3 2.709 2.755 2.762 2.768 2.774 2.780 2.786 2.792 2.798 2.80L 2.810 2.816 2.822 2.828 2.83 2.840 TANH 27 d/L 9862 -986L, 9865 -9867 -9869 +9870 9872 9873 9874 ©9876 9877 ©9879 -9880 - 9882 29883 ~9885 - 9886 «9887 9889 -9890 29891 9892 989k ©9895 «9896 9898 9899 +9900 9901 +9902 +990L +9905 +9906 +9907. -9908 29909 29910 09911 29912 “9913 991 09915 9916 09917 ©9918 “9919 +9920 09921 29922 ©9923 992h, 9925 9926 9927 ©9928 09929 ©9930 29930 ©9931 9932 Table C-l. SINH COSH H/H! Kk 27d/L 2m a/L 2 5.957 6.040 .9739 .1656 5.993 6.076 .9741 .16u6 6-029 6.112 .9743 .1636 6.066 6.148 .9745 .1627 6.103 6.185 .9748 .1617 6.140 6.221 .9750 .1608 6.177 6.258 .9752 .1598 6.215 6.295 = «975.1589 6.252 6.332 .9756 .1579 6.290 6.369 .9758 .1570 6.329 6.407 -.9761 .1561 6.367 6.hl5 .9763 .1552 6.406 6.483 .9765 1542 6.4b, 6.521 .9766 11533 6.484 6.561 .9768 .152h 6.525 6.601 .9770 .1515 6.564 6.640 .9772 .1506 6.603 6.679 .9774 .1h97 6.644 6.718 .9776 .1488 6.68, 6.758 .9778 .1480 6.725 6.799 .9780 .1h7i 6.766 6.839 .9782 .1h62 6.806 6.879 .978h .145h 6.849 6.921 .9786 .1hh5 6.890 6.963 .9788 .136 6.932 7.00, .9790 .1h28 6.974 7.0hK6 .9792 .1h19 WeO18) 7088! 979N" cae 7.060 7.130 .9795 .1h03 Tol (fey Hey aalstefh 7-1hK6 7-215 .9798 1386 7.190 7.259 .9800 .1378 7234 75303 .9802 .1369 7-279 7.349 .980h .1361 7325 70392 $9806 21353 (oske Talis, Cito} aly Velie - Teh S980) 62337 70457 7-524 .9811 1329 3503) | (570m wAgBlomelsel 7.550 7,616 981 1313 7.595 7.661 .9816 .1305 7.642 7-707 9818 .1298 7.688 7.753 9819 1290 7.735 7.800 9821 .1282 7.783 7.847 .9823 .127h 7-631 7.895 982) .1267 7.680 7.943 .9826 .1259 7.922 7.991 .9828 .1251 7.975 8.035 9829 .12hh 8.026 8.088 .9§30 .1236 8.075 8.136 9832 .1229 8:12, 8.185 9833 -l222 8.175 8.236 9835 .122h 8.228 8.285 .9836 .1207 8.274 8.334 .9838 .1200 8.326 8.387 .9839 © ©.1192 8.379 8.438 9841 .1185 8.427 8.486 9843 .1178 8.481 8.540 984) 1171 8.532 8.590 5846 .116h C=-13 Continued. 477 a/L 4.970 4.982 4.993 5.005 5.017 5.029 5.Ohl 5.053 5.065 5.077 5.089 5.101 5.113 5.125 5.137 5.19 5.161 5.173 5.185 5.197 5.209 Se2el! 5.233 5.25 5.257 5.269 5.281 5.294 5.305 5.317 5.329 5.3h1 5-353 5-366 5.378 5.390 5.402 5.414 5.426 5.438 5450 5462 5 47h 5486 5.499 5.511 5.523 5.535 5.5u7 5.560 5.572 5.58 5-596 5.608 5.620 5-632 5.6L4 5.657 5.669 5.681 SINH 477 a/L 71.97 72.85 73.72 7h.58 75.48 76.40 11.321 78.2u 719.19 80.13 81.12 82.07 83.06 8.07 85.11 86.1h 87.17 88.19 89.28 90.38 y1l.4h 92.54 93.67 94.83 95.95 97.13 98.29 99.52 100.7 101.9 103.1 104.4 105.7 107.0 108.3 109.7 110.9 112.2 113.6 115.0 16.4 117.8 119.2 120.7 122.2 123.7 125.2 126.7 128.3 129.9 131.b 133.0 134.7 136.3 137.9 139.6 141.h 143.1 W4h.8 146.6 COSH L/7a/L 71.98 72.86 73.72 7h.59 75.49 76.40 711.32 78.2) 19-19 80.13. &.12 82.08 83.06 84.07 85.12 36.14 87.17 88.20 89.28 90.39 Glob 92.55 93.67 94.83 95.96 97.13 98.30 99.52 100.7 101.9 103.1 10h.h 105.7 107.0 108.3 109.7 110.9 112.2 113.6 115.0 116.4 117.8 119.3 120.7 122.2 123.7 125.2 126.7 128.3 129.9 131.4 133.0 134.7 136.3 137.9 139.7 11.4 143.1 14.8 16.6 Table C-l. SINH on a/L 8.585 8.638 8.693 8.747 8.797 8.853 8.910 8.965 9-016 9.07 9-132 9-183 9.22 9.301 9.353 Gol3 9.472 92533 9-586 9.647 COSH 2 da/L 8.643 8.695 8.750 8.60) 8.854 8.910 8.965 9.021 9-072 92129 9.186 9.238 92296 9-35 90406 9.466 92525 9.585 9.638 9.699 9.760 9.821 9.877 9.938 10.00 10.07 10.12 10.18 10.25 10.31 10.37 10.3 10.50 10.57 10.63 10.69 10.76 10.83 10.90 10.96 11.03 11.09 11.16 11.2h 11.31 11.37 11.4h 11.51 11.59 11.65 11.72 11.80 11.87 11.95 12.02 12.09 12.16 12.24 12.32 12.39 H/H) 9847 9848 9849 9851 9852 ©9853 ©9855 29857 9858 29859 Continued. K un aft 21157 5.693 21150 5.705 1143 5.717 21136 5.730 01129 5.742 1122 5.754 e1115 5.766 -1109 5.779 21102 5.791 21095 5.803 -1089 5.815 1083 5.827 21076 5.8h0 21069 5.852 01063 5.864 +1056 5.876 -1050 5.868 21043 5.900 1037 5.912 ©1031 5.925 21025 5.937 21018 +5.9h9 21012 5.962 -1006 5.97 21000 5.986 09942 5. 09882 6 09698 6.018 -09641 6,060 209583 6.072 209523 6.085 209464 6.097 -09L05 6.109 209352 6.121 209294 6.134 209236 6.146 -09178 6.159 209121 6.171 -0906L 6.183 209010 6.195 -08956 6.208 -08901 6.220 20885 6.232 -08793 6.25 -087h) 6.257 -08691 6.269 208637 6.282 -0858) 6.294 -08530 6.306 -08477 6.319 20842 6.331 -08371 6.343 -08320 6.356 -08270 6.368 -08220 6.380 +08169 6.393 08119 6.405 -08068 6.417 C-14 SINH 4? a/L 148.4 150.2 152.1 15.0 155.9 157.7 159.7 161.7 163.6 165.6 167.7 169.7 171.8 173.9 176.0 178.2 180.4 182.6 184.8 187.2 189.5 191.8 194.2 196.5 199.0 201.4 203.9 206.5 209.0 211.7 21h.2 216.8 219.5 222.2 225.0 228.3 230.6 233.5 236.h 239.6 2h2.3 245.2 248.3 251.3 254.5 257.6 260.8 26.0 267.3 270.6 274.0 277.5 280.8 284.3 287.9 291.4 295.0 298.7 302.4 306.2 88 S33 388 B Serre r FMM e ee wo 00 0 “o c TANH 277 d/L +9968 ©9969 -9969 29970 +9970 ©9970 29971 29971 09971 “9972 39972 29972 -9973 ©9973 -9973 9974 9974 9974 9975 ©9975 29975 29976 +9976 29976 9976 09977 29977 299TT 29977 9978 ©9978 ©9978 29979 29979 09979 09979 9980 9980 9980 +9980 +9981 +9981 +9981 9981 ©9982 9982 ©9982 9982 9982 9983 ©9983 9983 9983 9984, -998h, -998L -998L 9984 9985 Table C-1. SINH 2m7d/L 12.43 12.50 12.58 12.66 12.74 12.82 12.90 12.98 13.06 13.14 13.22 13.31 13.39 13.47 13.55 13.6) 13.73 13.81 13.90 13.99 14.07 1.16 14.25 14.34 14.43 14.52 14.61 14.70 14.79 14.88 14.97 15.07 15.16 15.25 15.35 15.h5 15.5) 15.64 15.7h 15.8) 15.9h 16.0h 16.1h 16.24 16.34 16.Lh 16.5) 16.65 16.75 16.85 16.96 17.06 17.17 17.28 17.38 17.9 17.60 17.71 17.82 17.94 COSH 277 d/L 12.47 12.5h 12.62 12.70 12.78 12.86 12.94 13.02 13.10 13.18 13.26 13.35 13.43 13.51 13.59 13.68 13.76 13.85 13.94 14.02 1.10 14.19 14.28 1h.37 14.6 14.55 14.64 14.73 14.82 14.91 15.01 15.10 15.19 15.29 15.38 15.448 15.58 15.67 15.77 15.87 15.97 16.07 16.17 16.27 16.37 16.7 16.57 16.68 16.78 16.88 16.99 17.09 17.20 17.31 17.41 17.52 17.63 17.7h 17.85 17.97 H/H! ° 9914 “9915 “9915 29916 “9917 29918 -9919 29919 ©9920 ©9921 29922 9923 992), 9924 ©9925 +9926 29927 29927 9928 29929 +9930 +9931 29931 29932 © 9933 29933 993) 9935 9935 ©9936 ©9936 ©9937 9938 9938 ©9939 9940 -99L1 9941 992 9942 9942 “992 -99L3 994 99LL °99LS -99U5 99L6 © 997 9947 99L7 9948 299L9 “9949 9950 29950 29951 29951 29952 29952 C=15 Continued. K L77a/L -08022 6.430 -07972 6.42 207922 6.45) -07873 6.467 -0782k 6.479 -07776 6.491 -07729 6.50 -07682 6.516 -07634 6.529 207587 6.541 207540 6.553 -O7L94 6.566 -O7TLL9 6.578 -0740L 6.590 -07358 6.603 -07312 6.615 -07266 6.628 -07221 6.640 207177 6.652 -0713L 6.665 207091 6,677 -070L47 6.690 -07003 6.702 -06959 6.714 -06915 6.727 -06872 6.739 -06829 6.752 -06787 6.764 -067L6 6.776 -06705 6.789 -0666, 6.801 206623 6.814 206582 6.826 206542 6.838 206501 6.851 206461 6.863 -06420 6.876 206380 6.888 20631 6.901 -06302 6.913 -06263 6.925 -0622h 6.937 206186 6.950 -06148 6.962 -06110 6.975 206073 6.987 -06035 7.000 -05997 7.012 205960 7.025 205923 7.037 -05887 7.050 205850 7.062 -05814 7.07 -05778 7.087 205743 7.099 205707 7.112 -05672 7.12 -05637 7.136 -05602 7.149 -05567 7.161 SINH LWa/L 310.0 313.8 317.7 Syailey/ 325.7 329.7 333.8 337.9 32.2 346.4 350.7 355.1 359.6 364.0 368.5 373.1 377.8 382.5 387.3 392.2 397.0 402.0 406.9 412.0 417.2 422.4 427.7 433.1 438.5 hhh.o 49.5 455.1 460.7 L66.h 472.2 478.1 484.3 490.3 496.h 502.5 508.7 515.0 521.6 528.1 534.8 Sul. 58.1 554.9 562.0 569.1 576.1 583.3 590.7 598.0 605.0 613.2 620.8 628.5 636.4 644.3 2m d/L 3.587 3.593 3.600 3-606 3.612 3.618 3.62 3.630 3.637 3.63 3.649 3.656 3.662 3.668 3.674 3.680 3.686 3.693 3.699 3.705 3.712 3.718 3.724 3.730 3.737 3.743 3.749 3.755 3.761 3.767 3.77L 3.836 3.899 3.961 4.02) 4.086 4.1h9 4.212 4.27 4.337 4.400 4.462 4.525 4.588 4.650 4.713 4.776 4.839 4.902 4.964 5.027 5.090 5.153 5-215 5.278 5 .3h1 5404 5.467 5.529 5.592 SINH 27d/L 18.05 18.16 18.28 18.39 18.50 18.62 18.73 18.85 18.97 19.09 19.21 19.33 19.45 19.58 19.70 19.81 19.9 20.06 20.19 20.32 20.45 20.57 20.70 20.83 20.97 21.10 21523 21.35 21.49 21.62 21.76 23.17 24.66 26.25 27.95 29.75 31.68 33.73 35.90 38,23 40.71 43.34 46.14 49.13 52.31 55.70 59.31 63.15 67.2h 71.60 16.24 81.18 86.44 92.04 98.00 1ol.4 aiaten 118.3 126.0 134.2 Table C-l. COSH 277 d/L 18.08 18.19 18.31 16.142 18,53 18.64 18.76 18.88 19.00 19.12 19.2) 19.36 19.18 19.60 19.73 19.84 19.96 20.09 20.21 20.34 20.47 20.60 20.73 20.86 20.99 21.12 21.25 21.37 21.51 21.64 21.78 23.19 2h.68 26.27 27.97 29.77 31.69 33-7 35.92 38.2 40.72 43.35 46.15 49.14 52.32 Serine 59.31 63.16 67.25 71.60 76.24 81.19 86.4) 92.05 98.01 10.4 aaa ieal 118.3 126.0 13h.2 H/H! oO 9953 9953 9954 995k 9955 09955 29956 9956 9957 9957 9957 9958 -9958 9959 9959 =9960 -9960 9960 9961 9961 29962 29962 ©9963 29963 29963 996), 996 9964 29965 -9965 +9965 9969 +9972 29975 9977 +9980 -9982 -9983 +9985 9987 -9988 9989 ©9990 +9991 9992 ©9993 9994 +9995 9996 9996 9996 ©9996 9997 9997 ©9997 9998 9998 +9998 -9998 . 9998 C-16 Continued. K -05532 -05497 205463 205430 -05396 05363 -05330 -05297 0526) 205231 205198 -05166 205134 «05102 -05070 «0500 -05009 -04978 204947 204916 04885 204855 O82), -0479L -04764 7.473 204735 7.485 04,706 204677 04648 204619 -O591 -04313 204052 -03806 -03576 -03359 -03155 .0296), -0278h -02615 -02456 -02307 .02167 -02035 01911 -01795 -01686 -01583 -01487 -01397 -01312 201232 -01157 - 01086 01020 - 009582 . 009000 -008451 007934 -007454 hiTd/L SINH 477 a/L 7.17h 652.4 7.18 660.5 7.199 668.8 Tella mottee. 7.224 685.6 7.236 694.3 7.249 703.2 Te2Ol sles 7.27) 720.8 7.286 729.9 7.298 739.0 fost 7iieler e323) | 5TeD 7.336 767.0 7.348 776.7 7.361 786.5 7.373 796.4 7.386 806.5 7.398 816.5 7411 826.7 7.423 837.1 7.436 847.6 7.48 858.2 7.460 868.9 879.8 890.8 7.498 901.9 7.510 913.4 7-523 925.0 e535) 1930.5) 7.548 948.1 7.673 1,074 7.798 1,217 7.923 1,379 8.048 1,527 Seis) sal 8.298 2,008 8.423 25275 8.548 2,579 8.674 2,923 8.799 3,31b 8.925 3,757 9.050 ,258 9.175 4,828 9.301 5,h73 9.426 6,204 9.552 7,034 9.677 7,976 9.803 9,0h2 9.929 10,250 10.05 11,620 10.18 13,180 10.31 14,940 10.43 17,3h0 10.56 19,210 10.68 21,780 10.81 2,690 10.93 28,000 11.06 31,750 11.18 36,000 Table C-1. Concluded. a/L a/L 271 d/L TANH SINH COSH H/H! K tTd/L SINH COSH n cu/c M ° 2%a/L ed/t 24/L c Wa/L Ta/L Gio «9000 9000 52655 1.000 142.9 142.9 9999 007000 11.31 0,810 0,810 .5001 .5001 h.935 -9100 = .9100 5.718 1.000 152.1 152.1 -9999 200657 11.44 6,280 46,280 .5001 25001 4.935 +9200 9200 5.781 1.000 162.0 162.0 9999 .006173 11.56 52,470 52,470 .5001 .so91 1.935 ~9300 .9300 5-84 1.000 172.5 172.5 9999 ~.005797 11.69 59,500 59,500 .5001 .soo1 1.935 +9400 9400 5.9056 1.000 183.7 9183-7 = .9999 © -0054UK5 11.81 67,470 67,470 .5001 cool 1.935 +9500 9500 5.969 1.000 195.6 195.6 9999 .005114 11.9 76,490 76,490 .5001 .5001 h.935 -9600 .9600 6.032 1.000 208.2 2086.2 9999 .00h802 12.06 86,740 86,740 .5001 .5001 h.935 -9700 = .9700 = 6.095. 1.000 221.7 221.7 9.9999 .004510 12.19 98,380 98,340 .5001 .5001 1.935 -9800 .9800 6.158 1.000 236.1 236.1 .9999 .004235 12.32 111,500 111,500 .5001 .5001 1.935 -9900 .9900 6.220 1.000 251.4 251.4 1.000 .003977 12.4 126,500 126,500 .5000 .5000 1.935 1.000 1.000 6.283 1.000 267.7 267-7 1.000 .003735 12.57 113,00 13,400 .5000 .5000 h.935 after Wiegel, R.L., “Oscillatory Waves,” U.S. Army, Beach Erosion Board, Bulletin, Special Issue No. 1, July 1948. Table C-2. Functions of d/L for even increments of d/L (from 0.0001 to 1.000). d/L a/L 27 d/L TANH SINH COSH =H/H' K mdf, SINH COSH on C,/c, M ° 2md/L 2Td/L 2md/L cS yra/L kta/L 0 to) (e) 0 ) 1.0000 ©cO 1.000 C) to) 1.000 1.000 Co) co -000100 6.283 x 1078 .0006283 0006283 0006283 1.0000 28.21 1.000 .001257 .001257 1.000 1.000 .0006283 12,500,000 -000200 2.514 x 107” 4001257 001257 .001257 1.0000 19.95 1.000 .002513 .002513 1.000 1.000 .001257 3,125,000 -00030C 5.655 x 1077 .001885 001885 001885 1.0000 16.29 1.000 .003770 .003770 1.000 1.000 .001885 1,389,000 -000400 1.005 x 10° .002513 002513 002513 1.0000 14.10 1.000 .005027 .005027 1.000 1.000 .002513 781, 300 +000500 1.571 x 107© .003142 .003142 003142 1.0000 12.62 1.000 .006283 .006283 1.000 1.000 .0031)2 500 ,000 -000600 2.226 x 107° ,003770 .003770 .003770 1.0000 11.52 1.000 .007540 ~.007540 1.000 1.000 .003770 347,200 000700 3-079 x 10°© ,004398 .004398 © .004398 + 1.0000 10.66 1.000 .008796 .008797 1.000 1.000 .00)398 255,100 -000800 4.022 x 107© 005027 .005027 005027 1.0000 9.974 1.000 .01005 .01005 1.000 1.000 .005026 195, 300 -000900 5.090x 1 005655 .005655 .005655 1.0000 9.103 1.000 .01131 .01131 1.000 1.000 .005655 154, 300 001000 6.283 x 107° ,006283 006283 .006283 1.0000 8.92] 1.000 .01257 .01257 1.000 1.000 .006283 125,000 2001100 7,603 x 107° .006912 .006911 .006912 1.0000 8.506 1.000 .01382 .01382 1.000 1.000 .006911 103, 300 2001200 9.048 x 107° ,007540 .007540 007540 1.0000 8.1hb 1.000 .01508 .01508 1.000 1.000 .0075L0 86,810 2001300 .00001062 .008168 .008168 .008168 1.0000 7.824 1.000 .0163) .01634 1.000 1.000 .008168 713,970 2001400 00001231 .008796 .008796 .008797 1.0000 7.539 1.000 .01759 .01759 1.000 1.000 .008796 63,780 2001500 = .00001414 .009425 009425 009425 1.0000 7.284 1.000 .01885 .01885 1.000 1.000 .009\2h 55,560 +001600 .00001608 .01005 201005 «01005 1.0001 7.052 .9999 .02011 .02011 1.000 1.000 .01005 48,830 +001700 .00001816 .01068 201068 -01068 1.0001 6.842 .9999 .02136 .02136 1.000 1.000 .01068 43,260 -001800 .00002036 .01131 201131 201131 1.0001 6.649 .9999 .02262 .02262 1.000 1,000 .01131 38,580 2001900 =.00002269 .01194 201194 201194 1.0001 6.472 .9999 .02388 .02388 1.000 1.000 .0119h 3 , 630 C=17 27 d/L 201257 201319 201382 201445 01508 201571 20163) 201696 201759 201822 01885 01948 02011 +02073 02136 02199 -02262 202325 02388 -02450 202513 202576 202639 «02702 202765 02827 02890 202953 203016 03079 03142 -0320h -03267 203330 203393 203707 -03770 -03833 Table C-2. SINH 21d/L 201257 -01320 201382 201LK5 01508 -O1S71 -0163h 01697 -01759 01822 -01885 -01948 -O2011 202702 202765 202828 202890 202953 203016 203079 03143 -03205 203268 03708 03771 -0383h -03897 -03959 04022 04085 OOSH 27 d/L . gERE SREB BEEGE GES8E EERE ERREE le (reat * e Pre Re ees a el od dl od tte Ua bara peal et H/HS 6.308 6.156 6.015 5.882 5-159 5 642 52533 5.429 5.332 54239 5.151 5.067 4.987 4.911 4.838 4.769 4.702 Cc-18 K Continued. kmd/L 202513 02639 202765 202890 203016 03142 203267 OSLO), 205529 205655 205781 205906 06032 -06158 06283 +0609 06535 206660 06786 06911 07037 07163 -07288 eO7k1h «07540 -07665 PRR RR smipilelie eee S888 38888 ao g n Co/C, 201257 201319 201382 oOlLLS -01508 201571 -01633 -01696 201759 01822 201885 201947 202010 -02073 -02136 -02199 02261 202324 02387 202449 202511 202574 202637 -02700 202763 02 825 02688 -02951 -0301L 203076 203139 -03202 203265 03328 03391 -03L54 03517 203579 03642 2005226 -005589 2005963 -0063L7 2006746 007155 2007575 2008007 2008450 2008905 2009370 2009847 201033 201083 01134 201166 201239 201294 20139 201405 001463 2Td/L -05027 205089 05152 205215 205278 205341 205404 05466 205529 205592 205655 205718 TANH 27 d/L 205022 -05085 205147 205210 205273 205336 205398 205461 205524, 205586 205649 205712 205774 205836 05899 Table C-2. SINH 2 1d4/L 205029 205091 205154 205217 05280 20533 -054,06 205469 205533 205595 »05658 205721 COSH 211d/L 1.0013 1.0013 1.0013 1.0014 1.001) 1.001h 1.0015 1.0015 1.0015 1.0016 1.0016 1.0016 1.0017 1.0017 1.0017 1.0018 1.0018 1.0019 1.0019 1.0019 1.0020 1.002h, 1.0028 1.0033 1.0039 1.004 1.0051 1.0057 1.006 1.0071 1.008 1.009 1.010 1.011 1.011 1.012 1.013 1.014 1.016 1.017 1.018 1.019 1.020 1,022 1.023 1.02 1.026 1.027 1.029 1.030 1.032 1.033 1.035 WM, 3.157 3.137 3.118 3.099 3.081 3.062 3.0h4 3.027 3.010 2.993 2.977 Continued. K 4 ra/L 1005 -1018 1030 1043 21056 21068 -1081 SINH 4ra/t 1007 1020 -1032 +1045 1058 21070 1083 21095 +1108 1121 1133 -11L6 1158 1171 21184 21196 -1209 COSH Ld/t F 88888 88838 33 FNOEN Cory 1.0079 1.0096 1.0114 1.0134 1.0155 1.0178 1.0203 1.0229 1.0257 1.0286 1.032 1.035 1.038 1.02 1.06 1.050 1.054 1.058 1.063 1.067 1.072 1.077 1.082 1.087 1.093 1.098 1.104 1.110 1.116 1.123 1.129 1.136 1.143 1.150 1.157 1.164 1.172 1.180 1,168 1.196 ~05268 205332 -0539k 05456 205518 205580 05643 205706 205768 205830 205892 05955 206018 206080 20612 0620), 06267 -06890 -07511 -08132 208751 209369 09986 1060 1121 1183 ol2kh 21305 21365 o1h25 +1485 21545 e/L, 201521 201580 -01641 201702 201765 -01829 -01893 -01958 -02025 -02092 -02161 +02230 202300 202371 2 02UL4 202516 202590 -02665 202739 -02817 02895 02973 03052 03132 03213 20329 -03377 03460 203543 203628 +0371 -03799 203887 203975 -04,063 04152 20,242 04333 2OUL24 -04516 -04608 +0702 -04796 «04890 04985 -05081 -0S177 ~05275 -05372 -05470 TANH 2m1d/L Table C-2. SINH an d/L 3194 3260 3326 23392 23458 3525 COSH 2na/L 1.050 1.052 1.054 1.056 1.058 1.060 1.063 1.065 1.067 1.070 1.072 1.074 1.077 1.079 1.082 1.085 1.087 1.090 1.093 1.095 1.098 1.101 1.104 1.107 1.110 1.113 1.116 1.119 1.123 1.126 1.129 1.132 1.136 1.139 1.143 1.146 1.150 1.153 1.157 1.160 1.16h 1.168 1.172 1.176 1.160 1.164 1.168 1.192 1.196 1.200 1.20h 1.208 1.213 1.217 1.221 1.226 1,230 1.235 1.239 1.2k4 H/HS K 1.303 9526 1.291 .9508 1.281 .9L89 1.270 9470 1.260 =.9h51 1.250 .9431 1.2L1 9 .9h1) 1.231 8.9391 1.222 .9371 1.214 .9350 1.205 9329 1.197 9308 1.189 .9286 2.182 .9265 1.174. 9243 1.167 9220 1.160 .9198 1.153 .9175 1.147 9152 1.140 .9128 1.134 9105 1.128 = .9081 1.122 .9057 1.116 9033 1.110 .9008 1.105 8984 1.099 .8959 1.09h .893k 1.089 .8909 1.08, 8883 1.079 8857 1.075 8831 1-070 8805 1.066 .8779 1-061 .8752 1-057 .8726 1.053 8699 1.049 8672 1.045 .86LS 1.0k1 8617 1.037 .8590 1.034 6562 1.030 .853u 1.027 .8506 1.023 8478 1.00 8450 1.017 8421 1.014 8392 1.011 .836u 1.008 8335 1.005 .8306 1.002 .8277 09993 8247 29965 = 8218 99L0 =, 889 “9914 =, 8159 +9891 8129 +9865 8100 -9641 8070 29818 8040 C-20 Continued. Lad/L SINH COSH Lnd/L bb d/L -6705 1.20 -6857 1.213 +7010 1.221 27164 1.230 -7319 =:1.239 274751229 -7633 1.258 27791 = 1.268 27951 =-:1.278 6112 1.288 8275 1.298 6439 «1.308 860 1.319 -8770 =1.330 8938 1.31 -9107 1.353 -9278 1.34 9450 1.376 2962 =: 388 -9799 1.h00 29976 = 1.412 1.015 1.425 1.033 1.438 1.052. 1.51 1.070 1.46h 1.086 1.478 1.107 1.492 1.126 1.506 1.145 1.520 1.16L 1.53l 1.163 1.549 1.203 1.564 L223 1.580 1.243 1.595 1.263 1.611 1.283 1.627 1.30L 1.643 1.32h 1.660 1.346 1.676 1.367 1.693 1.388 1.711 1.410 1.728 1.431 1.746 1.453 1.764 1.476 1.783 1.498 1.801 1.521 1.820 1.5L 1.840 1.567 1.859 1.591 1.879 1.615 1.899 1.638 1.920 1.663 1.940 1.687 1.961 1.712 1.983 1.737 2.00 1.762 2.026 1.788 2.049 1.814 2.071 1.840 2.094 a/L +1100 21110 21120 «1130 21140 1150 21160 +1170 1180 1190 21200 1210 21220 1230 +12h0 -1250 +1260 21270 +1280 +1290 +1300 +1310 1320 1330 1340 21350 1360 21370 1380 1390 +1400 1410 1420 +1430 1440 +1450 +160 1470 1460 1490 +1500 1510 21520 21530 21540 +1550 +1560 21570 +1580 +1590 +1600 +1610 ~1620 1630 216L0 21650 21660 +1670 21680 21690 a/L, 06586 +06690 206795 -06901 207006 07113 07220 207327 -O7L34 20752 207650 207759 207868 -09773 -09888 1000 1012 1023 +1035 +1046 «1058 +1070 -1081 +1093 21105 1116 21128 21140 1151 1163 1175 1187 21199 -1210 1222 21234 2126 21258 1270 21281 21293 21305 21317 21329 2 4/L 5912 26974 TANH 2md/L 5987 26027 26067 -6107 6146 26185 26224 6262 +6300 26338 6375 6412 649 261,86 26520 -6558 Table C-2. SINH 277 d/L 7475 COSH 2n d/L 1.2h9 1.253 1.258 1.263 1.268 1.273 1.278 1.283 1.288 1.293 1.298 1.303 1.309 1.31 1.319 1.325 1.330 1.336 1.341 1.347 1.353 1.356 1.364 1.370 1.376 1.382 1.388 1.394 1.400 1.106 1.412 1.19 1.425 1.432 1.438 1.LU5 1.451 1.458 1.46 1.471 1.478 1.485 1.492 1.499 1.506 Nesp ls) 1.520 1.527 1.535 1.52 1.549 1.557 1.564 1.572 1.580 1.587 1.595 1.603 1.611 1.619 9617. 1735 29600 -770L 9583 = 7673 09567 1642 29551 7612 29535 7581 29520 T5L9 29505 +7518 29490 =» 7487 -9476 -« 7US6 9463 -7h2h 950-7393 +9437 «7362 -942h «7332 -94U12. «7299 29401 «7268 2923, 06672 09228 = o66L41 29222 6610 G=2 Continued. und/L 1,362 1.395 1.407 1.420 1.433 1.UL5 1.458 1.470 1.483 1.495 1.508 1.521 1.533 1.56 1.558 1.571 1.583 1.596 1.609 1,621 1.634 1.646 1.659 1.671 1.68) 1.696 1.709 1.722 1.73b 1.747 1.759 1.772 1.784 1.797 1.810 1.822 1.835 1.847 1.860 1.872 1.885 1.898 1.910 1.923 1.935 1.948 1.960 1.973 1.985 1.998 2.011 2.023 2.036 2.048 2.061 2.073 2.086 2.099 2.111 2.12h SINH 7 a/L 1.867 1.893 1.920 1.948 1.975 2.003 2.032 2.060 2.089 2.118 2.148 2.178 2.208 n at d/L 1.068 1.074 1.081 1.087 1.093 1.100 1.106 1.112 1.118 1.125 1.131 1.137 1.1 1.150 1.156 1.162 1.169 1.175 1.181 1,188 1.194 1.200 1.206 1.213 1.219 1.225 1.232 1,238 1.2u): 1.25 1.257 1.263 1.269 1.276 1,282 1.288 1.294 1.301 1.307 1.313 1.320 1.326 1.332 1.338 1.3L5 1.351 1.357 1.364 1.370 1.376 1.382 1.389 1.395 1.401 1.407 1.L1h 1.420 1.426 1.433 1.439 TANH oT a/L «7887 79. ©7935 27958 ©7981 -800), 8026 -8048 -8070 -8092 64 8135 ~8156 8177 6198 SINH 21 d/L 1.283 1.293 1.304 1.314 1.375 1.335 1.345 Table C-2. COSH 27a/L 1.627 1.635 1.643 1.651 1.660 1.668 1.676 1.685 1.693 1.702 1.711 1.720 1.728 1.737 1.7h6 1.755 1.764 1.773 1.783 1.792 1.801 1.611 1.820 1.830 1.640 1.849 1.859 1.869 1.879 1.889 1.699 1.909 1.920 1.930 1.940 1.951 1.961 1.972 1.983 1.99h 2.00 2.015 2.026 2.037 2.049 2.060 2.071 2.083 2.09 2.106 2.118 2.129 2.141 2.153 2.165 2.177 2.189 2.202 2.214 2.227 HAS K C-22 LMa/L 2.136 2.1h9 2.161 2.174 2.187 2.199 2.212 2.22h 2.237 2.29 2.262 2.275 2.287 2.300 2.312 2.325 Continued. SINH uta. 4.175 4.229 4.26h 4.30 4.396 4.453 4.511 L.S65 4.628 L688 4.79 4.819 4.872 4.935 4.999 5.063 5.129 5219 5-262 5.329 5.398 5467 5.538 5.609 5.681 5-75u 5.827 5-902 5-978 6.055 6.132 6.211 6.290 6.371 6.452 6.535 6.619 COSH 4 74/L L293 L.3L6 4.399 L.USh 4.508 4.564 4.620 L.677 U.735 h.793 4.853 4.918 L.974 5.035 5.098 5.161 5.225 «2300 22320 22330 22340 22350 +2360 +2370 22380 22390 »2L00 2410 +2420 22430 22440 +2450 «2460 «270 +2480 22490 +2500 «2510 22520 22530 22540 02550 22560 22570 22580 22590 22600 22610 22620 22630 22640 22650 22660 22670 22680 22690 22700 22710 ©2720 2730 22740 22750 -2760 22770 2780 22790 22800 22810 22820 22830 22640 22850 22860 2870 22880 2890 27 a/L 1.405 1.451 1.458 1.46 1.470 1.477 1.483 1.489 1.495 1.502 1.508 1.51b 1.521 1.527 1.533 1.539 1.56 1.552 1.558 1.565 1.571 1.577 1.583 1.590 1.596 1,602 1.609 1.615 1.621 1.627 1.634 1.640 1.646 1.653 1.659 1.665 1.671 1.678 1.684 1.690 1.697 1.703 1.709 1.715 1.722 1.728 1.734 1.7h0 1.747 1.753 1.759 1.766 1.772 1.778 1.78 1,791 1.797 1.803 1.810 1.816 TANH 2md/L Table C-2. SINH cosH H/H! K 2Md/L 2#d/L 2.003 2.239 9194. LL66 2.017 22252 9197) ub 2.032 2.264 29200 16 2.046 2.277 = 9203) 6391 2.060 2.290 9206 .4366 2.075 2.303 9209 .h3h2 2.089 2.316 9212 .4318 2.10h 2.329 9215 4293 2.118 2.343 9218 4269 20133 920356 0 92212 U2 2.148 2370 .9225 220 2.163 2.383 09228 = 44196 Bat) Past obey ahiliyd 2.193 2.410 9234 .b1k9 2.208 2.42) 9238 4125 2.22k 2.4368 9241 101 2.239 2.h52 .92bL .L078 2.255 2.466 9248 4055 2.270 2.480 .9251 .4032 2.286 2.495 9255 .4008 2.301 2.509 29258 .3985 2.317 2.52h 09202 ©3962 2.333 2.538 29265 = .3940 2.39 2.553 29269 = ,3917 2.365 2.568 .9273 .389k 2.381 2583 -9276 .3872 2.398 2.598 -9280 3849 2.414 2.613 = 9283 3827 2.430 2.628 9287 .3805 2.447 2.643 29291 =, 3783 2.6L 2.659 29294 =. 3761 2.1480 2.674 29298 43739 2.497 2.690 ©9301 3717 2.514 2.706 9305 .3696 2.531 2.722 9309 .367h 2.548 2.737 29313 =. 3653 2.566 2.754 9316 .3632 2.583 2.770 29320 ©3610 2.600 2.786 29324 =. 3589 2.618 2.803 09328 = 53568 2.636 2.819 9331 .35h7 2.653 2.835 = 9335-6 3527 2.671 2.852 29339 ©3506 2.689 2.869 29343 © 63485 2.707 2.886 29346 = 3465 2.726 2.903 .9350 .3hbh 2e7hL 2.920 19354 3424 2.762 2.938 29358 =o 340 2.781 2.955 9362 3384 2.799 2.973 oo) 23364 2.616 2.990 29369 = 3b 2.837 3.008 99373 = I32G 2.856 3.026 29377 = #3305 2.875 3.0L4 09381 = 3285 2.894 3.062 .936h 23266 2.913 3.080 .9388 .32h7 2.933 3.099 09392 3227 2.952 3.117 2939 = 3208 2.972 3.136 29400 43189 2.992 3.154 e940» 3170 C=23 UTafL 2.890 Continued. SINH Lraf 8.971 9.085 9.201 9.318 9 437 9.557 9.678 9.801 9.926 10.05 10.18 10.31 10.Lu 10.57 10.71 10.84 10.98 11.12 11.26 11.40 11.55 11.70 11.64 11.99 12.15 12.30 12.46 12.61 COSH urd 9.027 9.140 9.255 9.372 92489 9.609 9.730 9.852 9.976 10.10 10.23 10.36 10.49 10.62 10.75 10.89 11.03 11.17 11.31 11.45 11.59 11.74 11.89 12.04 12.19 12.34 12.50 12.65 12.81 12.98 13.14 13.31 13.h7 Table C-2. HAS C-24 Continued. sinh C-2. Continued. C-25 C-2. Continued. C-26 > oF a 5.152 5.165 5,177 5.190 5.202 5.215 5.228 5.240 5.253 5.265 5.278 5.290 5.303 5.316 5,328 5.341 5.353 5.366 5.378 5.391 5.404 5.416 5.429 5.441 5.454 5.466 5.479 5.492 5,504 5,517 5.529 5.542 5.554 5.567 5.579 5.592 5,605 5.617 5.630 5,642 5,655 5.667 5.680 5,693 5.705 5.718 5.730 5.743 5.755 5.768 5.781 5.793 5.806 $318 5.331 5.843 5.856 5.869 5,881 5,894 Table C-2. cosh 2nd L 9.609 9.669 9.730 9,791 9.852 9.914 9.976 10,04 10,10 10,17 10,23 10,29 10,36 10,42 10.49 10,55 10.62 10,69 10,75 10,82 10,389 10.96 11,03 11,10 11,17 11,24 11,31 11,38 11.45 11,52 11,59 11,67 11,74 11,81 11,89 11.96 12,03 12,11 12,19 12,26 12,34 12,42 12,50 12,57 12,65 12,74 12,81 12,89 12,98 13,06 13,14 13,22 13,30 13,38 13.47 13,56 13,64 13,72 13,81 13,89 09300 09241 209183 209126 209069 .09013 208957 208901 208845 208790 208736 208681 208627 208573 298519 208466 208413 208361 08309 08257 08205 208154 08103 08053 208002 97952 «07903 .07853 .07804 .07756 .07707 .07659 207611 207564 207517 .07469 207422 .07376 207330 07284 .07239 ~07194 C= 27], Continued. sinh 4nd L 183.7 186.0 188.3 190.7 193,1 195.6 198.0 200.5 203,1 205.6 208 ,2 210.9 213.5 216.2 219.0 221.7 224.5 227.4 230.3 233.2 236.1 239.1 242.1 245.2 248.3 251.4 254.6 257.8 261,1 264.4 267.7 271.1 274.5 278.0 281.5 285.1 288.7 292.4 296.1 299.8 303.6 307.4 311.3 315.4 319.2 323.3 327.4 331.5 335.7 339.9 344.2 348.2 353.0 357.5 362.0 366.6 371.2 375.9 380.3 385.5 C-2. HM," C-28 Continued. 207149 07104 207059 97016 06972 .06928 06885 06842 .06799 .06757 206715 06673 06631 206589 06548 06507 206467 206426 206386 206346 206306 06267 206228 206189 206150 06112 206074 206036 205998 205960 205923 205886 205849 205813 205776 205740 205704 205669 05633 205598 205563 205528 205494 205459 205425 205391 205358 205324 205291 05258 205225 205192 205160 205127 205095 205063 205032 205000 204969 204938 4nd sinh 4nd 4/L 1,000 d/Lo 1,000 3.707 3.713 3.720 3.726 3.732 3.739 3.745 3.751 3.757 3.764 3.770 3.833 3.896 3.958 4,021 4.084 4.147 4,210 4.273 4.335 4.398 4.461 4.524 4.587 4.650 4.712 4.775 4.838 4,901 4.964 5.027 5.089 5.152 5.215 5.278 5.341 5.404 5.466 5.529 5.592 5.655 5.718 5.781 5.843 5.906 5.969 6,032 6,095 6.158 6.220 6,283 sinh cosh 2nd 2nd L L 20.36 20,38 20.48 20.51 20.61 20.64 20,74 20.77 20.87 20.90 21,01 21,03 21,14 21,16 21.27 21,30 21,41 21,43 21,54 21,55 21.68 21.70 23.08 23,11 24,58 24,60 26,18 26,20 27.88 27,89 29.69 29,70 31,61 31.63 33.66 33,68 35.85 35,86 38.17 38,18 40.65 40,66 43.29 43,30 46.09 46,10 49.08 49,09 52,27 52,28 55.66 55,66 59.26 539,27 63.11 63,12 67.20 67,21 UT | ASI 76.21 76,21 81.14 81,14 86.40 86.40 92.01 92,01 97.98 97,98 104.3 104.3 111,1 111,1 118.3 118.3 126.0 126.0 134,1 134,1 142.8 142.8 152.1 152.1 162.0 162,0 172.5 172.5 183.7 183.7 195.6 195.6 208.2 208.2 221.7 221.7 236.1 236.1 251.4 251.4 267.7 267.7 C-2. Concluded. 29962 204907 29962 = _.04876 29962 204846 29963 = 04815 29963 04785 29964 204755 29964 204725 29964 204696 29965 204667 29965 204639 209966 204609 29970 =, 04328 29972 04065 29975 = ,03817 29978 03585 09980 = 03367 09982 203162 29984 02969 9985 02789 29987 202619 29988 .02459 29989 202310 29990 — ,02169 29991 — ,02037 29992-01913 29993 = 01796 29994 = .01687 29995 201584 09995 =. 01488 29996 = .01397 29996 = 01312 29997 01232 29997 01157 29997 01087 29998 ~01021 29998 =, 009585 29998 — ,009000 -9998 008453 .9998 .007939 29999 .007455 29999 .007001 29999 2006575 29999 006174 29999 ,005798 29999 2005445 29999 005114 29999 = .004802 29999 _.004510 9999 = 004235 £.0000 .003977 130000 = 003735 7.414 7.427 7.439 7.452 7.464 7.477 7.490 7.502 7.515 7.527 7.540 7.666 7.791 7.917 8.043 8.163 8.294 8.419 8.545 8.671 8.796 8,922 9,048 9.173 9.299 9.425 9.550 9.676 9.802 829,6 840.1 850.7 861.5 872.4 883.4 894.6 905.9 917.3 929.0 940.7 1067. 1210, 1371, 1555. 1754, 1999, 2267, 2571. 2915. 3305, 3748, 4250, 4819, 5464, 6195, 7025, 7966. 9032, 9.927 10240, 10,05 11610, 10,18 13170, 10,30: 14930, 10.43 16930, 10,56 19200, 10,68 21770, 10.81,24680, 10,93 27990, 11,06 31730, 11,18 35980, 11,31 40800, 11,44 46260, 11,56 52460, 11,69 59480, 11,81 67450. 11.94 76480, 12,06 86720, 12,19 98340, 12,32 111500,. 12,44 126400, 12,57 143400, 1754. 1999, 2267, 2571. 2915, 3305. 3748, 4250, 4819, 5464, 6195, 7025, 7966, 9032, 10240, 11610, 13170, 14930, 16930, 19200, 21770. 24680. 27990, 31730. 35980, 40800... 46260, 52460, 59480, 67450, 76480, 86720, 98340, 111500, 126400, 143400, after Wiegel, R.L., “Oscillatory Waves,” U.S. Army, Beach Erosion Board, Bulletin, Special Issue No. 1, July 1948. C=29 04 RPOBNDEFNOARHRENOAREFNOAHRAEFNODAENOAHDHENOBAHHENS ~ dono u On Go Om Oo 0. 000.0 O80 Hoon oo 6 Oa) old.5 a SCODOGOOGSGODDMMDBYYNNYYNNADAAADNVNVUUULS HLS LS EwWwWwWww a Eurail Table C-3. => —>s a CODD GCMBDIYNYNDAVHUVUNUUNS BO Gh onte devon ONOLOnd 6 O08 beor dnd WON ERENE RF RDUNDANODWON OD WV 10.6 - Deepwater wavelength (Log) and velocity (Co) as a function of wave period Cc-30 Lo (ft) 762.1 787.3 812.9 838.9 665.3 892.1 919.3 947.0 975.1 1003.5 1032.4 1061.7 1091.4 1121.5 1152.0 1182.9 1214.3 1246.0 1278.2 1310.7 1343.7 1377.1 1410.9 1445.1 1479.7 1514.7 1550.1 1586.0 1622.2 1658.9 1695.9 1733.4 W713 1809.6 1848.3 1887.4 1927.0 1966.9 20U7.2 2048.0 2257.9 2478.1 2708.5 2949.1 3200.0 3461.1 65070" BE ve MB ROREK Ze = ansoa fe teeeesTecestitcets esata WMA ye YEE Wy g He WAL We WHE, Lips Yy Yip Plate C-2. Relationship between wave period, length, and depth (upper graph shows metric, lower graph English units). c-31 *(satun ystTsuq qYysTA sy, OF fdTAZeW sMOYS JFZeT 9YyI 07 Yde1r3) YyIBUeTeAem pue potied taq10ys Jo saaem 10x yAdep pue ‘yA3ueT ‘potzed aaem usemjaq drysuotjzepTey °¢-9 e3eTg (44) 7 ‘yibuajaneny 00S O00r O00 002 ool Sf ase H pri gova pubes | ioral ap4-yidag sajom) | +} eine YY iil (S) 1 ‘pouag aney (W) 7‘yybuajaranmM OL O9 OS Ov o£ O02 Ol 0) |! 4 | a | t + 4 bt ‘ +f mp orebmtm fume ected rg feafect FO fd dt + , fSNTE G19 al ta Lee | | OF @ (SFO) Min) emo eal — so (S$) L*Ppolsad aADM ¢=32 *(sqtun ysTT3uq WYUSTI 34 07 ‘OTAJOW smOYS FFeT BY OF yders) yIdep pue ‘SAzTOOTAaA ‘potaed sAeM UsemMqeq dTysuoTIeTeEyY *4-9 e1eTd (W) p*yyded 1840M ET aN Sree vealoe s¢ o¢ Gz 02 S| Ol S 0 ‘paeog uorsoig yoeag ‘Away “S'f) ,,‘saaem Asoreyp1980,, “TY ‘Jadot Jaze (44)P ee Ja1eMy ool 50135. 09 Ob (SA}) 9 ‘Aris0jay ane 6/y)d ‘Al90/aA aneM c-33 *(sqTun ysT[suq JUusTA 9yR 07 ‘SdTIQZOU SMOYS 2J2eT 242 07 Yder3) JYyStTey eAaem pue ‘SyRB3UeTeAeEM SAB19UB VAeM UBEeMJEeq dTYySUOTIeTEY °*SG-9 eI1eTg (45) H*4yB18H enDm (W) H ‘}YyBiaH aADM vl e| dl I] Ol 6 8 Z 9 S v ts @ (0) 9 S D g é | 0) | | | | | | | Ty ! | T T LI if } CI J fata Ct | t t + } ttt t i ! ! ! “ff t Ke, = t t 2 ooo eet | SSge 56 Ft Peee a eet { t I ss i ooo Seat = +++ x< +t + t Ser a2 SeSee: : g= : Ee £ = = s ==) :5: 2, : =: : + Sf HSSSSSe + : : Senos : = ==== 35 s=7 55 b —- _ b S = S See f S = 7 t SocS==: 49 = : = 9 = == —— = J) : ‘Ss = + I = : a 25 == = 8 = = = £ = z 8 = = — = = is) ===== + == == = = ==5S=== fos ea = 3 < = = === =e= += : = 6 ro) | ~ T TT | 1 m ial | jl i I | a i if T 4 ae | a r 1 t < t t Cel T Tt = T T t T Tt Bate am 2 T “ Talor : 36 t T ft 0 t + o t + t =x = = + at os : € fe} =e = fo} t = 7 : == = - = b OR T = ° Sasa: = s 2 9 = ——— oe we = ==== = = = Se 8 f = SF 255 SS=S25SS55 [ S$ TH | 44 " t f + - r pOlX C-34 gOIX (W/P) $8849 JO 4ayaW Jad ‘13 ‘ABsaugZ annmM g01X o0l f 002 00 00S 009 o0L *SuTTeOYs ZuTpntTouT sanojuod yjdap TeTTered ‘3y8tez3s yIIM sedoTs uo uoTIOeIJeI 02 aNp AYSTey pue uoTeITp aaeM UT asuey) 9000'0 4000'0 0SZ o020G9 .09 216 ei 90°0 400 20°0 10°0 9000 %00'0 200'0 1000 tani] oma \ Water Ha a AEE LERAUS AG Wo i ust NSA ea ale I ii 1] \ \ \ \ Re Hee \ \ \ \ te Loy al tea SSRI LN FAURE aE a US Preece AEST HA MNT Hl val \ \ HEY \ | TREAT INT A Ped Aaa RUT \ I NREL \ WON rt ' a RTT tt \ A THAW in tana aR Ue EP SAAGRIIN NL HY TSOaNe IN NGA i | 1 \ \\ \ | [N Oo i 2 | ° Hf [7 Ne Ha a | | AWN] fy } if \ ot TINS Past i ma aN 1} | Ho Ne Te NEEEN \ | vie IN Ha tb i eX TX) HELEN Et | PEN 7 NWR TA AGH EYRE ie ae) SAAT INH | i Wiis El iat | aap Ieee FRAN, ALACRA EI HAM muita, TAY CNG INTE Cort | Ty vi 4 ita ty Fan NCA 4 ry neh et ye! ma | Do. as Sea INGEN /N EERE A TANS ENO LALA Le =e HUTA TSR ONG KE Va An ia ah / itt = lo mal N SN NY ARIS PAGINA REALTY PL TST CRS TRS / LA | Vr | V99p4) “RAN i L1H in ih ¢ | tt sale Soe il GS te Rese 1X7 A7\\24 | ry are oS /i/ / vA vi\ | 1 |i | ans ~~ 20000 1000°0 0 WH sy yy \ {Onba jo sauiq “1001 \ re) At 002 \ ae oO °“9-0 231d 43j0M daag Bul|as0yS C-35 Table C-4. Conversion factors: English to metric (SI) units of measurement The following conversion factors adopted by the U.S. Department of Defense are those published by the American Society for Testing and Materials (ASTM) (Standard for Metric Practice, December 1979), except that additional uerived conversion factors have been added. The metric units and conversion factors adopted by ASTM are based on the “International System of Units" (designated SI) which has been fixed by the International Committee for Weights and Measures. For most scientific and technical work it is generally accepted that the metric SI system of units is superior to all other systems of units. The SI is the most widely accepted and used language for scientific and technical data and specifications. In the SI system the unit of mass is the kilogram (kg) and the unit of force is the newton (N). N is defined as the force which, when applied to a mass of 1 kg, gives the mass an acceleration of 1 m/s“. Former metric systems used kilogram-force as the force unit , and this has resulted in the conversion of pound-force to kilogram-torce in many present-day situations, particularly in expressing the weight of a body. In the SI system the weight of a body is correctly expressed in newtons. When the value for weight is encountered expressed in kilograms, it is best to first convert it into newtons by multiplying kilograms by 9.80665 This provides consistent usage of the SI system, and will help to eliminate errors in derived units. Multiply By To Obtain Length inches . «+ 6 « © © © © © © © © @ oo 2094 ww « ee se 6UCentimeters Feet cw. sierexctiey chic, Shsmeiver eWierel @10sd04.6) sire erie, a ameter Yardsissniaysl esis sisi cre temerte. VOLQIS C4) 55, ss. 5 meters fathoms . . . s+ « « « - 1.8288... . . » meters statute miles (U.S.) ... ..- 1609.4....... #£4meters oe © © © © © © © 616609 34 ~~ «CKilometers nautical miles) ss sss 6 «s+ 1) 852.0! . <5 Ss. « meters sie. ont) GMepel ter or GNs852L: ees ot, kilometers Area square inches . « «2 « © © «© «© « « « 66451 6! * + + + « square centimeters square feet . . « « « « « © © e « « « 0.092 903 0 . . ~ ~ Square meters square yards . . « « « « © « © « © « « 06836 127 . . . « » Square meters ACES se sw oe ew we ww ew ww et 66404 687 . . . © . hectares oe © © 2 ce ce 4 046.87 « « - « - - © «Square meters square miles (U.S. statute) .... .- 2.589 99... . . square kilometers Volume cubic inches « . s+ se ee © © © © e «(160387 1 2 ww cubic centimeters cubic feet . . . « « « « «© « « « © « « 0.028 316 8 . . « « cubic meters cubic yards . =. - . «6s « «© «© «© « » 00764 555 . « « « « cubic meters cubic yards per foot . ~~... +. « « 2-508 38... . . cubic meters per meter Liquid Capacity fluid ounces (U.S.) . « « « « « « « 29.573 5. «. « « « » cubic centimeters eirotie) si lolNe/ncplelie! H29%e075:3ile. ete ee) milters liquid pints (U.S.) . 2. « « «ss ee O473 176... . ~ liters quarts (U.S.) « « « © © «© © © © © © © 606946 353 « «~~ « liters gallons (U.S.) « « « « « « © « « © © © Sef/8D SL ee © © «6Citers cubic feet . 2 2 0 0 es ee we we ee 2603168 « www liters acre-feet . . ss « « © © © © e «© 1 233.48 «. « ~ » » « » cubic meters Mass ounces (avoirdupois). .....+-.-s 28.349 5..... + grams pounds (avoirdupois) ....+-+-+-e-s. (064531592097 on are kilograms Sluga 2 cies yates <..6 us) 1. 2) eo oer tak L593),90209% British thermal units (Btu)... 1 055.06 .....2+46-s newton-meters” Power horsepower (550 foot-pounds-force per second)! . « « «se © « © 0) « J45%/00! 0) 0 « = 'o newton-meters per second® BEugse PeLMNOUL wie: olielie) leliiona cele: eile) Oe 295071) of jolie: ie newton-meters per second® foot-pounds-force per second... . « 1.355 82... . « mewton-meters per second® lgxact conversion value. 2the SI unit for a newton per square meter is a pascal. 3technically, mass/area-to-force/area conversion. 4technically, density-to unit weight conversion. the SI unit for a newton-meter is a joule. ®The SI unit for a newton-meter per second is a watt. C-37 Table C-5. Phi-millimeter conversion table Table C-5 is reproduced from the Journal of Sedimentary Petrology» with the permission of the author and publisher. It was taken from the Harry G. Page, "Phi-Millimeter Conversion Table," published in Volume 25, pp. 285-292, 1955, and includes that part of the table from -5.99 (about 63 mm) to +5.99 (about 0.016 mm) which provides a sufficient range for beach sediments. The complete table extends from about -6.65 (about 100 mm) to +10.00 (about 0.001 mm) . The first column of the table shows the absolute value of phi. If it is positive, the corresponding diameter value is shown in the second column. If phi is negative, the corresponding diameter is shown in the third column of the table. In converting diameter values in millimeters to their phi equivalents, the closest phi value to the given diameter may be selected. It is seldom necessary to express phi to more than two decimal places. The conversion table is technically a table of negative logarithms to the base 2, from the defining equation of phi: 9 = log.d » Where d is the diameter in millimeters Values of phi can also be determined with an electronic calculator having scientific notation by use of of the following relationship: log jo4 2 > = ~log.d =- log jo The table begins on the following page. Table C-5. Phi-millimeter conversion table ¢ (+¢) (—¢) ‘ (+¢) (-—¢) As (+¢) (-—¢) mm mm mm mm mm mm 0.00 1.0000 1.0000 | 0.50 0.7071 1.4142 | 1.00 0.5000 2.0000 01 0.9931 0070 51 7022 4241 01 4965 0139 02 9862 0140 52 6974 4340 02 4931 0279 03 9794 0210 53 6926 4439 03 4897 0420 04 9718 0285 54 6877 4540 04 4863 0562 05 9659 0355 55 6830 4641 05 4841 0705 06 9593 0425 56 6783 4743 06 4796 0849 07 9526 0498 57 6736 4845 07 4763 0994 08 9461 0570 58 6690 4948 08 4730 1140 09 9395 0644 59 9643 5052 09 4697 1287 0.10 9330 0718 | 0.60 6598 SG |} ates 4665 1435 11 9266 0792 61 6552 5263 11 4633 1585 12 9202 0867 62 6507 5369 12 4601 1735 13 9138 0943 63 6462 5476 13 4569 1886 14 9075 1019 64 6417 5583 14 4538 2038 15 9013 1096 65 6373 5692 15 4506 2191 16 8950 1173 66 6329 5801 16 4475 2346 17 8890 1251 67 6285 5911 17 4444 2501 18 8827 1329 68 6242 6021 18 4414 2658 19 8766 1408 69 6199 6133 19 4383 2815 0.20 8705 1487 | 0.70 6156 6245 | 1.20 4353 2974 21 8645 1567 71 6113 6358 21 4323 3134 22 8586 1647 72 6071 6472 22 4293 3295 23 8526 1728 73 6029 6586 23 4263 3457 24 8468 1810 74 5987 6702 24 4234 3620 25 8409 1892 75 5946 6818 25 4204 3784 26 8351 1975 76 5905 6935 26 4175 3950 27 8293 2058 77 5864 7053 27 4147 4116 28 8236 2142 78 5824 7171 28 4118 4284 29 8179 2226 79 5783 7291 29 4090 4453 0.30 8123 2311 | 0.80 5743 7411 | 1.30 4061 4623 31 8066 2397 81 5704 7532 31 4033 4794 32 8011 2483 82 5664 7654 32 4005 4967 33 7955 2570 83 5625 7777 33 3978 5140 34 7900 2658 84 5586 7901 34 3950 5315 35 7846 2746 85 5548 8025 35 3923 5491 36 7792 2834 86 5510 8150 36 3896 5669 37 7738 2924 87 5471 8276 37 3869 5847 38 7684 3014 88 5434 8404 38 3842 6027 39 7631 3104 89 5396 8532 39 3816 6208 0.40 7579 3195 | 0.90 5359 8661 | 1.40 3789 6390 41 7526 3287 91 5322 8790 41 3763 6574 42 7474 3379 92 5285 8921 42 3729 6759 43 7423 3472 93 5249 9053 43 3711 6945 44 7371 3566 94 5212 9185 44 3686 7132 45 7321 3660 95 5176 9319 45 3660 7321 46 7270 3755 96 5141 9453 46 3635 7511 47 7220 3851 97 5105 9588 47 3610 7702 48 7170 3948 98 5070 9725 48 3585 7895 49 7120 4044 99 5035 9862 49 3560 8089 een — —— —— ¢-39 Continued. (+¢) mim 0.3536 3511 3487 3463 3439 3415 3392 3368 3345 3322 3299 3276 3253 3231 3209 3186 3164 3143 3121 3099 3078 3057 3035 3015 2994 2973 2952 2932 2912 2892 2872 2852 2832 2813 2793 2774 2755 2736 2717 2698 2679 2661 2643 2624 2606 2588 2570 2553 2535 2517 (-¢) mm 2.8284 8481 8679 8879 9079 9282 9485 9690 9897 3.0105 0314 0525 0737 0951 1166 1383 1602 1821 2043 2266 2490 2716 2944 3173 3404 3636 3870 4105 4343 4581 4822 5064 5308 5554 5801 6050 6301 6553 6808 7064 7321 7581 7842 8106 8371 8637 8906 9177 9449 9724 (+¢) mm 0.2500 2483 2466 2449 2432 2415 2398 2382 2365 2349 2333 2316 2300 2285 2269 2253 2238 2222 2207 2192 2176 2161 2146 2132 2117 2102 2088 2073 2059 2045 2031 2017 2003 1989 1975 1961 1948 1934 1921 1908 1895 1882 1869 1856 1843 1830 1817 1805 1792 1780 (—¢) mm 4.0000 0278 0558 0840 1125 1411 1699 1989 2281 2575 2871 3169 3469 3772 4076 4383 4691 5002 $315 5631 5948 6268 6589 6913 7240 7568 7899 8232 8568 8906 9246 9588 9933 §.0281 0631 0983 1337 1694 2054 2416 2780 3147 3517 3889 4264 4642 5022 5404 5790 6178 (+¢) mm 0.1768 1756 1743 1731 1719 1708 1696 1684 1672 1661 1649 1638 1627 1615 1604 1593 1582 1571 1560 1550 1539 1528 1518 1507 1497 1487 1476 1466 1456 1446 1436 1426 1416 1406 1397 1387 1377 1368 1358 1350 1340 1330 1321 1312 1303 1294 1285 1276 1267 1259 (—¢) mm 5.6569 6962 7358 7757 8159 8563 8971 9381 9794 6.0210 0629 1050 1475 1903 2333 2767 3203 3643 4086 4532 4980 5432 5887 6346 0807 7272 7740 8211 8685 9163 9644 7.0128 0616 1107 1602 2100 2602 3107 3615 4110 4643 $162 5685 6211 6741 7275 7812 8354 8899 9447 0.1250 1241 1233 1224 1216 1207 1199 1191 1183 1174 1166 1158 1150 1142 1134 1127 1119 1111 1103 (-—4) mm 00,9) 0556 1117 1681 2249 2821 3397 3977 4561 5150 5742 6338 6939 7544 8152 8766 9383 .CODS 0631 1261 1896 2535 3179 3827 4479 5137 5798 6465 7136 7811 8492 9177 9866 -0561 1261 1965 2674 3388 4107 4831 $501 6295 7034 7779 8528 9283 0043 0809 1579 2356 Table C-5. Continued. (+¢) mm 0.0884 0878 0872 0866 0860 0854 08438 0842 0836 03830 0825 819 $13 0803 0802 0797 0791 0786 0780 0775 0769 0764 0759 0754 0748 0743 0738 0733 0728 0723 0718 0713 0708 (1703 0698 0693 0689 0684 0679 0675 0670 0665 0661 0656 0652 0647 0643 0038 0634 0629 Cc-41 0.0625 0621 Ae 18. 19. 20. Zire 22. Table C-5. Concluded. | - A (+¢) (-—¢) ¢ (+¢) (-—¢) é (+¢) (-¢) mm mm mm mm mm mm 4.50 0.0442 22.627. | 5.00 0.0313 32.000 | 5.50 0.0221 45.255 51 0439 785 OL 0310 223 51 0219 570 52 0436 943 02 0308 447 52 0218 886 53 0433 23.103 03 0306 672 53 0216 46.206 54 0430 264 04 0304 900 54 0215 527 55 0427 425 05 0302 33.128 55 0213 851 56 0424 588 06 0300 359 56 0212 47.177 57 0421 752 07 0298 591 57 0211 505 58 0418 918 08 0296 825 58 0209 835 59 0415 24.084 09 0294 34.060 59 0208 48.168 4.60 0412 251, | S.1O 0292 297 | 5.60 0206 503 61 0409 420 11 0290 535 61 0205 840 62 0407 590 12 0288 716 62 0203 49.180 63 0404 761 13 0286 35.017 63 0202 522 64 0401 933 14 0284 261 64 0201 867 65 0398 25.107 15 0282 506 65 0199 50.213 66 0396 281 16 0280 753 66 0198 563 67 0393 457 17 0278 36.002 67 0196 914 68 0390 634 18 0276 252 68 0195 51.268 69 0387 813 19 0274 504 69 0194 625 4.70 0385 992 | 5.20 0272 758) | S00 0192 984 71 0382 26.173 21 0270 37.014 71 0191 52.346 72 0379 355 22 0268 271 72 0190 710 73 0377 538 23 0266 531 73 0188 53.076 74 0374 723 24 0265 792 74 0187 446 75 0372 909 25 0263 38.055 75 0186 817 76 0369 27.096 26 0261 319 76 0185 54.192 77 0367 284 27 0259 586 17 0183 569 78 0364 474 28 0257 854 78 0182 948 79 0361 665 29 0256 39.124 719 0181 55.330 4.80 0359 858 | 5.30 0254 397 | 5.80 0179 Sy A Us) 81 0356 28.051 31 0252 671 81 0178 56.103 82 0354 246 32 0250 947 82 0177 493 83 0352 443 33 0249 40.224 83 0176 886 84 0349 641 34 0247 504 84 0175 57.282 85 0347 840 35 0245 186 85 0173 680 86 0344 29.041 36 0243 41.070 86 0172 58.081 87 0342 243 37 0242 355 87 0171 485 88 0340 446 38 0240 643 88 0170 892 89 0337 651 39 0238 933 89 0169 59.302 4.90 0335 857 | 5.40 0237 42.224 | 5.90 0167 714 91 0333 30.065 41 0235 518 91 0166 60.129 92 0330 274 42 0234 814 92 0165 548 93 0328 484 43 0232 43.111 93 0164 969 94 0326 696 44 0230 411 94 0163 61.393 95 0324 910 45 0229 713 95 0162 820 96 0321 31.125 46 0227 44.017 96 0161 62.250 97 0319 341 47 0226 426 97 0160 683 98 0317 559 48 0224 632 98 0158 63.119 99 0315 71719 49 0223 942 99 0157 558 c-42 Table C-6. Values of slope angle 9 and cot for various slopes. a: ) Slope Angle 0 Coe © (OW/X4) vA Slope (Y on X) 45° 00’ 1.0 100 1 on 1.0 42° 16’ oil 1 ones lyr SO LAY ere: HW ey Ne? 38° 40’ 25) lionelve25 Sy/2 BYAw io} lonteliS B50 32 1.4 lon 14 sg Gal 65) Ione e5 82° 00r 1.6 Ion 136 PO NSIS o/s) i @a io7/5 IAGO BAY 7330) 50 one 27.0 23° 587 Ze2D il @n 2oP5 PANO SSH V5) longi) 19S 597 ot 5) Ik 6a) 2o7/S) NEO A 3.0 355 iL Cnt Si5@ U7? Ola B25 Ionesis25 ISS Syl? 3}55) Ion 3 4a On 3o7/5 Ion 3.7/5 NAS (pny 4.0 25 1 on 4.0 WSO TAY ESD iL om, AgAs ees 20 oS} ron 475 iil? Sigh LED Ion 4575 WIS Ie} 5350) 20 Lon 5)0 10° 18’ B65) Ih Gyn 55} SoZ Sin 6.0 MOo7/ Ion610 Sear 492 625 iL oa, G55 8° 08’ 7.0 14.3 IL @ya 7/4(0) as Or Uo») on 7/5 7? O83? 8.0 65) 1 on 8.0 GAS! 85 Ion 85 65° DOM 9.0 Miko tt 1 on 9.0 @? Oil? 9.5 l on 9.5 BP ks 10.0 10.0 1 on 10.0 4° 46’ 12 8.3 Irony 12 HO (OY 14 Holl 1 on 14 sy Sy 16 6.25 1 on 16 Saeelil’ 18 a6 1 on 18 2? Be 20 5.0 1 on 20 il? $5; 30 313 1 on 30 he 26" 40 55) 1 on 40 len 9 50 2.0 1 on 50 On 57 60 a7, 1 on 60 0° 49’ 70 1.4 1 on 70 On 437 80 1225 1 on 80 0° 38’ 90 Sil 1 on 90 Oy 34" 100 1.0 1 on 100 C-43 a’ APPENDIX D Subject Index seamen © anole SP ai Mustang Island, Texas, 16 November 1972 ee oe Absecon Inlet, New Jersey, 4-91, 4-157 Active earth force, 7-256, 7-257, 7-259, 7-260 Adak Island, Alaska, 3-118 Adjustable groin, 1-24, 5-53 Adjusted shoreline (see Beach alinement) Airy, 2-2 Wave Theory, 2-2, 2-4, 2-25, 2-31 thru 2-33, 2-44, 2-46, 2-54, 7-103 thru 7-106, 7-111 thru 7-117, 7-135, 7-137, 7-139, 7-140, 7-142, 7-151 thru 7-155 Akmon, 7-216 Algae, coralline (see Coralline algae) Alongshore transport (see Longshore transport) American beach grass, 6-44 thru 6-50, 6-52, 6-53 Amsterdam, The Netherlands, 6-92 Anaheim Bay, California, 4-91, 5-9 Analysis, sediment (see Sediment analysis) Anchorage, Alaska, 1-6, 3-91 Anemometer, 3-30, 3-33, 3-52 Angle of internal friction (see Internal friction angle) wall friction, 7-257, 7-260 wave approach, 2-90, 2-91, 2-99, 2-116, 5-35, 7-198, 7-199, 7-201, 7-210 Angular frequency (see Wave angular frequency) Annapolis, Maryland, 3-116, 3-124 Antinode, 2-113, 2-114, 3-98, 3-99 Apalachicola, Florida, 3-92 Aransas Pass, Texas, 4-167 Armor stone, 1-23, 2-119, 6-83, 7-210, 7-236, 7-243, 7-247, 7-249, 7-251 thru 7-253 units (see also Articulated armor unit revetment; Concrete armor units; Precast concrete armor units; Quarrystone armor units; Rubble-mound structure; Stone armor units; Stability coefficient), 2-119, 2-121, 2-122, 6-88, 7-3, 7-4, 7-202 thru 7-225, 7-229, 7-231, 7-233 thru 7-240, 7-242, 7-243, 7-249, 8-50, 8-51, 8-59, 8-60, 8-73 akmon (see Akmon) cube, modified (see Modified cube) dolos (see Dolos) hexapod (see Hexapod) hol low square (see Hollow square) tetrahedron (see Hollow tetrahedron) interlocking blocks (see Interlocking concrete block) porosity (see Porosity) quadripod (see Ouadripod) stabit (see Stabit) svee block (see Svee block) tetrapod (see Tetrapod) toskane (see Toskane) tribar (see Tribar) types, 7-216 weight, 7-206, 7-240, 7-249, 7-250, 8-48, 8-50, 8-62, 8-67 thru 8-69, 8-71 Articulated armor unit revetment, 6-6 Artificial beach nourishment (see also Protective beach), 1-19, 4-76, 5-6, 5-7, 5-24, 5-28, 5-34, 5-55, 5-56, 6-16 tracers (see also Flourescent tracers; Radioactive tracers), 4-145 Asbury Park, New Jersey, 4-91, 6-83 Asphalt, 6-76, 6-83, 6-84, 7-139, 7-249 groin, 6-83 Assateague, Virginia, 1-17, 4-37 Astoria, Oregon, 3-118 SUBJECT INDEX Astronomical tides, 3-88, 3-89, 3-92, 3-104, 3-111, 3-119, 3-121, 3-123, 7-2, 7-81, 8-7, 8-10 thru 8-12, 8-46 Atchafalaya Bay, Louisiana, 3-92 Atlantic Beach, North Carolina, 4-91 City, New Jersey, 1-3, 1-9, 3-116, 3-124, 3-125, 4-11, 4-16, 4-31 thru 4-33, 4-37, 4-41, 4-77 thru 4-79, 4-180, 6-25 Intercoastal Waterway, 6-28 Atmospheric pressure (see also Central pressure index), 1-7, 2-21, 3-34, 3-35, 3-89, 3-96, 3-107, 3-110, 3-111, 3-121 Attu Island, Alaska, 3-118 Avalon, New Jersey, 6-9 See pLaie Backfill, 7-256, 7-257, 7-260, 8-81 Backshore, 1-2, 1-13, 1-17, 1-20, 1-23, 3-105, 3-109, 4-62, 4-76, 4-83, 4-108, 4-115, 4-120, 4-127, 4-128, 5-20, 6-31, 6-37, 7-233 protection, 3-105, 5-19 Bakers Haulover Inlet, Florida, 6-32 Bal Harbor, Florida, 6-32 Baltimore, Maryland, 3-116, 3-124, 3-125 Bar (see also Inner bar; Longshore bar; Offshore bar; Outer bar; Spits; Swash bar), 1-8, 1-13 thru 1-15, 1-17, 2-124, 2-125, 4-80, 4-82, 4-83, 4-149 thru 4-151, 5-6, 6-75, 7-14, A-49 Harbor, Maine, 3-116, 3-124, 3-125 Barnegat Inlet, New Jersey, 4-91, 4-170, 6-25 Light, New Jersey, 4-77, 4-79 Barrier (see also Littoral barrier), 1-6, 1-22, 2-75, 2-109, 2-112 thru 2-114, 3-122, 4-57, 4-136, 4-147, 4-154, 5-28, 5-31, 6-1, 6-72, 7-44, 7-232, 7-254 beach, 1-8, 3-110, 4-24, 4-165, 5-56, 6-36 inlet effect on (see Inlet effect on barrier beaches) island, 1-8, 1-9, 1-13, 1-16, 1-17, 3-123, 4-1, 4-3, 4-5, 4-6, 4-22, 4-24, 4-45, 4-108 thru 4-110, 4-112, 4-113, 4-115, 4-119, 4-120, 4-133, 4-140 thru 4-142, 4-167, 4-177, 6-32 deflation plain (see Deflation plain) Barrow, Alaska, 4-45 Bathymetry (see also Nearshore bathymetry; Offshore bathymetry; Shelf bathymetry), 2-60, 2-62, 2-122, 3-24, 3-123, 4-75, 4-147, 4-151, 4-174, 5-1, 7-13, 7-14, 7-17, 7-202, 8-1 Battery, New York, 3-116, 3-124, 3-125, 4-77 Bay County, Florida, 4-77, 4-79 Bayou Riguad, 3-117 Beach (see also Backshore; Berm; Deflation plain; Dune; Feeder beach; Pocket beach; Protective beach), 1-2 thru 1-4, 1-7, 1-9, 1-10, 1-12, 1-13, 1-19, 2-1, 2-112, 2-118, 3-100, 3-101, 4-108, 5-6, 5-30, 5-55, 5-56, 6-37, A-47, A-49 alinement, 1-14, 1-17, 5-1, 5-40 thru 5-46, 5-48 thru 5-50, 5-52, 5-54, 5-73, 8-32, 8-86 changes, 4-6, 4-23, 4-30, 4-45, 4-46, 4-77, 4-78, 4-108, 4-110, 4-126, 4-143, 6-26, 6-27 long-term, 4-6, 5-5 short-term, 4-6, 5-4 characteristics, 1-7, 4-79 composition, 2-1 erosion, 1-10, 1-13, 1-16, 1-23, 3-110, 4-76, 4-80, 4-83, 4-85, 4-89, 4-110, 4-114, 4-117, 4-129, 4-134, 4-148, 5-6, 6-16, 6-54, 6-61, 6-72 rate, 4-110, 4-130 SUBJECT INDEX Beach (Cont) face (see also Shoreface), 1-17, 4-1, 4-6, 4-27, 4-50, 4-59, 4-76, 4-83, 4-108, 5-9 fill (see also Artificial beach nourishment), 1-19, 4-12, 4-15, 4-58, 4-60, 4-80, 4-119, 4-121, 4-143, 5-4, 5-5, 5-8 thru 5-10, 5-13, 5-15, 5-19 thru 5-23, 5-71, 6-15, 6-16, 6-26, 6-28, 6-31, 6-32, 6-35, 6-36, 6-95, 8-90 erosion, 6-26 slopes, 5-21, 5-22 grasses (see also American beach grass; European beach grass; Panic grasses; Sea oats), 4-5, 4-108, 6-38, 6-44, 6-46 thru 6-48, 6-52, 6-53 planting summary, 6-47 seeding, 6-47 transplanting, 6-46 Haven, New Jersey, 4-9 nourishment (see also Artificial beach nourishment), 1-16, 1-19, 4-71, 4-173, 4-180, 5-22, 5-24, 5-34, 5-39, 5-73, 5-74, 6-14, 6-26, 6-32, 6-75 offshore bar (see Offshore bar) profile (see also Profile accuracy), 1-2, 1-9, 1-10, 1-16, 1-17, 4-1, 4-2, 4-5, 4-6, 4-27, 4-43, 4-45, 4-58, 4-60 thru 4-64, 4-76, 4-80, 4-86, 4-89, 4-117, 4-143, 4-147, 5-3, 5-4, 5-6, 5-8, 5-19, 5-20, 5-31, 5-35, 5-40, 5-43, 5-48 thru 5-51, 5-67, 6-26 terms, A-42 protection (see also Artificial beach nourishment; Beach grasses; Beach nourishment; Beach restoration; Shore protection), 1-8, 1-10, 4-23, 4-119, 6-75 vegetation (see Beach grasses; Vegetation) recovery, 1-13, 4-76, 4-78, 4-80, 4-83 replenishment, 4-119, 4-127 thru 4-129, 4-134, 5-6, 5-21, 6-30 response, 1-9 thru 1-11, 1-15 restoration (see also Artificial beach nourishment; Beach nourishment; Dune), 1-19, 1-22, 5-6, 5-7, 5-20, 5-23, 6-15, 6-16, 6-25, 6-28, 6-34 rock, 4-23, 4-24 sediment, 1-7, 1-13, 1-16, 2-60, 4-12, 4-15, 4-23, 4-27, 4-85, 5-12, 5-13, 5-21, C-38 slopes, 1-7 thru 1-9, 1-14, 2-129, 2-130, 2-135, 3-102, 3-105, 3-107, 4-44, 4-49, 4-54, 4-83, 4-87, 4-88, 5-20, 5-35, 5-49, 5-50, 5-64, 5-67, 5-71, 7-8, 7-194, 7-196, 7-197 stability, 1-15, 5-56, 6-54 storm effects (see Storm attack on beaches) surveys, 4-143 Beacon Inn, California, 4-10 Beaumont, Texas, 3-112, 3-113 Bedding layer, 7-227, 7-228, 7-240 thru 7-242, 7-245, 7-247 thru 7-249 Bedload (see also Suspended load), 4-58, 4-59, 4-65, 4-66, 4-147 Belfast, Maine, 3-92 Berm (see also Storm berm; Toe berm), 1-2, 1-3, 1-10, 1-12, 1-17, 3-100, 4-1, 4-10, 4-21, 4-62, 4-67, 4-80, 4-83, 4-108, 4-117, 4-120, 4-148, 5-5, 5-6, 5-20 thru 5-22, 5-24 thru 5-26, 5-28, 5-40, 5-41, 5-43 thru 5-46, 5-49 thru 5-53, 5-60, 6-26, 6-32, 6-39, 6-46; 6-84, 7-35 thru 7-40, 7-247 elevation, 1-7, 1-10, 4-76, 4-79, 4-86, 5-8, 5-20, 5-45, 5-50, 7-37 width, 1-7, 1-10, 5-20 thru 5-22, 5-45, 7-238 Biloxi, Mississippi, 4-35 Biscayne Bay, Florida, 6-36 Boca Grande Inlet, Florida, 4-149 Raton, Florida, 4-37 Inlet, 6-61 Bodie Island, North Carolina, 4-77, 4-79 Borrow areas, 4-119, 4-173, 5-10, 5-12, 5-19, 6-14 thru 6-16, 6-28, 6-36, 6-75 Borrow (Cont) material, 5-6, 5-8 thru 5-13, 5-16, 5-17, 5-19, 5-21, 6-16, 6-26, 8-90, 8-91 selection, 5-8, 5-9 Boston, Massachusetts, 3-90, 3-116, 3-124, 3-125, 4-35, Harbor, 4-119 Bottom friction, 2-2, 2-63, 3-55, 3-66 thru 3-68, 3-70, 3-75, 4-29, 4-30, 4-36, 4-124, 7-13, 7-14, 8-90 factor, 3-24, 3-67, 3-68 profile, 7-2, 8-5, 8-6 slopes, 2-6, 2-109, 2-126, 4-85, 7-16, 7-182, 7-237, 7-250 topography, 2-60, 2-62, 2-66, 2-74, 4-29, 4-31, 7-14 velocity, 1-10, 4-47, 4-49, 4-67 thru 4-69, 4-73, 5-37 Breaker (see Breaking wave) Breaking wave (see also Design breaking wave), 1-1, 1-2, 1-9, 1-14, 2-37, 2-73, 2-129, 2-130, 2-133, 2-134, 3-12, 3-15, 3-99, 3-105, 4-4, 4-49, 4-50, 4-53, 4-55, 4-57 thru 4-60, 4-67, 4-100, 4-107, 4-142, 4-143, 4-147, 5-3, 5-5, 5-63, 5-65, 6-88, 7-2 thru 7-4, 7-8, 7-11, 7-14, 7-17, 7-18, 7-38, 7-40, 7-45 thru 7-53, 7-100, 7-117, 7-119 thru 7-126, 7-157 thru 7-161, 7-164 thru 7-170, 7-180, 7-182, 7-191, 7-192, 7-198, 7-201 thru 7-204, 7-206, 7-207, 7-209, 7-212, 7-238, 7-246, 8-35 depth, 2-59, 2-130, 5-39, 7-37, 7-193, 7-196 forces (see also Minikin), 7-158 thru 7-160, 7-170, 7-181, 7-200 on piles, 7-100, 7-157 on walls, 7-100, 7-180, 7-182, 7-187 geometry, 7-5 height (see also Design breaking wave height), 2-37, 2-119, 2-121, 2-130, 2-135, 2-136, 3-15, 3-102, 3-104, 4-4, 4-22, 4-51, 4-54, 4-92, 4-98, 4-100, 4-104 thru 4-106, 7-4, 7-5, 7-8, 7-9, 7-11, 7-13, 7-112, 7-117, 7-118, 7-159, 7-181, 7-183, 7-186, 7-187, 7-192, 7-193, 7-204 jndex, 2-130, 2-131, 4-104, 7-7, 7-12 types, 1-9, 2-130, 2-133 thru 2-135, 4-49, A-44 Breakwater (see also Cellular-steel sheet-pile break- water; Composite breakwater; Concrete caisson break- water; Floating breakwater; Impermeable breakwater; Offshore breakwater; Permeable breakwater; Rubble- mound breakwater; Shore-connected breakwater; Steel sheet-pile breakwater; Stone-asphalt breakwater; Subaerial breakwater; Submerged breakwater), 1-5, 1-19, 1-22, 1-23, 2-75, 2-76, 2-90 thru 2-100, 2-109, 2-110, 2-115, 2-116, 2-119, 3-110, 5-28, 5-59, 5-64 thru 5-72, 6-1, 6-54, 6-59, 6-73, 7-1, 7-3, 7-61, 7-62, 7-64, 7-66, 7-67, 7-73 thru 7-75, 7-81 thru 7-85, 7-89, 7-92 thru 7-94, 7-100, 7-180, 7-181, 7-187, 7-198, 7-203, 7-207, 7-211, 7-225, 7-226, 7-229, 7-233, 7-236, 7-238, 7-239, 7-242, 7-246, 8-74, 8-75, 8-81 gaps, 2-92, 2-93, 2-99 thru 2-103, 2-107, 2-108, 5-64, 5-65, 5-67, 5-72, 5-73, 6-95, 7-89, 7-94 thru 7-98 Harbor, Delaware, 3-116, 3-124, 3-125 Brigantine, New Jersey, 4-37 Broken wave, 1-3, 1-9, 4-59, 7-2, 7-3, 7-16, 7-17, 7-100, 7-160, 7-161, 7-170, 7-192, 7-193, 7-195, 7-198, 7-200, 7-202, 7-204 Broward County, Florida, 6-74 Brown Cedar Cut, Texas, 4-167, 4-171 Brownsville, Texas, 3-114 Brunswick County, North Carolina, 5-15 Buffalo Harbor, Lake Michigan, 4-136 Bulkhead (see also Cellular-steel sheet-pile bulkhead; Concrete bulkhead; Sheet-pile bulkhead; Steel sheet- pile bulkhead; Timber sheet-pile bulkhead), 1-19 thru 1-21, 2-112, 2-126, 5-2 thru 5-4, 6-1, 6-6, 6-7, 6-14, 6-56, 6-73, 7-100, 7-198, 7-249, 7-254 Burrwood, Louisiana, 3-81 Bypassing sand (see Sand bypassing) Se Cae Caisson (see also Cellular-steel caisson; Concrete caisson; Nonbreaking wave forces on caissons), 5-56, 6-93, 7-105, 7-182, 8-75, 8-77, 8-81, 8-84 stability, 8-75, 8-81 Calcais, Maine, 3-92 Camp Pendleton, California, 4-91 Cantilever steel sheet-pile groin, 6-79, 6-83 Canyon (see also Submarine canyon), 4-124 Cape Canaveral, Florida, 6-15, 6-25 Cod, Massachusetts, 1-11, 3-110, 3-126, 4-24, 4-37, 4-44, 4-77, 4-79, 4-80, 4-110, 4-112, 6-38, 6-52 Fear North Carolina, 6-15, 6-16 River, 5-19, 6-22, 6-28 Hatteras, North Carolina, 4-35, 4-112, 4-120, 4-153, 8-86 Henlopen, Delaware, 4-124 Henry, Virginia, 3-92 Lookout, North Carolina, 4-120 National Seashores, 4-112 May, New Jersey, 3-92, 4-80, 5-54, 6-15, 8-28, 8-86 Mendocino, California, 3-92 Sable, Florida, 4-24 Romano, Florida, 4-24 Capillary wave, 2-5, 2-24 Carbonate loss, 4-124, 4-127, 4-128 production, 4-119, 4-127 thru 4-129 Carmel Beach, California, 4-10 Carolina Beach, North Carolina, 5-21, 5-22, 6-16, 6-21, 6-22, 6-25 thru 6-28 Inlet, 6-16, 6-28 Carteret, New Jersey, 3-123, 3-124 Casagrande size classification, 4-12 Cathodic protection, 6-88 Caustic, 2-74 Caven Point, New York, 3-124, 3-125 Cedar Key, Florida, 3-117 Cedarhurst, Maryland, 6-13 Celerity (see Wave celerity) Cellular-steel caisson, 6-88 sheet-pile breakwater, 5-61, 6-91 thru 6-93 bulkhead, 6-6 groin, 6-80, 6-83, 6-84 jetty, 6-87 structures, 6-88, 6-92 Central pressure index, 3-110, 3-126 Channel (see also Navigation channel), 1-24, 3-122, 4-154 thru 4-157, 4-161, 4-162, 4-164, 4-165, 4-177, 5-2, 5-26, 5-28, 5-56 thru 5-58, 6-56, 6-58 thru 6-60, 6-73, 6-74, 7-233, 7-250, 7-251, 7-253 Islands Harbor, California (Port Hueneme), 1-23, 2-77, 4-37, 4-90, 5-61, 5-62, 6-61, 6-64, 6-72 revetment stability, 7-249 shoaling, 1-24, 4-177, 4-180, 5-56, 5-58 Charleston, South Carolina, 3-92, 3-117, 3-124, 3-125, 4-35 Chatham, Massachusetts, 3-92, 4-169 Chesapeake Bay Bridge Tunnel, Virginia, 3-3 Maryland, 4-22, 4-141, 6-11, 6-15 SUBJECT INDEX Clapotis (see also Seiche; Standing wave), 2-3, 2-113, 2-114, 7-161 thru 7-163, 7-172 thru 7-174, 7-177, 7-178, 7-203 Clatsop Plains, Oregon, 6-52 Spit, Oregon, 4-110, 6-52 Clay, 1-7, 4-12, 4-13, 4-17, 4-18, 4-21, 4-22, 4-24, 4-115, 7-258, 7-260 Cleveland Harbor, Ohio, 7-226 Cliff erosion, 1-17, 4-45, 4-114, 4-115, 4-117, 4-127 thru 4-129 Cnoidal wave, 2-44 thru 2-48, 2-54, 2-57, 2-58, 7-117 theory, 2-2, 2-3, 2-31, 2-33, 2-44, 2-46, 2-54, 7-54, 7-55 Coast, 1-2 Coastal engineering (see also Planning analysis), 1-1, 1-2, 1-4, 4-64, 5-1 erosion (see Shoreline erosion) profile, 4-60 structures, 1-2, 1-17, 2-1, 3-126, 4-58, 4-74, 7-1, 7-58, 7-100, 7-241, 7-247 Cobble, 1-7, 4-12, 4-13 Coefficient (see Drag coefficient; Diffraction coeffi- cient; Energy coefficient; Expansion of ice coefficient; Friction coefficient; Hydrodynamic force coefficient; Inertia coefficient; Isbash coefficient; Layer coeffi- cient; Lift coefficient; Mass coefficient; Overtopping coefficient; Reflection coefficient; Refraction coefficient; Refraction-diffraction coefficient; Shoaling coefficient; Stability coefficient; Steady flow drag coefficient; Transmission coefficient) Cohesionless soil, 7-241 Cohesive material (see also Clay; Peat; Silt), 4-21 Cohesive soil, 7-260 Cold Spring Inlet, New Jersey, 4-90, 4-91 Columbia River, Washington, 3-92 Complex wave, 2-2 thru 2-4 Composite breakwater, 7-182, 7-242 slopes, 7-35 thru 7-37, 7-40 Computer programs, 2-71, 3-89, 5-44, 7-82, 7-88 Concrete (see also Interlocking concrete block; Unit weight--concrete), 1-23, 1-24, 5-2, 5-56, 6-1 thru 6-4, 6-6, 6-7, 6-10, 6-14, 6-76, 6-81, 6-83, 6-84, 6-95, 6-96, 6-98, 7-213, 7-214, 7-235, 7-236, 7-242, 7-249, 7-260, 8-47, 8-51, 8-54, 8-65, 8-69, 8-71, 8-73, 8-79 armor unit, 5-61, 6-88, 7-32, 7-202, 7-210, 7-212 thru 7-215, 7-225 thru 7-227, 7-231, 7-233, 7-235, 7-236, 7-239, 7-240, 8-47, 8-68 bulkhead, 6-6, 6-7 caisson, 5-59, 5-61, 6-88, 6-93 breakwater, 6-93 cap, 5-59, 6-12, 6-82, 6-89, 7-208, 7-229, 7-235, 7-236, 7-239 groin, 6-83, 6-84 pile, 1-20, 6-88 revetment, 6-6, 6-10 sheet-pile, 6-74, 6-75, 6-84, 6-88 groin, 6-81, 6-84 Consolidated material (see also Beach rock; Coral; Rock), 4-23 Construction, 6-95, 6-97 design practices, 6-95, 6-97 materials, 6-95 Continental shelf (see also Shelf bathymetry; Shelf profile), 3-122, 3-123, 4-17, 4-61, 4-65, 4-70, 4-71, 4-93, 4-117, 4-147, 6-15, 7-14 Convergence, 2-74 Conversion factors: English to metric, C-36 Coos Bay, Oregon, 4-37 Coquille River, Oregon, 4-37 Coquina, 4-24 D-3 SUBJECT INDEX Coral, 4-17, 4-22, 4-23, 7-246 Coralline algae, 4-23 Core Banks, North Carolina, 4-108, 6-38, 6-49, 6-50, 6-53 Coriolis, 3-24, 3-119 effects, 2-6, 3-115 force, 2-5, 3-24 parameter, 3-34, 3-38, 3-82, 3-84, 3-121 Corpus Christi, Texas, 3-112 thru 3-114, 4-37, 6-16 thru 6-18, 6-25 Corrosion, 6-88, 6-92, 6-96, 7-139, 7-149, 7-255 Coulomb equation, 7-259 Cover layer, 7-202, 7-205, 7-207, 7-211, 7-227 thru 7-229, 7-233, 7-235 thru 7-240, 7-242, 7-245 thru 7-249, 8-48, 8-49, 8-51, 8-58 thru 8-61, 8-69, 8-71 design, 7-204 stability, 7-238, 7-246 thickness, 8-48, 8-58, 8-59, 8-62, 8-74 Crane Beach, Massachusetts, 4-82, 4-83 Crescent City, California, 3-118, 6-89, 6-92, 7-226 Crest, wave (see Wave crest) Crib, 5-56, 5-59, 5-61, 5-62, 6-6, 6-14, 6-59, 7-242 Cube, modified (see Modified cube) Current (see also Density currents; Inlet currents; Littoral currents; Longshore current; Nearshore currents; Onshore-offshore currents; Rip currents; Salinity currents; Tidal currents), 1-3, 1-4, 1-6, 1-7, 1-13, 2-60, 2-62, 4-1, 4-4, 4-5, 4-12, 4-23, 4-48, 4-49, 4-55, 4-57, 4-58, 4-89, 4-105, 4-126, 4-147, 4-150, 4-157, 4-159, 4-177, 5-1, 5-2, 5-9, 5-21, 5-22, 5-35, 5-56, 5-57, 5-65, 5-73, 6-1, 6-56, 6-73, 7-241, 7-245 thru 7-247, 7-254, 8-1, 8-7 velocity (see also Longshore current velocity), 3-119, 3-121, 7-241, 7-246, 7-247, 7-249, 7-250, 8-12 Cuspate spit, 5-61, 5-63 thru 5-67, 5-69, 5-71 Cuttyhank, Massachusetts, 3-92 Cylinders, 7-102, 7-132 Cylindrical pile, 7-138, 7-157 342 DcatS d/L--Tables of Functions, 2-64, C-5, C-17 Dade County, Florida, 1-19, 1-22, 5-20, 6-16, 6-25, 6-32 thru 6-34, 6-36 Dams, 1-17, 7-254 Datum plane, 3-92 Daytona Beach, Florida, 1-8, 4-35, 4-37, 6-71 Decay, wave (see Wave decay) Deep water, 1-3, 1-5, 2-9, 2-15, 2-18, 2-20, 2-24 thru 2-28, 2-30 thru 2-32, 2-35, 2-37, 2-60, 2-62 thru 2-64, 2-66, 2-68, 2-70, 2-71, 2-74, 2-129, 3-11, 3-15, 3-18, 3-24, 3-39, 3-55, 3-77, 3-101, 4-29, 4-30, 4-95, 4-105, 4-107, 4-123, 4-124, 4-129, 6-92, 7-1, 7-2, 7-13, 7-15, 7-33, 7-63, 7-117, 7-119 thru 7-126, 7-157, 7-164, 7-167, 7-183, 8-26, 8-33, 8-34, C-3, C-35 significant wave height, 3-49, 3-50, 3-83 thru 3-86, 3-101, 3-105, 3-107, 4-85, 4-93, 4-99, 7-1, 7-15, 7-59, 7-242 wave, 2-10, 2-11, 2-17, 2-66, 3-2, 3-21, 3-24, 3-45, 3-46, 3-55 thru 3-66, 4-36, 4-46, 4-85, 4-94, 7-3, 7-7, 7-11, 7-14, 7-89, 7-110, 7-146, 8-26, 8-33, 8-36, 8-44, 8-85, 8-87 thru 8-89 forecasting equation, 3-48 height, 2-20, 2-64, 2-130, 2-135, 3-104, 3-107, 4-102, 7-5, 7-11, 7-13, 7-14, 7-16, 7-33, 7-35, 7-44, 7-54, 8-33 length, 2-130, 7-4, 7-93, 7-94, 8-34, C-3, C-30 prediction, 3-44, 3-49, 3-50, 3-66 Deflation, 1-16, 4-5, 4-124, 4-127, 4-128, 5-9 plain, 4-108, 4-109, 4-112 D-4 Del Mar, California, 4-10, 4-142 Delaware Bay, 4-140, 8-1, 8-7 thru 8-9, 8-12 thru 8-14, 8-17, 8-21, 8-22, 8-25, 8-26, 8-31, 8-32, 8-74 Delray Beach, Florida, 6-25 Density (see also Energy density; Mass density), 2-6, 3-6, 3-33, 3-121, 4-18, 4-50, 7-127, 7-236, 7-237 currents, 4-49, 4-164 Design, 7-149, 7-232, 8-1 analysis, 5-73, 5-74, 7-3 breaking wave, 7-11, 7-13, 7-187 height, 7-4, 7-8 thru 7-10, 7-13, 7-14, 7-204 hurricane, 8-7 practices (see Construction design practices) profile, 6-26 storm, 3-115, 3-126, 3-127 water level, 3-123, 3-126, 7-2, 7-3, 7-15, 7-16, 7-247, 7-260, 8-12 wave, 3-104, 5-5, 5-58, 6-83, 7-3, 7-4, 7-9, 7-14, 7-15, 7-17, 7-33, 7-35, 7-37, 7-105, 7-106, 7-112, 7-127, 7-129, 7-133, 7-140, 7-146, 7-149, 7-150, 7-152 thru 7-155, 7-173, 7-203, 7-208, 7-212, 7-243, 8-46, 8-47 conditions, 7-3, 7-16, 7-202 thru 7-204, 7-211, 8-25 height, 7-3, 7-4, 7-15, 7-118, 7-127, 7-133, 7-146, 7-203, 7-205, 7-207, 7-208, 7-211, 7-212, 7-237, 7-242, 7-243, 7-246, 7-247, 7-249, 8-46, 8-49 period, 5-5, 7-3, 7-127, 7-133, 7-146 Destin, Florida, 4-37 Diablo Canyon, California, 7-226 Diffraction coefficient (see also Wave diffraction), 2-77, 2-92 thru 2-98, 2-105 thru 2-107, 2-110, 7-89, 7-93, 7-94, 7-99 Dispersive medium, 2-25 wave, 2-25, 2-56 Diurnal tide, 3-89, 3-92 Divergence, 2-74 Doheny Beach State Park, California, 6-79, 6-81 Street Beach, California, 6-25 Dolos, 6-86, 6-88, 7-75, 7-206, 7-209 thru 7-212, 7-215 thru 7-217, 7-221, 7-225, 7-226, 7-231, 7-234, 7-236 thru 7-239 Drag coefficient (see also Steady flow drag coefficient), sa 7-101, 7-103, 7-133, 7-136 thru 7-139, 7-144, 7-1 forces, 7-106, 7-109, 7-116, 7-132, 7-133, 7-136, 7-138, 7-145, 7-146, 7-155, 7-157 Drakes Bay, California, 4-145 Dredges (see also Floating dredges; Hopper dredges; Pipeline dredges; Split-hull dredges), 5-32, 5-33, 6-14, 6-31, 6-36 Dredging (see also Land-based vehicles; Side-cast dredging), 1-17, 1-24, 1-26, 4-105, 4-117, 4-119, 4-124, 4-127 thru 4-129, 4-134, 4-176, 4-177, 4-179, 4-180, 5-28, 5-30, 5-31, 5-58, 5-73, 5-74, 6-30, 6-35, 6-36, 6-54, 6-72 thru 6-75 b plant (see also Land-based dredging plant), 5-19, 5-30 discharge line, 5-31, 5-33 Drift, littoral (see Littoral drift) Drum Inlet, North Carolina, 4-120, 4-121, 4-143, 4-153, 4-177 Duck, North Carolina, 4-77, 4-80, 4-81 Dune (see also Foredune), 1-8 thru 1-13, 1-16, 1-17, 1-19, 1-21, 1-25, 1-26, 3-71, 3-105, 3-106, 4-1, 4-5, 4-27, 4-44, 4-46, 4-76, 4-78, 4-83, 4-108, 4-110, 4-117, 4-118, 4-120, 4-127, 4-128, 5-24 thru 5-27, 6-1, 6-26, 6-37 thru 6-43, 6-48 thru 6-53 construction, 5-26, 6-43, 6-53 using sand fencing, 4-110, 6-38, 6-39 vegetation, 4-110, 6-43 formation, 4-5, 6-38, 6-48 SUBJECT INDEX Dune (Cont) migration, 4-124, 4-125, 5-24, 5-25 profile, 6-48, 6-51 stabilization, 5-24, 5-25, 6-38, 6-43, 6-44 trapping capacity, 6-41, 6-43, 6-51, 6-53 Duration, wind (see Wind duration) Durban, Natal, South Africa, 6-54 Dutch Harbor, Unalaska Island, Alaska, 3-91, 3-118 toe, 7-247, 7-248 Duval County, Florida, 6-25 Dynamic forces, 7-161, 7-180, 7-182, 7-187, 7-193, 7-197, 7-200 pressure, 7-193 thru 7-195, 7-200 ee Frogs Earth forces (see also Active earth force; Hydrostatic forces; Passive earth force), 6-76, 7-256, 7-259, 7-260, 8-83 pressure, 8-82 Earthquakes, 1-7, 2-56, 3-89, 3-92, 3-93, 7-1 East Pass, Florida, 4-179, 4-180, 6-61, 6-70 Eastport, Maine, 1-6, 3-116, 3-124, 3-125, 4-35 Ebb-tidal delta, 4-148 thru 4-152, 4-154, 4-155, 4-157, 4-160, 4-167, 4-173, 4-174, 4-177, 4-180 Echo sounder, 4-62 Ecological considerations, 5-73 Eddy shedding (see also Lift forces), 7-132 Ediz Hook, Port Angeles, Washington, 6-25 El Segundo, California, 4-91 Energy (see also Kinetic energy; Longshore energy; Potential energy; Wave energy; Wind energy), 2-5, 3-5, 3-11, 3-12, 3-14, 3-15, 3-20, 3-21, 3-79, 5-3, 5-65, 5-67, 5-69, 5-71, 7-2, 7-209 coefficient, C-4 density, 2-26, 3-11, 3-12, 3-14, 4-95, 7-67, 7-89, 7-93, 7-94, 7-99, 7-209 flux (see also Longshore energy flux factor), 2-26 thru 2-28, 2-109, 4-54, 4-92, 4-93, 4-96, 4-101, 4-147, 5-69, 8-89, 8-90 Engineering, coastal (see Coastal engineering) Englishman Bay, Maine, 3-92 Environmental considerations, 5-19, 5-74 Equilibrium geometry, 4-157 Erosion (see also Beach erosion; Beach fill erosion; Cliff erosion; Longshore transport; Shoreline ero- sion), 1-1, 1-3, 1-7, 1-12 thru 1-17, 1-19 thru 1-21, 1-24 thru 1-26, 2-60, 2-126, 4-1, 4-10, 4-44, 4-57, 4-60, 4-65, 4-77, 4-78, 4-80, 4-83, 4-85, 4-91, 4-113, 4-116 thru 4-118, 4-124, 4-131, 4-172, 4-173, 5-2, 5-4 thru 5-7, 5-24, 5-26, 5-28, 5-35, 5-43, 5-52, 5-53, 5-55, 5-56, 5-58, 5-60, 5-64, 6-1, 6-26, 6-27, 6-32, 6-46, 6-53, 6-54, 6-73, 6-95, 7-233, 7-241, 7-242, 7-245 rate (see also Beach erosion rate), 1-17, 4-6, 4-129, 4-133, 4-147, 5-22, 5-23, 6-51 Estuary, 1-2, 1-3, 1-7, 1-13, 1-26, 3-1, 3-107, 3-109, 3-115, 3-123, 4-5, 4-49, 4-117, 4-148, 4-166, 5-57 Eugene Island, Louisiana, 3-117 European beach grass, 4-110, 6-44, 6-45, 6-47, 6-52, 6-53 Evanston, Illinois, 4-91 Expansion of ice coefficient, 7-254 Extratropical storm, 3-11, 3-110, 3-119, 3-123, 3-126 Extreme events (see also Hurricane; Storm; Tsunami), 4-43, 4-44, 4-76, 7-2, 7-3, 7-242, 7-246 ot SES eg. Fall velocity, 4-18 thru 4-21, 4-28, 4-85 Fan diagrams (see Wave refraction analysis--fan diagrams) Father Point, Quebec, 3-95, 3-96 Feeder beach, 5-8, 5-23, 5-24, 6-72, 6-73 Feldspar, 4-21, 4-22 Fernandina, Florida, 3-117 Beach, 6-5, 6-82 Fetch, 1-6, 1-7, 1-13, 3-24, 3-33, 3-35, 3-36, 3-39, 3-41 thru 3-44, 3-47, 3-48, 3-51 thru 3-65, 3-67, 3-70 thru 3-72, 3-74, 3-76, 3-127, 4-29, 7-17, 7-161, 8-12, 8-17 delineation, 3-39 length, 3-42, 3-49 thru 3-51, 3-66 thru 3-68, 3-70, 3-71, 3-84, 7-1 width, 3-41 Filter blanket (see also Bedding layer), 7-229, 7-240 thru 7-242, 7-245, 7-249 Finite amplitude wave, 7-142, 7-154, 7-155 theory (see also Trochoidal Wave Theory; Stokes Theory), 2-2, 2-4, 2-6, 2-7, 2-34, 2-35, 7-108, 7-112, 7-137, 7-154 element models, 2-109 Fire Island Inlet, New York, 4-37, 4-142, 6-25, 6-61, 6-66 First-Order Wave Theory (see Airy Wave Theory) Fixed bypassing plant, 5-31, 6-53, 6-56 thru 6-58, 6-60 Lake Worth Inlet, Florida, 6-54, 6-56, 6-58 Rundee Inlet, Virginia Beach, Virginia, 6-54, 6-56, 6-60 South Lake Worth Inlet, Florida, 6-54, 6-57 groin, 1-24, 5-53 Flexible revetment (see Articulated armor unit revetment) structures, 6-6, 6-14, 7-3 Floating breakwater, 5-59, 6-93 bypassing plant, 5-28, 5-30, 6-54, 6-59 Channel Islands Harbor, California, 6-61, 6-64, 6-72 Hillsboro Inlet, Florida, 6-61, 6-67, 6-74 Jupiter Inlet, Florida, 6-59, 6-62, 6-72 Masonboro Inlet, North Carolina, 6-61, 6-68, 6-74 Perdido Pass, Alabama, 6-61, 6-69, 6-75 Ponce de Leon Inlet, Florida, 6-61, 6-71 Port Hueneme, California, 6-59, 6-61, 6-72 Santa Barbara, California, 6-61, 6-65, 6-73 Sebastian Inlet, Florida, 6-63, 6-73 dredges, 1-23, 5-30, 5-32, 5-33, 6-14, 6-59, 6-61, 6-72, 6-73, 6-93 Flood-tidal delta, 4-152, 4-174, 4-177 Flourescent tracers, 4-144, 4-146 Fluid motion, 2-2, 2-3, 2-15, 4-19, 4-49, 4-58, 7-132, 7-143 velocity, 2-12 thru 2-14, 2-45, 2-58, 4-18, 4-67, 7-101, 7-138 Force (see also Active earth force; Drag forces; Dynamic forces; Earth forces; Eddy shedding; Horizontal forces; Hydrostatic forces; Ice forces; Impact forces; Inertia forces; Lift forces; Passive earth force; Transverse forces; Uplift forces; Velocity forces; Wave forces), 1-4, 1-6, 1-7, 1-19, 1-21, 2-1, 2-60, 3-88, 3-89, 3-98, 7-1, 7-3, 7-101, 7-102, 7-105, 7-110 thru 7-112, 7-118, 7-128, 7-129, 7-131, 7-138, 7-144, 7-149, 7-150, 7-152 thru 7-161, 7-163, 7-170, 7-172, 7-173, 7-175 thru 7-178, 7-180 thru 7-182, 7-184, 7-186, 7-192, 7-194 thru 7-198, 7-200, 7-202, 7-245, 7-253, 7-255 thru 7-257, 7-260, 8-77, 8-80, 8-81, 8-83, 8-84 calculations, 7-143, 7-144 SUBJECT INDEX Forecasting (see also Deep water wave prediction; Hurricane wave prediction; Shallow water wave prediction; Wave hindcasting; Wave prediction), 3-1, 3-34, 3-55 curves, 3-45, 3-46, 3-55 thru 3-66 Foredune, 1-12, 4-5, 4-62, 4-108 thru 4-110, 4-112, 5-24, 5-26, 5-27, 6-37 thru 6-39, 6-45, 6-51 destruction, 6-38 Forerunner (water level), 3-111 Foreshore, 1-2, 1-3, 1-8, 1-10, 1-21, 4-62, 4-72, 4-76, 4-83, 4-86, 5-31, 5-35, 5-37, 5-40, 6-75, 6-76 slopes, 4-86 thru 4-88, 4-148, 5-8, 5-21, 6-16, 6-27 Fort Hamilton, New York, 3-124, 3-125 Macon State Park, North Carolina, 6-25 Myers, Florida, 4-35 Pierce, Florida, 6-15, 6-25 Point, Texas, 3-112 Pulaski, Georgia, 3-117 Sheridan, Illinois, 7-255 Foundation (see also Pile foundation; Rubble founda- tion; Rubble-mound foundation), 1-23, 6-6, 6-84, 6-88, 6-92, 6-93, 7-177, 7-179, 7-241, 7-242, 7-244, 7-256 conditions, 6-13, 6-14, 6-93, 7-240, 8-85 design, 5-73, 7-149 materials, 6-14, 6-84, 6-93, 7-241, 7-242 soil, 7-241, 7-242, 7-245, 8-75 stability, 7-229, 7-249 Freeport, Texas, 3-112 Frequency, wave (see Wave frequency) Friction (see also Angle of wall friction; Bottom friction; Internal friction angle), 3-20, 3-34, 3-74, 3-75, 3-98, 4-30, 8-33 coefficient, 4-55, 4-162, 7-260, 8-84 factor, 3-68, 3-72, 4-100, 4-164 loss, 3-55, 3-69 velocity, 3-25, 3-26 Friday Harbor, Washington, 3-118 Fully arisen sea, 3-24, 3-42, 3-49, 3-50, 3-53, 3-77 ss G) ene Gabions, 1-20, 7-242, 7-245 Galveston, Texas, 3-90, 3-111, 3-112, 3-114, 3-117, 4-35, 4-37, 4-41, 6-2, 6-15 Harbor, 4-144 Gay Head, Martha's Vineyard, Massachusetts, 4-23 Geostrophic wind, 3-25, 3-34, 3-35, 3-38, 3-40 Geotextile, 6-97, 7-241, 7-242, 7-247 filter, 6-1, 6-6, 6-13, 6-14, 7-241, 7-242, 7-247, 7-248 Gerstner, 2-2 Glossary of terms, A-1 thru A-40 Goleta Beach, California, 4-10 Government Cut, Florida, 6-32, 6-35 Gradient wind, 3-34 Grain size (see also Median grain size), 1-16, 4-12 thru 4-14, 4-18, 4-26, 4-66, 4-67, 4-71, 4-83, 4-85 thru 4-88, 4-145, 4-148, 4-180, 5-9 thru 5-12, 5-15, 5-19, 5-64, 5-67, 6-16, 6-26, 6-36, 6-39, A-41 Grand Isle, Louisiana, 3-117 Marais, Michigan, 6-87 Graphic measures, 4-15 Grasses, beach (see Beach grasses) Gravel, 4-12, 4-13, 4-21, 4-124, 6-6, 7-241, 7-242, 7-258, 7-260 Gravity wave, 2-4, 2-5, 2-9, 2-25, 2-31, 2-37, 3-88, 3-92, 3-107 Great Lakes, 1-13, 1-14, 3-19, 3-21, 3-23, 3-30, 3-32, 3-96, 3-99, 3-127, 4-78, 4-91, 5-21, 5-39, 5-56, 5-59, 6-83, 6-92, 6-93, 7-253, 8-26 Greyhound Rock, California, 4-136, 4-138 Groin (see also Adjustable groin; Asphalt groin; Canti- lever sheet-pile groin; Cellular-steel sheet-pile groin; Concrete groin; Concrete sheet-pile groin; Fixed groin; High groin; Impermeable groin; Low groin; Permeable groin; Rubble-mound groin; Sheet- pile groin; Steel groin; Steel sheet-pile groin; Terminal groin; Timber groin; Timber sheet-pile groin; Timber-steel sheet-pile groin; Transitional groin; Weir groin), 1-17, 1-19, 1-23, 1-24, 2-109, 3-110, 4-6, 4-58, 4-60, 4-76, 4-136, 4-139, 5-7, 5-22, 5-24, 5-32, 5-35 thru 5-56, 5-62, 6-1, 6-27, 6-56, 6-65, 6-76, 6-83, 6-84, 7-1 thru 7-3, 7-100, 7-198, 7-204, 7-239, 7-247 alinement (see also Beach alinement), 5-53 artificial filling, 5-7, 5-52, 5-54 construction, 4-6, 5-7, 5-39, 5-41, 5-52, 5-54 thru 5-56, 6-83 definition, 1-23, 5-35 design, 4-143, 5-35, 5-37, 5-40, 5-45, 6-84 dimension, 5-44 economic justification, 5-40 field (see Groin system) functional design, 5-39, 5-56 legal aspects, 5-56 operation, 5-35 system, 1-23, 5-7, 5-35, 5-39 thru 5-41, 5-43 thru 5-47, 5-52, 5-54 thru 5-56, 6-54, 7-255 types, 6-76, 6-84 Groundwater, 1-16, 7-241, 7-245, 7-249 Group velocity, 2-23 thru 2-25, 2-29, 2-31, 2-32, 3-43, 4-94, 4-95, C-3 eee Hear Haleiwa Beach, Hawaii, 5-62 Halfmoon Bay, 4-86 Hamlin Beach, New York, 2-111 Hammonasset Beach, Madison, Connecticut, 6-25 Hampton Beach, New Hampshire, 6-25 Harbor, New Hampshire, 4-169 Roads, Virginia, 3-90, 3-124, 3-125 Harbor protection, 1-22, 1-23, 5-1, 6-88, 6-93, 7-242 resonance, 2-75, 2-112 Harrison County, Mississippi, 5-20, 6-4, 6-25 Harvey Cedars, Long Beach Island, New Jersey, 6-83 Haulover Beach Park, Florida, 6-32, 6-35 Heavy minerals, 4-17, 4-18, 4-21, 4-22, 4-145 Height, wave (see Wave height) Hexapod, 7-206, 7-209, 7-215, 7-216, 7-224, 7-234 High groin, 1-23, 1-24, 5-37, 5-39, 5-40, 6-76 Hillsboro Inlet, Florida, 4-91, 5-30, 6-61, 6-67, 6-74 Hilo, Hawaii, 3-93 Hindcasting (see Wave hindcasting; Wave prediction) Holden Beach, North Carolina, 4-37 Holland, Michigan, 4-84 Hollow square, 7-216 tetrahedron, 7-216 Honolulu, Hawaii, 1-3, 3-94, 7-226 Hopper dredges, 1-26, 4-180, 5-32, 5-33, 6-14, 6-15, 6-32, 6-36, 6-71, 6-73, 6-75, 6-76 Horizontal forces, 7-127, 7-129, 7-150, 7-151, 7-153 thru 7-155, 7-157, 7-163, 7-177, 7-182, 7-255, 8-78, 8-81, 8-84 Houston, Texas, 3-114 SUBJECT INDEX Humboldt Bay, California, 6-86, 6-88, 7-226 Hunting Island Beach, North Carolina, 6-25 Huntington Beach, California, 3-3, 4-37, 4-41 Hurricane (see also Design hurricane; Hypothetical hurricane; Probable maximum hurricane; Standard Project Hurricane), 1-10, 3-1, 3-11, 3-77, 3-81 thru 3-87, 3-89, 3-101, 3-105, 3-110 thru 3-113, 3-123 thru 3-126, 3-128, 4-5, 4-31, 4-34, 4-35, 4-42 thru 4-45, 6-16, 6-27, 7-4, 7-16, 7-253, 8-7 thru 8-9 Agnes, 3-77 Allen, 6-53 Audrey, 3-81, 4-45 Beulah, 6-53 Camille, 3-77, 3-115, 4-43, 4-45, 6-4 Carla, 3-111 thru 3-115, 4-45 Carol, 3-123, 3-124 Cindy, 4-45 Connie, 3-80 David, 3-79, 6-35, 6-37 defined, 3-110 Diane, 3-80 Donna, 3-77, 3-115, 4-45 Ella, 3-81 Eloise, 4-77, 4-78 Fern, 4-110 Fredric, 1-8, 6-75 protection barriers, 7-253 storm tracks (see Storm tracks) surge (see Storm surge) wave, 3-77, 3-78 prediction, 3-83 wind field, 3-81 Hydraulic pipeline dredges (see Pipeline dredges) Hydrodynamic equations, 2-31, 2-59, 2-62, 3-119 force coefficient, 7-101 thru 7-103, 7-105, 7-136, 7-160 Hydrograph, 3-95 Hydrographic surveys, 4-62, 7-17 Hydrostatic forces (see also Uplift forces), 6-1, 6-6, 7-161, 7-163, 7-171, 7-186, 7-194, 7-195, 7-197, 7-198, 7-201, 7-260, 8-77, 8-81, 8-83 pressure, 7-171, 7-172, 7-182, 7-192, 8-80 Hypothetical hurricane, 3-126 slopes, 7-35, 7-38, 7-39 Ice (see also Expansion of ice coefficient), 7-253 thru 7-256 forces, 7-253, 7-255 Ijmuiden, The Netherlands, 6-92 Immersed weight, 4-96 Impact forces, 7-253 Imperial Beach, California, 1-3, 4-37, 5-9 Impermeable breakwater, 2-78 thru 2-89, 7-61, 7-64, 7-67, 7-71, 7-73, 7-77, 7-90 groin, 1-24, 5-52, 6-76, 6-83 slopes (see also Wave runup--impermeable slopes), 7-11, 7-16, 7-18 thru 7-23, 7-34, 7-49 structures, 7-16, 7-18, 7-33, 7-41, 7-54, 7-59, 7-73 Indian River Inlet, Delaware, 5-59 Rocks Beach, Florida, 6-25 Inertia coefficient, 7-101, 7-103 Inertial forces, 7-103, 7-106, 7-109, 7-115, 7-132, 7-136, 7-145, 7-146, 7-157 Initial water level, 3-111 Inlet (see also Tidal inlets), 1-3, 1-6, 1-8, 1-13, 1-14, 1-17, 1-24, 1-26, 2-60, 3-110, 4-1, 4-21, 4-44, 4-45, 4-58, 4-63, 4-78, 4-89, 4-90, 4-114, 4-120, 4-127 thru 4-133, 4-140, 4-142, 4-148 thru 4-150, 4-152, 4-153, 4-157 thru 4-159, 4-161, 4-162, 4-164 thru 4-167, 4-169, 4-173 thru 4-178, 5-24, 5-26, 5-28, 5-30, 5-32, 5-34, 5-35, 5-54, 5-56, 5-57, 6-72 thru 6-76 barrier beach (see Barrier beach) currents, 4-148, 4-161, 4-166, 5-24, 6-73 effect on barrier beaches, 1-14 inner bar (see Inner bar) middleground shoal (see Middleground shoal) outer bar (see Outer bar) stabilization (see also Jetty stabilization), 4-167, 5-5 Inner bar, 1-14, 5-28 Inshore (see Shoreface) Interlocking concrete block, 6-6, 6-12, 6-13 revetment, 6-6, 6-12, 6-13 Internal friction angle, 7-256 thru 7-258 Irregular wave, 2-108, 3-15, 3-19, 7-39, 7-41, 7-58, 7-59, 7-62, 7-67, 7-69 thru 7-72, 7-80, 7-81, 7-88 thru 7-90, 7-208, 7-209 Isbash coefficient, 7-253 Island (see also Barrier island; Offshore island), 1-8, 2-75, 2-109, 4-108, 4-110, 4-112 profile, 4-112 Isobar, 3-34, 3-35, 3-38, 3-39, 3-81 Isolines, 3-69, 3-85, 5-11, 5-14, 7-119 thru 7-126 So iS < Jetty (see also Cellular-steel sheet-pile jetty; Rubble- mound jetty; Sheet-pile jetty; Weir jetty), 1-3, 1-19, 1-24, 2-109, 3-110, 3-112, 3-113, 4-58, 4-76, 4-89, 4-136, 4-144, 4-151, 4-152, 4-158, 4-164, 4-167, 4-173, 5-22, 5-24, 5-28 thru 5-30, 5-32, 5-34, 5-56 thru 5-60, 6-1, 6-32, 6-54 thru 6-56, 6-58, 6-61, 6-64, 6-66, 6-67, 6-69 thru 6-72, 6-74, 6-84, 6-86, 6-88, 7-2, 7-3, 7-100, 7-203, 7-207, 7-212, 7-225, 7-226, 7-229, 7-233, 7-238, 7-239, 7-245, 7-247 construction, 4-6, 4-147, 6-53, 6-59, 6-61, 6-73, 6-84, 6-88 definition, 5-56 effect on shoreline, 5-58 siting, 5-57 stabilization, 5-28, 5-56, 6-56, 6-74 types, 5-56, 6-84 Johnston Island, Hawaii, 3-94 Joint North Sea Wave Project, 3-44 Jones Beach, New York, 4-11, 4-57, 4-77, 4-79, 4-110 Inlet, New York, 6-25 Juneau, Alaska, 3-118 Jupiter Inlet, Florida, 6-59, 6-62, 6-72 Island, Florida, 6-12, 6-25 Se (ees Kahului, Hawaii, 6-90, 6-92, 7-226, 7-235 Kakuda-Hama, Japan, 5-70 Kenosha, Wisconsin, 4-91 Ketchikan, Alaska, 3-91, 3-118 Keulegan-Carpenter number, 7-134 thru 7-137, 7-145 SUBJECT INDEX Key Biscayne, Florida, 6-25 West Florida, 3-90, 3-92, 3-117 Kill Devil Hills, North Carolina, 4-37 Kinematic viscosity, 7-101, 7-138, 7-139, 7-209 Kinetic energy, 2-25, 2-26, 2-29, 2-58, 3-20, 3-99 Kodiak Island, Alaska, 1-6, 3-118 Kure Beach, North Carolina, 6-22 er ea Lagoon, 1-2, 1-6 thru 1-8, 1-13, 1-14, 1-26, 4-4, 4-22, 4-57, 4-108, 4-110, 4-120, 4-127 thru 4-129, 4-133, 4-174, 4-177, 4-178, 5-19, 6-15 Laguna Point, California, 4-124, 4-125 La Jolla, California, 3-118, 4-51, 4-124 Lake Charles, Louisiana, 4-35 Erie, 2-116, 3-23, 3-95 thru 3-97, 3-99, 3-122, 6-15, 6-95 Huron, 3-95 thru 3-97 levels, 3-93, 3-97, 4-84, 6-95 Great Lakes, 3-93, 3-95 thru 3-97, 3-127 Michigan, 3-95 thru 3-97, 3-122, 4-83, 4-84, 4-110, 6-15 Okeechobee, Florida, 3-82, 3-110, 3-127, 3-128, 7-43 Ontario, 3-95 thru 3-97 St. Clair, 3-95, 3-96 Superior, 3-95 thru 3-97 Worth, Florida, 4-37, 4-41, 6-55 Inlet (see also South Lake Worth Inlet, Florida), 6-54, 6-56, 6-58 Lakeview Park, Ohio, 5-62, 5-72, 6-94, 6-95 Land based dredging plant (see also Landlocked plant), 5-28, 5-30, 5-31, 5-33 vehicles (see also Split-hull] barge), 5-28, 5-30, 5-33, 6-54, 6-75 subsidence, 1-16 Landlocked plant, 5-31 Lawrence Point, New York, 3-124, 3-125 Layer coefficient, 7-209, 7-233, 7-234, 7-237, 8-59 Length (see Fetch length; Wave length) Lewes, Delaware, 3-116, 8-9 thru 8-11 Lift coefficient, 7-136 forces, 7-132, 7-133, 7-135, 7-136 Lincoln Park, Illinois, 5-62 Line sinks, 4-113, 4-114 sources, 4-113, 4-114 Linear Wave Theory, 2-4, 2-11, 2-18, 2-22 thru 2-24, 2-31, 2-34, 2-46, 2-75, 2-112, 2-122, 2-124, 5-66, 7-55, 7-103, 7-117, 7-145 Little Creek, Virginia, 3-124, 3-125 Egg Harbor, New Jersey, 4-7 thru 4-9 Littoral barrier (see also Sand impoundment), 1-18, 4-134, 4-147, 5-8, 5-28, 5-29, 5-31 thru 5-33, 5-58, 5-60, 5-61, 5-64, 6-54, 6-55, 6-59, 6-61, 6-72, 6-75, 6-93 types, 5-28, 6-54, 6-55 currents, 1-24, 4-150, 5-28, 6-76 drift, 1-13, 1-19, 4-44, 4-89, 4-123, 4-129, 4-132, 4-142, 5-28, 5-30, 5-31, 5-35, 5-39, 5-43, 5-45, 5-52, 5-56 thru 5-58, 5-63, 5-64, 6-54, 6-56, 6-59, 6-61, 6-72, 6-73, 6-74, 7-254 Littoral (Cont) material (see also Cohesive material; Consolidated material; Sand; Sediment; Specific gravity--littoral material; Unit weight--littoral material), 1-1, 1-15, 1-17, 4-12, 4-14, 4-15, 4-17, 4-18, 4-21 thru 4-24, 4-26, 4-115, 4-119, 4-126, 4-173, 5-1, 5-2, 5-7, 5-24, 5-31, 5-40, 5-44, 5-56, 5-60, 6-56, 6-93 classification (see Soil classification) composition, 4-17, 4-26 immersed weight (see Immersed weight) occurrence, 4-24, 4-26 properties, 4-17 sampling, 4-26 sinks, 4-120, 4-123, 4-124, 4-126 size (see also Grain size; Mean diameter; Median diameter; Median grain size), 4-12, 4-15 distribution, 4-14, 4-15, 4-24, 4-26 sources (see also Sediment sources), 4-115, 4-126 transport (see also Bedload; Longshore transport; Onshore-offshore transport; Sediment transport; Suspended load), 1-1, 1-13, 1-17, 4-5, 4-30, 4-36, 4-43, 4-46, 4-55, 4-57, 4-58, 4-101, 4-112, 4-146, 4-150, 5-22, 5-23, 5-28, 5-34 rate, 5-55 sediment budget (see Sediment budget) seaward limit, 4-70, 4-71, 4-76, 4-147 tracers (see Tracers) trap (see Sand impoundment) wave Climate, 4-29 zone, 1-15 thru 1-17, 4-1, 4-4, 4-6, 4-12, 4-21, 4-22, 4-27, 4-29, 4-36, 4-40, 4-43, 4-46, 4-49, 4-50, 4-55, 4-57, 4-63, 4-71, 4-75, 4-89, 4-90, 4-114, 4-117 thru 4-120, 4-124, 4-127, 4-128, 4-134, 4-145 thru 4-148, 5-9, 5-58, 5-64 long-term changes, 4-6 short-term changes, 4-6 Load (see Bedload; Suspended load) Long Beach California, 6-95 New Jersey, 4-110, 4-180 Island, 4-11, 4-77, 4-79 Island, New York, 4-24, 4-25, 4-45, 4-63, 4-64, 4-120, 4-140, 4-144 Shores, 6-15 Sound, 4-22, 6-15 Longshore bar, 4-6, 4-49, 4-60, 4-62, 4-66 current, 1-7, 1-14, 1-16, 3-104, 4-4, 4-42, 4-44, 4-50, 4-53 thru 4-55, 4-59, 4-65, 4-100, 4-127, 5-21, 5-37, 5-38, 5-61, 5-65, 7-241 velocity, 4-50, 4-53 thru 4-56, 4-100 drift (see Littoral drift) energy, 4-92, 4-94, 4-96, 4-101, 4-107 flux factor, 4-93, 4-94, 4-96, 4-97, 4-100, 4-101 transport (see also Littoral transport), 1-7, 1-13, 1-14, 1-16, 1-17, 1-19, 1-23, 1-24, 1-26, 4-4, 4-6, 4-12, 4-29, 4-44, 4-45, 4-53, 4-57, 4-58, 4-60, 4-65, 4-89 thru 4-91, 4-102, 4-105, 4-113 thru 4-116, 4-123, 4-126, 4-128, 4-133, 4-134, 4-136, 4-140, 4-142, 4-145, 5-9, 5-22, 5-24, 5-28, 5-31, 5-32, 5-35, 5-37, 5-39, 5-41, 5-43, 5-45, 5-52, 5-54, 5-60, 5-63, 5-71, 6-27, 6-53, 6-75 direction, 1-14, 4-4, 4-134, 5-8, 5-29, 5-35, 5-36, 5-41, 5-43, 5-44, 5-60, 6-16, 6-57 reversals, 1-14, 5-44, 5-45 energy (see Longshore energy) nodal zones, 4-136, 4-139, 4-140 rate, 1-14, 4-6, 4-53, 4-60, 4-89 thru 4-93, 4-96 thru 4-99, 4-101, 4-104, 4-106, 4-134, 4-141, 4-146, 4-147, 5-8, 5-23, 5-31, 5-35, 5-39, 5-52, 5-58, 5-63, 5-64, 5-71 SUBJECT INDEX Longshore (Cont) transport (Cont) rate (Cont) gross, 1-14, 4-89, 4-92, 4-104, 4-105, 4-107, 4-114, 4-120, 4-126, 4-147, 5-1, 5-58 net, 1-14, 4-12, 4-89, 4-92, 4-120, 4-130, 4-167, 5-1, 5-8, 5-58, 5-60, 6-57, 8-90 potential, 4-104, 8-85, 8-87, 8-88 thru 8-90 tracers (see Tracers) wave energy (see Longshore energy) Los Angeles, California, 3-118, 6-95 Low groin (see also Weir groin), 1-24, 1-25, 5-39, 5-40, 6-76 Ludlam Beach, New Jersey, 4-77, 4-79 Island, New Jersey, 4-11, 4-37, 4-52 aa MS Maalea Harbor, 7-235 Malaga Cove (Redondo Beach), California (see also Redondo Beach (Malaga Cove), California), 5-33 Manahawkin Bay, New Jersey, 4-7 Manasquan, New Jersey, 4-91, 7-226 Mandalay, California, 4-37 Marine environment, 7-14, 7-17 Street, California, 4-10 structures, 2-57, 7-253, 7-255 Martha's Vineyard, Massachusetts, 4-24 Masonboro Beach, North Carolina, 6-22, 6-68, 6-74 Inlet, North Carolina, 6-16, 6-22, 6-61, 6-68, 6-74, 6-83 Mass coefficient, 7-101, 7-103 density (see also Specific gravity; Unit weight), 7-205, 7-233, 7-236, 7-243 sand, 4-90 water, 2-21, 3-121, 4-90, 7-205 transport, 2-4, 2-15, 2-18, 2-31, 2-36, 4-4, 4-48, 4-49, 4-59, 4-147 Massachusetts Bay, Massachusetts, 6-15 Matagorda, Texas, 3-112, 3-113 Materials, construction (see Construction materials) Mathematical models, 3-1, 3-19, 3-42, 3-77, 3-81, 3-83, 3-105, 3-115, 3-122, 3-126, 5-44, 5-45 Maximum probable wave (see Probable maximum wave) surge, 3-123 water level, 3-104, 3-123, 4-166 Mayport, Florida, 3-92, 3-117 Mean diameter, 4-15, 5-11, 8-91 water level, 2-6, 3-2, 3-95, 3-96, 3-99, 3-100, 3-105, 3-106, 3-108, 3-126, 7-162 wave height, 4-36, 4-37 Median diameter, 4-14, 4-15, 4-24, 4-25, 4-69, 4-181, 6-30 grain size, 4-12, 4-17, 4-86 thru 4-88 Merian's equation, 2-115, 3-98 Merrimack River Estuary, Massachusetts, 4-151, 4-160 Inlet, Massachusetts, 4-150, 4-151, 4-160 Miami, Florida, 4-35 Beach, 1-3, 1-19, 3-117, 6-15, 6-32, 6-36 Miche-Rundgren Theory, 7-161, 7-165, 7-166, 7-168, 7-169 Michell (wave steepness), 2-37, 2-129 Middleground shoal, 1-14, 4-120, 4-152, 5-15, 5-19, 5-26, 5-28, 6-56, 6-57 Miles-Phillips-Hasselmann Theory, 3-19, 3-21, 3-43 Millibar, 3-34, 3-35, 3-37 Milwaukee County, Wisconsin, 4-91 Minerals (see also Heavy minerals), 1-17, 4-21, 4-22, 4-144, 6-30 Minikin, 7-181, 7-182, 7-185, 7-187 thru 7-189 Mining, 4-114, 4-124, 4-127 thru 4-129 Misquamicut, Rhode Island, 4-37, 4-77, 4-79 Beach, 4-11 Mississippi River, 4-24, 4-115 Mobile, Alabama, 1-6 Modified cube, 7-206, 7-209, 7-215, 7-216, 7-223, 7-234 Mokuoloe Island, Hawaii, 3-94 Moments (see also Skewness; Standard deviation), 7-105, 7-111, 7-112, 7-118, 7-127, 7-129, 7-131, 7-149 thru 7-151, 7-155, 7-157 thru 7-159, 7-163, 7-166, 7-169, 7-170, 7-172 thru 7-181, 7-187, 7-193 thru 7-198, 7-202, 8-78, 8-80, 8-83 Monochromatic wave, 2-62, 2-74, 2-108, 2-112, 3-1, 3-15, 3-18, 3-101, 3-106, 7-16, 7-43, 7-58, 7-62, 7-65, 7-67, 7-68, 7-74, 7-76, 7-78 thru 7-81, 7-83 thru 7-90, 7-94, 7-101, 7-102, 7-208, 7-209 Monomoy-Nauset Inlet, Massachusetts, 4-169 Montauk, New York, 3-116, 3-124, 3-125 Point, 3-92 Monterey, California, 3-42 Morehead City, North Carolina, 3-117, 3-124, 3-125 Moriches Inlet, 4-45 Mugu Canyon, California, 4-123 Murrells Inlet, South Carolina, 1-24, 1-25, 4-37, 6-61 Mustang Island, Texas, 4-110, 4-112 Myrtle Beach, Connecticut, 4-11 Sound, North Carolina, 6-16 Sea dNiee= Nags Head, North Carolina, 3-13, 4-37, 4-41, 6-48, 6-83 Nantucket Island, Massachusetts, 4-24, 6-8 Naples, Florida, 4-37, 4-41 National Shoreline Study, 1-2, 4-24, 4-135 Natural Bridges, California, 4-37 tracers, 4-21, 4-144 Nauset Beach, Massachusetts, 4-108, 6-52 Spit, Cape Cod, Massachusetts, 1-11, 4-169 Navigation channel, 1-1, 1-23, 1-24, 1-26, 3-110, 4-58, 4-180, 5-28 thru 5-30, 5-57, 6-56, 6-73 thru 6-75 Nawiliwili, Kawai, Hawaii, 7-226 Neah Bay, Washington, 3-118 Nearshore bathymetry, 2-60 currents (see also Littoral currents; Littoral trans- port), 1-1, 1-2, 4-46, 4-49, 4-50, 4-51, 4-134 profile, 4-59 thru 4-64, 4-66, 4-75, 4-147, 6-32 slopes, 1-7, 1-9, 2-59, 2-136, 4-76, 4-143, 5-6, 5-9, 5-20, 6-16, 6-27, 7-4 thru 7-6, 7-9 thru 7-11, 7-45 thru 7-53, 7-182, 7-183, 7-186, 7-187, 7-201 wave climate, 4-31, 4-42, 4-89 zone, 1-2, 1-4, 1-6, 1-7, 1-13, 4-49, 4-50, 4-62, 4-65, 4-115, 4-119, 4-147 New London, Connecticut, 3-116, 3-124, 3-125 River Inlet, North Carolina, 6-75 York, New York, 3-90, 4-35 Bight, 4-57, 6-15 Harbor, 3-124, 4-136, 4-140, 4-180 SUBJECT INDEX Newark, New Jersey, 3-124, 3-125 Newport Beach, California, 6-25, 6-79 Rhode Island, 3-116, 3-124, 3-125, 4-23, 4-77 Nodal zones (see Longshore transport nodal zones) Node, 2-113, 3-97 thru 3-99 Nonbreaking wave (see also Miche-Rundgren Theory), 3-18, 7-2, 7-3, 7-14, 7-17, 7-45 thru 7-53, 7-100 thru 7-102, 7-117, 7-161, 7-163, 7-164, 7-166, 7-167, 7-169, 7-181, 7-202, 7-206, 7-207, 7-209, 7-211, 7-212, 7-238, 7-239, 8-47, 8-49, 8-58 forces (see also Sainflou Method), 7-161, 7-162, 7-165, 7-168, 7-170 on caissons, 8-76 on piles, 7-100 on walls, 7-161 height, 7-204 Noncircular pile, 7-102, 7-159, 7-160 Nonlinear deformation, 4-29, 4-30 Wave Theory (see Finite Amplitude Wave Theory) Nonvertical walls, 7-200, 7-201 Norfolk, Virginia, 3-117 Northeaster (see also Standard Project Northeaster), 3-110, 4-31, 4-44, 4-78, 4-157, 6-28 Nourishment, beach (see Artificial beach nourishment; Beach nourishment) Numerical models (see Mathematical models) SSO = Oak Island, North Carolina, 5-19 Ocean City Maryland, 4-91, 6-83, 8-85, 8-86, 8-90 Inlet, 1-18 New Jersey, 4-91 Beach, 6-25 wave, 1-4, 2-4, 2-74, 3-1, 3-2, 3-15, 6-32, 6-93 Oceanside, California, 4-10, 6-25 Harbor, 6-61 Ocracoke Island, North Carolina, 4-110, 6-49, 6-52 Offshore, 1-2, 1-3, 3-107, 4-72, 4-80, 4-147, 5-3, 5-9, 5-19, 5-21, 5-22, 5-55, 5-62, 5-64, 5-67, 5-69, 5-71, 5-73, 7-14, 7-17 bar, 1-3, 1-10, 1-13, 2-122, 4-78, 6-16 bathymetry, 1-7, 2-124, 3-123, 4-78 breakwater, 1-23, 2-105 thru 2-108, 4-167, 5-29, 5-30, 5-34, 5-61 thru 5-67, 5-69, 5-71, 5-73, 6-55, 6-61, 6-72, 6-93 thru 6-95 types, 5-59, 6-93 island, 4-30, 4-114, 4-117, 8-1 thru 8-3 slopes, 4-117, 4-120, 4-121, 4-127, 4-128, 5-5, 5-21, 5-22, 7-41 structures, 1-22, 2-108, 7-149 wave climate, 4-29, 4-42 zone, 4-55, 4-58, 4-60, 4-73, 4-121, 4-126, 4-129, 6-56 Old Point Comfort, Virginia, 3-124, 3-125 Onshore-offshore currents (see also Littoral currents; Nearshore currents), 4-49 profiles, 4-75 transport, 1-13, 4-57, 4-58, 4-65, 4-66, 4-71, 4-73, 4-74, 4-76, 4-83, 4-117, 4-133, 4-147, 5-35, 5-63 Orange, Texas, 3-112, 3-113 Organic reefs, 4-23 Orthogonal, 2-61 thru 2-66, 2-68 thru 2-75, 2-109, 2-110, 7-15, 7-156, 8-33 D-10 Oscillatory wave (see also Airy Wave Theory; Linear Wave Theory), 1-5, 2-4, 2-6, 2-9, 2-27, 2-55 thru 2-57, 2-59 Outer Banks, North Carolina, 6-41, 6-42, 6-48 bar, 1-14, 1-24, 4-152, 4-157, 4-173, 4-175, 4-177, 5-26, 5-28 Overtopping, 1-13, 2-119, 3-122, 4-44, 4-108, 4-110, 4-112, 5-3, 5-4, 5-20, 5-26, 5-58, 5-69, 5-73, 6-1, 6-48, 6-93, 7-16, 7-18, 7-33, 7-43 thru 7-54, 7-56, 7-58, 7-59, 7-61 thru 7-63, 7-67 thru 7-69, 7-73, 7-74, 7-80 thru 7-83, 7-89, 7-173, 7-205, 7-211, 7-212, 7-225, 7-227 thru 7-229, 7-231, 7-233, 7-235, 7-236, 7-238, 7-239, 7-248, 7-249, 8-48 coefficient, 7-67, 7-71, 7-72 Overwash, 1-13, 1-16, 1-17, 4-43, 4-80, 4-108, 4-110 thru 4-112, 4-114, 4-120, 4-122, 4-127, 4-128, 6-73 fans, 1-13, 1-16 Oxnard Plain Shore, California, 4-91 sa Pes Padre Island, Texas, 4-136, 6-37, 6-38, thru 6-53 Palm Beach, Florida, County, 6-72 Panic grasses, 6-44, 6-48, 6-53 Pass Christian, Mississippi, 3-115 Passive earth force, 7-257 Peahala, New Jersey, 4-8 Peak surge, 3-123, 8-9 Peat, 4-17, 4-22, 4-27 Pelican Island, Texas, 3-112, 3-113 Pensacola, Florida, 3-90, 3-117, 4-35 Inlet, 4-179, 4-180 Percolation, 2-2, 2-63, 3-55, 4-29, 4-36, 4-124 Perdido Pass, Alabama, 4-91, 6-61, 6-69, 6-75 Period, wave (see Design wave period; Significant wave period; Tidal period; Wave period) Periodic wave, 2-3, 4-58, 4-94, 7-11, 7-16 Permeable breakwater, 7-61, 7-64, 7-73, 7-80 thru 7-82 groin, 1-24, 5-52, 5-53, 6-76 Perth Amboy, New Jersey, 3-124, 3-125 Phase velocity (see also Wave celerity), 2-7, 2-23 thru 2-25, 2-31 Phi millimeter conversion table, C-38 units, 4-14, 4-15, 4-17, 4-25, 5-11 Philadelphia, Pennsylvania, 3-116, 3-124, 3-125 Pierson-Neuman-James wave prediction model, 3-43 Pile (see also Breaking wave forces on piles; Concrete pile; Concrete sheet-pile; Cylindrical pile; Non- breaking wave forces on piles; Noncircular pile; Sheet-pile; Steel sheet-pile; Timber pile; Vertical pile; Wave forces on piles), 5-53, 6-1, 6-76, 6-83, 6-84, 6-93, 7-101, 7-103, 7-106, 7-109 thru 7-111, 7-127, 7-129, 7-132, 7-138, 7-141, 7-147, 7-149 thru 7-155, 7-157, 7-159, 7-160, 7-256 diameter, 7-103, 7-131, 7-138, 7-140, 7-144, 7-146, 7-155 foundation, 4-27 group, 7-153 thru 7-155 Pinellas County, Florida, 4-91 Pioneer Point, Cambridge, Maryland, 6-10 Pipeline dredges, 5-32, 5-33, 5-54, 5-60, 6-14, 6-16, 6-30 thru 6-32, 6-56, 6-59, 6-61, 6-73, 6-76 Pismo Beach, California, 4-124 Planning analysis, 1-1, 5-1, 5-2, 6-14 1-11, 4-108 thru 4-111, 4-124, 6-40, 6-42, 6-43, 6-49, 6-51 4-37, 4-91, 5-9, 6-15 SUBJECT INDEX Plum Island, 4-151, 4-160 Pocket beach, 4-1, 4-3, 4-138 Pohoiki Bay, Hawaii, Hawaii, 7-226, 7-235 Point Arguello, California, 3-36, 4-124 Barrow, Alaska, 4-45 Conception, California, 4-145 Loma, California, 3-92 Mugu, California, 4-10, 4-37, 4-71, 4-74, 4-136, 4-137 Reyes, California, 4-10 sinks, 4-113, 4-114 sources, 4-113, 4-114, 4-117, 4-119 Sur, California, 4-10 Pompano Beach, Florida, 6-15, 6-25 Ponce de Leon Inlet, Florida, 6-61, 6-71 Ponding, 7-89, 7-90 Poorly- graded sediment, 4-14 sorted sediment, 4-14 Porosity, 4-66, 7-3, 7-18, 7-208, 7-215, 7-229, 7-234, 7-236 thru 7-238 Port Aransas, Texas, 3-112, 3-113 Arthur, Texas, 3-112 thru 3-114 Hueneme, California, 1-23, 4-91, 5-28, 6-59, 6-61, 6-72 Isabel, Texas, 3-92, 3-112, 3-113, 3-117, 4-35 Lavaca, Texas, 3-114 O'Conner, Texas, 3-112, 3-113 Orford, Oregon, 4-37 Sanilac, Michigan, 6-91, 6-92 Townsend, Washington, 3-92 Portland, Maine, 3-116, 3-124, 3-125 Portsmouth Island, North Carolina, 4-122 New Hampshire, 3-116, 3-124, 3-125 Virginia, 3-116, 3-124, 3-125 Potential energy, 2-25, 2-26, 2-29, 2-58, 3-15, 3-99, 3-107 Potham Beach, Maine, 1-21 Power, wave (see Wave power) Precast concrete armor units, 1-21 Prediction, wave (see Wave prediction) Presque Isle, Pennsylvania, 5-62, 5-63, 6-80 Pressure (see also Atmospheric pressure; Central pressure index; Dynamic pressure; Earth pressure; Hydrostatic pressure; Soil bearing pressure; Sub- surface pressure), 2-6, 2-43, 2-58, 3-34, 3-52, 3-81, 3-82, 3-84, 3-110, 4-28, 6-6, 7-161 thru 7-163, 7-173, 7-180, 7-181, 7-187, 7-193, 7-196, 7-198, 7-254, 7-256, C-3 distribution, 2-46, 7-161 thru 7-163, 7-173, 7-174, 7-178, 7-181, 7-182, 7-192, 7-256 gradient, 2-36, 3-24, 3-30, 3-33, 3-34, 4-50 profile, 3-82 pulse, 3-20 response factor, 2-22, 7-104, C-3 Pria, Terceria, Azores, 7-236 Probable maximum hurricane, 3-126 wave, 3-87 Profile (see also Beach profile; Bottom profile; Coastal profile; Design profile; Dune profile; Island profile; Nearshore profile; Onshore- offshore profile; Pressure profile; Shelf profile; Temperature profile; Wave profile; Wind profile), 2-39, 2-114, 3-20, 3-24, 3-97, 3-120, 4-6, 4-60, 4-61, 4-64, 4-65, 4-73 thru 4-78, 4-80, 4-83, 4-85, 4-117, 4-118, 4-143, 4-161, 5-5, 5-6, 5-9, 5-21, 5-22, 5-31, 5-35, 5-43, 5-45, 5-48, 5-49, 5-67, 6-26, 6-27, 6-80 Profile (Cont) accuracy, 4-62 closure error, 4-62, 4-63 sounding error, 4-62 spacing error, 4-62, 4-63 temporal fluctuations, 4-62 zonation, 4-73, 4-76 Progressive wave, 2-3, 2-6 thru 2-8, 2-10, 2-37 theory, 2-6 Prospect Beach, West Haven, Connecticut, 6-25 Protective beach (see also Artificial beach nourish- ment; Beach nourishment; Beach protection; Berm; Dune; Feeder beach; Groin), 5-2, 5-6, 5-7, 5-33, 5-35, 5-63, 6-1, 6-14 thru 6-24, 6-29, 6-30, 6-33 erosion (see Beach erosion) Providence, Rhode Island, 3-116 Provincetown, Massachusetts, 3-92 Puget Sound, Washington, 3-92 --Q-- Quadripod, 6-85, 6-88, 7-206, 7-209, 7-211, 7-215 thru 7-217, 7-219, 7-225, 7-226, 7-231, 7-234 Quarrystone, 1-21, 1-23, 1-24, 5-58, 5-61, 6-5, 6-6, 6-11, 6-97, 7-16, 7-26, 7-32, 7-202, 7-205, 7-206, 7-211, 7-212, 7-214, 7-215, 7-225, 7-230, 7-231, 7-233, 7-234, 7-236 thru 7-242, 7-245, 7-246, 8-47, 8-61 armor units, 1-24, 6-88, 6-97, 7-210, 7-212, 7-236, 7-241, 7-245, 7-247, 7-249 revetment, 1-21, 6-6, 6-11 slopes, 7-16, 7-26 weight and size, 7-230 Quartz, 4-18, 4-21, 4-22, 4-69, 4-73, 4-74, 4-124, 6-36 Quay, 8-75, 8-85 Quincy Shore Beach, Quincy, Massachusetts, 6-25 = = Ris = Racine County, Wisconsin, 4-91 Radioactive tracers 4-144, 4-145 Radioisotopic sand tracing (RIST), 4-145 Rainfall, 3-111, 3-115 Random wave, 3-106 thru 3-109, 7-62, 7-67, 7-74, 7-92, 7-95 thru 7-98 Rankine, 7-257, 7-259 Rayleigh distribution, 3-2, 3-5 thru 3-8, 3-10 thru 3-12, 3-81, 4-40, 4-93, 7-2, 7-39, 7-58, 7-67 Redfish Pass, Florida, 4-167, 4-168, 4-173 Redondo Beach (Malaga Cove), California (see also Malaga Cove (Redondo Beach), California), 4-91, 5-20, 6-14, 6-16, 6-25, 6-28 thru 6-32 Reefs, organic (see Organic reefs) Reflection coefficient (see also Wave reflection), 2-112, 2-116 thru 2-119, 2-121 thru 2-125, 7-73, 7-77, 7-82, 7-84, 7-85, 7-161 thru 7-163, 7-173, 7-179, 7-245, 7-246 Refraction analysis (see Wave refraction analysis) coefficient (see also Wave refraction), 2-64, 2-67, 2-71, 2-72, 2-110, 2-135, 2-136, 3-104, 4-94, 4-95, 7-14, 7-15, 7-33, 8-33, 8-35 thru 8-37, 8-76 diagrams (see Wave refraction analysis--diagrams) diffraction coefficient, 2-109, 2-110 template, 2-65, 2-66, 2-69 Rehoboth Beach, Delaware, 1-20 SUBJECT INDEX Relative depth, 2-9, 2-10, 2-32, 2-112, 2-129, 3-118, 7-10, 7-62, 7-113 thru 7-116 Resonant wave, 2-113 Revetment (see also Articulated armor unit revetment; Channel revetment stability; Concrete revetment; Interlocking concrete block revetment; Quarrystone revetment; Riprap revetment), 1-19 thru 1-21, 2-112, 2-116, 2-119, 2-121, 4-76, 5-2 thru 5-4, 6-1, 6-6, 6-14, 6-92, 7-100, 7-207, 7-212, 7-233, 7-237, 7-240, 7-241, 7-246 thru 7-252, 8-47, 8-69, 8-71 Reynolds number, 4-14, 7-101, 7-137 thru 7-139, 7-141, 7-143, 7-144, 7-149, 7-158, 7-208, 7-209 Ridge-and-runnel, 4-82, 4-84, 4-148 Rigid structures, 7-3, 7-133, 7-136 revetment (see Concrete revetment) Rincon Beach, California, 4-10 Island, California, 7-226 Rip currents, 1-7, 4-4, 4-49, 4-50, 4-52, 4-66, 5-37, 5-38, 5-54 Ripple, 1-4, 3-93, 4-48, 4-49, 4-58 thru 4-60, 4-62, 4-66, 4-72, 4-147 Riprap, 7-26, 7-30, 7-33, 7-34, 7-49, 7-73, 7-75, 7-205, 7-207, 7-229, 7-234, 7-237, 7-240, 7-247, 7-249 thru 7-251, 7-254, 7-255 revetment, 6-6, 6-14 slopes, 7-35, 7-229 RIST (see Radioisotopic sand tracing) Rivers (see also specific rivers), 1-3, 1-6, 1-7, 1-15, 1-17, 1-25, 3-41, 3-115, 3-122, 4-22, 4-114, 4-115, 4-117, 4-127, 4-128, 4-148, 4-166, 5-56, 6-30 Rock (see also Beach rock; Unit weight--rock), 4-23, 4-24, 4-136, 4-144, 5-59, 6-1, 6-35, 6-73, 7-207, 7-225, 7-227, 7-228, 7-258, 8-58, 8-61, 8-62, 8-67 Rockaway Beach, New York, 5-20, 5-22, 6-16, 6-23 thru 6-25 Rogue River, Oregon, 4-37 Rubble, 6-88, 7-63, 7-100, 7-241 thru 7-244, 7-255 foundation, 7-177, 7-178, 7-187, 7-242 thru 7-244 stability, 7-242 thru 7-244 slope, 5-3, 5-4, 7-31, 7-233 seawall, 5-4 structures (see Rubble-mound structure) toe protection, 2-112, 7-242 thru 7-244 Rubble-mound, 7-225, 7-227, 7-228 breakwater, 2-112, 2-117 thru 2-119, 5-59, 5-62, 6-72, 6-89, 6-90, 6-92 thru 5-95, 7-16, 7-61, 7-73, 7-75, 7-78, 7-79, 7-82, 7-86 thru 7-88, 7-90, 7-209, 7-210, 7-216, 7-235 construction, 1-24, 5-56, 5-59, 5-61, 5-93 foundation, 7-242, 7-246 groin, 5-40, 6-82 thru 6-84, 7-204 jetty, 6-84 thru 6-86, 6-88, 7-235 seawall, 6-5, 6-6, 6-28 structure (see also Wave runup--rubble-mound structure), 1-20, 6-84, 6-93, 7-3, 7-4, 7-18, 7-100, 7-200, 7-202 thru 7-204, 7-208 thru 7-210, 7-213, 7-214, 7-225, 7-229, 7-231, 7-233, 7-235, 7-236, 7-240 thru 7-242, 7-245, 8-59 cross-section example, 6-89, 6-90, 7-227, 7-228, 8-48 design (see also Armor units weight; Bedding layer; Concrete cap; Cover layer; Filter blanket; Layer coefficient; Underlayer), 7-202, 7-203, 7-225, 7-229, 7-231, 7-232 core volume, 8-65, 8-74 economic evaluation, 8-46, 8-65, 8-67 thru 8-73 layer volumes, 8-60 thru 8-66, 8-73, 8-74 number of armor units, 7-236, 7-237, 8-59, 8-73 stability, 7-202 Rudee Inlet, Virginia Beach, Virginia, 5-31, 6-54, 6-56, 6-59, 6-60 Runup, wave (see Wave runup) BS SS Sabellariid worms, 4-23 Safety factor, 7-136, 7-146, 7-149, 7-210, 8-84 Sainflou Method, 7-161 Size Augustine Beach, Florida, 6-75 Lucie Inlet, Florida, 4-176 Marks, Florida, 4-35 Mary's River, Florida, 4-167, 4-172, 4-173 Petersburg, Florida, 3-117 Thomas, Virgin Islands, 7-226 Salina Cruz, Mexico, 6-54 Salinity currents, 4-166, 5-57 Saltation, 6-38 Sampling sediment (see Sediment sampling) San Buenaventure State Beach, California, 6-25 Clemente, California, 4-37 Diego, California, 1-3, 3-118 Francisco, California, 3-91, 3-118, 6-3 Onofre, California, 4-10 Simeon, California, 4-37 Sand (see also Borrow areas; Littoral material; Specific gravity--sand), 1-7, 1-8, 1-10, 1-13 thru 1-16, 1-19, 1-23 thru 1-26, 4-5, 4-6, 4-12, 4-13, 4-17, 4-18, 4-21, 4-22, 4-24, 4-26 thru 4-29, 4-43 thru 4-45, 4-55, 4-57, 4-59, 4-60, 4-65, 4-66, 4-70 thru 4-74, 4-76, 4-80, 4-82, 4-83, 4-90, 4-108, 4-110, 4-113, 4-115, 4-117 thru 4-121, 4-124, 4-128 thru 4-130, 4-134, 4-136, 4-137, 4-139, 4-144, 4-147, 4-148, 4-173 thru 4-177, 4-180, 4-181, 5-6 thru 5-9, 5-11 thru 5-13, 5-15, 5-19, 5-24, 5-28 thru 5-31, 5-33, 5-35, 5-37, 5-40, 5-41, 5-43, 5-52, 5-53, 5-55, 5-64, 6-16, 6-26, 6-28, 6-30, 6-31, 6-37 thru 6-44, 6-51 thru 6-55, 6-61, 6-64, 6-73, 6-74, 6-83, 6-93, 7-1, 7-241, 7-247, 7-258, 7-260, 8-76, 8-81 thru 8-83, 8-91, 8-92 budget (see also Sediment budget), 1-1, 4-6, 4-114, 4-126, 4-128, 4-130 thru 4-133 bypassing, 1-17, 1-24, 4-134, 4-167, 5-24, 5-26, 5-28, 5-30, 5-31, 5-34, 5-37, 5-53, 5-58, 5-60, 6-1, 6-53, 6-54, 6-56, 6-59, 6-61 thru 6-75 plants (see Fixed bypassing plant; Floating bypassing plant) land-based vehicles (see Land-based vehicles) legal aspects, 5-33, 5-34 mechanical, 1-26, 5-28, 5-30, 6-54 methods, 6-54 composition, 1-7, 4-21 conservation, 1-25, 1-26 dune (see Dune) fence (see also Dune construction using sand fencing), 5-26, 6-38, 6-42 thru 6-44, 6-49, 6-50 heavy minerals (see Heavy minerals) Hill Cove Beach, Narragansett, Rhode Island, 6-25 impoundment, 1-23, 1-24, 4-5, 4-6, 4-174, 5-26 thru 5-29, 6-40, 6-43, 6-47 thru 6-49, 6-51, 6-53, 6-55, 6-59, 6-62, 6-63, 6-72, 6-73 motion (see Sediment motion) movement (see also Littoral transport; Longshore transport; Sediment transport), 1-14 thru 1-16, 1-23, 1-24, 1-26, 4-5, 4-23, 4-45, 4-66, 4-70, 4-104, 4-108, 4-114, 4-119, 4-120, 4-124, 4-126, 4-128, 4-144, 4-149, 4-150, 4-172, 4-180, 5-8, 5-26, 5-30, 5-35, 5-37, 5-61, 5-63, 6-37, 6-51, 7-242, 8-90 deflation (see Deflation) saltation (see Saltation) surface creep, 6-38 suspension, 6-38 Sand (Cont) origin, 1-7 size (see also Grain size; Mean diameter; Median diameter; Median grain size), 4-12, 4-14, 4-16, 4-17, 4-25, 4-79, 4-86, 4-97, 4-112, 7-180, 5-9, 5-35, 6-36 classification (see Soil classification) spillway, 6-74 tracers (see Tracers) SUBJECT INDEX Sediment (Cont) load (see Bedload; Suspended load) motion, 4-4, 4-17, 4-66 thru 4-70 properties, 4-66 sampling, 4-21, 4-142, 4-143 sinks (see Line sinks; Littoral material sinks; Point sinks) size (see also Grain size; Mean diameter; Median diameter; Median grain size), 1-7, 1-14, 4-12, 4-14, transport (see Sand movement) 4-28, 4-44, 4-66, 4-71, 4-112, 4-117, 4-147, 5-12, trap (see Sand impoundment) Bea Sandy Hook, New Jersey, 3-92, 3-116, 3-124, 3-125, sorting, 4-66 4-57, 4-77, 4-79, 4-90, 4-91, 4-121, 4-123, 4-134, loss, 4-121 4-135, 4-147, 5-54 sources (see also Line sources; Point sources), Santa 4-117, 4-119 Barbara, California, 1-23, 4-91, 4-180, 5-60, 5-62, 6-61, 6-65, 6-73 Cruz, California, 4-62, 6-85, 6-88, 7-226 Monica, California, 3-118, 4-91, 5-62 Mountains, 4-10 Sapelo Island, Georgia, 4-71, 4-74 Savannah Coast Guard Light Tower, 3-13 Georgia, 3-92, 3-124, 3-125 River, 3-90 Saybrook, Connecticut, 3-92 Scale effects (see Wave runup scale effects) Scour (see also Toe scour), 1-21, 3-110, 4-49, 4-172, 5-3 thru 5-5, 5-54, 5-73, 6-1, 6-5, 6-6, 6-14, 6-75, 6-93, 7-14, 7-129, 7-149, 7-237, 7-241, 7-242, 7-245 thru 7-249 Scripps Beach, California, 4-10 Canyon, California, 4-51 Pier, California, 4-10 Sea, 1-4, 1-7 thru 1-10, 3-1, 3-21, 3-51, 3-77, 3-106 thru 3-109, 3-120 Girt, New Jersey, 6-15, 6-32 Isle City, New Jersey, 5-54 level changes, 1-15, 1-16, 1-19, 4-5, 4-126 oats, 6-44, 6-45, 6-47 thru 6-53 Seacrest, North Carolina, 4-37 Seas (see also Fully arisen sea), 1-6, Seaside Park, Bridgeport, Connecticut, Seattle, Washington, 3-91, 3-118 Seawall (see also Rubble-mound seawall; Rubble slope seawall), 1-19 thru 1-22, 2-112, 4-80, 5-2 thru 5-4, 5-24, 5-62, 5-71, 6-1 thru 6-5, 6-14, 6-28, 6-32, 6-54, 7-16, 7-28, 7-29, 7-100, 7-170, 7-172, 7-198, 7-226, 7-233, 7-241 face, 1-21, 6-1 thru 6-4 tracers (see Tracers) transport (see also Littoral transport; Longshore transport; Sand movement), 1-16, 1-17, 4-4 thru 4-6, 4-17, 4-18, 4-29, 4-46, 4-48, 4-49, 4-55, 4-58, 4-65, 4-66, 4-71, 4-75, 4-76, 4-83, 4-114, 4-119, 4-136, 4-144, 4-146, 4-147, 5-21, 5-26, 5-61, 6-95 rate, 4-101, 4-126, 5-67 Seiche (see also Clapotis; Standing wave), 2-115, 3-88, 3-89, 3-93, 3-96, 3-98, 3-99 antinode (see Antinode) forced, 3-98 free, 3-98 node (see Node) Semirigid structures, 7-3 Setdown (see Wave setdown) Settling tube, 4-21, 4-28, 4-29 analysis, 4-27, 4-28, 5-10 Setup (see Surge; Wave setup; Wind setup) Seward, Alaska, 3-118 Shallow water, 2-2, 2-3, 2-6, 2-9, 2-10, 2-25, 2-26, 2-30, 2-32, 2-33, 2-44, 2-46, 2-57, 2-63, 2-64, 2-66, 2-68, 2-70, 3-2, 3-6, 3-11, 3-12, 3-15, 3-18, 3-24, 3-39, 3-44, 3-55, 3-66, 3-67, 3-89, 3-110, 3-122, 4-30, 4-46, 4-47, 4-49, 4-58, 4-93, 5-3, 5-33, 5-65, 7-3, 7-15, 7-63, 7-82, 7-85, 7-91, 7-117, 7-158, 7-159, 7-209, 7-237 thru 7-239, 7-246, 7-247, 8-26, C-3 structures, 7-246 wave, 2-17, 2-31, 2-126, 3-45, 3-46, 3-56 thru 3-65, 3-93, 4-29, 4-30, 4-47, 4-162, 7-3, 7-4, 7-14, 7-33, 7-109, 7-146, 7-157, 7-158, 8-33 prediction, 3-55, 8-12 Shark River Inlet, New Jersey, 4-91, 6-75 Sheet-pile, 5-3, 5-59, 6-1, 6-76, 6-83, 6-88 bulkhead, 6-6, 7-249 2-4 6-25 functional planning, 5-3, 6-1 groin, 6-84 purpose, 5-2, 5-4, 6-1 jetty, 4-165, 6-88 types, 6-1 Shelf Sebastian Inlet, Florida, 6-59, 6-63, 6-73 Sediment (see also Beach sediment; Poorly-graded sediment; Poorly-sorted sediment; Well-graded sediment; Well-sorted sediment), 1-7, 1-10, 1-13 thru 1-17, 1-19, 1-26, 2-18, 4-1, 4-28, 4-48, 4-50, 4-59, 4-60, 4-66, 4-67, 4-71, 4-72, 4-74 thru 4-76, 4-83, 4-85, 4-89, 4-117, 4-120, 4-121, 4-123, 4-134, 4-144, 4-145, 4-149, 4-174, 5-8, bathymetry, 4-31 profile, 4-60, 4-61, 4-64 Sherwood Island State Park, Westport, Connecticut, 6-25 Shesholik Spit, Alaska, 4-90 Shingle, 1-16, 4-21 Shinnecock Inlet, Long Island, New York, 4-45, 4-120, 4-140 Shipbottom, New Jersey, 4-7 5-9, 5-12, 5-13, 5-15, 5-17, 5-19, 5-21, 5-22, 5-28, 5-35, 5-37, 5-40, 5-43, 5-64 thru 5-65, 5-67, 5-71, 6-15, 6-76, 6-83, 7-246, 8-1 analysis, 4-28 budget (see also Sand budget), 4-58, 4-63, 4-113 thru 4-117, 4-119, 4-123, 4-124, 4-126, 4-129, 4-143, 4-146, 4-148 sinks (see Line sinks; Littoral material sinks; Point sinks) sources (see Line sources; Littoral material sources; Point sources; Sediment sources) classification (see Soil classification) Shoal (see also Middleground shoal), 1-14, 1-15, 1-17, 2-109, 2-122, 4-30, 4-65, 4-117, 4-119, 4-149, 4-152, 4-157, 4-173 thru 4-175, 4-177, 5-30, 5-60, 6-56, 6-72 thru 6-74 Shoaling (see also Channel shoaling), 1-24, 2-27, 2-60, D-13 2-74, 2-109, 3-93, 3-99, 3-110, 4-29, 4-30, 4-36, 4-49, 4-89, 4-92, 4-146, 4-157, 4-174, 4-176, 4-179, 4-180, 5-30, 5-56, 5-65, 6-16, 6-72, 7-1, 7-242, 8-45, C-35 coefficient, 2-28, 2-64, 2-67, 4-95, 4-97, 4-104, 4-105, 4-107, 7-13 thru 7-15, 8-33, 8-35 thru 8-37, C-3 water, 2-37, 2-46, 2-57, 2-58, 2-129 SUBJECT INDEX Shore, 1-2 thru 1-4, 1-6, 1-7, 1-9, 1-13 thru 1-15, 1-19, 1-23 thru 1-25, 3-1, 3-4, 3-30, 3-51, 3-81, 3-99, 3-101, 3-102, 4-66, 4-89, 4-117, 4-147, 4-181, 5-2, 5-3, 5-6 thru 5-8, 5-10, 5-23, 5-28, 5-32, 5-39, 5-40, 5-44, 5-45, 5-52, 5-55, 5-56, 5-58, 5-60 thru 5-62, 5-64, 5-66, 5-67, 5-71, 5-74 alinement (see Beach alinement) connected breakwater, 1-23, 5-29, 5-30, 5-58 thru 5-60, 6-55, 6-61, 6-88 types, 5-59, 6-88 protection (see also Beach protection), 1-1, 1-15, 1-22, 2-1, 2-2, 5-2, 5-6, 5-7, 5-62, 5-74, 6-6, 6-93, 7-16 Shoreface (see also Beach face), 1-2, 2-1, 4-67, 4-71 thru 4-73, 4-75, 5-9, 6-84 Shoreline, 1-2 thru 1-4, 1-7, 1-13, 1-15, 2-27, 2-71, 2-73, 2-126, 2-127, 2-136, 3-42, 3-99, 3-106, 3-119, 3-120, 3-123, 4-1, 4-3, 4-8, 4-23, 4-50, 4-53, 4-54, 4-57, 4-65, 4-75, 4-80, 4-82, 4-85, 4-89, 4-92, 4-94, 4-95, 4-113, 4-114, 4-134, 4-140, -142, 4-147, 4-148, 4-152, 4-154, 4-157, 4-167, -168, 4-170, 4-171, 4-173, 4-175, 4-180, 5-2 thru » 5-7, 5-22 thru 5-24, 5-26, 5-34 thru 5-44, » 5-53, 5-58 thru 5-63, 5-65 thru 5-67, 5-69, » 5-73, 6-27, 6-80, 6-93, 6-95, 7-2, 7-89, 5, 8-1, 8-26, 8-33, 8-34, 8-85, 8-90, A-48, 1-3 5-64, erosion, 1-10, 1-13, 1-15 thru 1-17, 4-5 thru 4-7, 4-9, 4-114, 4-117, 4-173 Side-cast dredging, 6-76 Sieve analysis, 4-17, 4-27, 4-28, 5-10 Significant wave, 3-2, 3-11, 3-71, 3-87, 3-104, 4-69, 7-14, 7-41, 7-59, 7-61, 8-36 height (see also Deep water significant wave height), 3-2, 3-6, 3-10, 3-21, 3-22, 3-39, 3-43, 3-52, 3-70, 3-71, 3-75, 3-77, 3-85, 3-87, 3-102, 3-104, 4-31, 4-37, 4-40, 4-41, 4-73, 4-74, 4-93, 4-94, 7-2, 7-3, 7-14, 7-41, 7-59, 7-67, 7-69, 7-72, 7-80, 7-93, 7-94, 7-99, 7-208, 7-245, 8-18, 8-25, 8-38 thru 8-41, 8-44, 8-45 period, 3-2, 3-6, 3-52, 3-77, 3-81, 3-84, 3-87, 7-1, 7-2, 7-67, 7-93, 7-94, 8-18, 8-38 thru 8-41 Silt, 1-7, 4-12, 4-13, 4-17, 4-21, 4-22, 4-71, 4-115, 7-258 Simple harmonic wave (see Sinusoidal wave) wave, 2-2, 2-3 Sinks (see also Line sinks; Littoral material sinks; Point sinks), 4-60, 4-114, 4-126, 4-129, 4-131, 4-132 Sinusoidal wave, 2-3, 2-6, 2-8, 2-10, 2-24, 3-5, 3-11, 3-18 Sitka, Alaska, 3-118 Siuslaw River, Oregon, 3-92 Size analysis, 4-27, 4-28 classification, sediment (see Soil classification) Skagway, Alaska, 3-118 Skewness (see also Moments), 4-15, 4-17, 5-12 Sliding, 7-254, 8-81, 8-84 Slopes (see also Beach fill slopes; Beach slopes; Bottom slopes; Composite slopes; Foreshore slopes; Hypothetical slopes; Impermeable slopes; Nearshore slopes; Offshore slopes; Quarrystone slopes; Rip- rap slopes; Rubble slope; Structure slope), 2-59, 2-67, 2-74, 2-116 thru 2-118, 3-99, 3-102, 3-107 thru 3-109, 3-119, 4-44, 4-65, 4-85 thru 4-88, 5-6, 5-9, 5-21, 5-22, 5-37, 5-40, 5-45, 5-49, 5-50, 5-67, 6-32, 6-46, 6-88, 7-4, 7-6, 7-8, 7-9, 7-18 thru 7-21, 7-24 thru 7-38, 7-40, 7-43, 7-44, 7-54, 7-56, 7-59, 7-63, 7-72, 7-82, 7-84, 7-183, 7-187, 7-202 thru 7-206, 7-210, 7-211, 7-235 thru 7-239, 7-241, 7-245 thru 7-247, 7-251, 7-257, 7-260, C-35, C-43 Small Amplitude Wave Theory, 2-2, 2-4, 2-6, 2-7, 4-46, 4-48, 4-65, 4-67, 4-68, 4-73, 4-92, 4-94, 4-105 Soil (see also Cohesionless soil; Cohesive soil; Founda- tion soil; Unit weight--soil), 5-6, 6-97, 7-240, iets 7-245, 7-248, 7-249, 7-256 thru 7-258, 7-260, 8-8 bearing pressure, 8-75, 8-81, 8-84, 8-85 classification (see also Casagrande size classifica- tion; Unified soil classification; Wentworth size classification), 4-13, A-41 mechanics, 4-18, 6-84, 7-256 Solitary wave, 2-4, 2-45, 2-49, 2-56 thru 2-59, 7-16 theory, 2-2, 2-3, 2-33, 2-44, 2-49, 2-55, 2-58, 2-130, 3-101, 4-94, 4-95, 7-117 Solomons Island, Maryland, 3-116, 3-124, 3-125 South Lake Worth Inlet, Florida, 4-144, 6-54, 6-57 Southampton, New York, 4-37 Southport, North Carolina, 3-117, 3-124, 3-125 Specific energy (see Energy density) gravity (see also Mass density; Unit weight), 4-18, 4-21, 4-22, 4-86, 6-97, 7-205, 7-207, 7-242, 7-243 littoral material, 4-17, 4-18 sand, 4-18 Speed, wind (see Wind speed) Spillway, sand (see Sand spillway) Spits (see also Cuspate spit), 1-8, 4-57, 4-90, 4-112, 4-121, 4-123, 4-129, 4-130, 4-132, 4-147, 6-74 Split-hull barge, 6-75, 6-76 dredges, 1-26 Spring tides, 4-45, 4-80, 4-152, 8-12 Spuyten Duyvil, New York, 3-124, 3-125 Stability (see also Beach stability; Caisson stability; Channel revetment stability; Cover layer stability; Dune stabilization; Foundation stability; Inlet stabilization; Jetty stabilization; Rubble foundation stability; Rubble-mound structure stability; Struc- tural stability; Toe stability), 3-25, 3-26, 3-30, 3-32, 3-33, 3-35, 3-52, 4-6, 4-112, 4-133, 5-6, 5-8, 5-10, 6-1, 6-13, 6-31, 6-83, 6-88, 6-92, 6-93, 7-200, 7-204, 7-206, 7-210, 7-215, 7-235, 7-236, 7-239, 7-242, 7-245, 7-247 thru 7-249, 7-254, 8-79 coefficient, 7-205, 7-207, 7-215, 7-225, 7-239, 8-49, 8-50 number, 7-207, 7-243, 7-244 Stabit, 7-216 Standard deviation (see also Moments), 3-11, 3-14, 3-15, 3-17, 4-14, 4-15, 4-17, 4-40, 4-77, 5-10, 6-26, 7-2, 7-145, 8-91 Project Hurricane, 3-126, 4-42 Northeaster, 3-126 Standing wave (see also Clapotis; Seiche), 2-3, 2-75, 2-113, 2-114, 3-89, 3-96 thru 3-98, 7-161 antinode (see Antinode) node (see Node) Staten Island, New York, 4-136, 4-139 Steady flow drag coefficient, 7-139 Steel, 1-20, 1-23, 1-24, 5-56, 5-59, 6-1, 6-84, 6-88, 6-96, 6-98, 7-149 groin, 6-76 thru 6-80, 6-84 sheet-pile, 5-56, 5-59, 5-62, 6-76, 6-80, 6-84, 6-88, 6-92, 7-242 breakwater (see also Cellular-steel sheet-pile breakwater), 6-91, 6-92 bulkhead, 6-6, 6-8 groin, 6-76, 6-84 Steepness, wave (see Wave steepness) Stevensville, Michigan, 4-110 SUBJECT INDEX Stillwater level, 1-5, 2-7, 2-55, 2-57, 3-1, 3-88, 3-99 thru 3-101, 3-104, 3-106 thru 3-108, 7-16, 7-33, 7-41, 7-106, 7-107, 7-109, 7-139, 7-162, 7-163, 7-171, 7-192, 7-193, 7-203, 7-204, 7-208, 7-211, 7-212, 7-243, C-3 line, 7-147, 7-192 thru 7-197 Stockpile (see Artificial beach nourishment; Beach replenishment; Feeder beach) Stokes, 2-2, 2-3, 2-37 Wave Theory, 2-31, 2-34, 2-44, 2-59, 7-110, 7-137, 7-145 Stone (see also Armor stone), 5-2 thru 5-5, 5-40, 6-5, 6-14, 6-36, 6-76, 6-83, 6-84, 6-88, 6-93, 6-97, 7-202, 7-205, 7-206, 7-212, 7-213, 7-225, 7-229 thru 7-231, 7-233 thru 7-237, 7-239 thru 7-242, 7-245 thru 7-247, 7-249, 7-250, 7-252, 7-253, 7-258, 7-260, 8-47, 8-59 armor units, 3-109, 3-110 asphalt breakwater, 6-92 Storm (see also Design storm; Extratropical storm; Hurricane; Northeaster; Thunderstorms; Tropical storm), 1-3, 1-4, 1-6 thru 1-10, 1-13, 1-15, 1-17, 1-19, 1-20, 3-1, 3-21, 3-26, 3-53, 3-77, 3-80 thru 3-83, 3-104, 3-107, 3-110, 3-111, 3-123, 3-126 thru 3-128, 4-6, 4-30 thru 4-35, 4-42 thru 4-46, 4-76 thru 4-78, 4-80 thru 4-83, 4-110, 4-134, 4-143, 4-147, 4-148, 4-169, 5-4, 5-6, 5-9, 5-20, 5-24, 5-26, 5-39, 5-40, 5-54, 5-63, 5-71, 6-38, 6-48, 6-95, 7-2, 7-4, 7-14, 7-16, 7-192, 7-211, 7-225, 7-247 attack on beaches (see also Wave attack), 1-10, 1-12, 1-13, 1-19, 4-76, 4-110, 5-24, 5-27 berm, 5-20, 5-26 surge, 1-1, 1-4, 1-6, 1-7, 1-10, 1-12, 1-13, 1-16, 1-19, 3-1, 3-74, 3-88, 3-89, 3-105, 3-107, 3-110 thru 3-112, 3-115, 3-119, 3-121 thru 3-124, 3-126, 3-127, 4-4, 4-5, 4-30, 4-44, 4-76, 4-78, 4-79, 4-147, 5-1, 5-4, 5-6, 5-24, 5-26, 5-57, 6-32, 6-34, 6-53, 7-16, 7-17, 7-204, 8-7, 8-9, 8-12, 8-46 prediction, 3-115, 3-123, 3-126 tide (see Storm surge) tracks, 3-77, 3-82, 3-83, 3-111, 3-123, 4-30, 4-31, 8-8 wave, 1-3, 1-10, 1-12 thru 1-17, 1-19, 1-21, 1-24, 3-106, 4-29, 4-31, 4-43, 4-44, 4-46, 4-62, 4-76, 5-6, 5-27, 5-54, 6-92, 7-59, 7-81, 7-202 Stream Function Wave Theory, 2-31, 2-33, 2-59, 3-15, 3-17, 7-110, 7-112, 7-118, 7-137, 7-145 Stress, wind (see Wind stress) Structural stability, 5-58, 6-83, 7-1, 7-3, 7-89, 7-236, 7-241 Structure (see also Cellular-steel sheet-pile struc- tures; Coastal structures; Flexible structures; Impermeable structures; Marine structures; Off- shore structures; Rigid structures; Rubble-mound structure; Semirigid structures; Shallow water structures; and specific types of structures), 1-19, 1-21, 1-25, 2-60, 2-124, 5-2, 5-4, 5-22, 5-60, 5-69, 5-74, 7-1 thru 7-4, 7-8, 7-10, 7-11, 7-14, 7-16 thru 7-21, 7-41, 7-44, 7-132, 7-136, 7-147, 7-161, 7-170 thru 7-174, 7-177 thru 7-180, 7-193, 7-194, 7-200, 7-202 thru 7-205, 7-211, 7-212, 7-249, 7-253 thru 7-256, 7-260, 8-79 damage, 5-58 design, 3-110, 7-82, 7-110, 7-149, 8-47 face (see also Seawall face), 5-4, 7-198, 7-206, 7-245, 8-48 head, 7-206, 7-212, 7-229, 7-238 scour (see Scour) Structure (Cont) slope, 2-116, 2-119, 2-121, 2-129, 5-69, 7-16, 7-18, 7-32, 7-35, 7-39, 7-41, 7-43, 7-44, 7-46, 7-50, 7-54, 7-61, 7-203, 7-205, 7-207, 7-215, 7-229, 7-236, 7-237, 7-246, 7-257, 8-47, 8-49, 8-54 thru 8-57, 8-64, 8-66, 8-68, 8-70, 8-72, 8-73 toe, 2-90, 2-119, 2-120, 2-126, 5-4, 5-5, 7-4, 7-8, 7-9, 7-16, 7-33, 7-35, 7-38, 7-41, 7-43, 7-44, 7-54, 7-162, 7-174, 7-182, 7-195, 7-197, 7-204, 7-237, 7-245 Subaerial breakwater, 7-64, 7-73, 7-76 Submarine canyon, 1-26, 2-73, 4-114, 4-123, 4-127 thru 4-129, 6-61 Submerged breakwater, 7-62, 7-64, 7-65, 7-73, 7-242 Subsurface pressure, 2-21, 2-32, 2-36, 3-33 Suffolk County, New York, 4-91 Summary of Synoptic Meteorological Observations, 4-42, 4-101, 4-104 Sunset Beach, California, 5-9, 5-22, 6-25 Surf zone, 1-2, 1-3, 1-10, 1-16, 1-24, 3-15, 3-89, 4-4, 4-5, 4-29, 4-30, 4-36, 4-46, 4-48 thru 4-50, 4-53, 4-54, 4-55, 4-58, 4-59, 4-60, 4-65, 4-66, 4-82, 4-92, 4-94, 4-96, 4-100, 4-104, 4-110, 4-112, 4-120, 5-67, 5-71, 6-75, 7-100, 7-160, 7-241, 7-247 Surfside, California, 5-9, 5-22, 6-25 Surge (see also Maximum surge; Peak surge; Storm surge), 1-6, 1-7, 1-16, 3-109, 3-110, 3-122, 3-123, 4-4, 4-5, 4-78, 5-59, 7-2, 7-238, 8-75 Surveys (see also Beach surveys; Hydrographic surveys; Profile accuracy), 4-63, 4-64, 4-77, 4-78, 4-80, 4-85, 4-90, 4-119, 4-180, 4-181, 5-8, 5-34, 6-27 Suspended load (see also Bedload), 4-58, 4-59, 4-65, 4-66, 4-91, 4-147 Svee block, 7-216 Sverdrup-Munk-Bretschneider wave prediction method, 3-44 Swash bar, 4-149 thru 151 Swell, 1-6, 1-13, 1-15, 2-4, 3-4, 3-24, 3-43, 3-77, 3-106, 5-26, 5-35, 7-89 Symbols (list of), B-1 thru B-22 Synoptic surface weather chart, 3-33 thru 3-36, 7-15 thru 7-17 a ee Tarpon Springs, Florida, 4-24 Temperature profile, 3-20 Template, refraction (see Refraction template) Ten Mile River Beach, California, 4-124 Terminal groin, 4-167, 5-40, 5-56, 5-62 Tetrapod, 5-59, 6-89, 6-92, 7-206, 7-209, 7-215 thru 7-218, 7-225, 7-226, 7-231, 7-234, 7-236, 8-47, 8-50, 8-51, 8-53, 8-56, 8-57, 8-59 thru 8-61, 8-63, 8-65 thru 8-67, 8-72, 8-73 Texas City, Texas, 3-112, 3-113 Theories, wave (see Wave theories) Thunderstorms, 3-26, 3-30, 3-33, 3-41 Tidal currents, 1-6, 1-8, 1-10, 3-88, 4-5, 4-49, 4-58, 4-127, 4-128, 4-147, 4-152, 5-24, 5-28, 5-32, 5-57, 6-74, 7-250, 8-12 thru 8-16 delta (see also Ebb-tidal delta; Flood-tidal delta), 4-153 inlets, 1-13, 1-14, 4-113, 4-148, 4-152, 4-157, 4-167, 4-177, 4-180, 6-53 period, 4-161, 4-162 prisms, 4-140, 4-152, 4-157, 4-158, 4-161, 4-165, 4-166, 4-174, 4-177, 5-57, 5-58, 6-73 SUBJECT INDEX Tidal (Cont) range, 1-6, 1-17, 3-92, 4-4, 4-83, 4-86, 4-128, 4-164 thru 4-166, 5-65, 5-66 thru 5-68, 5-73, 5-74, 6-74, 6-75, 6-96, 7-2, 7-17, 7-250, 8-9 wave (see also Tide; Tsunami), 3-92, 4-148, 4-166 Tide (see also Astronomical tides; Diurnal tide; Spring tide), 1-1, 1-4, 1-6, 1-7, 1-10, 3-1, 3-88, 3-89, 3-92, 3-93, 3-112 thru 3-114, 3-125, 4-1, 4-4, 4-5, 4-44, 4-76, 4-83, 4-152, 4-161, 4-162, 4-165, 5-1, 5-9, 5-20, 5-39, 5-40, 5-57, 5-66 thru 5-69, 7-192, 7-241, 7-250, 7-255, A-50 curves, 3-89 thru 3-91 gage record, 3-11, 3-93, 3-94 prediction, 3-88, 3-89 Tillamook Bay, Oregon, 4-37 Timber, 1-20, 1-23, 1-24, 5-56, 5-59, 5-61, 6-1, 6-76, 6-83, 6-93, 6-96 groin, 6-76 thru 6-78, 6-84 pile, 5-56, 5-59, 6-76, 6-88, 6-96, 6-97 sheet-pile, 6-84, 6-88 bulkhead, 6-6, 6-9 groin, 6-77, 6-84 steel sheet-pile groin, 6-76, 6-78 Toe (see also Dutch toe; Structure toe), 1-21, 2-92, 3-105, 5-21, 5-22, 5-26, 6-1, 7-175, 7-181, 7-182, 7-196, 7-197, 7-201, 7-237, 7-241, 7-242, 7-245 thru 7-248, 8-75 apron, 7-245 thru 7-249 berm, 7-228, 7-229, 7-237, 7-238, 7-249 protection, 5-5, 7-229, 7-245, 7-246 scour, 7-245, 7-248, 8-75 stability 7-238 Toledo, Ohio, 3-97 Tombolo, 1-23, 4-136, 4-138, 5-62 thru 5-67, 5-69, 5-71, 5-73, 6-95 Torrey Pines, California, 4-37 Toskane, 7-206, 7-215, 7-216, 7-222, 7-234, 7-239 Tracers (see also Artificial tracers; Flourescent tracers; Natural tracers; Radioactive tracers), 4-133 thru 4-145 Transition zone, 4-72, 4-73, 5-22, 5-23 Transitional depths, 2-10 groins, 5-45 thru 5-47 water, 2-9, 2-15, 2-24, 2-25, 2-31 thru 2-33, 2-37, 2-62, 2-64, 3-24, 3-55, 7-63, 7-117 Translatory wave, 2-4, 2-56 Transmission coefficient, 2-112, 7-62, 7-66, 7-67, 7-73, 7-80 thru 7-82, 7-88 wave (see Wave transmission) Transport (see Littoral transport; Longshore transport; Mass transport; Sand movement; Sediment transport) Transverse forces, 7-132, 7-133, 7-135 Treasure Island, Florida, 6-25 Tribar, 5-59, 6-90, 6-92, 7-81, 7-83, 7-206, 7-209, 7-211, 7-215 thru 7-217, 7-220, 7-225, 7-226, 7-231, 7-234, 7-239, 8-47, 8-50 thru 8-52, 8-54, 8-55, 8-59 thru 8-61, 8-63 thru 8-65, 8-67, 8-69, 8-70, 8-73 Trochoidal Wave Theory, 2-2 Tropical storm, 3-110, 3-119, 3-123, 3-126, 4-31, 4-34, 4-35 Tsunami, 1-1, 1-4, 1-7, 2-5, 2-56, 3-88, 3-89, 3-92 thru 3-94, 3-96, 4-46, 7-1 Tybee Island, Georgia, 6-25 ven ieee Umpqua River, Oregon, 4-37 Unalaska Island, Alaska, 3-118 Underlayer, 7-210, 7-227 thru 7-229, 7-236, 7-239, 7-240, 7-242, 7-246, 8-48, 8-63, 8-64, 8-66, 8-69, 8-71 thickness, 8-62, 8-63, 8-73 Unified soil classification, 4-12, 4-13 Unit weight (see also Mass density; Specific gravity), 4-18, 7-213, 7-214, 7-229, 7-233, 7-236, 7-257, 7-258, 7-260 concrete, 8-47, 8-49, 8-54 thru 8-57, 8-70, 8-72, 8-73 littoral material (see also Immersed weight), 4-18 rock, 7-237, 7-243, 8-58, 8-60 soil, 7-256 stone material, 8-59, 8-60 water, 7-205, 7-243, 8-49, 8-76 Uplift forces, 6-6, 6-97, 7-147, 7-235, 7-238, 7-260, 8-80 =awVia es Variability, wave (see Wave height variability) Vegetation (see also American beach grass; Beach grasses; Dune construction using vegetation; European beach grass; Panic grasses; Sea oats), 1-13, 1-17, 3-66, 3-72, 3-75, 4-5, 4-6, 4-76, 5-24, 5-26, 6-37 thru 6-39, 6-43, 6-44, 6-48, 6-51 Velocity (see also Bottom velocity; Current velocity; Fall velocity; Fluid velocity; Friction velocity; Group velocity; Longshore current velocity; Phase velocity; Water particle velocity; Wave celerity; Wind speed), 2-113, 3-12, 3-25, 3-35, 3-83, 3-84, 4-47, 4-48, 4-54, 4-55, 4-70, 4-146, 4-161 thru 4-163, 5-28, 7-102, 7-135, 7-138, 7-139, 7-249 thru 7-253 forces, 7-249 Venice, California, 4-37, 5-62 Ventura, California, 4-145, 7-226 Marina, 6-61 Vertical piles, 7-102, 7-110, 7-118, 7-127, 7-129, 7-135, 7-150, 7-157 walls, 1-17, 2-112, 2-113, 6-6, 7-45, 7-161, 7-162, 7-170, 7-174, 7-177, 7-178, 7-182, 7-187, 7-196, 7-199, 7-200, 7-203 Virginia Beach, Virginia, 4-37, 4-41, 6-7, 6-25, 6-54 Key, Florida, 6-25 Viscosity, water (see Kinematic viscosity) == Wis = Wachapreague Inlet, 4-159 Waianae Harbor, Oahu, Hawaii, 7-226 Waikiki Beach, Hawaii, 4-91, 5-62 Wallops Island, Virginia, 6-77 Walls (see also Angle of wall friction; Breaking wave forces on walls; Nonbreaking wave forces on walls; Nonvertical walls; Seawalls; Vertical walls; Wave forces on walls), 1-20, 2-126, 5-2 thru 5-6, 6-6, 6-14, 6-88, 7-3, 7-25, 7-45, 7-51 thru 7-53, 7-162, 7-163, 7-172 thru 7-174, 7-177, 7-178, 7-180 thru 7-183, 7-187, 7-190, 7-192 thru 7-197, 7-199 thru 7-201, 7-235, 7-242, 7-249, 7-256, 7-257, 7-260 Walton County, Florida, 4-77, 4-79 Washington, D.C., 3-116 Water depth (see also Deep water; Relative depth; Shallow water; Shoaling water; Transitional water), 2-2, 2-9, SUBJECT INDEX Water (Cont) depth (Cont) 2-10, 2-13, 2-46, 2-60, 2-62, 2-64, 2-90, 2-122, 2-124, 2-126, 2-128, 3-2, 3-17, 3-45, 3-46, 3-55 thru 3-67, 3-70 thru 3-72, 3-74, 3-76, 3-107, 3-119, 3-122, 4-53, 4-66 thru 4-71, 4-73 thru 4-75, 4-94, 4-166, 4-180, 5-5, 5-6, 5-34, 5-65, 5-73, 6-6, 6-88, 6-93, 6-95, 7-3 thru 7-5, 7-16, 7-35, 7-41, 7-43, 7-61, 7-62, 7-81, 7-94, 7-101, 7-105, 7-106, 7-110, 7-162, 7-202 thru 7-204, 7-243, 7-245, 7-246, C-3, C-31 thru C-33 level (see also Design water level; Initial water level; Maximum water level; Mean water level; Stillwater level), 1-6, 1-10, 1-15, 3-1, 3-88, 3-89, 3-93, 3-95, 3-96, 3-99, 3-101, 3-102, 3-104, 3-105, 3-107, 3-109, 3-110, 3-111, 3-115 thru 3-119, 3-122, 3-123, 3-126, 3-127, 4-5, 4-36, 4-43, 4-44, 4-49, 4-62, 4-108, 4-110 thru 4-112, 4-134, 4-161, 4-162, 5-3, 5-6, 5-20, 5-37, 5-39, 6-80, 7-1 thru 7-3, 7-14, 7-16, 7-62, 7-82, 7-163, 7-203, 7-245, 7-255, 8-7, 8-9 thru 8-12, 8-46, 8-81 fluctuations (see also Sea level changes), 1-1, 1-16, 1-17, 3-88, 3-89, 3-96, 4-62, 5-20 particle, 1-5, 1-6, 2-1, 2-2, 2-4, 2-15, 2-18, 2-20, 2-43, 2-55, 2-113, 2-114, 4-46, 4-47, 4-50, 7-203, A-43 displacement, 2-15 thru 2-18, 2-20, 2-32, 2-35 velocity, 2-7, 2-25, 2-32, 2-35, 2-36, 2-57, 2-59, 2-129, 7-101, 7-103, 7-142 Waukegan, Illinois, 4-91 Wave (see also Breaking wave; Broken wave; Capillary wave; Clapotis; Cnoidal wave; Complex wave; Deep water wave; Design breaking wave; Design wave; Dispersive wave; Finite-amplitude wave; Gravity wave; Hurricane wave; Monochromatic wave; Nonbreak- ing wave; Ocean wave; Oscillatory wave; Periodic wave; Probable maximum wave; Progressive wave; Random wave; Resonant wave; Seiche; Shallow water wave; Significant wave; Simple wave; Sinusoidal wave; Solitary wave; Standing wave; Storm wave; Translatory wave; Tsunami; Wind wave), 1-1, 1-4 thru 1-7, 1-16, 2-1 thru 2-6, 2-11, 2-56, 2-77, 2-90, 2-92, 2-99, 3-1, 3-20, 3-25, 3-42 thru 3-44, 4-1, 4-12, 4-57, 4-58, 4-76, 4-147, 4-148, 5-1, 5-2, 5-9, 5-20, 5-21, 5-35, 5-36, 5-57, 5-72, 7-5, 7-11, 7-13, 7-54, 7-55, 7-103, 7-138, 7-180, 7-202, 7-247, C-32 action, 1-1, 1-3, 1-8, 1-12, 1-13, 1-16, 1-23, 2-18, 2-71, 3-89, 3-99, 3-109, 4-1, 4-22, 4-43, 4-44, 4-66, 4-89, 4-110, 4-120, 4-148, 4-149, 4-150, 4-174, 5-2, 5-20, 5-21, 5-28, 5-30, 5-33, 5-55, 5-56, 5-59, 5-61, 6-1, 6-5, 6-6, 6-13, 6-14, 6-26, 6-32, 6-59, 6-72, 6-75, 6-83, 6-88, 6-93, 7-1 thru 7-4, 7-16, 7-100, 7-101, 7-149, 7-150, 7-160, 7-171 thru 7-173, 7-177, 7-203, 7-204, 7-208, 7-225, 7-235, 7-238 thru 7-240, 7-246, 7-254, 7-256, 8-47, 8-49, 8-50, 8-75 angular frequency, 2-7 approach (see also Angle of wave approach), 1-7, 2-66, 2-71, 2-78 thru 2-89, 2-92, 2-106, 5-35, 5-37, 5-40, 8-26, 8-34, 8-74 attack (see also Storm attack on beaches), 1-3, 1-6 thru 1-8, 1-10, 1-13, 1-20, 3-109, 4-23, 4-43, 4-76, 4-116, 5-3, 5-4, 5-24, 5-26, 5-27, 5-54, 5-63, 5-64, 6-39, 6-83, 6-92, 7-208, 7-210 celerity, 2-7, 2-10, 2-11, 2-14, 2-23, 2-25, 2-27, 2-32, 2-34, 2-37, 2-44, 2-46, 2-54, 2-55, 2-57, 2-59, 2-60, 2-62, 2-63, 2-129, 3-20, 4-47, 4-48, 4-70, 4-93, 5-65, 7-133, 7-192, 8-33, C-33 characteristics, 1-5, 2-9, 2-32, 2-34, 2-44, 2-112, 3-15, 3-24, 3-43, 4-4, 4-71, 5-55, 7-1, 7-3, 7-8, 7-14, 7-16, 7-44, 7-61, 7-170, 7-229, 8-43 Wave (Cont) climate (see also Littoral wave climate; Nearshore wave climate; Offshore wave climate; Wave condi- tions), 3-42, 4-4, 4-22, 4-23, 4-29, 4-30, 4-36, 4-40, 4-42, 4-44, 4-45, 4-63, 4-71, 4-73, 4-75, 4-115, 4-134, 4-140, 5-20, 5-21, 5-35, 5-37, 5-41, 5-65, 6-1, 6-16, 6-26, 6-59, 6-76, 7-14, 7-17, 7-231 conditions (see also Design wave conditions; Wave climate), 2-2, 2-54, 2-122, 3-1, 3-39, 3-44, 3-47, 3-51, 3-83, 3-87, 3-107, 4-1, 4-4, 4-6, 4-29, 4-36, 4-43, 4-46, 4-50, 4-68, 4-70, 4-73, 4-76, 4-78, 4-83, 4-86, 4-90, 4-92, 4-93, 4-108, 5-30, 5-64, 5-67, 5-71, 6-36, 6-73, 6-76, 7-1 thru 7-4, 7-8, 7-13, 7-14, 7-16, 7-58, 7-61, 7-81, 7-82, 7-93, 7-105, 7-109, 7-110, 7-131, 7-143, 7-161, 7-170, 7-172, 7-173, 7-180, 7-201 thru 7-204, 7-210, 7-211, 7-225, 7-237, 7-239, 8-12, 8-23, 8-26, 8-47 crest, 1-5, 2-7, 2-8, 2-25, 2-27, 2-28, 2-37, 2-38, 2-46, 2-55 thru 2-57, 2-59, 2-60, 2-62 thru 2-64, 2-67, 2-71, 2-73, 2-75, 2-76, 2-78 thru 2-89, 2-91, 2-92, 2-99, 2-100, 2-105, 2-106, 2-108 thru 2-110, 2-129, 3-104, 4-4, 4-30, 4-46, 4-53, 4-59, 4-92, 4-94, 4-160, 5-41, 5-63 thru 5-67, 5-71, 7-4, 7-106, 7-133, 7-141, 7-142, 7-150 thru 7-154, 7-171, 7-174, 7-180, 7-195, 7-199, 8-77, 8-78, 8-85, C-35 data, 4-32, 4-33, 4-42, 4-76, 4-78, 4-93, 4-134, 4-142, 4-147, 5-20, 5-32, 7-2, 7-3, 7-14, 7-15, 7-245, 8-12, 8-90 decay (see also Wave field decay), 1-6, 3-14, 3-21, 3-24, 3-66 thru 3-68, 3-70, 3-71, 3-75, 3-76, 4-29 distance, 1-6, 7-89 diffraction (see also Diffraction coefficient), 1-1, 2-75, 2-76, 2-90 thru 2-92, 2-99, 2-101 thru 2-103, 2-105, 2-106, 2-108, 2-109, 5-32, 5-65, 5-71, 7-89 analysis, 5-60, 7-16, 7-17, 8-74 calculations, 2-75, 2-77 diagram, 2-77 thru 2-90, 2-93, 2-99, 2-104, 2-105, 2-107, 2-109, 7-89, 7-92, 7-94 thru 7-98 direction, 2-60, 2-66, 2-67, 2-100, 2-109, 2-124, 3-14, 3-19, 3-39, 3-67, 3-71, 3-74, 3-80, 3-85, 3-87, 3-104, 4-29, 4-31, 4-36, 4-40, 4-65, 4-92, 4-103, 4-134, 4-143, 4-147, 4-148, 4-150, 5-55, 5-57, 5-64, 5-65, 5-67, 5-71, 7-2, 7-3, 7-12, 7-91, 7-92, 7-95 thru 7-98, 7-132, 7-151, 7-199, 7-210, 8-26, 8-37, 8-87, A-43, C-35 effects (see also Storm attack on beaches; Wave attack), 2-1, 2-124, 4-71, 4-73 thru 4-75 energy (see also Kinetic energy; Longshore energy; Potential energy; Wave power; Wave spectra), 1-9, 1-10, 1-14, 1-16, 1-17, 1-22, 1-24, 2-1, 2-2, 2-4, 2-5, 2-25 thru 2-31, 2-38, 2-44, 2-58, 2-60, 2-62, 2-71, 7-74, 2-75, 2-109, 2-112, 2-116, 2-119, 2-122, 2-124, 2-126, 3-5, 3-11 thru 3-13, 3-18 thru 3-21, 3-24, 3-39, 3-42, 3-43, 3-55, 3-78, 3-107, 4-6, 4-30, 4-43, 4-66, 4-71, 4-86,.4-90, 4-92, 4-149, 4-173, 5-3, 5-6, 5-7, 5-24, 5-61, 5-63, 5-64, 5-69, 5-71, 6-16, 6-88, 6-95, 7-2, 7-13, 7-61, 7-62, 7-64, 7-91, 7-179, 7-254, C-3, C-34 transmission, 2-26, 2-63 field, 2-90, 2-105, 2-108, 3-11, 3-12, 3-14, 3-19 thru 3-21, 3-24, 3-42, 3-77, 3-99, 4-69 decay, 3-21 forces (see also Breaking wave forces; Nonbreaking wave forces), 1-3, 1-20, 1-24, 2-12, 2-57, 7-100 thru 7-103, 7-143, 7-149, 7-151, 7-153, 7-162, 7-163, 7-174, 7-181, 7-187, 7-192, 7-193, 7-198, 7-200, 7-201, 7-204, 7-207, 7-245, 7-247, 7-254 on piles, 7-100, 7-101, 7-146, 7-156 on structures, 7-1, 7-3, 7-161 on walls, 7-100 SUBJECT INDEX Wave (Cont) forecasting (see Wave hindcasting; Wave prediction) frequency (see also Wave angular frequency), 2-4, 2-108, 3-19, 3-42, 4-102, 7-2, 7-132, 7-133 fully arisen sea (see Fully arisen sea) generation, 2-1, 3-1, 3-19 thru 3-21, 3-24, 3-26, 3-55, 3-77, 4-29 group velocity (see Group velocity) growth, 3-14, 3-20, 3-21, 3-24, 3-26, 3-27, 3-30, 3-41, 3-43, 3-44, 3-47, 3-51, 3-53, 3-55, 3-66, 3-70 height (see also Breaking wave height; Deep water significant wave height; Design breaking wave height; Design wave height; Mean wave height; Nonbreaking wave height; Significant wave height), 1-5, 2-3, 2-20, 2-27, 2-30, 2-31, 2-58, 2-67, 2-91, 2-105, 2-117, 2-119, 2-122, 3-39, 3-44, 3-45, 3-47, 3-55, 3-66, 3-74 thru 3-77, 3-80, 4-44, 5-65, 7-2, 7-33, 7-34, 7-39, 7-41, C-34, C-35 average, 3-2, 3-6 distribution, 2-75, 3-7 thru 3-11, 3-81, 4-43, 4-142, 4-143, 7-2, 7-39 Rayleigh distribution (see Rayleigh distribution) root-mean-square, 3-5, 4-93 statistics, 3-81, 4-40, 4-43, 4-105 variability, 3-2, 3-81 hindcasting (see also Wave prediction), 2-66, 3-1, 3-18, 3-21, 3-24, 4-42, 4-77, 4-78, 7-17, 8-26, 8-28 thru 8-30, 8-85, 8-90 length (see also Deep water wave length), 1-5, 1-6, 2-2, 2-7, 2-9, 2-18, 2-24, 2-25, 2-29, 2-32, 2-34, 2-37, 2-44 thru 2-46, 2-60, 2-62, 2-64, 2-66, 2-77 thru 2-99, 2-101 thru 2-105, 2-107, 2-108, 2-113, 2-115, 2-116, 2-119, 2-121, 2-124, 2-126, 3-2, 3-93, 3-98, 4-47, 4-85, 5-64, 5-65, 5-71, 5-72, 7-4, 7-35, 7-93, 7-94, 7-99, 7-101, 7-103, 7-104, 7-106, 7-108, 7-109, 7-144, 7-150 thru 7-152, 7-155, 7-181 thru 7-183, 8-33, C-3, C-31, C-32, C-34 mass transport (see Mass transport) mechanics, 2-1 motion, 1-1, 1-6, 1-9, 2-1, 2-59, 2-112, 2-115, 4-4, 4-46, 4-48, 7-138 nonlinear deformation (see Nonlinear deformation) number, 2-7, 2-30, 2-112 overtopping (see Overtopping) period (see also Design wave period; Significant wave period), 1-5, 1-6, 2-4, 2-7, 2-9, 2-24, 2-25, 2-31, 2-36, 2-42 thru 2-45, 2-54, 2-60, 2-66, 2-112, 2-122, 3-2, 3-13, 3-14, 3-39, 3-46, 3-51, 3-55 thru 3-65, 3-70, 3-71, 3-74, 3-77, 3-80, 3-81, 3-85 thru 3-87, 3-101, 3-105, 4-29 thru 4-31, 4-38, 4-44, 4-51, 4-68, 4-69, 4-74, 4-85, 4-94, 4-104, 5-69, 7-2, 7-9, 7-14, 7-15, 7-43, 7-54, 7-61, 7-62, 7-89, 7-92, 7-95 thru 7-99, 7-101, 7-105, 7-110, 7-144, 7-170, 7-174, 7-178, 7-182, 7-183, 7-187, 7-203, 7-204, 8-23, 8-33, 8-37, 8-74, 8-76, C-30 thru C-33 potential energy (see Potential energy) power (see also Wave energy), 2-25, 2-26, 2-44, 2-63, 3-5 prediction (see also Deep water wave prediction; Hurricane wave prediction; Shallow water wave prediction; Wave hindcasting), 1-1, 3-1, 3-19, 3-21, 3-24, 3-27, 3-32, 3-39, 3-41 thru 3-44, 3-47, 3-49, 3-50, 3-53, 3-67, 3-88 fetch (see Fetch) method (see Sverdrup-Munk-Bretschneider wave prediction method) models (see also Pierson-Neuman-James wave pre- diction model), 3-14, 3-26, 3-42 wind duration (see Wind duration) pressure (see also Pressure pulse; Subsurface pressure), 7-192, 7-193, 7-195, 7-241 profile, 2-2, 2-8, 2-10, 2-32, 2-37, 2-44 thru 2-46, 2-55, 3-15, 4-29, 7-5 propagation (see Wave transmission) Wave (Cont) reflection (see also Reflection coefficient), 1-1, 2-109, 2-111 thru 2-114, 2-116 thru 2-118, 2-122, 2-124, 3-98, 7-8, 7-62, 7-89 refraction (see also Refraction coefficent; Refrac- tion template), 2-60 thru 2-62, 2-64, 2-67, 2-71 thru 2-74, 2-126, 4-29, 4-30, 5-24, 5-32, 8-33, 8-35, 8-36, A-45 analysis, 2-62, 2-63, 2-68, 2-71, 2-135, 3-24, 5-60, 7-1, 7-11, 7-13, 7-16, 7-17, 8-26, 8-32, 8-36 computer methods, 2-71 diagrams, 2-64, 2-66, 2-70 thru 2-72, 2-74, 2-109, 7-14, A-46 fan diagrams, 2-70, 2-72, 7-14 orthogonal method, 2-66 R/J method, 2-70 wave-front method, 2-71 runup, 3-99, 3-101, 3-104 thru 3-106, 4-66, 4-76, 4-108, 4-110, 5-3, 5-4, 5-20, 5-58, 7-16, 7-18, 7-25, 7-28 thru 7-35, 7-37 thru 7-44, 7-55, 7-58, 7-59, 7-62, 7-67, 7-72, 7-73, 7-75, 7-192, 7-194, 7-196, 7-197, 7-210, 7-229, 7-239, 7-240, 8-48 composite slopes, 7-35, 7-36, 7-40 impermeable slopes, 7-16, 7-18 thru 7-23, 7-26, 7-27, 7-34 rubble-mound structure, 7-18 scale effects, 7-16, 7-18, 7-24, 7-34, 7-37, 7-55 setdown, 3-99, 3-101, 3-107, 3-109, 3-111 setup, 3-88, 3-89, 3-99 thru 3-102, 3-104 thru 3-109, 3-111, 3-115, 4-49, 4-50, 5-20, 5-37, 7-35, 8-12, 8-46 spectra (see also Wave energy), 2-108, 3-11 thru 3-14, 3-77, 3-78, 7-43, 7-89, 7-93, 7-94, 7-149, 7-209 steepness, 1-9, 1-10, 1-13 thru 1-15, 2-37, 2-60, 2-112, 2-116, 2-117, 2-119, 2-129 thru 2-131, 3-12, 3-15, 3-86, 3-107, 4-43, 4-44, 4-49, 4-85, 7-5, 7-7, 7-9, 7-16, 7-44, 7-64, 7-73, 7-101, 7-106, 7-162 swell (see Swell) theories (see also Airy Wave Theory; Cnoidal Wave Theory; Finite Amplitude Wave Theory; Linear Wave Theory; Progressive Wave Theory; Small Amplitude Wave Theory; Solitary Wave Theory; Stokes Wave Theory; Stream Function Wave Theory; Trochoidal Wave Theory), 1-1, 2-1 thru 2-4, 2-31, 2-33, 7-102, 7-105, 7-110, 7-117, 7-136, 7-141, 7-143, 7-144 regions of validity, 2-31, 2-33 train, 2-23 thru 2-25, 3-4, 3-11, 3-12, 3-14, 3-18, 3-21, 3-43, 3-77, 4-30, 4-31, 4-36, 4-39, 4-93, 7-3, 7-108, 7-209 translation (see Translatory wave) transmission (see also Transmission coefficient), 2-1, 2-3, 2-8, 2-14, 2-15, 2-26, 2-36, 2-38, 2-109, 2-119, 3-14, 3-20, 3-21, 3-122, 7-1, 7-16, 7-61 thru 7-65, 7-67 thru 7-69, 7-73, 7-74, 7-76 thru 7-87, 7-89, 7-150, 7-158, 7-192, 7-225 variability (see Wave height variability) velocity (see Wave celerity) Weir, 1-24, 5-34, 6-59, 6-61, 6-74, 6-75 groin, 5-40 jetty, 1-24, 1-25, 4-89, 5-30, 5-31, 5-34, 5-40, 6-59, 6-74, 6-75 Well- graded sediment, 4-14 sorted sediment, 4-14 Wentworth size classification, 4-12, 4-13 West Quoddy Head, Maine, 3-92 Palm Beach, Florida, 3-79 Westhampton, New York, 4-61, 4-77, 4-79 Beach, 2-61, 4-1, 4-2, 4-11, 5-54, 6-82 Willets Point, New York, 3-116, 3-124, 3-125 Wilmington, North Carolina, 3-117, 3-124, 3-125 Beach, 6-22 SUBJECT INDEX Wind (see also Geostropic wind; Gradient wind), 1-4, 1-6, 1-7, 1-10, 1-13, 2-62, 3-1, 3-20, 3-21, 3-24, 3-26, 3-27, 3-30, 3-32 thru 3-35, 3-37, 3-39, 3-42 thru 3-44, 3-51, 3-52, 3-55, 3-81 thru 3-85, 3-87, 3-96, 3-107, 3-110, 3-111, 3-119, 3-123, 3-126, 3-127, 4-1, 4-4, 4-5, 4-12, 4-29, 4-30, 4-42 thru 4-44, 4-48, 4-76, 4-101, 4-112, 4-119, 4-120, 4-127, 4-128, 5-1, 5-3, 5-4, 5-57, 6-37, 6-39, 6-40, 6-47, 6-49, 6-76, 7-44, 7-54, 7-61, 7-253, 7-254, 8-21, 8-22 action, 1-13, 1-16 data, 3-26, 3-30, 3-32, 3-33, 7-3, 7-17, 8-12, 8-21 thru 8-23 direction, 3-19, 3-21, 3-25, 3-43, 6-39, 7-43, 7-44, 8-21 duration, 1-6, 3-26 thru 3-29, 3-32, 3-33, 3-35, 3-41 thru 3-44, 3-47, 3-49 thru 3-53, 3-66, 3-77, 4-29, 7-1, 8-21 energy, 3-21, 3-54 estimation, 3-24, 3-26, 3-32 thru 3-35, 3-39, 3-41, field (see also Hurricane wind field), 3-21, 3-24, 3-25, 3-33, 3-39, 3-53, 3-81, 3-83, 3-126, 3-127 frequency, 8-21 frictional effects, 3-24 generated wave (see Wind wave) profile, 3-16, 3-20, 3-82 roses, 8-21, 8-22 sand transport (see Sand movement) setup (see also Surge), 1-7, 3-93, 3-96, 3-104, 3-107, 3-127, 4-110, 5-1, 5-57, A-51 speed, 1-6, 1-7, 3-20, 3-24 thru 3-27, 3-30 thru 3-36, 3-38 thru 3-44, 3-47, 3-49 thru 3-53, 3-66, 3-67, 3-70, 3-71, 3-74, 3-76, 3-77, 3-81 thru 3-84, 3-96, 3-110, 3-119, 3-121, 3-126 thru 3-128, 4-5, 4-29, 4-44, 4-48, 6-38 thru 6-40, 7-1, 7-43, 7-44, 7-57, 8-9, 8-21, 8-24 adjusted, 3-30, 3-66 duration (see Wind duration) stress, 1-6, 3-32, 3-42, 3-66, 3-70, 3-74, 3-89, 3-96, 3-119, 3-121, 3-127 factor, 3-30, 3-32, 3-33, 3-35, 3-44, 3-47, 3-49 thru 3-51, 3-53, 3-56 thru 3-66 velocity (see Wind speed) wave, 1-4 thru 1-6, 2-1, 3-4, 3-19, 3-24, 3-66, 4-77, 7-1, 7-39, 7-58, 7-81, 7-89 Winthrop Beach, Massachusetts, 5-62, 5-68 Woods Hole, Massachusetts, 3-116, 3-124, 3-125 Wrightsville Beach, North Carolina, 4-37, 5-21, 5-22, 6-16, 6-19, 6-20, 6-25, 6-68, 6-74, 6-83 on ee Yakutat, Alaska, 3-118 Yaquina Bay, Oregon, 4-37 Aw pas Zero Up Crossing Method, 3-2 4% U.S. GOVERNMENT PRINTING OFFICE: 1984-752-090 D=19 Ti fa ae REEL ET Peet et Soe ee Point Reyes National Seashore, California, 8 April 1969