U.S. Army Coastal Engineering ——— Research GATALIGRAI SAR SHORE PROTECTIO MANUAL Volume II DEPARTMENT OF THE ARMY CORPS OF ENGINEERS. : 1975 \\ Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. U.S. Army Coastal Engineering Research Center Kingman Building Fort Belvoir, Virginia 22060 GULF COAST OF FLORIDA — U UsUL UUbUrrU SHORE PROTECTION MANUAL VOLUME IL ( Chapters 5 Through 8 ) U.S. ARMY COASTAL ENGINEERING RESEARCH CENTER 1975 Second Edition —————————————————————— ee For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price $15.05 per 3-part set. (sold in sets only) Stock Number 008-022-00077-1 Catalog Number D 103.42/6:SH7/V.1-3 CHAPTER 1 1. 1.2 1:3 1.4 1.5 1.6 2 2.1 2.2 2.3 2.4 2.5 2.6 APPENDIX Dan, TABLE OF CONTENTS VOLUME I INTRODUCTION TO COASTALENGINEERING. . .- INTRODUCTION TO THE SHORE PROTECTION MANUAL THE SHORE ZONE. : THE SEA IN MOTION . : THE BEHAVIOR OF BEACHES . : EFFECTS OF MAN ON THE SHORE CONSERVATION OF SAND . MECHANICS OF WAVE MOTION INTRODUCTION . WAVE MECHANICS . WAVE REFRACTION . WAVE DIFFRACTION. WAVE REFLECTION . BREAKING WAVES . . REFERENCES AND SELECTED BIBLIOGRAPHY WAVE AND WATER LEVEL PREDICTIONS INTRODUCTION CHARACTERISTICS OF OCEAN WAVES . WAVE FIELD - WIND INFORMATION NEEDED FOR WAVE PREDICTION SIMPLIFIED WA VE—PREDICTION MODELS . WAVE FORECASTING FOR SHALLOW WATER . HURRICANE WAVES. . . WATER LEVEL FLUCTUATIONS cps. X6 REFERENCES AND SELECTED BIBLIOGRAPHY LITTORAL PROCESSES INTRODUCTION . LITTORAL MATERIALS. . . LITTORAL WAVE CONDITIONS NEARSHORE CURRENTS LITTORAL TRANSPORT . ROLE OF FOREDUNES IN SHORE PROCESSES . SEDIMENT BUDGET . . ENGINEERING STUDY OF LITTORAL PROCESSES REFERENCES AND SELECTED BIBLIOGRAPHY VOLUME III GLOSSARY OF TERMS LIST OF SYMBOLS. . . MISCELLANEOUS TABLES AND PLATES. SUBJECT INDEX SECTION un Anunununwnnnn Pee merste Wena: ue ar ote unUMnnnMYN ro) TABLE OF CONTENTS VOLUME II CHAPTER 5 - PLANNING ANALYSIS GENERAL . SEAWALLS, BULKHEADS AND REVETMENTS. FUNCTIONS . . LIMITATIONS .. . FUNCT IONAL PLANNING OF THE. STRUCTURE. USE AND SHAPE OF THE STRUCTURE. . . LOCATION OF STRUCTURE WITH RESPECT TO SHORELINE LENGTH OF STRUCTURE . HEIGHT OF STRUCTURE .. . ay at fo Foe Oe DETERMINATION OF GROUND ELEVATION IN FRONT OF A STRUCTURE . PROTECTIVE BEACHES. FUNCTIONS . LIMPPATIONS es... PLANNING CRITERIA . Z Direction of Longshore Transport aa ie ee eee ee Supply. wie Selection of poeean Meroe I. Berm Elevation and Width. Slopes. : : Feeder Beach ee ee : SAND DUNES. . FUNCTIONS . SAND BYPASSING. GENERAL . METHODS . Land-based peedeine Siete Floating Dredges. : Land-based Vehicles . LEGAL ASPECTS . GROINS. INTRODUCTION. DEFINITION. PURPOSE os: (2) utes TYPES OF GROINS . Permeable groins. Aununununnwnn 1 aAeBWWND Dw nnww ww i} CN Ww ON On ON ON SECTION nn on nen on non on on mon on on mon | ah nal ist, Wists) einen cree te] ited oil oil ain hile wn AnunnNunwww aun ananwnn DNANWAAOD OV High and Low Groins . Adjustable Groins GROIN OPERATION. . . DIMENSIONS OF GROINS. Horizontal Shore Section. Intermediate Sloped Section . Outer Section . Spacing of Groins . Length of Groins. ALIGNMENT OF GROINS . . . . ORDER OF GROIN CONSTRUCTION says LIMITATIONS ON THE USE OF GROINS. ECONOMIC DETERMINATION OF GROIN CONSTRUCTION. LEGAL ASPECTS . JETTIES . DEFINITION. TNOPES) 5 SIMUIUMG 5S og. oc EFFECTS ON THE. SHORELINE. BREAKWATERS - SHORE-CONNECTED . DEFINITION. LYPESHe SUUMUNG Sb. 5 c EFFECT ON THE SHORELINE : BREAKWATERS - OFFSHORE. DEFINITION. WARES 5 SIIMUNGG 6 6 10 EFFECTS ON THE. SHORELINE. Xa 6 . OPERATION OF AN OFFSHORE BREAKWATER ; OFFSHORE BREAKWATERS IN SERIES. HEIGHT OF AN OFFSHORE BREAKWATER. ENVIRONMENTAL CONSIDERATIONS. REFERENCES AND SELECTED BIBLIOGRAPHY. CHAPTER 6 - STRUCTURAL FEATURES INTRODUCTION. SEAWALLS, BULKHEADS, AND REVETMENTS . INGE Go 6 SELECTION OF STRUCTURAL TYPE. Foundation Conditions . Exposure to Wave Action . Availability of Materials . iv SECTION PAGE 6.5 PROTECGHEVEMBEACHESP eres vr SRR aoe oe; oe atyeaeeaiedee ey ORG Geol GENERAL. . . el Ree kone el Ee Tk 2, 3 GeO 6.52 EXISTING PROTECTIVE. BEACHES. tea RN Oe els. 3s DGEG Geo2 il Cariilana-Beach}.NortheCarolinalne] .. aye-aren 2... . PEREZ 6.322 Sea Girt, New Jersey. . iceikitions 3 « MOSZ9 G05235 Redondo eae (Malaga gore Gels Eornnes LPTs. «2 MGSS2Z 6.4 SANDS DUNES vites,. Stee ben 6 4c, Hersey we, fa eS Re eee ee co) OO 6.41 SANDEMOVEMENT Aw. «Sistiecak Lcecite ie Savecedc.| we eeeeitd o. -) 1O=50 6.42 DUNE FORMATION... 3 ae teae Se eee ta es CeO Soy 6.43 DUNE CONSTRUCTION - SAND FENCE «eA ERT AM. AQT SET. “tO= 3517 6.44 DUNEMGONSTRUGIION®=. VEGETATION) .95) BSw « ~ « Glaatecd = « Mo-4S 6.441 IBEbiersiesighe Ehal Drctolcesiiys 6 GF 6 5 oo 9 5 5 6 6 6 oO y OAS 6.442 SPUCINGA Hubeeeet PacASBESR. © cc ei Shek a re pg ie) ORE 6.443 NUERTENESE: See WEK cri. Key Sater 6 oes 1 a Lh KOO oo SOT 6.444 SCCUE Ste ss ays Sb, dacce Bleed Js te eae oats ae OR 6.445 Disease and press seaceee RA. HOLGER -eLe ees. SOm4o 6.446 Pieter (cha joc atta os G0 Seo De ovo Go cong co oc Go =4e 6.447 TrappingiGapact tyes we weeks) ti 20.0. CAA Crt. Oo 6.448 DuncwEdlevatione: Poms, Chectis.. ola =, sd elle dey eure a sa sae eQeee Om 6.449 CostPPactorse ees Fee Tees ath cin 9k wey ten oe Cue oa in ome ee ROO 625 SAND BYPASSING. . . Ce Oe ee Th) eee Sy! 6.51 FIXED BYPASSING PLANTS Ske Ras Bate, CoRR TS. ; GE De 6. 5d South Lake Worth Inlet, pailgri das b RO URI TAMIR; SonS6 6.512 LakesWortheinilet.. Eioriidact. 45 ce esimedioe oy 6) ok Gee. ~ ODO 6.52 BLOATING e BYPASSINGPLANES:. .«. «..% « «2 BROKEN BILTON... 2 MOES9) On 52) Port Hueneme, California... QO aNGIn AEteed -o, . F6LS9 G.o22 Channel Islands Harbor, Gea founiee Ul verter «=, < Gear 6.523 Santa Barbara, faint 23h RQRORSL VISE IR. a. BOS6S 6.524 Hitiishoromimleted Plorida ie, BG.gegie o> kiewiae <. os HOOD 6.525 Masionborosiniet, North Garoliana. .5. 0. 2) 3 «= «,+.s 8O=05 6.526 Perdido Pass, ANEBENe RE tare CIS MARD 2, GURU SYA “IG-65 5 47/ Other Floating Plant prajactsu ihn in tte) SOM IA See MOSOS OLaS LANDSBASED! VEHICLES: 4 = «6 @ «6 » eee eeeele RVR. ©) Ga76 6.6 GROTINS wcrc et be Poco eo sees mane eine ree hv ye tay Nae SALTS Soke ge ee EO LIG 6.61 TRE Sete Mate. k Ae ewe ue in a Ae bo ol Keer Bee OL 0 6.611 TimbersGroinsSie vs ws kw & 6 © w Sw whlew eit cite. ChCeEC Mien eo EORIZO 6.612 Steel. Groins Ks «© «0 « & «or & &. UCP ere oo OO 6.613 ConcenetesGroimsiot Bink RaLIe. LesDnOn tn. AOS eewes es ceo O5 6.614 Rubbille=Mound aGrOamSic, «x, mw sr 1, erty leaciine: Wen PeMMOEr. 6) OOS 6.615 DNS nenGes (Cretenne s Sag ab ob Poser wo iomiG do ob oo Gog OAS 6.62 SELEGIAONLOE SRY PEs a leks. 450 stil, A RO en ee arc. 2 OOS: Oni, JERIMESS, a 5 6 3 ono poo oo oo) 6 PHNSY TeS25 Wall on Rubble Foundation. . . aaNet ie Ay 7.55 BREAKING WAVE FORCES ON VERTICAL WALLS ie LO src ics oor VAS Post MinkinyMethod:) Breaking Wave Forcéese so. ses | . 7o1AG Ue SEV? Walslimoned Rub blemBouncdataloms: tm cues emnenChn -misMtcH on em ce on en 7.555 Wall ofeLowe Hed ohie.,." Rexcus Ion secm flair tomer etoRONE pM ce cp Se 7.34 BROKEN WAVES .... . STARS eee aS 7.341 Wall Seaward of Sin eee ianiok prey Fak Real CSE oh oe ah EMSS 7.342 Wall Shorewardvotpotillwater Wines Scan cutiime - - ~ 7-60 7255 EREEGI! OF VANGEES OF: WAVESARPROAGHS .tismcubit kite) Sines 2 4 7-4 Tie5© ERREGI" OFMAVNONVERTIGATMWALIM Tato tcnteo en Seeeiis of « 2 ) 764! Toil SPAR YS ORSRUBBEESSRRUGKURES! Creal seaeeete.) Sem 8 oe iO ipod 1 Generales .acechan « wa sta ot w o ot ROO SR Gd oe Sor aerow 2 Desmonsractorsee: .0 SCM SUA co) | OS Wieo 3 Hydraulics of Cover Layers Design A) orem serobMeis = 1 eles 7.374 Sellectionyor Stabvltty iGoctficientese wanule Riiseky 0 + 2 775 Tio S importance oO UnneaWeLoht lok lArmor.UnawtS cae -Macmied 2-157. Wows Concrete Armor Units = a) oe we oe eee ee co ES LoSii, Design of Structure Cross- Section. ae Mons 7-2 7.38 STABILITY OF RUBBLE FOUNDATIONS AND TOE PROTECTION ome 7200 Patent IDS atreany. Wemyss AgOsLes eS 6 Go bet oo ob eo 0 oo 6H Wt Stabilatey--Number wane Se creme tw at el wt ly et a a OT 7.383 ATMOLM SCONE herent ed a senee OMEN Loy ca ot Ma yeh ae gp ed op OS 7.4 VELOCITY FORCES - STABILITY OF CHANNEL REVETMENTS. . ... 7-203 WS HMI NCI? IONS SIGNS onto oo Ohonul ool oO oo. o of bee oo =Zt04l 7.6 IGE TRO) NCIS © BMS) OM BY so, Sorid idea dl Gta MS ASI 5 | SBOE Weil EVARUS ION CIES) 1 mat he RG ARS CST dies Pomme oe 6 7/208 esi INOIEINIE, RONCIEIS A 5 dla ie G6 Santa Gal -eon.cne Bans yeu Se weno oe §=—7= 208 IoVt PINSISHL is OAC mele oh oman? hla ec Geos on oyoMoters 7209 Und COHESIVE SOILS . . SSMS As 4 MOS 6 722 7.74 STRUCTURES OF IRREGULAR SECTION. Spa viceerniwaictom one, tos SDI UotS SWUNG EID) WAMUERUUNE Gh G9 GANG a og ii Geo oc a G96 SUG 6 6 FeZVIlZ 7.76 QIPIGINEY IORI S ge Sle ko touidniew 6) Ged soden owe wetiolowe mm ee 6 7H ZINE REFERENCES CAND SELECTED SBY BE VOGRAPEIY wp eemen =) ite) est ns me oe re vil SECTION CHAPTER 8 - ENGINEERING ANALYSIS - CASE STUDY 8.1 INTRODUCTION . Su2 DESIGN PROBLEM CALCULATIONS--ARTIFICIAL OFFSHORE ESUAND See eee GENERAL PROBLEM DESCRIPTION. , DESCRIPTION OF PHYSICAL ENVIRONMENT. Site Location and Conditions . Bathymetry at Site . : Water Levels and Currents. Hurricane Surge. Astronomical Tides . Tidal Currents . Wave Conditions. : Waves Generated in Delavares Bay. Waves Generated in Ocean . PRELIMINARY ISLAND DESIGN. 0 Revetment on Seaward Side of fein Selection of Armor Unit Type . : Quay Wall Caisson on Bay Side of island! Waves in Harbor--Diffraction . 2 Wave Forces During Construction. Earth) Forces ~ LONGSHORE TRANSPORT AT OCEAN CITY, MD. Hindcast Wave Data . Visual Wave Data... : BEACH FILL PROBLEM--OCEAN CITY, “MD 3 REFERENCES . LIST OF FIGURES FIGURE 5-1 General Classification of Coastal peers Prob lems 5-2 Effects of Erosion . 5 . 5-3 Equal Value Contours of yee, vs ‘Relative Differences between Barrow and Native Textural Paramececsarenn. 5-4 Stabilized and Wa eraeing Dunes 5-5 Schematic TCereee of Storm Wave Attack on “Beach and: Dune . 5-6 Types of Leona pereriene Where Sands cTmansten Systems have been Employed . Illustration of a Typical Groin. Factors in Determining Beach Width Updrift of a Groin. vill 5-7 9 5-8 General Shoreline Configuration for Two or More) Groins 0 5-9 PAGE ite i FIGURE Tails aby ot - © RSE GEN ETS he Saar cea RPrOANANBRWNPH i} = is) Groin System Operation with Reversal of Transport. Representation of Intermediate Sloped Groin Section Designed Perpendicular to the Beach -... Stabilized Shoreline Produced by Material Hic ed or Around Downdrift Groin. . . Determining Stabilized Downdrift Beach peoeule : Receded Shoreline oe an Erodible Bottom and Backshore. - . Effects of Engrance Weries. on Shoreline : ‘ Effects of Shore-Connected Breakwater on Shoreline : Siting of Offshore Breakwaters for Sere Harbor Entrance, 2) Siting Deeshosey Eredknceees eel oe Seawalils fort Protection . : Operation of Breakwater. in Diffraction of Wave Forces. Breakwater Acting as Complete Littoral Barrier Causing a Tombolo. Concrete Curved-Face Seawall . 4 oc Concrete Combination Stepped and Curved- Face Seawall Concrete Stepped-Face Seawall. Rubble-Mound Seawall... Rubble-Mound Seawall (Typical- Stage Pisce Concrete Slab and King-Pile Bulkhead . Steel Sheet-Pile Bulkhead. odes Timber Sheet-Pile Bulkhead . Concrete Revetment . Riprap Revetment . sd Interlocking Concrete- Block | Reyolmeues Interlocking Concrete-Block Revetment. Interlocking Concrete-Block Revetment. Protective Beach (Ocean City, New Jersey). Protective Beach (Ocean City, New Jersey). Protective Beach (Virginia Beach, Virginia). Protective Beach (Virginia Beach, Virginia). Protective Beach (Wrightsville Beach, North Carokinay: Protective Beach (Wrightsville Beach, North Carolina). Protective Beach (Carolina Beach, North Carolina). Protective Beach (Carolina Beach, North Carolina). Protective Beach (Harrison County, Mississippi). Protective Beach (Harrison County, Mississippi). Protective Beach at Sea Girt, New Jersey . Protective Beach at Sea Girt, New Jersey . Protective Beach (Redondo Beach, California) Protective Beach (Redondo Beach, California) Foredune System. Erecting Snow-type Sand Fencing. Snow-type Sand Fencing Filled to Capacity. Sand Fence Dune - Padre Island, Texas. i=) ! PrWoOANA UN BWN = DNANDNNADAAAAAA OV l! a Wh FIGURE 6-32 6-33 6-34 6-35 6-36 i DNDNDNDNDNAAANDA AAO i] vAnNununnbp fp HHH HH PWNrFOUOANIAUNHW Sand Fence Dune - Padre Island, Texas. . Sand Fence Deterioration Due to Exposure and Storms. Mechanical Transplanting of American Beachgrass. American Beachgrass Dune - Ocracoke Island, North Carolina . American Beachprass with pans Bence: = (Gore Banks, North Carolina . 0 Sea Oats Dune - Padre Tele Weias. chee Sea Oats Dune - Core Banks, North Carolina . F American Beachgrass Planting with Sand Fence, Core Banks, North Carolina (32 months after planting. Sea Oats Planting, South Padre Island, Texas es months after Planting). : European Beachgrass Dune - Clatsop Spit, Oregon. Types of Littoral Barriers Where Sand-Transfer lei have been Used . Fixed Bypassing Plant - “South Lake Worth Inlet, ‘Plorida. Fixed Bypassing Plant - Lake Worth Inlet, Florida: Sand Bypassing - Port Hueneme, California. ; Sand Bypassing - Channel Islands Harbor, California. Sand Bypassing - Santa Barbara, California . Sand Bypassing - Hillsboro Inlet, Floirda. Sand Bypassing - Masonboro Inlet, North Carolina . Sand Bypassing - Perdido Pass, Alabama . Sand Bypassing - Ventura Marina, California. Sand Bypassing - Fire Island Inlet, New York . Sand Bypassing - Oceanside Harbor, California. Sand Bypassing - Ponce de Leon Inlet, Florida pee ae Daytona Beach) Sand Bypassing - East "Pass, ‘Florida: ; > Sand Bypassing - Shark River Inlet, New esos c Sand Bypassing - Shark River Inlet, New Jersey . Timber Sheet-Pile Groin. ; Timber-Steel Sheet-Pile Groin. Cantilever Steel Sheet-Pile Groin. Cellular Steel Sheet-Pile Groin. Prestressed Concrete Sheet-Pile Groin. Rubble-Mound Groin . 5 5 Quadripod - Rubble-Mound Jetty : Dolos - Rubble-Mound Jetty . Cellular Steel Sheet-Pile Jetty. Tetrapod - Rubble-Mound Breakwater . Tirbar-Rubble-Mound Breakwater . Stone Asphalt Breakwater . - Cellular Steel Sheet-Pile and Sheet - Pile BreElnaten Perforated Caisson Breakwater. Rubble-Mound Breakwater. Definition of Breaker Geometry . FIGURE a and 8 vs Hp/gT*. . . ene Mette, ait eh ems Breaker Height Index, Hy /HS, vs a? Water Wave Steepness, Bpyiete: : Dimensionless Design Brookes Height vs poo heptane at SErUGEUTE. - Breaker Height idexs “Hy /Hs, vs Hy /gT?. ; Logic Diagram for Evaluation of Marine Evieounene : Definition Sketch, Wave Runup and Overtopping. Wave Runup on Smooth , Impermeable Slopes, d,/Hj = 0. . Wave Runup on Smooth, Impermeable Slopes, d,/H} * 0.45 Wave Runup on Smooth, Impermeable Slopes, d,/H} * 0.80 Wave Runup on Smooth, Impermeable Slopes, d,/Hj * 2.0. Wave Runup on Smooth, Impermeable sents d5/Hy! = 320% Runup Correction for Scale Effects : Wave Runup on Impermeable, Vertical Wall vs “HS / 72 2 Wave Runup on impermeable, Riprap, 1:1.5 Sean vs H3/gT? Sieh ls LIEBE. Aiea : Wave Runup on Impermeable, ure oe 1. a5 Slope vs H}/gT? c nite tele Wave Runup on ‘Curved Seawall vs “HS /gT? ; é Wave Runup on Recurved EN ie type) Seawall vs H/T? Wave Runup aad Rundown on ‘Graded Riprap, 1: 2 Slope, Impermeable Base, vs HS/gT?. Comparison of Wave Runup on Smooth Slopes, with Rene | on Permeable Rubble Slopes (data for d,/H} > 3.0) . Calculation of Runup for piesa Slope, Example of a Levee Cross Section. - - Successive Approximation to Runup on a Composite Slope - - Example Problem. Overtopping Parameters, a “and Qs (Smooth Vertical ‘Wall on a 1:10 Nearshore Slope). Overtopping Parameters, a and Q4 (Smooth 1:1. 5 Structure Slope on a 1:10 Nearshore Slope) : Overtopping Parameters, a and ey (Smooth 1: 3 Structure Slope on a 1:10 Nearshore Slope) : : Overtopping Parameters, a and Obs (Smooth 1: 6 senieruta Slope on a 1:10 Nearshore Slope) Overtopping Parameters, a and Q% (Riprapped 1: 1. 5 Structure Slope on a 1:10 Nearshore Slope) Overtopping Parameters, a and Q* (Stepped 1:1.5 Structure Slope on a 1:10 Nearshore Slope) . . Overtopping Parameters, a and Q% (Curved Wall ona 1: 10 Nearshore Slope) ; Overtopping Parameters, a aca Qe (Curved Wall on a 1: 25 Nearshore Slope) Overtopping Parameters, a and % (Recurved Wall on a 1: 10. Nearshore Slope) Wave Transmission over Submoaed and Gueseapped Semacenses: Range of d By Studied by Various Investigators Xi PAGE FIGURE 7335 7-34 7-35 7-36 7-37 7-38 Wave Transmission, Wave Transmission, Wave Transmission, Wave Transmission, Wave Transmission, Impermeable Rubble-Mound Breakwater . Impermeable Rubble-Mound Breakwater . Impermeable Rubble-Mound Breakwater . Permeable Rubble-Mound Breakwater . Permeable Rubble-Mound Breakwater . Classification of Wave Force Problems by Type of Wave Action and by Structure Type . Definition Sketch of Wave Forces on a Vertical Cylinder. Relative Wavelength and Pressure Factor vs d/gT? Wave Theory) ae Ratio of Crest Elevation aboue Geil ivakene teva ae Wave Height. Wavelength Correction Pactar for Finite “Amplitude spffects.. K;m vs Relative Depth, d/gT2 F Kpm vs Relative Depth, di eT! s a: Inertia Force Moment Arm, Sj,,, vs Retleeaue Depth, "d/eT?. Drag Force Moment Arm, Sp,, vs Relative Depth d/gT2. Breaking Wave Height and Regions of Validity Wave Theories. of of of of of a of a of a of a, Isolines Tsolines Isolines Isolines Isolines Isolines Isolines Isolines Variation of Gale, with H/gT2. Variation of iensvense (Airy Theory). vs vs vs vs vs VS VS vs H/gT2 H/ gT2 H/gT2 H/gT2 H/ gT2 H/ gT2 H/gT2 H/gT? and “d/gT2 Seeric d/gT2 d/gT d/gT? d/gT? d/gT? d/gT? d/gT? eoeeee eevee eeeee of Various Keulegan-Carpenter Number and Lift Force and Wave Profile Variation of Drag Gece etetents op: with Reynolds Nunber Deen een Sk6tch - iGalegiationr of Wave “Forees on “Groups of Structurally Connected Piles. Example Variation of Drag, Inertia and Total Wave. Forces with Phase Angle, Example Calculation Definition Sketch - Non-Vertical Definition of Terms 0, Pile. Pressure Distribution - Nonbreaking Waves. Miche-Rundgren Miche-Rundgren Miche-Rundgren Miche-Rundgren Miche-Rundgren Miche-Rundgren Nonbreaking Nonbreaking Nonbreaking Nonbreaking Nonbreaking Nonbreaking Waves; x = l. Wave Forces; Wave Moment; Waves; x = Wave Forces; Wave Moment ; ~< i x oil Wall of Low-Height - Pressure Distribution . ail ao) fora Circularsealle sy. : A of Total Force on a Two-Pile Graup . Calculation of Wave Forces on a - Nonbreaking Wave Forces. oo oa) to © FIGURE 7-72 7-73 7-74 7-75 7-76 7-77 7-78 7-79 7-380 7-81 7-82 7-83 7-84 Force and Moment Reduction Factors . Wall on Rubble Foundation - Pressure Distribution. Minikin Wave Pressure Diagram. Dimensionless Minikin Wave Pressure and Force. Dimensionless Minikin Wave Pressure and Force. Minikin Force Reduction Factor . Minikin Moment Reduction for Low Wall. : Wave Pressures from Broken Waves: Wall Beawawde a: Stillwater Line. an Na ey Wor Me Het Nel aw TD Wave Pressures from Broken Waves: Wall Landward of Stillwater Line. : Effect of Angle of Wave Approach - = Plan ‘View : Wall Shapes. 3 Weight of Armor Units x XG vs ‘Wave Hei ght for Various’ Slope Values (wy, = 140 tbs /ft3 and 145 lbs/ft3). Weight of Armor Units x Kp vs Wave Height for Various Slope Values (wy, - 150 1bs/ft? and 155 1bs/ft9). Weight of Armor Units x Kp vs Wave Height for Various Slope Values (w, = 160 lbs/ft? and 165 lbs/ft3). Weight of Armor Units x Kp vs Wave Height for Various Slope Values (wy, = 170 lbs/ft? and 175 lbs/ft3). Effect of Unit Weight es on nan Geka Paige of Armor Unit . o£ ; : - “ : Concrete Armor Units . Tetrapod Specifications. Quadripod Specifications . Tribar Specifications. Dolos Specifications . 3 : Modified-Cube Specifications : Hexapod Specifications . Rubble-Mound Section for Nonbreaking Wave iConditaent (zero to moderate overtopping conditions). : : Rubble-Mound Section for Vaiaae Wave Condition (moderate overtopping) Logic Diagram for Preliminary Design of Rubble Structure 5 Logic Diagram for Evaluation of Preliminary Design . Stability Number for Rubble Foundation and Toe Protection . . Velocity vs Stone Weight and Equivalent “Stone Diameter (Wi= 62sabs/ Ft?) : Definition Sketch for Coulomb Earth Fores: Equation 5 Active Earth Force for Simple Rankine Case . Location Plan - Offshore Island. Site Plan - Offshore Island. : Perspective View and Section Saar Island. Location of Bottom Profiles. Bottom Profiles through Island Site. Hurricane Storm Tracks in the Delaware Bay cer Xtii Bathystrophic Storm Surge Hydrograph . Bathystrophic Storm Surge Hydrograph - Comparison ice Peak Surges. c Astronomical Tides - Bronabaliey, Water revel Ha ine above a Given Level, Lewes, Delaware . Tidal Current Chart - Maximum Flood at Decne Pay Entrance . 5 Tidal Current Chart - ivecennn Ebb at fetenaces Bay Entrance . : Polar Diagram ef Tidal Currents. at Ts lands Site C Time Variation of Tidal Current Speed at Island Site . Calculation of Effective Fetch - Island Site at Delaware Bay Entrance. . Wind Data in the Vicinity of De lemaney Bay. a 3 ‘ Probability Distribution of Maximum Wind ce = Thom' Ss Fastest Mile Wind. 5 Frequency of Occurrence of Suen eteent Wave ‘Heights iar Waves Generated in Delaware Bay. 5 : Wave and Swell Big for a Location off Delawages Bay Entrance . : ; General Shoe Pe AaGlemmenth in n Vicinity of neieates Bay for Refraction Analysis. : Refraction - Shoaling Gperetetents as a JPaneiien, on Wave Direction and Wave Period . Frequency of Occurrence of paeanteveane Wave Heights “for Waves Generated in Ocean - Transformation by Refraction and) shoalaine 0%. Mean Bottom Profile from Deep “Water: to Mouth of Delaware Bay . at HCY chee Sete Engineering Data - Tribars : Engineering Data - Tetrapods . . Volume of Concrete Required per 100. feet of eee as a Function of Tribar eae Concrete Unit Weight and Structure Slope. Number of Tribars Required per 100 feet “of Structure as a Function of Tribar Weight, Concrete Unit oe and Structure Slope. A Volume cf Concrete peaoered ai "100 beeee of Gemieeure! as a Function of Tetrapod eg Concrete Unit Weight and Structure Slope. Number of Tetrapods Required per 100 rece of Bemnctore as a Function of Tetrapod Nacar: Concrete Unit iaienes and Structure Slopes . : Volume of First Underlayer per 100 Feet ice Structure as a Function of Tribar Pee Concrete Unit Weight and Structure Slope. : Volume of First Underlayer per 100 feet hoe Bernecare as a Function of Tetrapod Weight, Concrete Unit Weight and Structure Slope. be So ck GAR? ste se Are eae XIV 8-75 8-80 8-82 TABLE Volume of Core per 100 feet of Structure as a Function of Armor Unit Weight and Structure Slope . : Cost of Casting, Handling and Placing Concrete Armor Units as a Function-of Armor Unit ies and Structure Slope. Total Cost of 100 feet oe Bemaeeurel as a nee van Gea Tribar Weight, Concrete Unit ved and Structure Slope. c * Total Cost of 100 “feet of Structure as a Funetion “of Tetrapod tea Concrete Unit oer and Structure Slope. : Local Shoreline’ Alignment in » Vieinity of Genes city, Maryland . F Dimensionless Longshore “Component “of Wave. Beene as a Function of Deepwater Wave Steepness - Waves from Northeast at Ocean City, Maryland. LIST OF TABLES Applicability of Ryonz¢ Calculations for Various Combi- nations of the Graphic Phi Moments of Borrow and Native Material Grain Size Distributions . Beachgrass Planting Summary. Example Determination of Design Wave Heights . Steady Flow Drag Coefficients for sb ea Reynolds Numbers Experimentally Determined Values of on : Example Calculation of Wave Force Variation wait Phase Angle. : Comparison of Measured and Calculated Force. : Suggested Kp Values for Use in as sie Armor Unit Weight . H/Hp—9 and ra as a “Runetion of Gover! Layer. Damage and Type of Armor Unit . > Types of Concrete Armor Units. Use of Concrete Armors in the United States. Layer Coefficient and Porosity for Various Armor ees Quarrystone Weights and Dimensions . Effect of Ice on Marine Structures . : a). cell PEMERSE. tes Unit Weights and Internal Friction Angvios. Bo oho. 0. 8 Coefficients and Angles of Friction. XV PAGE 8-84 CHAPTER 5 PLANNING ANALYSIS DANA POINT, CALIFORNIA — CHAPTER 5 PLANNING ANALYSIS 5.1 GENERAL Coastal engineering problems may be classified into four general categories: shoreline stabilization, backshore protection (from waves and surge), inlet stabilization, and harbor protection. (See Figure 5-1.) A coastal problem may fall into more than one category. Once classified, there are various solutions available to the coastal engineer. Some of these are structural; however, other techniques may be employed, such as zoning and land use management. This Manual deals primarily with struc- tural solutions, but basic design factors may also apply to other types of solutions. Figure 5-1 indicates. structures or protective works that fit into the four general problem classifications and factors that must be considered in analyzing the problem. Hydraulic considerations include wind, waves, currents, tides, storm surge or wind setup and the basic bathymetry of the area. Sedimentation considerations include the littoral material and processes (i.e., direction of movement; rate of transport, net and gross; and sediment classification and characteristics) and changes in shore alignment. Navigation considerations include the design craft or vessel data, traffic lanes, channel depth, width, length and alignment. Control structure considerations include selection of the protective works eval- uating type, use, effectiveness, economics, and environmental impact. In selecting the shape, size, and location of shore-protection works, the objective should be not only to design an engineering work which will accomplish the desired results most economically, but also to consider effects on adjacent areas. Economic evaluation includes the maintenance costs and interest on and amortization of first cost. If any plan con- Sidered would result in enlarging the problem by extending its effects to a larger coastal stretch or prevent such enlargement, the economic effect of each such consequence should be evaluated. A convenient yardstick for comparing various plans on an economic basis is the total cost per year per foot of shore protected. Effects on adjacent lands are considered to the extent of providing the required protection with the least amount of disturbance to current and future land use, environmental factors, and aesthetics of the area. The form, texture, and color of material selected for the design should be considered as well as how the material is used. Proper planning analysis also requires consideration of legal and social consequences where shore protection measures may be expected to result in significant effects on physical or ecological aspects of the environment. The following sections describe the most common structural solutions now used to meet functional requirements, and provide guidelines for the application of these solutions. This manual treats only the structural solutions to problems. The environmental effects of all such solutions must, by law as well as normal engineering concerns, be studied. i oad | SUSTQOLg SUTTeSUTSUY TeISseOD JO UOTYISOTITSseT) Teseueyn ‘*T-G amsty $O1WwOU0dZ JDJUaWOsIAUA jobaq a4INJINIYS |O41,U0D UO!JOJUaWIPIS soljnoupAy soiwouo0dy JOJUaWOJIAUZ joba7q a4INjonsyS [OsJUoD *SNOILVYSCISNOD sd!wou0dy JDJUaWOIIAUZ NOILVINDYID AVE jobaq a4INJONIYS JOsJUOD udl}DJUaWIPAS soljnospAy solwouo0dy JOJUaWO4IAUZ jobaq a4INJINIYS }O1}U0D uOI}DBIADN UOIJOJUaWIPAS *SNOILVYAGISNOD so1wou0dg JOJUIWOIIAUG joba7q aduaUdJUIOW AINJINIYS [O1JU0D uOI}OBIADN So1no4pAy | AN3WL3A34 | (NOILVYOLS3Y LNOHLIM YO HLIM ) *SNOILVYSGISNOD INSWHSIYNON HOVSS SNAG GNVS NOILVOIAVN INAWL3A3Y HOV3AE SAILIALONd aQv3Hy1Nng Sa Sif ONISGSYG TIVMV SS TIVMV 3S NOIL043L0Ud NOILVZITIEGVLS NOILO3L0Ud NOILVZI1IGVLS YOSYVH LATNI JYOHSHOVE JINITSYOHS UOIJOJUBWIPAS soljnoupAy LA INI LV >SNOILVYSCISNOD ONISSVdAG GNVS So1jno4spAy *SNOILVYAGISNOD YAILVMAV INE JYOHS440 t YSLVMAVINS G3193NNO9-3YOHS Selva SW3I1804d INIYSANIONA IVLSVOD 40 NOILVOISISSV 19 5.2 SEAWALLS, BULKHEADS, AND REVETMENTS 5.21 FUNCTIONS Seawalls, bulkheads, and revetments are structures placed parallel, or nearly parallel, to the shoreline, to separate a land area from a water area. The primary purpose of a bulkhead is to retain or prevent sliding of the land, with the secondary purpose of affording protection to the upland against damage by wave action. The primary purpose of a seawall or revetment is to protect the land and upland property from damage by waves, with incidental functions as a retaining wall or bulkhead. There are no precise distinctions between the three structures, and often the same type of structure in different localities bears a different name. Thus, it is difficult to say whether a stone or concrete facing designed to protect a vertical scarp is a seawall or a revetment, and often just as difficult to determine whether a retaining wall subject to wave action should be termed a seawall or bulkhead. All these structures, however, have one feature in common, in that they separate land and water areas. These structures are generally used where it is necessary to maintain the shore in an advanced position relative to that of adjacent shores, where there is a scant supply of littoral material and little or no protective beach, as along an eroding bluff, or where it is desired to maintain a depth of water along the shoreline, as for a wharf. 5.22 LIMITATIONS These structures afford protection only to the land immediately behind them, and none to adjacent areas up- or downcoast. When built on a receding shoreline, the recession will continue and may be accelerated on adjacent shores. Any tendency toward loss of beach material in front of such a structure may well be intensified. Where it is desired to Maintain a beach in the immediate vicinity of such structures, companion works may be necessary. 5.23 FUNCTIONAL PLANNING OF THE STRUCTURE The planning of seawalls, bulkheads, and revetments is an elementary process, since their functions are restricted to the maintenance of fixed boundaries. Factors in designing such a structure are: use and overall shape of the structure, location with respect to the shoreline, length, height, and often stability of the soil and ground and water level seaward and landward of the wall. 5.24 USE AND SHAPE OF THE STRUCTURE The use of the structure dictitates the selection of the shape. Face profile shapes may be classed roughly as vertical or nearly vertical, sloping, convex curved, concave curved, reentrant, or stepped. Each cross section has certain functional applications. If unusual functional cri- teria are required, a combination of cross sections may be used. 5-3 A vertical or nearly vertical face structure lends itself to use as a quay wall, docking or mooring place. Where a light structure is required, a vertical face (of sheet piling, for example) may often be constructed more quickly and more cheaply than other types. This ease or speed of construction is important where emergency protection is needed. A verti- cal face is less effective against wave attack, and specifically against overtopping, than the concave curved and reentrant face. The use of vertical or nearly vertical face walls can result in severe scouring when the toe or base of the wall is in shallow water. Waves breaking against a wall deflect energy both upward and downward. The downward component causes scouring erosion of the material at the base of the wall. To pre- vent scouring, toe protection should be provided in the form of a toe or armor stone of adequate size to prevent displacement, and of such grada- tion as to prevent the loss of the foundation material through the voids of the stone and consequent settlement of the stone. Convex curved face and smooth slopes are least effective in reducing wave runup and overtopping. The rubble sloping seawall and revetment is effective in dissipating and absorbing wave energy, and reduces wave run- up and overtopping. Sloping face structures, generally reduce scouring, and may have an advantage over vertical face structures. Concave curved or reentrant faced structures are the most effective for reducing wave overtopping when onshore winds are light. Where the structure crest is to be used for a road, promenade, or other purpose, this design may be the best shape for protecting the crest and reducing spray. This is especially true if the fronting beach is narrow or non- existant, or if the water level is above the structure base, If onshore winds occur at the same time as high waves, a rubble slope should also be considered. A stepped-face wall provides the easiest access to beach areas from protected areas, and reduces the scouring of wave backwash. 5.25 LOCATION OF STRUCTURE WITH RESPECT TO SHORELINE A seawall, bulkhead, or revetment is usually constructed along that line landward of which further recession of the shoreline must be stopped. Where an area is to be reclaimed, a wall may be constructed along the sea- ward edge of the reclaimed area. 5.26 LENGTH OF STRUCTURE A seawall, bulkhead, or revetment protects only the land and improve- ments immediately behind it. These structures provide no protection to either up- or downcoast areas as do beach fills. Usually, where erosion may be expected at both ends of a structure, wing walls or tie-ins to adjacent land features must be provided to prevent flanking and possible progressive failure of the structure at the ends. Short-term beach changes due to storms, as well as seasonal and annual changes, are design con- siderations. Erosion updrift from such a structure will continue unabated after the wall is built, and downdrift erosion will probably be intensified. 5-4 5.27 HEIGHT OF STRUCTURE Seawalls, bulkheads, and revetments can be built so high that no water would overtop the crest of the structure, regardless of severity of wave attack and storm-surge levels, though it is sometimes not economically feasible to do so. Wave runup and overtopping criteria on which the height of a structure should be based can be estimated from data presented in Section 7,2 "WAVE RUNUP, OVERTOPPING, AND TRANSMISSION."' Specific model tests for the design case can be carried out if greater detail or accuracy is warranted, 5.28 DETERMINATION OF GROUND ELEVATION IN FRONT OF A STRUCTURE Seawalls and revetments are usually built to protect a shore from the effects of continuing erosion and to protect shore improvements from damage by wave attack. The exact effect of such a structure on erosion processes cannot be fully determined, but can be estimated by the method given in this section. For safety, even though erosion processes seem to have been halted or reversed, the designer must assume that they will continue. A determination of the beach profile that will exist after construction of the structure can be estimated through experience, obser- vations, and general guides. Scour may be anticipated at the toe of the structure as an initial short-term effect. Scour will form a trough with dimensions governed by the type of structure face, the nature of wave attack, and the resistance of the bed material. At a rubble-mound seawall, scour may undermine the toe stone, causing it to sink to an ultimately lower stable position. The resultant settl2ment of stone on the seaward face may be offset by over- building the cross-section to allow for settlement. Another method is to provide excess stone at the toe to fill the anticipated scour trough. The face of a vertical structure may be protected similarly against scour by the use of stone. A gravity wall must be protected from undermining by scour by providing impermeable cutoff walls at the base. As a general guide, maximum depth of a scour trough below the natural bed ts about equal to the hetght of the maxtmum unbroken wave that can be supported by the original depth of water at the toe of the structure. For example, if the controlling depth of water seaward of the face of the structure is 10 feet, the offshore bottom slope is 1 on 30, and a design wave period of 8 seconds is assumed, the maximum unbroken wave height that can be supported is 10.4 feet. (See Section 7.1.) Therefore, the maximum depth of scour at the toe of the structure would be 10.4 feet below the original bottom, or a total of 20.4 feet below the design water level. The place- ment of a rock blanket with an adequate bedding material seaward from the toe of the structure will prevent erosion at the toe, and will result in a more stable structure. (See Section 7.3 for design methods.) For long-term effects, it is preferable to assume that the structure would have no effect on reducing the erosion of the beach seaward of the wall. Such erosion would continue as if the wall were not there. Since the determination of scour can only be approximate, general guides are usually adopted. Consider the beach shown in Figure 5-2 where the solid line represents an average existing profile. It is desired to place a seawall at point A as shown. From prior records, either the loss of beach width per year or the annual volume loss of material over an area which includes the profile, is known, In the latter case, the annual volume loss may be converted to an annual loss of beach width by the general rule: loss of 1 cubte yard of beach material ts equivalent to loss of 1 square foot of beach area on the berm. This rule is applicable primarily at the ocean front. In shallow, protected bays, the ratio of volume to area is usually much less. +20 +10 Elevation (feet) i} ° Figure) 5-2. Effects) of Erosion. Nearshore slopes are usually gentle seaward of the bar. Slopes are steeper inshore of the bar, and may be as steep as 1 on 5 at the waterline with coarse sand. Analyses of profiles at eroding beaches indicate that it may be assumed that the slope seaward of a depth of 30 feet will remain nearly unchanged, that the point of slope break £# will remain at about the same elevation, and that the profile shoreward of the point of break in slope will remain nearly unchanged. Thus, the ultimate depth at the wall may be estimated as follows: (a) In Figure 5-2, let B represent a water depth of 30 feet, £F the point of slope break at the depth of about 5 feet, and C the present position of the berm crest. If it is desired to build a structure at A whose economic life is estimated at 50 years, and it is found that n is the annual loss of beach width at the berm, then in 50 years without the wall this berm will retreat a distance 50n to point D. (b) From D to the elevation of point £, draw a profile DF parallel to C #, and connect points B and F. This dashed line, DF B; will represent the approximate profile of beach after 50 years without the presence of the wall. The receded beach elevation at the wall's location will be approximated by point A’, Similar calculations may be made for 5-6 anticipated short-time beach losses caused by storms. Erosion caused by storms generally results in a greater loss of beach material above the mean low water level, because the superelevation of the water level (storm surge) allows storm waves to act on the upper part of the beach. Other factors in planning and design are the depth of wall penetra- tion to prevent undermining, tie backs or end walls to prevent flanking, stability against saturated soil pressures, and the possibility of soil slumping under the wall. 5.3 PROTECTIVE BEACHES 5.31 FUNCTIONS Beaches of suitable dimensions are effective in dissipating wave energy, and, when they can be maintained to proper dimensions, afford pro- tection for the adjacent upland, and are classed as shore-protection struc- tures. Such beaches dissipate wave energy without causing adverse effects. When studying an erosion problem, it is advisable to investigate the feasi- bility of mechanically or hydraulically placing borrow material on the shore to restore or form, and subsequently maintain, an adequate protective beach, and to consider other remedial measures as auxiliary to this solu- tion. The method of placing beach fill to ensure sand supply at the re- quired replenishment rate is important. Suitable beach material may be stockpiled at the updrift section of the problem area where stabilization of an eroding beach is the problem. The establishment and periodic replenishment of such a stockpile is termed artificial beach nourtshment. If the solution of a problem requires restoration of the eroded beach and its stabilization at the restored position, fill is placed directly on the eroded beach. Then artificial nourishment is accomplished by stockpiling. When conditions are suitable for artificial nourishment, long reaches of shore may be protected at a cost relatively low compared to costs of other adequate protective structures. An equally important advantage is that artificial nourishment directly remedies the basic cause of most erosion problems - a deficiency in natural sand supply ~ and benefits rather than damages the shore beyond the immediate problem area. An added consideration is that the widened beach may have value as a recreation feature. Under certain conditions, a properly designed groin system may im- prove a protective beach. This method must be used with caution, for if a beach is restored or widened by impounding the natural supply of litto- ral material, a corresponding decrease in supply may occur in downdrift areas with resultant expansion or transfer of the problem area. Detri- mental effects of groins may usually be prevented by placing artificial fill in suitable quantity concurrently with groin construction; such stock- piling is called filling the groins. Groins may be included in a beach restoration project to reduce the rate of loss and thus the nourishment requirements. When groins are considered for use with artificial fill, their benefits should be carefully evaluated to determine their justifi- cation. Such justification could be that groins would reduce annual nourishment costs in excess of the groin annual charges. (See Section 5.610 Economic Determination for Groin Construction.) Sad 5eo2 LIMITATIONS Whether to provide a protective beach, with or without groins, de- pends on the availability of suitable sand for the purpose. Artificial nourishment is usually quite costly on a unit length basis when applied to short segments of shore, because the widened beach protuding seaward of its adjacent shores erodes rapidly. This results in high nourishment costs, but is not necessarily a limitation if artificial nourishment over a short length of beach prevents the enlargement of that problem area to downdrift shores. However, difficulties could be encountered in financing a shore protection method which provides protection beyond the immediate problem area. Sis OS PLANNING CRITERIA Planning of a protective beach by artificial nourishment requires: (a) Determination of the predominant direction of longshore trans- port and deficiency of material supply to the problem area; (b) Determination of the composite average characteristics of the existing beach material or native sand in the zone between the 30-foot depth and the dune or cliff line (the zone of active littoral movement) ; (c) Evaluation and selection of borrow material for initial beach fill and periodic nourishment, including the determination of any extra amount of borrow material required for placement based on the comparison of the native beach sand and borrow material; (d) Determination of beach berm elevation and width; (e) Determination of wave-adjusted foreshore slopes; (£) Determination of feeder-beach (stockpile) location. 5.331 Direction of Longshore Transport and Deficiency of Supply. The methods of determining the predominant direction of longshore transport are outlined in Section 4.5. The deficiency of material supply is the rate of loss of beach material; it is the rate at which the material supply must be increased to balance the transport by littoral forces to prevent net loss, If no natural supply is available, as on shores down- drift from a major barrier to longshore transport, the net rate of long- shore transport will approximate the deficiency in supply. Comparison of surveys of impoundment or eroding areas over a long period of time is the best method of estimating the rate of nourishment required to maintain stability of the shore. Since surveys suitable for volume measurement are rarely available, approximations computed from changes in the shore posi- tion, as determined from aerial photographs or other suitable records, are often necessary. For such computations, the relationship in whtch 1 square foot of change in beach surface area equals 1 cubte yard of beach material appears to provide acceptable values on exposed seacoasts. For less ex- posed shores, this ratio would probably result in volume estimates in excess of the actual value. 5-8 { 5.332 Selection of Borrow Material. After the characteristics of the native sand and the longshore-transport processes in the area are deter- mined, the next step is to select borrow material for beach fill and for periodic nourishment. When sand is mechanically deposited on the beach, waves immediately start a sorting and winnowing action on the surface layer of the fill, moving finer particles seaward, and leaving coarser material at or shoreward of the plunge point. This sorting continues until a iayer of coarser particles compatible with the wave climate armors the beach and makes the slope temporarily stable for normal wave conditions. However, if this armor is disturbed by a storm, the under- lying material is again subjected to the sorting process. Because of these processes, beach fill with organic material or large amounts of the finer sand fractions may be used since natural pro- cesses will clean the fill material. This has been confirmed with fills containing foreign matter at Anaheim Bay, California, and Palm Beach, Florida, Material finer than that exposed on the natural beach face, if exposed on the surface during a storm, will move to a depth compatible with its size to form nearshore slopes flatter than normal slopes before placement. Fill coarser than the sand on the natural beach will remain on the foreshore, and may be expected to produce a steeper beach. The relationship between grain size and slope is discussed in Section 4.526. If borrow sand is very coarse, it will probably be stable under normal conditions, but it may make the beach less desirable for recreation. If the borrow material is much finer than the native beach material, a large amount will move offshore and be lost. The distribution of grain sizes naturally present on a stable beach represents a state of dynamic equilibrium between the supply and loss of material of each size. Coarser particles generally have a lower supply rate and a lower loss rate; fine particles are usually more abundant, but are rapidly moved alongshore and offshore. Where fill is to be placed on a natural beach that has been stable or oniy slowly receding, the size characteristics of the native material can be used to evaluate the suit- ability of potential borrow material. A borrow material with the same _ grain size distribution as the native material, or one slightly coarser, will usually be suitable for fill. If such borrow material is available, the volume required for fill can be determined directly from the project dimensions, assuming that only insignificant amounts will be lost through sorting and selective transport. Unfortunately it is often difficult to find economic sources of borrow material with the desired properties. When the potential borrow material is finer than the native material, large losses of the borrow material often take place immediately following its emplacement. Cur- rently there is no proven method for computing the amount of overfill required to satisfy project dimensions once the fill material has under- gone this initial sorting action and attained a stable configuration. Studies by Krumbein (1957) provide a quantitative basis for comparison on the material characteristics considered to have the greatest effect on this relationship. His subsequent work with James (Krumbein § James, 2-9 1965) developed a technique that may be used to indicate probable be- havior of the borrow material on the beach. The procedure requires enough core borings in the borrow zone and samples from the beach and nearshore zones to adequately describe the size distribution of borrow and beach material. Mechanical size analyses of the borings and samples are used to compute composite size distributions for the two types of material. These composite distributions are compared to determine the suitability of the borrow material. Almost any borrow source near the shore will include some material of suitable size. Since the source will control cost to a major degree, evaluation of the propor- tional volume of material of the desired characteristics in the borrow areas is important in economic design. Krumbein and James (1965) provide the design engineer with criteria for estimating an additional amount of borrow material required to meet project dimensions when the borrow mate- Tial does not match the characteristics of native sand or those required for a stable beach. These techniques have not been fully tested in the field, and should be used only as a general indication of possible fill behavior. The techniques have been evaluated in one field situation with favorable results (Section 6.3 PROTECTIVE BEACHES), but further investi- gations are required before the quantitative reliability of these tech- Niques can be assessed. The mathematical basis of the technique is straightforward. Given a borrow material with a size distribution different from the native or Stable material size distribution, the method determines the proportion of material which must be removed from each size class of the borrow material to produce a modified borrow material size distribution with the same shape as that of the native material. If size distributions of native and borrow material are known, and if there is some borrow material in each size class that comprises the native material, the computation could be made directly by finding the phi size class with the maximum ratio of native to borrow weight proportions. This ratio, called the critteal ratio (Rg erizt), Tepresents the estimated cubic yards of fill material required to produce one cubic yard of material having the desired particle size distribution (i.e., similar to native or stable material). In practice this procedure is usually not reliable. Several factors lead to errors in the estimates of weight proportions of both size distri- butions. These errors can be due to sampling inadequacy, estimation of composite properiies from individual samples, and laboratory error in mechanical analysis. Computation of the critical ratio is usually subject to less error if the first two graphic moments of each size distribution are computed, and these values substituted into the following equation: _ [Mon — Mos)” Go ee 2 (bn = op) (5-1) 0 crit On 5-10 where Ry crit = ratio of proportions of native material to the borrow material at the critical phi value (when phi value is that $ size with greatest ratio o£ the proportions of native sand to borrow material), a5. °- (gy - > )/2 Standard deviation is a measure of sorting. (See Section 4.2) (5-2) My = ogy + $4 ,)/2 phi mean diameter of grain size distribution. (See Section 4.2) (5-3) -h = subscript b refers to borrow material -, = subscript m refers to natural sand on beach ¢g, = 84th percentile in phi units $)¢, = 16th percentile in phi units e = (base of natural logarithms, 2.718) This formula assumes that both composite native and borrow material distributions are nearly lognormal. This assumption can be expected to be satisfied for the composite grain size distribution of most natural beaches and for naturally deposited borrow material that is almost homo- geneous. Pronounced skewness or bimodality might be encountered with borrow sources that contain alternating horizons of coarse and fine material, such as clay-sand depositional sequences, or in borrow zones that cross cut flood plain deposits associated with ancient river channels. The formula for Rg crit is not applicable to all possible combina- tions of grain size moments for borrow and native material. The possible combinations can be subdivided into the four basic cases given in Table 5-1, and indicated as quadrants in Figure 5-3. Table 5-1 shows that, Rg crit is assumed to have direct application in only one of the four cases. In Case 1, the borrow material has an average grain size finer than that of the native material, but the borrow material is more poorly sorted. The basic prerequisite is satisfied that there is some borrow material present for each of the size classes which contain native material. There will be some coarser size classes beyond which this supply will be more than adequate. However, a large part of the borrow material is finer than that expected to remain in the active littoral zone. The best esti- mate of the overfill ratio is the critical ratio calculated by Equation 5-1. This should be a conservative estimate since overage quantities in all size classes other than that for Rg erit would not all be expected to be completely lost from the active area. S-l1 ee aa jeieqeur aatgeu ISIE] oq Ajqeqoid TE 3nq porrpead aq youuvd ssoj [fT ‘poyoqeut oq JOUUS sUOTINGISIP ou], UU} IOUT ST TeIIOIVUT MOTO SpA |e d “On < Tw jereqeur aataeu uvya parsos 19939q ST [eT19IVUE MOIIOg _——————— ‘T[y Jo 207 Sunuoy perroyeur oaTIeU petsoqeul aatyeu jo Inoos poppe sonpul Aeur ‘ayqe3s 9g q[e pinoys yererew [py aya nq ULY} JOSIVOD ST [eTIIIeUI MOTO payo3yeu aq Jou sUCTINGIASIP OY. uP > CON ¢ ant [etoqeur oatzeu i 4149 ry 10} pondwios 3ey3 weYs ULY} JOSIVOD ST [eIIOIVUT MOTO os | 1 ssaq Atqeqoad st o13ea []1J19A40 posmnbay [elzoqew saryeu ue) uo > Irn | V4 a Te) poszos Ayiood asour st petoyeU MOOG bh ee ud qe yetioqeur aateu 4149 dy 4g uoat8 st a UvY} IOUT} ST [elsoIeUT MOIIOG oni [[y10A0 posnbas jo oyeurrasa sag “bw < 1 Ww I I le-g “Sq um) quvrpend | ase As0391e— uoIYy SUIIIOg 01 ssuodsay suoneIAa prepuras 1Yyq JO drysuonepoy suvay Ty JO diysuonepoy “SUOTINGIISIC] 9ZIS UIeID [eo] PANN pue Mog jo squomropy Tyg WydesryH ay3 Jo suoTIRUTGUIOD SNOTIeA OF suone[nsyeoD 122 Ore zo Aypiqvoyddy *1—¢ 29°%L oY borrow / Ty native i \\ Guadrart a\ Quadrant | “Upper Bound Medd Fe Estimated Overfill Ratio ‘Overfill | -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 re) LOwis 20, 713 0ein4O 5-5 Oes GO Md borrow-M@native Td native Quadrant 3 Quadrant 4 Estimated Overfill Ratio =| Unsuitable-Overfill Ratio Cannot be Computed Figure 5-3. Equal Value Contours Ry eritical Versus Relative Differences Between Borrow and Native Textural Parameters In Case II (Table 5-1), the borrow material is also more poorly sorted than the native material, but the larger part of borrow material is coarser than the average grain size of the native material. Since the sorting processes that modify the grain size distribution of the fill material are most active on the finer size classes, much of the excess coarse material included in the initial fill will remain in the stabi- lized beach profile. In this case, the grain size distribution of the stabilized fill is not expected to completely match that of the original native sand. It is expected that part of borrow material lost from the fill will be less than that calculated from Ry erit: The computed value of the critical ratio can be assumed to represent an upper bound. In Case IV (Table 5-1), the borrow material is finer and better sorted than the native material. The equation for Ry oy;~ does not apply in Case IV, because the equation denotes a minimum rather than a maximum in the ratio of native to borrow weight proportion at the critical phi value. This indicates that borrow material of this type is unsuitable as fill material, The native and borrow size distributions cannot be matched through selective sorting processes. The mathematics imply that none of the original fill material will remain as stable fill after the initial sorting. This implication is not totally realistic, and the instability of borrow material of this type in a fill depends on the degree of differ- ence between the average grain size of the stable and borrow materials. If borrow material of this type is selected, large initial losses should be expected, but no method in current use provides even a crude estimate of loss. In Case III, borrow material is coarser and better sorted than the native material. The equation for Ry eypjz¢ does not apply for the same reason it does not apply to borrow material in Case IV. Practical impli- cations in Case III are the opposite of those for IV. In III, there is a marked deficiency of material in the finer size classes which are more responsive to the sorting processes. Hence the borrow material is stable from the outset, and no significant losses are to be expected. The over- fill ratio may be assumed to be unity. If the material has a large coarse fraction, foreshore slopes may be steepened enough to alter wave runup and reflection and induce scour and loss of existing native material fronting the toe of the coarse fill. It may also result in a beach fill having profile slopes and textural properties not well suited for recrea- tion. The engineering application of the techniques discussed above require that basic sediment size data be collected in both the potential borrow zones and in the project area. Estimation of the composite grain size characteristics of native material should follow the guidelines set forth by Krumbein (1957). The estimation of composite distribution of properties of material in the borrow zone depends upon the heterogeneity of the tex- tural properties in the zone. If material in the borrow zone exhibits large vertical or horizontal gradients in textural properties, extensive coring may be required to obtain reliable estimates of the composite properties of the borrow material. Practical guidelines for reliable 5-14 { estimation of borrow material properties have not been established when the borrow zone is heterogeneous. Hence special attention must be given when suitable borrow material from homogeneous deposits cannot be found, The relationship between the critical ratio and the relative diver- gence between the phi moments of native and borrow materials is shown in Figure 5-3. The horizontal axis is a dimensionless measure of the relative difference between borrow and native phi means. It is computed as the borrow phi mean minus the native phi mean divided by the native phi stand- ard deviation, The vertical axis (plotted on a logarithmic scale) is the ratio of borrow phi standard deviation to native phi standard deviation. Any value plotting to the right of the origin indicates a borrow material finer than the native material (M ob > M onde Any point plotting above the horizontal axis ae a BoreuN Saeed more poorly sorted than the native material bb > O nds Hence the four categories discussed above are separated sll zie foie quadrants on this plot. The curves in Figure 5-3 indicate equal-value contours of the criti- cal ratio. Contours are dashed lines in quadrant 2, because here the critical ratio is assumed to be an upper bound to the true loss ratio. In quadrant 1, the critical ratio is assumed to be a conservative esti- mate of the true loss ratio and the curves are solid lines. No curves are plotted in quadrants 3 and 4, because the computed value of critical ratio has no meaning when the borrow material is well sorted in compari- son to the native material. This plot shows the general behavior of the critical ratio as func- tions of the differences in textural characteristics between borrow and native materials. The following relationships are noteworthy: (a) For any fixed ratio between the sorting of borrow and native material, the critical ratio changes only slowly with small differences in phi means, then more rapidly as this difference becomes larger. (b) For larger ratios of the sorting parameter o,, the stability of the computed critical ratio is greater, i.e., if the ratio of borrow to native sorting is large the computed critical ratio is nearly insensi- tive to the difference in phi means. (c) For any fixed finite difference in phi means, there will be some ratio of borrow to native sorting for which the critical ratio will be a minimum. For sorting ratios less than this value, the critical ratio rises rapidly and approaches infinity as the sorting ratio approaches unity. For sorting ratios larger than this optimal value, the critical ratio increases slowly. These relations indicate that the computed value for critical ratio is generally more sensitive to the phi sorting ratio than to differences in phi means. If the borrow material is poorly sorted in comparison to the native material, errors in determination of the difference in phi means will not cause significant errors in the computation of the critical ratio. 9-15 Conversely, if the borrow and native materials have nearly equal phi sort- ing values, small errors in determining the difference in phi means can cause enormous errors in computation of the critical ratio. As an example, where the ratio of borrow phi sorting to native phi sorting is 1.25, the normalized difference in phi means is 0.5 unit so that the true difference is 1.0 unit. The true critical ratio is about 3.0 which means twice as much borrow material is required than that estimated with the erroneous value. On the other hand, where the sorting ratio is 3, the same "erro- neous" and ''true'' values apply to the normalized difference in phi means. Here the two critical ratios are approximately 3.05 and 3.20, a difference of only 5 percent. This example indicates that selecting a poorly sorted borrow material may be safer when the borrow material must be finer than the native material. Application of the above techniques is demonstrated below with two example problems. Re RRR eT ee re eR RK EE AMPILEO PROBLEM er Re Ge Ree GIVEN: Composite native beach material phi parameters bg, — 2.47 @ (0.180 mm), $6 = 1.41 @ (0.376 mm). composite borrow material parameters bg, = 3.41 ¢ (0.094 mm), 16 1.67 @ (0.314 mm). FIND: (a) Ry enit (b) Applicable case for computing overfill ratio (c) Interpreted overfill ratio (cy fill/cy project requirements) SOLUTION: (a) Using Equation 5-3 $64 + 6 Mg = fr tte ‘ Mon = a = 1.94 (0.261mm) , and Buhari a7 Mgp = a ey = 2.54 (0.172 mm) . 9-16 Using Equation 5-2 & $34 16 i) = 2 : sf 247 — VA eRe Cn = 2 7 . ’ and geek T Loo. Ob = 2 = BEST Using Equation 5-1 Gb Ke - va Rb crit = Gy = 206m — 95) Sees 95a) ae oes e |2((0.53) — (0.87)*) @ crit 53 y 0. Rg cri¢ = (1-64) (1.46) = 2.40 . (b) Mgp > Mgn (2-54 > 1.94) and oyp > og, (0.87 > 0.53). Hence from Table 5-1 this is Case I. (c) Ry erit is the best estimate of the overfill ratio. This project requires 2.40 cubic yards of fill of this borrow material to satisfy each cubic yard demanded by the project dimensions. CE ee i ec am, Te a ote Ringe ek er We, alee A em he Sa He ee ee TE ur ee ewe ae em = SE i ea ar 5 ke eK KK RK RK K KK K * * * EXAMPLE PROBLEM * * * * * * * *¥ ® *¥ ¥ ®¥ ® KF GIVEN: Composite native beach material phi parameters O34 = oA 45 $16 — 1.86. Composite borrow material phi parameters G4 oon, $4, = 0.17 (a) Ry erit (b) Applicable case for computing overfill ratio (c) Interpreted overfill ratio SOLUTION: (a) Using Equation 5-3 ee $34 * 46 2 ; a, S10 aes Mon = ia NO ==) 2948) (One79)mm)- and B25) se R17 Mgp = Fees = 1.71 (0.306 mm). Using Equation 5-2 our — On of) = 7 , 5.ue GAD Vem CSOns ane on 3 ; and PPS 2a eee 4 bb = 2 = 1.5 : Using Equation 5-1 Gb = Vea E as Sais 2(8n — 9) | By aries eae 2((0.62)? — (1.54)"]]_, Rg crit = (2-48) (1.16) = 2.88 . (b) Mop < Mon and op > Oy Using Table 5-1, this is Case alive a= 18 (c) Overfill ratio is less than 2.88. It is expected that project demands will be met with less than 2.88 cubic yards of borrow for each cubic yard of fill needed. ees aes ke ee eck ee, RO) SEER SORE e A oe eS ae: Ee ES RO, Rel ee er er ae ees ee se? ee ae As indicated previously, this procedure involves the procurement of core borings in the borrow area and samples from the beach and nearshore zones, and size analyses of all borings and samples. Readily available sources of borrow material have frequently been in bays and lagoons where the material is finer than the native beach material. In such cases, a required volume of borrow material several times the needed in-place volume on the beach would not be uncommon. Because of less availability of bay and lagoon material, and ecological considerations in its use, future planning is looking toward the use of offshore sources of fill material, Since the source of borrow material will control the cost of a beach fill to a major degree, evaluation of the required volume of material from available areas is an important factor in economic design. Ecological considerations in the borrow area are also important. 5.333 Berm Elevation and Width. Beach berms are formed by the deposit of material by wave action. The height of a berm is related to the cyclic change in water level, normal foreshore and nearshore slopes, and the wave regime. Some beaches have no berms; others have one or several. Figure A-1 of Appendix A illustrates a beach zone with two berms. The lower berm, the natural or normal berm, is formed by the uprush of normal wave action during the ordinary range of water-level fluctuations. The higher bern, or storm berm, is formed by wave action during storm conditions. During most storms the water level will be higher than normal on the beach. Wave overtopping may completely obliterate the normal beach berm, if over- topping lasts long enough. The degree of protection to the backshore depends greatly on the effectiveness of the storm berm. Beach berms must be given careful consideration in the planning of a beach fill. If a beach fill is placed to a height lower than the natural berm crest, a ridge will form along the crest, and high water and high waves may overtop the berm crest causing ponding and temporary flooding of the backshore. Such flood- ing, if undesirable, may be avoided by filling the berm to a height slightly above the natural berm crest. Several alternative techniques may be em- ployed to estimate the height of the berm for design purposes. (See Section 7.2 WAVE RUNUP, OVERTOPPING AND TRANSMISSION.) If a beach exists at the site, the natural berm crest height can be measured, and an estimate of future berm elevations can be made. An estimate also may be made by comparison with other sites with similar exposure characteristics (waves and tides) and beach material. If enough wave data (either developed from synoptic surface weather charts or actual records) are available and appli- cable to the project site, these data may be applied to the relationships of wave runup, given by Savage (1959) which are discussed in Section 7.2, to establish an estimated design berm crest height. Criteria for specifying berm width depend upon several factors. If the purpose of the fill is to restore an eroded beach to protect backshore 9-19 improvements from damage by major storms, the width may be determined as the protective width which has been lost during storms of record plus the minimum required to prevent wave action from reaching improvements. Where the beach is used for recreation, justification for the increased width of the beach may be governed by the area required for recreational use. The current (1972) U.S. Government standard is 75 square feet of dry beach per bather. Where the beach fill serves as a stockpile to be periodically replenished, the berm should be wide enough to provide for expected re- cession during the intervals between replenishment operations. 5.334 Slopes. The toe of a stockpile of beach material should not extend so deep that material on the surface of the stockpile would not be moved alongshore in sufficient quantities by wave action. There is no firm specification for this maximum depth, but depths of about 30 feet below low-water datum on seacoasts and about 20 feet on the Great Lakes are appropriate. The initial slope of any beach fill will naturally be steeper than that of the natural profile over which it is placed. Subsequent behavior of the siope depends upon the characteristics of the fill material and the nature of the wave climate. In practice, the initial fill slope is designed parallel to the local or comparable natural beach slope above low-water datum. The design of the slope should be determined after care- ful investigation of all pertinent data from low-water datum to about the 30-foot depth. The design slope is derived through synthesis and averaging of existing data within and adjacent to the problem area, and is usually significantly flatter than the foreshore slope. Design slopes based on such data are usually in the range of 1:20 to 1:30 from low-water datum to the intersection with the existing bottom. However, they are used for computation of quantities only. It is unnecessary and usually impracti- cable to grade beach slopes artificially below the berm crest since they will be shaped naturally by wave action. Fills placed to a desired berm width but with steep initial slopes will quickly adjust to a natural slope, narrowing the berm and leaving the impression that much of the fill has been lost, although it has only moved to establish the natural slope. 5.335 Feeder Beach Location. Dimensions of a stockpile or feeder beach are generally governed primarily by economic consideration involving com- parisons of costs for different replenishment intervals. Therefore, planning a stockpile location must generally be considered in conjunction with stockpile dimensions. If the problem area is part of a continuous and unobstructed beach, the stockpile is located at the updrift end of the problem area. Until the stockpile material is transported by litto- ral forces to the beach zone downdrift of the stockpile location, that beach zone may be expected to recede at the same rate as determined from historical survey data. If economically justified, stockpiles may be placed at points along the problem area. Such placement decreases the time interval between stockpile placement and complete nourishment of the area. Stockpile lengths from a few hundred feet to a mile have been employed successfully. If the plan involves a feeder beach just down- drift from a coastal inlet, wave refraction and inlet currents must be considered to locate the feeder beach so that a minimum of material is 5720 lost into the inlet. A supplementary structure (as a groin) may be needed to reduce material movement into the inlet caused by either tidal currents or change in longshore transport. The nearly continuous interception of littoral materials on the up- drift side of an inlet and mechanical transportation of the materials to a point on the downdrift shore (sand bypassing) constitutes a form of stockpiling for artificial nourishment to the downdrift shore. In this type of operation, the stockpile or feeder beach will generally be small in size as the stockpile material will be transported downdrift by nat- ural forces at a rate about equal to or greater than the rate of deposi- tion. For the location of the stockpile or feeder beach for this type of operation, see Section 6.5, SAND BYPASSING. The need for a jetty or groin between the stockpile or feeder beach and the inlet to prevent return of the material to the inlet must be evaluated where such struc- tures do not already exist. 5.4 SAND DUNES 5.41 FUNCTIONS Sand dunes are an important protective formation. The dune ridges along the coast bar the movement of storm tides and waves into the area behind the beach. Dunes prevent storm waters from flooding the low in- terior areas. Dune ridges farther inland also protect, but to a lesser degree than foredunes. Well-stabilized inland ridges are a second line of defense against water erosion should the foredunes be destroyed by storms. Use of native vegetation may be desirable to stabilize dune sand that might migrate over adjacent areas and damage property. (See Figure 5-4.) Stabilizing dunes also prevents the loss of their protection. At locations with an adequate natural supply of sand, and which are subject to inundation by storms, a belt of dunes can provide protection more effectively at a lower cost than a seawall. (See Section 6.4, SAND DUNES.) Sand dunes near the beach not only protect against high water and waves, but also serve as stockpiles to feed the beach. Sand accumulating on the seaward slope of a dune will extend or build the dune toward the shoreline. This sand, once in the dune, may be returned to the beach by a severe storm and thus nourish the beach. Figure 5-5 is a schematic diagram of storm wave attack on the beach and dune. As shown, the initial attack of storm waves is on the beach berm fronting the dune. When the berm is eroded waves attack the dune. If the wave attack lasts long enough, the dune can be overtopped by waves with resultant lowering of the dune crest. Much of the sand eroded from the berm and dune is transported directly offshore and deposited in a bar formation. This process not only helps to dissipate incident wave energy during a storm, but offshore deposits will normally be transported back to the beach by swells after the storm, Onshore winds transport the sand from the beach toward the foredune area and the dune building proceeds on another natural cycle. This dune build- ing, however, is generally at a very slow rate unless supplemented by fences or vegetation. 5-2! i ae High, well- stabilized barrier dune Migration of unstabilized dune across a road Figure 5-4. Stabilized and Migrating Dunes a-22 Dune Crest Profile A — Normal wave oction Profile B — Initial attock of storm waves A SE Profile A is Crest ’ : Lowering Profile C — Storm wave attock ( of foredune Gr aS MOIGW. | Crest == ACCRETION Bio Profile A Profile D — After storm wave attock, Normal wove action ACCRETION Profile & Figure 5-5. Schematic Diagram of Storm Wave Attack on Beach and Dune 35m) SAND BYPASSING 5.51 GENERAL An inlet is a short narrow waterway connecting the sea or major lake with interior waters. Inlets, either natural or improved to meet navigation requirements, interrupt sediment transport along the shore. Natural inlets have a well-defined bar formation on the seaward side of the inlet. A part of the sand transported alongshore ordinarily moves across the inlet by way of this outer bar - natural sand bypassing. How- ever, the supply reaching the downdrift shore is usually intermittent rather than regular, and the downdrift shore is usually unstable for a considerable distance. If the tidal flow through the inlet into the in- terior body of water is strong, part of the material moving alongshore is carried into and permanently stored in the interior body of water as a middleground shoal, reducing the supply available to nourish downdrift shores. The outer bar normally migrates with a migrating inlet, but the middleground shoal does not. Thus the middleground shoal increases in length as the inlet migrates, and the volume of material stored in the inlet increases. When an inlet is deepened by dredging, through the outer or inner bars or through the channel, additional storage capacity is created to trap available littoral drift, and the quantity which would naturally pass the inlet is reduced. If the dredged material is deposited in deep water or beyond the limits of littoral currents, the supply to the down- drift shore may be nearly eliminated. The resulting erosion is propor- tional to the reduction in rate of supply. An often-used method of inlet improvement has been to flank the inlet channel with jetties or breakwaters. These structures form a barrier to longshore transport of littoral drift. Jetties have one or more of the following functions: to block the entry of littoral drift into the chan- nel, to serve as training walls for inlet tidal currents, to stabilize the position of the navigation channel, to increase the velocity of tidal cur- rents and flush sediments from the channel, and to serve as breakwaters to reduce wave action in the channel. Where there is no predominant direction of longshore transport, jetties may stabilize nearby shores, but only to the extent that sand is impounded at the jetties. The amount of sand avail- able to downdrift shores is reduced, at least until a new equilibrium shore is formed at the jetties. Usually, where longshore transport predominates in one direction, jetties cause accretion of the updrift shore and erosion of the downdrift shore. Stability of the shore downdrift from inlets, with or without jetties, may be improved by artificial nourishment to make up the deficiency in supply due to storage in the inlet. When such nourishment is done mechani- cally by using the available littoral drift from updrift sources, the pro- cess is called sand bypassing. Types of littoral barriers (jetties and breakwaters) which have been generally employed in connection with inlet and harbor improvement are 59-24 shown on Figure 5-6. Where littoral transport predominates in one direc- tion, any of these types would cause accretion to the updrift shore and erosion of the downdrift shore, unless provision is made for sand bypass- ing. At a jettied inlet, Figure 5-6 (Type I), bypassing can normally be performed best by a land-based dredging plant or land vehicles. A floating plant can be used only where the impounding zone is subject to periods of light wave action, or by breaking into the landward part of the impound- ment and dredging behind the beach berm thus leaving a protective barrier for the dredge. Such an operation was performed at Port Hueneme, Cali- fornia, in 1953 (See Section 6.5 SAND BYPASSING.) In any of the types of operations at such a jettied inlet, it is unlikely that bypassing of all of the littoral drift can be attained, and some material will pass around the updrift jetty into the channel, especially after the impound- ing capacity of the jetty has been reached. To ensure more complete bypassing of the littoral drift, the combi- nation of the jettied inlet and offshore breakwater, Figure 5-6 (Type II), was developed. In this design, a floating plant works effectively, com- pletely protected by the breakwater and nearly all of the sand moving in- shore of the offshore breakwater is bypassed. Practically no shoaling of the channel by sand would be expected. Although this type is considered the most effective type of improvement for both navigation and sand by- passing, it is also normally the most costly. The shore-connected breakwater with impoundment at its seaward end, Figure 5-6 (Type III), has been used effectively. Bypassing is performed by a floating plant, although heavy wave action could cause delays when the outer portion of the impoundment is being removed. Nearly all of the sand transported alongshore would be bypassed, either naturally or mechanically, but some shoaling of the navigation channel is likely between dredging operations. The shore-connected breakwater or jetty with a low sill or weir and impounding zone or deposition basin behind the breakwater, Figure 5-6 (Type IV), was designed in an effort to provide for bypassing of the lit- toral drift moving inshore of the seaward end of the weir by a floating plant, thus not permitting any of that part of the littoral drift to shoal the navigation channel. Although weir jetties have been construc- ted at three inlets and partly installed at another inlet, none of them has been in operation long enough to provide complete assurances concern- ing their performance. A successful bypassing operation at Hillsboro Inlet, Florida, (Hodges, 1955), where a basin behind a natural rock ledge is dredged periodically, formed the basis of this design. 5.52 METHODS Several techniques have been employed for mechanically bypassing sand at inlets. Sometimes a combination of techniques has proved to be most practicable and economical. The basic methods are: land-based dredging plants, floating dredges, and land-based vehicles. 3-25 CLEELLLILLE B Littoral Barrier (Jetty) Downdrift Shoreline TYRE ?iswE TaWED INERT Updrift Shoreline impounding Zone (First Stage) Littoral Barrier (Shore connected Breakwater) 2 {mpounding.. Hips Lone Downdrift Shoreline TY. PEstEcSHORE CONNECTED BREAKWATER (Impounding Zone at Seaward End of Breakwater) Figure 5-6. Updrift Shoreline Littoral Barrier (Offshore Breakwater 4 Se Ge Z L477 447 447 Downdrift Shoreline TYPE IL. JETTIED INLET AND OFFSHORE BREAKWATER Updrift Shoreline Low Sill (Weir) Breakwater 757 ?Zone GLE 07 ELLE GOLGI SIS, le, ALLL LLOOA A Fi Ee Downdrift Shoreline TYPE IW. SHORE CONNECTED BREAKWATER (Impounding Zone at Shoreward End of Breakwater) ( Watts,1965) Types of Littoral Barriers where Sand-Transfer Systems have been Employed 26 5.521 Land-based Dredging Plants. a. Plant Considerations. This type of operation usually employs a dredging plant at a fixed position near the beach from which the sand transported alongshore is intercepted as it moves within reach of the plant. Presently, plants are of the pump type and operate basically as an ordinary suction dredge. Plants are positioned on an existing struc- ture; however some are on an independent foundation. Moveable plants located on a pier with capability of dredging along the length and on both sides of the pier have been proposed, but none has been built to date. Such a plant would have a mich larger littoral reservoir or depo- sition basin to accumulate the littoral drift during storm periods when the rate of transport exceeds the pumping capacity of the plant. A plan, using an eductor and pumps located in an impoundment area updrift of an inlet and capable of being moved within that area, is a possible method of bypassing for large-scale operations. Although not used for that pur- pose, an operation of this nature was used at Los Angeles (El Segundo), California, to level ancient dunes well behind the shoreline and trans- port the sand to the beach. Shore processes at a littoral barrier must be studied critically to design and position a fixed bypassing plant. The average annual rate of longshore transport moving to the barrier must be known. This annual rate will normally be the controlling criterion for determining the capa- city of the pumping plant. The average annual impoundment of littoral materials by the littoral barrier is equal to the minimum quantity that must be supplied to the downdrift shores to achieve stability. Short-term fluctuations of the actual rate of littoral material movement to the barrier as on an hourly, daily, or weekly basis may be many times greater or less than the estimated annual rate reduced arithmetically to an hourly, daily, or weekly basis. Therefore, even though a bypassing plant may be designed to handle the total amount of drift reaching a barrier on an an- nual basis, there will be occasions during the year when the quantity of sand reaching the barrier will greatly exceed the pumping capacity of the plant and occasions when the plant may operate well below capacity due to an insufficiency of material reaching the barrier. To establish design criteria, a detailed study must be made of the beach profile updrift of the littoral barrier to determine the best location for the plant along the profile. A comparison of foreshore pro- files over a period of time will aid in predicting the future position of the foreshore and allow a determination of the best position of the plant. Location of the plant too far landward may result in a land-locked plant when the rate of transport reaching the barrier in a short interval of time exceeds the plant's pumping capacity. Such a location may also result in large losses of material around the barrier. A location too far seaward may result in ineffective operation until sufficient materials have been impounded by the barrier and are within reach of the intake mechanism. The disadvantage of the fixed position plant has led to consideration of a movable dredging unit on a trestle with the capability of dredging a long deposition reservoir on both sides. This would increase the capacity fo Fed ay of the littoral reservoir and reduce the possibility of land-locking the plant. Mobility of a land-based dredging plant may overcome some defi- ciencies of a fixed plant, but this has not been demonstrated in field installations. It seems unlikely that such a mobile plant would be able to bypass all material when the rate of arrival at the site is high. Therefore, some material would be lost around the barrier. b. Discharge Line Considerations. The best alignment of the dis- charge line from the fixed plant to the downdrift side of the littoral barrier or inlet is controlled by local conditions. The discharge line must traverse a channel maintained for vessel traffic, and a floating discharge line is impracticable. If the line is positioned on the channel bottom, allowance must be made for protection of the line against damage by pitching ships and by maintenance dredging of the channel. Also, a sub- merged line may need a special flushing system designed to keep the line from clogging when the pumps are shut down, The point of discharge on the downdrift side of the littoral barrier may be of critical importance. The discharge point is not critical in an area with unidirectional longshore transport. However, in areas with trans- port reversals, some of the material at the point of discharge is trans- ported back toward the littoral barrier or into the inlet during periods of transport reversal. This should be kept to a minimum to reduce channel Maintenance, and, where transport reversals occur, a detailed study must be made of the distribution of littoral forces downdrift of the barrier. Tidal currents toward the inlet may frequently predominate over other forces and produce a strong movement of material toward the downdrift jetty, or into the inlet particularly if no downdrift jetty is included in the plan. In this case, the best discharge point will be a point on the shore just beyond the influence of the downdrift jetty and littoral forces tending to move material in an updrift direction. Establishment of this point requires the use of statistical wave data, wave refraction and diffraction diagrams, and data on nearshore tidal currents. If such currents are present, they may sometimes dominate the littoral processes immediately downdrift of the littoral barrier. Alternative points of dis- charge nearer the barrier may also be considered, using groins to impede updrift movement of material at the discharge point. Such alternative considerations are of value in determining the most economical discharge point. 5.522 Floating Dredges. The operation of floating dredges may be classi- fied in two general categories, hydraulic and mechanical. Hydraulic dredges include the suction pipeline dredge with plain suction or with cutter-head for digging in hard material, and the self-propelled hopper dredge. Mechanical types include the dipper and bucket dredges. The pipeline dredges employ a discharge pipeline to transport dredged material to the point or area of placement. Booster pumps may be used in this line if required by distance to discharge point. The standard hopper dredge, although its bins are filled hydraulically, usually discharges by dumping the dredged material out of the bottom of the bins. This type of 5-28 dredge requires disposal areas with enough depth to allow dumping. The hopper dredge is not suitable for bypassing operations unless it dis- charges in an area where the material may be rehandled by another type of dredge or is equipped to pump the material ashore. Since about 1960, a number of hopper dredges have been equipped to pump the material from their bins; thus the hopper dredge has greatly increased in importance in bypassing operations. Mechanical dredges require auxiliary equipment (such as dump scows, conveyors and eductors) to transport material to the point of placement. Equipment and techniques are continually being improved in the transpor- tation of sand; therefore, incorporating a mechanical-type dredge to by- pass material may be most favorable in some cases. In considering a floating dredge for a bypassing operation, each type of dredge plant must be evaluated. This evaluation should include: first, the feasibility of using various types of floating dredges; second, the operational details; and finally, the economics to determine which floating plant will transfer the material at the least unit cost. Local site conditions will vary, and factors to be considered for each type of floating plant cannot be stand- ardized. Some of the more important factors to evaluate follow: a. Exposure of Plant to Wave Action. Wave action limits the effec- tive operation of a floating dredge; the exact limitation depends on plant type and size, and intensity of wave action. This factor is particularly critical if the dredge will be exposed to open waters where high waves may be expected. No standard criteria are available for the maximum permissi- ble wave action for operation of various types of dredges. Such data must be obtained from dredge operators who are familiar with the dredge plant and the area in question. However, as mentioned in Section 6.3 PROTECTIVE BEACHES, a specially designed pipeline dredge has been used successfully at Malaga Cove (Redondo Beach), California, for pumping sand to the beach from offshore in an exposed location. Hopper dredges may be operated in higher waves than the other types of floating dredge plants. Pipeline dredges exposed to hazardous wave action are subject to damage of the ladder carrying the suction line, breakage of spuds, and damage of the pontoon-supported discharge pipe. Thus, estimates must be made of the probable operational time with and without manmade structures or natural ground features to protect the dredge and auxiliary equipment. Determi- nation of the time of year when least wave action will prevail will allow estimates to be made for plant operation under the most favorable conditions. Also, protection of the plant during severe storms in the area of the pro- ject must be considered. b. Plant Capacity. Use of a floating dredge of a specific capac- ity is generally controlled by economic consideration. If the impounding zone of a littoral barrier is large, a periodic bypassing operation may be considered in which a large plant is scheduled and utilized for short periods of time, An alternative would be the use of a small-capacity plant for longer periods of time. If long pumping distances to the dis- charge point necessitate too many booster pumps, a larger plant may pro- vide most economical operation. The choice sometimes depends on avail- ability of plant equipment. c. Discharge Line. See Section 5.521-b. 5.523 Land-Based Vehicles. Local site conditions may favor the use of wheeled vehicles for bypassing operations. Typical factors to be consid- ered and evaluated would be the existence or provision of adequate road- ways and bridges, accessibility to the impounding zone by land-based equipment, the volume of material to be bypassed and the time required to transport the material. Factors involved in locating deposition areas are also the same as discussed in Section 5.521-b. SoS LEGAL ASPECTS The legal consequences stemming from any considered plan of improve- ment are many and complex. Legal problems will vary dependent upon the physical solution employed as well as the jurisdiction in which construction is to occur. The complexities of the legal problems are due not so much to the fact that legal precedent will differ from jurisdiction to jurisdiction, but rather from the application of any given factual setting to a particular body of law. It should also be noted that insofar as the Federal Govern- ment is concerned, liability for personal or property damage will be deter- mined by reference to the Federal Tort Claims Act. Where there is an accumulation at an inlet, whether due to an exist- ing jetty system or as a result of natural action, and where it is desir- able to transfer some of that material to the downdrift beach by whatever method is most feasible, it does not follow that any agency - Federal, State or local - has the right to make the transfer. The accreted land is not necessarily in the public domain. In at least one case in the State of New Jersey, for example, it was decided that an accumulation (although clearly due to an existing inlet jetty system) was owned by the holder of the title to the adjacent upland. The court stated that "gradual and im- perceptible accretions belong to the upland owners though they may have been induced by artificial structures." The phrase ''gradual and imperceptible accretions" is open to legal determination since it would be unusual for one to stand on a beach and clearly see an accretion taking place. Accretion might be detected by surveys at intervals of a month or more. Thus, any agency contemplating bypassing must consult the local legal precedent. At an inlet employing a weir jetty and a deposition basin, updrift accretion may be uncertain. If the weir so interferes with littoral trans- port that it causes the beach initially to fill to the elevation of the top of the weir, it is conceivable that there will be a gradual advance of beach elevations well above the elevation of the weir. This will cause movement of material over the weir to decrease, and there will be accre- tion for some distance updrift of the jetty with consequent legal ques- tions concerning ownership. As impairment of movement over the weir reduces effectiveness of bypassing, it will be desirable to take steps to restore the efficiency of the weir. Such action will inevitably result in loss of updrift accretions, and again legal considerations may arise. 5-30 If the deposition basin in the lee of an offshore breakwater is not cleared of accumulations regularly, it is possible that continuing accre- tion may ultimately produce land from the former shoreline out to the breakwater. Resumption of bypassing operations may then require ownership determination. Legal considerations may even arise on the downdrift beach receiving bypassed sand despite the obvious advantages to most property owners. Another case involved a pier used for fishing, located on a beach that had been artificially nourished. Before this work was commenced, water of adequate depth existed for fishing, but after beach nourishment was commenced, depths decreased along the pier to such an extent that fishing was greatly impaired. The owner then brought suit seeking payment for the loss of value to his pier. It is not the purpose here to set forth a comprehensive discussion of the legal problems encountered in connection with sand bypassing. The above discussion is merely to alert the planner that such problems do arise, and it is therefore prudent to seek legal counsel at the earliest stages of project formulation. Dae GROINS 5.61 INTRODUCTION The groin is probably the type of structure most widely used for shore protection purposes; yet the detailed operation of the groin is poorly understood. Groins or groin systems in many locations have achieved the intended purpose. In other locations, only negligible benefits have resulted, or damaging recession of the downdrift shore- line has been caused, even when groins were apparently successful in accomplishing the design objective. Failures can be traced to a lack of understanding of the functional design of groins and the littoral pro- cesses to which the structures are subjected. 5.62 DEFINITION A groin is a shore protection structure designed to build a pro- tective beach or to retard erosion of an existing or restored beach by trapping littoral drift. Groins are usually perpendicular to the shore and extend from a point landward of predicted shoreline recession into the water far enough to accomplish their purpose. Groins are narrow, and vary in length from less than 100 feet to several hundred feet. Since most of the littoral drift moves in the zone landward of the normal breaker zone (for example about the 6-foot contour on the Atlantic coast), extend- ing a groin seaward of that depth is generally uneconomical. The normal breaker zone for the Gulf coast and less exposed shores of the Great Lakes ranges from 3- to 4-foot depths; more exposed shores of the Great Lakes approach the 6-foot depth. The Pacific coast ranges from 7- to 10-foot depths depending on exposure. Groins may be classified as permeable or impermeable, high or low, long or short, and fixed or adjustable. They are constructed of timber, steel, stone, concrete, or other materials. Impermeable groins have a solid or nearly solid structure which prevents littoral drift from passing through the structure. Permeable groins have openings through the struc- ture big enough to permit passage of significant quantities of littoral drift. Some permeable stone groins are made impermeable by heavy marine growth. A series of groins acting together to protect a long section of shoreline is called a groin system or groin field. Groins differ from jetties structurally and functionally. Jetties are larger with more massive components, and are used primarily to direct and confine the stream or tidal flow at the mouth of a river or inlet, and to prevent littoral drift from shoaling the channel. 5.63 PURPOSE The purpose of groins is to provide or maintain a protective or recreational beach. Groins may be used to: (a) Build or widen a beach by trapping littoral drift; (b) Stabilize a beach, subject to excessive storms or seasonal periods of advance and recession, by reducing the rate of loss; (c) Reduce the rate of longshore transport out of an area by re- orienting a section of the shoreline to an alignment more nearly perpen- dicular to the predominant wave direction; (d) Reduce losses of material out of an area by compartmenting the beach, usually a relatively short section of beach artificially filled seaward of adjacent shores; and (e) Prevent accretion in a downdrift area by acting as a littoral barrier. These ends are attained by reducing the longshore transport rate which decreases the quantity of drift reaching downdrift shores. This can lead to the need for downdrift extension of the system or for arti- ficially nourishing the downdrift shore, unless the system is artificially filled initially and suitably renourished. 5.64 TYPES OF GROINS 5.641 Permeable Groins. Permeability helps avoid.the abrupt offset in shore alignment found at impermeable groins. Part of the littoral forces and materials pass through the groin, and induce sand deposition on both sides of the groin. Many types of permeable groins have been employed. The degree of permeability above the ground line affects the pattern and amount of deposition within the limits of the groin's influence. Insuffi- cient empirical data have been compiled to establish quantitative relation- ships between littoral forces, permeability, and resulting shore behavior. S32 Until such data are available to develop a functional design of permeable groins similar to that in Sections 5.65 through 5.68 for impermeable groins, evaluation and design of permeable groins will be inexact. In general, the desired degree of sand passing the groin can be achieved as effectively and economically by appropriate design of groin height and length, or by notching or lowering the groin on the shore end. Permeable groins are not normally used to retain fill placed to restore or widen a beach. Permeable groins are used in rich-drift areas to widen or prevent recession of specific beach areas and to reduce scalloping (saw-tooth shape) of the shoreline. 5.642 High and Low Groins. The amount of sand passing a groin partly depends on the height of the groin. Groins based where it is unnecessary or undesirable to maintain a sand supply downdrift of the groin, may be built high enough to completely block sand moving in the zone influenced by the groin. Such groins are called terminal groins. Where it is neces- sary to maintain a sand supply downdrift, the groin may be built low enough to allow overtopping by storm waves, or by waves at high tide. Such low groins serve a purpose similar to that of permeable groins. 5.643 Adjustable Groins. Nearly all groins are permanent, fixed struc- tures. However, in England and Florida, adjustable groins have been used. These groins consist of removable panels between piles. These panels can be added or removed to maintain the groin at a specific height (usually 1 to 2 feet) above the beach level, thus allowing a part of the sand to pass over the groin and maintain the downdrift beach. However, if these structures undergo even slight movement and distortion, removal or addi- tion of panels becomes difficult or even impossible. 5.65 GROIN OPERATION A groin is a barrier to sand moving in the zone between its seaward end and the limit of uprush. Height, length, and permeability of the groin determine its effect on longshore transport. ‘The way a groin modifies the littoral transport rate is about the same whether the groin operates singly or as one of a system, provided spacing between adjacent groins is adequate. However a single groin or the updrift groin of a system, may impound less than the other individual groins of a system. The typical groin, illustrated in Figure 5-7, extends from a point landward of the top of the berm to the normal breaker zone (for instance, the 6-foot depth contour on the Atlantic coast). The predominant direction of wave attack shown by the orthogonals will cause a predominant movement Ole toralidnittt. The groin acts as a partial dam that intercepts a part of the normal longshore transport. As material accumulates on the updrift side, supply to the downdrift shore is reduced, and the downdrift shore recedes, This results in a progressively steepening slope on the updrift side and a flattening slope on the downdrift side, since both slopes reach a common elevation near the end of the groin. Since the grain size of the beach = 59 material normally increases to establish a steeper than normal slope, the residual accreted material is probably, by selective processes, the coarser fraction of the material that was in transport. When the accreted slope reaches ultimate steepness for the coarser fraction of available material, impoundment stops, and all littoral drift passes the groin. If the groin is so high that no material passes over it, all transport must be in depths beyond the end of the groin. Because of the nature of transporting currents, the material in transit does not move directly shoreward after passing the groin, and transport character- istics do not become normal for some distance on the downdrift side of the groin. Thus, a system of groins too closely spaced would divert sediment offshore rather than create a widened beach. The accretion fillet on the updrift side of the groin creates a de- parture from normal shore alignment, tending toward a stable alignment perpendicular to the resultant of wave attack. The impounding capacity of the groin thus depends on the stability slope and stability alignment of the accretion fillet. These in turn depend upon characteristics of the littoral material and the direction of wave attack. Figure 5-8 shows the general configuration of the shoreline expected for a system of two or more groins. It assumes a well-established net longshore transport in one direction. 5.66 DIMENSIONS OF GROINS Groin dimensions depend on wave forces to be withstood, the type of groin, and the construction materials used. The length, profile, spacing of groins in a system, direction of wave approach, and rate of longshore transport are important functional considerations. The length of a groin is determined by the distance to depths off- shore where normal storm waves break, and by how much sand is to be trapped. The groin should be long enough to interrupt enough material to create the desired stabilization of the shoreline or accretion of new beach areas. Damage to downdrift shores must be considered in determining the groin length. For functional design purposes, a groin may be considered in three sections: (a) horizontal shore section, (b) intermediate sloped section, and (c) outer section. 5.661 Horizontal Shore Section. This section extends far enough land- ward from the desired location of the crest of berm to anchor the groin and prevent flanking. The height of the shore section depends on the degree to which it is desirable for sand to overtop the groin and replen- ish the downdrift beach. The minimum height for a groin is the height of the desired berm, which is usually the height of maximum high water, plus the height of normal wave uprush. Economic justification for building a groin higher than this is doubtful except for terminal groins. With stone groins, a height about 1 foot above the minimum is sometimes used to re- duce passage of sand between large cap stones. The maximum height of a 5-34 Original Shoreline / Adjusted Shoreline adie + —_»— Direction of Longshore Transport WATER eae Hates Foot Contour Wave ee) PL Original Profile Updrift Profile ___MHW + MEW Groin Profile SECTION Figure 5-7. Illustration of a Typical Groin LAND Resulting Shoreline Original paeniag Groin System a Direction of Longshore Transport WATER Figure 5-8. General Shoreline Configuration for Two or More Groins groin to retain all sand reaching the area (a high groin) is the height of maximum high water and maximum wave uprush during all but the most severe storms. This section is horizontal or sloped slightly seaward, paralleling the existing beach profile or the desired slope if a wider beach is desired or a new beach is to be built. 5.662 Intermediate Sloped Section. The intermediate section extends be- tween the shore section and the level outer section. This part should approximately parallel the slope of the foreshore the groin is expected to maintain. The elevation at the lower end of the slope will usually be determined by the construction methods used, the degree to which it is desirable to obstruct the movement of the material, or the requirements of swimmers or boaters. 5.663 Outer Section. The outer section includes all of the groin extend- ing seaward of the intermediate sloped section. With most types of groins, this section is horizontal at as low an elevation as is consistent with economy of construction and safety, since it will be higher than the de- Sign updrift bottom slope in any case. The length of the outer section will depend on the design slope of the updrift beach. 5.664 Spacing of Groins. The spacing of groins in a continuous system is a function of the length of the groin and the expected alignment of the accretion fillet. The length and spacing must be so correlated that when the groin is filled to capacity, the fillet of material on the up- drift side of each groin will reach to the base of the adjacent updrift groin with a sufficient margin of safety to maintain the minimum beach width desired or to prevent flanking of the updrift groin. Figure 5-9 shows the desirable resultant shoreline if groins are properly spaced. The solid line shows the shoreline as it may develop when erosion is at a maximum at the updrift groin. The erosion shown occurs while the up- drift groin is filling. At the time of maximum recession, the solid line is nearly normal to the direction of the resultant of wave approach and the triangle of recession, a, is approximately equal to the triangle of accretion, b. The dashed line mn _ shows the stabilized shoreline that will obtain after material passes the updrift groin to fill the area between groins and, in turn, commences to pass the downdrift groin. The fillet of sand between groins tends to become and remain perpendicu- lar to the predominant direction of wave attack. This alignment may be quite stable after equilibrium is reached. However, if there is a marked variation in the direction and intensity of wave attack, either season- ally or as a result of prolonged storms, there will be a corresponding variation in the alignment and slope of the shore between groins. Where there is a periodic reversal in the direction of longshore transport, an area of accretion may form on both sides of a groin as shown in Figure 5-10. Between groins, the fillet may actually oscillate from one groin to the other as shown by the dashed lines, or may form a U-shaped beach somewhere in between, depending on the rate of supply of littoral mate- rial, With regular reversals in the direction of longshore transport, the maximum line of recession would probably be somewhat as shown by the solid line, with the triangular area a plus triangular area ¢ about 5-36 Berm Crest at Point of Fi Maximum Recession Direction of Leo) aay, WATER ../ fant Direction of Predominant Wave Approach Figure 5-9. Factors in Determining Beach Width Updrift of a Groin Original Shoreline Wave Orthogonals Figure 5-10, Groin System Operation with Reversal of Transport equal to the circular segment b. The extent of probable beach recession must be taken into account in establishing the length of the horizontal’ shore section of groin and in estimating the minimum width of beach that may be built by the groin system. As a gutde to the spacing of grotns, the following general rule ts suggested: The spacing between groins should equal two to three times the groin length from the berm crest to the seaward end. 5.665 Length of Groin. To determine the horizontal shore and inter- mediate sloped section shoreline position adjacent to a groin, it is necessary to predict the ultimate stabilized beach profile on each side of the groin. Total length, including the horizontal outer (seaward) section, is based on projected position of the breaking zone for normal waves. The steps involved for a typical groin are: (a) Determine the original beach profile in the vicinity of the groin. (b) Determine the direction of longshore transport. (See Section 4.5, Littoral Transport.) (c) Determine the shape of the accretion fillet by the shape of the average impounded fillet over a sufficient period of time at an exist- ing structure where the shore has similar orientation and exposure. If no such structure is available, an estimate may be made by plotting a re- fraction diagram for the mean wave condition, i.e., the wave condition which would produce the greatest rate of longshore transport, and drawing the shoreline or berm crest normal to the orthogonals. (d) Determine the minimum beach width desired updrift of the groin. This may be a width desired to provide adequate recreational area; adequate protection of the backshore area; or with a groin system, adequate width of beach at the next groin updrift to prevent flanking of this groin by wave action. The last condition is shown at point m on Figure 5-9, if line mn represents the berm crest of the beach. (e) The position and alignment of the desired beach relative to the groin under study is indicated by the line mn, Figure 5-9, the line being constructed approximately to the orthogonals based on mean wave con- ditions from m to n. (f) Apply the distance cm from Figure 5-9 to Figure 5-11; this distance plus enough length landward of e¢ to prevent flanking, will represent the length of the horizontal shore section. (g) The slope of the ground line from the crest of the berm sea- ward to about the mean low water line will depend on the gradation of the beach material and the character of the wave action. This section of groin, the intermediate sloped section, Figure 5-11, is usually designed parallel to the original beach profile. The ground line will assume the slope of the groin section mp or a steeper slope if the material trapped is 9-38 coarser than the original beach material. The length of the outer section pr depends on the amount of littoral drift it is desired to intercept. It should extend deep enough for the new profile ps to intercept the old profile ¢e@ds within the toe of the groin. (h) The final beach profile on the updrift side of the typical groin shown in Figure 5-11 is indicated by the line enps. Until the groins are filled, the shoreline on the downdrift side of a groin will be different for an intermediate groin in a system than it will for a single groin or for the farthest downdrift groin in a system. If the system is properly planned and constructed, the shorelines would be about the same for the single and downdrift groins. Considering first an intermediate groin in a groin system, the maxi- mum shore recession on the downdrift side of the groin would occur before the updrift groins fill. During this time the maximum recession would occur when the shoreline between the intermediate groin and the next down- drift groin has reoriented to a position normal to the predominant wave orthogonals such that area a = area b in Figure 5-12. To determine the profile of maximum recession of the downdrift side of the groin, draw the proposed groin on the original beach profile as in Figure 5-12. From the crest of berm at d, lay off distance fd taken from Figure 5-12. Draw the foreshore from crest of berm f to datum plane (MLW) parallel to the original beach slope, and connect that point of intersection with the original profile at the seaward end of the groin. After the line of maximum recession has been reached, as shown by fg on Figure 5-12, the shoreline will begin to advance seaward, main- taining its alignment perpendicular to the net wave orthogonals until enough material flows around or over the downdrift groin to produce a Stabilized shoreline as shown by the line mn in Figure 5-12. To determine the stabilized downdrift line, see Figure 5-13. From the crest of berm at d, lay off the distance dm taken from Figure 5-12. Draw the foreshore slope from the crest of berm f to datum plane (MLW) parallel to the original beach line, then connect that point of intersection with the original profile at the seaward end of the groin. Considering a single groin or the downdrift groin of a system, the maximum recession that could occur may be determined by assuming that the downdrift area loses an amount equal to the full rate of longshore trans- port for the period required for the groin to fill to capacity. It is known that a percentage of the total littoral drift moves seaward of the seaward ends of the groins. It is also known that an additional percent- age of the material moving shoreward of the seaward ends of the groins will bypass the groin before it is completely filled. Accordingly, to approximate the position of the downdrift ground line, it is believed safe to reduce the net longshore transport by some amount depending on 9-39 Horizontal Shore Intermediate Section Sloped Section Outer Section Beach Profile on Updrift Side Original Beach Profile of Groin (c-n-p-s) (c-d-s) Figure 5-ll. Representation of Intermediate Sloped Groin Section Designed Perpendicular to the Beach Line of Maximum Reoriented Berm Crest : Original Berm Crest ef] fe eee Wave Orthogonals Figure 5-12. Stabilized Shoreline Produced by Material Flowing Over or Around Downdrift Groin 5-40 the type of groin constructed. Percentage of net longshore transport considered conservative for computing downdrift losses due to certain groin types based on the normal breaker zone occurring at the 6-foot depth contour (Atlantic coast) is given as follows: (a) For high groins extending to a depth of water 10 feet or more, use 100 percent of the total longshore transport. (b) For high groins extending to a depth of 4 to 10 feet below mean low water (or mean lower low water), or for low groins extending to a depth greater than 10 feet, use 75 percent of the total longshore trans- port. (c) For high groins extending from mean low water to 4 feet below mean low water (or mean lower low water), or for low groins extend- ing to a depth less than 10 feet below mean low water, use 50 percent of the total annual rate of longshore transport. The following steps can now be used to determine the position of the downdrift shoreline or berm crest line: (a) Estimate the time required for the updrift side of the groin to £111), (b) Draw receded shoreline, de (Figure 5-14) with an align- ment determined for the updrift fillet such that area dee in square feet is equal to the volume of littoral material in cubic yards (reduced according to groin type) determined by the time for the groin to fill. (c) Plot the original bottom profile, and show the groin on this profile as in Figure 5-13. Plot ed as the maximum recession to be expected. This method assumes an erodible bottom and: backshore. Wherever a nonerodible substance is encountered, recession would halt at that point. This would also be true where the groins are tied to a seawall or bulk- head. In this case the expected profile seaward of the seawall would be determined as if the seawall were not there or in a similar manner as for scour at a seawall. The position of the bottom where it intersects the seawall would determine the approximate scour to be expected in front of the wall. The deficiency in material would tend to be made up by reces- sion of the shoreline beyond the downdrift end of the seawall. 5.67 ALIGNMENT OF GROINS Examples may be found of almost every conceivable groin alignment, and advantages are claimed by proponents of each type. Based on the theory of groin operation, which establishes the depth to which the groin extends as the critical factor affecting its impounding capacity, maximum economy in cost is achieved with a straight groin perpendicular to the shoreline. Various modifications such as a 7- or L-head are usually designed with 5-4! Groin (dm-Figure 5-12) Stabilized Downdrift Beach Profile Original Profile Profile of Maximum Recession Two Slopes Meet at End of Groin Figure 5-13. Determining Stabilized Downdrift Beach Profile Wave Orthogonals Figure 5-14. Receded Shoreline Assuming an Erodible Bottom and Backshore the primary purpose of limiting recession on the downdrift side of a groin. While these may achieve the intended purpose, the zone of maxi- mum recession is often simply shifted downdrift from the groin, and benefits are thus limited. Storm waves will normally produce greater scour at the seaward extremities of the Z- or L-head structures than at the end of a straight groin perpendicular to the shore, delaying the return to normal profile after storm conditions have abated. Curved, hooked, or angle groins have been employed for the same pur- poses as the 7- or L-head head types. They also invite excessive scour, and are more costly to build and maintain than the straight, perpendicu- lar groin. Where the adjusted shore alignment expected to result from a groin system will differ greatly from the alignment at the time of con- struction, it may be desirable to align the groins normal to the adjusted shore alignment to avoid angular wave attack on the structures after the shore has stabilized. This condition is most likely to be encountered in the vicinity of inlets and along the sides of bays. 5.68 ORDER OF GROIN CONSTRUCTION At sites where a groin system is under consideration, two condi- tions arise: (a) The groin system will be filled artificially, and it is desired to stabilize the new beach in its advanced position; and (b) Littoral transport is depended upon to make the fill, and it is desired to stabilize the existing beach or build additional beach with a minimum of detrimental effect on downdrift areas. With artificial fill, the only interruption of longshore transport will be between the time the groin system is constructed and the time the artificial fill is made. For economy, the fill is normally placed in one continuous operation, especially if it is being accomplished by hydraulic dredge. Accordingly, to reduce the time between groin construction and deposition of fill, all groins should preferably be constructed concur- rently. Deposition of fill should commence as soon as the stage of groin construction will permit. When depending on littoral transport no groin can fill until all of the preceding updrift groins have been filled. Any natural filling will reduce the supply to downdrift beaches. The time required for the entire system to fill and the material to resume its unrestricted movement down- drift may be so long that severe damage will result Accordingly, to reduce downdrift damage, only the groin or group of groins at the down- drift end should be constructed initially. The second groin, or group should not be started until the first has filled and material passing around or over the groins has again stabilized the downdrift beach. Although this method may increase costs, it will not only aid in reducing damage, but will also provide a practicable guide to spacing of groins to verify the design spacing. 5.69 LIMITATIONS ON THE USE OF GROINS Because of its limitations, a groin should be used as a major protective feature only after careful consideration of the many factors involved. Principal factors to be considered are: (a) The adequacy of natural sand supply to ensure that groins will function as desired. (b) Where the supply of littoral drift is insufficient to permit the withdrawal from the littoral stream of enough material to fill the groin or groin system without damage to downdrift areas, artificial place- ment of fill may be required to fill the groin or groin system and thus minimize the reduction of the natural littoral drift to downdrift shores. As previously mentioned, any groin system will reduce the rate of long- shore transport to some degree. (c) The adequacy of shore anchorage of the groins to prevent flank- ing as a result of downdrift erosion. (d) The extent to which the downdrift beach will be damaged by a reduction of material supply if groins are used. (e) The economic justification for groins in comparison with stabi- lization by nourishment alone. Groins are usually considered in areas where the supply of littoral drift is less than the capacity of the littoral transport forces. In these areas, a shoreline adjustment resulting from the installation of a groin or groin system may not reduce the actual transport rate but result only in a reduction of the expected additional losses from the beach fill within the groin system. However, for this to occur, the groins must extend to the surf zone thereby diverting some of the littoral material to the offshore zone resulting in adverse affects to downdrift beaches. Where littoral drift supply satisfies the capacity of transporting forces, the adjustment in the shore alinement resulting from a groin system may result in a reduction in capacity of longshore transport forces at the groined site. Thus, less material is transported along- shore than was the case prior to the construction of the groins, and a permanent adverse effect to the downdrift shore would result. Adverse effects on adjacent shores described above are not necessarily a measure of the effectiveness of the groin or groin system since these groins might well have diverted some of the longshore transport to deep water which in turn has deprived the downdrift beach from receiving a full amount of longshore transport and produced the adverse effect (erosion). 5.610 ECONOMIC DETERMINATION OF GROIN CONSTRUCTION Beaches exposed to wave action constantly change due to variation in wave direction and wave characteristics. In spite of the constant movement of beach materials, a beach will be stable if the rate of loss from an area does not exceed the 5-44 rate of supply to that area. If the rate of supply is less than the rate of loss, erosion and recession of the beach will occur. An eroding beach can be restored by artificially placing a protective beach and subsequently stabilized by artificial nourishment, that is artificial placement of sand to make up the deficiency in rate of supply, or by artificial nourishment supplemented by structures (groins) to reduce the rate of loss. Justifi- cation of groins must be based on the relative costs of the two methods of shore stabilization. On long straight beaches, making up the deficiency of supply presum- ably affects and stabilizes much of the entire reach of shore. A groin system for such a long reach is obviously expensive, but requires less artificial nourishment, especially where nourishment of the shore down- drift of the reach is not required. A method sometimes used for economic determination of such a groin system is to estimate the annual cost of the system, including the annual cost of artificially nourishing the reach with groins and the downdrift shore, to find if this annual cost is less than the estimated annual cost of stabilizing by artificial nourishment alone. No firm guide is available on the reduction in nourishment require- ments where a complete groin system is built. Where the littoral transport rate is high, a groin system will not require artificial nourishment while the groins and offshore area are filling. After filling, no nourishment will be required if the littoral transport rate has not been reduced. The volume required to fill the groin system is easily estimated; the volume required to fill the off- shore area, which is equally important, is difficult to estimate. There- fore, the time needed for complete filling is difficult to estimate, but it may take several years for long groins: During this long time, the downdrift shore will erode unless it is artificially nourished. This nourishment volume will be equal to the volume impounded by the groin system and its offshore area plus any deficiency suffered before groin construction. After complete filling and shore realignment at the groin system, the littoral transport rate will probably be reduced from that required during the filling period and the downdrift shores may require more nourishment. Another approach for economic determination of a groin system for a long reach of shore is to estimate the annual cost as before, and convert this cost to the equivalent quantity of sand that could be placed annually at the estimated cost of sand over the life of the project. This will indicate how much the groins must reduce annual nourishment requirements to be at the break-even point. A judgment is then made as to whether the groin system will actually reduce annual nourishment requirements below the break-even point. The groin system would be justified only if its costs (including reduced nourishment costs) are less than the costs of artificial nourishment alone. Where it is necessary to widen a short beach, perhaps 1 mile or less, it becomes impracticable to maintain the increased width by artificial nourishment of that beach alone. The nourishment material would rapidly 5-45 spread to adjacent shores, and the desired widening of the beach would not be maintained. Here groins are necessary to stabilize the widened beach within the limited reach. This justification by comparison of the estimated annual costs with and without the groin system is therefore impracticable. At the downdrift end of a beach, where it is desired to reduce losses of material into an inlet and stabilize the lip of the inlet, a terminal groin is used. Such a groin must often be justified by benefits from the stabilized shore, as no other method of stabilization would be as suitable and available for a comparative cost. Terminal groins should not be long enough to perform the functions of jetties, but should impound only enough littoral drift to stabilize the lip or edge of the inlet. 5.611 LEGAL ASPECTS’ The legal considerations discussed previously under Section 5.53 are applicable as well to the construction of groins. Legal problems which arise are varied and often complex, due to the diversity of legal precedent in different jurisdictions and the application of the factual setting to a particular body of law. Previous sections covering the functional design of groins emphasize the fact that adverse downdrift shore erosion can be expected if the up- drift side of the groin is not artificially filled to its impounding ca- pacity at the time of groin construction. Liability for property damage insofar as the Federal Government is concerned will be determined with reference to the Federal Tort Claims Act. It is therefore incumbent on the owner of groin-type structures to recognize the legal implications of this coastal structure, and to plan, design, construct and maintain the structure accordingly. It is thus prudent to seek legal counsel at the earliest stages of formulation. So7/ JETTIES Deri DEFINITION A jetty is a structure extending into the water to direct and con- fine river or tidal flow into a channel, and to prevent or reduce the shoaling of the channel by littoral material. Jetties located at the entrance to a bay or river also serve to protect the entrance channel from wave action and cross currents. When located at inlets through barrier beaches, they also stabilize the inlet location. 5.72. TYPES. In the United States, jetties built on the open coast are generally of rubble-mound construction. In the Great Lakes, jetties have also been built of steel sheet-pile cells, caissons, and cribs using timber, steel, or concrete. In sheltered areas, a single row of braced and tied Wake- field timber piling and steel sheet piling have been used. 59-46 5973" 7" SITING The proper siting and spacing of jetties for the improvement of a coastal inlet are important. Careful study, including model studies in some cases, must be given to the following hydraulic, navigation, control structure, sedimentation, and maintenance considerations: a. Hydraulic Factors of Existing Inlet. (1) The tidal prism and cross-section of the gorge in the natural state; (2) Historical changes in inlet position and dimensions (i.e., length, width, and cross-section area of the inlet throat); (3) Range and time relationship (lag) of tide inside and out- side the inlet; (4) Influence of storm surge or wind setup on the inlet; (5) Influences of the inlet on tidal prism of the estuary and effects of fresh water inflow on estuary; (6) Influence of other inlets on the estuary; and (7) Tidal and wind-induced currents in the inlet. b. Hydraulic Factors of Proposed Improved Inlet. (1) Dimensions of inlet (length, width and cross-section area) ; (2) Effects of inlet improvements on currents in the inlet, and on the tidal prism, salinity in the estuary, and on other inlets into the estuary; (3) Effects of waves passing through the inlet; and (4) Interaction of the Hydraulic Factors (item b.) on Naviga- tion and Control Structure Factors, (item c. and d.). c. Navigation Factors of the Proposed Improved Inlet. (1) Effects of wind, waves, tides and currents on navigation channel; (2) Alignment of channel with respect to predominant wave direction and natural channel of unimproved inlet; (3) Effects of channel on tide, tidal prism and storm surge of the estuary; (4) Determination of channel dimensions based on design vessel data and number of traffic lanes; and (5) Other navigation factors such as: (a) Relocation of navigation channel to alternative site; (b) Provision for future expansion of channel dimensions; and (c) Effects of harbor facilities and layout on channel alignment. d. Control Structure Factors. (1) Determination of jetty length and spacing by considering the navigation, hydraulic, and sedimentation factors; (2) Determination of the design wave for structural stability and wave runup and overtopping considering structural damage and main- tenance; and (3) Effects of crest elevation and structure permeability on waves in channel. e. Sedimentation Factors. (1) Effects of both net and gross longshore transport on method of sand bypassing, size of impoundment area, and channel maintenance; and (2) Legal aspects of impoundment area and sand bypassing process. (See Section 5.53.) f. Maintenance Factor. Dredging will be required, especially if the cross-section area required between the jetties is too large to be main- tained by the currents associated with the tidal prism. 5.74 EFFECTS ON THE SHORELINE Effects of entrance jetties on the shoreline are illustrated by Figure 5-15. A jetty (other than the weir type) interposes a total littoral barrier in that part of the littoral zone between the seaward end of the structure and the limit of wave uprush on the beach. Jetties are sometimes extended seaward to the position of the contour equivalent to project depth of the channel. Accretion takes place updrift from the structures at a rate proportional to the longshore transport rate, and erosion downdrift at about the same rate. The quantity of the accumu- lation depends on the length of the structure and the angle at which the resultant of the natural forces strikes the shore. If the angle that the shoreline of the impounded area makes with the structure is acute, the 5-48 impounding capacity is less than it would be if the angle were obtuse. Structures perpendicular to the shore have greater impounding capacity for a given length, and thus are usually more economical than those at an angle, because perpendicular jetties can be shorter and still reach the same depth. If the angle is acute, channel maintenance will be re- quired sooner due to littoral drift passing around the end of the struc- ture. Planning for jetties at an entrance should include some method of bypassing the littoral drift to eliminate or reduce channel shoaling and erosion of the downdrift shore. (See Section 5.5 - SAND BYPASSING.) a fork ae Sty ey Direction of Net Longshore Transport Shi oS Ballona Creek, California-Jan. 1946 Figure 5-15. Effects of Entrance Jetties on Shoreline. 5.8 BREAKWATERS - SHORE-CONNECTED 5.81 DEFINITION A breakwater is a structure protecting a shore area, harbor, anchor- age, or basin from waves. Breakwaters for navigation purposes are con- structed to create calm water in a harbor area, and provide protection for safe mooring, operating and handling of ships, and protection for harbor facilities. Decze WLYPES Breakwaters may be rubble mound, composite, concrete-caisson, sheet- piling cell, crib, or mobile. In the United States, breakwaters built on the open coast are generally of rubble-mound construction. Occasionally, 59-49 they are modified into a composite structure by using a concrete cap for stability. Precast concrete shapes, such as tetrapods or tribars, are also used for armor stone when rock of sufficient size is not obtain- able. In the Great Lakes area, timber, steel, or concrete caissons or cribs have been used. In relatively sheltered areas breakwaters are occasionally built of a single row of braced and tied Wakefield (triple lap) timber piling or steel sheet piling. Several types of floating breawaters have been designed and tested, but few are in use at this time (1972). 5.83 SITING Shore connected breakwaters provide a protected harbor for vessels. The most important factor of siting a breakwater is to determine the best location that will produce a harbor area with minimum wave and surge action over the greatest period of time in the year. This determination is made through the use of refraction and diffraction analyses. Other siting factors are the direction and magnitude of longshore transport, the harbor area required, the character and depth of the bottom material in the pro- posed harbor, and available construction equipment and operating capability. Shore-connected structures are usually built with shore-based equipment. (See Section 5.73 - JETTIES - SITING.) 5.84 EFFECT ON THE SHORELINE The effect of a shore-connected breakwater on the shoreline is illustrated by Figure 5-16. As does a jetty, the shore arm of the break- water interposes a total littoral barrier in the zone between the seaward end of the shore arm and the limit of wave uprush until the impounding capacity of the structure is reached and natural bypassing of the littoral material is resumed. The same accretion and erosion patterns result from the installation of this type of breakwater. The accretion, however, is not limited to the shore arm, but eventually extends along the seaward face of the sea arm, building a berm over which littoral material is trans- ported to form a large accretion area at the end of the structure in the less turbulent waters of the harbor. This type of shoal creates an ideal condition for sand bypassing. A pipeline dredge can lie in the relatively quiet waters behind the shoal, and transfer accumulated material to nourish the downdrift shore. (See Section 5.5, SAND BYPASSING.) Sio8) BREAKWATERS - OFFSHORE SoS DEFINITION An offshore breakwater is a structure designed to protect an area from wave action. Offshore breakwaters may serve as an aid to navigation, a shore-protection structure, a trap for littoral drift, or may serve a combined purpose. 5592 o sier Almost without exception, offshore breakwaters in the United States are of rubble-mound construction. 5-50 eter Accretion a Breakwater ‘Accretion : m Direction of Net Longshore Transport Sr Santa Barbara, alifornia— 1948 Figure 5-16. Effects of Shore-Connected Breakwater on Shoreline 5.93 SITING Offshore breakwaters are sited to provide shelter to a harbor entrance, or to create a littoral reservoir. They may also provide a calm area where small craft may seek refuge or where a pipeline dredge can operate to pump sand to downdrift shores (see Section 5.5, SAND BY- PASSING). An example of this type of siting or use is illustrated in Figure 5-17, which shows Channel Island Harbor entrance at Ventura, California. Offshore breakwaters have also been sited seaward of massive seawalls to provide a first line of defense as illustrated in Figure 5-18. 5.94 EFFECTS ON THE SHORELINE The effects of an offshore breakwater on a shoreline are illustrated by Figure 5-19, Offshore breakwaters are probably the most effective means of completely intercepting movement of littoral material. They are usually positioned in water significantly deeper than the seaward ends of jetties or groins. This makes it possible for them to control a wider part of the littoral zone than structures tied to the shore. Because longshore trans- port is the direct result of wave action, the extent to which the breakwater intercepts the movement of littoral drift is directly proportional to the extent of wave attenuation by the breakwater. 5.95 OPERATION OF AN OFFSHORE BREAKWATER An offshore breakwater initially causes littoral drift to deposit on the shore in its lee by dissipating the wave forces that cause littoral ool ‘s Channel Islands Harbor — Port Hueneme, California - Sept. 1965 > / ae ey oi oa / Sy Mey, LM by U.S NAVAL CONSTRUCTION iia y, je > QV 60! BATTALION CENTER te, ES 7 2 me wy SU \ (Ga RS Spe ae Z Deecuaan = pote J, Feeder beach (i Hueneme area Existing seawall / eILZi_ AN Silver Strand ' MHW. Existing east jetty Existing entrance channe/ Hueneme / 1 SE Xisti tt te \ ate ee ff Existing west jetty: ube 1 Trap ntrance Channe/ ; Conyon Offshore Breakwater 1 4, lean ne y 30 GiCvE ts i Figure 5-17. Siting of Offshore Breakwaters for Sheltering Harbor Entrance Doe uoT}9e}01g 1OJ sTTeMees JO pleMeVS SABeMYPeIg e10YSJJO BuTITS 6b6l-SsisasnyoDssow ‘ydDeqg dosysuIM jJodsupi| asoysbuo07 JON JO UO!JIe1IG - i My i Pe ANY Vd f em j a ray - HL ri a i) iu I CHAPTER 6 STRUCTURAL FEATURES 6.1 INTRODUCTION This chapter provides illustrations of various structural features and detailed discussions of selected coastal engineering projects. This chapter complements discussions in Chapter 5, Planning Analysis. Sections 6.2 through 6.9 provide details of typical seawalls, bulk- heads, revetments, protective beaches, sand dunes, groins, jetties, and breakwaters. These details form a basis for comparing one type of struc- ture with another. They are not intended as recommended dimensions for application to other structures or sites. Section 6.10, Construction Materials, discusses materials for shore structures. Section 6.11, Miscellaneous Design Practices, lists recommendations concerning prevention or reduction of deterioration of concrete, steel and timber waterfront SELUCEULES Ts 6.2 SEAWALLS, BULKHEADS, AND REVETMENTS Onde weES The distinction between seawalls, bulkheads and revetments is mainly a matter of purpose. Design features are determined at the functional planning stage, and the structure is named to suit its intended purpose. In general, seawalls are the most massive of the three, because they resist the full force of the waves. Bulkheads are next in size; their function is to retain fill, and they are generally not exposed to severe wave action. Revetments are the lightest, because they are designed to protect shore- lines against erosion by currents or light wave action. A curved-face seawall and a combination stepped and curved-face sea- wall are illustrated in Figures 6-1 and 6-2. These massive structures are built to resist high wave action and reduce scour. Both seawalls have sheet-pile cutoff walls to prevent loss of foundation material by wave scour and leaching from overtopping water or storm drainage beneath the wall. The curved-face seawall also has an armoring of large rocks at the toe to reduce scouring by wave action. The stepped seawall (Figure 6-3) was designed for stability against moderate waves. The tongue groove provides a space between piles that may be grouted to form a sandtight cutoff wall. Instead of grouting this space, a plastic filter cloth can be used to line the landward side of the sheet piling. The filter-cloth liner provides a sand-tight barrier, and eliminates the buildup of hydrostatic pressure which is relieved through the cloth and the joints between the sheet piles. The rubble-mound seawall (Figure 6-4) was built to withstand sev- ere wave action. Although scour of the fronting beach may occur, rock 6-| SA —— “ aS SERIE TS Galveston, Texas (1965) | 12:0" -K=M.L.Water ‘ ee EI. 1.00 Sheet piles Figure 6-1. Concrete Curved-Face Seawall H- beams 20-0"o.c | 5+0" me 50" SECTION A-A 10" rage Crosswalls = BeOS ae hale SECTION B-B 10 El SECTION © D-D nN VY a Figure 6-2. 7" 6" tubing 20*0" Scupper : Extreme high tide Ni | I | I + 4 _ | | 1-O concrete | | wall between | | sheetpilling Mean sea level =i H | and beam | | Cross walls are to stop at | | | this line, ———_—_—_ | | Two bulb piles replace +o" pedestal pile when sheetpiles « | conflict with pedestal pile. D | | : | = D bass 3-1"x 3°!" pedestal —___ == SECTION C-C each line ‘2 1" I 8"underdrain | and outlet a | 0" a | iA idaenel! | Interlocking sheet piles < =e Concrete Combination Stepped and Curved-Face Seawall oS 9 Treads @18"=13'-6" an i} 8'-o" Original Ground Surface(Variable) eee — sose—8 Steps @ 12 Mean Gulf Level o = £ | a a = Ko} ele ' o — s= = 3 g a ) = c 3 o 23 | . Ss - or Detail of oy ra) NG Sheet Pile Figure 6-3. Concrete Stepped-Face Seawall Harrison County, Mississippi (1 953 Fernandina Beach, Florida (December 1964) Ocean Beach Cap stone 200 Ibs. to 1500 Ibs If the existing beach surface is higher than El. 5.0' MLW. excavation £L. 110’ MLW. shall be required to place the ocean side toe at El. 50'MLW. Elevation varies according to beach surface Core material 200 Ibs. to chips min. 25% > 50 Ibs Note Where walls exist modify section by omitting rock on land side Figure 6-4. Rubble-Mound Seawall comprising the seawall can readjust and settle without causing structural failure. Figure 6-5 shows an adaptation of the rubble-mound seawall shown in Figure 6-4; the stage placement of A and B_ stone utilizes the bank Material to reduce the stone required in the structure. SITIIRISISINT ES TSR Note: Dimensions and details to be a determined by particular site Cut \ ate ) conditions. Large Riprap Stone Figure 6-5. Rubble-Mound Seawall (Typical-Stage Placed) Three structural types of bulkheads (concrete, steel and timber) are shown in Figures 6-6 through 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 verti- cal 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. Exces- sive scouring may endanger the stability of the wall. Structural types of revetments used for coastal protection in exposed and sheltered areas are illustrated in Figures 6-9 through 6-13. There are two types of revetments: the rigid, cast-in-place concrete type illus- trated in Figure 6-9, and the flexible or articulated armor unit type illus- trated in Figures 6-10 through 6-13. A rigid concrete revetment provides excellent bank protection, but the site must be dewatered during construc- tion to pour the concrete. A flexible structure also provides excellent bank protection, and can tolerate minor consolidation or settlement with- out structural failure. This is true for the riprap revetment and to a lesser extent for the interlocking concrete block revetment. Both the articulated block structure and the riprap structure allow for the relief of hydrostatic uplift pressure generated by wave action. The underlying plastic filter cloth and gravel or a crushed-stone filter and bedding layer provide for relief of pressure over the entire foundation area rather than through specially constructed weep holes. Interlocking concrete blocks have been used extensively for shore protection in the Netherlands and England, and have recently become popular 6-6 Virginia Beach, Virginia (March 1953) 20-0" 5" Concrete walkway Headwall cast in place Access Stairs 30' Pile Mean Sea Level SECTION A-A Precast slab 30' Pile Precast king pile 15-6" 10-7 Figure 6-6. Concrete Slab and King-Pile Bulkhead = Nantucket Island, Massachusetts ( 1972) Photograph, Courtesy of U.S. Steel A splash apron may be added Dimensions and details to be next to coping channel to ; determined by particular site reduce damage due to overtopping conditions Coping channel Top of bulkhead Sand fill Former ground surface SIRT SIRT Tide Range Dredge ibaa Round timber pile Timber wale Steel sheet piles Figure 6-7. Steel Sheet-Pile Bulkhead Top Elevation of Bulkheod = Average Height of Highest Yearly Storm Tides Plus Wove Runup. Anchor Pile SECTION ELEVATION NOTE: Dimensions @ Detoils To Be Tie Rod Determined By Porticulor Site Conditions. PLAN Figure 6-8. Timber Sheet-Pile Bulkhead Nace? Pioneer Point, Cambridge, Maryland (before 1966) Courtesy of Portland Cement Association @ expansion joi 4@ expansion joint El. 9.00! 3'6.1. dowel! | 12" SECTION AT JOINT 4" Flap valve H.Water El. 4.60’ Figure 6-9. Concrete Revetment 6-10 a oe gi Chesapeake Bay, Maryland (1972) Topsoil and Seed 4'-6" Rounding 1'-6" min. Elev. 9.00’ Elev. 8.75° oD. iO min. Stone Rip-Roap 2 Ft. Thick Oe (25% > 300 Ibs., 25 %< 30lbs. a 50% wt. >150 Ibs.) 2 oured Concrete ; (Contraction Jt. every 10 ) Gravel Blanket | Ft. Thick (200 Sieve to 3",50%=I-1/2") Over Regraded Bank Elev. - 1.00’ Existing Beach a Elev. 0.00' MSL. Figure 6-10. Riprap Revetment 6-11 Jupiter Island, Florida (1965) Courtesy of Carthage Mills Inc. Erosion Contral Division +1 49) ft. Plastic filter . cloth Interlocking blocks Reinf. conc. cap 16°? 2 to 4-Ton stones Loft 0.5" to 1.0"Gravel on plastic filter cloth, + 8" thick au 5" Plastic filter cloth as far down as possible. E picpav ie Prestressed concrete piling i's) 36 | __=t Section A-A GG “io tock Ship-lap_ “tA ae Joint pas = Section A-A 101234 5ft * “FT 14" block Scole Figure 6-11. Interlocking Concrete-Block Revetment 6=t2 5 eit , Benedict, Maryland (October 1964) Wood railing Concrete sidewalk 3-0" x 6' thick Original ground line_ Ship-lap Joint —%S you Nw MLW Stone toe protection " " digg lie 6 Layer 5} to 15 stone Hardpan 2"x 6" Timber Toe cutoff wall would be required for a sand beach. Figure 6-12. Interlocking Concrete-Block Revetment GIs as 4 - mae & Ps Cedarhurst , Maryland (1970) Etev.43.13 Tongue and Groove Joint 3"Cl. all faces _— ss a 4-*4 as shown th Discontinuous at Joints : = Place | Man Stone Toe Protection as Directecd by Engineer. Average Min. Weight of Stone Placed Shall be 300 Ibs. per Linear Foot of Revetment. Plastic Filter Cloth Elev-2.0 3/4X5' Galv. Rods @ 5' Yc 6"X 8" Timber Liner Figure 6-13. Interlocking Concrete-Block Revetment 6-14 in the United States. Typical blocks are generally square slabs with ship-lap type interlocking joints as shown in Figures 6-11 and 6-12. The joint of the ship-lap type provides a mechanical interlock with adjacent blocks. Stability of an interlocking concrete block depends largely on the type of mechanical interlock. It is impossible to analyze block stability under specified wave action based on the weight alone. However, prototype tests at CERC on blocks having ship-lap joints and tongue-and-groove joints indicate that stability of tongue-and-groove blocks is much greater than the ship-lap blocks. (Hall, 1967.) An installation of the tongue-and- groove interlock block is shown in Figure 6-13. 6.22 SELECTION OF STRUCTURAL TYPE Major considerations for selection of a structural type are: founda- tion conditions, exposure to wave action, availability of materials and costs. The following paragraphs illustrate a procedure for reviewing these factors. 6.221 Foundation Conditions. Foundation conditions may have a significant influence on the selection of type of structure, and can be considered from two general aspects. First, foundation material must be compatible with the type of structure. A structure that depends on penetration for stabi- lity is not suitable for a rock bottom. Random stone or some type of flex- ible structure using a stone mat or plastic filter cloth could be used on a soft bottom, although a cellular steel sheet-pile structure might be used under these conditions. Second, the presence of a seawall, bulkhead or revetment may induce bottom scour and cause failure. Thus, a masonry or mass concrete wall must be protected from the effects of settlement due to bottom scour induced by the wall itself. 6.222 Exposure to Wave Action. Wave exposure may control the selection of both structural type and details of design geometry. In areas of severe wave action, light structures such as timber crib or light riprap revetment should not be used. Where waves are high, a curved, reentrant face wall or possibly a combination of a stepped-face wall with a recurved upper face might be considered over a stepped-face wall. 6.223 Availability of Materials. This factor is related to construction and maintenance costs as well as to structural type. If materials are not available near the construction site, or are in short supply, a particular type of seawall or bulkhead may not be economically feasible. A cost com- promise may have to be made or a lesser degree of protection provided. Cost analysis includes the first costs of design and construction and annual costs over the economic life of the structure. Annual costs include interest and amortization on the investment, plus average maintenanc costs. The best structure is one that will provide the desired protection at the lowest annual or total cost. Because of wide variations in first cost and maintenance costs, comparison is usually made by reducing all costs to an annual basis for the estimated economic life of the structure. 6-15 6.3 PROTECTIVE BEACHES 6.31 GENERAL Planning analysis for a protective beach is described in Section 5.3. Protective beaches may be built with land-hauled sand fill or by pumping sand with a floating dredge through a pipeline to the beach. The dredge picks up the material at the borrow area and pumps it directly to the fill area. The direct pumping method is better suited where the borrow area is not exposed to wave action, although a specially equipped dredge was used successfully in an exposed location in Redondo Beach, Malaga Cove, Calif- ornia. (See Section 6.323.) This dredge was held in position by cables and anchors rather than spuds, and used a flexible suction line with jet agitation rather than the conventional rigid ladder and cutterhead. Dredges with a rigid ladder and cutterhead were used on beach fills at Pompano Beach and Fort Pierce, Florida, where the borrow area was off- shore and exposed to the open ocean. Some hopper dredges are now available with pump-out capability. Hopper dredges load at the borrow site, (normally offshore), move close to the fill site, and then pump from the hoppers through a submerged pipe- line to the beach. (See Section 6.322.) The choice of method depends on the location of the borrow source and availability of suitable equipment. Borrow sources in bays and lagoons may become depleted, or unexploitable because of injurious ecological effects. It is now necessary to place increased reliance on offshore sources. CERC is studying the geomorphology, sediments, and structure of the Inner Continental Shelf with the primary purpose of finding sand deposits suitable for beach fill. Results are published as they become available. (Duane and Meisburger, 1969, Meisburger and Duane, 1971, Meisburger, 1972.) Sand from offshore sources is frequently of better quality for beach fill, because it contains less fine grain size materials. However, equipment suitable for dredging and transporting sand to the beach is not yet readily available. As equipment becomes available, offshore borrow areas will become more important sources of beach fill material. 6.32 EXISTING PROTECTIVE BEACHES Restoration and widening of beaches have come into increasing use in recent years. Examples are Ocean City, New Jersey (Watts, 1956), Virginia Beach, Virginia (Watts, 1959), (Wrightsville Beach and Carolina Beach, North Carolina (Vallianos, 1970), and Harrison County, Mississippi (Escoffier and Dolive, 1954 and Watts, 1958.) Figures 6-14 through 6-23 illustrate details of these projects with before-and-after photographs. A test of beach widening and nourishment from an offshore source by hopper dredge, in 1966, at Sea Girt, New Jersey is described in Section 6.322.’ In 1968, beach widening and nourishment from an offshore source was accom- plished by a pipeline dredge at Redondo Beach, California. (See Section 6.323.) Of the projects mentioned, Carolina Beach, Sea Girt and Redondo Beach are discussed. 6-16 ( 6.321 Carolina Beach, North Carolina. A protective beach was part of the project at Carolina Beach, and is used to illustrate the planning of such a beach. (See Figures 6-20 and 6-21.) The project included hurricane pro- tection, but the illustration of protective beach planning will include only the feature which would have been provided for beach erosion control alone. The report on which the project is based was completed in 1961 (U.S. Army Engineer District, Wilmington, 1961), and the project was partly constructed in 1965. The predominant direction of longshore transport is from north to south. This conclusion was based on southerly growth of an offshore bar at Carolina Beach Inlet, and shoaling at Cape Fear, 12 miles south of Carolina Beach. Subsequent erosion south of Carolina Beach Inlet and accretion north of a jetty at Masonboro Inlet, about 9 miles north of Carolina Beach, have confirmed the direction. The long-term average annual deficiency in material supply for the area was estimated in the basic report at about 4 cubic yards per linear foot of beach, This esti- mate was based on the rate of loss from 1938 to 1957, from the dune line to the 24-foot depth contour. Carolina Beach Inlet, opened in 1952, appar- ently had little effect on the shore of Carolina Beach before 1957; there- fore, that deficiency in supply was considered the normal deficiency with- out regard to the new inlet. For planning, it was estimated that 60 percent of the material in the proposed borrow area in Myrtle Sound (behind Carolina Beach) would be com- patible with the native material on the beach and nearshore bottom, and would be suitable for beach fill. This estimate assumed that 40 percent of the borrow material was finer in size characteristics than the existing beach material and therefore would be winnowed due to its incompatibility with the wave climate. The method of Krumbein and James (1965), was con- Sidered for determining the amount of fill to be placed. However, insuffi- cient samples were taken from the foreshore and nearshore slopes to develop characteristics of grain-size distribution for the native beach sand. Although samples taken from the beach after construction may not be entirely indicative of the characteristics of the native sand, they do represent to some extent the borrow material after it has been subjected to wave action, presumably typical of the wave climate associated with sorting on the natural beach. Samples taken from the original borrow material and from the active beach profile in May 1967 were therefore used to estimate the amount of material lost from the original fill as a result of sorting action. The estimate was made by computing the eritical ratio (Roerit) > defined as the ratio of the volume required to be placed to the volume retained on the beach in equilibrium with shore processes assuming the specific gravities of the borrow and native materials are the same. ° (Mon — Moo)” b 5 Rent ag ~ 295) (6-1) 6— h7 Ce eg \ “y \ Intracoastal ¢69 AN Waterway 1 ral ot Borrow oS Area i; Terminal Groin Stone Groins N & ay X SCALE OF FEET 1000 0 1000 2000 oS os ee Figure 6-14. Protective Beach (Ocean City, New Jersey) 6-18 After Restoration (1952) Figure 6-15. Protective Beach (Ocean City, New Jersey) 6-19 -!==s>\ Laskin Rd. ee (US-58) Restored Beach 25th Normal High Tide Eroded Beach E1-6.0 AT TYPICAL SECTION ARTIFICIALLY RESTORED BEACH 21 Groins Construction Deferred Pacific Ln a= ES z SCALE: NONE US-58(Bus.) Fishing Pier Project Includes: Restoration and periodic nourishment of beach between Rudee Inlet and 49th Street, and deferred con- struction of system of groins. Fishing Pier Borrow Area for Periodic Beach Nourishment ‘eis — RUDEE INLET SCALE IN FEET 500 O 500 1500 Figure 6-16. Protective Beach (Virginia Beach, Virginia) 6-20 OCEAN AshtvANT IC Before Restoration (1951) After Restoration (1960) Figure 6-17. Protective Beach (Virginia Beach, Virginia) “[\a. are XN od \ Future Borrow aN Harbor Island SCALE IN FEET t 500 0 500 1000 1500 In 1 é@ Le 2 = ee | Masonboro Figure 6-18. Protective Beach (Wrightsville Beach, North Carolina) Before Restoration (February 1965) “s ae A By 965) Figure 6-19. Protective Beach (Wrightsville Beach, North Carolina) - After Restoration (June | +/ Masonboro Beach Fishing Piers pee ° “Ser Lim; its i Sto "0 y *00 f} Wilmington Beach Figure 6-20. 6-24 Protective Beach (Carolina Beach, North Carolina) Before Restoration (1964) wy After Restoration (1965) Figure 6-21. Protective Beach (Carolina Beach, North Carolina) 6-25 Park oEESee Seawall anit \ \ Gulfport eo Harbor Noa XS ss aa Seawall Be PASS CHRISTIAN Ss > a HENDERSON ; z 1S cul Pp P ore M CAT ISLAND \ SCALE IN MILES GULF OF MEKIE?O \ 10 ee 250 on Restored Beach EL. 5.0 Ane \ of 50 Profile of Beach Figure 6-22. Protective Beach (Harrison County, Mississippi) Before Restoration (1950) at aaa After Restoration (1952) Figure 6-23. Protective Beach (Harrison County, Mississippi) 6-27 in which Tob and Gyn are the standard deviation in 9 units of the borrow and native materials (in this case 1.28 and 0.91, respectively) and Mop and Mon are the $ means of the borrow and native materials (in this case 0.88 and 1.69 respectively). The critical ratio was computed to be 2.1, indicating that for every cubic yard of material on the active profile in 1967, 2.1 cubic yards of borrow material should have been placed. In April 1965, approximately 2,632,000 cubic yards of borrow material were placed along the 14,000 linear feet of shore fronting Carolina Beach. (Vallianos, 1970.) Figure 6-21.shows the before-and-after conditions of the beach. The fill consisted of a dune having a width of 25 feet at an elevation of 15 feet above mean low water, fronted by a 50-foot wide berm at an elevation of 12 feet above mean low water. Along the northern-most 3,700 feet of the project, (Figure 6-20), the berm was widened to 70 feet to provide a beach-nourishment stockpile. Following construction, rapid erosion occurred along the entire length of the beach fill. Initial adjustments were expected based on the use of Roenit = 2.1 which resulted in an excess of 1,350,000 cubic yards of fill being placed on the beach to account for the unsuitability of part of the borrow material, However, the actual rates of change, particularly those evidenced along the onshore section of the project, were much greater than originally anticipated considering that all of the fill had not been sub- jected to winnowing by wave action. In the first 2 years, erosion persisted along the entire length of fill. The erosion along the southern 10,000 feet of the project was less than that along the northern 4,000 feet. During these years (1965-1967), approximately 712,000 cubic yards, of the 1,652,000 cubic yards initially placed, were moved from the southern 10,000-foot section to depths seaward of the 22-foot contour. This loss was about 43 percent of the total fill placed. Therefore, in terms of fill, protection was reduced by 43 percent. Beach changes resulted in an 82-foot recession of the high water line, and the loss of the horizontal berm of the design profile. By the end of the second year, the southern 10,000 linear feet of project was stabilized, and remained in about the same condition as of 1972. In the first 2 years after the placement of 980,000 cubic yards of fill, erosion along the 4,000-foot northern section was greater than that in the 10,000-foot southern section. About 550,000 cubic yards of fill were lost from the active profile, amounting to a 56 percent reduction in the total in-place fill. By March 1967, the high water line along this section receded 140 feet, resulting in the complete loss of 1,500 linear feet of original fill, and the severe loss of an additional 1,200 feet of fill. This erosion progressed rapidly in a southward direction and threat- ened the more stable southern section of the project. In March 1967, emergency measures were taken. The north end was restored by placing about 360,000 cubic yards of fill, and by building a 405-foot groin near the north end. The groin was necessary, because there was a reversal in the predominant direction of longshore transport at the north end. In the next year, approximately 203,000 cubic yards of emer- gency fill eroded, and most of the shoreline returned to about where it was before the emergency work. The shoreline immediately south of the groin, for a distance of about 400 feet, has remained nearly stable, and the loss of emergency fill along this small segment was about 42 percent less than the loss along the remaining emergency section. Survey records from 1938 to 1957 (reported in the original project report), show that the average annual recession rate was about 1 foot per year, with a short-term maximum rate of 2.8 feet from 1952 to 1957, when the area had been exposed to four major hurricanes. The annual loss of material for the entire active profile was estimated to be about 4 cubic yards per linear foot. During the 2 years following the fill, the effects of shore processes were radically different from processes determined from historical records, During April 1965--April 1966 and April 1966--April 1967, the shoreline receded 67 and 15 feet, respectively, with corresponding losses of 370,000 and 342,000 cubic yards. In the third year, April 1967--April 1968, a marked change occurred in the response of the fill. The rate of shoreline recession dropped to 5 feet per year, and the volume change of material amounted to a slight accretion of about 17,000 cubic yards. Surveys in 1969 indicated that the project was in nearly the same condition as in 1968. Full verification of the project performance will depend on future surveys. However, it can be assumed that the project required 2 years of exposure to reach a state of equilibrium with the prevaiiing enviornment. Rapid recession of the shoreline during the first 2 years was a result of profile adjustment along the active profile which terminates at depths of profile adjustment along the active profile which terminates at depths between -22 and -30 feet mean low water, as well as net losses in volume resulting from natural sorting action which displaced fine material to depths seaward of the active profile. The foreshore and nearshore design profile slope of 1 on 20 was terminated at a depth of 4 feet below mean low water. The adjusted project profile of April 1968 shows the actual profile closing at a depth of about 22 feet below mean low water, with a characteristic bar and trough system. Thus, displacement of the initial fill with the accompanying reduction of the beach design section was the result of normal sorting action and the reestablishment of the normal profile configuration. 6.322 Sea Girt, New Jersey. The feasibility of pumping sand to a beach from an offshore source by hopper dredge was tested from 28 March to 20 May 1966. (U.S. Army Engineer District, Philadelphia, 1967, and Mauriello, 1967). The beach site at Sea Girt, (Figure 6-24) was selected because it was State owned, required nourishment, and a typical ocean environment would be encountered. Other factors which influenced selection of the 6=29 ATLANTIC Mooring Barge Submerged Pipeline > 2 HOPPER DREDGE anise may (Tea = MOORING BARGE ANCHORED ABOUT 2000 FT. OFFSHORE PIPE SLED— WEIGHTED TO OCEAN FLOOR. Figure 6-24. Protective Beach at Sea Girt, New Jersey 6-30 Atter Restoration (June 1966) Figure 6-25. Protective Beach at Sea Girt, New Jersey 6-911 site were an adequate area for assembly of pipeline, the nearness of off- shore sand deposits to the beach, and enough depth (about 30 feet) close to shore to float the dredge and reduce the length of the submerged pipe- Taner The hopper dredge, Goethals (bin capacity, 5,623 cubic yards), dredged sand from the ocean bottom and transported it to an anchored barge where sand in the bins was pumped out through a submerged 28-inch pipeline onto the beach. (See Figure 6-24.) About 250,000 cubic yards were deposited on 3,800 linear feet of beach.. Operations were interrupted by sea conditions and failure of the pipeline connection system. However, total accomplishment of the project was successful, providing information required for improvement of the equipment, and verifying the feasibility of replensihment of beaches by hopper dredges. Figure 6-25 illustrates, with before-and-after photographs, the beach restoration. 6.323 Redondo Beach (Malaga Cove), California (Fisher, 1969, and U.S. Army Engineer District, Los Angeles, 1970). An authorized beach restora- tion project at Redondo Beach, California, provided another opportunity to use an offshore sand source. (See Figure 6-26.) The availability of sand below the 30-foot contour immediately seaward of the project was in- vestigated in two stages. The first stage, a geophysical survey with an acoustic profiler, indicated that enough sand was available for the pro- ject. In the second stage, core samples were obtained from the ocean bottom using a vibrating core-extraction device. Analysis of the core samples verified an underwater sand source of acceptable quantity and quality. This source covered an area 1.4 miles long by 0.5 miles wide about 1,100 feet offshore (shoreward limit). It would produce 2,500,000 cubic yards of sand if it could be worked to a depth 52 feet below MLLW between the 30- to 60-foot isobaths. An additional 2,500,000 cubic yards of sand could be recovered by extending the depth of excavation to 60 feet below MLLW. The median diameter of the beach sand was 0.5 millimeter; the median diameter of the offshore sand ranged from 0.4 to 0.7 millimeter. The offshore sand was considered an excellent source of material for beach replenishment. Several land sources were also investigated, and found Suitable in quantity and quality. Bids, received in August 1967 for land hauling or ocean-bottom re- covery, ranged from $1.07 per cubic yard to more than $2.00 per cubic yard. A contract was awarded to remove the sand from the ocean source. The con- tractor used a modified 16-inch hydraulic dredge, with a water-jet head on the end of a 90-foot ladder. Although the water-jet technique had been used in excavating channels, filling and emptying coffer dams, and pros- pecting for minerals in rivers, its application to dredging in the ocean appears to be unique. Actual dredging began in early December 1967. On 17 December, ocean swells rose to a height of 7 feet. With the dredge heading into the swells, the 90-foot ladder and dredge vessel as a unit could not respond to the short-period waves. Water came into the hold shorting out electrical equipment. Air in the fuel and ballast tanks kept the dredge afloat, and it was towed into Redondo Harbor for extensive modi- fications to make it watertight and seaworthy. Ultimately the dredge 6-32 operated in seas up to 5 feet; at 6-foot seas it proceeded to Redondo Harbor for shelter. The dredge was held in position with its beam to the sea by an arrange- ment on the stern and bow lines. On the end of the dredge ladder was a combination head that provided both cutting action and suction action. The force to lift the suspended material was provided by a suction pump in the well of the dredge, assisted by water jets powered by a separate 250 horsepower pump. Sand was removed by working the head down to the bottom of the cut and keeping it in that position until the sandy material stopped running to the head. The head was then raised and the dredge would pivot about 40 feet to the next position in the cutting row, where the process would be repeated. The dredge could cut a row 250 feet wide. At the com- pletion of a row, the dredge was moved ahead on its lines about 40 feet for the next row cut. For most of the project, it was possible to excavate to -55 to -65 feet, with a cut bank of 20 to 30 feet. This is desirable for high pro- duction because it reduces moving and swinging of the dredge. The sand slurry was transported ashore through a combination pontoon and submerged line. The pontoon line was a 16-inch diameter pipe supported in 60-foot lengths by steel pontoons; each section was joined with a ball- joint coupling. At every third coupling, a 15-foot-long rubber hose was inserted to provide greater flexibility. The pontoon line was connected to the dredge by a quick-release couple that allowed the dredge to be moved swiftly to shelter if a storm arose. The submerged line was steel pipe (with a wall thickness of 3/8 inch) joined to the floating line by a flex- ible rubber hose. As the beach fill progressed, the submerged line was moved by capping the shore end of the discharge, and then pumping water out of the line. This created a floating pipeline that was towed to the next discharge position. As pumping resumed, the pipeline filled and sank to the bottom. The submerged line was connected to the beach fill pipe on shore with a bolted connection. The fill was accomplished by a double-pipe system. The system consisted of a yoke attached to the discharge line, and by use of a double-valve arrangement, the discharge slurry was selectively distri- buted to one pipe or the other or to both pipes simultaneously. The beach was built by placing the first discharge pipe at the desired final elevation of the fill, in this case at +12 MLLW (Figure 6-26) and pumping until the desired elevation was reached. During this pumping peri- od, the second line was built parallel to the first. The valve controlling the first line was closed and the valve to the second line was opened. The first pipe was then advanced to the next discharge point. By alternating between these two discharge lines, the beach width of 200 feet was built to the full cross section as they advanced, (See Figure 6-27.) The final placement totaled 1.4 million cubic yards at a cost of $1.5 million. Between 4,000 and 15,000 cubic yards per day were placed on the beach, averaging 8,000 cubic yards per day. Recent measurements indicated only minor beach changes, and the beach has been relatively stable. 6-33 So, % . 5. AVN a, s %, Yo Harbor r) Co; ic TORRANCE sapseA SCALE IN FEET 500 0 500 1000 VERDES Distance From Base Line (Feet) +20' 0 100 200 300 400 500 600 700 800 900 1000 1100 1200, 1300 1400 of Quantities Elevation "sting = Ce r. Sore Typical Cross Section of Existing and Improved Beach Figure 6-26. Protective Beach (Redondo Beach, California) 6-34 Before Restoration (April 1962) Figure 6-27. After Restoration (September 1968) Photographs Courtesy of Shellmaker Corporation Protective Beach (Redondo Beach, California) @= 35 This project was the first in the United States in which an unprotec- ted hydraulic pipeline dredge was operated. successfully in the open sea. Although highly successful in this project, this procedure has a critical limitation--the necessity for a nearby harbor. Experience gained on this project and the hopper-dredge operation at Sea Girt, (Section 6.322) pro- vides the techniques for further recovery of valuable beach sand from off- shore sources. 6.4 SAND DUNES Foredunes (Fig. 6-28) form just behind the beach and perform an im- portant role in littoral processes. (See Sections 5.4 and 4.6.) Fore- dunes function as a reservoir of sand to nourish eroding beaches during high water, and as a levee to prevent waves from damaging backshore areas. As such, they are valuable nonrigid shore protection structures. Fore- dunes are created naturally by the combined action of sand, wind, and biota. Behind sandy beaches, foredunes often form a continuous line to resist overtopping by high water and wave action. Figure 6-28. Foredune System 6.41 SAND MOVEMENT Winds with sufficient velocity to move sand particles deflate the exposed beach, and transport sand in three ways: (a) Suspension. Small or light grains are lifted into the air stream and carried appreciable distances; (b) Saltation. Individual particles are carried by the wind in a series of short jumps along the beach surface; and (c) Surface Creep. Particles are rolled or bounced along the ground as a result of wind forces or impact of descending saltating particles. These three ways of transportation effectively sort the original beach material. Smaller particles are removed from the beach and dune area. Larger particles remain on the beach. Medium-sized particles form the foredunes. Although most sand particles move by saltation, surface creep may account for 20 to 25 percent of the sand moved. (Bagnold, 1942.) 6.42 DUNE FORMATION Dune building begins when an obstruction causes deposition of sand grains. As the dune builds, the seaward slope may become so steep that saltating or creeping particles come to rest there. With higher wind velocities, particles move up the face of the dune, settle in the lee of the dune, and cause the dune to migrate in the direction the wind is blow- ing. Foredunes are often created and maintained by the action of the beachgrasses in trapping and stabilizing sand blown off the beach. Foredunes may be destroyed by the waves and tides of severe storms, by drought or disease destroying the beachgrasses, or by overgrazing that reduces the vegetative cover permitting local "blowouts." Foredune manage- ment has two divisions--stabilization and maintenance of naturally occur- ring dunes, and creation and stabilization of protective dunes where they do not exist. Although dunes can be constructed by mechanical structures, a preferred procedure is to create a stabilized dune through the use of vegetation. 6.43 DUNE CONSTRUCTION--SAND FENCE Various mechanical methods, such as fencing made of brush or by driving individual pickets into the sand, have been used to construct a foredune. (Blumenthal, 1965, Jagschitz and Bell, 1966a, McLaughlin and Brown, 1942, Gage, 1970.) Relatively inexpensive, readily available slat- type snow fencing (Figure 6-29) is used almost exclusively in artificial dune construction. Plastic fabrics have been investigated for use as sand fences. (Savage and Woodhouse, 1969.) Although some preliminary results were encouraging, these fabrics have not been tested sufficiently to pro- vide an adequate evaluation. Satisfactory, but short-term results have been obtained with jute-mesh fabric. (Barr, 1966.) Studies to develop techniques for constructing dunes of a desired size and profile through use of sand fences have been conducted at Cape Cod, 6-37 Massachusetts; Core Banks, North Carolina; and Padre Island, Texas. Con- clusions and recommendations based upon these studies are: (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 2 inches in width. (b) Only straight fence alignment is recommended. (See Figure 6-30.) Fence configurations with side spurs or a zigzag alignment do not increase the trapping effectiveness enough to be economical. (Savage, 1962.) (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 vegeta- tion line or foredune line prevalent in the area. This distance is usually greater than 200 feet shoreward of the berm crest. (d) The fence should parallel the shoreline. It need not be per- pendicular to the prevailing wind direction. The fence will fill if con- structed with some angularity to sand-transporting winds. (e) If sand moves on the beach, sand fencing with 50 percent poros- ity 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 grain size and wind velocity. (f) More than one lift of fence can be filled within a year, if the fill rate is closely observed. The rate of fill is not constant and varies with local conditions. A fence may nearly fill during a short period of high wind velocities. If the next lift of fence is erected shortly after the filling of the existing fence, it also may be filled within the same season, (g) Installation time and positioning of the succeeding lifts of sand fence depend on the objectives, i.e. to increase the dune height, the width of the dune base, or both. Dune height is increased by erecting succeeding lifts of fence at the crest of the existing dune. (See Figure 6-31.) The effective height increase gained by positioning the fence at the crest is nearly 3 feet with a 4-foot fence as shown by the second lift in Figure 6-31. Note that the effective height gained from the third lift is much less. The third lift was initially erected at the crest of the dune shown by the 24-month profile. Dry, high winds occurred for several days following installation. Turbulence at the dune crest eroded so much sand from the base of the fence that support posts had to be reset to keep the fence upright. Thus the effective height was reduced to 1 foot. Dune width is increased by erecting succeeding lifts of fence parallel to and away from the existing fence. The second lift is placed shoreward or landward of the existing fence depending on the direction the dune is to be constructed. The offset distance between fence lines should be about 6-39 SDX9] ‘PUD|S| aIPOgG--aUNG a2Ua4 puDS |¢-9 aINBI4 (429)) auly aspg wos} aduD}sig (oy 001 08 09 Ov AWNING HEEL can « Ht + Q 1) Hitt SNGE : ANE HEN CHA EE IA ua cueae ma tt Et al + = : AGese Bt iit ages ev v0! ¢ be Le 19 é él pe ye | (0) 0) 0) Joqunn 417 (SyjUOW) awit JDAJaJU] =—- BALD] NwWND NOILO3SY3 JON34 JINGSHOS ( yopaq 40 “44 ul] / “SpA “nd ) JWNIOA GNVS | 2 v| 9 9¢ b2 Z| 0 (SyjuoW) awit (422) TSW aAogn uol}DAa| 3 6-40 SDXa| ‘puD|S| aIPDg--aUNGg adUe4 puDS ‘2¢-9 aNbI4 (4a9}) aul] aspg wo) aouDjsiq 002 08 | 09! Ov! 02! Baie are saa ra ay +5. — a JOQUNN 4317 — (SyJUOW) aWIL NOILO3Y3 3ON33 31NG3SHOS lv g9 v2 v2 v2 Z| 0 0 0 JDAJAJU] = BAIJDJNwWND (SyjuoW) awit ( yoDaq jo 44 ‘ul] / “sph “no ) JWNIOA GNVS (489) ) TSW aAogD uoljDAa} a 6-41 four times the fence height. A 4-foot fence requires fence lines to be 16 feet apart, see third and fourth lifts in Figure 6-32. This arrange- ment is most efficient in trapping sand, and forms a more uniform dune. Positioning the second lift on the slope of the existing dune will increase both its height and width. The actual sequence of installation of the fence may alternate between a position on the crest, along the slope, or offset to the existing dune. (h) The trapping capacity of the initial installation and succeed- ing lifts of a 4-foot high sand fence averages between 2 and 3 cubic yards per linear foot. (See Figures 6-31 and 6-32.) (i) CERC's experience has been that on the average 6 man-hours were required to erect 235 feet of wooden, picket-type fence or 185 feet of fabric fence when a six-man crew had materials available at the site and used a mechanical posthole digger. (j) Unless maintained, dunes created by fencing are short-lived, because of corrosion of wire, deterioration of wood (Figure 6-33), and vandalism. (k) 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. Figure 6-33. Sand Fence Deterioration Due to Exposure and Storms 6-42 (1) The best way to maintain a fence-constructed dune is to plant it with vegetation. 6.44 DUNE CONSTRUCTION - VEGETATION Few plant species survive in the harsh beach environment. Those that thrive along beaches are adapted to conditions that include abrasive and accumulating sand, exposure to full sunlight, high surface temperatures, occasional inundation by salt water, and drought. The plants that do sur- vive 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 only a few plant species 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 beach grass (Amnophila 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 beach grass (Ammophila arenaria) along the Pacific Northwest and California coast (Brown and Hafenrichter, 1948; McLaughlin and Brown, 1942; Kidby and Oliver, 1965; USDA, 1967) sea oats (Untola paniculata), along the South Atlantic and Gulf coast (Woodhouse, Seneca, and Cooper, 1968: Woodard, et al., 1971); panic beach grasses (Panteum amarum) and (amarulum) along the Atlantic and Gulf coasts (Woodhouse, 1970; Woodard, et al., 1971.) 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 - sites subject to erosion. Most critical areas require densely spaced transplants to ensure successful stabiliza- tion. A mechanical transplanter mounted on a tractor is recommended for flat or moderate slopes. (See Figure 6-34.) Steep and irregular slopes must be planted by hand. Seeding is practical only when protection from eroding and drying winds can be provided by mulching or frequent irrigation, and is there- fore not applicable to most beach areas. Beach grass seeds are not avail- able from commerical sources, and must be wild harvested during the fall for spring seeding. Table 6-1 summarizes much of the information about transplanting and sand-trapping ability of the beach grasses. Additional factors for success- ful transplanting are harvesting and processing of transplants, proper placement of dune, and planting transplants. 6.441 Harvesting and Processing. The plants should be dug with care so that most roots remain attached to the plants. The clumps should be sep- arated into transplants having the desired number of culms (stems). Plants should be cleaned of most dead vegetation and trimmed to a length of 18 to 20 inches to facilitate mechanical transplanting. Plants dug while dormant and held in cold storage may be used for late spring plantings. 6-43 Figure 6-34. Mechanical Transplanting of American Beachgrass 6.442 Spacing. The vulnerability of a site to erosion determines trans- plant spacing and culm number. The more vulnerable a site is to erosion, the greater the number of culms per transplant and the closer the plant spacing. (See Table 6-1.) Also, if dense first-year growth is essential, plant spacing should not exceed 18 inches. 6.443 Nutrients. Where field tested, beach grasses have responded to supplemental nutrients by increased foliage production. This in turn, provides greater sand-trapping capacity. Rates of fertilizer are provided in Table 6-1. If first-year growth is satisfactory, the fertilizer program may be reduced to fewer applications and less fertilizer. 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.) 6.444 Seed. American beachgrass can be seeded only on protected sites. Seeding is less expensive than transplanting. However, costs for harvest- ing, chilling and storing seed, plus costs of mulching after seeding, if required, reduce the cost difference. Harvest in the fall from a good stand of American beach grass should yield about 32 pounds of seed to the acre. (Jagschitz, 1960.) After harvest the seed should be chilled at 40°F under moist conditions for 3 to 4 weeks in the northern part of its geo- graphic zone and 2 weeks or less in the southern part. (Seneca, 1969, 6-44 Table 6-1. Beach Grass Planting Summary Species Beach Grass Sea Oats* Planting Season Late fall to early winter Mid-Winter Late winter to early spring optimum Early spring to mid-spring yes Available Source Transplants Commercial Wild-harvest Seed Commercial Wild-harvest Planting Density (maximum and minimum values) (Stem number x plant center spacing in inches) Eroding site 5x6 —3x1i8t|] 5x6 —3x18 J] 1x6 —1x184 3x12—1x18 Noneroding site 3x18 —1x 36 3x18—1x 36 1x18 —1x 48 1x18—1x 48 Fertilizer -MPK £ Rate Ibs./acre (annual) 200-60-0 NET§ Frequency (applications/year) 3 NFT Average Annual Sand-Trapping Rate (cubic yards per lineal foot of beach) Padre Island, Texas NA|| NA 3 (2) Core Banks, N.C. 2(7)£ NA NFT Ocracoke Island, N.C. 2 (7) NA NET Clatsop Spit, Oregan NA 5 (33) NA Annual Rate of Increase in Dune Dimensions (feet) Lateral 7 (7) NFT Elevation | 1 (7) 0.7 (33) * Illegal to harvest in some states. +t 5x6 — 3x18 is5 stems on 6-inch centers to 3 stems on 18-inch centers. = NPK— Nitrogen Phosphorus Potassium. § NFT — Not Field Tested. || NA —Not Applicable. £ Number in parenthesis represents years of record, 6-45 Seneca and Cooper, 1971.) After cold treatment, the seed should be dried and stored under cool, dry conditions until planting. Seeding date should coincide with temperatures best for germination--65°F night, and 85°F days. Best growth of seedlings occurs with daytime temperatures between 80°F and 90°F. (Seneca and Cooper, 1971.) 6.445 Disease and Stress. Beach grasses vary in their tolerance to drought, heat, cold, disease, and parasites. Plantings of a species out- side its natural geographic zone are vulnerable during periods of environ- mental stress. American beach grass is more susceptible to scale infesta- tion when exposure to sand blasting is reduced. Deteriorating stands of American beach grass, due to scale infestation (Ertococcus caroltnea), have been identified from New Jersey to North Carolina. (Campbell and Fuzy, 1972.) South of its natural geographic zone (Nags Head, North Carolina), American beach grass is susceptible to heat (Seneca and Cooper, 1971), and a fungal infection (Marasius blight) is prevalent. (Lucas, etal. 5 19715) South of Virginia, mixed species plantings are desirable and necessary. The slow natural invasion (6 to 10 years) of sea oats into American beach grass dunes (Woodhouse, Seneca and Cooper, 1968), may be hastened by mixed species plantings. Thus with better vegetation cover, the chance of over- topping during storms is reduced. Sea oats and panic beach 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. 6.446 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 edge of the dune and a narrow-based dune is formed. If the plant spacing along the seaward edge 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 edge will be effective. The following example illustrates the interrelationship of planting width, plant spacing, sand volume, and rate of plant growth. American beach grass planted on the Outer Banks of North Carolina at 18 inches and outer spacing of 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 extensive along the seaward face of the dune that most sand was being trapped within the first 25 feet of the dune. American beach grass typically spreads outward by rhizomatous (under- ground stem) growth, and when planted in a band parallel to the shoreline 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 is shown in Figures 6-35 and 6-36. This phenomenon has not occurred with the sea oats plantings in south Texas (Figure 6-37) or Core Banks, North Carolina. (See Figure 6-38.) 6-46 ) oz iain DUI|OJDD YJJON “PUuD|S| 84090190 -- aung ssoiJbyo0ag UDIIJaWY “G¢-9 aInBI4 ( $99} ) aul] asDg Wody adUD\sIq 08! 09) Or! 0d! 001 08 09 Ov tt jo) ett + FEET tH CHEER t t HEE | t ay mam Perret + tT t t t 1 if EEE 3 nage oh tt | } 1 i t i ae + Hf it 4 { t t 1 pad beeanae t { i a a EERE Et HE 959 9°G] 08 6¢ 06 1S 1°¢ I'S v2 0) (0) 0) JOAJajU] = AALYD|NWND (Syjuow) awit ( yoDaq JO 4} Ul] / SpA “nd ) JWNIOA GNVS S&S @ o Tv (42983) TSW eA0gD uol}DAa] J 6-47 > DUIJOJDD YJJON ‘S¥UDg 2405 -- 99Ua4 PUDS JIM ssoJBydDeg UDDIIaWY ‘9¢-9 aINbI4 (4994) aul] aspg wo1y aoudjsig 021 00! ev vel 08 vv 16 SG Z0 Lv Ge 0) 0 0 JOAJaju] = @ALJD]NWND (SyjuoW) awit ( yodaq yo y4 ul] / “SpA “nd ) JWNIOA GNVS 22}) TSW eA0gD uol}DAa]|R 48 SAND VOLUME (cu. yds./ lin. ft. of beach ) Interval Cumulative Time (Months) aa | . TA 4 dudd 0 Fah eae Eadie Hite HEH Hi pectvay eta AT) Hi ea ii — erect ee aii Te EA IHIiue ott cauauane ja aH: aibiditi ie tie Hi Hi ide ‘ E i = +t i ~ i i Tt 5 6 : A 4 eeseueceesucce anon | eC Sdesenae i a} T ng Repes see fa peede eet a8 H ro aa or TELL CLL ELEL eeeeeett een ws oe ae sages o ween } } SPO RRGee Ghee a oa Be PUSH AGNES Aedes eae i janet 7 ws it 1H ol sa ase oes id Bee 6 ale are a a rt mt r 444 SERS owen Tee FE t —S—— — oa rt Geena prea ~ +44. Tt HRS Ee ae a 4 tt t i + HH oI bachet ot i He Ley 6 rere + Hine Tr af dessadett canis ftoaa tied eee ee Et rt : | } rs 2 wo es 4 weeees . at ie oo serenchasn: Pe FS i sk HI Ht Distance from Base Line (feet) Figure 6-37. Sea Oats Dune -- Padre Island, Texas DUI]OJDD YJsJoN ‘SyUDG 2409 -- auNG S}00 DAS ‘gE-9 ainbl4 (}90}) aul asog woody aouD}sig 02! pons | ee: 9¢ 0? 02 ae 0) (0) 0) |DAJ9}U] aAl}D]NWND (SYJUOW)) BwIY ( yoDaq 40 44 ul] /"spf ‘no | SJWMIOA GNVS (488}) TSW anogp uolj0Aa]3 =50, The rate of spread for American beach grass has averaged about 3 feet per year on the landward side of the dune and 7 feet per year on the sea- ward slope of the dune as long as sand was available for trapping. (See Figures 6-35 and 6-36.) The rate of spread of sea oats is considerably less, 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 100-foot wide planting. (See Figure 6-39.) Some sand was trapped while the American beach grass began its growth, but afterwards little sand was trapped by this fence. Figure 6-36 shows how the central part of the planting had a limited increase in elevation due to the reduced amount of sand reaching it. The seaward edge of the dune trapped nearly all of 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. 6.447 Trapping Capacity. Periodic cross-section surveys were made of the plantings to determine the volume of trapped sand, and to document the pro- file of the developing dune. The annual average rate of sand trapped is 2 to 3 cubic yards per linear foot of beach by American beach grass in North Carolina, (Figures 6-35, 6-36), and by sea oats (Figures 6-37 and 6-40), and panic beach grass in Texas. The annual average rate of sand trapped by sea oats in North Carolina is 1 cubic yard. (See Figure 6-38.) European beach grass annual trapping rate on Clatsop Spit, Oregon, has averaged about 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 Figure 6-41.) These rates are much less than the rates of vigorous grass plantings. Small plantings (100 feet square) of American beach grass trapping sand from all directions have trapped as much as 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 vol- ume of sand available for dune construction over a long beach, it does indicate the potential trapping capacity of American beach grass. Similar data for sea gats or panic beach grass are not available. However, obser- vations on the rate of dune growth on Padre Island, Texas following Hurri- cane Beulah (September 1967) indicate that the trapping capacity of sea oats and panic beach grass is greater then the 3 cubic yard 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. 6.448 Dune Elevation. The crest elevation of the constructed dunes is 12 feet MSL on Ocracoke Island (Figure 6-35), 13 feet MSL on Core Banks (Fig- ure 6-36), 10 feet MSL on Padre Island (Figure 6-37) and 37 feet MSL on Clatsop Spit (Figure 6-41). This is an increase of nearly 8 feet for dunes in North Carolina, 6 feet on Padre Island, and 27 feet on Clatsop Spit. Pessoa (See Figure 6-36 for Profile ) 4 Figure 6-39. American Beach Grass Planting with Sand Fence, Core Banks, N.C. (32 months after planting) mw) ies Pa - a - Pe (See Figure 6-37 for Profile) Figure 6-40. Sea Oats Planting South Padre Island, Texas (38 months after planting) 6-92 uobaio ‘4y1ds dosyo|9 -- aung ssosbyo0eg upvadoing “|p-9 ainbi4 (}99)) aul] asog Woy aduDdjsiq 0002 008! 0091 00¢1 oa QO! 008 0 Hie aaa A Hp HEL 7 BAHL | oo HERES EHaHEh STE ae i a aA a See ae HE oo a HE aE tian n+ nr ail Buas pegeape, ie a a a _ : iE HUET ue Binnie a co ae “ Ee nae aa en een a | He HEE EE Ee a cE ee ae Hu Fa eu Te Ga eg ee a Ne Wo at mee - EEE ee orora | ee EEE et al Leia ae EGE, ea nee ae HH EE EE Ee HEE HE EE Ee EE EEE EE EE Ol [o) N (488}) TSW arcgp uoljDAa|Z 6-93 The average annual increment in elevation for 40 cross-sections on Ocra- coke Island since 1964 is 1.01 feet. The average on Core Banks is less-- 0.17 feet for 18 cross-sections since 1965. The elevation increment for 20 cross sections on Clatsop Spit is 0.7 feet per year for 33 years. Undoubtedly the latter average was much higher during the first 5 to 10 years, but survey information is lacking. For the first 3 years on Padre Island, the average increase in elevation has been 2 feet per year. 6.449 Cost Factors. 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 survival rate. Harvesting, processing, and transplanting of sea oats requires one man-hour per 130 hills, panic beach grass requires one man-hour per 230 hills, For example, a 50-foot wide, 1-mile long planting of sea oats on 24-inch centers requires about 500 man-hours for harvesting, processing, and transplanting if plants are locally available. Using a mechanical transplanter, 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 beach grass. 6.5 SAND BYPASSING Several techniques have been used for mechanically bypassing sand at littoral barriers. The type of littoral barriers--breakwaters and jetties --determines the method of sand bypassing that should be employed. The four types of littoral barrier where sand transfer systems have been used are illustrated in Figure 6-42. The basic methods of sand bypassing are: Fixed bypassing plants, floating bypassing plants, and land-based vehicles. Various features combining types of littoral barriers and methods of bypass- ing are illustrated by descriptions of selected projects. 6.51 FIXED BYPASSING PLANTS Fixed bypassing plants have been used at the following Type I (Fig. 6-42) inlet improvements in the United States: Rudee Inlet, Virginia Beach, Virginia; South Lake Work Inlet, Florida; and Lake Worth Inlet, Florida. In other countries, fixed bypassing plants were used at Salina Cruz, Mexico, (U.S. Army, Beach Erosion Board, 1951), Durban, Natal, South Africa, (U.S. Army, Beach Erosion Board, 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, Beach Erosion Board 1952, 6-54 Updrift Shoreline Direction of Net Longshore Transport Littoral Barrier (Jetty) flo Direction of Net Longshore Transport Downdrift Shoreline Downdrift Shoreline TYPE IL. JETTIED INLET AND TYPE 1. VETTIED INLET OFFSHORE BREAKWATER Updrift eh Saas ma Updrift Direction of Net Shoreline ' g Shoreline Longshore Transport Direction of Net Low Sill ( Weir) Littoral Barrier Longshore ys (Shore Connected Transport Breakwater LAA ASSAF LAAAS SEAS? 1 CAAA AAAS FS <\mpounding. CLALEL “7, SALE e oy Zone 277 £65 77" Downdrift Shoreline Downdrift Shoreline TYPE; RRS SHORE TYPE IW. SHORE CONNECTED CONNECTED BREAKWATER BREAKWATER (Impounding Zone at Seaward End of Breakwater) (Impounding Zone at Shoreward End of Breakwater) ( Watts, 1965) Figure 6-42. Types of Littoral Barriers where Sand-Transfer Systems have been used 1955.) At Durban, the plant bypassed about 200,000 cubic yards of sand per year from 1950 to 1954; afterward the amount decreased. The plant was removed in 1959 when not enough littoral drift reached it. No appar- ent 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 and booster pumps along the beach. 6.511 South Lake Worth Inlet, Florida. (Watts, 1953). South Lake Worth Inlet, about 15 miles south of Lake Worth Inlet and about 10 miles south of Palm Beach, was dredged, and two entrance jetties were constructed in 1927. The primary purpose of this inlet was to create a circulation of water in the south end of Lake Worth, to lessen a stagnant water condi- tion. The inlet channel also permits passage of craft drawing up to 6 or 8 feet. It is 125 feet wide and 600 feet long. The entrance jetties are 250 feet long. Their top elevation is 12 feet above mean low water. After jetties were built, the downdrift beach south of the inlet eroded. Construction of a seawall and groin field failed to stabilize the shore- line. A fixed sand bypassing plant began operation in 1937. (See Figure 6-43.) The initial plant was designed to bypass enough sand over 2 years to fill the groins and protect the seawall. Design capacity did not in- clude consideration of total longshore transport. The plant consisted of an 8-inch suction line, a 6-inch centrifugal pump driven by a 65-horsepower diesel engine, and about 1,200 feet of 6-inch discharge line that crossed the inlet on a highway bridge. The outfall was located on the beach south of the south jetty. The plant, with a capacity of about 55 cubic yards of sand per hour, pumped an average of 48,000 cubic yards of sand a year for 4 years. The net north-to-south longshore transport rate was estimated to be about 225,000 cubic yards a year. After 5 years (1937-1941), the beach was partially restored for more than a mile downcoast. During the next 3 years (1942-1945), pumping was discontinued, and the beach south of the inlet severely eroded. In 1945, the plant resumed operation, and the shore immediately south of the inlet was stabilized. To reduce shoaling in the inlet channel, the size of the bypassing plant was increased to an 8-inch pump with a 27-horsepower diesel engine with a capacity of about 80 cubic yards of sand per hour. This plant bypassed about one- third of the available littoral drift. The remainder, about 150,000 cubic yards, was transported by waves and currents to the offshore zone, the middleground shoal, and the downdrift shore. 6.512 Lake Worth Inlet, Florida. (Zermuhlen, 1958, and Middleton, 1959). Lake Worth Inlet is at the north limit of Palm Beach, Florida. The fixed bypassing plant is a two-level, reinforced concrete structure near the end of the north jetty. (See Figure 6-44.) On the lower level (1 foot below MLW) are a centrifugal dredge pump, a 400-horsepower electric motor, and a power transformer. The upper level houses controls and ventilating equipment. The pump has a 12-inch suction and 10-inch discharge, and is designed to handle 15 percent solids at more than 60 percent efficiency. Design capacity was about 170 cubic yards per hour. The suction line is 6-56 (December 1955) ATLANT/C OCEAN Direction of Net Longshore Transport SOUTH LAKE WORTH INLET Pumping Plant Beng ne Pipeline Updrift Downdrift 7 Ne 37 = C Middle Ground Shoal \ ‘N \ 5 arn p----7 ~~ Highway AIA \ aa ee yo 1) Lue LAKE WORTH Intracoastal Waterway Figure 6-43. Fixed Bypassing Plant - South Lake Worth Inlet, Florida 6-57 (Circa, 1961!) ATLANTIC OCEAN North rm Main Pumping Station g Low Groin — Berm Crest ™ South Jetty Scale( Feet) 400 0 400 800 1200 LAKE WORTH INLET a Direction of Net Longshore Transport Discharge Line a Pox Discharge Outfall High Water ee eect _™ _ Figure 6-44. Fixed Bypassing Plant - Lake Worth Inlet, Florida supported by a 30-foot movable boom. The discharge line is 1,750 feet long, and is made of steel pipe with a 1/2-inch wall thickness, except for an 800-foot section of wire-reinforced rubber hose submerged line that crosses the navigation channel. This section can be removed during channel maintenance. Safety features were installed to reduce the possi- bility of clogging the submerged discharge line. The plant began operating in August, 1958. It was estimated that 71,400 cubic yards of sand were bypassed in 451 hours of operation during 8 months, or a rate of about 100,000 cubic yards per year, almost half of the estimated annual littoral transport rate. 6.52 FLOATING BYPASSING PLANTS All four types of littoral barriers (Figure 6-42) have used float- ing plants for harbor and inlet improvements. Floating bypassing plant operations have been used at the following places: TYPE SL Port Hueneme, California TYPE Ef Channel Islands Harbor, California Ventura Marina, California TYPES LULL Fire Island Inlet, New York Santa Barbara, California Oceanside Harbor, California TYPE IV Hillsboro Inlet, Florida Masonboro Inlet, North Carolina Ponce de Leon Inlet, Florida East Pass, Florida Perdido Pass, Alabama 6.521 Port Hueneme, California. (Savage, 1957). This harbor is about 7 miles south-southeast of the mouth of the Santa Clara River. The harbor, constructed in 1940, was acquired by the U.S. Navy in 1942. The 35-foot- deep entrance channel is protected by two converging rubble-mound jetties. (See Figure 6-45.) Littoral drift moves southeast at a rate estimated between 800,000 and 1,200,000 cubic yards a year. (Herron, 1960.) Although the west jetty impounded a substantial amount of sand, its greatest effect was to divert the sand into the Hueneme Canyon, thus pre- venting this material from reaching the shores southeast of Port Hueneme. Before harbor construction, the downdrift shore was exceptionally stable. After construction, the rate of erosion was about 1,200,000 cubic yards per year from 1940 to 1953. In 1953 an emergency project was started at this harbor to reduce downdrift erosion by nourishing the downdrift beaches. 6-59 (Circa, 1953) Accretion Direction of Net Longshore Transport Phase 2 Dredging Area Primary Feeder Beach Proposed Dredge Entry Route Scale (Feet) Dredge Entry Route PACIFIC OCEAN 1000 0 1000 2000 3000 Figure 6-45. Sand Bypassing - Port Hueneme, California Sand trapped by the updrift jetty was pumped to the downdrift beach through a floating pipeline dredge. The dredging procedure used was unique. The outer strip of the impounded beach was used to protect the dredge from wave action during the initial phase. Land equipment exca- vated a hole in the beach, and then a small pipeline dredge enlarged the hole enough to permit a larger dredge to enter from the open sea. The larger dredge completed the Phase 1 dredging, leaving a protective strip of beach for the final operation. In dredging the barrier strip of beach, cuts were made from the Phase 1 area to the mean lower low water line at an angle of about 60 degrees to the shoreline. These diagonal cuts gave the dredge more protection from waves than perpendicular cuts. Since it was necessary to close the dredge entrance channel to prevent erosion of the protective barrier, water had to be pumped into the Phase 1 dredging area to supply the dredge. This problem might have been avoided had the proposed entry route from inside the harbor been used and left open during Phase 1 dredging, rather than the entry route from the open sea. (See Figure 6-45.) From August 1953 to June 1954, 2,033,000 cubic yards of sand were bypassed to two downdrift feeder beaches through a discharge line sub- merged across the harbor entrance. A survey indicated an erosion rate downdrift from the harbor of about 2 million cubic yards from June 1955 to June 1956. Subsequent development of Channel Island Harbor, discussed below, provided periodical nourishment to the downdrift beaches. 6.522 Channel Islands Harbor, California. This harbor, designed to shelter about 1,100 private small craft, was constructed about a mile northwest of the entrance channel to Port Hueneme. (See Figure 6-46.) The design objectives of the littoral barrier were to trap nearly all of the southward moving littoral drift, to prevent losses of drift into the Hueneme Canyon, to prevent shoaling of the harbor entrance, and to protect a floating dredge from waves. The sand bypassing opera- tions transfered dredged sand across both the Channel Islands Harbor entrance and the Port Hueneme entrance to the eroded shore downdrift (southeast) of Port Hueneme (U.S. Army Engineer District, Los Angeles, 1957). The general plan is shown in Figure 6-46. The project consisted of an offshore breakwater and two entrance jetties. The breakwater, 2,300 feet long and located at the 30-foot (September 1965) “ Feeder beach area Vie Dri 5Existing seawall } “Existing east jetty Existing entrance channe/ es P Se Direction of Net jae Th 2.5. Stewlsting west jettycnanne eg ee Longshore Transport: a’. Trap \eptrancethannel” Spee Conyon \ yaa Oe ta Basis por D0 ZO Scale (Feet) N 1000 0 1000 2000 3000 4000 fA 0 € Figure 6-46. Sand Bypassing - Channel Islands Harbor, California. The photo was taken just after 3 million cubic yards had been dredged from the trap 6-62 contour, is a rubble-mound structure with a crest elevation 14 feet above mean lower low water. Its location and orientation enable it to trap almost all of the downcoast littoral drift. The breakwater provides pro- tection from waves for the dredge and for the small craft entering the harbor. The rubble-mound entrance jetties have a crest elevation of 14 feet above mean lower low water, and extend to about the 14-foot isobath. They prevent shoaling of the entrance channel which has a project depth of 20 feet. A floating dredge has cleaned the trap periodically since 1960. In 1960-61, dredging of the sand trap, the entrance channel, and the first phase of harbor development provided about 6 million cubic yards of sand. In 1963, 2 million cubic yards were dredged; in 1965, 3 million cubic yards were transferred. In the Port Hueneme operation (Section 6.521), 2 million cubic yards were transferred in 1953. This total of 13 million cubic yards had stabilized the eroded downdrift shores by 1965. Since 1965, bypassing has continued at intervals of about 2 years. 6.523 Santa Barbara, California. (Wiegel, 1959). The Santa Barbara sand bypassing operation was necessitated by the construction of a 2,800-foot breakwater, completed in 1928, to protect the harbor. (See Figure 6-47.) The breakwater resulted in accretion on the updrift side (west) and ero- sion on the downdrift side (east). Bypassing was started in 1935 by hopper dredges which dumped about 202,000 cubic yards in 22 feet of water about 1,000 feet offshore. Surveys showed that this sand was not moved to the beach. The next bypassing was done in 1938 by pipeline dredge. A total of 584,700 cubic yards of sand was deposited in the feeder beach area shown in Figure 4-47. This feeder beach was successful in reducing erosion downdrift of the harbor, and the operation was continued by placing 4,475,000 cubic yards periodically from 1940 to 1952. The city of Santa Barbara decided in 1957, not to remove the shoal at the seaward end of the breakwater, because it provided additional pro- tection to the inner harbor. A channel is being maintained around the inshore end of the shoal by a small floating dredge. Wave and weather conditions limit operations to about 72 percent of the time. With a capa- city of about 1,600 cubic yards per 8-hour shift, dredging is adequate on a yearly basis, but inadequate to prevent some shoaling of the channel during storms. (August 1965) = anner ly ‘ G 1s) SHOAL \ BREAKWATER FLOATING \—-A SS ‘\ DREDGE Gb ~ w “N G I Q Direction of Net Longshore Transport Figure 6-47. Sand Bypassing - Santa Barbara, California 6-64 6.524 Hillsboro Inlet, Florida. (Hodges, 1955). This inlet is about 36 miles north of Miami Beach, Sand bypassing operations have been by a pipeline dredge. (See Figure 6-48.) This method is well suited for this location, because the littoral material moving to the south is impounded in an area sheltered by a rock reef and rubble-mound jetty. The rock reef and jetty form what has been termed a sand spillway. Dredging the sand behind the spillway and depositing it on the downdrift beach has helped keep the inlet open and has provided nourishment to the downdrift beach. Experience has indicated that about 75,000 cubic yards of sand should be bypassed each year. This plan is the original wetr jetty, and forms the basis for the Type IV design concept. 6.525 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 of the littoral drift has been partly constructed. The part completed in 1966, comprised the north jetty and deposition basin. (See Figure 6-49.) The jetty consists of an inner section 1,700 feet long of concrete sheet piles, of which 1,000 feet is the weir or spillway section, and a rubble-mound outer section 1,900 feet long. The elevation of the weir section (about half-tide level) was established low enough to pass the littoral drift, but high enough to protect a dredge in the deposition basin, and to control tidal currents in and out of the inlet. The elevation appears to be suitable for this location where the mean tidal range is about 4 feet. The basin was dredged to a depth of 16 feet, mean low water, and 367,000 cubic yards of sand were removed. It was planned to redredge the basin at 2-year intervals, and deposit the material to nourish and stabilize downdrift shores. A south jetty, intended to prevent material from entering the channel during periods of longshore transport reversal, has not been built. Without the south jetty, sand that enters the inlet from the south has caused a northward migration of the channel into the deposi- tion basin and against the north jetty. Because migration of the channel has caused navigation problems, model studies are presently in progress to establish the final design of the inlet including the alignment and dimensions of the south jetty. 6.526 Perdido Pass, Alabama. This weir-jetty project was completed in 1969. (See Figure 6-50.) Since the direction of longshore transport is westward, the east jetty included a weir section 1,000 feet long at an elevation 1/2 foot above mean low water. The diurnal tidal range is about 1.2 feet. A deposition basin was dredged between the weir adja- cent to the 12-foot-deep channel. Scour along the basin side of the concrete sheet pile weir was remedied by placing a rock toe on the weir. Nearly all the littoral drift crosses the weir. The deposition basin filled so rapidly that the fill encroached on the channel. Redredging of the basin was necessary in 1971. 6.527 Other Floating Plant Projects. Other sand bypassing projects using floating dredges are at the following locations: 6-65 dl pee: Tes =, | : “* / j ‘ou ee eC 9 i Le val rn a YY ; Yi yy ‘ny Ao A ZA Direction of Net impounding Area (Rock at 15 +) Discharge Line \ \ Uy iy My, Granite Jetty UW \ "Yboo, Jetty \ 500 0 Sand Bypassing - Hillsboro Inlet, Florida Figure 6-48. 6-66 Longshore Transport yf Natural Sand Spillway ATLANTIC OCEAN yO Tiber SCALE (FEET) 00 a ae ( August 1971) =< Sey ae [ J ee ATLANTIC Sip) EES oa Sl Ween De # Soars : OCEAN Soundings in feet referred toMLW °“"" «+. , i % Seo = Surveyed July 1966 icc 500 0 500 1000 Figure 6-49. Sand Bypassing - Masonboro Inlet, North Carolina 6-67 (October 1970) GU Lite OR MEX/CO Direction of Net Longshore Transport Florida Point Cotton fs => Bayou C : \ SCALE (FEET) - = ZN C : $00.4 ° 300 600 900 Figure 6-50. Sand Bypassing - Perdido Pass, Alabama 6-68 i. aoe Z. ventura - 7 . te, ON y = ie __ 7 j// oe aes > _ erieicrion Aca Yar ke North Jetty Ulf Uy e Yi: OCEAN Grass Island Deposition Reservoir 3 e Existing deity “ff emscrat Peiat / f Fira isiond Stote Park Light ———_ Direction of Net SN Longshore Transport Littoral Reservoir Scale (Feet) Jetty Extention 1000 0 1000 2000 3000 4000 5000 te eta ATLANTIC OCEAN Figure 6-52. Sand Bypassing - Fire Island Inlet, New York 6-70 7 Figure 6-53. Ve, % z 4G YY Nan Wy, GAG G4G ig Yui + Ys Z Yyy Si, Mayfly Meryyy NS X\ (Circa, 1968) ZZ My \ “UmyygnY “ % SS OCEAN SCALE (FEET) 600 1200 Sand Bypassing - Oceanside Harbor, California 6-7. (April 1971) oo ea er Halifax River Auece Lighthouse —-US.Coast Guard Reservation <—yion of Net Direction otransport Longshor il wie » ees Fismairn, ae OCEAN one. ts 8 eas ee P [J sas scam SCALE (FEET) ly 1000 ° 1000 2000 3000 4000 Figure 6-54. Sand Bypassing - Ponce de Leon Inlet, Florida, just south of Daytona Beach 6=—f2 (Circa, July 1958) Trestie No 37 oh3 =a AREA Boardwatk Wy » Rock Groin tui] >il/ Trestie No 2.|* Ps < AVON ra ATLANTIC OCEAN » Rock Groin a ray Trestle Not rm Scale (Feet) we SoS 200 0 200 400 600 \ Mi bt Sift dp ===’ North Jetty BSELMAR ee Direction of Net Longshore Boordwaik Transport Sand Bypassing - Shark River Inlet, New Jersey ( Angas, 1960) Figure 6-56. 6-74 Excavating sand from the borrow area ( Angas, 1960) Sand dumped on the beach is distributed by wave action at high water Figure 6-57. Sand Bypassing - Shark River Inlet, New Jersey 6=795 Type II Ventura Marina, California....Figure 6-51 Type III Fire Island Inlet, New York...Figure 6-52 Type III Oceanside Harbor, California..Figure 6-53 Type IV Ponce déeyLeon, Florida..2.... - Figure 6-54 Type IV .. East Pass), 7 Floridarictiy cet nc)] =5 Figure 6-55 6.53 LAND-BASED VEHICLES A bypassing operation at Shark River Inlet, New Jersey (Angas, 1960) used land-based vehicles. The project consisted of removing 250,000 cubic yards of sand from an area 225 feet south of the south jetty and placing this material along 2,500 feet of beach on the north side of the inlet. (See Figures 6-56 and 6-57.) On the south side of the inlet a trestle was built in the borrow area to a point beyond the low water line allow- ing trucks access from the highway to a crane with a 2 1/2-yard bucket. (See Figure 6-57.) Three shorter trestles were built north of the inlet from which the sand was dumped on the beach allowing wave action to distribute it to downdrift beaches. 6.6 GROINS 6.61 TYPES As described in Section 5.6, groins are classified principally 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 sand-filled nylon bags have also been used to a limited extent. Various structural types of groins built with different construction materials.are illustrated in Figures 6-58 through 6-63. | 6.611 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 6-58. The round timber piles forming the primary structural support should be at least 12 inches in diameter at the butt. Stringers or wales, bolted to the piling, should be at least 8 by 10 inches, preferably cut and drilled before being pressure treated with creosote. The sheet piles are usually either of the Wakefield, tongue and groove, or ship-lap type, supported in a vertical position between the wales and secured to the wales with nails. AI1l timbers and piles used for marine construction should be given the maximum recommended pressure treatment of creosote or creosote and coal-tar solution. 6.612 Steel Groins. A typical design for a timber-steel sheet-pile groin is shown in Figure 6-59. 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 6-76 Plonks staggered piling Round pile VIEW-AA Clinched nails pala 2"x8" 2"x8" VIN TIDS wm RRHEN +— G.I. bolt Woter level datum Timber sheet NOTE Dimensions and details tobe determined by particular site conditions Clinched se 4 SHIPLAP TONGUE AND GROOVE WAKEFIELD Wallops Island, Virginia (1964) Variable Variable Variable Water Level Datum Timber Sheet Piling = Vertoble PROFILE , Woshers( PLAN Figure 6-58. Timber Sheet - Pile Groin 77 o \ (1958) VARIABLE VARIABLE VARIABLE G.1.BOLT WATER LEVEL DATUM WATER LEVEL DATUM STRAIGHT WEB PILE 2% STEEL SHEET PILES ARCH WEB PILE PROFILE SECTION A-A G.1.BOLT OUND PILES, ai G.1.BOLT ey) TIMBER WALE a I Sree NG) NAY NAY AEN SAY SHEET PILING 2 Se NOTE: ct) €) TIMBER WALE Dimensions and details to be ye determined by particulor site Z PILE TIMBER BLOCK conditions. PLAN Figure 6-59. Timber-Steel Sheet-Pile Groin 6-78 eit, Evanston, Illinois ( before 1960) Riprap Along North Face of Groin Steel Cap Riprap Along South Face of Groin +8' Sand Fill wi : Haun H u pitti Assumed Clay Line Z-38 Piles Steel Cap ISC 33.9 in Sand Fill | Assumed Clay Line | to 3 Ton Stone Placed Pell Mell Steel Sheet Piling SECTION A-A Figure 6-60. Cantilever Steel Sheet-Pile Groin Presque Isle, Pennsylvania ( October 1965) Shoreline Concrete ,rock,or asphalt cell cap may be used to cover sand or rock filled cells Steel sheet piles Varies Note: Dimensions and details to be determined by particular site conditions. Water level [> ~ PROFILE Figure 6-61. Cellular Steel Sheet-Pile Groin 3 eee eT 1 EA ae rey vey it bey iy en] ia von Lie) ey 1 1 1 bat 1 : t ; H ; a) t | Pile length varied from hey ; | 1 1 22'-0" to 44'-0" od We if Vis au iar bi eit It It ta! ey) et ‘Maa ant Pel el tet at ies Lea i to \ io Lea . 1 pag \ oy, Fm | 1 lin} il eat: \ I ul Te - ! H i 1 1 i imal i yt ies at io Ww ay 7 (al pal ' Il Gl tint I, Ay iol Veal fe er eal lilt ! Jer hell 1 ret i) ‘lel 14 1 | rite nt “ee ! to es vis ah Seal Beach, California (July 1959) 3/4" Chomfer * 3" Clear #4 bor @12"0c 6- #4 Continuous Bend all bors into pile cap as shown Concrete Sheet Piling I" @ Bolt CONCRETE PILE CAP Cast Iron O.G. Washer , 6x 6"x 1/4" steel plate ty x12" Slot for bolt in pile TIMBER WALE (Alternative Design ) 3° Clear . 34° Chomfer CONCRETE PILE SECTION 12" pile dimension voried from 9" to |'-10" depending or. differential loadings. Figure 6-62. Prestressed Concrete Sheet-Pile Groin 6-8! Long Island, New York (circa 1971) Variable Water Level Datum a Qs ‘a- & 2 PROFILE NOTE: Dimensions and details to be Varies determined by particular site conditions CROSS-SECTION Figure 6-63. Rubble-Mound Groin 6-82 of sheet-piles depends on the earth forces to be resisted. Where the forces are small, straight web piles can be used. Where forces 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 arch web sections. The round pile and timbers should be creosoted to maximum treatment for use in waters with marine borers. Figure 6-60 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. The cellular type of steel sheet-pile groin is used on the Great Lakes where adequate pile penetration cannot be obtained for foundation. A typical cellular type groin is shown in Figure 6-61. This groin is comprised of cells of varying sizes, each consisting of semicircular walls connected by cross diaphragms. Each cell is filled with sand or stone to provide structural stability. Concrete, asphalt, or stone caps are used to retain the fill material. 6.613 Concrete Groins. Previously, the use of concrete in groins was generally limited to permeable-type structures that permitted passage of sand through the structure. Many of these groins designs are discussed by Portland Cement Association (1955) and Berg and Watts (1967). A more recent development in the use of concrete for groin construction is illus- trated in Figure 6-62. This groin is an impermeable, prestressed concrete- pile structure with a cast-in-place concrete cap. At a more recent instal- lation at Masonboro Inlet, North Carolina, a double timber wale was used as a cap to provide greater flexibility. 6.614 Rubble-Mound Groins. Rubble-mound groins are constructed with a core of quarry-run material including fine material to make them sand- tight, and covered with a layer of armor stone. The armor stone should weigh enough to be stable against the design wave. A typical rubble- mound groin is illustrated in Figure 6-63. If permeability of a rubble-mound groin is a problem, the voids between stones can be filled with concrete or asphalt grout. This sealing 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, 1969.) 6.615 Asphalt Groins. Experimentation in the U.S. with asphalt groins began in 1948 at Wrightsville Beach, North Carolina. During the next decade, sand-asphalt groins were built at Fernandina Beach, Florida, 6-83 Ocean City, Maryland (Jachowski, 1959), Nags Head, North Carolina, and Harvey Cedars, Long Beach Island, New Jersey. The behavior of sand-ashpalt groins, of the type used to date demon- strates definite limitations of their effectiveness. This is partly due to the limitation of extending the structures beyond the low waterline, and early structural failure of the section seaward of the beach berm crest. The failure in this zone is the result of normal seasonal vari- ability 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. 6.62 SELECTION OF TYPE After planning has indicated that the use of groins is practicable, the selection of groin type is based on varying interrelated factors. No universal type of groin can be prescribed because of the wide variation in conditions at each location. A thorough investigation of foundation materials is essential to selection. 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 of structure of concrete, timber, or steel sheet-piles should be considered. Availability of materials affects the selection of the type of groin because of costs. The economic life of the material and the annual cost of maintenance to attain that economic life are also selection factors. The first 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 much longer life than do the timber or steel sheet-pile groins. These factors, the amount of funds available for initial construction, the annual charges, and the period during which protection will be required, must all be studied before deciding on a particular type. Go) JERRLES 6.71 TYPES The principal construction materials are stone, concrete, steel, and timber. Asphalt has occasionally been used as a binder. Some structural types of jetties are illustrated in Figures 6-64 through 6-66. 6.711 Rubble-Mound Jetties. The rubble-mound structure is a mound of stones of different sizes and shapes either dumped at random or placed in courses. Side slopes and stone sizes are designed so that the structure 6-84 Santa Cruz, California ( 1963) CHANNEL SIDE SEAWARD SIDE Concrete Cap B- Stone Concrete Filled EL. +15.0' 15 N @ EL. + 60' 4 MLLW._EL.0O' 2. é u EEE COme oS 5 te es ARS es {-} FY : Single Row a) 12 B-Stone Chinked ey $Y 25-Ton Quadripods ace eS C-Stone Core Existing Ground SYS SUSY SS SY SSS SS Stone Avg. lOton, Min. 7 ton Stone 50% >60004, min.4000# -Stone 4000# to 4" 50% > 500# Figure 6-64. Quadripod-Rubble-Mound Jetty = hae sy Osi = ots heal Humboldt Bay, California (197!) Existing Concrete Cap 42 Tons Dolos (2 Layers) 10-14 Ton Stone 4' Thick Bedding Existing Structure Layer (after Magoon and Shimizu, 1971) Figure 6-65. Dolos-Rubble-Mound Jetty 6-86 Typel Cells 58.89' Dia. Type I Cells =46.15' Dia. Cover Stone (3 Ton Min) 8' for all cells Type S-28 Steel Sheet Piling 600.0' Stone Mattress x ] =: od ; bet— Stone Mattress Existing Bottom Figure 6-66. Cellular Steel Sheet-Pile Jetty will resist the expected wave action. Rubble-mound jetties illustrated in Figures 6-64 and 6-65 are adaptable to any depth of water and most foundation conditions. Rubble-mound structures are used extensively. Chief advantages are: settlement of the structure results in readjust- ment of component stones, and increased stability, rather than in failure of the structure, damage is easily repaired, and rubble absorbs rather than reflects wave action. Chief disadvantages are: the large quantity of material required, the high first cost if satisfactory material is not locally available, and the wave energy propagated through the structure if the core is not high and impermeable. Where rock armor units in adequate quantities or size are not eco- nomically available, concrete armor units are used. Section 7.376, Concrete Armor Units, discusses the shapes that have been tested and are available, Figure 6-64 illustrates the use of Quadripod armor units on the rubble-mound jetty at Santa Cruz, California. Figure 6-65 illustrates the use of the more recently developed Dolos armor unit where 42- and 43- ton dolos were used to rehabilitate the seaward end of the Humboldt Bay jetties against 40-foot breaking waves. (Magoon and Shimizu, 1971). 6.712 Sheet-Pile Jetties. Timber, steel and concrete sheet-piles have been used for jetty construction where waves are not severe. Steel sheet- piles are used for jetties in various ways. These include: a single row of piling with or without pile buttresses, a single row of sheet-piles arranged so that the row of piles acts 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 which are modifications of the double-wall type. An example of a cellular steel sheet-pile jetty is shown in Figure 6-66. Cellular steel sheet-pile structures require little maintenance and are suitable for construction in depths to 40 feet 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 stone is used to fill the structure, the life will be longer than with sand filling, because holes that corrode through the web have to be big before the stone will leach out. Corrosion is the principal disadvantage of steel in sea water. Sand and water action abrade corroded metal and leave fresh steel exposed. The life of piles in this environment may not exceed 10 years. However, if corrosion is left undisturbed, piles may last more than 35 years. Plastic protective coatings and electrical cathodic pro- tection have effectively extended the life of steel sheet-piles. 6.8 BREAKWATERS--SHORE-CONNECTED Siete TING RENS In exposed locations, breakwaters are generally some variation of a rubble-mound structure. In less severe exposures, both cellular steel and concrete caissons have been used. Figures 6-67 through 6-70 illus- trate structural types of shore-connected breakwaters used for harbor protection, 6.811 Rubble-Mound Breakwaters. The rubble-mound breakwaters in Figures 6-67 and 6-68 are adaptable to almost any depth, and can be designed to withstand severe waves. Figure 6-67 illustrates the first use in the U.S. of tetrapod armor units. The Crescent City, California, Breakwater was extended in 1957 using two layers of 25-ton tetrapods. (Deignan, 1959.) Figure 6-68 illustrates the use of tribar armor units on a rubble- mound structure. The 18-ton tribars were used to rehabilitate the 2,150- foot Nawiliwili breakwater in 1959. (Palmer, 1960.) In 1965, 35- and 50-ton tribars were used in the repair of the East Breakwater at Kahului, Hawaii. 6.812 Stone-Asphalt Breakwaters. (Kerkhoven, 1965 and Asphalt Institute, 1969). At Ijmuiden, the entrance to the port of Amsterdam, The Netherlands, the existing breakwaters were extended in 1964 to provide better protection and enable larger ships to enter the port. (See Figure 6-69.) The southern breakwater was extended 6,890 feet, and now projects 8,340 feet into the open sea to a depth of about 60 feet. These breakwaters had to be heavily protected to withstand wave attack. The Rijkswaterstaat (a government agency of The Netherlands) decided to construct rubble breakwaters in the open sea with a core of heavy stone blocks weighing 660 to 2,200 pounds, Since such blocks were not heavy enough to be stable against prevailing wave attack, a protective cover was needed. Application of a normal sand mastic grouting of the stone core was not possible because the dimensions of the stones and consequently the interstices were too large. A new material called stone-asphalt was developed to protect the stone core. The stone-asphalt contained 60 to 80 percent by weight stones 2 to 20 inches in size, and 20 to 40 percent by weight asphaltic concrete mix with a maximum stone size of 2 inches. The stone-asphalt mix was pourable and required no compaction. During construction the stone core was protected with about 1 ton of stone-asphalt grout per square yard of surface area. For this application the composition was modified, so that it was possible to obtain some pene- tration into the surface layer of the stone core. This stone-asphalt grout was effective and demonstrated the outstanding properties of this material for protection against wave attack. The final protection of the stone core was a layer or revetment of stone asphalt about 7 feet thick. The structure side slopes are 1 on 2 above water and 1 on 1.75 under water. (See Figure 6-69.) The stone-asphalt was manufactured by a double mixing procedure. An asphaltic concrete type of mix was made in a normal hot mix plant and then 6-89 Cresent City, California (1957) SEAWARD SIDE HARBOR SIDE Bray Stone Chinked 7 B'***Concrete Stone Grour / 1 B>* Stone 2-3 Ton EL +200° Concrete Cap EL. + 25.0' EL +18.0' EL.- 30.0, . s "D" Stone é = (Quarry Run ) "B'* stone 1000-2000 Lbs "A" Stone Min. 7 Ton, Avg. 12 Ton % ou B>— One ton variation to 7 ton max enon B3- 1/2 ton to | ton min.- 7 ton max. as available. eH "B" — | ton to 7 tons or to suit depth conditions at seaward toe Figure 6-67. Tetrapod-Rubble-Mound Breakwater Reinforced concrete post !.8 Cede ¢ i by 5 feet high at 5 feet centers 18-ton tribars ( uniformly placed ) Figure 6-68. Tribar-Rubble-Mound Breakwater i" Ijmuiden, The Netherlands (1964) NORTH SEA COAST LINE EXTENSION OF NORTHERN BREAKWATER EXTENSION OF SOUTHERN BREAKWATER CEMENT -CONCRETE CROWN ELEMENT STONE ASPHALT SAND-MASTIC- GROUTED RUBBLE ABOVE ETIER’ FIRST PROTECTION OF STONE CORE WITH A RELATIVELY THIN LAYER OF STONE ASPHALT GROUT MEAN WATER LEVEL STONE ASPHALT UNDER WATER ScaLE eres (after Asphalt Institute,1969) Figure 6-69. Stone Asphalt Breakwater 6-92 blended with dried and preheated stones. Because of the special mixing plant and equipment necessary, this material can be used only on large projects. At Ijmuiden, specially designed 22-ton vehicles transported the stone-asphalt mix to buckets of the same capacity. These buckets were lifted by crane for placing the mix either above or under water. (See Figure 6-69.) A specially designed plot system was used to ensure accurate placement of the mix. Because large amounts were dumped at one time, cool- ing was slow, and successive batches flowed together to form one monolithic revetment. Extension of the breakwaters started in 1964. By the completion of the project in 1967, about 1 million tons of stone asphalt had been used. To date regular maintenance has been required to deal with settle- ments in the stone-asphalt revetment, especially during the summer, but it is expected that a steadily decreasing amount of maintenance will be required. 6.813 Cellular Steel Sheet-Pile Breakwaters. These breakwaters have been used where storm waves are not too severe. The shores of the Great Lakes have moderately high wave exposure. A cellar steel sheet-pile and steel sheet-pile breakwater installation at Port Sanilac, Michigan, is illustrated in Figure 6-70. Cellular steel sheet-pile structures require little maintenance and are suitable for construction in depths up to about 40 feet and into various types of sedimentary foundations. Steel sheet-pile structures have advantages of economy and speed of construction, but are vulnerable to storm damage during construction. Corrosion is the principal dis- advantage of steel in sea water. 6.814 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. Figure 6-71 illustrates the patented perforated type of caisson break- water. (Jarlan, 1961.) The installation at Baie Comeau, Quebec (Stevenson, 1963), utilizes the caisson as a wharf on the harbor side. The holes or perforations on the seaward side reduce the undesirable conditions of a smooth vertical face wall (wave overtopping and wave reflection) by partly dissipating the wave energy within the wave chamber (Marks, 1967), (Marks and Jarlan, 1969), (Terrett, et al., 1969), (Richey and Sollitt, 1969.) 6-93 Figure 6-70. Depth /0 Feet Depth 6 Feet SCALE (FEET) 100 0 100 200 300 400 LAKE SIDE Stoel Sheet Piling LAKE SIDE Steel Sheet Piling 4” Bituminous Cop 4” Bituminous Cop f-—2s 67+} TYPE "A" ~~ Entrance Channel Depth 12 Feet LAKE SIDE LAKE SIDE Steel Sheet Piling Silseiseve Steel Shee! Piling a a 1576.8 £15768 Driven length variable, Average cation 1St1 Oriven length joble. Average /+——- 28 05’ —_-]_ Penetration 611, TYPE “ D>” TYPE Ce TYPICAL SECTIONS OF BREAKWATER SCALE (FEET) A es Se 10 () 10 20 30 40 50 Cellular Steel Sheet-Pile and Sheet-Pile Breakwater 6-94 Baie Comeau, Quebec, Canada (August 1962) ——————————————— —— — éo'-¢° — SSS =e 24 OAin relief hole El. 250 '-O Compacted crushed stone 5'-6" ize 2" Max. siz E1250 Slope - fe) El. 260 4" > scupper- H.W. LOST. ELI5.0 q A Fresh water SY pipe Steel grating air relief hole 2i'-0" Wave Chamber Quarry Run Fill 75 12" L.W.LOST. tA Rubber ELO: 3'-0" @ Holes, |"chamfer ender all around =i 7-4" =t- 7-44 © eS ee) 7-4" = 7'-4"—4 4" © Drain holes E 4-8" Figure 6-71. Perforated Caisson Breakwater 6-95 Caissons are generally suitable for depths from about 10 to 35 feet. The foundation must support the structure and withstand scour, and usually consists of a mat or mound of rubble stone. (See Section 7.38.) 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. 6.9 BREAKWATERS--OFFSHORE GOT YEES Offshore breakwaters can also be classified into two types: rubble- mound and cellular steel sheet-pile. Selection of the type for a given location is dependent on the comparative cost which is dependent on the depth of water, availability of material and wave action. 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 better choice. Figures 6-46 and 6-51 illustrate the use of rubble-mound offshore breakwaters to trap littoral material, to protect a floating dredge, and to protect the harbor entrance. Figure 6-72 illustrates the structural details of the rubble-mound breakwater at Marina Del Rey, Venice, California. Probably the most notable offshore breakwater complex in this country is the 8 1/2-mile-long Los Angeles-Long Beach breakwater built between 1899 and 1949. Other offshore breakwaters are located at Santa Monica, California, built in 1934; Venice, California, built in 1905; and Winthrop Beach, Massachusetts, built in 1933. 6.10 CONSTRUCTION MATERIALS The selection of materials in the structural design of shore protec- tive works depends on the environmental conditions of the shore area. Discussions of criteria that should be applied to materials commonly used follow. 6.101 Concrete. Proper quality concrete is required for satisfactory performance in a marine environment. The quality is obtainable by use of 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, a necessity in freezing climate; adequate cover over reinforcing steel; durable aggregates and proper type of portable cement for the exposure condition. Factors affecting durability of concrete in a marine environment have been reported by Mather (1957). The requirements for durable concrete, consisting of water-cement ratio, air-entrainment, durable aggregate and type of portland cement are discussed in an engineering manual (U.S. Army, Office, Chief of Engineers, 1971b). Details of reinforcing steel are discussed in an engineering manual (U.S. Army, Office, Chief of Engineers, 1971la). 6-96 Marina Del Rey, Venice, California ( before 1966) HARBOR SIDE OCEAN SIDE MLLW. E100 "A-4" Stone "Cc" Stone "A" — Stone — I6 tons or greater "A-1" Stone — 13 tons or greater "A-2" Stone — 8 tons or greater. "A-3" Stone — 6 tons or greater "A-4" Stone — 500 Ibs. to 8 tons "B" Stone — Core stone varies from quarry -run stone to pieces of | ton to 4 tons "Cc" Stone — Core stone varies from quarry - waste to pieces of 1,500 Ibs. to 4 tons. Figure 6-72. Rubble-Mound Breakwater 6-97 6.102 Steel. Where steel is exposed to weathering, allowable working stresses must be reduced to account for corrosion and abrasion. Certain steel chemical formulations are available which offer greater corrosion resistance in the splash zone. 6.103 Timber. Allowable stresses for timber should be those for timbers more or less continuously damp or wet. These working stresses are discussed in U.S. Department of Commerce publications dealing with American lumber standards. 6.104 Stone. Stone for protective structures should be sound, durable, and hard. It should be free from laminations, weak cleavages, and un- desirable weathering, and should be of such character that it will not disintegrate from the action of air, sea water, or in handling and placing. All stone should be angular quarrystone. The greatest dimension should be no greater than three times the least dimension. All stone should conform to the following test designations: apparent specific gravity, ASTM C 127; and abrasion, ASTM C 131. Density is in pounds per cubic foot (solid cubic foot without voids). In general, it is desirable to use stone with a high specific gravity to decrease the volume of material required in the struc- ture. 6.11 MISCELLANEOUS DESIGN PRACTICES Experience with the deterioration of concrete, steel and timber in shore structures may be summarized in the following guidelines: (a) Within the tidal zone, the elimination of as much bracing as is practicable is desirable; maximum deterioration occurs in that zone. (b) Round members, because of a smaller surface area and better flow characteristics, generally have a longer life than other shapes. (c) All steel (c) All steel or concrete deck framing should be located above normal spray level. (d) Untreated timber piles should not be used unless protected from marine-borer attack. (e) The most effective injected preservative 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 creosote and coal-tar solutions is recommended in accordance with standards of the American Wood-Preservers Association. (f) Boring and cutting of piles after treatment should be avoided. Where unavoidable, cut surfaces should receive field treatment. (g) Untreated timber piles encased in a gunite armor and properly sealed at the top will give economical service. 6-98 (h) The lower the water-cement ratio, the more durable the con- crete will be in salt water. (i) Coarse and fine aggregates must be selected carefully for density of gradin, and to avoid unfavorable chemical reaction with the cement. (j) Maintenance of enough concrete cover over all reinforcing steel during casting is very important. (k) Smooth form work and rounded corners improve the durability of concrete structures. (1) Steel in and above the tidal range will last longer if pro- tected by coatings of concrete, corrosion-resistant metals or organic and inorganic paints (epoxies, vinyls, phenolics, etc). f . cy * ofa | D . Neg ‘ “ate tin oh ‘30 eH SEs eG ei ae hvenh af ian Seataphgs Tumi a ea Lasax F 1a"o te 709 |S where yuo na 1 oon: tm) a ay 3 a. + a Ss i rite k O24 Hy Me vin fre Tay ade et Fea * a> nit, : rye enn joiner ‘ ‘we uk Chey ¢ de abr Cerise hh) OOP EVO Thanh! ree eye Lard es BYE! say ret ake " i Zz hoews on a ; F a =F, oF Ges entobite. @ bed ‘ ei.un y , Ai4 yeh ow Ths) gE Laon dLaens Mare Ih OP L871 y Fat (shtt) oy vd lth Raccablad 1 bpeeee 3h va ‘his a) og A) ony zhajyan pase iée : i Hey 7 t +4 s#54067 fo Caw a . tye ‘hy a) ey fed EAs j ier ¥* : { ue * fasy iar ‘ : . lar vaguhi DS a ae eB ile kl i Ll a REFERENCES AND SELECTED BIBLIOGRAPHY ANGAS, W.M., "Sand By-Passing Project for Shark River Inlet," Journal of. the Waterways and Harbors Dtvitston, ASCE, Vol. 86, WW3, No. 2599, Sept. 1960. ASPHALT INSTITUTE, "Sentinel Against the Sea," Asphalt, Jan. 1964. ASPHALT INSTITUTE, "Battering Storms Leave Asphalt Jetty Unharmed," Asphalt, Oct. 1965. ASPHALT INSTITUTE, ''Asbury Park's Successful Asphalt Jetties," Asphalt Jetties, Information Series No. 149, Jan. 1969. AUGUSTINE, M.T., et al., "Response of American Beachgrass to Fertilizer," Journal of Sotl and Water Conservation, Vol. 19, No. 3, 1964, pp. 112- TUS BAGNOLD, R.A., The Phystes of Blown Sand and Desert Dunes, William Morrow, New York, 1942, 265 pp. BARR, D.A., 'Jute-Mesh Dune Forming Fences," Journal of the Sotl Conser- vatton Service of New South Wales, Vol. 22, No. 3, 1966, pp. 123-129. BERG, D.W., and WATTS, G.M., "Variations in Groin Design," Journal of the Waterways and Harbors Diviston, ASCE, Vol. 93, WW2,No. 5241, 1967, pp. 79-100. BLUMENTHAL, K.P., ''The Construction of a Drift Sand Dyke on the Island Rottumerplatt,'' Proceedings of the Ninth Coastal Engineering Conference, ASCE, Ch. 23, 1965, pp. 346-367. BROWN, R.L., and HAFENRICHTER, A.L., "Factors Influencing the Production and Use of Beachgrass and Dunegrass Clones for Erosion Control: I. Effect of Date of Planting," Journal of Agronomy, Vol. 40, No. 6, 1948, pp. 512-521. CAMPBELL, W.V., and FUZY, E.A., ''Survey of the Scale Insect Effect on American Beachgrass,'' Shore and Beach, Vol. 40, No. 1, 1972, pp. 18-19. DEIGNAN, J.E., "Breakwater at Crescent City, California," Journal of the Waterways and Harbors Dtviston, ASCE, Vol. 85, WW3, No. 2174, 1959. DUANE, D.B., and MEISBURGER, E.P., "Geomorphology and Sediments of the Nearshore Continental Shelf, Miami to Palm Beach, Florida," TM-29, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Washington, D.C., Nov. 1969. ESCOFFIER, F.F., and DOLIVE, W.L., "Shore Protection in Harrison County, Mississippi," The Bulletin of the Beach Erosion Board, Vol. 8, No. 3, July 1954, 6-10] FISHER, C.H., "Mining the Ocean for Beach Sand," Proceedings of the Con- ference on Civil Engineering in the Oceans, II, ASCE, 1969, pp. 717-723. GAGE, B.O., "Experimental Dunes of the Texas Coast", MP 1-70, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Washington, D.C... Jan. 1970. HALL, J.V., Jr., "Wave Tests of Revetment Using Machine-Produced Inter- locking Blocks," Proceedings of the 10th Coastal Engineering Conference, ASCE, Ch. 60, 1967, pp. 1025-1035. HAWK, V.B., and SHARP, W.C., "Sand Dune Stabilization Along the North Atlantic Coast," Journal of Sotl and Water Conservation, Vol. 22, No. 4, 1967, pp. 143-146. HERRON, W.J., Jr. ''Beach Erosion Control and Small Craft Harbor Develop- ment at Point Hueneme," Shore and Beach, Vol. 28, No. 2, Oct. 1960, pp. 11-15. HODGES, T.K. "Sand By-Passing at Hillsboro Inlet, Florida," Bulletin of the Beach Erosion Board, Vol. 9, No. 2, Apr. 1955. JACHOWSKT, R.A. "Behavior of Sand-Asphalt Groins at Ocean City, Maryland," MP 2-59, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., May 1959, JAGSCHITZ, J.A., "Research to Rebuild and Stabilize Sand Dunes in Rhode Island,'' Shore and Beach, Vol. 28, No. 1, 1960, pp. 32-35. JAGSCHITZ, J.A., and BELL, R.S., "Restoration and Retention of Coastal Dunes with Fences and Vegetation," Bull. No. 382, Agricultural Experi- ment Station, University of Rhode Island, Kingston, R.I., 1966a. JAGSCHITZ, J.A., and BELL, R.S., 'American Beachgrass (Establishment-- Fertilization--Seeding),'' Bull. No. 383, Agricultural Experiment Station, University of Rhode Island, Kingston, R.I., 1966b. JARLAN, G.L.E., "A Perforated Vertical Wall Breakwater," The Dock and Harbour Authority, Vol. 41, No. 486, Apr. 1961, pp. 394-398. JARLAN, G.L.E. "Note on the Possible Use of a Perforated Vertical-Wall Breakwater,'' Unpublished Manuscript, Hydraulic Laboratory, National Research Council, Ottawa, Canada. KERKHOVEN, R.E., "Recent Developments in Asphalt Techniques for Hydraulic Applications in the Netherlands," Proceedings of the Associatton of Asphalt Paving Technologists, Vol. 34, 1965. KIDBY, H.A., and OLVER, J.R., "Erosion and Accretion Along Clatsop Spit," Coastal Engineering, Santa Barbara Spectalty Conference, ASCE, 1965, pp. 647-672. 6-102 KRUMBEIN, W.C., and JAMES, W.R., "A Lognormal Size Distribution Model for Estimating Stability of Beach Fill Material,"' TM-16, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Washington, DGayeNov. 1965). LUCAS, L.T., et al, '"Marasmius Blight, A New Disease of American Beach- grass,'' Plant Disease Reporter, Vol. 55, No. 7, 1971, pp. 582-585. MAGNUSON, N.C., "Planning and Design of a Low-Weir Section Jetty at Masonboro Inlet, North Carolina," Coastal Engineering, Santa Barbara Spectalty Conference, ASCE, Ch. 36, 1966, pp. 807-820. MAGOON, O.T., and SHIMIZU, N., "Use of Dolos Armor Units in Rubble- Mound Structures, e.g., for Conditions in the Arctic," Proceedings from the First Internattonal Conference on Port and Ocean Engtneer- tng Under Arctte Condittons, Technical University of Norway, Trondheim, Norway, Vol. II, 1971, pp. 1089-1108 (also CERC Reprint R. 1-73). MARKS, W., "A Perforated Mobile Breakwater for Fixed and Floating Appli- cations ," Proceedings of the 10th Conference on Coastal Engineering, ASCE, Vol. 2, 1967, pp. 1079-1129. MARKS, W., and JARLAN, G.L.E., "Experimental Studies on a Fixed Perfor- ated Breakwater," Proceedings of the 11th Conference on Coastal Engi- neering, ASCE, Vol. 2, 1969, pp. 1121-1140. MATHER, B., ''Factors Affecting Durability of Concrete in Coastal Struc- tures ,"" TM-96, U.S. Army, Corps of Engineers, Beach Erosion Board, June 1957. MAURIELLO, L.J., "Experimental Use of Self-Unloading Hopper Dredge for Rehabilitation of an Ocean Beach,'' Proceedings of the World Dredging Conference, 1967, pp. 367-396. McLAUGHLIN, W.T., and BROWN, R.L., "Controlling Coastal Sand Dunes in the Pacific Northwest," Cir. No. 660, U.S. Department of Agriculture, Washington, D.C., Sept. 1942, pp. 1-46. MEISBURGER, E.P., "Geomorphology and Sediments of the Inner Continental Shelf, Chesapeake Bay Entrance," TM-38, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Washington, D.C., June 1972. MEISBURGER, E.P., and DUANE, D.B., ''Geomorphology and Sediments of the Inner Continental Shelf, Palm Beach to Cape Kennedy, Florida,'' TM-34, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Washington, D.C. , Feb. 1971. MIDDLETON, S.R., "Installation and Operation of Fixed Sand Bypassing Plant at Lake Worth Inlet, Florida," Shore and Beach, Vol. 27, No. 9., June 1959. 6-103 PALMER, R.Q., "Breakwaters in the Hawaiian Islands," Proceedings of the American Soctety of Ctvtl Engineers, Waterways and Harbors Division, ASCE, Vol. 86, WW2, No. 2507, 1960. PORTLAND CEMENT ASSOCIATION, "Concrete Shore Protection," 2nd ed., 1955, (Ist ed., 1939). RAYNER, A.C. and MAGNUSON, N.C. ''Stabilization of Masonboro Inlet," Shore and Beach, Vol. 34, No. 2, 1966, pp. 36-41. RICHEY, E.P., and SOLLITT, C.K., "Wave Attenuation by a Porous Walled Breakwater,"' Proceedings of the Conference on Civil Engineering in the Oceans--II, ASCE, 1969, pp. 903-928. SAVAGE, R.P., "Sand Bypassing at Port Hueneme, California," TM-92, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, DaGo sg Wewes IS\s7/, SAVAGE, R.P., "Experimental Study of Dune Building with Sand Fences," Proceedings of the Eighth Conference on Coastal Engineering, ASCE, Council on Wave Research, 1962, pp. 380-396. SAVAGE, R.P., and WOODHOUSE, W.W., Jr., "Creation and Stabilization of Coastal Barrier Dunes," Proceedings of the 11th Conference on Coastal Engineering, ASCE, 1969, pp. 671-700. SENECA, E.D., "Germination Response to Temperature and Salinity of Four Dune Grasses from the Outer Banks of North Carolina," Ecology, Vol. 50, 1969, pp. 45-53. SENECA, E.D., and COOPER, A.W., "Germination and Seedling Response to Temperature, Daylength, and Salinity by Ammophila breviligulata from Michigan and North Carolina," Botantcal Gazette, Vol. 132, No. 3, 1971, pp. 203-215. STEVENSTON, C.A., "Set a Wave to Catch a Wave," Canadian Consulting Engtneer, June 1963. TERRETI, FtL., OSORTOSJieDiC: 5 “and LEAN; G.H.)5 "Modell (Studilesso£ ayRertor= ated Breakwater," Proceedings of the 11th Conference on Coastal Engt- neering, ASCE, Vol. 2, 1969, pp. 1104-1120. U.S. ARMY, CORPS OF ENGINEERS, "Bypassing Littoral Drift at a Harbour Entrance ,"' The Bulletin of the Beach Erosion Board, Vol. 5, No. 3, July 1951. U.S. ARMY, CORPS OF ENGINEERS, "Sand Bypassing Plant at Salina Cruz, Mexico," The Bulletin of the Beach Erosion Board, Vol. 6, No. 2, Noes IMS 2e 6-104 U.S. ARMY, CORPS OF ENGINEERS, ''Status of Sand Bypassing Plant at Salina Cruz Harbor, Isthmus of Tehantepec, Mexico," The Bulletin of the Beach Eroston Board, Vol. 9, No. 1, Jan. 1955. U.S. ARMY, CORPS OF ENGINEERS, ''Beach Erosion at Durban, South Africa," The Bulletin of the Beach Eroston Board, Vol. 10, No. 2, July 1956. U.S. ARMY, CORPS OF ENGINEERS, ''General Design for Harbor and Shore Pro- tection Works Near Port Hueneme, California,'' California Region, Engi- neer-Disitrict,, Los Angeles, CGalif.; 195,7- U.S. ARMY, CORPS OF ENGINEERS, "Cooperative Research and Data Collection Program of Coast of Southern California, Cape San Martin to Mexican Boundary, Three-Year Report, 1967-69,'' Beach Erosion Control Report, California Region, Engineer District, Los Angeles, Calif., 1970. U.S. ARMY, CORPS OF ENGINEERS, "Study on Use of Hopper Dredges for Beach Nourishment ,'' Hopper Dredge Improvement Program, No. 10, North Atlantic Region, Engineer District, Philadelphia, Pa., 1967. U.S. ARMY, CORPS OF ENGINEERS, "Details of Reinforcement--Hydraulic Structures ,'' EM 1110-2-2103, Office, Chief of Engineers, May 197la. U.S. ARMY, CORPS OF ENGINEERS, ''Standard Practice for Concrete," EM 1110- 2-2000, Office, Chief of Engineers, Nov. 1971b. U.S. ARMY, CORPS OF ENGINEERS, ''Carolina Beach and Vicinity, North Carolina; Combined Report on an Interim Hurricane Survey and Coop- erative Beach Erosion Control Study," South Atlantic-Gulf Region, Engineer District, Wilmington, N.C., 1961. U.S. ARMY, CORPS OF ENGINEERS, "Atlantic Intracoastal Waterway Between Norfolk, Virginia and the St. Johns River, Florida, Wilmington District," South Atlantic-Gulf Region, Engineer District, Wilmington, N.C., 1970. U.S. DEPARTMENT OF AGRICULTURE, ''Sand Dune Control Benefits Everbody: The Bodega Bay Story," Soils Conservation Service Pamphlet, Portland, Oreg., 11967. VALLIANOS, LIMBERIOS, ''Recent History of Erosion at Carolina Beach, North Carolina,"' Proceedings of the 12th Coastal Engineering Conference, ASCE, Molle 2. “Che 77, 19704 pp. 1223-1242. WATTS, G.M., "A Study of Sand Movement at South Lake Worth Inlet, Florida," TM-42, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, DeGo5 Wee, ASS. WATTS, G.M., ''Behavior of Beach Fill at Ocean City, New Jersey," TM-77, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Mar. 1956. 6-105 WATTS, G.M., "Behavior of Beach Fill and Borrow Area at Harrison County, Mississippi," TM-107, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Aug. 1958. WATTS, G.M., "Behavior of Beach Fill at Virginia Beach, Virginia," TM-113, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., June 1959, WATTS, G.M., "Trends in Sand By-Passing Systems," Coastal Engineering, Santa Barbara Spectalty Conference, ASCE, Ch. 34, 1966, pp. 779-804. WIEGEL, R.L., "Sand By-Passing at Santa Barbara, California," Journal of the Waterways and Harbors Diviston, ASCE, Vol. 85, WW2, June 1959. WOODARD, D.W., et al, "The Use of Grasses for Dune Stabilization Along the Gulf Coast with Initial Emphasis on the Texas Coast," Report No. 114, Gulf Universities Research Corporation, Galveston, Tex., 1971, (for the U.S. Army, Coastal Engineering Research Center). WOODHOUSE, W.W., Jr., "Use of Vegetation for Dune Stabilization," Proceed- tngs of the Coastal Processes and Shore Protection Seminar, Coastal Plains Center for Marine Development Services, Wilmington, N.C., Seminar Series No. 1, 19170), pp: 56-39" WOODHOUSE, W.W., Jr. and HANES, R.E., "Dune Stabilization with Vegetation on the Outer Banks of North Carolina," TM-22, U.S. Army, Corps of Engi- neers, Coastal Engineering Research Center, Washington, D.C., Aug. 1967. WOODHOUSE, W.W., Jr., SENECA, E.D., and COOPER, A.W., "Use of Sea Oats for Dune Stabilization in the Southeast," Shore and Beach, Vol. 36, NOG Aa UES, do UWHoeIke ZURMUHLEN, F.H., "The Sand Transfer Plant at Lake Worth Inlet," Proceed- ings of the Sixth Conference on Coastal Engtneering, ASCE, Council of Wave Research, 1958. 6-106 CHAPTER 7 STRUCTURAL DESIGN - PHYSICAL FACTORS PRAIA BAY, TERCEIRA, AZORES — 2 March 1970 CHAPTER 7 STRUCTURAL DESIGN -. PHYSICAL FACTORS 7.1 WAVE CHARACTERISTICS Wind-generated waves produce the most critical forces to which coastal structures are subjected (except for seismic sea waves). A structure exposed to wave action should be designed to withstand the highest wave expected at the structure, if such a design is economically justified. Economic evaluations depend on frequency of occurrence of extreme events such as, height and duration of extreme waves, damage potential of high waves, and permissible risk. Wave characteristics are normally determined for deep water, and then propagated shoreward to the structure. Deepwater Significant wave height Ho and significant wave period Tg may be deter- mined if wind speed, wind duration, and fetch length are known. (See Sections 3.5 and 3.6) This information, with water-level data, is used with refraction 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 struc- ture. Structures 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 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 obtained from statistical analysis of Synoptic weather charts is the significant height, Hg. Assuming a Rayleigh wave-height distribution, Hg may be further defined in approxi- mate relation to other height parameters of the statistical wave-height distribution: H,/3 or H, = average of highest 1/3 of all waves, Hy = 1.27 Hg = average of highest 10 percent of all waves (7-1) H, ~ 1.67 Hs average of highest 1 percent of all waves (7-2) T-! 7.11 DETERMINATION OF WAVE CONDITIONS All wave data applicable to the project site should be evaluated for possible use as design criteria. Visual observation of storm waves, while difficult to confirm, may provide an indication of wave height, period, direction, storm duration, and frequency of occurrence. Instru- mentation has been developed for recording wave height and period at a point. Instrumentation for recording wave direction is presently in the development stage, thus direction data must be obtained from visual obser- vations. Wave direction is usually necessary for design analysis. If reliable visual shore or ship observations of wave direction are not available, hindcast procedures (Sec. 3.5, SIMPLIFIED WAVE PREDICTION MODELS) must be used. Where reliable, statistical deepwater wave data are available, these can provide the necessary shallow-water wave data. If wave data are not directly available at the site, the best available procedure must be employed, with sound engineering judgment, to transform available deepwater and extreme offshore wave data to the structure site. (See Section 2.238, Wave Energy and Power, and Sections 2.3, WAVE REFRAC- TION, and 2.4, WAVE DIFFRACTION.) 7.12 SELECTION OF DESIGN WAVE The choice of a design wave height depends on 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 are known, the next step is to determine if wave height at the site is controlled by water depth. (See Section 2.6, 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 con- ditions should be determined 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 be found at a location other than the seaward end of the structure. The possibility of such conditions should be considered in establishing design waves and water levels. If breaking in shallow water does not limit wave height, a non- breaking 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 rigtd, semirigtd, or flexible. As a rule of thumb, the design wave is selected as follows. For rzgtd structures, such as cantilever steel sheet-pile walls, where a high wave within the wave train might cause faulure of the entire structure, the design wave is normally based on H,, the average height of the highest 1 percent of all waves. For semirigid structures, the design wave is selected from a range of H to H,. Steel sheet-pile cell structures are semirigid, and can absorb wave pounding; therefore, a design wave height of H,) may be used. For flextble structures, such as rubble-mound or riprap Structures, the design height is usually the Significant height H,. Waves higher than H, impinging on flexible f2 structures seldom create serious damage for short durations of extreme wave 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. It may be un- economical to build a structure that would withstand the hurricane condi- tions without damage, hence H, may be a more reasonable design wave height. On the North Pacific coast of the United States, the weather pattern is more uniform; severe storms are likely each year. The use of H, asa design height under these conditions could result in extensive annual damage and frequent maintenance because of the higher frequency and duration of waves greater than H, in the spectrum. Here, a higher design wave of about H,, may be advisable. Selection of the design height between H, and Hj, is based on the following factors: (a) degree of structure damage allowable and associated maintenance costs, (b) availability of armor materials, and (c) comparative alternate size or type of armor unit and their costs, 7.121 Breaking Waves. Selection of a design wave height also depends on whether a structure is subject to attack by breaking waves. It has been commonly assumed that a structure sited at a water depth dg (measured at design water stage), will be subjected to breaking waves if d, < 1.3 H 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 Section 2.6, 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 process. 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 break- ing wave height by 20 to 80 percent depending on deepwater wavelength or period. Galvin (1968,69) indicated a relationship between the distance traveled by a plunging breaker and the wave height at breaking Hp. The relationship between the breaker travel distance Xp and the breaker height Hz, depends on the nearshore slope and was expressed by Galvin (1969) as: Keg 7 Hy = (4.0 —9.25 m) H, (7-3) where m is the nearshore slope (ratio of vertical to horizontal distance) and a (4.0 - 9.25 m) is the dimensionless plunge distance. (See Figure 7-1.) Region where Breaking Starts Xp = Breaker Travel fe Distance = Tb LAT eh ee Hp 4 Proposed Structure ( Effect of Structure on Breaking has not been Considered ) Xp Wave Profile at Start of Breaking __SWL Wave Profile when Breaking is Nearly Complete Figure 7-1. Definition of Breaker Geometry 7-4 Analysis of experimental data shows that the relationship between depth at breaking dj, and breaker height Hp is more complex than indicated by the equation dpb = 1.3 Hp. Consequently, the expression dy = 1.3 Hy should not be used for design purposes. The dimensionless ratio d,/Hp varies with nearshore 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 7-2. The curve of a vs. Hp/ eT? repre sents an upper limit of experimentally observed values of dz,/Hp hence a = (dp/Hp)mar- Similarly, 8 is an approximate lower limit of measure- ments of dp/Hpb; therefore, 8 = (db/Hb)min. 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. KOK ROKK * KOK * *.% * -* * RYAMPLE PROBLEM * */* 8 Xo * * * & *Ok R * KH * GIVEN: A wave with period T = 10 seconds, and an unrefracted deepwater height of ie = 5 feet advancing shoreward over a nearshore slope of m = 0.050 (1:20). FIND: The range of depths where breaking may start. SOLUTION: The breaker height can be found in Figure 7-3. Calculate, He 5 =e eee? ES gE 32:2) (110)? : and enter the figure to the curve for an m= 0.05 or 1:20 slope. Hp/HO is read from the figure ie = = aOE [eo] Therefore, Bp. = )1.65°H, = )1.65.(5.0)) = 8:3 ie: Hp/gT* may now be computed. Por eB = ———— = 0.0026. eT? (32.2) (10)? Entering Figure 7-2 with the computed value of Hy,/gT? the value of a is found to be 1.51 and the value of 8 for a beach slope of OS050 zs 0293: Then, (d,) max ~ aH, 1518(8-3) 25 Reo, and (d;) min = BH, = 0.93 (8.3) Tel. Et... NOTE: When results of computations are used in subsequent problems or steps of the same problem, the number of significant digits carried is the number of digits that can be read ona slide rule. Final answers should be rounded to reflect the accuracy of the original given data and assumptions. L=5 2 16/9H snsia\ gf pud D “2-2 ainbiy zif (2261 ‘105B9m 19440) 4 0200 8100 9100 v100 2100 0100 8000 900°0 000 2000 (o) jan S0SS SESS eee 0) SE ere ae a ines + | oa eect SG SIL PEE it o See TSE Sse tal ate AEROS RE aaoo rata eet Pt 1A H FELCH Reece } 10) jataiala ia ich EEE aa EHEEH fe | ie i T L one felalatalar ie nok eee zi eae dG R ORES aaa ae! ialal Ste ops atat HH “-H cH SEE EEA +4 Cece i atalat alae 4 BECEEE EEE EEE EEE Cee eee EEEEEEEECEEEEEE EH SEES ag saerd Ht SESS ae Beene Sec0R000800 Elma coe : Pepe S080 0000 000580 S0S50050055505s0855 055055500 siatessensvavarazavaresesetetatates Sreseostteceetocsetavararteoctza: faye ater ata Smieia insta r ial IS ESA oe Talatetefabersslata +H ro aa IGE Seaei HHH t ft islelala f Pee Soc Gaame fase ea ITE Sooe oo nt 1 els (Slelefelaiatsts|ale EHH roo EEE EEE EH Brad otosazovarsatetesazezeststatesazareneetasasarane= Sessuanitasedectaseassitii ieee eoceessstiiieteetcccceessstiteeedttttessssnateineeetettteersoce mie pet \ it i He dt 9as/}}) <— (2 }) om 0.03 0.02 (after Goda, 1970) 0.01 0.004 0.006 0.002 0.001 0.0004 0.0006 55 z= ce : 5 5 Zz mH 4 rH aa Be ia) 5 E= == as A ao #3 =e =e BS = ea an Pa wa Ll 0.6 O.8 1.0 0.3 04 0.2 0.03 0.04 0.02 0.01 Versus Deep Water 1 (0) Figure 7-3. Breaker Height Index, Hp/H /gT@ Ho ? Wave Steepness Where wave characteristics are not significantly modified by the presence of structures, incident waves generally will break when the depth is slightly greater than (dp)mj,. 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 (HE = 5.0 feet, T = 10 seconds) could be subjected to waves breaking directly on it, if the depth at the structure toe were between (dp)niy = 7.7 feet and (dg)mgy = 12.5 feet. CM Tee ie ee I a Se i DR a, i A MM i a ee, a ee RT MES a ee 7.122 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 Hp 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 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: ’ (7-4) where dg is depth at the structure toe; 8 is the ratio of breaking depth to breaker height dz/Hp; mis the nearshore slope, and Tp is the dimensionless plunge distance Xp/ Hp from Equation 7-3. The magnitude of 8 to be used in Equation 7-4 cannot be directly evaluated since it depends on breaking wave steepness that cannot be known until Hp, is evaluated. To aid in finding Hp, Figure 7-4 has been derived from Equations 7-3 and 7-4 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. Ko * Ree UK eK KK eek Ee EXAMPLE PROBLEM * * * % * * * * *) e * (% ees GIVEN: (a) Design depth structure toe, dg = 7.5 feet. (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 = 6 sec (minimum) iT 10 sec (maximum) FIND: Maximum breaker height against the structure for the maximum and minimum wave periods. (2261 ‘I GINJINIJS 4D YYdaq aAIOJaY SNsyaA jyblaH 4ayD91g UbIsaq ssajuolsuawWIg “p-J asnbi4 e66em 104)0) 8100 8000 9000 v00'0 CH Bi iti sisstiias Poy 222——. Coo ——_ miaia Cr a om AT TY rH Eee eee @d0|s 9J0yssDeN “MS ubjseq — 2000 aoonan Ves 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 dg/gT2. ag. bbe gs oT? (32.2) (6)? Enter Figure 7-4 with the computed value of de / ete and determine value of Hp/d, from the curve for a slope of m= 0.050. = 0.0065 . (T = 6 sec.) d. Hy, gl = 0.0065 ; i = 1.12, (T = 6 sec.) Ss Note that Hp/dg is not identical with Hp/dp where dz, is the depth at breaking and d, is the depth at the structure. In general, because of nearshore slope, d, < dp; therefore Hp/d, > Hp/dp. For the example, breaker height can now be computed from, Ey = vada de eieli2i(7e5) 6.40 fe. (T = 6 sec.) For the 10-second wave a similar analysis gives, Epa) 1eS0ide 9 1-3007.5) = 9:75 sft: (T = 10 sec.) 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 poeeee and nearshore slope is found by entering Figure 7-4 with d a/ela Oo” (infinite period). For the example problem, d, H, — = 0; == 141 (m= 0.050), gT d. Fie pleated) — feel (725) 10-6) fe) i ee MT a a i ek ee I ee oer i thee ue ee eC Ct ye Dr G3 It is often of interest to know the deepwater wave height associated with the design breaker 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 Section 2.3, WAVE REFRACTION.) Figure 7-5 is based on observations by Iversen (1952a, 1952b), as modified by Goda (1970), of periodic waves breaking on impermeable, smooth, uniform laboratory slopes. Figure 7-5 is a modified form of Figure 7-3. Tih) 0.004 0.006 0.001 0.0004 0.0006 1970) (after Goda 0.2 i Ht | it EEEEEE nr 0.01 0.6 0.8 1.0 0.3 04 © 2 fo) 0.03 0.04 0.02 (ft/sec2) al T2 Versus Hp/gT ¢ ' ie} vHip/ A Figure 7-5. Breaker Height Index Tih kk ke ek kk eK kK kK * & * *& * EXAMPLE PROBLEM * * * * * * * * & ® * * ¥ *® * GIVEN: (a) H, = 84 ft, CTP1=16 sees) and H, = 9.8 ft . (see previous example) (T = 10 sec.) (b) Assume that refraction analysis of the structure site gives, by, Kp i) = 0.85 , (T = 6 sec.) Rae OP oL. (T = 10 sec.) and for a given deepwater direction of wave approach. See Section 2.3, WAVE REFRACTION. ) FIND: The deepwater height H, of the waves resulting in the given breaker heights Hp. SOLUTION: Calculate Hp/gT* for each wave condition to be investigated. H b 8.4 ap Se oe 00072: (T = 6 sec.) eT (32.2) (6) With the computed value of Hp/gT? enter Figure 7-5 to the curve for a slope of m= 0.05 and determine Hp/H, which may be considered an ultimate shoaling coefficient or the shoaling coefficient when breaking occurs. Hy, Hy, eee = 0.0072 aa Eee (Gt es 6 see.) eT Hi, With the value of Hp/Hg 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 7-5. Hy o Deis (H, /H3) Hj is the actual deepwater wave height, while HS is the wave height in deep water if no refraction occurred (Ho = unrefracted, deepwater height). Where the bathymetry is such that significant wave energy H (7-5) T-l2 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 Section 3.7, HURRICANE WAVES, for a discussion of wave height attenuation by bottom friction. Applying Equation 7-5 to the example problem gives: 8.4 H. = ——— = 8.3 ft. T = 6 sec. 2 Vgiesdig 7 C e) A similar analysis for the 10-second wave gives, H, = 83 ft. (T = 10 sec.) 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 feet in front of the structure. Waves with a deepwater height less than the Hg computed above could break directly against the structure; however, the corresponding breaker height will be less than the destgn breaker hetght determined from Figure 7-4. eRe, i Ae Ae cee Cae ae aie, et ee oe aire ee eae I A ee) eae a ides del ae) eye 7.123 Nonbreaking Waves. Since statistical hindcast wave data are normally available for deepwater conditions (d> Lo/2) or for depth conditions some distance from the shore, refraction analysis is necessary to determine wave characteristics at a nearshore site. (See Section 2.3, 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 Section 3.7, 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 refractton 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 Section 2.3, 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 coefficients, that gives the highest significant wave height at the structure would 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 7-1. (Gale) Table 7-1. Determination of Design Wave Heights Significant | Wave Period | Combined Refraction | Refracted Wave Height Deepwater and Shoaling to Nearest Wave Height Coefficients * One-half Foot * Refraction coefficient, Ky — Vb, /b at design water level. Shoaling coefficient, Keg H/H/ at design water level. + 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. Column 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. 7-14 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 refrac- tion 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. 7.124 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, result- ing 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, 1963), and Chesnutt (1971), provide information for estimating changes in depth. A general rule for estimat- ing the scour at the toe of a wall is given in Section 5.28. 7.125 Summary - Evaluating the Marine Environment. The design process of evaluating wave and water level conditions at a structure site is summa- rized 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 can reasonably be assumed to occur simultaneously at the site. Where hurricanes 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 reasonable combinations of water level and wave action are required for an adequate economic evaluation of any proposed shore protection scheme. 7.2 WAVE RUNUP, OVERTOPPING AND TRANSMISSION 7.21 WAVE RUNUP The vertical height above the stillwater 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. T-l5 DETERMINE DESIGN DEPTH AT STRUCTURE Considerations: 1) Tidal ranges meon spring 2) Storm surge 3) Variations of above factors along structure NOTE: Greatest depth ot structure will not necessarily produce the most severe design condition! DETERMINE BATHYMETRY AT SITE Existing hydrographic charts or survey data BATHYMETRY DESIGN DEPTHS DETERMINE DESIGN WAVE 1S WAVE DATA AVAILABLE ? AT WHAT LOCATION ? Gage dato or visual observations SUPPLEMENT DATA BY HINOCASTING Considerations: 1) Synoptic weather charts 2) Wind dota 3) Fetch data Offshore DEPTH IN GENERATING AREA Shallow HINDCASTING TO DETERMINE WAVE CLIMATE Considerations: Visual observations or available hindcost dato HINDCASTING TO DETERMINE WAVE CLIMATE Considerations: 1) Synoptic weather 1) Wind dato chorts 2) Fetch dota 2) Wind dota 3) Hydrography 3) Fetch dota SIGNIFICANT WAVE HEIGHT, RANGE OF PERIODS (MsyHioyMy) ond Spectrum) Figure 7-6. DETERMINE DESIGN WAVE AT STRUCTURE SITE Refraction dato available ° (aerial photographs) Refraction analysis Diffraction analysis DESIGN WAVE HEIGHT, DIRECTION AND CONDITION (Breaking, non-breoking or broken) AT STRUCTURE SITE FREQUENCY ANALYSIS ( Determine frequency of occurrence of design conditions ) Logic Diagram for Evaluation of Marine Environment 7-16 Runup depends on structure shape and roughness, water depth at structure toe, bottom slope in front of a structure, and incident wave characteris- tics. Because of the large number of variables involved, a complete de- scription is not available of the runup phenomenon in terms of all possi- ble ranges of the geometric variables and wave conditions. Numerous lab- oratory 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 rough- ness and slope permeability. Miller (1968) investigated runup of undular and fully broken waves on three beaches of different roughnesses. LeMéhauté (1963) and Freeman and LeMéhauté (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 wave runup on smooth impermeable slopes. (Saville, 1958a.) The curves are in dimensionless form for the relative runup R/H, as a func- tion 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 pre- dicted by Figures 7-8 through 7-12 are probably less than the runup on prototype structures because of a scale effect due to the inability to scale roughness effects in small-scale laboratory tests. Runup values from Figure 7-8 through 7-12 ean be adjusted for scale effects by using Figure 7-13. Point of maximum wave runup Design SWL Ho Figure 7-7. Definition Sketch, Wave Runup and Overtopping (pallite ae eee ga Esse Sass Caseastiel entity SUG veaed ceri creel esses te Gai Sae goat tatesfoee ed | neers 7 Jere pe Eat Hs } fe _ See Figure oe correction fon ft acon 5 =a - model sedlereftee ey sasiiice isin gems eaeelpaesisseesiai ce | | BeEHe | } seaeuuhese| } } paeaa teas } tert iti i fi I | bo { | | | | t | { | | t {2 | tt , ess Baek Fern thas ith ——}- Hs fost ft : Depkss Leash Hin) Berean ou oa } Rdumecnonataeny } { teen | | | FER] | | } it | } aan! | | | } aa | I | nes oogs eee tli | | ca OS) 04 OFS10'G en O!saaO Sn 220 3.0 40 5060 8.0 Slope ( cot @) Figure 7-8. Wave Runup on Smooth, Impermeable Slopes, ds/Ho =0 (Structure Fronted by a 1:10 Slope ) TN8 10.0 | = iSSeabsasd utereieiis eetetn ces ga Ohad beat stadt toes ye bexas| | See) Figure 7-13, correction for | ay | model scaleeffect ieee ee eas SS os } | } ease $0520 1144s Hes; Soearu aeebd Eaaes Leek isi ; | i } | en ae a 0.14 . 0.1 ONS O82 Oy 404 0'5'0'6; “Os 0 1:5: 120 3.0 40 5060 8.0 10.0 Slope ( cot @) Figure 7-9. Wave Runup on Smooth, Impermeable Slopes, ds / Hg * 0.45 (Structure Fronted by a 1:10 Slope) Vel 10.0 SEEEEEERE ee EE Ee it OEE 0.3 04 05 06 si ceesbrr AG cal aE EE etl A aa 0.8 1.0 1.5 Slope (cot @) 3.0 4.0 50 6.0 8.0 10.0 Figure 7-10. Wave Runup on Smooth, Impermeable Slopes, ds/Ho * 0.80 (Structure Fronted by a I:10 Slope ) 7-20 O'Z# °H/Sp ‘sadojs ajqpawsedw] ‘yyoows uo dnuny aanm ‘||-2 esnbi4 (0 G61 ‘aii!aos ) (@ 409) adois os O1l06080L 09 OS OF o¢€ 02 (2288/4) Ores OH 7Sp *‘sado|s ajqoewiedwj ‘yyoows uo dnuny arom ‘Z|-Z aunbi4 (9 8561 ‘ai!!A0s) (@ 402) adojs 01060802 09 OS OF o¢€ o2@ 0160802090 SO +0 T ae 09 - — ae 0.888 i EC a aepeeepr tortie 1.25 0.7 —f settee ete preter pet tod | 43 0.6 Hee 1.67 ° a ™ fo} [e) 1 2.50 Slope (tangent @ ) Slope ( cotangent @) 3.33 45.00 0.1 10.0 fe) --- 1.00 1.04 1.08 Bla Runup Correction Factor, k Figure 7-13. Runup Correction for Scale Effects i—25 Runup on impermeable structures having riprap slopes and runup on vertical, stepped, curved and Galveston-type recurved seawalls have been studied on laboratory-scale models by Saville (1955, 56). The results are shown in Figures 7-14 through 7-18. Effects of using graded riprap on the face of an impermeable structure (as opposed to riprap of uniform size for which Figure 7-15 was obtained) are presented in Figure 7-19 for a lon 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,/gT? 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 Figures 7-19 and 7-20 are assumed directly applicable to prototype structures without correction for scale effects. The use of the figures to estimate wave runup is illustrated by the following example. ee RK RK RK RK KE KK & *F & * EXAMPLE PROBLEM * * * * * * * * * & & X F ¥'X GIVEN: An impermeable structure has a smooth slope of 1 on 2.5 and is subjected to a design wave, H = 7 ft. measured at a gage located in a depth d= 15 ft. Design period is T = 8 sec. Design depth at structure toe at high water is dg = 10 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 nie the shallow water wave height H = 7 ft. must be converted to an equivalent deepwater value. Using the depth where the wave height is measured, calculate, abetipentenct | ans aeanisits Ey ho siior as We Sola)? = 0.0458 . 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H/ Hi, The runup, uncorrected for scale effects, is R= 92.7, (Ho R = 2.7°6.74)) = 18.2 ft . The scale correction factor k can be found from Figure 7-13. The slope in terms of m= tan 6 is 1 tan? = — = 0.40. Ded) The corresponding correction factor for a wave height, Ho. = 10.74) £01 Liss eS 7 e Therefore, the corrected runup is R= 71.17 (18:2) = 21-32te T=32 (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 struc- tures with different slopes. From an analysis similar to the above, the runup, wicorrected for scale effects, on al on1.5 smooth, impermeable slope is, R = Shi. / H, smooth From Figure 7-15 (riprap), entering with H/gT? = 0.0033 and using the curve for dg/H, = 1.5 which is closest to the actual value of | = 45 Hy riprap The reduction in runup is therefore [R/H] riprap __—i14.5 = 31 = 0.48 . [R/H: J smooth Applying this correction to the runup calculated for the 1 on 2.5 slope in the preceding part of the problem, R = 0.48R = 0.48 (21.3) = 10.3 ft . riprap smooth Since the scale-corrected runup (21.3 ft.) was multiplied by the factor 0.48, the correction for scale effects is included in the 10.3 ft. 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. eae eee ee US ae er see eee ae: | eae Sotelo Sb a) Ab “ae en) EY Se Ta ee ee ee ae 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 by 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. (35 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 increased by wave setup (see Sections 3.8 and 3.85) such as a reef, the wave runup is based on the water depth on the berm or reef. x ke Ke kK eK RK RK K * * * * * EXAMPLE PROBLEM * * * * * * * * & *¥ *¥ ¥ * E * GIVEN: A smooth-faced levee (cross section shown in Figure 7-21) is sub- jected to a design wave having a period T = 8 sec. and an equivalent deepwater height HE = 5 ft. The depth at the structure toe is d, = 4 ft. FIND: Using the composite-slope method, determine the maximum runup on the levee face by the design wave. SOLUTION: The runup on a 1 on 3 slope is first calculated to determine whether the runup will exceed the berm elevation. Calculate, ‘s See H 5 = and Hs 5 From Figure 7-10 for es = 0.8 Hi, ios with 1 BoA ae : and / z = 0.0024 , ° This runup is corrected for scale effects by using Figure 7-13 with e tan 6 = 0.33 and H =5 £t. A correction factor of k = 1.15 is obtained) oa R = 2.8 k H) = 2.8 (1.15) (5), Res TG ie. which is 10.1 .feet above the berm elevation. (See Figure 7-21.) Therefore, the composite-slope method must be used. 7-34 UOT}DES SSOID BOADT B FO atduexg ‘odotg 9a3tsodwu,) LOF dnuny JO uoT4e[nNoTe) “*T7Z-L aIn3s ty 02 POC CZZZZLL LL ¢ 1v6'9="P so art Ty eee le <7 y'8:| adols , vO Ee 0°9:| adoig*” Vf | ¢ ado|s pewnssp we Socal Cine 772 1] ys4iy 404 AV : Sendo adojs pawnsso jS4l} 40} XV=1'6E! T-30 The breaker depth for the given design wave is first determined. With 7 bi = 0.0024 1 ak calculate, H, H, — = 27 —, = 6.28 (0.0024) = 0.015 . L, gT? Enter Figure 7-3 with HL /gT? 0.0024, using the curve for the given Slope of m= 0.050 (1:20), and find H b SS 1.46. H, Therefore, Byes 146) = 7.50 ft 7 Calculate, H Ba Lye eT? 3222)\(8) Then, from Figure 7-2, from the curve for m= 0.05, 2 = 0.95 H, ; and d= _0:95 Hy = 0:95 (7-30) 6.947. Therefore, the wave will break a distance (6,94-4.0)/0.05 = 58.8 ft. in front of the structure toe. The runup value calculated above is a first approximation to the actual runup, and is used to calculate a hypothetical slope that is used to determine the second approximation to the runup. The hypo- thetical 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). Ax Then, 58.8'+ 30' + 20' + 30.3’ = 139.1 ft, and, the change in elevation is Ay and therefore cot 0 6.94 + 16.1 23.04 ft, AG SGS8:1) Ay (23.04) f-36 This slope may now be used with the runup curves (Figures 7-10 and 7-11) to determine a second approximation to the actual runup. Calculate d,/H, using the breaker depth dp, d 4 SSS / oO Interpolating between Figures 7-10 and 7-11, for He — = 0.0024, eT eee ae, H Correcting for scale effects using Figure 7-13, k = 1.07, and R = 1.55(1.07)5 = 8.3 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 is nearly zero. The sequence of runup approximations for the example problem is R, = 161 ft, Re) egos cite R, = 6.04 ft, Ryo 5.26-ft, Rem = "xe@ 4:3tee 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. Re, I) Be eee ke Or a ee Re EK ee de oR Se UR BR kei i ae ke ee 7.22 WAVE OVERTOPPING 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 x Mae 6 \ Limit of runup ona 1:3 slope First approximate eis ee To ORS te obtain Breaker location Ore second R. SWL ae Limit of runup on a |: 6.0 slope Limit of runup on a I:7.6 slope Second approximate slope to obtain R3 ee 8.3'= Ro \ c (Runup on a I:5.7 slope) Breaker location SWL Breaker location Limit of runup ona 1:8.4 slope < ULLLUYAIS TON Og Berm US See Final approximate slope ales 1 “vere aes 5.26':R, 6.0 “c aia 6.04": Rs SWL det ” AS Babe lect. £ Note: Final runup calculation will ep a CUTER indicate minor runup onto Cie laven berm at 6.0° Figure 7-22. Successive Approximations to Runup on a Composite Slope -- Example Problem 7-38 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 sections (Saville, 1958b.) A reanalysis of Saville's data indicates that the overtopping rate per unit length of structure can be expressed by, 0.217 _, [h-d 13\% - tanh s Q = (¢Q3 H!?) e a R , in which (7-6) or equivalently by, 0.1085 Rth—d, Aeresli3 yan al mee log. Q= (g Q H;,) e a R—h+d, }} , in which in) 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 (Section 7.21, WAVE RUNUP), and a and Qs are empirically determined coefficients that depend on inci- dent wave characteristics and structure geometry. Approximate values of a and Qs as functions of wave steepness H,/gT? and relative height d,/H, for various slopes and structure types are given in Figures 7-23 through 7-31. The numbers beside the indicated points are values of a and Qs (Q% in parentheses on the figures) that, when used with Equation 7-6 or 7-7, predict measured overtopping rates. Equations 7-6 and 7-7 are valid only for 0 < (h-d,) < R. When (h-d,) > R the overtopping rate is taken as zero. 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 hd. R he tes Wr | ats ol sin 6, (7-8) t-39 itt (2998/44) oy [oo] o Tt mM nN _ So © + nl - oOo 0 o oO ° ° : fo) OF Ou CO) On oo © - © © 6 EES Ors ett Eat OOBSONI seis | *ooro) |e Bae | 0) seer t ow —- © o Tt nu —- @ o st (o) fo) (oy (5) fo) ° fo) eS (2) ro) o 5S ea © (o) fo) ° o Oo (Ss) fo) fo) [o) [o) fo} oO. © fo} fo) fo) fo) (o) 216 © o t+ LP) oO [o) [o) [e) SS) o 98 (SI oO {2} oO 0 oO mo es = o = t= — °o fo) ine) Oo (‘= WwW _— *x O-~ wo Bi ie So aS je de OW 3 w Cas 4c; no ~ ae wol-—o sls ES te) Sz = ty is} > (al, (S) ope iS Fa te) [ob f= ° (eo) fo) — _ ea = Ss Ks) os 0 ne) o [aN] 1 Nm o = =) [@) o oF vie 0.0002 0.0001 40 0.02- 0.0002 0.000] 0) ie EARS en 0.067 0135) oi Saal SSS SES. ooseo\ a5 0 3 16-065: 0.0 aa B00) | p } } } {——--—+}—-—-} Figure 7-24. Overtopping Parameters, a and aS (Smooth I: 1-1/2 Structure Slope on a |:10 Nearshore Slope ) 2.0 oil oH (2988/14) 200 £00 b0'0 90'°0 800 me) 20 £0 b0 9°0 80 O'| or —_ ( adojg asoyssDaN O}:| D UO adojs aunjonijs €:| yyoows ) 20 pud oD ‘SsajyawDdIDd BHulddojsang “GZ-Z aunbi4 SH Sp Gb Ob Gue os G2 oz cul onl $0 00 1000'0 aoe eee ee ee --(0b20'0)- sascecsceas 2000°0 — (0001°0): } | 900 ¥, f E Sek | SES : = aESe 0910°0 (00S1'0) : : SenaEs case ianeeceaaeeen seace ¥000°0 (0220'0) a een {000 0) SSSSyasane SEE : : 80000 seue : (2600.0) . = 100'0 (061 0 0) (01¢0'0) 600@ ee : : : (OG10:0)--- ~ 40°0-- : 900°0 -—-=fsal s[pog pws seiousg'@ = —s—Ci—C buiynaig (adojs sJ0ySIDEN Of: a pw puiyoaig sr 70'0 t-42 malt °H (2998/44) (ado|S as0yssDaN Q|:| D UO edojs aunjonss 9:| yyoows ) °0 pub d ‘sudjawDdd Buiddojsang “92-2 aunbi4 i io HEU RU A LU f oo Tt T i eee Pett EEE EEE aoe ae Ty i See = eee HREEHETE Bose eaeeeeueeeey caeeaeeeauseeee See JuE SSS pee Sh00 0) ane a] Hit ate I mm TERA roi aa nN aan | int iit i A La EI nT ih iT Isvo00) E E 1a = 18 Seer HH siete nae itt ae = ssn HH _ (oda wh buposig Hitt oo pee ee PASSA cE ae Sr sie ill Ic Det Hr | TT gol er aS Fi im Hn T- 43 0.04 0.02 ty Riprap roughly 4 3 ft.in diameter 0.0002 Figure 7-27. Overtopping Parameters, a and Gn (Riprapped |:I-1/2 Structure Slope ona !:!0 Nearshore Slope ) ina i if ( ft/sec?) Ho Hui gat i ate ett oreo ee ee : "Ttg.0160).... | to food BNE See le feted er ete ane gee aG Figure 7-28. Overtopping Parameters, a and Q5 ( Stepped |: Structure Slope on a 1:10 Nearshore Slope ) 7-45 (ft/sec?) Ho T? fu (2998/14) oH (Curved Wall * oO Co ao) (= (oS) B® = oo 2 (ep) ® _ rs) = wn — 'S) o 2 ie) Figure 7-29. Overtopping Parameters onal: 46 2.0 Figure 7-30. Overtopping Parameters, a and Q3 on a 1:25 Nearshore Slope ) 0.04 1.0 | : eo 0.8 | t } i } | ; } E tia ate Fe 0082 a). 0.01 0.3 0.008 si 0.006 0.2 0.004 : a 0.1 Hi 0.08 ‘> 0.002 E=s ; # 0.06 ae 0.001 mee 0.0008 0.0006 0.02 0.0004 0.01 0.008 0.0002 0.006 0.004 0.0001 0.0 0.003 ds Ho (Curved Wall (ft/sec?) Ho T? © (ft/sec? ) H iN} Os Ho Figure 7-31. Overtopping Parameters, a and Q6 (Recurved Wall ona 1:10 Nearshore Slope ) where Wr is a coefficient depending on wind speed, and 9 is the structure slope (6 = 90° for Galveston walls). For onshore wind speeds of 60 mph or greater Wr = 2.0 should be used. For a wind speed of 30 mph, Wr = 0.5; when no onshore winds exist, Wr = 0. Interpolation between values of Wr given for 60, 30, and 0 mph will give values of Wr for intermediate wind speeds. Equation 7-8 is unverified, but is believed to give a reasonable estimate of the effects of onshore winds of significant magnitude. For a wind speed of 30 mph, the correction factor k’ varies between 1.0 and 1.55 depending on the values of (h-d,)/R and sin 6. Values of a and Qs larger than those in Figures 7-23 through 7-31 should be used if a more conservative (higher) estimate of overtopping rates is required. Calculation of wave overtopping rates is illustrated by the following example. kk eK kK kK RK KR KK K K * * * EXAMPLE PROBLEM * * * * * * * * * *¥ *® *¥ ® K GIVEN: An impermeable structure with a smooth slope of 1 on 2.5 is subjected to waves having a deepwater height HS =) 5) cft.5 Handa: period T = 8.sec. The depth at the structure toe is d, = 10 ft; crest elevation is 5 ft. above SWL. Onshore winds of 35 mph are assumed, FIND: Estimate the overtopping rate for the given wave. SOLUTION: Determine the runup for the given wave and structure. Calculate, / Hy d 2 ae ie 5 From Figure 7-11, since d Se == aS PAY 6 He R =) 2.9 (uncorrected for scale effect) . (eo) Since Hp = 5 ft., from Figure 7-13 the runup correction factor ais approximately 1.17. Therefore, = f17- (2.9) = 34; oh | and R = 3.4 H’ = (3.4) (5) = 17.0 ft. The values of a and Qs for use in Equation 7-6 can be found by interpolation between Figures 7-24 and 7-25. From Figure 7-25 for a 1 on 3 slope for small-scale data, a = 0.09 Q* = 0.033 Also from Figure 7-25 for larger scale data, a 0.065 d, Hy at "ayn 02:55) and oe 002s He eT Q* = 0.040 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 d, ae = 2.0, and He = 0.0024 eT? 4 : From Figure 7-24 for small-scale data on a 1 on 1.5 slope, a = 0.067 d, H, ats = is and ——=— 0.0016): He gt? QF = 020135 Large-scale data are not available for a 1 on 1.5 slope. Since larger values of a and Q& give larger estimates of overtopping, interpola- lation by eye between the data for a 1 on 3 slope and a 1 on 1.5 slope gives approximately, a = 0.08, Qt = 0.035. hz50 From Equation 7-6, 0.217 aa = tania OS Ea =) es ie x |], 0.217 is & ys = tanh S Q = [(32.2) (0.035) (5)3]* e | 0.08 = The value of To evaluate tanh7! [(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! [(h-d,)/R] from column 3. Therefore, tanh? (0:294) = 0.31). Calculating the exponent, OPATA(Os 1) = 0.84 ; 0.08 therefore, Ost Seer? 11.9, (0.431) = 5.1. ft? /(sec-tt) . For an onshore wind velocity of 35 mph, the value of Hie is found by interpolation. 30 mph; We = 0.5, 35 mph; Wr = 0.75, 60 mph; We = 2.0. From Equation 7-8, ieee Kravis Wp => (sal |}) iar (ee where h-id, = 0.3, R 1 5 (= ea! || SS DW 25 and Sy QA? = 0.317 Therefore, ko =f 0.75 (0352 0-8) 0:37 — 11 | and the corrected overtopping rate is, ll Q, = FQ, 1.11 (5.1) = 5.7 ft3/(sec-ft), Q 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. Oe KR Roe KR & Ke Rk Ok KO OR ROK KR KR OK ROR OK OK OK OR OF OR Xa Oe ake ie XE aioe 7.23 WAVE TRANSMISSION When incident waves hit a breakwater, wave energy will be either reflected from, dissipated on, or transmitted through the structure. The way incident wave energy is partitioned between reflection, dissipa- tion and transmission depends on incident wave characteristics (period, height and water depth), breakwater type (rubble or smooth faced, per- meable or impermeable), and the geometry of the structure (slope, crest elevation relative to SWL, and crest width). Ideally, harbor breakwaters should reflect or dissipate all wave energy approaching from the sea, and dissipate any wave energy approaching from the harbor. (See Section 2.5, WAVE REFLECTION.) Transmission of wave energy over or through a break- water should be eliminated to prevent damaging waves and resonance within a harbor. When a permeable or low-crested breakwater must be considered, an estimate of the transmitted wave height is necessary. For impermeable structures, crest elevation and crest width are important in determining transmitted wave heights. Jeffreys (1944) and Fuchs (1951) studied the transmission of waves over impermeable, submerged breakwaters (crest elevation below the SWL) using linear, small-amplitude wave theory. Because of the small-amplitude assumption, their equations predict no wave transmission when the structure crest elevation is at the SWL. For finite-amplitude waves, energy is transmitted over breakwaters by overtopping even if the crest is above the SWL but below the limit of maximum runup. (See Section 7.21, WAVE RUNUP.) Jeffreys (1944) theoretically analyzed transmission of waves over an offshore bar which is similar to transmission of wave energy over a 52 wide, submerged, impermeable breakwater. His equation for the trans- mission coefficient, ratio of transmitted wave height to incident wave height Hz/Hz, is given by Ss ((7-9) A tae et te 0.25 ‘ eee is ( 1 : ee = |= oa oe Se | Sa, d.—h d, Jet \dj—h where dg is the depth below the SWL at the structure toe, h is the height of the structure above bottom, b is crest width, g is acceler- ation of gravity, and T is wave period. The development of Equation 7-9 does not consider energy dissipation, and therefore does not consider waves breaking on the structure or energy loss by friction. In addition, the equation is valid only for shallow-water waves when d/gT* < 0.00155, and should not be used when h/d > 0.8. When crest width is small relative to structure height (say b/h < 0.5) the value of H;/H; given by the equation may be too large. Fuchs (1951) presented an equation for calculating wave transmission over a rigid, thin vertical barrier by considering power transmission across the barrier. The equation is based on linear wave theory, and cannot be used when transmission is by overtopping. Fuchs' equation is Hy) _Gahity + sinh GahyL) H; sinh (41d,/L) + (4nd,/L) ° (7-10) and is assumed valid in water of any depth, provided the wavelength L corresponds to the depth dg. In shallow water, Equation 7-10 reduces to (7-11) for ae 00155) gT? and in deep water Equation 7-10 reduces to (7-12) for d, nae > 0.0793 . eT For 0.00155 < d,/gT* < 0.0793 Equation 7-10 must be used. 1-395 When submergence of a crest is small (h/d, > 0.8 for shallow water) or when transmission is by overtopping, the results of hydraulic model studies must be used to evaluate transmission coefficients. The range of ds/ 21 values included in numerous laboratory investigations are summarized in Figure 7-32. Figures 7-33 through 7-35 show some experi- mental results obtained by Saville (1963) for an impermeable rubble-mound breakwater. Interpolation between curves permits an estimate of wave heights on the leeward side of similar prototype structures. If experi- mental results in Figure 7-32 are used to determine wave transmission, transmission coefficients obtained by several investigators should be computed and compared for the appropriate value of d,/gT? whenever possible. Figures 7-36 and 7-37 show experimental values of the transmission coefficient for the permeable rubble-mound breakwater sections investi- gated by Saville. Higher transmission coefficients result for permeable structures than for similar impermeable structures, since part of any incident wave energy is transmitted through a permeable structure in addition to the energy transmitted over it. Because of the difficulty of modeling permeability in laboratory studies, transmission coefficients obtained by interpolation between the curves of Figures 7-36 and 7-37 should be considered as estimates of the true transmission coefficient. The data shown in Figures 7-36 and 7-37 can be supplemented by the experimental results of Jackson (1966), Hudson and Jackson (1966), Dai and Jackson (1966), and Davidson (1969) for wave transmission through typical rubble breakwater sections. The use of Equations 7-9 and 7-10 and Figures 7-33 through 7-37 to obtain transmitted wave heights is illustrated by the following example problems. xe ek kK kk eK * * * * * EXAMPLE PROBLEM * * © * * * 3 x) ¥) ke Kin EKEE GIVEN: A design wave with H = 6 ft, T = 8 sec and a submerged impermeable breakwater with a crest width of b = 30 ft. Depth in front of the structure is d, = 15 ft, the height of the crest above bottom is 10 ft, and seaward and landward slopes are 1 on 2. FIND: Wave height on the leeward side of the breakwater assuming no energy dissipation at the structure. SOLUTION: Calculate: Qu. ss le = ——— _ = 0.0073 , eT? (32.2) (8) ie which is greater than d,/gT? = 0.00155, hence the wave is not a shallow-water wave and Equation 7-9 cannot be used. Assuming that 1-54 SIOJLSTISOAUT SNoTIeA Aq poetpnas zi13/°P Jo o8uey ‘soinzon13g peddoj1eAQ pue pesLowqns I9AO UOTSSTUSUPT] OARPM °7E-Z OANSTY 216 Sp jDUO!}ISUDIy 10°0 J8;0M da0g ime) TTY J®40M MO||OUS 100'0 (1261) 44!110S @ $8019 | | (8961) 4910 (9961) 10 48 ‘ounwoyoN s$s!00;0- — — — — — 216 *p (€961) @1I!ADS (8S6I) 48®l4d £62010 —— ——-—— (1G61) UOSI4OW B SyoNy ‘UOSUYyoP (Ov61) 119H 8 11OH (As08y1) atoa.. F — — — > an PCCM Tac Game A Ot ad | | (KsoeyL) | | (pv6l) skesssar Lie) (after Saville , 1963) au h Figure 7-33. Wave Transmission, Impermeable Rubble- mound Breakwater 56 BEESA sesauer 1nsgusaice=2== = = 355 SSS 5 5555 5=5SS=> == 2=2============ ee 2 S=SS5 SSeS S=SS=S==== 88 25225 b= fee see=2 28 522e2e== eaeeee==es 0.8 oe e5¢ 50222 £2252 2222222522 22222 2222222222 SESSEE==SS=S=S=ESS : = : See ree ees ng Rene neta ene eoees overs Cesar CanEEneeae SSEaS5 =e pe a 0.2 0.09 0.08 0.07 F 0.06 0.05 0.04 3.5 4.0 b (after Saville, 1963) Figure 7-34. Wave Transmission, Impermeable Rubble-mound Breakwater fDi 0.6 H ? aaa (Oe) gt 0.4 0.3 OZ 0.03 0.02 re = 0.00403 ga-0 O15! iT = =0 00239 2.0 Fe clei =0.00345. oe 0.00648 (B38) 3.0 (after Saville , 1963) Figure 7-35. Wave Transmission, Impermeable Rubble - mound Breakwater G5) 4.0 a ro) a i) fo) 2.5 3.0 3.5 4.0 b (after Saville, 1963) Figure 7-36. Wave Transmission, Permeable Rubble- mound Breakwater (after Saville, 1963) Figure 7-37. Wave Transmission, Permeable Rubble-mound Breakwater j 7-60 the structure is a rigid, thin barrier, calculate L in a depth dg = 15 ft. using Equation 7-10. gI? 2 c= = Fee. = 328 tte _ oe (8) and i. AS gb aes iD 328 ; ; From Table C-1, Appendix C, setting dg = d, 4nd ind er OReR eae ior ok ‘atl = 1.378, a L jb and calculate, I SLT ea L dul sea ’ ‘ Find 0.751 in Column 9 of Table C-1, Appendix C and read sinh (41d/L) from Column 10. Hence, sn (#2) 0.825 . L From Equation 7-10, H, (4mh/; ) + sinh (4mh/y ) Hy {sinh (nd) + (4nd) ) te) ie _ (0.751) + (0.825) H, (1.378) + (1.127) ° Hy 1.576 _ x == — F50g = V0.370 = 0.609 The transmitted wave height is H, = 0.609 H, , H, = 0.609 (6) = 3.67 ft., say H, po kt. The calculated value can be assumed to exceed the true value, since the finite structure crest width will decrease the transmitted wave height and some energy dissipation will occur. CT ee ee Tae Oren ee So a iia ale di a, lid le li i ae tal lu ge hal ae Ee a A I De a a, 7-6I * ke kK kK kK RK kK KK K * F * * EXAMPLE PROBLEM * * * * * * ®* * *¥ ®¥ ¥ ¥ & F & GIVEN: A design wave with H = 6 ft and T = 8 sec is incident on a rubble structure with a cross section as shown in Figure 7-34, situated in a depth d, = 10 ft. The crest of the structure is b = 10 ft wide and is 1 ft above the SWL. (a) The height of the wave transmitted over the structure by over- topping if the structure is permeable. (b) The reduction in transmitted wave height if an impermeable core is included in the structure. SOLUTION: Calculate: h = dg + crest height above SWL = 10 + 1 = 11 feet, then, b 10 — = — = 0.909 , h 11 a Ne bol d, 10 sg SM cea 0.0029 gi? 1 %(G2:2)\(8) ; ; d 10 — = = 0.0048 . eT? (32.2) (8)? For a permeable structure, find the corresponding H¢/Hz values for b/h = 0.909 by interpolating between h/dg = 1.033 in Figure 7-36 and h/d, = 1.133 in Figure 7-37, and using the curve for H;/gT? 0.00269 and d,/gT* = 0.00455 in Figure 7-36 and the curve for H;/gT* = 0.00249 and d,/gT? = 0.00414 in Figure 7-37. For h/dg,g = 1.033 from Figure 7-36, Hz/H; = 0.44 and for h/d, = 1.133 from Figure 7-37, H¢/Hz = 0.31; therefore, AOS) 3 Hence, H, = (0.35) H; = 0.35 (6) = 2.1 ft. 7-62 By a similar analysis for an impermeable breakwater, using Figures 7-34 and 7-35, and Hy = (0.33) H) =>0533,(6), So1.98 ft. 5 =sayie2, tt. The presence of an impermeable core in this instance does not provide a significant decrease in transmitted wave height. Most of the wave energy is transmitted by overtopping for the example conditions. See Sie ae eee PS PIS Ae eter he Bok ek ecto de are aK eae! eck eet Ae Rink ie Kents ce ede aie Oe) RR i 7.3 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 7-38 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 3 NON-BREAKING BREAKING BROKEN Seaward of surf zone In surf zone Shoreward of surf zone P W R PILE, SUPPORTED RUBBLE Piers, offshore platforms Seawalls, bulkheads, etc. Groins, jetties, etc. Classification by Type of Structure Figure 7-38. Classification of Wave Force Problems by Type of Wave Action and by Structure Type 7-63 Rubble structure design does not require differentiation between 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 pre- sented in Section 7.31, FORCES ON PILES. Nonbreaking, breaking and broken wave forces on vertical (or nearly vertical) walls are considered in Sections 7.32, NONBREAKING WAVE FORCES ON WALLS, 7.33, BREAKING WAVE FORCES ON VERTICAL WALLS, and 7.34, BROKEN WAVES. Design of rubble struc- tures is considered in Section 7.37, STABILITY OF RUBBLE STRUCTURES. 7.31 FORCES ON PILES 7.311 Introduction. Frequent use of pile-supported coastal and offshore structures makes the interaction of waves and piles of significant practi- cal 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 problen. Variables important in determining forces on circular piles subjected to wave action are shown in Figure 7-39. 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 acceler- ations 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 ¢€ are important variables describing the pile. In this discussion, the effect of the pile on the wave-induced flow is assumed negligible. Intui- tively, 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 by: H : a = dimensionless wave steepness, 8 d f : = = dimensionless water depth, g D : : : = = ratio of pile diameter to wavelength (assumed small), = = relative pile roughness, and HD . ae = a form of the Reynolds' number. Vv 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 mecha- nism 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 present. Two dimensionless force coeffi- cients, an inertia or mass coefficient Cy and a drag coefficient Cp, are used to establish the wave-force relationships. These coefficients are determined by experimental 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 Cy and Cp are known, and illustrates the calculation of forces on verti- cal cylindrical piles subjected to monochromatic waves. A discussion of the selection of Cy and Cp follows in Section 7.315, Selection of Hydrodynamic Force Coefficients, Cp and Cy. Experimental data are avail- able primarily for the interaction of nonbreaking waves and vertical cylin- drical piles. Only general guidelines are given for the calculation of forces on noncircular piles. Zz () a) Figure 7-39. Definition Sketch of Wave Forces on a Vertical Cylinder r- 69 7.312 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 ‘as, (See Figure 7-39 for definitions.) mD? du 1 fey S04 sil SNC De, Sey NC ye -ronDr ula: (7-13) where, f; =" inertial force per iunst length of pile, fy = drag force per unit length of pile, p = density of fluid (2 slugs/ft? 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) du : ‘ } — = total horizontal water particle acceleration at the axis of dt the pile, (calculated as if the pile were not there) Che hydrodynamic force coefficient, the ''Drag'’ coefficient, and 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 (fp 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 ulu|). Although these remarks Support the soundness of the formulation of the problem as that given by Equation 7-13, it should be realized that expressing total force by the terms £; and fp ts an assumption justi- fied only if it leads to sufficiently accurate predictions of wave force. From the definitions of u and du/dt, given in Equation 7-13 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 1-66 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, D/Ly 5 and shows the force to be about proportional to the acceleration du/dt for small values of D/Lqg (Lg is the Airy approximation of wavelength). Taking their result as indicative of how small the pile should be for Equation 7-13 to apply, the restriction is obtained that D — < 0.05. (7-14) L, Figure 7-40 shows the relative wavelength Ly/L, and pressure factor K versus d/gT? for the Airy wave theory. ke eK KK kK kK RK RK K F * * EXAMPLE PROBLEM * * * * * * * * * *¥ ® F KK * GIVEN: A wave with a period of T = 5 sec., and a pile with a diameter D= TiS. in S.ft. of water. FIND: Can Equation 7-13 be used to find the forces? SOLUTION: oo ll 5.12 T? = 5.12(25) = 128 ft., ae — = —— = 0.0062 , eT? 32.2 (5)? which, using Figure 7-40, gives L A — = 0.47 L, L, = 047L, = 0.47 (128) = 60 ft., D 1 ii — 0.017 —.0105 Dye ty 60 Since D/Ly satisfies Equation 7-14, force calculations may be based on Equation 7-13. ee) eee. Cie See eee ke ee ae see kel rae ee Ere der ie. bie ae ees Coe ae ie ede: es del aes Pele The result of the example problem indicates that the restriction expressed by Equation 7-14 will seldom be violated for pile force calcula- tions. However, this restriction is important when calculating forces on dolphins, caissons, and similar large structures that may be considered special cases of piles. ——e——— Oe (Asoay] arom Asi) 216/p SNSJAA JOJID4 a4nssaid pud uD yjbua}aanm GAI}DJAY “Op-LZ aunbi4 eoe 0 100° 0 90000 vOOO'O ae nt Ha ay Say ea PRES TE aaae|40 ee abso SES 600 0, - ~ —=— pub i il 010 vy puDd } Sle al it a eee ra ae ey 001 0'8 O9 ao ce “ae ae Ol £0 slo 10 800 90°0 ene) Ta z00 S100 10°0 (2988/14}) 68 Two typical problems arise in the use of Equation 7-13. (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 Cp and Cy ? 7.313 Calculation of Forces and Moments. Jt ts assumed in thts sectton that the coefficients Cp and Cy are known and are constants. (For the selection of Cp and Cy see Section 7.315, Selection of Hydro- dynamic Force Coefficients Cp and Cy.) To use Equation 7-13, 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 7-39, the equations from Chapter 2 for surface elevation, (Equation 2-10), horizontal velocity (Equation 2-13), and acceleration (Equation 2-15), are LH, (2m n= 5 cos Tt |? (7-15) 2-H er cosh [27m (z + d)/L] 2nt hee i) Seach ard] (7 i (7-16) du du ___ gH cosh [2m (z + d)/L] = __ 2mt poe & cosh [2nd/L] ey fa (7-17) Introducing these expressions in Equation 7-13 gives 1D? m cosh[2m(z+dV//L]] . 2mt = aoe ee Ne SS 7-18 f, = Cy Pg 4 H | ae ] | = ( ) ( ) ¥ iy » |g? (cosh [2m (z + d/L}\” 2mt 2nt p “p 2 tae a ( cosh [21d/L] ) lees ea re ( = Slime Equations 7-18 and 7-19 show that the two force components vary with elevation on the pile z and with time t. The inertia force fz is maximum for sin (- 27t/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 7-18, 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 ; however, the decrease with depth is more rapid since the attenuation factor, cosh[27(z+d)/L]/cosh[21d/L], 1-69 is squared. For a quick estimate of the variation of the two force components relative to their respective maxima, the curve labeled K = 1/cosh[21d/L] in Figure 7-40 may 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 hetght - water depth ratio. The influence of steepness on crest elevation n, and wavelength is presented graphically in Figures 7-41 and 7-42. The use of these figures is illustrated’ by the following examples. kK RK RK kK kK kK kK kK kK kK K * F EXAMPLE PROBLEM * * * * * * * *® * * * ® * * * GIVEN: Depth d= 15 ft., wave height H = 10 ft., and wave period T = 10 sec. FIND: Crest elevation above stillwater level, wavelength, and relative variation of force components along the pile. SOLUTION: Calculate, d 15 eee ae eT? —- 32.2 (40) H 10 = = 01003: eT? ui 32.2 (10)? From Figure 7-40, Eg = 0-40 ES = 4612) 07 2a Onte:. K =09. From Figure 7-41, Ne = 0.845 H = 8.45 ft. From Figure 7-42, T= 1165) 324 opte and K = UC 0.9 £0) fp (z = —d) K? = ———= 0.81 . fp (z=0) }YBlaH aADM Of [AAI] 4aJDM||IS BAOGD UOIDAa]Z 4S919 4O O1NDY “|p -Z asnbi4 £0 20 10800 900 v0O0 £00 200 10°0 9000 000 2000 1000 90000 000°0 'bL20'0 Ht : ae 119420N, ‘yeas: 'yided JejoMiS = Pp apace “spudoes * BIE ME 0d ee ee a 94 “jy618H eADM = rH | | | | Np1wi] As04110S anoay colierdt3 #8019 | | | SH ai oo! o8 O'9 OP AOsE o2 OSs! o!1 80 90 pO £0 20 = 06sl0 10 80:0 900 vOO £0°0 200 si0'0 (299S/}}) — SO 20 10'0 $JD9JJJ OPNyljdwy ajiuij 0} 104904 u01yDa1I09 yybuay aaDM “2p-ZL ainbi4 aio P500°0 00°0 COUT AEEE) QO TE CON EDEL SOR ee | I “ell 5 RTT <<“ £0 20 10800 900 00 £00 200 100 2000 100°0 9000°0 70000 00°! sO! Ol'l G2'l O¢'| oo!l o8 oO9 Ov O€ o2 OS! ol 80 90 110) £0 zo 8 6SI0 0 800 900 voo £00 zoo SI00 10'0 zi (298S/4}) =ore Note the large increase in n, above the Airy estimate of H/2 = 5.0 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. er ee wee Kae oe tae: ey oy Je. Ae ee A Rh ei ite Ae IE I ik he ee oe ie ee ie Kis EE es ke RK RK KK KK RK KF KF K *F * EXAMPLE PROBLEM * * * * * * * *¥ ®¥ *®¥ ®¥ ®¥ F * * GIVEN: Same wave conditions as preceding problem H = 10 ft. and T = 10 sec.; however, the depth d= 100 ft. FIND: Crest elevation above stillwater level, wavelength, and the relative variation of force components along the pile. SOLUTION: Calculate, eed gs ae gr: 32:2\(10)" a a H 10 a ee OOO SIE eT? 32.2 Giop2 From Figure 7-40, Ly = 0:89) 1. = 895-12) T= 455ift., K = 046. From Figure 7-41, N, = 0.52 H = 5.2 ft. From Figure 7-42, L = 1.01 L, = 460 ft. and FS (ceed) SS ES iG =o) K2 = fp (@ = -d) = 0.21. fp (2 = 0) Note the large decrease in forces with depth. The wave condition approaches that of a deepwater wave. RRR yk ee eee eee Re ee Oe OR ee ee ee a ee: Oe OR ee oe. f=75 For force calculations, an appropriate wave theory should be used to calculate u and du/dt. Skjelbria, 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 fp with time (values are given for time intervals of 2mt/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, 1965) are to be published by CERG in 1973. (ean, 1973:) For structural design of a single vertical pile, it is often unneces- sary to know in detail the distribution of forces along the pile. Total horizontal force acting on the pile and total moment of forces about the mudline z= -d are of primary interest. These may be obtained by inte- gration of Equation 7-13. n r= f gar [ f, dz="F) UF, (7-20) =d n (Zr d) £) dz | (+d) 45, dz-— M; + Mp. (7-21) ad K Il | a In general form these quantities may be written fl ™D? Ee = Cae pe ae EK. (7-22) Fp = Cp > pg DH Kp, (25) * TD? M; = Cy pg HK, dS,=F, dS, (7-24) = 1 2 = Bp 15) Fy EE es Kid Spy apne Spl (7-25) in which Cp and Cy have been assumed constant, and where K;, Kp, S; and Sp are dimensionless. When using Airy theory (Equations 7-18 and 7-74 7-19), the integration indicated in Equations 7-20 and 7-21 may be per- formed if the upper limit of integration is zero instead of n. This leads to Sarl Qnd\ . __ 2mt eS = tanh = tT)? (7-26) 1 4nd/L 2nt 2nt == (1+——— — — Kp = 3 ( a aa eee 5 ) = GZ 1 mt amt = in lees [|= I/|| Ges [==] 4 T lt 1 — cosh [27d/L] ll Shwe ni ocoed/t cia lon WD ee 1 n pe en a 1 — cosh [42d/L] D = 2 2n\2 ~~ (4nd/L) sinh [47d/L) ]* @=29) where n = Cg/C has been introduced to simplify the expressions. From Equations 7-26 and 7-27, the maximum values of the various force and moment components may be written mD? Fim = Cy 08 —- H Kim , (7-30) Fom = Cp - pg Bsr? tee (7-31) (ey Age Cae (7-32) Mes pe Sp: (7-33) where K;, and Kp, according to Airy theory, are obtained from Equations 7-26 and 7-27 taking t = -T/4 and t = 0, respectively, and S; and Sp are given by Equations 7-28 and 7-29 respectively. Equations 7-30 through 7-33 are general. Using Dean's stream-function theory (Dean, 1973), the graphs in Figures 7-43 through 7-46 have been prepared and may be used to obtain Kym, Kpm, Sim and Spm. Sz and Sp, as given in Equations 7-28 and 7-29 for Airy theory, are independent of wave phase angle 9 and thus are equal to the maximum values. For stream-function and other finite amplitude theories S; and Sp depend on phase angle; Figures 7-45 and 7-46 give maximum values, Sm and Spm. The degree of nonlinearity of a wave can be described by the ratio of wave height to the breaking height, which may be obtained from Figure 7-47 as illustrated by the following example. 7-75 216/p‘ysdad anijojay snsiaA “!y “Ebh-2 ainbi4 (€26] ‘uDag 424)0) IGG Gt IORSiZ Oe INCNSMZ ONES ao f! afate tates} i i 11 i t i ERS PRD Bt 1 ++ 1 i £70 Wly 0) 8 OS BOS I 9000 %00°0 10°0 + shetty thr i 0 EU GEO EAE os’! i 900 poo £00 zoo SI00 et p (2988/44) 76 (€261 ‘upaqg 4ayjo ) Sa 1 ag ae 2 16/p ‘yydag anijojay snsian a fal | oe OS’! Ol £0 i itt PCE nit aioe Ebceitasiat AEH a al UT - + Pe Li) = Ht fe vi f| HEEEorie Siocenitit i = HA FA 20 one) 10 800 900 zt (2998/43) > VO0E TRUE Gee “dy ‘pp-2 ainbi4 HR poo £00 THT TST = 200 SIi00 HK LEH En ERG LL ROG LEGG Co 100 Ee ee 9000 %00°0 2 16/p ‘yydaqg anijojay snsua, ‘“!S ‘way juaWwoW 90404 DIJJau] “Gp-2 ainbi4 (€26| ‘uoag 43440) ,-O1X Ox O20 1 0180 90 60 €0 20 Slo 10 800 900 all (2998/11) + v0'0 £00 7-78 216/p (€261 ‘uDaq 18440 ) ;-Oll X INGRSI 20} “CRY, g t yjdaqg arljDjay snssaA ‘Ws twiy juawoW ads04 601g “9b 216 2 ainbi4 o£ Oca ail Ol ORS ORS Op OF o'? aseee caer ae os’! O01 80 90 pO €0 20. =6SGi zi 2as cies (229S/1}}) 7 0 0 800 90°0 v00 £00 "9 * ek kk ke kK kK RK KK KF * * EXAMPLE PROBLEM * * * * * * * * FF ¥K FR KR GIVEN: A design wave H = 10 ft. with a period T= 8 sec. ina depth d = 40 ft. FIND: The ratio of wave height to breaking height. SOLUTION: Calculate, 40 ¢ See OA. eT? (32.2) (8)? Enter Figure 7-47 with d/gT* = 0.0194 to the curve marked Breaking Limit and read, sues 0.015 gl? : : Therefore, Hy = 0-015 eT? = 0.015 (32.2) (8)? = 30.1 ft. The ratio of the design wave height to the breaking height is H 10 Sa = 033: Ea cod ee ORS te Eo Oe ORR ese Ye oR RR ok OK) Peek Ree ee eee ee By using Equations 7-30 through 7-33 with Figures 7-43 through 7-46, the maximum values of the force and moment components can be found. To estimate the maximum total force F, Figures 7-48 through 7-51 by Dean (1965a) may be used. The figure to be used is determined by calculating, ve, (7-34) and the maximum force is calculated by 1p he wCpH?D, (7-35) where $m is the coefficient read from the figures. Similarly, the maximum moment My can be determined from Figures 7-52 through 7-55 which are also based on Dean's stream-function theory. (Dean, 1965a.) The figure to be used is again determined by calculating W _ by Equation 7-34 and the maximum moment about the mud line (z = -d) is found from Mn = %m WCpH?Dd, (7-36) m where a, is the coefficient read from the figures. Calculation of the maximum force and moment on a vertical cylindrical pile is illustrated by the following example. 7-80 Huet Ge So ea Be HH Se Hes Hoes eee [| tab Sena eee eae RN EE 0.02 0. 04 0.06 0.1 0.01 0.02 004 006 O11 0.2 04 06 08 1.0 2.0 40 6080100 <= (ft/sec?) (after Le Mehauté, 1969) Figure 7-47. Breaking Wave Height and Regions of Validity of Various Wave Theories 7-8 1.0 08 0.6 0.4 0.2 0.1 0.08 0.06 0.04 H T2 0.02 0.01 0.008 0.006 4 0.002 — 0.001 (ft/sec?) zi H (2988/43) (SO';O=M) ~~ 216/P pud ,16/H snssaq “> Jo sauljos| “‘gp-2 e4nbi4 (06961 ‘uoag 12430) ae e S460 ; eos apne HE 3: tHe = ¥0000 20:0 9000'0 8000°0 £0°0 100°0 ¥0'0 ° 90°0 200'0 80:0 i 1 0 é £000 00'0 20 900°0 800°0 £0 100 v0 90 200 80 oO £00 —J +00 cere SHIN Se 00108 09 Ob OF P v0 v00 £00 200 10'0 Jl z (2998/15) 2 T- 82 z= ( 2908/4)) = (10 =M) (0596) ‘uDag Jajjo ) cca ogee (shea eae! Ett | it if taf OEE LEE eS 2 + fatten ie) oe ui! Biacrists 215/p pubD 216/H SNsjo/ 80'0 900 0" gif P 100 Wd Jo Sauljos| 9000 %000 z00'0 ‘6b-2 enbi4 9000'°0 0000 a eae Hulae ih eseaGee £0000 v0000 90000 80000 1000 UM iii L, Oy 2000 nn wn oo1 08 O9 Ov OF SNA Gaui eesteesee tty o1 80 90 vo £0 (2008/45) 2 0 10 800 900 ¥O0 £00 200 100 1-83 zt H (2988/33) (SO=M) ae ‘upag 424j0) v0 20 as eS at ae Soe y Mh Wy Fs yy, yy 4 Ye 90000 ’0000 — £000°0 THELELA Spa pees =EEES To 800 30 il 2 (2298/45) =— $00 00" 200 T- 84 zi H (2988/43) (O'1l=M) "2167p pud 5167} snssaa Yd yo sauljos| "|G-2 e4nbl4 teaeg eae 4a4j0) p i 10°0 900°0 +000 2000 100°0 90000 +0000 £000°0 ee LAST AA? AE A a Hi 5 eas SE Sea NR a EE ae io det a Bi LAA MLE + Lys i Mp me TTT Tm a C) o Sep Hee Sebel: SSSSESSSS (07 Pe ae nN A ae aa 7 cE ae ite ae oor os o9 Ov OF o7e o!1 80 90 v0 10 800 900 vo00 £00 200 a (2988/44) p 285 zi (229S/1}) |= 200 £00 00 Ht 90°0 80°0 10 20 £0 555 ie e a Hitt { i v0 9°0 a ! 80 o'1 (SOO =M) 216/p pud ,16/7H snssaQ “Yo Jo sauljos| “ZG-2 ainbi4 (0 G96] ‘uoag 4440) v0 £0 20 200 900° +000 200°0 cr 1000 9000°0 00! 0 (2988/1)) £0 ai p 10 800 900 v 00 00 200 £0000 ¥000°0 9000°0 80000 1000 2000 £000 7000 200 1-86 zi H (2988/43) (1O0=M) (0 G96) ‘uoag 124)0) via 800 900 rene ,16/p puo 3 15/H snsiaA “no jo sauljos| “¢G-2 eunbi4 HUDSEESS ea SLY! | | quae: Ul 6y7/// cael Hee ee Ee ALL pe eB i LL +t ze t t SR ses 1g eG ae Aue ANN \\ oe #00 £00 200 Hinceee. Ff Zo Ae reistey et AAS Ly My Mi ye VW /, aaa EE i ae it a A Oo! 80 90 v0 EL (2988/13) ae £0 9000 000 2000 1000 90000 ROO W// ae ee Was Pe aPaCe a ict ani a WEL Ve api Gaara es ee Aa ae Li er ¢ ia C tis a + 2 O Os 1 eB _ bai ro ao 300 ni £00 200 (87 (SO=M)"" 216/p pud , 16/7} snssaq “Yo Jo sauljos| “pG-2 asnbi4 (0 G96) ‘uoag 4a4j0) bo ¢0 20 ; : : ’ : : 9000°0 80000 100°0 2000 £00°0 47000 9000 8000 10°0 200 £00 v00 HAI HTH Ei wt 90 ( To 800 300-600 £007 200100 (2988/13) <— a=) 7-88 at H (2988/43) (0g Eu + x a Sto paper ett Es } T coos H it 1H tt (O'l= 96] ‘uoag 4a4j0) M) tenes HT : ge i BB HH PEERS SHE EE SESE BEES 216/p pup 10 80°0 woe v00 £00 215/H snssaA “vd jo sauljos| GG-y einbi4 200 00 9000 +000 2000 TE Ad ae ae ae at Wy YY, YY Wy Yi Bees! XQ \\ Soe: EE a Te en £0 10 80:0 900 v00 £00 200 Too ul (2998/44) S— ot 200'0 Ere (ar a 4 ll ps 90d 9 “yee vam tt 0 cela moo | +400 z 16 1-89 * ek kK KK RK RK kK kK kK kK K * * RXYAMPLE PROBLEM * * * * * * * * *® ® ® & kK kK GIVEN: A design wave with height H = 10 ft. and period T = 10 sec. ‘acts on a vertical circular pile with a diameter D = 1 ft. in depth d = 15 ft. Assume that Cy = 2.0 and Cp = 0.7. Selection of Cy and Cp is discussed rel Miereealorn 7 SilS, FIND: The maximum total horizontal force and the maximum total moment around the mudline of the pile. SOLUTION: Calculate, d iS) — = ———__—_ = 0.00466, gT? (32.2) (10)? and enter Figure 7-47 to the breaking limit curve and read, Hy, aye WWE YE eT Therefore, H, = 0.00357 eT? = 0.00357 (32.2) (107) = 11.5 ft., and H 0 SS See ONS Hy iL) From Figures 7-43 and 7-44, using d/gT? = 0.00466 and H = 0.87 Hp, interpolating between curves H = Hp and H = 3/4 Hp to find, Kym and Kpm: K. = 0.38, 1m Ke = 0.70" From Equation 7-30: ic nD? Ea Pe. tae mT 1a Fim = (2) (2) (32.2) - (10) (0.38) = 384 Ibs. and from Equation 7-31: 1 = = 2 Emer op sre eek Fn (0.7) (0.5) (2) (32.2) (1) (10)? (0.7) = 1,580 Ibs. 7-90 From Equation 7-34, compute CLD W = lee EDR ene 0.29. ChH (7) (10) Interpolation between Figures 7-49 and 7-50 for 4, is required. Calculate a ee, 0031 eT? (32.2) (10)? ; and recall that d as 0.00466 eT Find the point on Figures 7-49 and 7-50 corresponding to the computed values of H/gT? and d/gT? and determine $, . Figure 7-49 Wo= 0 Oe 0.35, Interpolated Value W = 0.29; ¢,, © 0.365, Figure 7-50 W= 0.5 ; 9, = 0.38. From Equation 7-35, the maximum force is EF, = %m WCpH2D. ea 0.365 (64) (0.7) (10)? (1) = 1,635 lbs. say | Sige lief) lbs. To calculate the inertia moment component, enter Figure 7-45 with d — = 0.00466, gt? and H = 0.87 Hp, interpolate between H = Hp and H = 3/4 Hp to find, Sian Ui ae Similarly from Figure 7-46 for the drag moment component, determine Saar a Oz: 791 Therefore from Equation 7-32, Min = Fim & Sim = 384 (15) (0.81) = 4,670 Ib.-ft., im and from Equation 7-33, Mpm = Epm4 Spm = 1:580 (15) (1.02) = 24,170 lb.-ft. m The value of a, is found by interpolation between Figures 7-53 and 7-54 using W = 0.29, H/gT2 = 0.0031 and d/gT? = 0.00466. Figure 7-53 Wes 0 het 70534, Interpolated Value W = 0.29; Cea O35 Figure 7-54 Wr F015 i iar s=10- 367 The maximum total moment about the mudline is found from Equation 7-36. M =a w CpH?Dd, m m 0.35 (64) (0.7) (10)? (1) (15) = 23,520 lb.-ft. = ll say = I 23,500 lb.-ft. The moment arm, measured from the bottom,is the maximum total moment M, divided by the maximum total force F,; therefore, If it is assumed that the upper 2 feet of the bottom material lacks Significant strength, or if it is assumed that scour of 2 feet occurs, the maximum total horizontal force is unchanged, but the lever arm is increased by about 2 feet. The increased moment can be calculated by increasing the moment arm by 2 feet and multiplying by the maximum total force. Thus the maximum moment is estimated to be (Mn). ff. Belownnudline = (14.1 ar 7)) ES = 16.1(1,635) = 26,320 lb.-ft., say (Min). ft. below mudline — 26,300 lb.-ft. We ik ee ee oe eT es Ke Oe Re OK ORR Re oe Ke Oe ee es CR OR er ee eee kk RK kK eK kK KE RK kK FE KF & * * EXAMPLE PROBLEM * * * * * * * * * ®& *¥ FE KE GIVEN: A design wave with height H = 10 ft. and period T = 10 sec. acts on a vertical circular pile with a diameter D=1 ft. ina depth d= 100 ft. Assume Cy = 2.0 and Cp = 1.2 792 FIND: The maximum total horizontal force and the moment around the mudline of the pile. SOLUTION: The procedure used is identical to that of the preceding problem. Calculate, d 100 — = ——— = 0.031, eT? (32:2), (10)? and enter Figure 7-47 to the breaking-limit curve and read H b ae 0.0205. g Therefore H, = 0.0205 gT? = 0.0205 (32.2) (10)? = 66 ft., and From Figures 7-43 and 7-44, using d/gT* = 0.031 and interpolating between H ~ 0 and H = 1/4 Hp, for H = 0.15 Hp, ee Oar Knm = 0-20 . From Equation 7-30, " nD? Fim = Cy PS W HK,» m(1)? 4 esl Il ‘in = 20 (2)(32:2) (10) (0.44) = 445 lbs. and from Equation 7-31, 1 Fom = Cp 5 PDH’ Kp Fom = 1.2 (0.5) (2) (32.2) (1) (10)? (0.20) = 773 lbs. Compute W from Equation 7-34, re) 2d) Ww = = = Guy We i1.21@0) Onl": Interpolation between Figures 7-49 and 7-50 for $, gives Om = 011. From Equation 7-35 the maximum total force is = 2 FE = 0, Vp iD: F 0.11 (64) (1.2) (10)? (1.0) = 845 lbs. m say FP = 850\lbs. From Figures 7-45 and 7-46, for H = 0.15 Hp, Sim = 0:57 5 and Soe Or6oN. From Equation 7-32, Me in ds fs COO 57) = 235,370 lb.-ft., and from Equation 7-33, Mom = Fom 4 Spm = 773 (100) (0.69) = 53,340 lb.-ft. Interpolation between Figures 7-53 and 7-54 with W = 0.16 gives a, = 0.076. The maximum total moment about the mudline from Equation 7-36 is, M,, = %m W CpH?Dd, m = ll 0.076 (64) (1.2) (10)? (1.0) (100) = 58,370 lb.-ft, say M m 58,400 lb.-ft. If calculations show the pile diameter to be too small, noting that Fim is proportional to D* and Fpm 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 2-foot-diameter pile the forces become, 4 s (ie it Fim (DD S25ft) Fin (D = 1 ft.) (che 445 (4) = 1,780 lbs., 2 Fpm (D = 2 ft.) = Fom (p= 1 ft) 7 = 77302) = 1,546 lbs. 1-94 The new value of W from Equation 7-34 is CyP 2.0 (2.0) pe eS See Ses CpH 1.2 (10) and the new values of $4, and a, are, po) = s0RIS., and a, = 0.093. m Therefore, from Equation 7-35, (Fn) 2’ diamaaeeer w Cp)H?D s (Fn) 2° diam, = 0-15 (64) (1.2) (10)? (2) = 2,300 Ibs., and from Equation 7-36, (Mn) 2' diam. ~ %" W Cp) H* Dd , (Min) 2’ diam, = 0-093 (64) (1.2) (10)? (2) (100) = 142,800 Ib.-ft., say (M,,) 2’ diam, = 143,000 Ib.-ft. We knee ee dee ee) fel ae? ee aie ee eee ae ee el ie ie oe Oe eee ee ee ie ie oe ae 7.314 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 lift forces, although they do not act vertically but perpendicular 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 from the other resulting in a laterally oscillating force. i 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 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 pore only to rigtd 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 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 proportional 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 7-37 may be used. Ps FF, = Epcos 74) Cr = DH? Kp cos 20. (7-37) where Fr is the lift force, Fry, is the maximum lift force, 6 = (2mx/L - 27t/T), and Cy is an empirical lift coefficient analogous to the drag coefficient in Equation 7-31. Chang found that Cz depends on the Keulegan-Carpenter (1956) number Ung, T/D where Ug, is the maximum horizontal velocity averaged over the depth. When this number is less than 3, no significant eddy shedding occurs, and no lift forces arise. AS Umgy; T/D increases, Cy increases until it is approximately equal Cp (for rigid piles only). Bidde (1970, 1971) investigated the ratio of the maximum lift force to the maximum drag force FZm/FDm which is nearly equal to C;/Cp if there is no phase difference between the lift and drag force (this is assumed by Equation 7-37). Figure 7-56 illus- trates the dependence of Cr/Cp on U,g, T/D. Both Chang and Bidde found little dependence of Cz; on Reynolds Number R, = Uae D/\, or the ranges of Re investigated. The range of Re 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 Gy) ania: seitent SOE. The use of Equation 7-37 and Figure 7-56 to estimate lift forces is illustrated by the following example. xk kk kK kK kK kK K kK * * * * * BXYAMPLE PROBLEM * * * * * * * * * ®¥ ¥ *¥ ® FF GIVEN: A design wave with height, H = 10 ft. and period, T = 10 sec. acts on a vertical circular pile with a diameter, D = 1 ft., ina depth, d = 15 ft. Assume Cy = 2.0 and Cp = 0.7. FIND: The maximum traverse (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. 216/H pud saquinn 4ajuadi09-udbajnay yyIM 05/19 yo uolyDIuDA “9G-Z asnbi4 OWI —upbajnay abpian (0261 ‘eppia 40430) G/, *©4n ‘yequiny s9}ueds09 -udbajney Vv 02 8 9 | él Ol 8 9 ; (0) Sous eoad dese toeH food foes fond foot ood and fondant ecdtacsiond fasitecdstciocy SSE euaseetataetd teat teeta faet ase ettaeePtSee ae EEE a Uae sees fs is | ac PFET Ae ] a@ [S Sssaatasad foctftocatfosastacat ecati Erne eee dE EECEEEEEEEE EEE ECEE EEE EEE EEC By 2aneauuuuaeur 4 SSEEEe act tact tvaseeetaet dete deer eitpeetiio fer Hee EES ste Gece geet NHR SECT ELEY Sussdassadautesaceatacestoseetansafavestarsatauea o> -afuzentazsetansater’ Hy Bogs aces ce ou SeeeTeer SeGeTeeETaseTase "ces 7oseraeea/ sevaseusasuese “ance | Scrat DSSS SUE Sh eee sees aH aeae Lit 1 a H+ 4 | |_| Sob uaa ese" 00see a] 0GSSSRECger -( THEESEEETECcoeT 7 TCGeeeEsGGe/,cusSaeeGEeeECee EEC oy ae tae ane cae tae ae tae ac Haeee Aaeeeae atest at aa eae Srasecastoastar fae? cat tones tecetens eaatesstt setter ductgocazecasecst east faantacetecttecatiacdl BEES EECEEEEEEEEEEEEEEEEEEEEE EEE SSE EEE tt SedgocetandecadSozt evi acstant fantesstostcasttestt oe? ceatand facttantesstecasaciacetecttacticcttacdt SEdgecadtecadessdfas eovat ast anateasttacateas’ coat ocateaateanttenat endi iaanlcrirar tert fasta SH asvevazatetcenasaiavciacze2-ugeeasuuhanst>7 ganesataenenenenenas dt oud ae dua peub cacesaeteesasuaed! sauuceceds eu sseudessuveeeseee sscensccesleceTecerceseseserassriasszass secereseet 0) vO e70) 90 1-97 SOLUTION: Calculate, H 10 — = ——— = 0.0031, eT? (32.2) (10)? ee ee BES Tg eT? (32.2) (10)? and the average Keulegan-Carpenter number ae T/D using the maximum horizontal velocity at the SWL and at the bottom to obtain Umax ° Therefore, from Equation 7-16 with z= -d, H eT 1 2 Ly, cosh Pree ; 10 (32.2) (10 = 2022100) (0.89) = 6.66 ft./sec., bottom 2 215 ("max) bottom (“naz where Ly is found from Figure 7-40 by entering with d/gT* and read- ing Ly/Lo = 2nLy/gT* = 0842. Also, 1/coshs (27d/ Li) asmthen skevaliie on Figure 7-40. Then, from Equation 7-16 with z=0 , aes (Ymax) spp Lat 10 (32.2) (10) = — ——— = 7.49 ft./sec. (Umax) spr 2 215 Wey The average velocity is therefore, 4 i (“max bottom (max) SWL | man 2 ay 6.66 + 7.49 14.15 7.08 ft./ u SS ere ha) Pa . »/SEC., max 2 2 2 and the average Keulegan-Carpenter number is Umax | 7.08 (10) D 1 = [Vets The computed value of Uo T/D is well beyond the range of Figure 7-56, and the lift coefficient should be taken to be equal to the drag coefficient (for a rigid structure). Therefore, From Equation 7-37, pg (sap al Or oy DH? Kp in cos 20 = F,,, cos 20. The maximum transverse force Fy, occurs when cos 26 = 1.0. Therefore, (2) (32.2) Ere ee Old. ice tig (1) (10)? (0.7) = 1,580 Ibs., 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, Fs Fim ee ee ma cagase | O07 - which occurs about when the crest passes the pile. The time variation of lift force as given by, F, = 1,580 cos 28, is shown in Figure 7-57. eee ae Ae! ode? ae) ie cei oi et i ee ae a Oe Se es ee SE) ee ES AS ee ee 7.315 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 (1973) or Skjelbria, et al. (1960) along with the appropriate Cy and (Cp. a. Factors influencing Cp. The variation of drag coefficient Cp with Reynolds Number R, for steady flow conditions is shown in Figure 7-58. The Reynolds Number is defined by, e eee ADs (7-38) Vv t- 39 aaa dpgeuaaned isssassa7 7 gaa Rudd gEERS Faaagaanad SunaTEazE CELE fH H HH un H EH {i aoee Ho i a {I FH inne aeacseue os a oa i aaa at i ENE Eeeeetna idee arene 2 di ame Salers H 3 San oo eV Cy -\. | Wave Profile | / ingaa. Po | sia ifs totes Tee flees ro) 7 (ft) (Airy Profile) -5 ara ree ea aS ain ine i age “| cnt: ie ai oe oe } rH rH H ai \ \a cenee f Li Foe H] i H a Bau je ER neces He ty art Hop a ied SEGRG oma wa HEE HH He Hee mein ele (ae tee etuii es ue oo Heil - 120 160 200 240° 280 320° a @ (degrees) sabes Figure 7-57, Variation of Transverse Lift Force and Wave Profile (Airy Theory) 7-100 Ay ‘yaqunn spjoukay yyim ‘99 ‘yuaioijja09 Bog JO UOIJDIUDA “QG-Z s4nbi4 9O0IX ¢OIX pOlXx [Sas Bas € 2 IN6n8 29s Se Ty ¢£ 2 [Eset A: eT £ 2 | jabiaqjaseim TT a (8961) YoDqueyoy ‘syuawisadxy 81045 Appays wos saul] paysog dDSIDM puod abo | HRT ERCRE SH ma I$aq 10} papuawwosay aulq |jn4 } | | os oe oe | t | Ws s9x01S. He Goei) suap3 pup hokssapby ina | — Kioays- Kary {2961} ‘10.48 jabaim- M1 ¢]- ae — | —-}—)} ——} Ksoaut ADBUI|UON * Peetiiainiiit 3) platy Hi ca otjouns woes‘ (0261) pipoboy pup uoag g | | AY | L ae alien (oes Ua Kou Aiiy (2S61) 4optonups}oid Hh (9961) aioe cs cake uobainey > | t | CUBES CURE ee a si + ai ema tu raat | (8961 ) yooqueyoy F161 where u = velocity, D = “pile diameter; vy = kinematic viscosity (approximately 1.0 x 10-5 ft.2/sec. for sea water.) Results of steady state experiments are indicated by dashed lines. (Achenbach, 1968.) Taking these results, three ranges of Rg exist: (1) Subcritical; R, < 1x 10° where Cp is relatively constant (=1.2), (2) Transitional; 1 x 10° < R, < 4 x 10° where Cp varies, and (3) Supercritical; \Roi> 4 x 10°; where Cp is relatively constant (~0.6 - 0.7). Thus, depending on the value of the Reynolds number, the results of steady state experiments show that the value of Cp may change by about a factor of 2. The steady-flow curves shown in Figure 7-58 show that the values of R, defining the transitional region vary from investigator to investi- e g g g gator. Generally, the value of R, at which the transition occurs de- pends on the roughness of the pile and the ambient level of turbulence in the fluid. A rougher pile will experience the transition at a smaller R,. In the subcritical region, the degree of roughness has an insignifi- cant influence on the value of Cp. However, in the supercritical region, the value of Cp increases with increasing surface roughness. The varia- tion of Cp with surface roughness is given in Table 7-2. The preceding discussion was based on experimental results obtained under steady, unidirectional flow conditions. To apply these results to the unsteady oscillatory flow conditions associated with waves, it is necessary to define a Reynolds number for the wave motion. As Equation 7-16 shows, the fluid velocity varies with time and with position along the pile. In principle, an instantaneous value of the Reynolds number could be calculated, and the corresponding value of Cp used. However the accuracy with which Cp is determined hardly justifies such an elaborate procedure. Keulegan and Carpenter (1956), in a laboratory study of forces on a cylindrical pile in oscillatory flow, found that over most of a wave cycle the value of the drag coefficient remained about constant. Since the maximum value of the drag force occurs when the velocity is a maximum, it seems justified to use the maximum value of the velocity Ue when f102 Table 7-2. Steady Flow Drag Coefficients for Supercritical Reynolds’ Numbers ; ; Average Drag Coefficient Surface of 3-Foot-Diameter Cylinder R, =1X 10° to 6X 108 Smooth (polished) Bitumasticx glass fiber, and felt wrap Bitumastic, glass fiber, and felt wrap (damaged) Number 16 grit sandpaper (approximately equivalent to a vinyl-mastic coating on a 1- to 2-foot-diameter cylinder) Bitumastic, glass fiber, and burlap wrap (approximately equivalent to bitumastic, glass fiber, and felt wrap on a 0.78 1- to 2-foot-diameter cylinder) Bitumastic and oyster shell coating (approximately equivalent to light fouling on a 1- to 2-foot-diameter 0.88 cylinder) Bitumastic and oyster shell with concrete fragments coating (approximately equivalent to medium barnacle 1.02 fouling on a 1- to 2-foot-diameter cylinder) Blumberg and Rigg, 1961 *Bitumastic is a composition of asphalt and filler (as asbestos shorts) used chiefly as a protective coating on structural metals exposed to weathering or corrosion. (Webster’s Third) f-103 calculating a wave Reynolds number. Furthermore, since the flow near the stillwater level contributes most to the moment around the mudline, the location at which u,,, is determined is chosen to be z= 0. Thus, wave Reynolds number is a (7-39) where v = kinematic viscosity of the fluid (v ~ 1.0 x 107° for salt water), Ung, = maximum horizontal velocity at z = 0, determined from Airy theory, is given by Unax — — (7-40) ¥ The ratio Lyg/Lo can be obtained from Figure 7-40. An additional parameter, the importance of which was cited by Keulegan and Carpenter (1956), is the ratio of the amplitude of particle motion to pile diameter. Using Airy theory, this ratio A/D can be related to a period parameter = T)/D (introduced by Keulegan and Carpenter) by, (nas ee (7-41) D 27 D When z= 0 Equation 7-41 gives L H 1 H (Ki ye es eps (7-42) The ratio L,/L, is from Figure 7-40. In a recent laboratory study by Thirriot, et al. (1971), it was found that for A = > 10, Cy = Cp (steady flow) ; A le = < 10, Cp > Cp (steady flow) . Combining this with Equation 7-42, the steady state value of Cp should apply to oscillatory motion, provided —=——>10, (7-43) 7-104 or equivalently, SS 7) == - = (7-44) * ek kk kK kK kK K kK * ® * * * EXAMPLE PROBLEM * * * * * * * *¥ * * ¥ ®¥ ® ¥ * GIVEN: A design wave with height, H = 10 ft., period, T = 10 sec. ina depth, d = 15 ft. acts on a pile of diameter, D = 1 ft. FIND: Is the condition expressed by the inequality of Equation 7-44 satisfied? SOLUTION: Calculate, d — qi 0.00466 . eT From Figure 7-40: L, —— = 0.41 iv Then, H 10 uA Se lO Oh a= 82 D 1 IL oO Therefore, the inequality is satisfied and the steady state Cp can be used. Rey RRS ote! Ke ea tee Te A Re ee ae eR ee OI ee. es SR Re Fe Re ney ee CRE, ee oe Thirriot, et al. (1971) found that the satisfaction of Equation 7-44 was necessary only when Rp, < 4 x 10+. For larger Reynolds numbers, they found Cp approximately equal to the steady flow Cp, regardless of the value of A/D. It is therefore unlikely that the condition imposed by Equation 7-44 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 Cp's obtained by Keulegan and Carpenter (1956) is (CD) avg = 1.52, The results plotted in Figure 7-58 (Thirriot, et al., 1971) that account for the influence of A/D show that Cp *1.2 is a more representative value for the range of Reynolds numbers covered by the experiments. 42105 To obtain experimental values for Cp 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 Cp (and Cy) obtained from prototype-scale experiments depend critically on the wave theory used to estimate fluid flow fields from measured surface profiles. kK eK RK kK kK kK kK kK kK K *K FE * EXAMPLE PROBLEM * * * * * * * *¥ * ¥ ¥ ¥ F EK ta GIVEN: When the crest of a wave, with H = 10 ft. and T = 10 sec., passes a pile of D= 1) ft., in 15 £t. of water, a force’ F =) Fp, — D,500%ibs. is measured. FIND: The appropriate value of Cp. SOLUTION: From Figure 7-44 as in the problem of the preceding section, Kp = 0.7 when H = 0.87 Hp. The measured force corresponds to Fp,, therefore, rearranging Equation 7-31, cow 3 Ppm >” (ih) oD H Kp, 1500 C= = 0.66 (1/2) (2) (32.2) (1) (10)? (0.7) If Airy theory had been used (H ~ 0), Figure 7-44 with d/gT? = 0.0047 would give Kp, = 0.235 and therefore K ( Dm) 1 =0.87 H, 0.7 eae a (ln =a47 1 & ) eae OF Dm) airy (H ©) CM See ear tek SC Ta a a a a SO a a a er el a Oe eC ik i he ae Te Ne eT Tor LSS ke eK kK kK RK KK K * * * * EXAMPLE PROBLEM * * * * * * * * ®¥ ¥ ®¥ ¥ KK F GIVEN: Same conditions as preceding example, but with a wave height, Hi= 50 £t., acdepth, d’= 100 £t.; and F = Fp, = 30,000 Ibs. FIND: The appropriate value of Cp. SOLUTION: From Figure 7-47 Hp = 66 ft; then H/Hp = 50/66 = 0.76. Entering Figure 7-44 with d/gT* = 0.031, Kp, = 0.38 is found. Therefore, from Equation 7-31, C = D 1/5 pe Dak 30,000 ne 1/y (2) (32.2) (1) (50)? (0.38) Cp = 0.98 . 7-106 If Airy theory had been used Kp, = 0.17, and (“pm) 1 = 0.76 ‘hit (0.38) (“D) sry ¥ [Co n=0.76 A a (Kin) siny (0) Some of the difference between the two values of Cp is 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 is because Airy theory is unable to describe accurately the water- particle velocities of finite-amplitude waves. Semmes ie, eae ae oe ie oe ie oe ode Ye ede Se See ee ae de ee) ete aie) oe. Se Oe) Se ee, eee The two examples show the influence of the wave theory used on the value of Cp determined from a field experiment. Since the determina- tion of wave forces is the inverse problem, i.e., Cp and wave conditions known, tt ts tmportant 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 7-58. The solid line is generally conservative, and is recommended for design along with Figures 7-44 and 7-46 with the Reynolds number defined by Equation 7-38. x RK kK eK RK RK RK RK KR K * *K * * EXAMPLE PROBLEM * * * * * * * * * * *¥ *® * * * DETERMINE: Were the values of Cp used in the preceding example problems reasonable? SOLUTION: For the first example with H = 10 £t.; T = 10 sec., d = 15 ft. and D = 1 ft., from Equation 7-40, e =) Eon =|\—— S| 7 10 1 Unae = Sa Wr = 7.66 ft./sec. nats AG AOMIniR 8 ee From Equation 7-39, Py ii Bbw D, R= (7.66) (1) RS a ES 7S SOO S iL S20 f= lO” From Figure 7-58, C, = 0.7, which is the value used in the preced- ing example. For the example with H.=.50 ft. (T= 10 seeiyrd = l00fee and D= 1 £ft., from Equation 7-40, m(10) (1) = = 3.5 ft/sec. Mb ioe! (10) (0.9) 3.5 ft./sec From Equation 7-39, (3.5) G) UE ee SE Co IID e (EOCM10F 51) : From Figure 7-58, Cp = 0.9 which is less than the value of Cp = 1.2 used in the force calculation. Consequently, the force calculation gave a high force estimate. FB Rok SE BF HOH *K a KOK FOR BF BUS CR ORTH KCTS ORK CRE Eee ee b. Factors Influencing Cy. MacCamy and Fuchs (1954) found by theory that for small ratios of pile diameter to wavelength, (aia wea (7-45) 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 Cy 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 7-41, will drastically alter the flow pattern around the cylinder, and invalidate the analysis leading to Cy = 2.0. The factors influencing Cp also influence the value of Cy. No quantitative dependence of Cy on Reynolds number has been established, although Bretschneider (1957) indicated a decrease in Cy with increasing Rg. However for the range of Reynolds numbers (Re < 3 x 10*) covered by Keulegan and Carpenter (1956), the value of the parameter A/D plays an important role in determining Cy. For A/D < 1 they found Cy ~2.0. Since for small values of A/D _ the flow pattern probably deviates only slightly from the pattern assumed in the theoretical development, 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 minimum Cy ~0.8, for A/D ~ 2.5, and found that Cy increased from 1.5 to Mey ator’ () PVA 5 X OZ. with Re defined by Equation 7-39. Table 7-3. Experimentally Determined Values of Cur Approximate R, | Approximate, | Gy" _ [Type of Expeiment and Theory Used Type of Experiment and Theory Used Per a nrcsasee), and Carpenter (1956) <3 X104 1.5 to 2.5 | Oscillatory laboratory flow (A/D 6) Bretschneider (1957) 1.6 X10° to 2.3X 10° | 2.26 to 2.02] Field experiments 3.8X 10° to6X10° | 1.74 to 1.23] Linear Theory Wilson (1965) large (>5 X 10°) 153 Field experiment, spectrum Skjelbreia (1960) large (>5 X 10°) 1.02 + 0.53 | Field experiments, Stokes’ Fifth Order Theory Dean and Aagaard (1970) 2 X10° to 2x 10° 1.2 to 1.7 | Field experiments, Stream-function Theory Evans (1970) large (>5 X 10°) ore A Field experiments, Numerical Wave Theory or Stokes’ Fifth Order Theory Wheeler (1970) large (>5 X 10°) : Field experiments, Modified spectrum analysis using C, =0.6 and C,,= 1.5 the standard deviation of the calculated peak force was 33 percent * Range or mean + standard deviation. f=109 The values of Cy given in Table 7-3 show that Skjelbria (1960), Dean and Aagaard (1970) and Evans (1970), used almost the same experimen- tal 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 7-58 is generally conservative, from Equation 7-46 the recom- mended choice of Cy for Rg > 5x 10° corresponds approximately to the average of the reported values. This possible lack of conservatism, how- ever, is not significant since the inertia force component is generally smaller than the drag force component for design conditions. From Equa- tions 7-30 and 7-31 the ratio of maximum inertia force to maximum drag force becomes Ea 2 Cy H Kp» For example, if Cy ~*~ 2 Cp and a design wave corresponding to H/Hp, = 0.75 is assumed, the ratio F;,/Fp, may be written (using Figures 7-43 and 7-44 as ( ) She) H (deep water 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 com- ponent for shallow-water waves, and the two force components will be of comparable magnitude only for deepwater waves. 7.316 Example Problem and Discussion of Choice of a Safety Factor. ee RK kK RK kK kK kK K * *F * * EXAMPLE PROBLEM * * * * * * * ®¥ *® * ® * * * GIVEN: A design wave with height, H = 35 ft. and period, T = 12 sec, acts on a pile with diameter, D = 4 ft. in water of depth, d = 85 ft. FIND: The wave force on the pile. SOLUTION: Compute, i) ppm aes, 0.00755 eh aae(G2.2)\(2)e) ee : and d 85 — = ——— = 00183. AE ee NGL) Ue 7-110 From Figure 7-40, for d/gT* = 0.0183, Ly = 0. L 72). and 2 0.75 L, = 0.75 a = 0 32.2) (12)? o/s) er2Mi2e ==" 554) ft. 20 = BN ll From Figure 7-41, for d/gT* = 0.0183, n 70.68, H and therefore, 1. = 0.68 H = 0.68 (35) = 23.8 ft., say if) ea oe The structure supported by the pile must be 24 feet above the still- water line to avoid uplift forces on the superstructure by the given wave. Calculate, from Equation 7-14, D 4 —= = — 00072 <"0:05 Therefore Equation 7-13 is valid. From Figure 7-47, Ay ar? = 0.014 ft./sec?, H H oT 2. 0.00755 — = (8T’/H, | = ——" = 0.54. H, ne 0.014 gT? From Figures 7-43 through 7-46, Kim = 0-405 Kee 0.07 Su = 0162 Soe go Tat From Equations 7-39 and 7-40, L, 1 |< ee ft./sec., Umax 4p iby 12 0.75 and Una De pi(2:2)i(4) RS ee anloce e v 1X 1075 From Figure 7-58, Cy es Us and from Equation 7-46, with Re > 5 x10°, Cy = See Therefore, = 7D? Fin — Cy PS caw H Kin» Fe = CCGA 2 ree = we (35) (0.405) = 17,200 lbs., 1 Fom = Cp 7 0g DH Kp,» ps II Din (0.7) (0.5) (2) (32.2) (4) (35)? (0.37) = 40,800 lbs., = i a Qu Y | = (17,200) (85) (0.62) ll 906,000 ft. Ibs., Mp m a Ba d Spm From Equation 7-34, (40,800) (85) (0.82) = 2,840,000 ft. Ibs. SC) CyH 0.735) Interpolating between Figures 7-49 and 7-50 with H/gT? = 0.00755 and d/ot~ = 0.0185, W = 0.245 . Gm = 0-20. Therefore, from Equation 7-35, le m lI Pm Ww Cp H2D, E m (0.20) (64) (0.7) (35)? (4) = 43,900 lbs. Whe Interpolating between Figures 7-53 and 7-54 gives ams=) 0:16". m Therefore, from Equation 7-36, Me aw Cy H? Dd , M,, = (0.16) (64) (0.7) (35)? (4) (85) = 2,985,000 lb.-ft. , say M,, = 2,990,000 Ib.-ft. ee OY Re a) See ie Pe ie, ee ey ey ee ek CD ee Rk) se ee el Re eR ee ei CAT RP CR eek Before designing the pile or performing the foundation analysis, 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 and 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 design wave ts unlikely to occur, it ts recommended that a safety factor of 1.5 be applied 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. If 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 super- critical Reynolds numbers (Table 7-3) 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 TIT3 oscillation is such that a significant amount of energy in the wave spec- trum 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 the roughness and effective diameter of the member, and increases forces on the member. Guidance on selecting a drag coefficient Cp can be obtained from Table 7-2. However, the increased diameter must be carried through the entire design procedure to determine forces on a fouled member. 7.317 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 7.312 must be generalized. Figure 7-59 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. Choosing a reference pile located at x = 0, the x-coordinate of each pile in the group may be determined from, x= 2 cos.an, (7-49) where the subscript n refers to a particular pile, and 2%, and a, are as defined in Figure 7-59. 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 7.312, 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. it 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 js ===, (7-50) where L is wavelength, the formulas given in Section 7.313 (equations 7-18 and 7-19) for a pile located at x = 0 may be written in general form by introducing 6, defined by 2mx/L - 2mt/T in place of - 2nt/T. 7-114 Reference Pile Figure 7-59. Definition Sketch - Calculation of Wave Forces on a Group of Piles that are Structurally Connected Using tables (Skjelbreia, et al., 1960, and Dean, 1973), it is possi- ble to calculate the total horizontal force F(x) and moment around the mudline 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 = xp relative to the design wave crest the total force, or moment around the midline, is obtained by summation, Naa Frotal = an 15 Ba ee (7-51) NS Nis 7-52 Total — wei (x, X,)>° (7=52) where N = total number of piles in the group, x. = 705 x, = from Equation 7-49 , x. = location of reference pile relative to wave crest . Repeating this procedure for various choices of x, it is possible to determine the maximum horizontal force and moment around the mudline for the pile group. 7-115 Fp(8) is an even function, and F;(@) is an odd function, hence By CO) Scr G Bs (7-53) and BE Ghar, Gia): (7-54) and calculations need only be done for 0 < @< 7m radians. Equations 7-53 and 7-54 are true for any wave that is symmetric about its crest, and are therefore applicable if the wave tables of Skjelbria, et al. (1960) and Dean (1973) are used. When these tables are used, the wavelength computed from the appropriate finite amplitude theory should be used to transform @ into distance from the wave crest, x. The procedure is illustrated by the following examples. For sim- plicity, Airy theory is used and only maximum horizontal force is con- sidered. The same computation procedure is used for calculating maximum moment. eK Ue) SURAT ok ok ok Ok Fe RYAMPILE PROBILEM © % # % Xo ee ek eK ee GIVEN: A design wave with height, H = 35 ft. and period, T = 12 sec. in a depth, d = 85 ft. acts on a pile with a diameter, D = 4 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 7.315, G = 0-7, and Cin = Loe: From Figures 7-43 and 7-44 using the curve for Airy theory with d 85 [=a = apa = UOlsoR: eT SW old( (117) Re Oo Sine isto. and from Equations 7-30 and 7-31, m(4)? 1.5 (2) (32.2) —[= (35) (0.378) = 16,100 Ibs., @ Il 0.7 (0.5) (2) (32.2) (4) (35)? (0.195) = 21,500 Ibs. Ww ll Combining Equations 7-22 and 7-26 gives Fa Be risie s 1 7-116 and combining Equations 7-23 and 7-27 gives Fp = Fm cos 0 | cos |, where 9 = 2Ux _ 2m L iva The wavelength can be found from Figure 7-40, Lp pat ft. From Table 7-4 or Figure 7-60 the maximum force on the example pile occurs when 20° < 6 < 40°, and is about Fy, ~ 25,000 lbs. Table 7-4. ae Calculation of Wave Force Variation with Phase se 21,500 21,500 21,500 ath 19,000 24,500 13,500 10,350 12,600 22,950 2,250 13,950 5,370 19,220 —8,580 15,850 650 16,500 —15,200 15,850 —650 15,200 —16,500 55950 —5,370 8,580 —19,220 10,350 —12,600 —2,250 —22,950 5,500 —19,000 —13,500 —24,500 0 —21,500 —21,500 —21,500 Co” URC HC, te Re Pm Ta IR et Ge ca gh a ee WR ee i Pe i ee Oe Te ieee, aC, eMC, Yalkeh ea ee , P Ta a x eK KK RK kK kK kK RK kK eK K F * EXAMPLE PROBLEM * * * * * * * * * * * * OR F GIVEN: Two piles each with a diameter, D = 4 ft., spaced 100 ft. apart are acted on by a design wave having a height, H = 35 ft., a period, T = 12 sec. in a depth, d = 85 ft. The 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 8 was computed from Airy theory for the preceding problem and is given in Figure 7-60 and Table 7-4. Figure 7-60 will be used t=Neg alld 4IDINIIID D JO} ‘9 ‘ajbuy BSOUd YIM $99J04 BADM |DJO] PUD DI JJau| ‘BOI 40 UOIJDIIDA ajdwoxy —CEgQ-y ainbi4 (seeibap) g Oc- Ove O8I- 00! 08 000‘0¢- 09 os! O9! Ovi O02! a0 L ia ae sai 000'sz- “i Oo DS SRe Ree jseeonanaad aausaee He ae sueae boss t tet ater 000°0| Shs 7 (sq| ) 99104 to compute the maximum horizontal force on the two-pile group. Compute the phase difference between the two piles by Equation 7-49, x, — &, cosa, — 100\(cos 30°), n n 86.6 ft. Xn From the previous example problem, L ~ Lg = 554 ft. ford = 85 ft. and T = 12 secs. Then from the expression, en ib 2a 6.6 GL se COs SEES) a eae adds roy 554 or 360° (86.6 ee a Oo n 554 Figure 7-60 can be shifted by 56.3° to represent the variation of force on the second pile with phase angle as shown in Figure 7-61. The total horizontal force is the sum of the two curves (F, = 42,000 lbs). The same procedure can be used for any number of piles with one curve for each pile. Table 7-4 can be used similarly simply by offsetting the force values by an amount equal to 56.3°. The procedure is also appli- cable to moment computations. Figure 7-61 shows the maximum force to be about 42,000 lbs. when the wave crest is about 8° or [(8°/360°) 554] ~ 12 ft. in front of the refer- ence 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 struc- tures 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 the example, the forces on a single pile are (from preceding example problems) , (Fm) finite amplitude = 43,900 lbs. , and (Fra) giny = 254000 Ibs. Gauls) iG Ht a on Het tere Bete maa FF eS ut at f-3} fi Gite Gav Raa ie te ~ ~ i Je y ° i=) io) lo} fo} jo} fo) ie) °o ° fo} fo} jo} °o o- 2 o So So. So o ie] fo) io) So °o fo} oO! a 8 8 & & & 2S 2 fo Ba a © jo) lo} o fo} fo) fo} fo} fo) fo} °o fe} jo) BE Ee a en tae @ = re W120 Figure 7-61. Example Calculation of Total Force on a Two-Pile Group Therefore, the total force on the 2-pile group, corrected for the finite amplitude design wave, is given by, & (Fr finite amplitude [Frotat]2-piles . (F ) [Frotai] 2-piles (corrected mi Airy (computed for finite from Airy amplitude theory) design wave ) 43,900 FFrotailzpites = 35 99 (42:000) = 73,750 Ibs., say 73,800 Ibs. AU Sk A ie We ee ke Oe a ee ae ee ee Oe Re ee This approach is an approximation, and should be limited to rough calcula- tions for checking purposes only. The use of tables of finite amplitude wave properties (Skjelbria, et al., 1960 and Dean, 1973) ts recommended for destgn calculattons. As the distance between piles becomes small relative to the wave- length, 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 diam- eter. A few investigations evaluating the effects of nearby piles are summarized by Dean and Harleman (1966). 7.318 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 7-62. Since forces are perpendicular to the pile axis, it is reasonable to calculate forces by Equation 7-13 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 follow- ing procedure is recommended for calculating forces on nonvertical piles. For a given location on the pile (x), Yo, Zo in Figure 7-62), 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. ke Re kk RK kK RK kK K * * * * EXAMPLE PROBLEM * * * * * * * * * ¥ *¥ ¥ ®¥ KF GIVEN: A pile with diameter D = 4 ft. at an angle of 45° with the horizontal in the x-z plane is acted on by a design wave with height H= 35 ft. period T = 12 isec.\am a depth d = 855ft. Tiel 2 ee a ey L fmds ett (Xo Yor Zo) a Note: x,y and z axes are AG orthogonal Figure 7-62. Definition Sketch - Calculation of Wave Forces on a Nonvertical Pile FIND: The maximum force per unit length on the pile 30 ft. below the SWL (z = -30 ft.). SOLUTION: For simplicity, Airy theory is used. From preceding examples, Cy = 1.5, Cp = 0.7, and L = Lg = 554 feet. From Equation 7-18, with sin (-2nt/T) = 1.0, gee Alle ™D? m cosh [2m (d + z)/L] im M PS 4 IL cosh [27d/L] nm (4)? 1 =. 2) — (0.8) = apie f 5i@)G222) D (35) 554 (0.8) 193 lbs./ft From Equation 7-19, with cos (2mt/T) = 1.0, 4 pg gT? a [27 (d+ 2vull! f= Sepsis Dm “p 2 oH AL? cosh [27d/L] (2) (32.2) (32.2) (1:2)2 f = 1 —— A Se (US ./ft. Din (0.5) (4) (35) (4) (554)2 (0.8) 267 |b./ft tali22 The maximum force can be assumed to be given by F =e mz mo" Dm , Fpm where F, and Fp, are given by Equations 7-35 and 7-31. Substituting these equations into the above gives $, WCp H?D 2b fone ae ——____—___——_- = f — D D : a . Cp (e 8/ 2 )H? DK “y Kom From Equation 7-34, Interpolating between Figures 7-49 and 7-50 with H/gT* = 0.00755 and d/gT* = 0.0183, it is found that 9, = 0.20 From a preceding problem, or o.GA Hy Enter Figure 7-44 with d/gT* = 0.0183 and using the curve labeled 1/2 Hp read Knm = 0-35- Therefore, 2¢ fa pk = ’ Dm 2 (0.20) £367 = = 305 lb/ft: me 0.35 say f= 300 lbefit. The maximum horizontal force per unit length at z = -30 ft. on the fictitious vertical pile is f, = 300 lbs./ft. This is also taken as the maximum force per unit length perpendicular to the actual inclined piles a cat eee Le Ree eK KOR kad ee eek ee ee CRE RE ROR Ra ea Res a, ha23 7.319 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 7.312 by using the generalized graphs with H = Hp. This approach is recommended for waves breaking in deep water. (See Section 2.6, 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 approximately 1 Fn ~ Fom = Cp 5 pg DH? Kp,, (7-55) m Figure 7-44, for shallow-water waves with H = Hp, gives Kp, = 0.96 = 1.0; consequently the total force may be written 1 Fm = Cp 5 68D HE (7-56) m From Figure 7-46, the corresponding lever arm is dpSp, ~ dp (1.11) and the moment about the mudline becomes Wyle = Let (1.11 d,) (7-57) m m Small-scale experiments (Rp ~ 5 x 10* by Hall, 1958) indicate that B= Spe D HE (7-58) and Me ee Hy (7-59) Comparison of Equation 7-56 with Equation 7-58 shows that the two equations are identical if Cp = 3.0. This value of Cp is 2.5 times the value obtained from Figure 7-58. (Cp = 1.2 for R, > 5 x 10*.) From Section 2.6, since Hp generally is smaller than (1.11) dp , it is con- servative to assume the breaker height approximately equal to the lever arm, 1.11 dy. Thus, the procedure outlined in Sectton 7.312 may also be used for breaking waves in shallow water. However, Cp should be the value obtained from Figure 7-58 mltiplted by 2.5. Since the Reynolds number generally will be in the supercritical region, where according to Figure 7-58, Cp = 0.7 it is recommended to calculate breaking wave forces using C = 2.5(0.7) = 1. 7-60 ( D) breaking Oe) ee) ( ) The above recommendation is based on limited information; however, large-scale experiments by Ross (1959) partially support its validity. 7-124 For shallow-water waves near breaking, the velocity near the crest approaches the celerity of wave propagation. Thus, as a first approxima- tion the horizontal velocity near the breaker crest is Ucrest ~ Ved, AN gH, (7-61) where Hp is taken approximately equal to dz, the depth at breaking. Using Equation 7-61 for the horizontal velocity, and taking Cp = 1.75, the force per unit length of pile near the breaker crest becomes f. ~ 1 2 Dm ~ Cp 2 PDUZ oot ~ 0.88 pg DH,. (7-62) Table 7-5 is a comparison between the result calculated from Equation 7-62 with measurements by Ross (1959) on a 1-foot diameter pile (ie) =). 30x,10°),, Table 7-5. Comparison of Measured and Calculated Breaker Force* Breaker Height fom t a (ft.) (Ibs./ft.) (Ibs./ft.) * Values given are force per unit length of pile near breaker crest. + Calculated from Equation 7-62. t Measured by Ross, 1959. Based on this comparison, the choice of Cp = 1.75 for Rg, > 5 x 10° appears justified for calculating forces and moments due to breaking waves in shallow water. 7.3110 Calculation of Forces on Noncircular Piles. The basic force equation (Equation 7-13) can be generalized for piles of other than circular cross section, if the following substitutions are made D2 : ‘ ie = volume per unit length of pile , (7-63) where D = area perpendicular to flow direction per unit length of pile. aes Substituting the above quantities for a given noncircular pile cross section, Equation 7-13 may be used. The coefficients K;,, etc., depend only on the flow field, and are independent of pile cross-section geometry; therefore, the generalized graphs are still valid. However, the hydro- dynamic coefficients Cp and Cy, depend strongly on the cross-section shape of the pile. If values for Cp 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 oscil- lating flows, Equation 7-13 in the form applicable for a circular cylin- der, with D taken equal to the width of the plate gave OES A and for as = 10 (7-64) ies (eae, (7-65) If reflection is complete, and the reflected wave has the same amplitude as the incident wave, then x= 1, and the height of the clapotis or standing wave at the structure will be 2H;. See Figure 7-63 for defini- tion of terms associated with a clapotis at a vertical wall. The height of the clapotis crest above the bottom is given by il oP 3% Ye te Gn lier ag H; (7-66) The height of the clapotis trough above the bottom is given by, il sPp5% Ven deck he = at H; (7-67) fem, wae: of Clapotis Mean Level (Orbit Center ge of Clapotis ) ‘ li: (ee ly a Incident Wave 2 i \ a Seats (Hi + a ih ete i re "4 as Yc L =(1+%) Hj Trough of 4 Muster 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 7-65 and 7-68) Yo = Depth from Clapotis Crest = d+ ho + (3) Hj y; = Depth from Clapotis Trough = d + ho - ( Lik ) Hj 2 b = Height of Wall Figure 7-63. Definition of Terms--Nonbreaking Wave Forces 7-128 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 tech- niques, 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 x= 1. Where wales, tiebacks or other struc- tural elements increase the surface roughness of the wall by retarding vertical motion of the water, a lower value of x may be used. A lower value of x 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 destgn purposes. Pressure distributions of the crest and trough of a clapotis at a vertical wall are shown in Figure 7-64. When the crest is at the wall, pressure increases from zero at the free water surface to wd + pj at the bottom, where p, is given as 1+ x w H; p. = |—| ———— (7-68) 1 2 cosh (2md/L) Crest of Clapotis at Wall Trough of Clapotis at Wall = = ho ae mS Aa Actual Pressure Distribution Hydrostatic Pressure Distribution Hydrostatic Pressure Distribution Actual Pressure Distribution N Figure 7-64. Pressure Distributions - Nonbreaking Waves (pais) When the trough is at the wall, pressure increases from zero at the water surface to wd — Pp, at the bottom. The approximate magnitude of wave force may be found if the pressure is assumed to decrease linearly from the free surface to the bottom when either the crest or trough is at the wall. Figures 7-65 through 7-70 permit a more accurate determination of forces and moments resulting from a nonbreaking wave at a wall. Figures 7-65, 7-66, and 7=67 show the dimensionless height of the clapotis orbit center above stillwater level, dimensionless horizontal force, and «limen- Sionless moment about the bottom of the wall for a reflection coefficient, x = 1. Figures 7-68 through 7-70 represent identical dimensionless param- eters for x = 0.9. The use of the figures to determine forces and moments is illustrated in the following example. * OX * Oe ek OK LK) Ok) 1k ee eX SEXAMPLE PROBLEM * * * > * 0% % Xp oe ¥) Peee GIVEN: (a) Smooth-faced vertical wall (x = 1.0). (b) Wave height at structure if structure were not there, H; = 5.0 feet. (c) Depth at structure, d = 10.0 feet. (d) Range of wave periods to be considered in design, T = 6 sec. (minimum) T = 10 sec. (maximum) 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, i 5.0 i 5.0 = = = 05, —3 = => = 000043 (hears d 10.0 eT2 32:2(6)2 : ) Enter Figure 7-65 (because the wall is smooth) with the computed value of H-/gT*, and determine the value of h./H, from the curve for H;/d = 0.5. (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.) H; hy ere === = (0/001 - =a OSs @ oT? H, ro) 1 iT] 6 sec.) Therefore, h, = 0.70 (Ey =" 0-7 05.0)) — 325 dite (T = 6 sec.) ic) 7-130 O'| =X !saanm Bbulyoosquoy uasbpuny-oeydiw Gg-2 anbl4 216 alge £b000 $S1000 £00 Gz0'0 200 S100 10:0 Soo 0! ; 0) eye 4 (299S/4}) Ty | 60 80 20 90 iene) ve) £0 20 i ie OF }—} ft i 4 | | } | 4040M deeq han 80°81) = art | | } FEE DjDQ @ADM BulyDeig pansasag o} adojanuy TIS 21NJONI}S 4D 4S9I9 @ADM | a4njonsjs yo yBnoi) aadM 2) (ft/sec Hj T2 2 0.025 0.03 0.0 .O 0.015 (0) .005 De kel ©) Rundgren Nonbreaking Wave Forces -66. Miche - Figure 7 Noe t ainjonsyS 4D $Sa419 aADM aINJONsyS yo yBnos] aAnM T ss pes Sises se: Hi (ft/sec?) T2 0.03 0.025 0.02 0.01 X=1.0 ? Wave Moment -Rundgren Nonbreaking iche Figure 7-67. M also £00 $200 "60 =X ‘SaADM bulyDasquon uasbpuny-aysiw “gg-y aunbi4 200 S100 100 S000 O Jt z (299S/}}) Tg) lapel ee i = gh run add } | | | | 1-134 oe . eee id | Reine Hae 7 ann it prt! = ee = 0 01 0.2 Os «104 g5" ~~ 206 07 08 09 Hi, (ft/ 2) T2 sec 0 0.005 0.01 0.015 0.02 0.025 Hi gT? Figure 7-69. 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Bau carga sects cgesstsessnaes teense a 3 Poo p : - - 2 r +t : +] 33 es : g: ~ ; 7 3 3 es E — ; . ; sErseseasees ro) 0.1 Fee ts ne eeieeesses = tt eT yesebeara pes Es + fo) t FEyeery: = 3 33 3B @ i ese : st 7 Bgl esazenect tet suertat : egesi staat te © & + + +] Lanes a :: = J seseszs! rs Biri re 2 ° it + + SEH HEE S 2 ] 2 ~ : = # : + aE Sense ; : SS cf tht race Segsesers tas au taess Ht oH =n OS” 10m 0.5 0.6 07 0.8 H; ai (ft/sec?) ° © 0) 0.005 0.01 0.015 0.02 0.025 0.03 Figure 7-70. Miche-Rundgren Nonbreaking Wave Moment; X = 0.9 7T=|36 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 7-66 and 7-67, il ap 3% y= d + beet aes H; , gad il ars age eT Bae Feros 0 21 ya= 10 3.50 + (1) (5) = 18.5cit., (T = 6 sec.) Va 210) 13,50 — (1) (5) = 18:5 te. A similar analysis for the 10-second wave gives Yo19.5 ft.,, (T = 10 sec.) ¥, =. 9:5 ft. The wall would have to be about 20 feet high if it were not to be over- topped by a 5-foot high wave having a period of 10 seconds. The horizontal wave forces may be evaluated using Figure 7-66. Entering the figure with the computed value of Hejl, 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* = 0.5) will give the dimension- less force when the crest is at the wall, F,/wd? ; the lower family of curves (below F/wd* = 0.5) will give the dimensionless force when the trough is at the wall, Fz/wd*. For the example problem, with H;/gT* = 0.0043, and H;/d = 0.50, Leh F t mas = 1.25; vd? = 0.29. (T = 6 sec.) Therefore, assuming a weight per unit volume of 64.0 lbs./ft? for sea water, F c F, The horizontal line in Figure 7-66 (F/wd* = 0.5) represents the hori- zontal hydrostatic force against a wall in still water of depth, d. For the example problem, if the water depth on the leeward side of the wall is also 10 feet and there is no wave action, the maximum seaward acting horizontal force will be Fg = 0.5 wd*. Therefore, the net horizontal force will be, 1.25 (64) (10)? 8,000 lbs./ft., (T = 6 sec.) 0.29 (64) (10)? 1,860 lbs./ft. Eeee =. 1-25 (64) (0)? — "0:5: (64) (10)? Fo, = (1.25—0.5). (64) (10)? = 4,800 Ibs./ft. (T= 6 sec.) GAlSy 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 F, - Fy, with F, and Fz determined for the appropriate wave conditions. Assuming for the example problem that the wave action is identical on both sides of the wall, Frop = 1.25 (64) (10)? — 0.29 (64) (10)? Fe (1.25) 0-29) Gs) (10)? = 6,144 lbs./ft. say Fe 0; LOO Mlbs:/tt: (T = 6 see] The moment about point A at the bottom of the wall (Fig. 7-64) may be determined from Figure 7-67. The procedures are identical to those given for the dimensionless forces. However, in this case the hori- zontal line, M/wd? = 0.167 indicates the hydrostatic moment about the toe resulting from still water of depth d. Continuing the example problem, from Figure 7-67, with H;/gT? = 0.0043 and H;/d = 0.50 M M c t aaa 7/55 2 eet 0.80 (T = 6 sec.) Therefore, lb.-ft. Me = 05755564) (10)? = 48,300 fs (T = 6 sec.) lb.-ft. M, = 0.080 (64) (10)? = 5,120 fi When there is still water of depth d on the leeward side, the maximum moment Me Me 0:67 wde © net Therefore, the resultant moment about A is Mo: = 0-799" (64) (10)? — 0.167 (64) (10) nN lb.-ft. ft. The maximum moment when there is wave action on the leeward side of the structure will be M, - Me with M, and My evaluated for the appropriate wave conditions. For the example problem, if identical wave conditions prevail on both sides of the structure lb.-ft. M,o¢ = (0.755 — 0.080) (64) (10)? = 43,200 ft. Figures 7-68, 7-69, and 7-70 are used in a similar manner to determine forces and moments on a structure which has a reflection coefficient of x = 0.9. M ee = MOTD O67) (G4) (10)? = 37,600 (T= 6 sec.) (T = 6 sec.) CN TU i DS Ta, eH ee eet ee hg OSS 7-138 7.324 Wall of Low Height. It is often not economically feasible to design a structure to provide a nonovertopping condition by the design wave. Consequently, 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 7-71. The resulting pressure distribution is shown by the shaded area, and the force resulting from it is F’. The magnitude of F’ is proportional to F, the force that would act against the wall if it extended up to the crest of the clapotis (the force determined from Figures 7-66 or 7-69). The relationship between F’ and F is given by F’ = rfF , (7-69) where Tr is a force reduction factor given by b b b faa =| when =< 120). yi yf y and (7-70) tr, = 1.0 when Ligne aye y where b and y are defined in Figure 7-71. The relationship between TF and b/y is shown in Figure 7-72. ah. of Clapotis P, Figure 7-71. Wall of Low Height - Pressure Distribution Similarly, the reduced moment about point A is given by M’ = r,.M, (7-71) where the moment reduction factor fr, is given by b.\? b b ro ice (eae 32 when = SolOy, y y, y and (7-72) b Bo 10 when ae LO y T-I39 HH Pore 0.9 | eee | | ty 0 en | pet -t~-4-4 Boe pate eee pear oe La 1.0 Force and Moment Reduction Factors -72. Jaryey ns) 7/ 7-140 The relationship between r, and b/y is also shown in Figure 7-72. Equations 7-69 through 7-72 are valid, when either the wave crest or wave trough are at the structure, provided the correct value of y is used. ke eK KK RK RK RK kK K KF * & * EXAMPLE PROBLEM * * * * * * * *® * ® ® ® * * GIVEN: (a) Wall height, b = 16.0 feet. (b) Incident wave height, H; = 5.0 feet. (c)’ Depth at structure toe, d = 10.0 feet. (d) Wave period, T = 6 sec. (minimun), T = 10 sec. (maximum) FIND: Determine the reduced wave force and moment on the given vertical wall, SOLUTION: From the example problems in Section 7.323, 7.18.50 itm (l= 6)secs) ¥,.— 8.50 ft. Compute b/y for each case b 16.0 : — = = 0.865 ve 18.50 (T = 6 sec.) 16.0 = a ee CO ete Yt 50 Entering Figure 7-72 with the computed value of b/y, determine the values of Tp and r, from the appropriate curve. For the wave with ie=— 65SEC... b ——='="05865 ; therefore, ee 0.981;r, = 0.950, m Ye and b == Sil therefore, aS Wem SS 1). Yt f BS 7-14) Reduced forces and moments may be calculated from Equations 7-69 and 7-71 using the values of F and M_ found in the example problem of the previous section; for T = 6 sec. F. = 0.981 (8,000) = 7,850 Ibs./ft ; lb.-ft. M’, = 0.950 (48,300) = 45,900 Tears F, = 1.0 (1,860) = 1,860 Ibs./ft. ; M! = 1.0 (5,120) = 5,120 P= de > a fee 2 Again assuming that the wave action on both sides of the structure is identical, so that the maximum net horizontal force and maximum over- turning moment occurs when a clapotis crest is on one side of the structure and a trough is on the other side Bie = E = E = 7,850 — 1,860 = 5,990 lbs./ft. , say (T = 6 Secs) Fey = 6,000 lbs./ft. , and Big en Maa RA (ER . x lb.-ft. Mo M M, =.49,900 —.5,420.=- 40,730 ae say (T = 6 sec.) as lb.-ft. M, 4, = 41,000 rae A similar analysis for the 10-second wave gives, 1san = 6,065 lbs./ft. , (T = 10 sec.) ives lbs.-ft. Mp a 445/00 peak Ce ee a ee ee a er a, ee ee, et SO ee eC er SS 7.325 Wall on Rubble Foundation. Forces acting on a vertical wall built on a rubble foundation are shown in Figure 7-73, and may be computed in a manner Similar to computing the forces acting on a low wall if the comple- ments of the force and moment reduction factors are used. As shown in Figure 7-73, the value of b which is used for computing b/y ts the height of the rubble base and not the hetght of the wall above the foundation. The equation relating the reduced force F" against the wall on a rubble foundation with the force F which would act against a wall extending the entire depth is, F’= (1 sf) lee (7-73) 7-142 The equation relating the moments is, Mao (tates), M (7-74) m) where M/ is the moment about the bottom (point A on Figure 7-73). Usually, the moment desired is that about point B which may be found from Foca ame ty BN em) Ee or (7-75) Mz = M, — bF” The values of (1 - Cn and (1 - re) may be obtained directly from Figure 7-72. Crest of Clapotis Figure 7-73. Wall on Rubble Foundation - Pressure Distribution k kok kok kok ko * * * * * & EXAMPLE PROBLEM * * * * * * * # HK KOKO * * GIVEN: (a) A smooth-faced vertical wall on a rubble base. (b) Height of rubble foundation, b = 9 ft. (c) Incident wave height, Hi = 5 ft. (d) Design depth at the structure, d = 10 ft. (e) Wave period, T = 6 sec. (minimum), T = 10 sec. (maximum) 1-143 FIND: Determine the force and overturning moment on the given wall on a rubble foundation. SOLUTION: For this example problem Figures 7-65 through 7-67 are used to evaluate hos F and M even though a rubble base will reduce the wave reflection coefficient of a structure by dissipating some incident wave energy. Values of h., F, and M used in this example, have been determined in the example problem of Section 7.323, ae US (T = 6 sec.) eS eae ie Compute b/y for each case, remembering that b now represents the height of the foundation. b 9.0 — = —— = 0.486 yz 18.50 (T = 6 sec.) b 9.0 =a = === = 1.058) Sair0 y, 8.50 Enter Figure 7-72 with the computed values of b/y and determine corresponding values of (1 - r¢) and (1 - ae For the 6-second wave, b = = 0486; (1 Srey = 70.264 5 (tr = 0.521 - (ay (1% ) and a Yt From Equation 7-73, = 1.0); (1 — tf) = OWig Gasset =" 0:0 2,100 lbs./ft. ai i 0.264 (8,000) (T = 6 sec.) 0.0 (1,860) = 0 Ibs./fe. wil = I For the 10-second wave, a similar analysis gives, Be 2,620 lbs./ft. ( (T = 10 sec.) 0 lbs./ft. 7 ev The overturning moments about point A are, from Equation 7-74, lb.-ft. ft. (M4), = 0.521 (45,900) = 23,900 (T - 6 sec.) lb. (M’i), = 0.0 (5,120) = 0 —— and for the 10-second wave, yi lb.-ft. (Mi). = 32,000 ——, (T = 10 sec:) nerd lb.-ft. (Mia)¢ = 43 fe The overturning moments about point B are obtained from Equation 7-75, lb.-ft. ft. (Mz)_ = 23,900 — 9.0 (2,100) = 5,000 ’ Pe egeiGe (Mz), ~ 0 fc. and for the 10-second wave, (Mz), = 8,400 ——, (Mz), ~ 0 a: As in the examples in Sections 7.323 and 7.324, various combinations of appropriate wave conditions for the two sides of the structure can be assumed and resulting moments and forces computed. Er ene ok. ep eR eo aed ie Oe tae tema, oe Se ade eS “Se ee de es ee eee oe ee en ee aye 7.33 BREAKING WAVE FORCES ON VERTICAL WALLS Waves breaking directly against vertical-face structures exert high, short duration, dynamic pressures that act near the region where the wave crests hit the structure. These impact or shock pressures have been studied in the laboratory by Bagnold (1939), Denny (1951), Ross (1955), Nagai (1961 b), Carr (1954), Leendertse (1961), Kamel (1968), Weggel (1968), and Weggel and Maxwell (1970 a, and b). Some measurements on full-scale breakwaters have been made by deRouville, et al., (1938). Wave tank experi- ments by Bagnold (1939) led to an explanation of the phenomenon. Bagnold found that impact pressures occur at the instant that the vertical, front face of a breaking wave hits the wall and only when a plunging wave entraps a cushion of air against the wall. Because of this critical dependence on wave geometry, high impact pressures are infrequent against prototype structures. However, the possibility of high impact pressures must be recognized, and considered in design. The high impact pressures are short (of the order of hundredths of a second), and their importance in the design of breakwaters against sliding or overturning is questionable. However, lower dynamic forces which last longer are important. 7-145 7.331 Minikin Method: Breaking Wave Forces. Minikin (1955, 1963) developed a design procedure based on observations of full-scale break- waters and the results of Bagnold's study. Minikin's method can give wave forces that are extremely high, as much as 15 to 18 times those calculated for nonbreaking waves. Therefore, the following procedures should be used with caution, and only until a more accurate method of calculation is found. The maximum pressure assumed to act at the SWL is given by H, d b p= 101 w — —(D+d), (7-76) m ED s where p, is the maximum dynamic pressure, Hp is the breaker height, d, is the depth at the toe of the wall, D is the depth one wavelength in front of the wall, and Lp is the wavelength in water of depth D. The distribution of dynamic pressure is shown in Figure 7-74. The pressure decreases parabolically from P,, at the SWL to zero at a distance of Hp /2 above and below the SWL. The force represented by the area under the dynamic pressure distribution is Pm Hy KK = ae (force resulting from dynamic component of pressure) (7-77) and the overturning moment about the toe is Pm Hy 4, eS Re. ek er (moment resulting from dynamic component of pressure) (7-78) The hydrostatic contribution to the force and overturning moment must be added to the results obtained from Equations 7-77 and 7-78 to determine total force and overturning moment. The Minikin formula was originally derived for composite breakwaters comprised of a concrete superstructure founded on a rubble substructure. Strictly, D and Ly in Equation 7-76 are the depth and wavelength at the toe of the substructure; d, is the depth at the toe of the vertical wall (i.e., the distance from the SWL down to the crest of the rubble substruc- ture). For caisson and other vertical structures where no substructure is present, the formula has been adapted by using the depth at the structure toe as d,; D and Lp are the depth and wavelength a distance one wave- length seaward of the structure. Consequently, the depth D can be found from D=d,+1,™, (7-79) 7-146 where Lg is the wavelength in a depth equal to dg, and m is the near- shore slope. The forces and moments resulting from the hydrostatic pres- sure must be added to the dynamic force and moment computed above. The triangular hydrostatic pressure distribution is shown in Figure 7-74; the pressure is zero at the breaker crest (taken at Hp,/2 above the SWL), and increases linearly to w(d, + Hp/2) at the toe of the wall. The total force is 2 Ree=eR, 4) Ree ee (7-80) =M, + ™,. (7-81) The last terms on the right side of Equations 7-80 and 7-81 (Rg and M,) are the hydrostatic contributions. Pm — -~ ~ Dynamic Component a Bees Component ds x x Combined Total Bare Figure 7-74. Minikin Wave Pressure Diagram Calculations to determine the force and moment on a vertical wall are illustrated by the following example. ke ke ke Kk F KE ke & & * * EXAMPLE PROBLEM * * * * * * * * * ® ® ® ® * GIVEN: A vertical wall, 14 feet high is sited in sea water with d, = 7.5 feet. The wall is built on a bottom slope of 1:20 (m= 0.05). Reasonable wave periods range from T = 6 sec. to T = 10 sec. 7-147 FIND: (a) The maximum pressure, horizontal force and overturning moment about the toe of the wall for the given slope, and (b) the maximum pressure, horizontal force, and overturning moment for AN 6-second wave if the slope were 1:100. SOLUTION: (a) From the example problem in Section 7.122, the maximum breaker height for a design depth of 7.5 feet, a slope of 0.05, and wave periods of 6- and 10-seconds are H, = 84 ft; (T = 6 sees) H, = 9.8 ft. (T= 10/seem) The wavelength at the wall in water 7.5 feet deep can be found with the aid of Table C-l, peponess C. (The following calculations are for the 6-second wave.) irst calculate the wavelength in deep water (T = 6 sec.), ile 2 L, = 2— = 5.12 (6)? = 184 ft. 4 20 ‘) Then d us = = =— = 0:0408, L, 184 and from Table C-1, Appendix C, d — = 0.084, L and > Lay Fa ool: From Equation 7-79 DU = dt 7 is 7.5 + 89.1 (0:05). = 01.96 ft. and using Table C-1, as above, D D =) 020650 ae — Oe OO L, Lp hence D 11.96 Lp = ae = 0.1091 — el OOMEES Mp say LS 110 ft. 7-148 Equation 7-76 can now be used to find py». Hy d, Bo 10i-w-—— (pd. m i iD s}> ‘D 8.4 Wes py = 101 (64) qasie ioe (196-575) = 6,050 lbs./ft. (T = 6 sec.) A similar analysis for the 10-second wave gives, Pin = 31300 Ibs./ft? (CE-= 0" sec.) The above values can be obtained more rapidly by using Figure 7-75, a graphical representation of the above procedure. To use the figure, calculate for the 6-second wave, err See ace rd aes VR’A (3) at Enter Figure 7-75 with the calculated value of deVelts using the curve for m= 0.05, and read the value of p,,/wHp. Pin Saas ae RS: Using the calculated values of H,, p, = 11.3 w H, = 11.3 (64) (8.4) = 6,075 lbs./ft? , (T = 6 sec.) m For the 10-second wave, p Siw oH, = 35.3 (64) (9:8) =~ 3,300 Ibs./ft? (ix=s108Secs)) m The force can be evaluated from Equation 7-77 RS 900 Ibs /tt.-, (Tl =16, sees) and 1 etme 2110) lbs./ft. (= 10 ¥seck) 7-149 35 30 25 2 El= 20 ai mo) Cc or o Ee N FETT TT ++ = ss {/& Ct in HE obeletaiet Hit daseaiitiaee 4 1 jt ya i Hl Pate Po 10 FEE A al HEH ' saan x aE SEEEEE EEE Ht CJ ace + FH EHH is Hy SESSESS HERREEEEEE ECccosatttat 5 ; f | = } | 7 Beet 4 ot (2 +44 " 1 EG ue BEEP EE EEE EEE EEE Poet +H 5 Booeoe! slomta fal afat a5) is PECEEEE EEE EEE aaa I miele Pr als | a 0 — ————L 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 a (ft/sec2) (0) 0.005 0.01 0.015 0.02 ds gT? Figure 7-75. Dimensionless Minikin Wave Pressure and Force 7-150 The overturning moments are given by Equation 7-78 as, ft.-lbs. Mm = Ryd, = 16,900 (7.5) = 126,800 ~~ , (T = 6 sec.) and ft.-lbs. Mj, = 86,300 “= . (T = 10 sec.) For the example, the total forces, including the hydrostatic force from Equations. 7-80 and 7-81, R, =R,, +R, ; t 8.4\? 64 bs at oa Z. R, = 16,900 + — = 16,900° + 4,380 = 21,280 lbs./ft. say R, = 21,300 Ibs./ft. (T = 6 sec.) R, = 16,400 lbs./ft. Gis l0nsec.) Then M, = M,, sr M, 4 8.4\3 64 (7.5 +S M, = 126,800 + = 126,800 + 17,100 , lb.-ft M, = 143,900 —— , (T = 6 sec.) say lb.-ft. M, = 144,000 —— , ft. and ft.-lb. M, = 106,600 — (T = 10 sec.) Galoil (b) If the nearshore slope is 1:100 (m = 0.01), the maximum breaker heights must be recomputed using the procedure of Section 7.122. For a 6-second wave on a 0.01 slope the results of an analysis similar to the preceding gives, H, = 6.3 ft. (d, = 7.7 ft.>d,), Pores 6,050 lbs./ft? , (l= 6 sees) and R_, = 12,700 lbs./ft. m The resulting maximum pressure is about the same as for the wall on a 1:20 sloping beach (p,, = 6,075 lbs./ft.*); however, the dynamic force is less against the wall on a 1:100 slope than against the wall on a 1:20 slope, because the maximum possible breaker height reaching the wall is lower on a flatter slope. BR OR CK FOR ORK a ROR KOR OK OR CR RK RRR RC AR OX Ke eee 7.332 Wall On a Rubble Foundation. The dynamic component of breaking wave force on a vertical wall built on a rubble substructure can be esti- mated with either Equation 7-76 or Figure 7-76. The procedure for calcu- lating forces and moments is similar to that outlined in the example problem of the preceding section. However, the ratio d,/D is used instead of the nearshore slope when using Figure 7-76. Minikin's equa- tion was originally derived for breakwaters of this type. For expensive structures, hydraulic models should be used to evaluate forces. 7.333 Wall of Low Height. When the top of a structure is lower than the crest of the design breaker, the dynamic and hydrostatic components of wave force and overturning moment can be corrected by using Figures 7-77 and 7-78. Figure 7-77 is a Minikin force reduction factor to be applied to the dynamic component of the breaking wave force equation, Ro SR (7-82) U m mm Figure 7-78 gives a dimensionless moment reduction factor a for use in the equation = T (7-83) m? dik, == (diceay (team or = T mi Bn, Em (Gectaal aly (7-84) T1152 [eT T TIN | THN TIN i 2a ee’ rosa a | Gas as 0.02 OR NEP. i fe HH 0.015 0.01 0.005 ds gt? Figure 7-76. Dimensionless Minikin Wave Pressure and Force 7155 Minikin Force Reduction Factor Figure 7-77. -154 7 "a" factor for use in equation Mm=dsRm—(ds ta) (I-tm) Rm Figure 7-78. Minikin Moment Reduction for Low Wall 7-155 ke eK kK RK RK RK Kk RK kK eK * * * EXAMPLE PROBLEM * * * * * * * * ®% *® ® * kk * GIVEN: (a) A vertical wall 10 feet high in a water depth of d, = 7.5 feet on a nearshore slope of 1:20 (m= 0.05), and (b) aed bi wave periods of T = 6 sec. and T = 10 sec. FIND: Determine the reduced force and overturning moment because of the reduced wall height. SOLUTION: moments are given in preceding example problems. problems, Hy, = 8.4 ft. ) R,, = 16,900 lbs./ft. M, = 126,800 P=: we ; ft. and Hy, = 9.8 ft. ’ Rae e200 lbs./ft. Eon tetas A lbs.-ft. 1 emia ft. Calculations of the breaker heights, unreduced forces and From the preceding ad. —'8:9irt. anes b ‘s (T = 6 sec.) (4, = 9.2 ft.>d,), (T = 10 sec.) For the breaker with a period of 6 seconds, the height of the breaker crest above the bottom is H (+) ~ (75424) = 2 2 as defined in Figure 7-77 is 6.7 feet (i.e., the minus the height obtained by subtracting the wall The value of b/ breaker height Hy crest elevation from the breaker crest elevation). i ey/Pette Calculate (T = 6 sec.) 7-156 From Figure 7-77, r, = 0.94 , m therefore from Equation 7-82, Ri, = tmRimn = 0-94 (16,900) = 15,900 lbs. (T= 6isee.] m From Figure 7-78, entering with b/H, = 0.798, of 20173 Hy : hence 0.73 (8.4 and from Equation 7-84, = T Rin [fm (4, +a) — a] = 16,900 [0.94 (7.5 + 3.07) — 3.07] . lb.-ft. oe A similar analysis for the maximum breaker with a 10-second period gives = i 16,900 [6.87] = 116,000 (T = 6 sec.) ha 0.90 , ao 3.08 ttn. Ri, = 10,350 lbs./ft. , M,, = 73,800 eet : (T = 10 sec.) The hydrostatic part of the force and moment can be computed from the hydrostatic pressure distribution shown in Figure 7-74 by assuming the hydrostatic pressure to be zero at Hp/2 above SWL, and taking only that portion of the area under the pressure distribution which is below the crest of the wall. Cte eet aii OR, eee Tul ile “aia la” Sam Te eam” a a Ea ie et Nat ae asl ie Sa Pe SS ee, a rE a lr he, Mo) eC 7.34. 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 C-NOF wave parameters, and it is necessary to make simplifying assumptions about the waves to estimate design forces. If more accurate force esti- mates 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 7.21, WAVE RUNUP. Model tests have shown that for waves breaking at a shore approxi- mately 78 percent of the breaking wave height Hz, is above the still- water level. (Wiegel, 1964.) 7.341 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 7-79.) Figure 7-79. Wave Pressures from Broken Waves: Wall Seaward of Stillwater Line Using the approximate relationship C = vgdz, for the velocity of wave propagation C where g is the acceleration of gravity and dp is the 7-158 breaking wave depth, wave pressures on a wall may be approximated in the following manner: The dynamic part of the pressure will be wC2 wd, pe | , (7-85) where w is the unit weight of water. If the dynamic pressure is uni- formly distributed from the stillwater level to a height he above SWL, where h, is given by ie= 0:78 Ee (7-86) then the dynamic component of the wave force is given by wd,h bac Raos Pinte = 735" 4 (7-87) and the overturning moment caused by the dynamic force by h, M,, = Rm dot 5 ; (7-88) where dg is the depth at the structure. The hydrostatic component will vary from zero at a height hg, above SWL to a maximum at the wall base. This maximum will be given by, ee (d, + h,) : (7-89) The hydrostatic force component will therefore be w (4, +h)? Rent a ane (7-90) and the overturning moment will be, d.+h we (di-+ h.)3 M.=R (s pew gol e g (7-91) Ss Ss 3 6 The total force on the wall is the sum of the dynamic and hydrostatic components; therefore, Re Ree eRe (7-92) and My = Me reo: (7-93) Tel59 7.342 Wall Shoreward of Stillwater Line. For walls landward of the still- water line as shown in Figure 7-80 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, poe eee ean v=C ' = = /ed, ( =, (7-94) and the wave height h' above the ground surface by, ; xy hii eor Ges ; (7-95) where x, = distance from the stillwater line to the structure, X> = distance from the stillwater line to the limit of wave uprush; Xo = 2Hp cot B = 2Hp/m Note: (The actual wave runup as found from the method outlined in Section 7.21 could be substituted for the value 2Hzp.) 8 = the angle of beach slope, and m = tan 8. INSERT Assumed locus of wave crest See insert for wave pressure Shoreline Figure 7-80. Wave Pressures from Broken Waves: Wall Landward of Stillwater Line 7-160 An analysis similar to that for structures located seaward of the still- water line gives for the dynamic pressure, 12 wd, x,\? wv b 1 = = == [1S = i 7-96 The dynamic pressure is assumed to act uniformly over the height h, hence the dynamic component of force is given by, wd,h x Buc 1 R,, = p_h' = i=-= 7-97 piemee 5 = (7-97) and the overturning moment by, h’ wd, he x,\ M =R, -= ae 7-98 we ToD 4 x ( ) The hydrostatic force component is given by, ihe whe x, Re ae = ee 7-99 Ss bo) 9) x, ( ) and the moment resulting from the hydrostatic force by, h! wh? x, 3 M, = R, = = 1-— (7-100) Zire) 6 The total forces and moments are the sums of the dynamic and hydrostatic components; therefore, as before, R, =R, +R (7-101) Ss and, ll = ete = M, a : (7-102) 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 stillwater 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. 7-161 Kk) ek) Re oe ok eX EX AMP IE PROBLEM! tte 0 at) soe nee Seen peo eee GIVEN: The elevation at the toe of a vertical wall is 2 feet above the mean lower low water (MLLW) datum. Mean higher high water (MHHW) is 4.3 feet above MLLW and the beach slope is 1:20. Breaker height is Hy = 9.0 ft., wave period is T = 6 sec. FIND: (a) The total force and moment if the SWL is at MHHW. (Wall seaward of stillwater line.) (b) The total force and moment if the SWL is at MLLW. (Wall landward of stillwater line.) SOLUTION: (a) The breaking depth d, can be found from Figure 7-2. Calculate, Hees 39:0 sae eee = 020078, eT? 322 (6)* and the beach slope, 1 m = tanpB = — = 0.05 20 Enter Figure 7-2 with H,/gT* = 0.0078 and using the curve for m = 0.05, read, Therefore, d= 1 10eri — 1).10'(O10)) 9.9 tt. From Equation 7-86, h, = 0.78 H, = 0.78 (9.0) =7.02 ft The dynamic force component from Equation 7-87 is wd,h 4(9 Ree wes = ee) = 2,200 lbs./ft. and the moment from Equation 7-88 is Man UR ea: =92900 Bae eee ies oO m MEENGS| PD S ; 2 : fr.” 7-162 (b) where d, = 2.3 is the depth at the toe of the wall when the SWL is at MHHW. The hydrostatic force and moment are given by Equations 7-90 and 7-91, d +h + f; (A, Fh) pyng 2 ee lb.-ft. The total torce and moment are therefore, Roa Bn de Beg 22200 7 80 | 4,980 lbs./ft. , lb.-ft. M, = M,, 3F M, = 12,900 + 8,640 = 21,540 ek : When the SWL is at MLLW, the structure is landward of the still- water line. The distance from the stillwater line to the struc- ture x, is given by the difference in elevation between the SWL and the structure toe divided by the beach slope, 2.0 So eet!) ft. 0.05 The limit of wave runup is approximately, 2H b 2 (9.0 oS Ss ses a m 0.05 The dynamic component of force from Equation 7-97 is, wd, h rae bic 1 64 (9.9) (7.02 40 R, = ie = eed CEBU) fra = 1,560 lbs./ft. , Ks 2 2 360 X and the moment from Equation 7-98 is, wdy he al _ 64(9.9) (7.02)? ( a so) lb.-ft. = Afi) == . X, 4 360 The hydrostatic force and moment from Equations 7-99 and 7-100 are, wh? xe \2 2 2 64 (7.02 40 R, = — (=) ee pS = 1,250 Ibs./ft. , 2 x, 2 360 and 3 wh? x) 64 (7.02)? 40\3 Ib.-ft. M, = — [1-—] = ——— (1-—] = 2,590 ——. 6 x, 6 360 ft. 7-163 Total force and moment is given by, R, = R,, + RB, t 1,560 + 1,250 = 2,810 lbs./ft. lb.-ft. 4,870 + 2,590 = 7,460 —— CH KS ee ee Tee eC oes tee ro eo TE ee ey Cp RR RS ne M II = +M t m Ss 7.35 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 dynamite 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, R’ = R sin?a (7-103) 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, R is the dynamic force that would occur if the wave hit perpendicular to the structure. The development of Equation 7-103 is given in Figure 7-81. Force reduction by Equation 7-103 should be applied only to the dynamic wave-foree component of breaking or broken waves and should not be applted to the hydrostatic component. The reduction ts not applicable to rubble structures. 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. 7.36 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 7-82 (a), the horizontal component of the dynamic force due to waves breaking either on or seaward of the wall should be reduced to, R” = R’ sin? 6 (7-104) where 68 is defined in Figure 7-82. The vertical component of the dynamic wave force may be neglected in stability computations. For design calculations, forces on stepped structures as in Figure 7-82 (b) 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. 7-82 (c)) and reentrant curved face walls (Fig. 7-82 (d)) may also be considered as vertical. 7-164 sin @ Woy. Vertical Wall ~~ wles3 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 Ry= Component of R Normal to Actual Wall. Rn=R sind W = Length Along Wall Affected by a Unit Length of Wave Crest. W= Vein a R = Dynamic Force Per Unit Length of Wall| R R sind Raye = A = R sin? a /sing R'= R sin? @ Figure 7-81. Effect of Angle of Wave Approach--Plan View 7-165 aes arn (b) Stepped Wall ~s (d) Reentrant Face Wall Figure 7-82, Wall Shapes we * kK kk kK kK & kk * * * EXAMPLE PROBLEM * * * * * * * * * * ¥ ¥ RR GIVEN: A structure in water, dg = 7.5 ft. on a 1:20 nearshore slope is subjected to breaking waves, Hp = 8.4 ft., and period T = 6 secs. 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 (neglect the vertical component of the hydrostatic force). SOLUTION: From the example problem of Section 7.331 for the given wave conditions, Ry, = 16,900 Ibs./ft. M.. = 126,800 oe Ul ‘ ft. R, = 4,380 lbs./ft. and lb.-ft. M. = 17,100 ft. 7-166 Applying the reduction of Equation 7-103 for the angle of wave approach, with Res eRe R' = R,, sin? a = 16,900 (sin 80°)? , R' = 16,900 (0.985)? = 16,400 lbs./ft. Similarly, M' = M,, sin? a = 126,800 (sin 80°)? , ; lb.-ft. M’ = 126,800 (0.985)? = 123,000 ic Applying the reduction for a nonvertical wall, the angle the face of the wall makes with the vertcal is, 6 = arctan (10) = 84°. Applying Equation 7-104, R"” = R’ sin? 6 = 16,400 (sin 84°)? , Ree 16,400 (0.995)? = 16,200 lbs./ft. Similarly for the moment, M” = M' sin? @ = 123,000 (sin 84°)? , lb.-ft. 123,000 (0.995)? = 121,800 Tipe The total force and overturning moment are given by the sums of the reduced dynamic components and the unreduced hydrostatic components. Therefore, M” R, = 16,200 + 4,400 = 20,600 lb./ft., lb.-ft. M, = 121,800 + 17,100 = 138,900 Fars Ct a a a I TT Se a ee ee Oe Te a ay ee a SS Te ee a I 7.37 STABILITY OF RUBBLE STRUCTURES 7.371 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 quarry stones or specially shaped concrete units. Armor units in the cover layer may be placed in an orderly manner TI67 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 indivi- dual 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. 7.372 Design Factors. A primary factor influencing wave conditions at a structure site is the bathymetry in the general vicinity of the struc- ture. Depths will partly determine whether a structure is subjected to breaking, nonbreaking, or broken waves for a particular design wave con- dition. (See Section 7.1, WAVE CHARACTERISTICS. ) Variation in water depth along the structure axis must also be con- sidered 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 may: (a) break completely, projecting a jet of water roughly perpen- dicular to the slope, (b) partially break with a poorly defined jet, or (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 for a rubble structure is usually the significant wave. Damage from waves higher than the significant wave is progressive, but the displacement of several individual armor units will not neces- sarily result in the complete loss of protection. A logic diagram for the evaluation of the marine envrionment is presented in Figure 7-6, and summarizes factors involved in selecting the design water depth and wave conditions to be used in the analysis ofa rubble structure. 7.373 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 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 engineer- ing judgment. 7-168 Following work by Iribarren (1938, 1950), comprehensive investiga- tions were made by Hudson (1953, 1959, 1961 a, and 1961 b) 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 3 w, H oe See 7-105 Kp (S, — 1)? cot 0 C , where W = weight in pounds of an individual armor unit in the primary cover layer. (When the cover layer is two quarry stones in thickness, the stones comprising the primary cover layer can range from about 0.75 W to 1.25 W with about 75 percent of the individual stones weighing more than W. 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, lbs. /ft3, H = design wave height at the structure site in feet. (See Section 7.372.), Sp, = specific gravity of armor unit, relative to the water at the structure, (Sp = Wy/W,). Ww, = unit weight of water, fresh water = 62.4 lbseyceay sea water = 64.0 lbs./ft3, 8 = angle of structure slope measured from horizontal in degrees, and Kn = 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 7-6.) Equation 7-105 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 available. Cover layer slopes steeper than 1 on 1.5 are not recommended by the Corps of Engineers. Figures 7-83 through 7-86 provide a graphical solution of Equation 7-105. i=(69 Table 7-6. Suggested Kp Values for Use in Determining Armor Unit Weight No-Damage Criteria and Minor Overtopping Armor Units n * |] Placement Structure Trunk Structure Head Breaking | Nonbreaking |} Breaking | Nonbreaking wave wave 2) ie) } is) oO Quarrystone Smooth rounded random 2.4 ilo@/ 1.9 Smooth rounded |] >3 random See, Dal 78) Rough angular random + 2.9 it Drs) 2.9 Rough angular random Rough angular random : ; Rough angular special £ : : F Tetrapod 5.9 2 and random 8.3 Be) 6.1 Quadripod 4.0 4.4 8.3 9.0 Tribar random 10.4 7.8 8.5 7.0 Veal Dolos random 25.0 9 15.0 16.5 Sh) 15.0 Modified Cube random — 5.0 Hexapod random 5.0 7.0 Tribar uniform U8) 9.5 Quarrystone (K R R) Graded angular random * nis the number of units comprising the thickness of the armor layer. + The use of single layer of quarrystone armor units subject to breaking waves is not recommended, and only under special conditions for nonbreaking waves. When it is used, the stone should be carefully placed. £ Special placement with long axis of stone placed perpendicular to structure face. § Applicable to slopes ranging from 1 on 1.5 to 1 on 5. || Until more information is available on the variation of K,, value with slope, the use of K,, 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 K,,-slope dependence. 4 Data only available for 1 on 2 slope. £ Slopes steeper than 1 on 2 not recommended at the present time. %=THO COmMarwownwn t+ {4618} aADM (1983) (cH4/S41Sb1 PUD olJ/SqI Ob) = 4M) SanjoA adojs snol4DA 40} jybiay aADM snssaA Ty x SyiUP JOWsY Jo JyBIEM Cg-2 ounbIY (SQ1) 94 XM 40 San|DA @arwown t+ ANGE) Fy a a AOlGGN9=G b Ge JIBOZ DG tp Be ANGLE 1 Ez pl6esl9ag» <¢ 2 ol ] ] Ps ogi Hits 2 OG PRM ae | oe ss faith i } + 2 Ht . +1. saas sSaak Et + + ‘ gH JM” SSS SSS SH Ba geees cere eRe Geille ieee Ob ii Ejoe Gin iii obese cy arise fetta ey det ee passes snd! iiaqeeinuaed aarieetreeeresees ffl a oS iit tt ti SeSs ESS ESS SS ha it Miciibestsa itt east etstsestttd (9 to = 90! pol68l96 6 eOl6é829¢ 2016829 S (S4|) 99 xM JO sanjoA =| 71 1 }4BiaH aaom (4984) (4984) 44618H annm (cf}/SQ1 GSI PUD o1J/S4] OSI = 4M) sanjoA adojs snolinA 404 jybia}y aADM sns4aA Ty x sylup soWsy 10 jyBIEM “PE-Z a4nbi4 (Sq!) 94 XM JO san|DA gOl68L9G b € pOl68L9G b € 2 eOl68 L9G b ¢ 20168 L9G b ¢€ oOmD~aron T+ oO N fo} mo ¢ 0l6el9 90168296 b ¢ XM JO San[DA COmOrwown < 1YyBiay aaom (4284) NE Tt 1y818H eADM (4984) s0l6BL9N GS pOlI68L9 G b sOUS GL 9) 9 * Ss @ cOlE8L9OS + | Tr TT , ' - N mo omoarown tt (14/41 GO] PUD -14/S4) 09] = 7M) SAN|DA adojs sNolDA 40y sybIa}y eADM sns4aQ Fy x syluM soWsY Jo yyblam “GE-Z e4nBi4 (S41) 9M XM JO SanjoA a{DM j|0S. 4 Ds 0} ig ; \\ ee 4 Ve ee a A Bs Be SAY pOl682l9 (sql) 9 (4294) 4sy61a}H aaDM (4224) 44619 aA0M (cH / S41 GL] PUD .1}/S| OL| = 7M) SaN|DA ado Snol4DA 10} }YbIaH aADM snsseA Ty x SyiuA JOWJY Jo jybIam “9g-y aunBI4 (Sq|) 94 XM JO San|oA SOGEA EG tp 43 rj sOl68L9G bp € 2 PONG BELTS) Give ne 2 AMIEL) Gate ts 2 2016829 G bp ¢€ 2 ol | i r Hl m COnOoaronwn + o N " adojs ¢ | uo PO]: er A n° 2 sOl6E82 9 S & 2 SOGEL Qt 4 AS 2 eOl68L9G b ¢€ 4 z0l68L9 SG b &€& 2 Ol (S41) °¥XM Jo sanjoA t-174 $yB1aH aADM (4994 ) Equation 7-105 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: Ww, H3 Wi eae 7-106 a Krp (S, — 1)? cot é ( ) The symbols are the same as defined for Equation 7-105 except that Ws 9 is the weight of the 50-percent size in the gradation. The maximum weight of graded rock is 3.6 Ws 9; the minimum is 0.22 Wcsp. Kpp is a stability coefficient for angular graded riprap, similar to Kp. Values of Kpp are shown in Table 7-6. These values allow for 5 percent damage. (Hudson and Jackson, 1962.) Use of graded riprap cover layers is generally more applicable to revetments than to breakwaters or jetties. A limitation for the use of graded riprap is that the design wave height should be less than about 5 feet. For waves higher than 5 feet, it is usually more economical to use the more uniform-size armor units as indicated in Equation 7-105. 7.374 Selection of Stability Coefficient. The dimensionless stability coefficient Kp in Equation 7-105 accounts for all variables other than structure slope, wave height, unit weight of armor units, 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 layers of armor units, (3) manner of placing armor units, (4) surface roughness and sharpness of edges of armor units (degree of interlocking of armor units), (S) type of wave attacking structure (breaking or nonbreaking), (6) part of structure (trunk or head), (7) angle of incidence of wave attack, (8) model scale (Reynolds number), (9) unit weight of armor units, (10) distance below stillwater level that the armor units extend down the face slope, (11) size and porosity of underlayer material, lies (12) core height relative to stillwater level, (13) crown type (concrete cap or armor units over the crown and extending down the back slope), (14) crown elevation above stillwater level relative to wave height, and (15) crest width. Hudson (1959, 1961 a, and b) and Hudson and Jackson (1959) have conducted numerous laboratory tests with a view to establishing values of Kp 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 Kp are those from (1) through (8). While the angle of wave approach may be important in the stability of armor units especially when the waves are breaking directly on the struc- ture, sufficient information is not available to provide firm guidance on angle effect of the stability coefficient. The data of Hudson and Jackson comprise the basis for selecting Kp, although a number of limitations in the application of laboratory results to prototype conditions must be recognized. These are: (1) Laboratory waves were monochromatic and did not reproduce the variable conditions of nature. Laboratory studies by Ouellet (1972) and Rogan (1969) have shown that action of irregular waves (wave spectrum) on model rubble structures can be modeled by monochromatic waves if the mono- chromatic wave height corresponds to the significant wave height of the spectrum. The validity of this comparison depends somewhat on the shape of the wave spectrum, with the best agreement for a narrow band spectrum (narrow range of frequencies or periods) when the wave heights are dis- tributed according to a Rayleigh distribution. (See Section 3.2.) (2) Preliminary analysis of large-scale tests has indicated that the scale effect is probably unimportant, and can be made negligible by the proper selection of linear scale for the tests (Reynolds Number, Ro > 6 x 10*). (3) The degree of interlocking obtained in the special placement of armor units in the laboratory is unlikely to be duplicated in the pro- totype. Above the water surface in prototype construction, it is possi- ble 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 Kp values. (4) Numerous tests have been performed for nonbreaking waves, but only limited tests are available for plunging waves. Limited test re- sults for breaking waves indicate that the Kp value for breaking waves is proportional the Kp value for nonbreaking waves. Therefore, Kp values for armor units not tested for breaking waves have been obtained by applying a reduction factor to the Kp value for nonbreaking waves. 7-176 (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 subject to overtopping. A part of the head is usually subject to direct wave attack regardless of wave direc- tion. 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 struc- ture. Based on available data and the discussion above, Table 7-6 pre- sents recommended values for Kp. Because of the limitations discussed, values in the table provide little or no safety factor. The experience of the field engineer may be utilized to adjust the Kp value indicated in Table 7-6, but deviation to less conservative values should be fully evaluated. A two-unit armor layer is recommended. If a one-unit armor layer is considered, the Kp values for a single layer should be ob- tained from Table 7-6. 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 design. The values given in Table 7-6 are indicated as no-damage criteria, but actually consider up to 5 percent damage. If some degree of damage to the cover layer is acceptable, slightly larger values of Kp can be used for design. The deliberate selection of a larger value of Kp than recommended in Table 7-6 may be partly justified by the fact that settlement of the structure and readjustment of the interlocking between armor units can result in a more stable structure than the original structure. It is possible that structural damage will occur to indi- vidual concrete armor units during movement and rekeying of the units. However, a structure designed to resist waves of a moderate storm, but which may suffer damage without complete destruction during a severe storm, will have a lower annual cost than one designed to be completely Stable for larger waves. Values of kK, as a function of percent damage to the rubble structure have been determined for several of the armor unit shapes. (See Table 7-7.) These values, together with statistical data concerning the frequency of occurrence of waves of different heights, should be used to determine the annual cost as a function of the accept- able percent damage without endangering the functional characteristics of the structure. Table 7-7 shows the results of damage tests where H/Hp=9 and Kp are functions of the percent damage D for various armor units. H is the significant wave height corresponding to damage D. Hp-9 is the Lalit significant wave height corresponding to O0- to 5-percent damage, gener- ally referred to as no-damage condition. Kp is the stability coeffi- cient for the respective armor unit and damage condition. Table 7-7. Hp <9 and K, as a Function of Cover-Layer Damage and Type of Armor Unit Damage (D) in Percent 1.00 1.08 2.4 3.0 3.6 H oe 1.00 | 1.08 1.19 Kp 4.0 4.9 1.09 ae 10.8 1.00 1.11 1.25 1.36 1.50 1.59 10.4 14.2 19.4 26.2 35.2 41.8 Breakwater Trunk, n = 2, Random Placed Armor Units, Nonbreaking Waves, d Armor Units, Nonbreaking Waves, and Minor Minor Overtopping pping Conditions. Quarrystone (smooth) Quarrystone (rough) Tetrapods & Quadripods The percent damage is based on the volume of armor units displaced from the zone of active armor unit removal for a specific significant wave height. This zone, as defined by Jackson (1968 a), extends from the middle of the breakwater crest down the seaward face to a depth equivalent to one zero-damage wave height Hp-j below the stillwater level. Once damage occurred, testing was continued for the specified wave condition until slope equilibrium was established or armor unit displacement ceased. The following example illustrates the ways in which Table 7-7 may be used. x eK kK kK KK KK KK K K F * EXAMPLE PROBLEM * * * * * * * ¥ * * & ® & FF GIVEN: Rough two-layer quarrystone breakwater designed for nonbreaking ~ wave and minor overtopping from a no-damage design wave of Hp=9 = 8 feet and a Kp = 4.0. FIND: (a) Anticipated percent damage from a wave height H = 9 feet, (b) anticipated percent damage from using a value of K_ = 8.2 in the stability analysis instead of Kp = 4.0, and P (c) appropriate values of wave height, H and stability coefficient, Kp for acceptable 30- to 40-percent damage. 7-178 SOLUTION: (a)) Calculate, ee Seenaas Lath: 8 . . Using Table 7-7, the value of H/Hp-g for rough quarrystone falls between 5- to 10-percent and 10- to 15-percent damage, therefore the anticipated damage for a 9-foot wave would be about 10 percent. (b) Table 7-7, using a value of Kp = 8.2 for rough quarrystone, shows a percent damage range of 15 to 20 percent. (c) From Table 7-7 for D = 30 to 40 percent, H == = 1,47, Hp=0 or BH = 81-47) -11.8-te. and Kp = 126. Therefore if the structure were designed for a wave height, Hp = 8 feet and a no-damage stability coefficient Kp = 4.0 and subsequently attacked by waves H = 11.8 feet, the anticipated damage to the struc- ture's armor layer could be between 30 and 40 percent. On the other hand, if the structure were only designed for a 5.4-foot wave (Hp), but an 8-foot wave could occur, then 30- to 40-percent damage should be anticipated from the 8-foot wave. If the structure were designed for H = 8 feet and Kp = 12.6 instead of the no-damage value of Kp = 4.0, 30- to 40-percent damage could be anticipated as the result of the occurrence of an 8-foot wave. Ree oe. Re Re ee Die, Be eee eee Sey ok! BAS ae, bak lees ELE Se ee i ie ee ae) ae te ee ee, 7.375 Importance of Unit Weight of Armor Units. The basic equation used for design of armor units for rubble structures indicates that the unit weight w, of quarrystone or concrete is important. Designers should carefully evaluate the advantages of increasing unit weight of concrete armor units to effect savings in the structure cost. Brantzaeg (1966) cautioned that variations in unit weight should be limited within a range --say 120 lbs./ft? to 180 lbs./ft3 Unit weight of quarry-stone 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 140 pef and 155 pcef. It can be made higher or lower through the use of special heavy or light weight 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 @2179 Method CRD-3 of the Handbook for Concrete and Cement published by the U.S. Army Engineers Waterways Experiment Station. Figure 7-87 illustrates the effect of varying the value of the unit weight w, on the weight of the armor unit W in Equation 7-105. The weight factor of armor unit f TS thes racvonoit, The effect of varying the unit weight of concrete is illustrated by the following example problem. * ke kK kK kK kK RK kK kK kK kK & * & EXAMPLE PROBLEM * * * * * * * * * * *¥ ¥ F KF XK GIVEN: A 36-ton concrete armor unit is required for the protection of a rubb le-mound structure against a given wave height. This weight was determined using a unit weight of concrete wy, = 145 lbs./f£t3 FIND: Determine the required weight of armor unit for w, = 140 lbs./ft3 and wy = 170 lbs./ft? concrete. SOLUTION: Using the lower curve in Figure 7-87, the weight factor for f (w, = 140 lbs./ft.%) ll a QW co f (w, = 145 lbs./ft.3) Il — — co f (w, = 170 lbs./ft.3) = 0.62 . Thus for, wy» = 140 lbs./ft3, W 36 X 128 ADA = re F ons , 1S say W = 42 tons. and for W, = 170 1bs./ft?, 0.62 W 3600 ae So Oe tons™ 1.18 say W = 19 tons. Ce i a ee J, 2, ee a ee a a Se ee ee ee eh Se ee SE I! oS 7.376 Con@rete Armor Units. Many different concrete shapes have been developed as armor units for rubble structures. The major advantage of concrete armor units is that they usually have a higher stability coef- ficient value, thus permitting the use of steeper structure side slopes or a lighter weight of armor unit. This has particular value when quarrystone of the required size is not available. 7-180 sean painine FECA (944/SQ1)' 7M ‘]D14940W JO JYBIOM 41UN af Weight Factor of Armor Unit Effect of Unit Weight Changes on Required Figure 7-87. it Weight of Armor Un Sil Table 7-8 lists the concrete armor units that have been cited in literature and shows where and when the unit was developed. One of the earlier non-block concrete armor units was the tetrapod. It was devel- oped and patented in 1950 by Neyrpic, Inc., of France. The tetrapod is an unreinforced concrete shape with four truncated conical legs project- ing radially from a center point. (See Figure 7-88.) International patent coverage requires a royalty be paid per cubic yard of concrete used in the unit. A general patent license agreement now exists between Neyrpic, and the U.S. Government regarding the royalty payment for use of tetrapods and quadripods. Figure 7-89 provides volume, weight, thickness of layers, and dimen- sions of the tetrapod unit. The quadripod (Fig. 7-88) was developed and tested by the United States in 1959; details are shown in Figure 7-90. 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 Figure 7-88.) The need for steel reinforced concrete in tribars depends on the techniques of placement and the size of the unit. Generally, when using land-based equipment, steel rein- forcement is not required for units weighing less than 20 tons. Placing any type of armor unit from a floating plant subject to wave action can result in bumping of units resulting in overstress of the concrete. Some form of reinforcement may be required for tribars weighing about 10 tons or more when placed by floating equipment. Figure 7-91 provides tribar details on the volume, weight, thickness of layers and dimensions. Accord- ing to the patent rights of the tribar, the U.S. Government is granted royalty-free use, The Dolos armor unit was developed in 1963 by E. M. Merrifield, Republic of South Africa. (Merrifield and Zwamborn, 1968.) The Dolos is illustrated in Figure 7-88. This concrete unit closely resembles a ship anchor. Generally, reinforcement is not required for units weighing up to 20 tons, but for units over 20 tons reinforcement is required. (Magoon and Shimizu, 1971.) This armor unit is not patented in the United States. Detailed dimensions are shown in Figure 7-92. As noted in Table 7-6, various other shapes have been tested by the Corps of Engineers. Other shapes are the modifted cube and the hexapod. Details of the modified cube and hexapod are shown in Figures 7-93 and 7-94 respectively. Projects using tetrapods, tribars, quadripods, and dolosse in the United States, are listed in Table 7-9. 7.377 Design of Structure Cross-Section. A rubble structure is nor- mally comprised of a bedding layer and a core of quarry-run stone cov- ered by one or more layers of larger stone and an exterior layer(s) of large quarrystone or concrete armor units. Typical rubble-mound cross sections for nonbreaking and breaking waves are shown in Figures 7-95 7-182 Table 7-8. Types of Concrete Armor Units Name of Unit Akmon Bipod Cob *Cube *Cube (modified) *Dolos Dom Gassho Block Grabbelar Hexaleg Block *Hexapod Hollow Square Hollow Tetrahedron N-Shaped Block *Pelican Stool *Quadripod *Rectangular Block Stabilopod Stabit *Sta-Bar *Sta-Pod Stalk Cube Svee Block *Tetrahedron (solid) *Tetrahedron (perforated) Tetrapod Toskane Tribar Trigon Tri-Long Tripod Development of Unit Country Netherlands Netherlands England United States South Africa Mexico Japan South Africa Japan United States Japan Japan Japan United States United States Romania England United States United States Netherlands Norway United States France South Africa United States United States United States Netherlands The units have been tested, some extensively, at the Waterways Experiment Station (WES). + 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 two centuries. The cube was tested at WES as early as 1943. £ Solid tetrahedrons are known to have been used in hydraulic works for many years. This unit was tested at WES in 1959. 7-183 Bottom 2 QUADRIPOD Elevation Plan Bottom DOLOS (DOLOSSE, plural) Elevation Figure 7-88. 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Where there will be no overtopping, crest width is not critical. Little study has been made of crest width of a rubble struc- ture subject to overtopping. As a general guide for overtopping condi- tions, 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, eal (7-107) r where, By = erestwaldthe, att n = number of stones (n = 3 is recommended minimum) k, = layer coefficient (Table 7-10) W = weight of armor unit in primary cover layer, lbs. Wp» = unit weight of armor unit, 1bs./ft3 The crest must be wide enough for construction and maintenance equipment operated from the structure. Table 7-10. ves Coefficient and Porosity for Various Armor Units Quarrystone ( ore conetenicethh random Quarrystone (rough) random Quarrystone (rough) random Cube (modified) random Tetrapod random Quadripod random Hexapod random Tribar random Dolos random Tribar uniform Quarrystone random b. Concrete Cap for Rubble-Mound Structures. Poured-in-place concrete has been added to the cover layer of rubble-mound jetties and breakwaters. Such use ranges from filling the interstices of stones on the cover layer, on the crest, and as far down the slopes as wave action permits, to casting large monolithic blocks of several hundred tons. This concrete may serve any of three purposes: (1) to strengthen the crest; (2) to increase the crest height; and (3) to provide roadway access along the crest for construction or maintenance purposes. 1-196 Massive concrete caps have been used with cover layers of precast concrete armor units. The cap provides a rigid backup to the top row of armor units at the crest. Instead of a concrete cap, solid or permeable parapets have been used. (See Figure 6-68.) The breakwater at Pria, Terceria, Azores was repaired using large quarrystone to support the primary tetrapod armor units instead of the concrete cap on the crest. 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. To evaluate the need for a massive concrete cap for increasing struc- tural stability against overtopping, consideration should be given to the cost of including a cap versus the cost of increasing dimensions to pre- vent overtopping and for construction and maintenance purposes. For a structure of concrete armor units subject to overtopping, a massive con- crete cap is not necessary for structural stability when the difference in elevation between the crest and the limit of wave runup on the projec- ted slope above the structure is less than 15 percent of the total wave runup, unless a substantial saving would result from the use of concrete. For this purpose, an all-rubble structure is preferable. Maintenance costs for an adequately designed rubble structure are likely to be lower than for any alternative composite type structure. Experience indicates that concrete placed in the voids on the struc- ture 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 mainte- nance costs. For a roadway, a concrete cap can usually be justified if frequent maintenance of armored slopes is anticipated. c. 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: W 1/3 Le eon ka = (7-108) WwW Lp where r is the total layer thickness in feet, n is the number of layers of quarrystone or concrete armor units comprising the cover layer, W is the weight of individual armor units in pounds, and w, is the unit weight in pounds per cubic foot. P w 2/3 NWA an (1- = (=) (7-109) where N, is the required number of individual armor units for a given surface area, A is surface area in square feet, k, is the layer co- efficient, and P is the average porosity of the cover layer in percent. PeeMy Values of ky, and P, determined experimentally, are presented in Table 7-10. The average dimension for a range of quarrystone weights based on a unit weight of 165 pounds per cubic foot is shown in Table 7-11. Table 7-11. ee and Size Dimensions of jaa NOTE: Average Dimension (ft.) is the solution for Equation 7-108, where n = 1, w, = 165 Ibs./ft? and ka = 1.15 for quarrystone. (See Table 7-10.) d. Bottom Elevation of Primary Cover Layer. The armor units in the cover layer (the weights are obtained by Equation 7-105) 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 7-95. When the structure is in a depth < 1.5H, armor units should be extended to the bottom as shown in Figure 7-96. Toe conditions at the intersections of slope with bottom may be critically unstable. Model studies should be made when economically feasible. e. 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 50 to 150 feet from the struc- ture end. This distance depends on such factors as structure length and crest elevation at the seaward end. 7-198 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 overtop- ping, theoretically, the weight of armor units on the back slope cover layer should depend on the lesser wave action on the lee side and the porosity of the structure. When overtopping is anticipated, primary armor units should be extended down the back slope to minimum SWL. When both side slopes receive similar wave action (as with groins or jetties), both sides should be of similar design. Lording and Scott (1971) tested an overtopped rubble-mound structure that was subjected to breaking waves in water levels up to the crest ele- vation. Maximum damage to the lee side armor units occurred with the stillwater 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. f. Secondary Cover Layer. The weight of armor units in the secondary cover layer, between -H and -1.5H, should be greater than about one-half the weight of armor units in the primary cover layer. Below -1.5H, the weight requirements can be reduced to about W/15 for the same slope condition. (See Figure 7-95.) When the structure is located in shallow water (Fig. 7-96), that is depth d < 1.3H, armor units in the primary cover layer should be extended down the entire slope. The above ratios between the weights of armor units in the pri- mary and secondary cover layers are applicable only when quarrystone units are used in the entire cover layer for the same slope. When pre- cast concrete units are used in the primary cover layer, the weight of quarrystone in the other layers should be based on the equivalent weight, W of quarrystone armor units. The secondary cover layer (Figs. 7-95 and 7-96) from -H to the bottom should be as thick or thicker than the primary cover layer. Thus, based on the preceding ratios between the armor weight, W in the pri- mary cover layer and the quarrystone weight in the secondary cover layer, if n= 2 for the primary cover layer (two-quarrystones thick), then n= 2.5 for the secondary cover layer from -H to -1.5H, and n= 5 for that part of the secondary cover layer below -1.5H. g. Underlayers. The first underlayer (directly beneath the pri- mary armor units) should have a minimum thickness of two quarrystones (n = 2), and these should weigh about one-tenth the weight of the over- lying armor units (W/10). (See Figure 7-95.) This applies where (a) cover layer and first underlayer are both quarrystone, (b) first under- layer is quarrystone and the cover layer is concrete armor units with a Stability coefficient K, < 12. When the cover layer is of armor units with Kp < 20, the first underlayer quarrystone should weigh about W/S f-139 or one-fifth the weight of the overlying armor units. The second under- layer for this part of the structure should have a minimum thickness of two quarrystones; these should weigh about one-twentieth the weight of overlying quarrystones (1/20 x W/10 = W/200). The first underlayer for that part below -1.5H should have a minimum of two thicknesses of quarrystone; these should weigh about one-twentieth the overlying second- ary armor unit (1/20 x W/15 = W/300). The second underlayer for that part below -1.5H, and the core material, can be as light as W/6,000, or quarry-run, For a graded riprap cover layer, the weight of the first underlayer, if required, should be about W. 9/20 to prevent the material from washing through the voids of the cover layer. h. Bedding Layer or Filter Blanket. Foundation conditions for marine structures require thorough evaluation. Wave action against a rubble structure may scour the natural bottom and the foundation of the structure, even at depths usually considered unaffected by such action. A rubble structure may be protected from excessive settlement resulting from leaching, undermining, or scour, by the use of either a bedding layer or filter blanket. Depending on the weight of quarrystone used, a plastic filter cloth may be used instead of a bedding layer or with a thinner bedding layer. It is advisable to use a bedding layer or filter blanket 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 foundation is a cohesive material, a filter blanket may not be required. However, a layer of quarry spalls or other crushed rock or gravel may be placed as a bedding layer or apron to reduce scour of the bottom or settlement of the structure. Foundations of coarse gravel may not require a filter blanket. When the rubble structure is founded on sand, a filter blanket should be provided to prevent waves and currents from removing sand through the voids of the rubble and thus causing settlement. 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 settle- ment. This, in turn, can provide a stable foundation. Gradation requirements of a bedding layer depend principally on the size characteristic of the foundation material. However, quarry spalls, ranging in size from 1 to 50 pounds, will generally suffice. Layer thick- ness depends generally on the depth of water in which the material is to F200 be placed and the size of quarrystone used, but should not be less than 12 inches to ensure that bottom irregularities are completely covered. It is common practice to extend the bedding layer at least 5 feet beyond the toe of the cover stone. Details of typical rubble structures are shown in Chapter 6, STRUCTURAL FEATURES. 7.38 STABILITY OF RUBBLE FOUNDATIONS AND TOE PROTECTION Forces of waves on rubble structures have been studied by several investigators. (See Section 7.37.) 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 struc- tures. 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 superstruc- ture might consist of concrete or timber cribs founded on the core material. Finally, the apron and side slope of the core would be pro- tected from erosion by a cover layer of armor units. The cover layer should have a minimum thickness of two armor units. An alternative method of constructing the superstructure would be to drive a pair of parallel-tied walls of steel sheet piling into the rubble core. 7.381 Design Wave Heights. For a composite breakwater with the super- structure 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, for design of such structures, it is suggested that the selected design wave height H should 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 H, expected, based on the significant deepwater wave height Ho corrected for refraction and shoaling. (Early breaking might prevent the l-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 Hj9 and Hj are acceptable, The design wave for rubble toe protection is also between Hj9 and Hj. 7.382 Stability Number. The stability number 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, ds. The relation between the depth ratio, dj,/dg> and Ng is indicated in Figure 7-99. The cube value of the stability number has been used in the figure to facilitate its substitution in Equation 7-110. 7-201 3) Ce) Sys) fe)) oO ft oO Minimum Design Stability Number (N ol ro) Rubble as Toe Protection Rubble Toe Protection k Wr H> N2(s,-1)5 and B=0.4d, Rubble as Foundation EER (o> was BPS SOS Rubble Foundation 0.1! Ore "OS OL Oor re OPO. ON ias Ons (After Brebner and Donnelly, 1962) Depth Ratio gy ds Figure 7-99. Stability Number for Rubble Foundation and Toe Protection 7-202 7.383 Armor Stone. The equation used to determine the armor stone weight is a form of Equation 7-105, 3 WUE a Sean 7-110 ca v50 where, W = mean weight of individual armor unit, lbs. Wp, = unit weight of rock (saturated surface dry), lbs./ft2 H = design wave height (the incident wave height causing no damage to the structure). Sp» = specific gravity of rubble or armor stone relative to the water on which the structure is situated (S, = w,/w,). Wy = unit weight of water, fresh water = 62.4 Ubsay £65 sea water = 64.0 lbs./ft? N. = design stability number for rubble foundations and toe protection. (See Figure 7-99.) 7.4 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, and Cambell, 1966.) The maximum velocity of tidal currents in midchannel through a navigation opening as given by Sverdrup, Johnson. and Fleming (1942), can be approximated by the following formula: SS ) where V is the maximum velocity of tidal current at the center of the opening, T is the period of tide, A is the surface area of harbor basin, S is the cross-section area of openings, and h is the range of tide in the basin. The current in midchannel is about one-third swifter than at each side of the channel. If the stable stone weight T eos W= 6 dy W,, (7-112) where do is the diameter of a stone sphere of equivalent weight, and = Ya oN ray . y, y, V=y (2 ) === || (gH — sii @) d, : (7-113) Ww 7-203 then combining the two equations for y = 1.20 (embedded stone) yields, Vow.w, 3 We er (7-114) T5235 XaOS (w, — Wy)? (cos 8 — sin 0)? ” where W = minimum weight of the stable stone, pounds V = velocity of water acting directly on stone, feet per second Wp = unit weight of stone, pounds per cubic foot W, = unit weight of water, pounds per cubic foot g = acceleration of gravity, 32.2 feet per second? = angle of structure slope with the horizontal in the direction of flow da = equivalent minimum stone diameter, feet IW d, = 1.24 ar = ig w, (7-115) y = Isbash constant 1.20 and 0.86 for embedded and nonembedded stone, respectively. A graphical solution of Equations 7-112 and 7-113 for the equivalent stone diameter and stone weight is shown in Figure 7-100. For salt water, the curve would be adjusted accordingly. The curves are considered appli- cable to conditions where turbulence is not excessive, and the stones are either embedded or nonembedded. 7.5 IMPACT FORCES Impact forces are an important design consideration for shore struc- tures, because of the increased use of thin flood walls and gated struc- tures as part of hurricane protection barriers. High winds of a hurri- cane 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 conditions require the inclusion of impact forces in the design, other measures should be taken either to limit the depth of water against the face of the structure by providing a rubble-mound absorber against the face of the wall, or a partly submerged structure seaward of the structure that will ground floating masses, and 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 force should be evaluated from impulse-momentum considerations. 7-204 "Sqi(M) $y61aM au0}S (g33/°S4I 779 = (8961 ‘X09 4e4}7) Oo! o8 og90S OF “™) LeqZowetq 9u0IS JUSTeATNbY pue 3YStTOM auc IS SNSsIAA AUTIOTOA 492} (5p) sajawnig auoys jDo14ayds juajpainb3 of Oz 01 80 9050 #0 £0 270 10 800 900 ¥%00 £00 O01 80 O90S Ov OF o2 o!1 80 90950 #0 €°0 : 20 10800 900 vo'O0 £00 2 'Sq| 82 =M 40 14 2E'O= "p * 4 4ad ‘sq) p79 =m =A 0 —— : : ¢€ (98°0=4) eu0}S pappaquiz UON Jas Jad WJ=A cay 4ad sq] GQ|= 4m auaym (02'1=4) eucys peppaquig aU0{S peppequig ‘adojs jane7 6 ajdwioxy z2”p = (Gus 908)))2)( 1 T a Lye Lu) “OOI-Z ean3Ty 200 10:0 4m g5p Yy =m Tw) 2(82) =m ( puodas sad 429}) Aylo0jaA f—205 7.6 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, and Peyton, 1968.) There are many ways ice can affect marine structures. In Alaska, great care mist 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 7-12. The amount of expansion of fresh water in cooling from 39°F, to 32°F. is 0.0132 percent. In changing from water at 32°F. to ice at 32°F, 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 -8°F., it is subjected to pressures greater than about 30,000 pounds per square inch. Excessive pressure, with temperatures above -8°F., causes the ice to melt. With the temper- ature below -8°F., the change to a denser form at high pressure results in shrinkage which relieves pressure. Thus, the probable maximum pres- sure that can be produced by water freezing in an enclosed space is 30,000 pounds per square inch. Designs for dams include allowances for ice pressures of as much as 45,000 to 50,000 pounds per linear foot. The crushing strength of ice is about 400 pounds per square inch. Thrust per linear foot for various thicknesses of ice is about 28,800 pounds for 6 inches, 57,600 pounds for 12 inches, etc. Structures subject to blows from floating ice should be capable of resisting 10 to 12 tons per square foot (139 to 167 1bs./sq.in.) on the area exposed to the greatest thickness of floating ice. Ice also expands when warmed from temperatures below freezing to a temperature of 32°F. without melting. Assuming a lake surface free of snow with an average coefficient of expansion of ice between -20°F. and 32°F, equaling 0.0000284, the total expansion of a sheet of ice a mile long for a rise in temperature of 50°F. would be 3.75 feet. 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. 1-206 Table 7-12. Effect of Ice on Marine Structures A. Direct Ice Forces on Structures. ile 3; 4. ne WN FE 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. . 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. Diaphram bending forces during water level change of ice sheets frozen to structural elements. e. Superstructure icing by ice spray. . Second,Order Effects. a. Motion during thaw of that ice frozen to structural elements. b. Expansion of entrapped water within structural elements. c. Jamming of rubble between structural framing members. . Indirect Ice Forces on Structures. IL Ze Floating ice sheets impinging on moored ships. Unusual crane loads caused by the difficulty in maneuvering work boats in ice covered waters. Impact forces by ships during docking which are larger than might normally be expected. Abrasion and corollary corrosion of structural elements. . Low Risk but Catastrophic Considerations. iL. Pax Collision by a ship caught in fast-moving, ice-covered waters. Collision by extraordinarily large ice masses of very low probability of occurrence. . Operational Considerations. . Problems of servicing offshore facilities in ice covered waters. . Limits of ice cover severity during which ships can be moored to docks. . Ship handling characteristics in turning basins and while docking and undocking. . The extreme variability of ice conditions from year to year. . The complacency to be expected by operators in anticipating 100-year occurrences in severity of ice conditions. . The necessity of developing an ice operations manual to outline the operational limits for preventing the overstressing of structures. Peyton, 1968 7-207 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 pro- tection 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, there- fore, the quantity of material reaching an impounding structure is re- duced. 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. 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 attached members such as wales, and then being forced upward by a rise in water stage or wave action. 7.7 EARTH FORCES Various texts on soil mechanics such as Andersen (1948), Hough (1957), and Terzaghi and Peck (1967), adequately discuss the subject. The forces exerted on a wall by soil backfill depend on the physical characteristics 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 indetermin- ate because of the factors noted, approximations of their influence must be made. 7.71 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 active earth force. Retaining walls are generally designed to allow minor rota- tion 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: aa wh? csc @ sin (0 — @¢) Z a 2 sin (0+ 6) + [ sin (@ + 8) sin (¢ — i) $ sin (9 — i) 7-208 (7-116) where, P, = active force per unit length (lbs./linear ft. of wall) = unit weight of soil (lbs./ft3) h = height of wall or height of fill at wall if lower than wall (feet) 8 = angle between horizontal and back slope of wall (degrees) i = angle of backfill surface from horizontal (degrees) > = internal angle of friction of the material (degrees) 6 = wall friction angle (degrees) These symbols are further defined in Figure 7-101. Equation 7-116 may be reduced to that given by Rankine for the special Rankine conditions where 6 is considered equal to i, and 6 equal to 90° (vertical wall face). When, additionally, the backfill surface is level (i = 0°), the reduced equation is a 2 - aie tan? [ass— 3) C71} Figure 7-102 shows that Pa from Equation 7-117 is applied horizontally. Unit weights and internal friction angles for various soils are given in Table 7-13. The resultant force for Equation 7-116 is inclined from a line per- pendicular to the back of the wall by the angle of wall friction 6. (See Figure 7-101.) Values for 6 can be obtained from Table 7-14, but should not excéed the internal friction angle of the backfill material $4. and for conservatism, should not exceed (3/4)¢. (U.S. Army, Corps of Engineers, 1961.) 7.72 PASSIVE FORCES If the wall resists forces that tend to compress the soil or fill behind it, then the earth must have enough internal resistance to trans- mit these forces. Failure to do this, will result in rupture; a part of the earth will move sideways and upward away from the wall. This resis- tance of the earth against outside forces is called passtve earth forces. The general equation for the passive force is : _ wh? csc 0 5 eee Pee Se a) a a Fry ce V sin (9 +5) — Vsin (0 + 5) — |sin(@—5) sin@ +i). sin (@ + i) EHS) sin (6 — i) f=209 Figure 7-101. Definition Sketch for Coulomb Earth Force Equation Pa Ee Figure 7-102. Active Earth Force for Simple Rankine Case 7-210 Table 7-13. Unit Weights and Internal Friction Angles of Soils Unit Weight (Ib/cu ft) Min. Max. (loose) | (dense) Classification | | | Submerged Min. Max. (loose) | (dense) GRANDULAR MATERIALS 1. Uniform Materials Standard Ottawa SAND Es Clean, uniform SAND (fine or Medium) Uniform, inorganic SILT 2. Well-graded Materials Silty SAND Clean, fine to coarse SAND Micaceous SAND Silty SAND and GRAVEL MIXED SOILS 1, Sandy or silty CLAY 2. Skip-graded silty CLAY with stones or rock fragments 3. Well-graded GRAVEL, SAND, SILT and CLAY mixture CLAY SOILS 1, CLAY (30 to 50 percent clay sizes) 2. Colloidal CLAY (—0.002 mm. >50 percent) ORGANIC SOILS 1, Organic SILT 2. Organic CLAY (30 to 50 percent clay sizes) pike : Unit Weight (Ib/cu ft) Friction Density or Angle } Consistency Equivalent Fluid Coarse SAND or SAND and GRAVEL compact firm loose Medium SAND compact firm loose Fine SAND compact firm loose Fine, silty SAND or sandy SILT compact firm loose Classification Fine, uniform SILT compact firm loose CLAY-SILT medium soft Silty CLAY medium soft CLAY medium soft CLAY medium soft (after Hough, 1957) Te2illl It should be noted that Py 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 Figure 7-101.) For the Rankine conditions given in Section 7.71, Equation 7-118 reduces to h2 P= oe tan? [is +5): (7-119) Equation 7-119 is satisfactory for use with a sheet-pile structure, assuming a substantially horizontal backfill. Table 7-14. Coefficients and Angles of Friction Surface, Pe: ae + ie Sens Dhak Gamera Coefficient of Friction, u | Angle of Wall Friction, 6 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 of friction, £ would equal the tangent of the new angle, 6. 7.73 COHESIVE SOILS Sections 7.71 and 7.72 dealt with forces in cohesionless soil. A cohesive backfiil may be necessary, and reduces the active fcrce. How- ever unless the soil can move continuously to maintain the cohesive resistance, it may relax. Thus, the wall should be designed for the active force in cohesionless soil. 7.74 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 computed by Equations 7-116 and 7-118 by substituting an approximate average wall batter or slope to determine the angle, 86. 7.75 SUBMERGED MATERIAL Forces due to submerged fills may be calculated by substituting the unit weight of the material reduced by buoyancy for 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 7-13. f212 7.76 UPLIFT FORCES For design computations, uplift forces should be considered as full hydrostatic force for walls whose bases are below design water level or for walls with saturated backfill. W213 REFERENCES AND SELECTED BIBLIOGRAPHY ACHENBACH, E., "Distribution of Local Pressure and Skin Friction Around a Circular Cylinder in Cross-Flow Up to Re = 5 x 10," Journal of Fluid Mechanics, Vol. 34, Part 4, 1968. AGERSCHOU, H.A., and EDENS, J.J., "Fifth and First Order Wave-Force Coefficients for Cylindrical Piles," Coastal Engineering, Santa Barbara Spectalty Conference, ASCE, 1965. ANDERSEN, P., Substructure Analysts and Destgn, Ronald Press, New York, 1948. BAGNOLD, R.A., "Interim Report on Wave Pressure Research," Journal of the Institution of Civil Engineers, Vol. 12, London, 1939. BATTJES, J.A., "Runup Distributions of Waves Breaking on Sloping Walls," Report, Department of Civil Engineering, Delft, The Netherlands, 1969. BATTJES, J.A., '"'Runup Distributions of Waves Breaking on Slopes," Journal of the Waterways, Harbors and Coastal Engineering Division, ASCE. Vol. 97, No. WW1, Proc. Paper 7923, 1971, pp. 91-114. BIDDE, D.D., "Wave Forces on a Circular Pile Due to Eddy Shedding," HEL 9-16, Hydraulic Engineering Laboratory Research Report, University of California, Berkeley, Calif., 1970. BIDDE, D.D., "Laboratory Study of Lift Forces on Circular Piles," Journal of the Waterways, Harbors and Coastal Engineering Division, ASCE, WW 4, Paper No. 8495, Nov. 1971. BLUMBERG, R., and RIGG, A.M., "Hydrodynamic Drag at Super-Critical Reynolds Numbers ,'' Paper Presented at Petroleum Session, American Soctety of Mechanteal Engineers, Los Angeles, Calif., 1961. BRANDTZAEG, A., ''The Effect of Unit Weights of Rock and Fluid on the Stability of Rubble-Mound Breakwaters,"' Proceedings of the 10th Conference on Coastal Engineering, ASCE, Vol. II, 1966. BREBNER, A., and DONNELLY, P., "Laboratory Study of Rubble Foundations for Vertical Breakwaters,'' Engineer Report No. 23, Queen's University at Kingston, Ontario, 1962. BRETSCHNEIDER, C.L., "Modification of Wave Height Due to Bottom Friction, Percolation and Refraction," TM-45, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Sept. 1954a. BRETSCHNEIDER, C.L., "Field Investigations of Wave Energy Loss in Shallow Water Ocean Waves," TM-46, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Sept. 1954b. 7-214 BRETSCHNEIDER, C.L., "Evaluation of Drag and Inertial Coefficients from Maximum Range of Total Wave Force," Technical Report No. 55-5, Depart- ment of Oceanography, Texas A&M University, College Station, Texas, 1957. BRETSCHNEIDER, C.L., "On the Probability Distribution of Wave Force and an Introduction to the Correlation Drag Coefficient and the Correla- tion Inertial Coefficient," Coastal Engineering, Santa Barbara Speetalty Conference, ASCE, 1965. BURSNALL, W.J., and LOFTIN, L.K., “Experimental Investigation of the Pressure Distribution About a Yawed Cylinder in the Critical Reynolds Number Range,'' Technical Note 2463, National Advisory Committee for Aeronautics, 1951, CAMBELL, F.B., "Hydraulic Design of Riprap,'' Misc. Paper No. 2-777, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1966. CARR, J.H., "Breaking Wave Forces on Plane Barriers,'' Report No. E 11.3, Hydrodynamics Laboratory, California Institute of Technology, Pasadena, Callies, 195A CHANG, K.S., "Transverse Forces on Cylinders Due to Vortex Shedding in Waves," M.A. Thesis, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1964. CHESNUTT, C.B., "Scour of Simulated Gulf Coast Sand Beaches in Front of Seawalls and Dune Barriers," Report No. 139, Coastal and Ocean Engi- neering Division, Texas A&M University, College Station, Texas, 1971. COX, R.G., "Velocity Forces on Submerged Rocks," Misc. Paper No. 2-265, U.S. Army, -Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1958. CROSS, R.H., and SOLLITT, C.K., 'Wave Transmission by Overtopping," Technical Note 15, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1971. DAI, Y.B., and JACKSON, R.A., "Designs for Rubble-Mount Breakwaters, Dana Point Harbor, California," Misc. Paper No. 2-725, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., June 1966. DAI, Y.B., and KAMEL, A.M., "Scale Effect Tests for Rubble-Mount Break- waters,"' TR No. H-69-2, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., Dec. 1969. DANEL, P., and GRESLOU, L., ''The Tetrapod," Proceedings of the Eighth Conference on Coastal Engineering, ASCE, Council on Wave Research, The Engineering Foundation, 1963. 1-215 DAVIDSON, D.D., "Stability and Transmission Tests of Tribar Breakwater Section Proposed for Monterey Harbor, California," TR No, H-69-11, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicks- burg, Miss., Sept. 1969. DAVIDSON, D.D., ''Proposed Jetty-Head Repair Sections, Humboldt Bay, California," TR H-71-8, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1971. DEAN, R.G., "Stream Function Representation of Nonlinear Ocean Waves," Journal of Geophystcal Research, Vol. 70, No. 18, 1965a. DEAN, R.G., "Stream Function Wave Theory; Validity and Application," Coastal Engineering, Santa Barbara Specialty Conference, ASCE, Ghel2eeL96S5eby. DEAN, R.G., "Evaluation and Development of Water Wave Theories for Engineering Application,'' U.S. Army, Corps of Engineers, Coastal Engineering Research Center. (To be published in 1973). DEAN, R.G., and AAGAARD, P.M., "Wave Forces: Data Analysis and Engineer- ing Calculation Method," Journal of Petroleum Technology, Vol. 22, No. 3, 1970. DEAN, R.G., and HARLEMAN, D.R.F., "Interaction of Structures and Waves," Ch. 8, Estuary & Coastline Hydrodynamics, A.T. Ippen, ed., McGraw-Hill, New York, 1966. DE CASTRO, D.E., '"Diques de escollera (Design of Rock-Fill Dikes) ," Revtsta de Obras Publtceas, Vol. 80, 1933. DENNY, D.F., "Further Experiments on Wave Pressures," Journal of the Institution of Civil Engineers, Vol. 35, London, 1951 DICK, T.M., "On Solid and Permeable Submerged Breakwaters," C.E. Research Report No. 59, Department of Civil Engineering, Queens University, Kingston, Ontario, 1968. DOMZIG, H., "Wellendruck und druckerzeugender Seegang," Mitteilungen der Hannoverschen Versuchsanstalt ftir Grundbau und Wasserbau, Hannover, West Germany, 1955. ERGIN, A., and PORA, S., "Irregular Wave Action on Rubble-Mound Break- waters," Journal of the Waterways, Harbors and Coastal Engineering Division ASCE, Vol. 97, No. WW2, Proc. Paper 8114, 1971, pp. 279-293. EVANS, D.J., "Analysis of Wave Force Data," Journal of Petroleum Tech- nology; Vol. 22, No. 35/1970. FREEMAN, J.C., and Lé6éMEHAUTE, B., "Wave Breakers on a Beach and Surges on a Dry Bed," Journal of the Hydraultes Diviston, ASCE, Vol. 90, 1964, pp. 187-216. 7-216 FUCHS, R.A., see Johnson, Fuchs and Morison (1951). GALVIN, C.J., JR., "Horizontal Distance Traveled by a Breaking Wave," National Meeting on Transportation Engineering, ASCE, San Diego, Callie Ss Eeb.s L963). GALVIN, C.J., JR., ''Breaker Travel and Choice of Design Wave Height," Journal of the Waterways and Harbors Diviston, ASCE, WW2, Vol. 95, Paper 6569, 1969. GODA, Y., "A Synthesis of Breaker Indices," Transacttons of the Japanese Soctety of Civil Engineers, Vol. 2, Pt. 2, 1970. GODA, Y., and ABE, T., "Apparent Coefficient of Partial Reflection of Finite Amplitude Waves," Port and Harbor Research Institute, Japan, 1968. GRESLOU, L., and MAHE, Y., "Etudé du coefficient de reflexion d'une houle sur un obstacle constitué par un plan incliné," Proceeding of the Fifth Conference on Coastal Engtneering, ASCE, Grenoble, France, 1954, HALL, J.V., and WATTS, G., "Laboratory Investigation of the Vertical Rise of Solitary Waves on Impermeable Slopes," TM-33, U.S. Army Corps of Engineers, Beach Erosion Board, Washington, D.C., Mar. 1953. HALL, M.A., 'Laboratory Study of Breaking Wave Forces on Piles," TM-106, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Aug. 1958. HALL, W.C., and HALL, J.V., ''A Model Study of the Effect of Submerged Breakwaters on Wave Action,'' TM-1, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., May 1940. HEDAR, PER ANDERS, "Rules for the Design of Rock-Fill Breakwaters and Revetments," 21st Internattonal Navigatton Congress, Stockholm, Section II, Subject 1, 1965. HENSEN, W., 'Modellversuche tiber den Wellenauflauf an Seedeichen im Wattengebiet,'' Mitteilungen der Hannoverschen Versuchsanstalt ftir Grundbau und Wasserbau, Franzius-Institut, Hannover, West Germany, 1954, HO, D.V., and MEYER, R.E., "Climb of a Bore on a Beach-(1) Uniform Beach Slope," Journal of Fluid Mechanics, Vol. 14, 1962, pp. 305-318. HOUGH, B.K., Baste Sotls Engineering, Ronald Press, New York, 1957. HUDSON, R.Y., "Wave Forces on Breakwaters," Transactions of the American Soetety of Civil Engineers, ASCE, Vol. 118, 1953, p. 653. HUDSON, R.Y., "Design of Quarry-Stone Cover Layers for Rubble-Mound Breakwaters," RR No, 2-2, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1958. elim HUDSON, R.Y., ''Laboratory Investigations of Rubble-Mound Breakwaters," Proceedings of the Amertcan Soctety of Civil Engineers, ASCE, Water- ways and Harbors Division, Vol. 85, No. WW3, Paper No. 2171, 1959. HUDSON, R.Y., 'Wave Forces on Rubble-Mound Breakwaters and Jetties," Misc. Paper 2-453, U.S. Army, Corps of Engineers, Waterways Experiment Sta- tion, Vicksburg, Miss., 196la. HUDSON, R.Y., 'Laboratory Investigation of Rubble-Mound Breakwaters," Transactions of the Amertean Soectety of Civtl Engtneers, ASCE, Vol. 126, Pt. IV, 1961b. HUDSON, R.Y., and JACKSON, R.A., "Stability of Rubble-Mound Breakwaters," T™ No. 2-365, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1953. HUDSON, R.Y., and JACKSON, R.A., "Design of Tetrapod Cover Layer for a Rubble-Mound Breakwater, Crescent City Harbor, Cresent City, Calif.,"' T™ No. 2-413, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1955. HUDSON, R.Y., and JACKSON, R.A., "Design of Tribar and Tetrapod Cover Layers for Rubble-Mound Breakwaters,'' Misc. Paper 2-296, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., O59. HUDSON, R.Y., and JACKSON, R.A., ''Design of Riprap Cover Layers for Railroad Relocation Fills, Ice Harbor and John Day Lock and Dam Projects; Hydraulic Model Investigation," Misc. Paper 2-465, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss. , 11962. HUDSON, R.Y., and JACKSON, R.A., "Stability Tests of Proposed Rubble- Mound Breakwaters, Nassau Harbor, Bahamas," Misc. Paper No. 2-799, U.S. Army, Corps of Engineers, Waterways Experiment Station, Mar. 1966. IPPEN, A.T., ed., Estuary and Coastline Hydrodynamics, McGraw-Hill, New York, 1966. IRIBARREN CAVANILLES, R., "A Formula for the Calculation of Rock-Fill Dikes,"' Revista de Obras Publtcas, 1938. (Translation in The Bulletin of the Beach Eroston Board, Vol. 3, No. 1, Jan. 1949.) IRIBARREN CAVANILLES, R., and NOGALES Y OLANO, C., ''Generalization of the Formula for Calculation of Rock Fill Dikes and Verification of its Coefficients," Revista de Obras Publicas, 1950, (Translation in The Bulletin of the Beach Eroston Board, Vol. 5, No. 1, Jan. 1951.) IRIBARREN CAVANILLES, R., and NOGALES Y OLANO, C., "Report on Breakwaters,"' 18th Internattonal Navigatton Congress, Ocean Navigation Section, Question 1, Rome, 1953. 7-218 IVERSEN, H.W., "Laboratory Study of Breakers," Circular No. 521, U.S. National Bureau of Standards, Washington, D.C., 1952a. IVERSEN, H.W., "Waves and Breakers in Shoaling Water," Proceedings of the Third Conference on Coastal Engineering, ASCE, Council on Wave Research, 1952b. JACKSON, R.A., 'Design of Quadripod Cover Layers for Rubble-Mound Break- waters,'' Misc. Paper 2-372, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1960. JACKSON, R.A., "Designs for Rubble-Mound Breakwater Repair, Morro Bay Harbor, California," TR No. 2-567, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1961. JACKSON, R.A., 'Designs for Rubble-Mound Breakwater Construction, Tsoying Harbor, Taiwan,'' TR No. 2-640, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1964a. JACKSON, R.A., "Designs for Rubble-Mound Breakwaters Repair, Kahului Harbor, Maui, Hawaii,'' TR 2-644, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1964b. JACKSON, R.A., "Stability of Rubble-Mound Breakwaters, Nassau Harbor, Nassau, New Providence Bahamas,'"' TR No. 2-697, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1965. JACKSON, R.A., "Designs for Rubble-Mound Breakwater, Noyo Harbor, California," Misc. Paper No. 2-841, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., Aug. 1966. JACKSON, R.A., "Stability of Proposed Breakwater, Burns Waterway Harbor, Indiana,'' TR No. 2-766, U.S. Army, Corps of Engineers, Waterways Expriment Station, Vicksburg, Miss., Mar. 1967. JACKSON, R.A., "Limiting Heights of Breaking and Nonbreaking Waves on Rubble-Mound Breakwaters,'" TR No. H-68-3, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., June 1968a. JACKSON, R.A., "Design of Cover Layers for Rubble-Mound Breakwaters Subjected to Nonbreaking Waves," RR No. 2-11, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1968b. JACKSON, R.A., HUDSON, R.Y., and HOUSLEY, J.G., "Designs for Rubble-Mound Breakwater Repairs, Nawiliwili Harbor, Nawiliwili, Hawaii," Misc. Paper No. 2-377, U.S. Army, Corps of Engineers, 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. w29 JEN, Y., "Laboratory Study of Inertia Forces on a Pile," Journal of the Waterways and Harbors Diviston, ASCE, No. WW1, 1968. JOHNSON, J.W., FUCHS, R.A., and MORISON, J.R., '"'The Damping Action of Submerged Breakwaters,"' Transacttons of the American Geophysical Union, Vol. 32, No. 5, 1951, pp. 704-718. KADIB, A.L., "Beach Profile as Affected by Vertical Walls," Hydraulic Engineering Laboratory, University of California, Berkeley, Calif., 1962. (also in TM-134, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., June 1963.) KAMEL, A.M., "Water Wave Pressures on Seawalls and Breakwaters," R.R. No. 2-10, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1968. KELLER, H.B., LEVINE, D.A., and WHITHAM, G.B., ''Motion of a Bore Over a Sloping Beach," Journal of Fluid Mechantes, Vol. 7, 1960, pp. 302-315. KEULEGAN, G.H., and CARPENTER, L.H., ''Forces on Cylinders and Plates in an Oscillating Fluid," NBS Report No. 4821, National Bureau of Standards, Washington, D.C., 1956. LAIRD, A.D.K., "Water Forces on Flexible, Oscillating Cylinders," Journal of the Waterways and Harbors Diviston, ASCE, Aug. 1962. LAIRD, A.D.K., JOHNSON, C.H., and WALKER, R.W., "Water Eddy Forces on Oscillating Cylinders," Journal of the Hydraulics Diviston, ASCE,- Nov. 1960. LAMB, SIR HORACE, Hydrodynamics, Cambridge University Press, 6th ed., 1932. LAMBE, T.W., and WHITMAN, R.V., Sotl Mechanics, Series in Soil Engineering, Wiley, New York, 1969. LEENDERTSE, J.J. "Forces Induced by Breaking Water Waves on a Vertical Wall," Technical Report 092, U.S. Naval Civil Engineering Laboratory, 1961. LEMEHAUTE, B., "Periodical Gravity Wave on a Discontinuity," Journal of the Hydraulies Diviston, ASCE, Vol. 86, No. HY 9, Part 1, 1960, pp. 11-41. LEMEHAUTE, B., "On Non-Saturated Breakers and the Wave Runup," Proceedings of the Eighth Conference on Coastal Engineering, ASCE, Mexico City, Council on Wave Research, 1963, pp. 77-92. 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. %=220 LORDING, P.T., and SCOTT, J.R., "Armor Stability of Overtopped Breakwater," Journal of the Waterways, Harbors and Coastal Engineering Diviston, ASCE, Vol. 97, No. WW2, Proceedings Paper 8138, 1971, pp. 341-354. MacCAMY, R.C., and FUCHS, R.A., "Wave Forces on Piles: A Diffraction Theory,'' TM-69, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Dec. 1954. MAGOON, O.T., and SHIMIZU, N., "Use of Dolos Armor Units in Rubble-Mound Structures, e.g., for Conditions in the Arctic," Proceedings from the First Internattonal Conference on Port and Ocean Engineering Under Aretie Conditions, Vol. II, Technical University of Norway, Trondheim, Norway, 1971, pp. 1089-1108. (also CERC Reprint 1-73). MERRIFIELD, E.M., and ZWAMBORN, J.A., ''The Economic Value of a New Break- Water Armor Unit," Proceedings of the 10th Conference on Coastal Engineering, ASCE, Tokyo, 1968, p. 885. MICHE, R., "Mouvements ondulatoires de la mer in profondeur constante ou decroissante," Annals des Ponts et Chaussees, Paris, Vol. 114, 1944. MILLER, R.L., "Experimental Determination of Runup of Undular and Fully Developed Bores,'' Journal of the Geophysical Research, Vol. 73, 1968, pp. 4497-4510. MINIKIN, R.R., "Breaking Waves: A Comment on the Genoa Breakwater," Dock and Harbour Authority, London, 1955, pp. 164-165. MINIKIN, R.R., Winds, Waves and Maritime Structures: Studies in Harbour Making and in the Protection of Coasts, 2nd rev. ed., Griffin, London, 1963, 294 pp. MORRISON, TR, et al., ''The Force Exerted by Surface Waves on Piles," Petroleum Transactions, 189, TP 2846, 1950. NAGAI, S., "Experimental Studies of Specially Shaped Concrete Blocks for Absorbing Wave Energy," Proceedings of the Seventh Conference on Coastal Engineering, ASCE, Council on Wave Research, The Engineering Foundation, 196la. NAGAI, S., "Shock Pressures Exerted by Breaking Waves on Breakwaters," Transacttons, ASCE, Vol. 126, Part IV, No. 3261, 1961b. NAGAI, S., "Stable Concrete Blocks on Rubble-Mound Breakwaters,"' Proceed- tings of the American Soctety of Civil Engineers, ASCE, Vol. 88, WW3, 1962, pp. 85-113. NAKAMURA, M., SHIRAISHI, H., and SASAKI, Y., "Wave Damping Effect of Submerged Dike," Proceedings of the 10th Conference on Coastal Engineering, ASCE, Tokyo, Vol. 1, Ch. 17, 1966, pp. 254-267. T-22Il QUELLET, YVON, "Effect of Irregular Wave Trains on Rubble-Mound Break- waters," Journal of the Waterways, Harbors and Coastal Engineering Divtston, ASCE, Vol. 98, No. WW1l, Proc. Paper 8693, 1972, pp. 1-14. PAAPE, A., and WALTHER, A.W., "Akmon Armour Unit for Cover Layers of Rubble-Mound Breakwaters,"' Proceedings of the Eighth Conference on Coastal Engineering, ASCE, Council on Wave Research, 1962. PALMER, R.Q., "Breakwaters in the Hawaiian Islands," Proceedings of the American Soctety of Civil Engtneers, ASCE, Waterways and Harbors Division, Vol. 86, No. WW2, Paper No. 2507, 1960. PECK, R.B., HANSON, W.E., and THORNBURN, T.H., Foundatton Engineering, Wiley, New York, 1967. PEYTON, H.R., 'Ice and Marine Structure," Ocean Industry Magazine, Parts I = 3, Mars, Sept., andiDec.; 19638. PRIEST, M.S., "Reduction of Wave Height by Submerged Offshore Structures," Bulletin No. 34, Alabama Polytechnic Institute, Engineering Experiment 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. ROGAN, A.J., "Destruction Criteria for Rubble-Mound Breakwaters," Proceedings of the 11th Coastal Engineering Conference, ASCE, London, 1969, pp. 761-778. ROLLINGS, A.P., "Stability of Crescent City Harbor Breakwater, Crescent City, California," Misc. Paper No. 2-171, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1956. ROSS, C.W., "Laboratory Study of Shock Pressures of Breaking Waves," TM-59, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, De Ceay Feb 1955. ROSS, C.W., "Large-Scale Tests of Wave Forces on Piling," TM-111, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., May 1959. ROUSE, H., ed., Engineering Hydraulies, Wiley, New York, 1950. ROUVILLE, A., de, BESSON, P., and PETRY, P., "ftat Actuel des Etudes Internationales sur les Efforts dus aux Lames," Annals des Ponts et Chaussees, Paris, Vol. 108, No. 2, 1938. RUNDGREN, L., "Water Wave Forces," Bulletin No. 54, Royal Institute of Technology, Division of Hydraulics, Stockholm, Sweden, 1958. f=22e RUSSELL, R.C.H., and INGLIS, C., "The Influence of a Vertical Wall on a Beach in Front of It," Proceedings of the Minnesota International Hydraulies Convention, International Association of Hydraulic Research, Minneapolis, 1953. SAINFLOU, M., "Treatise on Vertical Breakwaters,'"' Annals des Ponts et Chaussees, Paris, 1928. (Translated by W.J. Yardoff, U.S. Army Corps of Engineers.) SAVAGE, R.P., ''Laboratory Study of Wave Energy Losses by Bottom Friction and Percolation,'' TM-31, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., 1953. SAVAGE, R.P., "Wave Runup on Roughened and Permeable Slopes," Journal of the Waterways and Harbors Divitston, ASCE, WW3, Paper No. 1640, 1958. SAVILLE, T., JR., "Laboratory Data on Wave Runup and Overtopping on Shore Structures,'' TM-64, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Oct. 1955. SAVILLE, T., JR., "Wave Runup on Shore Structures," Journal of the Water- ways and Harbors Division, WW2, Vol. 82, 1956. SAVILLE, T., JR., "Wave Runup on Composite Slopes," Proceedings of the Stxth Conference on Coastal Engineering, ASCE, Council on Wave Research, 1958a. SAVILLE, T., JR., "Large-Scale Model Tests of Wave Runup and Overtopping, Lake Okeechobee Levee Sections,"'' Unpublished Manuscript, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., 1958b. SAVILLE, T., JR., "Discussion: Laboratory Investigation of Rubble-Mound Breakwaters by R.Y. Hudson," Journal of the Waterways and Harbors Diviston, WW3, Vol. 86, 1960, p. 151. SAVILLE, T., JR., "An Approximation of the Wave Runup Frequency Distribu- tion," Proceedings of the Eighth Conference on Coastal Engineering, ASCE, Mexico City, Council on Wave Research, 1962, pp. 48-59. SAVILLE, T., JR., "Hydraulic Model Study of Transmission of Wave Energy by Low-Crested Breakwater," Unpublished Memo for Record, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C., Aug. 1963. SAVILLE, T., JR., and CALDWELL, J.M., "Experimental Study of Wave Over- topping on Shore Structures," Proceedings of the Minnesota Inter- nattonal Hydraulies Convention, Minneapolis, International Association of Hydraulic Research, 1953. SAVILLE, T., JR., GARCIA, W.J., JR., and LEE, C.E., "Development of Break- water Design," Proceedings of the 21st International Navigation Congress, Sec. 11, Subject 1, "Breakwaters with Vertical and Sloping Faces," Stockholm, 1965. f-223 SHEN, M.C., and MEYER, R.E., "Climb of a Bore on a Beach, (3) Runup," Journal of Fluid Mechanics, Vol. 16, 1963, pp. 113-125. SINGH, K.Y., "Stabit, A New Armour Block," Proceedings of the 11th Conference on Coastal Engineering, ASCE, Vol. II, 1968. SKJELBRIA, L., et al., "Loading on Cylindrical Pilings Due to the Action of Ocean Waves," Contract NBy-3196, 4 Volumes, U.S. Naval Civil Engineering Laboratory, 1960. STRIEGL, A.R., "Ice on the Great Lakes and its Engineering Problems," Presented at a Joint Conference of the American Meteorological Soctety and the Amertcan Geophystecal Union, 1952. SVEE, R.A., TRAETTEBERG, A., and TORUM, A., ''The Stability Properties of the Svee-Block," Proceedings of the 21st International Navigation Congress, Sec. 11, Subject 1, Stockholm, 1965. SVERDRUP, H.U., JOHNSON, M.W., and FLEMING, R.H., The Oceans; Their Physics, Chemistry, and General Biology, Prentice-Hall, Englewood Cliffs, N.J., 1942. TANAKA, S., et al., "Experimental Report of Hollow Tetrahedron Blocks," Chisui Kogyo Co., Ltd., Osaka, Japan, 1966. TERZAGHI, K., and PECK, R.B., Sotl Mechanics in Engineering Practice, Wiley, New York, 1967. THIRRIOT, C., LONGREE, W.D., and BARTHET, H., "Sur la Perte de Charge due a un Obstacle en Mouvement Periodique," Proceedings of the 14th Congress of the International Association of Hydraulic Research, 1971. THOMSEN, A.L., WOHLT, P.E., and HARRISON, A.S., ''Riprap Stability on Earth Embankments Tested in Large- and Small-Scale Wave Tanks," TM-37, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Washington, D.C., June 1972. U.S. ARMY, CORPS OF ENGINEERS, "Stability of Rubble-Mound Breakwaters," Technical Memorandum No. 2-365, U.S. Army, Corps of Engineers, Waterways Experiment Station, Vicksburg, Miss., 1953. U.S. ARMY, CORPS OF ENGINEERS, "Retaining Walls," Engineer Manual, Engineering and Design, EM 1110-2-2502, May 1961. (rev. 1965.) 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. WATKINS, L.L., "Corrosion and Protection of Steel Piling in Seawater," TM-27, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Washington, D.C., May 1969. 7-224 WEELE, B., VAN, "Beach Scour Due to Wave Action on Seawalls," Report No. 45, Fritz Engineering Laboratory, Lehigh University, Bethlehem, Pa., 1965. WEGGEL, J.R., "The Impact Pressures of Breaking Water Waves,'' Thesis presented to the University of Illinois, Urbana, Illinois, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, (Unpublished, available through University Microfilms, Ann Arbor, Michigan). WEGGEL, J.R., 'Maximum Breaker Height," Journal of the Waterways, Harbors and Coastal Engineering Diviston, ASCE, Vol. 98, No. WW4, Paper 9384, V972.. WEGGEL, J.R., "Maximum Breaker Height for Design,'' Proceedings of the 13th Conference on Coastal Engineering, Vancouver, B.C., 1973. WEGGEL, J.R., and MAXWELL, W.H.C., ''Numerical Model for Wave Pressure Distributions ,'' Journal of the Waterways, Harbors and Coastal Engineering Diviston, ASCE, Vol. 96, No. WW3, Paper No. 7467, 1970a, pp. 623-642. WEGGEL, J.R., and MAXWELL, W.H.C., "Experimental Study of Breaking Wave Pressures," Preprint Volume of the Offshore Technology Conference, Paper No. OTC 1244, 1970b. WHEELER, J.D., "Method for Calculating Forces Produced by Irregular Waves," Journal of Petroleum Technology, Vol. 22, No. 3, 1970. WIEGEL, R.L., Oceanographtcal Engineering, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1964. WIEGEL, R.L., BEEBE, K.E., and MOON, J., "Ocean Wave Forces on Circular Cylindrical Piles," Journal of the Hydraultes Division, ASCE, Vol. 83, NOR HY 2%), L957. WILSON, B.W., "Analysis of Wave Forces on a 30-inch Diameter Pile Under Confused Sea Conditions,'' U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Technical Memo No. 15, 1965. ZUMBERG, J.H., and WILSON, J.T., “Effects of Ice on Shore Development ," Proceedings of the Fourth Conference on Coastal Engineering, Chicago, Illinois, pp. 201-206, 1953. T>225 7 SOC 1 : a ) Hoe bea ah “esi i itis , adic és Ji" Seehn rf at es rere, ‘ weeny "Ante pleut? cbfisaats of bon Weg to x : ‘ gover mi | att ae wooo’ ( iQ 7 tol Lodsan’h u ee eee Porson’ “5 NE a oF : bolt Sit Sree Seer aiaal | ie rE 7) mi’ | erty, wt : Pabveill ft Lh dines OT ry. ee ov Wit. Be ge A is vlog va Ome) ME "yams brit ; a4 Why (ats iid take) A eit ge) il ae } “iy toad ‘ : Nines Ve tayconie Te ftdee Ss ond) he Med ene 1) WgbDs! " bi, iy pd) (yr, ant P 4d, Gaiyall o ‘ ‘ A 1 T2ei Aue mut B uw uA Wave fianup belt eee ae Heer oen Rape f i . mney CHAPTER 8 ENGINEERING ANALYSIS - CASE STUDY REDONDO - MALAGA COVE, CALIFORNIA — 23 January 1973 CHAPTER 8 ENGINEERING ANALYSIS - CASE STUDY 8.1 INTRODUCTION This chapter presents a series of calculations for the preliminary design of a hypothetical offshore island in the vicinity of Delaware Bay. It serves to illustrate the interrelationships between 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 not complete; 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 investi- gations at the island site would be required to establish the physical environment. These studies would include a determination of engineer- ing and geological characteristics of local sediments, as well as measure- ment of waves and currents. The results of these studies would then have to be evaluated prior to beginning a final design. While actual data for the Delaware Bay site were used when avail- able, specific numbers used in the calculations should not be construed as directly applicable to other design problems in the Delaware Bay area. Calculations are presented as examples of the techniques pre- sented in this manual. [Pageno: | 2 of 133) Ah Se 1a'e Caleuiaied by:| J. RW. Checked by: ea {Mar 73 Design Problem General ae aes x General Problem Descriptign References A 300 acre artificial offshore Island 1s pro- posed in the Atlantic Ocean just outside the mouth of Delaware Boy. If is reguired to develop char - acteristics of the physical environment at the proposed island site_and to develop a preliminary design for the island. The calculations are pre - sented as follaws: Table _of Contents page no. A. Description of Physical Environment .... 3 | f. Sife. LOCATION .G CONGITFIONS# = ti") 30 2 3 2, Bathymetry at Site.-........... 7 | SiWater* levels’ & CUnfenis.. "ss IO QMHORFICONC SUNGG as ne, ere 10 | be ASTTONGMI CON NGES. esse open ee € Fidel CUnreniSrene a ss. ay Stee 2! 4 WOVE. CONG LLONS Bay anata 404 ch mye EE 26 ! qa. Waves Generated in Delaware Bay... 26 ! b. Waves Generated in Ocean....... 37 | ; 1) Wave Sfatistics & Refraction. .... 37 _ 2) Herricane Waves... . ae ae B. Freliminary Tsiang Oesign .... ). sae | l 1. Revetment on Seaward Side of Island . 65 | @. Sélection of Armor Unit Type... ... G2 * Z. adey Wall Caisson on Bay Side of Island. 93 ' 9. Waves in Harbor- diffraction. .... 93 | b. Wave Forces during Construction. ... 95 CAVEQIT FOr COS. Fearon, 1. oh aha wee C. Longshore Transport at Ocean City,Md.. . . /07 LooHind cost (WAVE Dolan... 3k. he Oe 2 WASUB) WAVE DOIQI se. i Wade ins yee D. Beach Fill Problem- Ocean City, Ma. ...,.129 E. References. ea a a IRE ME eas yf * References pertain to Spee e sections of Shore Protection Manual or to numbered referencés on page 8-132 of design calculations. YS a Checked by: Rey ! Mar 73 Site Description The following pages present information on the general physical conditions at the proposed island site. Site plans showing the island /ocation, surrounding shorelines and bothyme?try are given. 40° 40° NAUTICAL MILES Roo at 3 v? fee char 1219). aie U cas FRE FANON cation wy; ” ‘Gp FI (4) #30 a ey BE REM23 29 nia ei ite \ fuse chart 1220) i Bh a inwe_ 5 22 yay 84.5) Waesne au ree “eine “ys 4 rae Teal 58m . \ 38° F iinet 1150 ) i S rN A Fee NO Sg Chart 1109. (use chart 1221)" ‘ 7 arbh . 4320 ‘ Ta i | 76° 74° USC & GS Chart No.1000 Note: The following pages present general descriptive information about the site such as site plans and bathymetry in the region of the island. Figure 8-1. Location Plan - Offshore Island PpueTS] eL0YsFFO - UeTd 93TS oSd 8121 ON $4049 SO BOSN ae SE WAVY Sescct * Je,DMyDe1g ° Sate i ¥ o” ie ss ONNOBN/ = -INWT Z iets ie ,OSoB8E J 9104205) ¥ 7: 4S > 940 "7-8 omnsTy 01 0S2 04 Da we cs & (¢ 210U 295) WI" AYYNOLLN) * TINNY Id eld S3ITIW TWOLLNWN pue[s~T ysnoryz uoTzeg pue META aatqoedszeg *¢-g OANSTY puoj/s, yono1y; UOIf{IaS Siem GurgsiXZ A oe Wid apis uo0aI0 juauyanay PUO/S!~ uossrog jioM fone JSoMY{ION DUTYOOT Mal/ | 8-6 a Lp ©) —— GF 5 i) Za Wy, LD f2 f Ve S55 SIO) SOTTFOLIg WoOG FO uoT}eI0T ‘p-g oINdTY (8) eouedazay oS J a ” Sa! (alii QNNOBLNO” NYT DNssvaL wis," (0 2104201) WIS ABPNOIL y = o INOZ © NOLLV WIS o © fe . ONNOQNI INV] =Ds4VHL & eo Ff w o 09 o8€ 0S 08e 3 hd “we = ° “> & 2) % » z A o6€ Lt iS mer tor S30IN TWOILNWN 8-7 rom rl 1 Ol 6 8 wh 9 S v € (a | ($984) eouDISIG 000‘08 000‘O2 000'09 000'0S 000‘0+ o00‘oe 000'02 000'O! Semis ee eee | | EEEEEEEEEH | | | | RE t a Feil A Le Dae t MW JAMO ugdo,ueH ado oO aN YW BHI PUD|Ss| YBnosys sellyosd WOHOg “S-g ‘eanB! 4 ; (Saj!w joo14NDU) 4aMOL ADW ado wody aoUD\sIG puDd|s} pasodoig yooimM {0 dol — De ee ee eee a oirelac te Jamo] Apw edop OOol- | os- OOol- Os- OS (4993) MW MOjeq uol}DAe|R @4IS puD|Ss|] YyBnosyy sejlyord WO}Jog—panulju0g “G-g e4NbI4 (Sejiw jo91ynDU) 4eMO, ADW edDdD WOs, aduD{sSIG a él I Ol 6 8 Z 9 S v € é | (e) (4904) eouD}SIGg 000'02 000'Ov ooo‘oe 00002 i Ul eas | nf a tt (4923) MW ®A0GD U0!4DAa|3 8-9 10 of 133 Page no: Calculated by: Checl:¢ by: Date: Design Problem Physical Environment Water Levels - Storm Surge and Astronomical Tides The follawing 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 References 5 616. Estimate of Storm Surge - Nomograph Method Note: The nomograph method can only provide a rough estimate far the present | problem since the Island site 1s in about 40 ft. of water in an estuary. entrancé. The nomograph method will give peak surge on the open coast (a high estimate for the is/ond site). Chapter 3 Sect 3.865 b(1)(b) Design Hurricanes for illustrative purposes use hurricanes “A” 6"8" given by Bretschneider in References 5616. Hurricane A Refs. 56,16 Radius to maximum winds = R= 33.5 nm. Central pressure Mp 2Z.2 in. of mercury Forward spead = y-=/5 to 25 knots (us@ Ve= 25 knots) Maximum gradient wind, Unay = 0.868{73 (Pr- Po) R(O575F)} where for latitude 40°N, f= 0.338 7 Umax= 0.868 73 (2.2)? 33.5(05750.336)} Umax,= 88.3 knots (102 mph) Maximum sustained wind for Ve= 25 knots Up = 0.865 Ungy + 0.5 Ve Up = 0.865 (88.3) t05(25) = 88.9 knots (1/02 mph) PATHS OF STORMS OF TROPICAL QRIGIN DATE LEGEND AuGusT 1635 NOT SHOWN AUGUST 17668 NOT SHOWN SEPTEMBER 1815 NOT SHOWN SEPTEMBER tert SEPTEMBER 1969 NOT SHOWN OCTOBER 187@ NOT SHOWN aucusT 1079 ———e SEPTEMBER ‘sco ——— avoustT 1093 NOT SHOWN OCTOBER 10040 ———- SEPTEMBER 1903 NOT SHOWN SEPT.-ocT 1929 august 1933 SEPTEMBER 1930 SEPTEMBER i944 auoust i964 SEPTEMBER 1954 1954 198s 1965 1956 1958 SEPTEMBER 1958 SEPTEMBER 1960 FIGURES IN CIRCLES REPRESENT THE POSITION OF THE STORM ON THE DAY OF THE MONTH INDICATED. JAMAICA ae SCALE IN MILES Figure 8-6. Hurricane Storm Tracks in the Delaware Bay Area 8-I| ne ee ne no: 12 of 133 | Design Problem. Physical Environment Nomograph Method (cont.) Hurricane 8 Refs Seam R= 33.5 nm. Ve = 25 knots Umax = 5 mph greater than hurricane A (5 mph = 4.34 knots) Calculate Ap for Umay= 88.3+ 4.34 knots UP 92.6 knots —_— (107 mph) Rearranging £9 3-35, 2 ap= {5b [glnse + R(05754)} £.3°35 2 Apr < st 33.5 (0575X0.338)]| Ap = 2.4 in. of mercury Peak Surge on Open Coast -Hurricane A bp = 2.2 in. of aL AS (1 millibar = Q0295 in. of mercury ) =e ee 27017: oe (4°) pinivars 0.0295 n/mp ae 7» From Figure 3-51 for R= 33.5n.m.= 38.5 mi. 5, = 16.5 ft From Figure 3-53 for Cape May, NJ. k= 09 From Figure 3-54, assuming hurricane moves | Fig. 3-54 perpendicular to coast (= 90°), for Ve=25 Knots (28.8 mph) lav m 1.3 Fig. 3-51 Fig. 3-53 Peak Surge Sp= StF Ay = 16.5 (0.9)(1.3)= 19.3 Ft. Pace no: eee — AB orf Tt F ; ; Calculated by:) uf. R- W. Design Problem Physical Environment [Checked by: |R YT Date: 2 Mar 73 Nomograph Method (cont) Peak Surge _on Open Coast - Hurricane B 3 = 18.0 Ff f= OS fy, >= 1.30 = Sr Fy = 18.0 (0.9) (1.30) = 21.1 ft. £q. 3-78 Note: The computed values of Sp are believed high for the Island site since the 1sland is in 40 ft. of water and at an estuary entrance; not at thé coast as assumed by the nomogra ph method. Estimate _of Storm Surge ~ Reference § Ref. 5 bretschneider (Ref 5) gives an empirical relationship between maximum sustained wind speed and surge height (both pressure and wind induced) at the Delaware Bay entrance. (Applicable only to Delaware Bay) Equation 11 from Reference 5 for peak surge a mere Ref. 5 (So) = 200085 + 10% Ee (Ug in mph) Hurricane A Ug= 0.865 Umay +05 Ve Eq, 3-34 = 0.865 (88.3) +0.5 (25) = 88.9 knots (102 mph) (So), = 0.00085 (102) = 8.04ft say (So), = 90ff. £ 1 ft. Hurricane _ B (So)max™ 0-00085 (107) = 9.7 ft. say (So)...~ 10.0 ft t 1 ft max 14. of 133 . ; : J. RW. Design Problem Physical Environment RH. Date: Estimate _of Storm Surge - Bathystrophic Method | Sect. 3.865 The figures on the following pages present Piya) the results of a detailed analysis of the storm surge at the entrance to Delaware ret using the Bathystrophic Mode]. (Section 3.865 (1G, Summary _of Storm Surge Estimates Nomograph Method Hurricane A Sp = 19.3 ft. Hurricane B Sp = 21.1 ft Empirical Equation of Reference § Hurricane A (So) ray= 2OF10 ft. Hurricane B (So)may™ 10.0 #1.0 Ft. Bathystrophic Method ; Hurricone A Sp = tt c to Hurricane Bb Seo = 12.0 fi “Astronomical component subtracted, Hurricane A Sp=13.07~-2.07 11.1 ft. Hurricane B Sp= 14.09-2.0 * {2./ ft. Height above MLW (feet) St Otrrete tater stal a a + | 4 ie se ihe ap i he = FA ims] Foams Ta T GN AGRY PGT GREG WE] 7; ST (POU ST Desa Ba +6 FH +41 +2 —_{nitial Setup Figure 8-7. onshore Soinponent ch Astronomical Tide — {assumed uniform) Time (hours) Bathystrophic Storm Surge Hydrograph (4984) MTW eAogD 44 Time (hours) Comparison of Peak Surges Bathystrophic Storm Surge Hydrograph Figure 8-8. 8-16 IT of 133 | TRA Checked by: |. A.J | 2 Mar: 73 | Design Problem Physical Environment Observed Water Level Data - Breakwater Harbor ha ay able 3- Lewes, Delaware aket iD i Length of Record: 1936 to present (1973) 2. Mean Tidal Range: 4.1 ft. 3. Spring Range: 4.9 ft 4. Highest Observed Water Levels: a) Average yearly highest: 3.0 ff. above M.H.W. b) Highest observed: 5.4 ft. above M.H.W. (@ March 1962) 5. Lowest Observed Water Levels: a) Average yearly lowest: 25 ft below MLW. b) Lowest observed: 3.0 ft. below M.LW. (28 March 1955) Graphical Summary a +10 195 Highest observed water /eve/ (@ March 1962) +71 + Average yearly highest +5 Poe oo +44 +- Mean high water *| Mean lrange —*24 Mean sea leve/ Mean low water ~ Of datum of O (USC & GS chart datum) Ret. 5 Sit Average yeorly lowest -3.0 Lowest observed water level — (28 March 1955) Elevation (ft above M.L.W.) 8-17 Calculated by:| J/. R. W. Analysis of Predicted Astronomical Tides Using the predicted high tides for Breakwater Harbor, Lewes, Delaware for the. years 1962, 1967, 1966 and 1972, the probabilities that the water level will be above a given level at any time were generated (by computer) based on the following scheme. Design Problem Physical Environment Predicted high tides Fitted sine curves ty Zoe (ese eas | | | | hig 2.4 ft pn ee Eel ae | ~ 124 hr__| alzhhr__| datum S emi-diurnal tide The probability the water level will be above z at any time Is given by, P(Z=z)= 2 ti 1 where Ty 1s the length of the record analysed . and Zt; js the amount of time the water level is above z. The results of the analysis are given on the following pages. weet ee eee wee ew oe eee . Based on this analysis, a water level above #+5,0 ft. (ML.W. datum) is exceeded 10% of the time. (See Figure 8-39) Astronomical Tide-Water Level Statistics Based on Sine Curve Fit to Predicted High Tides —Lewes, Delaware (1967) Elevation above MLW (z) feet 2.60000 2.70000 2.80000 2.90000 3200000 3-10000 3.20000 3230000 3240000 3.50000 3.60000 3.70000 3.80000 3.90000 4.00000 4.10000 4.20000 4.30000 4.40000 4250000 4.60000 4.70000 4.80000 4.290000 5.00000 5.10000 5.20000 5.30000 5240000 5.50000 5.60000 5.70000 5.80000 (1967 data) (1) Number of Hours per year 3539.20154 3356-93503 3162-84706 2966216526 2750-04381 2530-95381 2307-68068 2096-8781) 1897.91885 1700-23383 1537.76783 1368.22078 1217.94634 1071-54007 934.1357] 784.60798 670.06012 5602-42541 462-52767 3702-94314 295240660 223257539 169.21023 129.63847 92.5188] 67-31568 41.81988 31244437 18.56210 8.99619 3217861 0.92306 0200064 (2) Fraction of Time P(Z2>=z) 0.40420 ° 38338 «36122 © 33875 231407 228905 226355 2° 23948 221675 19418 °17562 e 15626 - 13910 -12238 - 10668 0896) 207652 - 06400 205282 © 04236 ©03374 202553 ©01932 001481 ©01057 00769 © 00478 e00359 °00212 e00103 © 00036 200011 200000 (1) Number of hours per year water level above given elevation (2) Fraction of time water level above given elevation 8-19 (M1W aAogD 4924) Z | Calculated by: Checked by: j Date: Design Problem Physical Environment renee S Mar: 73 Design Water Level Summary For purposes of the design problem the following water levels will be used. The criteria used here should not be assumed generally applicable since design water /evel criteria will vary with the scope and purpose of a particular project. 5 ; tT 1. Astronomical tide: use + 5.0 ft (ML.W) 2. Storm surge: USEF J LOM ar 3. Wave setup: (a function of wave conditions ) 16.0% ft. (above M.L.W) Sect. 3,85 t Exceeded 1.0% of time. Tidal Currents at Delaware Bay Entrance iRefs. 9 ent. / Carre neers) * For spring tides Example charts from Reference 9 and a summary of tidal current velocities are given on the following pages. PHILADELP! T TIDAL CURRENT CHART DELAWARE BAY AND RIVER Red arrows show the direction and red figures the mpring velocity in knots of the cur- rent at time indicated at bottom of chart. Thia chart is dexigned for use with the Tables published each year by the U.S. Coast and Geodetic Survey. Complete instructions are inside the front cover of thia set of charts, NOTE Full predictions of the current In Chesapeake and Delaware Canal for every day in the year are given in the Atlantic CoastCurrent Tables, MAXIMUM FLOOD AT DELAWARE BAY ENTRANCE. Figure 8-10. Tidal Current Chart-Maximum Flood at Delaware Bay Entrance 8-22 =|: TIDAL CURRENT CHART DELAWARE BAY AND RIVER Red arrows show the direction and red figures the mpring velocity in knots of the cur- rent at time indicated at bottom of chart. This chart is designed for use with the each year by the U.S. Coast and Geodetic Survey. Complete instructions are inside the front cover of this set of charts. NOTE Full predictions of the current In Chesapeake and Delaware Canal for every day in the year are given in the AtianticCoastCurrent Tables, MAXIMUM EBB AT DELAWARE BAY ENTRANCE. Figure 8-11. Tidal Current Chart-Maximum Ebb at Delaware Bay Entrance 8-23 330° 340° S5Oume o° 10° 20% 30° se > ~ RKO anh < ste A \ ‘A i nt we ASIANS . AU ya A Maximum Flood 2-7 feet second \\ iw S ewe QS Want aah \ ayant | vir) ox i \ SO eo “ ‘ “4 Nee os ) 210° 200° 190° 180° 170° 160° 150° Figure 8-12. Polar Diagram of Tidal Currents at Island Site 140° atIS pup|s| $0 paedS juadiND |OP!] JO UO!fOIIDA OWI] “¢EI- (S4noy) awl) g eunbl4 (puodes jad 4904) | AI Seo 26 of 133 j . : Calculated by: Design Problem physical Environment [Checked by: [R77 _| [Date: | 5 Mar73 Wave Conditions on Bay Side_of Island Wave data on waves generated in Delaware Bay are not available for the island site. Consequently, wind data and limited fetch, shallow water wave forecasting techniques will be used to estimate wave conditions. Calculation of Effective Fetch (See Figure 8-14 on next page) fe = 22.54n.m., 6080 ft _ 137/00 # nm i say F = 140,000 ft. * Angle measured clockwise from central radial. **® Distance along centralradial im naviical miles. NITED TATION yey CMT, SW UKRSIEY LAW AMA DELAWARE BAY (Orlawere Bar) CHGS 1218 Reference (8) Figure 8-14. Calculation of Effective Fetch - Island Site at Delaware Bay Entrance SOUNDINGS IN FEET 8-27 Design Problem Physical Environment Wave Conditions on Boy Side of Is/ana_(cont.) Significant Wave Height and Period as a Function) Sect. 3.6! of Wind speed Wind from N.N.W. along central radial. Average Depth Along Central Radial | Approx. 48 nm. | Chart datum 7 MSL _+2./ ft fis ae ye i “" —\ Shoal } & ie “ +d iS 8 Wy Main channel 42 gk \° 0.283 U- gd i f aai2s (2) ————— fanh | 0.53 tanh FF tod GIST. g 120] 0530[) fan fanhfa.s3o/ 94)" rte), ¢ — pgdy@ 0 aor ($6) 5 9 an |ass a tanh An ncaa ee (24 eae) 29 of 133 Design Problem Physical Environment [Dote: 6 Mar 73 Wave Conditions on Bay Side of Island (cont) U= 50mph_ (73.3 ft/sec.) F, = 140,000 ft. (2652s) d = 34 ft gf = 32.2 (140,000) - (73.3)? gF _ _32.2 (34) " (73.3)? 0.283 (73.3) 32.2 = 839.0 = 0204 ig Ps 0.2/8 = 472 tanh [al6/ ] tonh ——————_ M HELE Zs tanh (0.161) Hp 2169218: (7¥t-) 0.077(839) = 12 (6.26)(784 (6.28 (743) tanh [0.833(0204) "Hon ro : ba 32.2 tonh[0s3(0204) Jj 7, = 17.15 tanh[a833 (oss tanh. O414 tanh [0831(0.551)] to SIO Sec: Note: See tabulation on next page. , [Date: | G Mar-73 | Wave Conditions an Bay Side of Island (cont.) fF, = 140,000 ff. 5; d = 34 ff. 3/ of 133 Calculated by:| /. R.W. Checked by: | A. 7. J Date: 6 Mar TS Wave Conditions _an Bay Side_of Islond (cont) Frequency Analysis Design Problem Physical Environment Wind Data Wind roses tor the Delaware Bay | Ref. 14 area are given an the next page. Assume that sizeable waves occur primarily when wind is blowing along central radial | fram NW. This 1s the predominant wind direction for the Delaware Gay area. Wind is from the NW. gpproximately 16% of the time. : The maximum observed wind in 18 years of record was q 70 mph gale from the NW (aally maximum 5 minute wind speed) Thom’s Fastest-Mile -Wind Frequency, Ref. 8 In the absence of tabulated wind data (other than that given on the following page) the wind speed frequencies of Thom, adjusted for wind direction, will be used. Thom’s wind speed frequencies ore multiplied by 16 to adjust for direction. This assumes that winds from the NW are distributed the same as are winds when all directions are considered. Thom's Wind Speeds- Delaware Bay Area Quantile | Recurrence| Adjusted ~ Interval | Recurrence (yrs) Interval yrs) eee 0.5 Zz 12.5 0.02 50 S25 100 0.01 625.0 * Adjusted for direction (col.2 divided by 016) *™* Extreme fastest-mile- wind WIND DATA DELAWARE BREAKWATER, DEL. MOTE: DATA WERE OBTAINED FROM US. WEATHER BUREAU, PHILA, PA FOR PERIOD 1924-1941 THE INTENSITY DIAGRAMS REPRESENT WINDS OF GALE FORCE (3OMRH) OR GREATER, AND ARE BASED OW DAILY MAXIMUM 5 MINUTE VALUES. THE INTENSITY OF GALES IS INDICATED BY LENGTH OF LINE, AND WIDTH ALONG BASE SHOWS, TO THE SCALE INDICATED, THE NUMBER OF DAYS DURING THE 18 YEAR PERIOD HAVING WINDS OF & GIVEN INTENSITY RANGE. THE WIND DURATION DIAGRAM INDICATES THE AVERAGE NUMBER OF DAYS PER YEAR FOREACH DIRECTION, BASED Om HOURLY WiWD RECORDS. PREVAILING WINDS WIND ROSES SHOW AVERAGE WINDS FOR S* SQUARE OVER ENTIRE PERIOD OF RECORD ARROWS PLY WITH THE WIND. FIGURES AT END OF WS INDICATE PERCENT OF COSERVATIONS WIND MAS BLOWN FROM THAT DIRECTION. ER OF FEATHERS REPRESEN AGE FORCE, BEAUFORT SCALE. FIGURE IM CIRGLE REPRESENTS PERCENTAGE OF CALMS, LIGHT AIRES AWD VARIABLES. BASED ON SHIP OBSERVATIONS AS COMPILED BY THE NAVY HYDROGRAPHIC OFFICE FOR 10 YEARS PERIOD, 1932-1942 WIND DATA ATLANTIC CITY, N. J. YEARLY AVERAGES AV. HO.OF DAYS YR. s 1923-1952 1936 — 1952 LEGEND LEGEND MILES PER HOUR PERCENT OF TOTAL WIND MOVEMENT —— 0 To 13 SSS =9 PERCENT OF TOTAL DURATION — 147020 ——— — AVERAGE VELOCITY IN MILES PER HOUR aS 29+ THE DATA SHOWN WERE DERIVED FROM HOURLY RECORDS OF WIND DIRECTIOM AND VELOCITY AS OBTAINED GY THE U.S. WEATHER BUREAU FROM AN ANEMOMETER ATOP THE ABSECON LIGHTHOUSE AT ATLANTIC Ci Y, M.J. AT AW ELEVATION OF I72 FEET wS.L Figure 8-15. Wind Data in the Vicinity of Delaware Bay 8-32 Page no: 33 of /33 , : E Calculated ty:| J. RW. Design Problem Physical Environment {Checked by. |W | Date: 7 Mar 73 Wave Conditions on Bay Side_of Island (cont) Duration of Fastest- Mile-Wind Samer GO min. U (mph) Ar. t = duration of wind in minutes re) 50 100 150 200 U (mph) Nate: Since the durations under consideration here are not sufficiently lang to gen- erate maximum wave conditions, Thoms wind data will result ina high estimate of wave heights and periods. Dashed fine an. following page will be used to establish frequency of | occurrence of given wave conditions. Calculated wave height recurrence intervals will be conservative. ia JDAJO4U] BOUDJINDaY PUTM STTW 3Seqseq Ss, WoUT, peeds putM unupxey Jo uot InqTzista AITTTqeqoig ‘*9T-g ean3Ty (4noy Jed sajiw) paeds ae OSIOvl O22! Oll OO! O6 O8 09 SS OS Sb Or 002 ooo! S660 TTL MMM GUANA UUUTCOOUUUOUND’ JOMOU EERE SA TANG ULCNS TCU TUNNTINUNYcOUNNORTOROEPGHEREE PREC AA 2 FEES PA fant sion aouDpaedXy 40 Ajljiqnqoid 8-34 ° : ! Calculated by: Design Problem Physical Environment by: Wave Conditions on Bay Side of Isfand (cont) From dashed curve on previous page and graph on page 8-30for H; andi; as a function of U. Recurrence| Probability Interval | of Exceedance SAANAG sh ‘o _ The computed wave heights plot as a straignt line on log-normal probobility paper (See Figure 8-17 , next page). Note: Economic considerations as well as the | purpose of a given structure will determine the design wave conditions, The increased protection afforded by designing fora higher wave would have to be weighed against the increase in structure cost. For the illustrative purposes of. this problem, the significant wave height with a recurrence interval of loo yrs. will be used. Therefore, for design, fig Os Deft. = 6.6 Séc. for waves generated in Delaware Bay. 2B, Rae Tete Ol ee cuenta ae ane : 1 D Tees MUNI InTtTHSssSSeS SSeS ee EeeEs te Het 4] ocd, LE TRGReRarM HH tH He Hbfeteersten eames \ggaeee' Bp tii be HHT pace eee enue — ; Cee ere ee me IIOP LS ET een eeeen caeee olen escnee a. 2 ° ho oe Gieetiaueieeer teeszaee fe SS eis: pee ease si aera uiestzese Sipe ietes ogg oS sees tee 80 oar a 50 ui 50 77120 90 95 alts it 4 : ee ~ Deena abt + ; i} TT : r et Te babqUvRERA REA a a o ee =e atin a sacsecaee tt CCRETE BRE a BeSee! + nh OGG a PS ae wee i Te) ° ae i o @ o w ne) “ =o ) = =! Frequency of Occurrence (percent) Frequency of Occurrence of Significant Wave Heights for Waves Generated in Delaware Bay Figure 8-17. | | Design Problem Physical Environment Checked by: | fe. fF > oe Date: Man Wave Conditions on Ocean Side of Island Ref. 7 Hindcast wave statistics are available for severa/ U.S. East Coost locations in Reference 7. Linear interpolation between the New York and. | Chesapeake Bay stations was used to determine statistics for the Delaware Bay region (see next page). Since the data are given for deep water, @ refraction analysis is required fo transform the statistics to the island site. Idealized Refraction Analysis Sect 2.3 : For purposes of this problem, refraction by straight paralle/ bottom cantours will be Aes a oe 2.32 Azimuth of shoreline = 30 (See Figure 8-19) Angle Between Wave Direction 6 Shoreline Wave Directions Direction of Wave Approach -75° (0790 neglect) +/5.0° * &,= 75° | aio Ap = $2.5 %o= 300° +625 Xo= 75° + 105.0 Ao= 15.0 + 127.5 . «o™ 375 t 150.0, %e= 60.0 +1725, %o~ 825° + 195.0 (40790; neglect) * A, 1s the angle between the direction of wave approach and a normal! fo the shoreline. ** Used for typical refraction calculations given on following pages. STATISTICAL WAVE HINDCAST FOR NORTH ATLANTIC COAST ASSUMED STATION OFF DELAWARE BAY (INTERPOLATED FROM NEW YORK HARBOR AND CHESAPEAKE BAY HINDCASTS) Duration given in hours. Height and period groupings include lower value but not the upper. BI =e ca ssl Ls] [Ssal Al a APE tf fh a fl pepe re EF er ERR Per ere BI Fy ar ERE| WAVE DATA ASSUMED LOCATION OFF DELAWARE BAY ENTRANCE 40% 35% 0% LEGEND 25% 14 AND OVER 12 TO 14 20% 10 TO 12 TO 10 e eto 8 15% w w 4To6 10% = * 5% 2104 J 3 o% = . NE = 0870 2 CALM OR HEIGHT 3 LESS THAN 0.5 FT. 36.75% THE DATA, WHICH SHOW PERCENT OF TIME WAVES OF DIFFERENT HEIGHT OCCUR FROM EACH DIRECTION, WERE DERIVED BY HINDCASTING METHOOS- ANO USE OF SYNOPTIC WEATHER CHARTS FOR THE THREE-YEAR PERIOD 48-1950. DATA WERE COMPILED BY B.E.B. AND ARE INTERPOLATED O@- TWEEN VALUES FOR LOCATIONS OFF WEW YORK HARBOR AND CHESAPEAKE Gay ENTRANCES. SWELL DIAGRAM nN PERCENT PERCENT s LEGEND LOW SWELLS (1-6 FEET) MEDIUM SWELLS (6-i2FEET) a Ean GRBs sweris (oven izreer) THE LENGTH OF BAR DENOTES THE PERCENT OF TIME THAT SWELLS OF Each SITE NAVE GEEN MOVING FROM OR WEAR THE GIVER DIRECTION. TH URE IW THE CEMTER OF THE DIAGRAM INDICATES THE PEACENT OF CALMS. THE DIAGRAM APPLIES TO THAT AREA OF THE ATLANTIC OCEAN WEST OF LONGITUDE 70° AMD MORTH OF LATITUDE S0°M, THE INTERSECTION OF WHICH [9 ABOUT £35 MILES SOUTHEAST OF BARNEGAT INLET. BASED ON OBSERVATIONS BY THE U.S. MAVY HYDROGRAPHIC OFFICE FOR IO YEAR PERIOD, 932-1942. Figure 8-18. Wave and Swell Diagrams for a Location off Delaware Bay Entrance 8259 WY, LLL S i NAUTICAL MILES ol! 23 AREK nee Ory 36°/-\_ “4 2 a Figure 8-19. Ww Bans Ty 74° mee 2% cancer W91R wo | Pafeven yrered tos 982” (@ rw ee "= aan ey a wa = EL Ls a, , an yWaves From East™™, a +0 Location of Interpolated » Deep Water Wave Data 38° General Shoreline Alignment in Vicinity of Delaware Bay for Refraction Analysis 8-40 Page no: Calculated by: Checked by: Date: Wave Conditions on Ocean Side of Island (cont) Typical Refraction Calculations Oepth at structure: Use 40.0 ft Design Problem. Physical Environment BAS "7 Mar 73 Shoaling coefficient q eer peice. 3 7 sinh (47d) equ! valently, at 2 $ “| Cy i gT | Mae ———— = ———————— Z2nC 49nL Retraction coefficient and angle £q. 2-44 4 ee 5 BHT =~ 511s fg 278a Note: Equation 2-76qa is written between deep water and d= 4oft since bottom contours and shoreline have been assumed straight and parallel. For straight paralle/ bottom contours the expression for the refraction coefficient reduces to; ui Hi K, = be a { COS Ao Is R b COS X Recall, 97? Lo= Oe (deep water) £q..2-6 and L Cc t 2rd Lo -€a ( L ) q Typical refraction -shoaling calculations are given : on the next page. Caleu/qtions for various directions and tor q range of periods follow. 42 of 133 ; J. RW. Design Problem Physical Environment jess Wave Conditions on Ocean Side of Island (cont) Example Calculations for waves from South (Angle between direction of Wave approach and normal to shoreline in deep woter=4.= 60°) from Equation 2-8 40 f#t/ column (2) : Equation 2-44 or Table C1, Appenaix C. Table C-1, Appendix C Ves = tanh (222 fquation 2-78a Kr = Column (4)« column (7) * KeKs can also be obtained from Plate C-6, Appendix C. Tv€6%° 4069E° 7OLEE°l €€69e° Taleo ot 20%69° L06tS* yOLEE°t e9tec° 668El°ot TL096° esetze vOLEE’T 4etse® FETED oT S2zs0°T L06L° HOLEE*T ve0te* 6fL6l°el AS PT 629L%7° SSOLE° 9€see°l T9st€° Z20€80°ST 61699° 60T2s° 9€se2e°t 22L0e° y1209°LT 0%7926° €L0eL° 9g€seert LS%l2° ByTEL°ST Leetort SL26L° 9esee°t ToOtse® ESTSE vt oe 906S%° LseLe* 9t2ee°t SUPE AS 06888°6T 9€S%9° 9L€eS° glzee°t €eLlee® 929S€°6l 79168° 79E2L° 9l2ee°t eLt0e® 22l82°Lt 90086° 0”S6L° 9Izte°t TaSze° SL96L°ST A SJUSTITFFOOD) BUTTBOYS } UOTIIeIFOY pue seTBuy Loyeerg Fo otTqey S67? 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EcBBS°E B802T°y vf zt 20688° 2S8c6° 0SLS6° 2220%° 2€S70°€2 0zST6° 4€9S6° 0S1S6° vELEE® CovS.°el 891%76° 71686° 0S1S6° T2z9T? 0708S°6 60SS6° 1%166° 0S1S6° €0780° elylB°y of SUCIPOL DN60ET® =2%Jc 0s0ze° 6%7668° zte86° 859%6° %ZS16° 1L866° C5616° 2€226° £686° 6£E8"° 2279S° L2z1s9° 16S69°L2 SEELy*Ce 96HlE°LE 0000S°zE 00000°0% et06ee? G0606° s9e86° 86196° 19S86° 0€666° £9616° 2€226° "€686° e9lee® 101%? Liles? *9l97°22 %769€6°92 01098°62 00000°0€ 00000°0% Le2te* BE616° 61686° S9266° 18966° S8666° £9616° 2€226° "€686° Tegel? 0L9€2° 19092° Os9ec°Il 98l9S°El TEseea: 00000°ST 00000°0% B6L16° 19126° leeee o¥Y 02866° €2666° 96666° = £9616° 2¢226° "€686° =F 28660° HSBIL® paneOet® 2X 626TL°S §=S9T6L°9 gi 289n° La) g 9 295 Val o0N00S*L = %o H 00000°0%2D (penutjuo)) s,USTOTFJO0D ButTTeoys Y UOTJOeAIFOY pue soTSuy Ioyeerg Jo sTqey 8-44 Summary_of Refraction Analysis - d= 40.0 ft. Wave Conditions on Ocean Side of Island (cont) (Numbers given in Table are K;Ke) | Wave Period (sec) Refraction: shoaling coefficients are summarized 1 { 0.411\0394 10 39610410 |0.42510.442 |0.459|0476|0493 graphically on next page. | Transtormation of Wave Statistics b Refraction and Shealing. The above refraction-shoaling coefficients will be used to transform the interpolated deepwater wave statistics given on page 8-38. The resulting statistics will only be an Qpproximation since only the significant wave is condidered in the analysis. The actua/ sea surface 1s made up of many wave periods or frequencies cach of whieh results ina different refraction- shoaling coefficient. The analysis given here 1s only for the highest waves of the wave statistics on page 8-38. Amore complete analysis would consider the entire table of statistics, ve ‘Ppoldad @ADM PUD UO!JOBIIG BADM 40 UOlJOUN4 D SD SjUaIdI¥Je09 (spuodes) | pOllead eADM 9| v | él Ol HuljobouS—uolJoD4Jay OZ-g ds4nbi4 HEH aE SEsdaccasdocasdtcetttocattccstitastttacitiecsittee'ss Beene + alsin - mit 4 a : - +++} Seed z HR HESEsHaHes eocotHta bocsatiibeeess aa TF i} 1 NS [ ks EEE SEE EH EEL seme: title ae : fone ee aa ise ale pate E f H FE j tHE Ez E E Hes : 4BHe E B ageaee er cz_atteeenene ecuebed peta Ta Soh abeaadaGupeee“ca¥aauaeratvasaeraeratassaeretrarie 7 “e ae 7 ane E ee feet | SEEEEEEEE EEE HEE elalele eeeeeee (ASA ae asae ace HEE eRe ee she Coe eer eee PERE HH SSS Rae eae) ee ete a - oneee Ossie fala Tea | ie oo ot a 20 O'| 8-46 Page no: . ; ; Calculated by: Design Problem Physical Environment | Checked by: Wave Conditions on Ocean Side of Island (cont) Table _of Transformed Wave Heights Significant height & period in a =40ft explanation of numbers in table on next page) Deepwa Wave Period (sec) Hel eal Direction | 9 a of utd Page no: 48 of 133 J. RW. Design Problem Physical Environment awe: Date: 8 Mar 73 Wave Conditions on Qcean Side of Island (cont) Explanation of numbers in table on preceding page. 1. Numbers represent transformed wave height. For example, a 30ft high deep- water wave with a period of 23 séc. approaching from the ENE (in deep water) will be 312 ff high at the islond site (in @ depth, d= 40 ft.). 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 25 and 30 ff. in height with a period of 23 sec were experienced for 2 hours in the three years of hindcast data. Eguivalently, the wave height at the structure site for the iven deepwater wave statistics will bé between 26.0 and 312 ft. for 2 hours. 49 of 133 Calculated by:| J. R.W. Checked by: Date: Design Problem Physical Environment Wave Conditions on Ocean Side of Island (cont Number of hours wave height at structure is in given height interval. Wave Height at Structure (ft.) o46* Table continued on next page. * Example: For waves = 30ft. high, 23 séc. period from ENE, fram table,page 8-47, wave height at structure is between 31.2 and 26.0 ft. for 2 Ar. There fore, wave height is above 30 ft for £2 (2)=a46 hr. Page ne: 50 of 13. . : ; Calculated by: J. = = Design Problem Physical Environment — [Checked by: a ae 73 Wave Conditions on Ocean Side of Is/and (cont) Wave Height at Structure oe 5.05 1.33 1.05 O74 6.66 5 2 ee 347 complete Total hours in record: 26,304 hr (Includes 4,667 hrs. calm) Height | Total hrs. 0.0000175 0.000788 0.00470 0.0068! *« *¥ ¥ Subtotal from previous page. *«¥ Would require that above tables be extended to entire range of table on page 8-38. Calculated by: Design Problem Physical Environment Checked by: Wave Conditions on Ocean Side of Island (cent.) Deepwater Wave Statistics (witheut consideration of direction) Significant | Cumulative | Probability Wave Height| Hours* of (feet) Exceedance * Number of hours wave height will equal or exceed given value. «x 60 Ars /26304 hrs in record = 0.00228 To obtain higher woves of spectrum: Flip oie Hs Ay 161i, Note: Curves showing deepwater wave heght statistics and transformed statistics are given an next page. MUIPYYSD PYM BUTEA” AG UULEUWMAUZSUNAL —UD800 Ul pa}DJaUed SOADM 40} SJYBHIOH SADM jUDOIJIUBIS Jo aoUasIND00 Jo Aouanbes4 (HEH) d 10000 fH ‘12-8 e4nbi4 1000 loye) (0) Ol S| (4984) H 02 Ge oe g¢ 8-52 [53 of 133 | sted by: | J. K vA | Checked by: | betes a Design Problem Physical Environment aa Dae 3 5 WOR A mies Wave Conditions on Ocean Side of Istand (cont) Se a7 Hurricane Waves The waves associated with hurricane & Ref. 5 of Reference 5 will be determined and routed across the continental shelf to the Island site. Characteristics of Hurricone B Ap =24 in. of mercury R= 33:5 1m. Ye = 25 knots Umnax= 92.6 knots Up= 0865 Uma+O5 Ve =92.6 knots £q 3-34 Significant wave height at point of maximum winds 1n deep water. Hy = 16.5 ere | —— I Up | | | | eee) 0.208 Les (Assume X=1.0) |£q. 3-3! H,= 16.5eE 100 [1+ 926 i= SOO at Significant wave period at paint of maximum winds, kap % = 86e%7 [ os Eg. 3-32 V Uz 0.402 k=86e [1 4 0.104. (1.0)(25) 92.6 Is= 163 Sec: Check by Equation 3-36, k= 2130 Hy = 2137568 =16.1 sec. OK. Design Problem Physical Environment SCS PRIN ee ERE 8 | Wave Conditions on Ocean Side of Island (cont) Hurricane Waves (cont) _ The relative distribution of wave heights within the hurricane can be obtained from Figure 3-34. Calculation of Probable Maximum Wave The time required for a length equal to the radius of maximum winds fo passa point if hurricane is moving with a forward speed equal to Ve. R 335 7m. = 2 oe = 1344 c Ve 25 knots G fr. The number of waves in 4824 sec. Ale oe 4824 sec = 296 Waves i 16.3 sac. From, Equation 3-39 for n=1, the probable maximum wave IS, H, = 0.707 H, ¥ 10g. = (Approximate ) H,., ~ 9-707 (56.8) ¥ lag, (296) Ha, = 95.8 ft. (approximately) Note: The above wave conaitions ore for deepwoter conditions. Because of energy dissipation the Wave heights will be lower at the island site. The hurricane will be routed across the continental shelf using the bottom profile given on next page(trom Reference 5) Haus EEE SESE 7 aa Ee Ferg le § a a a Tea : pf oe aaeee = oo ane - a ce : ; Distance from Coast in Nautical Miles Mean Bottom Profile from Deep Water to Mouth of Delaware Bay =22) 8-55 Lae i a a eel oO ie) 12) fe) fo) 8 Oo ie) 8 8 oO oO = ia] r- t+ wo © ~ 49} u! yidag Figure 8 —_——— Calculated by: Checked by: | Design Fropiem. Physical Environment Wave Conditions on Ocean Side of Island (cont) Hurricane Waves (cont.) Routing Hurricane Across Continental Shelf Typical Calculations Calculations for first row of table an page 8-6! following. Column 1: Distance from coast in nautical miles Fig. 8-22 Column 2: Depth below MLW at end of section. |Fig. 6-22 Column 3: Depth at beginning of section te mean water surface (including astronomical tide and storm surge). The astronomical tide and storm surge are assumed to vary across the shelf as below. combined astronomical & storm tide. > | Opprox. cage | of elf | Elevation above MLW. (ft) (e) 10 20 30 40 50 G 10 8 Distance from Coast (nm) Note: These water surface elevations are assumed to vary as shown for purposes of this example. Column 4: Depth at end of section to mean water surface. Column 5: Average depth m section = aie Design Problem Physical Environment Wave Conditions on Ocean Side of Island (cant) Hurricane Waves (con?) Column 6: Effective fetch, for first step | aio NS (Deep water) © l 90555Upg 2 56.8 = i = mM. © 100555 (920) {22 7™ For subsequent steps, 2 always sess ee j——_| Poy amavis thon oF equal 0.0555 (Ug) to 122 4m) £q. 3-40 Column 7: Deepwater wave height, given by Hy = 0.0555 Up VE ( Eguation 3-40, rearranged) Ho = 0.0555 (92.6) 7/22 = 56.8 ft Column 8: Deepwater significant wave period, = 213-1Ho Ip = 2137508 = 16.1 sec. Column 9: From column 5 @ column 8, 2 2 To = (16.1) = 0458 sec*/ft- d, 563 £q. 3-40 £9. 3-36 Column 10: From Table 3-3, for ®/ 7 = 0456 | Table3-3 read Ks= 0.98! Column it: Friction loss parameter, fr Ho Ks Ax (d,)- £g. 3-4) 58 of 133 Calculated by:! ¢/. R.A Design Problem Physical Environment RW 12 Mar 73 Wave Conditions on Ocean Side of Island (cont. Hurricane Waves (cont.) where f, = friction factor = OO! AX = reach length 1n ft. Snm x 6080 ft. = 30,400 ft. AM. Hy from column 7 d, from column § He 2.01 (56.8)(0.981) (30,400) _ 0.0534 (563)? Column 12: From Figure 3-35, for A= 0.0534 Fig. 3-35 and To'/d, = 0467, Kp= 10 (by extrapolation) (negligible energy dissipation) Column 13: Equivalent deepwater wave height Hp = Kg Ho where Kg 1s fram column 12. He = 10 (56.8) = 56.8 ft (Refraction coefficient, Kp =1.0 has been assumed) Column 14: Effective fetch for He, given by, ’ ripe 2 = o - E ean Eq. 3-40 | 2 de t s0GBex \ee 122 nm. e 0.0555 (92.6) s : ; Calculated by: Design Problem Physical Environment [Checked by: | Date: Wave Conditions on Ocean Side of Island (cont. Hurricane Waves (cont) Column 15: Significant period corresponding to H,, from Eguation 3-36, To =2137/He Fg. 3-36 Tp = 2.13 756.8 = 16! sac. Column 16: Fram columns 4 6 15, 1\2 2 (%) A = = 0608 sec*/ ft. d, 42 . \2 Column 17: From Table 3-3, with (70) /d, = 0608, Ky, = 2.956 Column 18: Significant wave height at end of reach (7o nm. from coast) Hy = Kza Hy H,= 0956 (56.8) = 54.3 ft. Column 19: N = number of waves N= eaeed Le _4624 = 300 waves £q. 3-38 if 16.1 Calumn 20: Probable maximum wave height, Equation 3-39 with n=, Hp, = 2.707 H, | !%e M Eq. 3-39 | cps 0.707 (54.3)1/ loge 220 = 91,7 ft | (approximate) w See page 8-54 of calculations. 8-59 Design Problem Physical Environment [Checked by: (RW | hater te The Moar: 73 Wave Conditions on Ocean Side of Island (cont) Hurricane Waves (cont.) Column 21: Height of /0% wave (average height of the highest 10% o waves) Hyg = 1.27 Hg Hip = 1.27 (54.3) = 69.0 ft fg. Tk Column 22: Height of 1% wave (average height of the highest 1% of waves) H, = 1.67 H, H, = 1.67 (54.3).= 903, fi. Note: Values given on next pa i were computed by slide rule and ima differ in the last significant figure from ca/cu/ations made by des calculator, Gf of 133 | Page no: 4 A : Calculated by: Design Problem Physical Environment est by: IR ee | Date: 13 Mar. 73 Wave Conditions on Ocean Side of Islana (cont.) Hurricane Hurricane Routing Across Shelf Across Shelf sf es we Vo) a Ks ie es 0.458 2981 2053 Beyan AWN ~ nh (21) Wed Wave Conditions on Ocean Side of Island (cont) Hurricane Waves (cont) Time Variation of Significant Wave Height at_ structure Design Problem Physical Environment ** Value of (tL) = 16.7ft +«* A time lag of 025 hr has been assumed. eR = 335 19: Note: Time variation of H, only approximote. 20 7 ot Hs gz 16.7 Ft. 15 | | aS 0.25 hr. lag = retry " landfall of 3) max. winds | 4 al ~# big 0221 GSt | WOOT GHM eZ lanl] OF Time after landfall of max. winds (hrs) 8-62 Page no: G3 of 133 | Design Problem Preliminary Design Daic: Selection of Design Waves and Water Levels The selection of design conditions js 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 af first cost). This optimum design wave height will give the most economical design. ES \ most economical design i ; tofal average annual &| \ cost U La ecu : Y S 7 IW ape te: we = \ ; Be % z D Pee g n> SRO Dile uCme & repair costs | amortized — first cost gesign wave height giving { Design Wave Height Intangible considerations such as the environmental conseguences of a structural fai/ure 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: : ae. tnd ’ Calculates by: | Jf. RW design Problem. Preliminary Design mae: Selected Design Conditions The following design conditions are assumed for the tllustrative purposes of this problem. | Water Levels (MLW datum) Use 110 ft 2. Astronomical tide (use water level exceeded 1% of time.) 1. Storm surge (less astronomical tide) | GSE. St Orn 3. Wave setup (assumed negligible since structure is jn rela Ase deep water and not at beach) Wave Conditions on Bay Side_of Island witerval. Use H,= &9 ft 15 ="6.6 Sec. Wave Conditions on Ocean Side of Island 1. Hurricane 8 waves Fig = 1607S hag. Tg ped, (SOG. 2. From hindcast statistics (wave height exceeded 1% of time) Fie =f Lomre Use ‘hH, = {8:0 41. | ! 1 I. Use conditions with 100 yr recurrence | | ie) Design Problem freliminary Design Revetment Design - Ocean Side of Island The ocean side of the island will be protected by a revetment using concrete armor units * Type_of Wave Action The depth at the site required to initiate breaking of the 18 ft. design wave is: For q slope in front of the structure mn Oo Hp = 276 fof ae = He 0.78 Since the depth at the structure (d,= 40 ft) is greater than the computed breakin depth (d)= 23.1), the structure will be subjected to non- breaking waves. ~ 148 _ 237 # O78 Selection between Alternative Designs The choice of one cross section and/or armor unit type over another is primarily an economic decision reguiring evaluation of the costs of various alternatives. A comparison of several alternatives follows. Type of Armor Unit: Tribars vs. Tetrapods Structure Slope: 121.5, 1:2, 1:2.5 and 1:3 Concrete Density: 150 /b/ FF 160 /b/ #f°g | 70 lb/ft? * The use of concrete armor units will depend on the availability of suitable quo and on the economics of using concreté as opposed to stone. Sect 7.21 Page no: Calculated by: Checked by: Design Problem Preliminary Design if SS 7] Mar or 73 Revetment Design (cont) Preliminary Cross Section Sect. 7.377 Modified from Figure 7-95 PIG Tia crest elev. varies ‘bottom eley ©-40 — Crest Elevation Established by maximum runup. Runup estimate Sect 7.21 H,= 16 ft d= 5G ft. 7 = ? (use point on runup curvé giving maximum runup) ith = = 3. Use Figure 7-20 * Waves over {6 ft. will result in some overtopping. 8- 66 Page no: te) L >) > Rd : ee _ RW. Design Problem Preliminary Design 15 Mar: 73 Revetment Design (cont) Armor Unit Size - Primary Cover Layer Sect. 7.373 3 ‘ we Kp (5.-1)*cote £Q. 7-105 H= design wave height = 16 # nw, = Unit weight of concrete ; 150 Ib/ft?, 160 Ib/ft3 and 170 |b/ft cot@ = structure slope 15, 2.0,2.5 and 3.0 Sp? Wr = ratio of concrete unit weight fo Ww = unit weight of water. OS stobility coefficient (depends on type of unit, type of wave action and structure s/ope) The calculations that follow are for the structure trunk subjected to non-breaking — wave action. Stability coefficients are obtained fram Table 7-6. [Page no: _—*| 68 | Calculated by:| /. [Checked by: | #. (Date: 1 aw f 133 7 or: 73 lt Design Problem preliminary Design = Revetment Design (cont) Required Armor Unit Weights Structure Trunk Wr s/ope Kp * W | 150 15 10.4 A Tribars * Kp from Table 7-6 for loyer 2 units thick. **¥ Represents the damage under sustained wave action of waves as high as the 1% wove, not the damage resulting from a few waves in the spectrum having a height equal to Hy =167H;, f eae ; Calculated by:; J, RW. Design Problem Preliminary Design Checked by: |=. AG Daie: 15 Mar 73 ww Revetment Design (cont) 69 of 133 Yolumes of Concrete - Primary Cover Layer Structure Trunk Armor Number | Volume layer area/iao | (tons) ft of structure % (#2) 11860 15,120 17,720 20,200 Area = (30+ crest Per sin@_ where crest elevation 1s from runup analysis on page 8-66. Number of units ond concrete volumes determined from figures on next two pages. These figures were derived from Figures 7-91 and 7-89. sipqi4] —Djo0q Bulsaeulbuy ‘¢zg-g s4nbi4 ¢ 1984 40d spunod Ovl=2M ‘(SU0}) 4OGI4, |ONpIAIpul yo 4YBIEM vl 2498} OOO! Jed syiun yo saquinn (suo}) aoqi4y jo yybIaMm 8-70 24885 OOO! Jed sy!uN 40 saquiny Ovi oO9| spodnija| — djoq BHulsesuibuy pe-g ainbi4 ¢ 1824 49d spunod Op|=7M ‘(su0}) podosja) jONpiAipul 40 ;yBiem vl cil 9 9 (suos) sy61em Si (il Ta ENSIT es, im Vel a ‘On VONSTIGNT oTTUCTUre TOPE. Pat pala fe) = [estate nt Concrete | ny, VOncrere | Ne 0 Tr Const (¢499J 40 SpuDsnoy}) esnyon4ys 40 420} OO! 49d e4as0U0D JO BUIN|OA Weight of Tribars (tons) Figure 8-25. Volume of Concrete Required per |OO feet of Structure as a Function of Concrete Unit Weight and Structure Slope Tribar Weight, 8-72 51 Concrete! Density Fant: LL Lt ne OT CONSTANT. 1é 01 r_Cons (Speipuny) ainjonsjs 40 409} OO| Jed pesinbay syiuQ soWsy yo saquinn Weight of Tribars (tons) Figure 8-26. Number of Tribars Required per |OO feet of Structure as a Function of Concrete Unit Weight and Structure Slope Tribar Weight = 7S) $20} OO! Jed ajasdu0g jo (¢489} 40 SpuDsnoy}) eanjonsys fo 16 Weight of Tetrapods (tons) Figure 8-27. Volume of Concrete Required per |OO feet of Structure as a Function of Tetrapod Weight, Concrete Unit Weight and Structure Slope 8-74 is | } | | | f Ta ee jogs} T it wt a | (el | 1 | 18 4 12 10 8 (Spespuny) einjonsys JO 490} OO! Jad pesinbey spodoije, Jo JequinN © t+ Weight of Tetrapods (tons) Concrete Unit Weight and Structure Slope Number of Tetrapods Required per |OO feet of Structure as a Function of Tetrapod Weight, Figure 8-28. GS-75 * k, « £ from Toble 7-10 Poge nc. 16 otf of 133 r ; meme : aula ee W. Design Problem Freliminary Design Checked by: | RWS ries ase 15 Kar. 72 ve Revetment Design (cont) Thickness _of Armor Layer & First Underlayer | GOK. (# E 7-108 r = loyer thickness in ft n = number of stones or armor units comprising the layer (either armor layer or first underlayer) W = weight of inaivioual stones making up the layer in pounds. we = unit weight of stone moterial (concrete or guarrystone) Number of Stones Reguired 2 =; aes . Wr )3 Ank, (1 aE) WwW! Eq. 7-109 Nr = number of armor units or stones. A = area in ft? P= porosity in percent Thickness of Armor ee es Tribars iF Ma? = 107 ft = 1084 R= 1084 Ft | Ig =10.62 =10.62 ft. *k, = 102 4 /a20 P= 54%, Table continued on next page Calculated by: Checked by: Date: 77_0f 133 | URW rc oe | 16 Mar: 73 Design Probiem Preliminary Design Revetment Design (cont) Thickness of Armor ee eee Aare (n=2) (cont) Type of BRE Armor De oi Wier: 170 Ibs /#P Thickness of First Underlayer Quarrystone ky= 415 (rough guarrystone) fiat Fe we = 165 /bs /ft? = S peal ES arial x «¥ * k, @ P from Table 7-10 *« From Equotion 7-108 *®* From Equation 7-109 with A= 1000 ft* Page no: 78 cf 73 Calculated by:} J. R.W. Design Problem Freliminary Design 7 ae Date: 16 Mar 73 Revetment Design (cont.) Equation for Volume of First Underlayer iG Me E30 F+307 1 £252} + so] : 2 sing 2siN@ sine Equation derived from preliminary geometry of cross-section on page 8-66. F = crest elevation (# obove MLW) i = thickness of armor layer (ft) G = thickness of first under/ayer (ft) = yolume of first underlayer per ft of structure (f7?) Equation for Volume of Core 2 ae | eee j 40.+£ -—-— 7(15 +core Ve #{ cosOo ( ) Eguation derived from preliminary geometry of cross-section an page 8-66. Page no: 79 of 133 | Revetment Design (cant) Yolume_of First Underloyer -Tribars Volume per 100 ft of structure (thousands of ##*) Tribar S/ze Cres per Tee} igs (per Teer _=ifoO i poun te $90} JO SUOI||JW) S4NJoN4yS 4O 42804 OO | Jed sahd|JapuN yssi4 yo awnjor Weight of Tribars (tons) 29. Volume of First Underlayer per |OO feet of Structure as a Function of Figure 8- Concrete Unit Weight and Structure Slope ? Tribar Weight 80 Page no: 8/ of /33 | Calculated by:| J. A. im Checked by: [A | Date: "6 Mar 7: 16 Mar. 7 | Design Problem Preliminary Design Revetment Design (cont) | ! Yolume_of First Underlayer -Tetrapods Volume per 1ooft. of structure thousands of ft) 8-8! } SORES Some (¢#804 40 SuOIJIW) e4nyon44s 40 4894 OO! Jed 4eXd|JepUuy 4s414 40 eUIN|OA Weight of Tetrapods (tons) Figure 8-30. Volume of First Underlayer per |OO feet of Structure asa Function of Tetrapod Weight, Concrete Unit Weight and Structure Slope 8-82 ge Nn | 83 of 133 | vi) ine iv ! Volume of Core - Tribars 6 Tetrapods Volume per 100 ff. of structure (thousands of ##°) Tribor or ———— eee oe ee Cost Analysis the illustrative purposes of this problem. Actua! costs for a particular project would have fo be based on the Pade costs in the raject area. Costs will vary with location, . time and the availability Of suitable materials. Unit Costs of Concrete Ss The following cost data will be assumed for Wr Cost ,| Cost , (lbs/ff°) | per yd?| per ft Sata acl 70g be 7081 A cet JOE 150 | %40% | 14% 160 42 170 $5 2 LS IQ 12 Volume of Core per 100 feet of Structure (millions of feet>) Sesresatestecstostesttostnsiieatts SSS ee Soeeuns Seu seGEs Ta CeESGeeesueesTeeeesacerieeteiee BEGDEU EG CORSEEEETEEGESTOEESEOSEETTSCETTaSETTeaEraeeereaaeraaees sudesdasteatnas tect fast toateattastecttastesstasttestesttesterttestecttast bac eeesteeeessansesaeesri ESRESTOSEITGS Srireeceee eT BIEEEIES one He at ee eees besuas ESSELESEEIENSE He EEE Fs os fs ffi Pos a on i es fp fe Stites eet 1 HBSS ot HHH HEH Bt HH EEE eee CCC Ps QRPREREERARRO OE aeaao Me ft ts EEE = a CI H ee eee eee eee HERE EEE-EEEEEHEH PSS a SESSSR00R 00858 PoP dea eee bl sane — 14.9 ft. TI; = 6.6 sec. * d= 40.0 +6.0 ft d = 46 ft. « Probability of extreme surge during canstruct- ion assumed negligible. 8-95 Design Problem Prejiminary Design Quay Wall Caisson (cont) Stability During Construction Le ke Sh eley. +20.0 | bay side seaward side (protected) ’ a ‘g elev. -40.0 “compact sandy bottom® For preliminary analysis, assume 75% voids filled with seawater Wy = 64 /bs/ff> Non-breaking Wave Forces on Caisson 1. Incident Wave Height: H,; = 149 ft. 2. Wave Period: T= 6.6 sec. 3. Structure Reflection Coefficient: [sto 4. Depth: d, = 46.0 fe. Ai, 14.9 te ——s= 0342 TT? (eg 97 of 133 . a u Calculated py: Design Problem. Preliminary Design RH [Date: ss: 19 Maar 73 Quay _Wall Caissan_(cont.) 5. Height of orbit center obove S.WL.: tre _ 0.3! H t he = O31 H; = 0.31 (149.9) = 4.62 fF. 6. Height of wave crest above bottom: Ye thet FF ry Ye= 460+ 4.624149 = 65.5 ft. Wave will overtop caisson by 5.5 #t., therefore assume that structure is not 100% reflective, Use X= 09 and recalculate h, fe, a2 he = 028H; =028(149)= 4./7 ft. 110? Ye = 460447 + (14.9) = 64.3 fr. say Y.= 64Ft 7. Dimensionless Force (wove crest ot structure): for aoe a342; ae 0324 & 129, 5 066 Wd. = 0.68 (64)(46)'= 92,100 Fe = 92 eI Ft [Page no: | 98 of 13 } Cateutated by: Design Problem prenminary Design — (Checked by: [RAT au ) 19 Mar: 73 Quay Wall Caisson (cont) 8. Force reduction for low height: b= 400 #20.0 =GO.O ft Yo= 64 ft. b whe Zo = 094 From Figure 7-72, i= 0996 E= RE = 09%(92.1)= 91.7 k/#t 9. Hydrostatic force on leeward side: a wd". G4(46)- 677 k/ft 10. Net horizontal Piles (due to presence of woves): Fey = OT ~ G77 = 2Gk/#4 ii. Bens ea wave crest at for ie 0.342, ae 0324 6 1=aQ9, fF} Me wd, a4 OZ95, 3 M, = 02%wd, = 0295(64)(a6)'= 1,838,000 = 1, 838 ft-k/ft. 12, Moment reduction for ope height : Fig. 7-72 From Figure 7-72, with a = 0.94 lm = 0.990 Me = SnM = 0990(1,838) = 1,820 ft-k/ft. Design Problem freliminary Design Quay Wall Caissan_ (cont) 13. Hydrostatic moment on leeward side: 3 3 M= Ws _ 64(46)_ j038 f-k/p 6 G 44, Net overturning moment abaut bottom (due to presence of waves): Mne¢ = 1820-1038 = 782 #-k/ft. Stability Computations Overturning: Le | cre = S ; f Pied: a aan Mnet = (82 tt K/tt. | A Pz hae |: Pr R= reaction force fs Weight per unit width per unit length of structure. Concrete, w= 150 Ibs/f? (25% of crea) Water in voIdS, Wy= 64 Ibs/ft° (75%. of area) Height =60.0 ft. ‘ 6 [Page no: | 100 of 133 ~ RW. Design Prablem Preliminary Design AT Ne Se ae ee a ae Cate: 20 Mor. 73 Quay Wall Caisson (cont) Equation for Weight/unit length W= GOL, {(025)(150) +0 75)(64)} W= 5130 L, /b/ft = S13Le k/ft. 2. Uplift per unit length of structure Poy tle eee ' 2 cosh (27d) 2 2 [,= BE 2) 22 eer 2197 2 (3.146) A206 L= Ay = 0230 0230 cosh (21d/,) = 2.242 - 1409 (64)(14.9) _ faggot 2.142 P,= 0.404 K/ ft? 4.04, Ibs /ft? Po Wd — (hydrostatic uplift) P2> 64(46) = 2,944 Ibs/ft™ Po = 2.944 k/ft* Eguation for Uplift Forces/unit length By = fle = 0.202 Le k/tt. B= Pale = 2.9441, K/t. 8-100 /Of of 133 ‘ 2 he Calcuiated by: Design Problem Preliminary Design Checked by: R.A ; 20 Mar. 73 Quay Wall Caisson _(cont.) Summation of vertical forces B, +B, -W +h, =0 O2Z0OLIAE ZILLA SS ASE. +RY=O Ry = 1984Le k/tt. Summation of Moments about A. 2 B, 3 4c + By Le —~WHle¢ t Rote * Myer 0 0.202/E)le +2944) le -—513(2)Le + 1964 (LL + Jaz 30 ys = ABZ = B54 0. 15 ae Let 2 en. Width required to prevent negative soil bearing pressure under Caisson. (Reaction “within midale third) Assume | i 56 Fr Sliding Coefficient of friction (concrete on sand) Ms = 240 Table 7-14 Vertical Force for L.= 36 ft. W= 5131, = 513 (36) = 184.7 k/ft 6; --0 202 1.=-0.202 (36) = — 7.3. k/fi. * Ry = vertical component of RK. 8-10] Puge no: 102 of 133 ‘ Ry Caisson will not slide. | ] | | | | \ | | Summary - The preceding calculations illustrate «the type of calculations required to determine the ALD of the proposed . . guay wall. Many additional /oading conditions aiso require investigation as do the foundation ¢ soil conditions. Field investigar- ions to defermine soil conditions are required in addition to hydraulic model studies to determine wave effects on the proposed island. | * Ry = horizontal component of reoction, R. *% Factor Of sofety against sliding should be 23; hence Fu = 2 Ry for Die dein eee shout be widened. 8-106 Page no: 107 of 133 Computation of Longshore Component of Wave Energy_& Potential Transport Rates Using the hindcost deepwater wave dota from page 8-38, the netand gross potential sand trans port rotes will be ‘estimated for the beaches south of Ocean City, Maryland. (See map on next page) Assume refraction is by straight, parallel! bottom contours. ee Corresponds to mid-interval values on Table, page 6-38 of calculations. Table of Deepwater Wave Steepnesses, Ho/gT* is asia a Me Ole) (023) (029) plete) h aoaeceae (.098)| (./30)| (167) | .208)| (.241) | (.2768)| (.315)| (.352) (25 (50a) |c609)| (77D), ce \ ze (360) (463) | (566) tees) (772) (875) = Pinon all ot ) 00870|.0044 ae ae 0013 | .0010 mo 20 | sa | C700)| (908) c10)| 030 | fa | fer) O12 | 0057 ais os 017 0012 ot rao | (mel cael am nl 2 eer ma j (1.74) | (2.24)| (2.74) | (324)| (474) | (4.24) |4.73) | (5.23) 3 (5. 5.92) Pele 695. ino | to | ar a ee (244) | (3./3) | (3.83)| (4.52)| (5.22) | (: (6.6/)| (7.30 150 0095 |. 0038 |.0028 / |.001G | .00/3\.Q010 (3.24) a 05 /0)\ (6.02) )| (7.88)| (8.80) (273) OO -0044| .0031 |.0023 | .00/8|.00/5 |.00/2 (10 | teeta ra|ia9|Gonias ceo) | a 0073 |.0049 2085 .0026|.0020 C016 “0013 ; (6.69)| (8.18)| (9.66)| (11.1) | (12.6)| (/4./) | 15.6) 225 | [etal ta eee ee la ae (9.38) (U5) (36) (5.6) (77) (19.8) 219) (240) 215 COT! | -0051\ .0038 | .0030) .0024\.0019|-00/6 (17.1) | (20.2)! (23.4)| (26.5 ae! (32.7)\(35.8) “Numbers in paren theses are wg HsT x10~* 8-107 75°30" 75° DELAWARE FI Nanna euch Gp evn + TB temporary buoy Or orange C can vr Wed hard bh black ay arey thy rocky br bromn 6 ah 90h by blue Sh. ahalte wth stechy an green Wreck, rock obstruction, oF shoal amupt clear to the depth indicated. Rocks inet corer and uncover with heights in fewt abore 4: fn “pa FL 1Snec 165191 19M, ?! HEIGHTS, Heights in feat above Mean High Water AUTHORITIES and topography by the Coast and Geodetic Survey NAUTICAL MILES ° ! EEE ee CAUTION UNITED STATES — EAST COAST CAPE MAY TO CAPE HATTERAS SOUNDINGS IN FATHOMS AT MEAN LOW WATER (For offshore navigation only) Mercator Projection Scale 1:416,944 at Lat. 37°00 vp +4 » ots 2 and 3 for 2 this area Refer re Olea Eg ee Mohtahoat will) area designat gna Region of Interest YO UT ATLANTIC OCEAN Figure 8-35. Local Shoreline Alignment in Vicinity of Ocean City, Maryland 8-108 39° 38°30 38° Design Problem Longshore Transport Longshore Wave Energy (cont) Azimuth of shoreline =20° 2eepwater Wave Angle (Ao) Angle wave crest makes with shoreline (egual to angle wave ray makes with normal to shoreline ) Compass airection| Deepwater of Wave Approach angle [= 4 northwerd southword * Disregard as contributing little to longshore energy. S=109 Design Problem longshore Transport Longshore Wave Energy (cont) Typical Calculations for Waves from NE. Use Figure 4-35 to determine longshore wave energy. Subtotal 1498.8 x 10° y From page 8-/0]7 of calculations *%* From Figure 4-35 (See curve on next page derived from Figure 4-35 ) #*¥# Column 2 x Column 3 t From Toble, page 8-38 (for 3yfs. of hindcast dofo) tt Column 4* column 5 «3600 (ft-lb/ft-3yr) 8-110 puodjAsnp ‘AjIQ UDBDO 4D JSDAYJION WO1} SAADM — SSeUdaa{S SADA Ja,omdeeq 40 uolfouny D sp Absaug aADM 4O JUaUOdWOD a10YsbUO 7 ssajuoIsuaWwIq ‘9¢-g a4Nbl4 900'0 vooo 2000 90000 7000'0 z0000 pee HH | dt | l AAG OS ol Biel {tt UT i Rise ii t TATE PEEP EEE EEC Ee EEE EEE it 4 tt [TEESE im ae Ce HEY Het HH} J Baus eee Biewe 4 ' THT E ee i THTRTER TE REET EEE EEE EEE EEC ee tet EEC THOT rH HEH TEC {ih ttt tt - ' HE c -xoe0e HCCC IRE sates i a ed 2 aa aceet ORCUTT TUTE | mt a ey See 1 4 ala nue 5 al dials A ee qi Tht j i rT Poe fa INAS See nau nee THA efi eat 18 x ; oth oH ¢0! | Macaunane Ht rH aL ie | Gnainae tity Lat a a TE BSL } TTT rr nue Ree ee a mo] it ~ - IS Nasal scnene 3, | is s&s HEE EEE ilcaeel nase sieen = ode NOONE HAE bow i atalats | BASS | Buen tit | H t cOlxe it aa E a5 - 00 LN GL OY LAU TLGOG POOH TONG GO Tr ioe lal ih feat Hi i a 4 mshi tL HV L004 RRSNEENOG EEO DEM BHO oo inal gape ay ae i fi una OTT TT ere Coe SHUT UTEATE TT HTNGNEL i HAO B GB Se hi fal Th iM uit | i i nu i r (lil tt | aa EEC Hn TERE ECE TH a ET ses nueuees EEE 8 [Pace no: | Af2 of 133 | A, (tt/b/f}se¢) 10.04 Ho412.0 | BO0