U8, ABN Coad. at Res. Gh led. Rep, KEUR-C > REPAIR, EVALUATION, MAINTENANCE, AND Ezy REHABILITATION RESEARCH PROGRAM US Army Corps of Engineers TECHNICAL REPORT REMR-CO-7 METHODS TO REDUCE WAVE RUNUP AND OVERTOPPING OF EXISTING STRUCTURES by John P. Ahrens Coastal Engineering Research Center DEPARTMENT OF THE ARMY Waterways Experiment Station, Corps of Engineers PO Box 631, Vicksburg, Mississippi 39181-0631 October 1988 Final Report Approved For Public Release; Distribution Unlimited Prepared for DEPARTMENT OF THE ARMY US Army Corps of Engineers Washington, DC 20314-1000 Under Civil Works Research Unit 32328 The following two letters used as part of the number designating technical reports of research published under the Repair, Evaluation, Maintenance, and Rehabilitation (REMR) Research Program identify the problem area under which the report was prepared: Problem Area Problem Area Cs Concrete and Steel Structures EM Electrical and Mechanical GT Geotechnical El Environmental Impacts HY Hydraulics OM Operations Management co Coastal Destroy this report when no longer needed. Do not return it to the originator. The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. COVER PHOTOS: TOP — Rib cap on breakwater at Hilo, Hawaii. BOTTOM.— Waves overtopping seawall at Roughans Point, Mass. SECURITY CLASSIFICATION OF THIS PAGE Form Approved REPORT DOCUMENTATION PAGE OMB NONO7Z08 .O188 Exp. Date Jun 30, 1986 1a REPORT SECURITY CLASSIFICATION 1b. RESTRICTIVE MARKINGS Unclassified 2a, SECURITY CLASSIFICATION, AUTHORITY 3. DISTRIBUTION / AVAILABILITY OF REPORT Approved for public release; distribution 2b. DECLASSIFICATION / DOWNGRADING SCHEDULE unlimited. 4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5. MONITORING ORGANIZATION REPORT NUMBER(S) Technical Report REMR-CO-7 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL | 7a. NAME OF MONITORING ORGANIZATION USAEWES, Coastal Engineering (If applicable) Research Center 6c. ADDRESS (City, State, and ZIP Code) 7b. ADDRESS (City, State, and Z/P Code) PO Box 631 Vicksburg, MS 39181-0631 8a. NAME OF FUNDING / SPONSORING 8b. OFFICE SYMBOL | 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZATION (If applicable) US Army Corps of Engineers 8c. ADDRESS (City, State, and ZIP Code) 10. SOURCE OF FUNDING NUMBERS PROGRAM PROJECT TASK WORK UNIT ELEMENT NO. | NO NO ACCESSION NO Washington, DC 20314-1000 32328 11. TITLE (Include Security Classification) Methods to Reduce Wave Runup and Overtopping of Existing Structures 12. PERSONAL AUTHOR(S) Ahrens, John P. 13a. TYPE OF REPORT 13b. TIME COVERED 14. DATE OF REPORT (Year, Month, Day) |15. PAGE COUNT Final report From Sep 84 To Sep 86 October 1988 44 16. SUPPLEMENTARY NOTATION See reverse. 17 COSAT!I CODES 18. SUBJECT TERMS (Continue on reverse if necessary and identify by block number) GROUP SUB-GROUP Breakwaters Wave overtopping Revetments Wave runup Seawalls 19. ABSTRACT (Continue on reverse if necessary and identify by block number) Problems occurring on coastal structures related to wave runup and overtopping are identified and categorized. Three general problem areas include: wave runup and over- topping of breakwaters and jetties causing excessive wave action on the leeside, wave runup and overtopping of seawalls and bulkheads causing either flooding or erosion or both behind the structures, and wave runup and overtopping of revetments jeopardizing the integrity or possibly causing failure of the structure. A number of approaches to reducing wave runup and overtopping of coastal structures is presented. Plans to use laboratory model tests to quantify and refine the most promising approaches are discussed. 20. DISTRIBUTION / AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION Gd UNCLASSIFIED/UNLIMITED (J SAME AS RPT © otic users Unclassified 22a, NAME OF RESPONSIBLE» INDIVIDUAL 22b. TELEPHONE (Include Area Code) | 22c. OFFICE SYMBOL DD FORM 1473, 84 MAR 83 APR edition may ve used until exhausted SECLIRITY CLASSIFICATION OF THIS PAGE All other eaitions are obsolete Unclassified SECURITY CLASSIFICATION OF THIS PAGE 16. SUPPLEMENTARY NOTATION (Continued). A report of the Coastal problem area of the Repair, Evaluation, Maintenance, and Rehabili- tation (REMR) Research Program. Available from National Technical Information Service, 5285 Port Royal Road, Springfield, VA 22161. Unclassified SECURITY CLASSIFICATION OF THIS PAGE PREFACE This report was prepared as part of the Coastal Problem Area of the Repair, Evaluation, Maintenance, and Rehabilitation (REMR) Research Program. Initial work was conducted under Civil Works Research Work Unit 32328, "Tech- niques of Reducing Wave Runup and Overtopping on Coastal Structures." Mr. William F. McCleese, US Army Engineer Waterways Experiment Station (WES) was overall manager of the REMR Research Program. The REMR Coastal Problem Area Technical Monitor was Mr. John H. Lockhart, Jr., Office, Chief of Engineers (OCE), and WES Coastal Problem Area Leader was Mr. D. D. Davidson, Coastal Engineering Research Center (CERC). This work was conducted at WES during the period September 1984 to September 1986 under general supervision of Dr. James R. Houston and Mr. Charles C. Calhoun, Jr., Chief and Assistant Chief, respectively, CERC; and under direct supervision of Mr. C. E. Chatham, Jr., Chief, Wave Dynamics Division, and Mr. Davidson, Chief, Wave Research Branch (CW-R). Messrs. John P. Ahrens, Oceanographer, Dennis G. Markle, and Robert D. Carver, Lead Hydraulic Engineers, and various junior engineers and technicians of CW-R collected and organized information from Corps District offices which provided a significant contribution to this effort. This report was prepared by Mr. Ahrens, typed by Mrs. Myra Willis, Secretary, CW-R, and edited by Ms. Shirley A. J. Hanshaw, Information Technology Laboratory, Information Products Division, WES. Commander and Director of WES during report publication was COL Dwayne G. Lee, CE. Technical Director was Dr. Robert W. Whalin. PREFACE.. CONTENTS CONVERSION FACTORS, NON-SI TO SI (METRIC) UNIEES MO Ra MBA SUREMENT Severe rote veleretelle/sisie e) seve ecelel'srsi'ci'e)(sxeiiey;e1(a) clone) sie, evenel elles sieteieiae ere PART I: PART II: PART III: PN TRODUCTMON PR csaicveroheie/ciaiciatelcrcvelevois or elocaietarolelsheteveretsl etsy evolerelerenetencicte WAVE RUNUP AND OVERTOPPING OF BREAKWATERS AND JETTIES CAUSING EXCESSIVE WAVE ACTION ON THE LEE SIDE......cccceves WAVE RUNUP AND OVERTOPPING OF SEAWALLS, SEA DIKES, AND BULKHEADS CAUSING FLOODING AND/OR EROSION......cceeccees Methods to; Reduce Wave Overtopping sic A 0. 0) 2 4 6 8 10 INCIDENT Hmo, FT Figure 4. Transmitted wave heights versus incident wave height for reef breakwaters, in water depth of 20 ft, exposed to inci- dent wave spectrum with period of peak energy density of 8.0 sec 10 LEGEND O hc=144FT A, > 476 FT? 4 QO he= 156 FT Ay > 542 FT? O bc -168FT Ay, 612 FT? TRANSMITTED Hmo, FT INCIDENT Hino, FT Figure 5. Transmitted wave height versus incident wave height for reef breakwaters, in water depth of 12.0 ft, exposed to inci- dent wave spectrum with period of peak energy density of 8.0 sec | | LEGEND A D «3 . 4 Ay = 1127 FT? a QO 1-6 O A, = 1355 FT? o oO 1712 7 4 Az = 1810 FT? I 3 + . O TRANSMITTED Hmo, FT \\ C) > ol 0 2 4 a o °o INCIDENT Hmo, FT Figure 6. Transmitted wave heights versus incident wave height for reef breakwaters, in water depth of 20 ft, exposed to inci- dent wave spectrum with period of peak energy density of 8.0 sec 11 through the structure that the transmitted wave heights are slightly higher for the reef breakwater with 8,000-1b stone than the reef with 5,000-1b stone. This comparison illustrates that larger stones create larger void spaces which allows slightly higher transmission through the structure (all other factors being equal). When transmission is dominated by overtopping, the transmitted wave heights are about the same. 11. Figure 5 uses the reef transmission model with wave conditions and stone size the same as those in Figure 2 but with a water depth reduced from 20 to 12 ft and the crest heights of the reefs reduced in proportion to the water depths. Comparison of Figures 2 and 5 indicates that the wave trans- mission is slightly greater for a reef in a 12-ft water depth than it is fora reef in a 20-ft water depth because the cross-sectional area of the structure has been reduced more in changing from a water depth of 20 to 12 ft than the reduction in wave length. The cross-sectional area of the structure is im- portant both for transmission through the reef and for transmission by over- topping. A wider structure is more effective in reducing transmission than a narrower reef breakwater with the same height. Since it might be easier to rehabilitate a structure by increasing the width rather than by increasing the height to achieve a desired level of transmission, this approach is explored using the reef transmission model in Figure 6. Figure 6 has the same wave conditions and stone size as used for Figure 2, but in Figure 6 only one crest height of 24 ft is shown having three different cross-sectional areas. The various cross-sectional areas were obtained by using crest widths of 3, 6, and 12 stone diameters which give cross-sectional areas for the reef of 1,127, 13355; and 1810 pe respectively. In Figure 2 the reef with a crest height of 28 ft (the lowest transmission trend) has a cross-sectional area of 1,482 fed Comparison of Figures 2 and 6 shows that the reef with a height of 28 ft and a cross-sectional area of 1,482 ee allows less wave transmission than the reef with a crest height of 24 ft and a cross-sectional area of 1,810 ft. The comparison suggests that it is more effective to reduce trans- mission by repairing the reef's crest than increasing its width. Of course, other factors would have to be considered such as the relative difficulty of increasing the crest height versus increasing the cross-sectional area without increasing the crest height. 12. An example of the reef transmission model applied to an existing structure is furnished by the wave transmission occurring at Burns Harbor, 2 Indiana, on Lake Michigan. Burns Harbor frequently experiences greater than desirable wave action in the harbor. Transmission by overtopping has in- creased because of high lake levels in 1985 and 1986, and transmission through the structure appears to be high due to the large size of the stone used in the armor. Unless special placement of the armor is used, large armor stone leave large void spaces, allowing greater wave transmission through the break- water. Ahrens (1987) provides a quantitative relation for this occurrence. Figure 7 shows wave transmission caused by a storm at Burns Harbor and pre- dicted wave transmission using the reef breakwater transmission model. Fig- ure 8 shows wave action at the Burns Harbor breakwater generating transmitted waves in the harbor. Predicted transmission using the model is greater than the observed transmission since the reef transmission model was developed from physical model tests of very permeable rubble mounds with no core. However, the model follows the trend of the observed data quite well. 13. A physical method developed within the US Army Engineer Division, Pacific Ocean, to cope with crown stability and overtopping during heavy wave overtopping of rubble mounds is a ribbed concrete cap. Concrete armor units key into the ribs and improve the stability of the crest, and the presence of the ribs adds resistance to wave overtopping flow thereby reducing transmis- sion (Markle 1982 and Markle and Herrington 1983). Figure 9 shows the con- crete rib cap on the breakwater at Hilo, Hawaii. The reef transmission model is not applicable to concrete cap breakwaters without further experimental work. 14. Figures 2 through 7 give a rough idea of the value of a rather sim- ple wave transmission model which was developed from conceptual ideas and cal- ibrated and refined through the use of physical model tests. The reef trans- mission model makes it very easy to investigate the influence of a variety of variables on the transmitted wave height. Further, the model could be used to project how the deterioration of a rubble structure might affect wave trans- mission or how various rehabilitation concepts would improve the transmission characteristics of the structure. The reef transmission model was not in- tended as a rehabilitation tool, and many of the examples shown were using the model outside the range of calibration, i.e. outside the range of conditions of the laboratory tests. However, the model provides logical trends in Fig- ures 2 through 7, even outside the range of calibration, because of improved understanding of the wave transmission process (Ahrens 1987). In developing a 13 WAVE HEIGHT, FT LEGEND O INcIDENT & PREDICTED TRANS O ACTUAL TRANS 3 6 9 12 HOURS FROM DEC 23, 1985, @ 2350 Figure 7. Incident and transmitted wave heights Burns Harbor, Indiana Figure 8. Wave action against breakwater at Burns Harbor, Indiana, April 1986 14 15 Figure 9. Rib cap on breakwater at Hilo, Hawaii wave transmission model for REMR use, the reef transmission model will provide a logical starting point. There are numerous other approaches and models for wave transmission which can provide insight for improving the reef model and adapting it for REMR use. Some of the most important sources of additional information are Calhoun (1971), Goda (1969, 1985), Keulegan (1973), Madsen and White (1976), Sollitt and Cross (1976), Johnson, Fuchs, and Morison (1951), Thornton and Calhoun (1972), and Seelig (1980). The work of these investiga- tors and others to be identified should be coupled with proposed laboratory tests specifically oriented toward REMR objectives to provide improved guidance on methods to reduce wave transmission by overtopping. 15 PART III: WAVE RUNUP AND OVERTOPPING OF SEAWALLS, SEA DIKES, AND BULKHEADS CAUSING FLOODING AND/OR EROSION 15. The approach to be used in this section will be to build on the findings made during the recent model study of wave overtopping of the Roughans Point seawall and subsequent model tests of the Cape Hatteras and Virginia Beach seawalls, (Ahrens, Heimbaugh, and Davidson 1986). Other sources of information such as that by Douglass (1986), the extensive study of seawalls and sea dikes conducted at the Hydraulic Research Station, Wallingford, England, and research at the Port and Harbor Research Institute, Yokosuka, Japan, will be investigated. Important recent foreign references are Owen (1982a, 1982b) and Goda (1985). 16. Findings from the Roughans Point and Cape Hatteras seawall tests will be summarized here because they are a starting point for study of this general problem area, and they provide a conceptual framework for further progress in developing strategies for reducing wave overtopping of seawalls and related coastal structures. The primary purpose of the Roughans Point study was to conduct laboratory tests to determine the overtopping rates for various seawall/revetment configurations. This information will be used to develop a cost-effective plan to reduce flooding due to wave overtopping in the community of Roughans Point, Massachusetts (Hardy and Crawford 1986). Additional Cape Hatteras seawall tests were conducted to extend the findings made during the Roughans Point study to somewhat different seawall profiles, including severely recurved and vertical walls. One of the most important findings from the Roughans Point study was that all of the overtopping data for a revetment/seawall configuration could be consolidated into a single, well defined trend through the use of a new dimensionless freeboard parameter. This parameter seems to be effective even for test series that included several or more water levels and a wide range of irregular wave conditions. The new freeboard parameter F' is defined as follows: BS a (1) where 16 F = freeboard of the structure, h. - d, = crest height of the seawall = still-water depth at the toe of the wall or the toe of the revetment fronting the wall L_ = Airy wave length calculated using d. and ae H = incident zero moment wave height at or near the toe of the structure Equation 1 can be thought of as the ratio of the freeboard to the severity of the local incident wave conditions. 17. A very valuable characteristic of the freeboard parameter is that it combines a lot of information about the structure, water depth, and wave conditions into one variable. The parameter F' has higher correlation with the overtopping rate for the Roughans Point data than any other parameter which could be identified, including the parameter BAH. » suggested by the work of Goda (1969) and Seelig (1980) or the dimensionless freeboard parameter F/(T eH.) used by Owen (1982b), where qT, -is the zero-crossing wave period, g is the acceleration of gravity and, He is the significant wave height of the spectrum. Figure 10 shows a plot of the overtopping rate as a function of PROFILE VIEW OVERTOPPING RATE, Q, M3/M, SEC 0.25 0.35 0.45 0.55 0.65 0.75 RELATIVE FREEBOARD, F Figure 10. Overtopping rate versus relative freeboard for the Roughans Point seawall with no revetment (configuration RP-1) 17 F' for the existing seawall configuration at Roughans Point without a riprap revetment protecting the wall. Considering the complexity of the irregular wave overtopping process, the ability of F!' to consolidate the overtopping data into a well-defined trend is surprising. 18. A simple exponential model using F' was found to be very useful for evaluating the overtopping performance of a seawall/revetment configura- tion or for comparing the performance of two or more configurations. The model can be written = ' Q = Q, exp (C)F') (2) where o is a coefficient with the same units as the overtopping rate, i.e., volume per unit time per unit length of seawall crest, and C is a dimen- 1 sionless coefficient. Both oe and C are determined by the data for a 1 particular seawall/revetment configuration either by regression analysis or occasionally by subjective curve fitting, if that seems more appropriate. A regression curve fit to the data using Equation 2 is shown in Figure 10. Since a regression equation of the form of Equation 2 tends to reduce the in- fluence of the conditions with high overtopping rates, as compared to a linear equation, it was sometimes convenient to subjectively fit an equation of the form of Equation 2 to obtain a better fit to the data having high overtopping rates. In Figure 1l, a comparison is shown between a regression curve and a subjectively fit curve for a seawall with a 1.0-ft cap fronted by a revetment with a berm. In Figure 1l the nonregression curve fits the data with high overtopping rates better than the regression curve. For many configurations, the regression curves seem quite satisfactory, but for some cases, a nonre- gression curve provides a more conservative trend which would be preferable for design purposes. Possibly a more suitable approach would be to use an equation with the form of Equation 2 with a weight function proportional to either the overtopping rate or F' . In any event the form of Equation 2 fits the data well and is similar to the form used by Owen (1982b) in a study on irregular wave overtopping of sea dikes. Data trend curves of the form of Equation 2 provide a simple way to evaluate the effectiveness of various seawall/revetment configurations, i.e, the less area under the curve the more effective the configuration is at reducing overtopping. 19, The various seawall/revetment configurations discussed in this 18 ON" PROFILE VIEW oot 0.010 0.006 OVERTOPPING RATE, Q, M?/M, SEC OVERTOPPING RATE,Q,CFS/ET 0.002 PEGRESSION 0.02 0.0 0.0 5 Ore 0.3 0.34 0.38 0.42 0.46 0.5 0.54 0.58 0.62 RELATIVE FREEBOARD, F' Figure 11. Overtopping rate versus relative freeboard for the Roughans Point seawall fronted by a wave absorber revetment with a berm and a 1.0-ft cap on wall (configuration RP-7) report are listed in Table 1. Table 1 also gives the value of the overtopping coefficients used in Equation 2 and an overtopping rating coefficient for the configuration (to be discussed later). For the Roughans Point seawall tests the number in the designation is consistent with the configuration number given by Ahrens, Heimbaugh, and Davidson (1986). 20. Onshore winds can increase the overtopping rate by blowing spray over the seawall or by wind stress on the runup mass on sloped structures. If " the additional amount a seawall is being heavily overtopped by "green water, carried over the crest by wind effects is probably not important. However, the portion of overtopping contributed by wind can be expected to increase as the proportion of waves overtopping the wall decreases. The only quantitative guidance on wind effects is in the SPM (1984). A recent brief study* suggests en nee LUE EEE EEE IESE SESS * "Assessment of Wind Effects on Wave Overtopping of Proposed Virginia Beach Seawall,"' Memorandum from Donald T. Resio to Joan Pope, Coastal Engineering Research Center, US Army Engineer Waterways Experiment Station. 19 Table 1 Seawall Revetment Configurations and Coefficients a ee a Study Configuration No.* RP-1 RP-2 -RP-4 RP-7 RP-8 CH-1 CH-2 CH-3 Description Seawall with no fronting revetment Seawall fronted by a standard riprap revetment Seawall fronted by a wide berm, absorber revetment Seawall fronted by a wide berm, absorber revetment, cap on wall Seawall fronted by a wide berm, absorber revetment, double cap on wall Severely recurved wall with extensive toe protection Moderately recurved wall with extensive toe protection Vertical wall with extensive toe protection Hydraulic Overtopping Rank Coefficients Parameter Q. (cfs/ft) Cy A. (cfs/ft) 76.55 -14.08 0.0797 30.54 -13.43 0.0404 439.22 -21.62 0.0310 305.82 -23.07 0.0131 93.04 -22.15 0.0055 394.62 -20.68 0.0386 93.25 -14.75 0.0757 8.80 -6.33 0.2078 * RP indicates Roughans Point seawall (Ahrens, Heimbaugh, and Davidson 1986). CH indicates Cape Hatteras seawall (Grace and Carver 1985). 20 correction given in the SPM overestimates the amount of water carried over the wall by wind. Methods to Reduce Wave Overtopping Recurved walls 21. One method to reduce wave overtopping is to use a recurved wall instead of a vertical wall. The Roughans Point seawall is vertical with a small recurve at the crest. Observations indicate that the recurve is effec-— tive when the waves are small enough and the water depth at the wall great enough to allow a reasonably coherent standing wave system to be established. This system causes a vertical flow regime at the wall which is thrown seaward by the recurve (Figure 12). The recurve is not effective when the crest Figure 12. Wave overtopping the seawall at Roughans Point, Massachusetts height of the incident wave approaches the elevation of the crest of the sea- wall because the large, partial clapotis which forms for a moment in front of the wall then spills over in large volumes of "green" water literally inun- dating the seawall for a short time. 22. For the inundation mode it is difficult to envision how any surface feature of the wall could be very effective in reducing the overtopping rate. For tests conducted in the Roughans Point study, the inundation mode of over- topping occurred frequently when F' was less than 0.3. Thus, comparisons of 2a the data trends for F' less than 0.3 were not made and would probably not be meaningful. 23. Data analysis of the seawall/revetment configurations referred to as the Cape Hatteras types is in a preliminary stage. This test series in- cludes both vertical and recurved seawalls which have rather extensive revet- ment toe protection (Figure 13). Overtopping data trend curves of the form of Equation 2 are used in Figure 14 to compare the performance of the three Cape Hatteras seawall/revetment configurations. The poor performance of the verti- cal seawall compared to the walls with recurvature is clearly shown in Fig- ure 14. Figures 15 and 16 show laboratory tests of the Cape Hatteras seawalls with a typical curve and a vertical wall, respectively, that illustrate the considerable difference in wave action that can occur at the wall for dif- ferent structure geometries. It can be seen in Figure 14 that the wall with severe recurvature is somewhat better than the wall with more moderate re- curvature. In Figure 17, the overtopping trend curves for the Roughans Point seawall profile shown in Figure 10 are compared to those for the vertical wall Cape Hatteras profile shown in Figure 13. Figure 17 indicates that even a rather small recurve can be effective since the Roughans Point overtopping trend curve falls considerably below the corresponding curve for the vertical Cape Hatteras seawall configuration. Figures 14 and 17 illustrate the value of the overtopping model, defined by Equations 1 and 2, for evaluating the performance of a single configuration and for making comparisons between and among configurations. It should be noted that Equation 2 does not take into account water blown over the wall by onshore winds which are usually present during overtopping conditions. Therefore, a recurve which throws water sea- ward and possibly even downward will control windblown overtopping better than a vertical wall that throws the water straight upward. Figure 18 shows how energetic wave action can send large quantities of spray to impressive heights when waves encounter a steep barrier. Figure 18 was taken at Neach Bay, Washington, with long-period waves propagating shoreward from the Strait of Juan de Fuca and crashing against a riprap revetment with a slope of 1 on 2. Fronting rubble and revetments 24. A second method to reduce wave overtopping rates is to use rubble in front of the wall. The purpose of the rubble might be toe protection, but if enough rubble is used, the dissipation of wave energy will be sufficient to reduce wave overtopping. The extensive toe protection used for the 22 17,2’ 8.0" Figure 13. SEA SIDE a. Configuration designation CH-1l Cape Hatteras seawall configurations (Continued) 23 10.9° SEA SIDE 8.0° SIMULATED CUT-OFF WALL | b. Configuration designation CH-2 MATERIAL CHARACTERISTICS MODEL PROTOTYPE W, = 0.37-LB STAPODS AT 167 PCF W, = 0.86-TON STAPODS AT 150 PCF WwW, = 0,.71-LB STONE AT 165 PCF Wo = 1.6-TON STONE AT 165 PCF W3 = 0 28--LB STONE AT 165 PCF W, = 0.65-TON STONE AT 165 PCF W, = 0.01-LB STONE AT 165 PCF W, = 46-LB STONE AT 165 PCF SEA SIDE SIMULATED CUT-OFF WALL | c. Configuration designation CH-3 Figure 13. (Concluded) 24 OVERTOPPING RATE, Q, CFS/FT L—f a es 0.42 0.46 a RELATIVE FREEBOARD, F’ Figure 14. Comparison of overtopping trend curves for the three Cape Hatteras seawall/revetment configurations (CH-1l, CH-2, and CH-3) Cape Hatteras seawall provides an illustration of the effectiveness of toe protection rubble in reducing overtopping of the wall. Figure 19 shows over- topping data for the Cape Hatteras profile with a vertical wall. A number of the data points fall conspicuously below the overtopping trend established by regression analysis. Analysis of the data indicates that these points are all associated with the lowest water level tested. Since the dimensionless free- board defined by Equation 1 takes the water level into consideration, data collected at all water levels should all follow the same trend in figures like Figure 19 unless there is a strong influence from another factor. Additional analysis indicates that when there is relatively shallow water over the rubble toe protection the rubble is quite effective in dissipating wave energy and reducing wave overtopping even when the wall is vertical. However, there appears to be a point when a small increase in water depth will make the toe protection rubble much less effective in reducing overtopping. This effect is demonstrated in Figure 19 where the data collected at the lowest water level 25 APEHATTERAS | SE AMAL STABILITY | STUDY MODEL SCALE 25 PLAN R482 WAVE ACTION Figure 15. Laboratory tests of wave action against a Cape Hatteras seawall with a moderate recurve Figure 16. Laboratory tests of wave action against a Cape Hatteras seawall, vertical configuration 26 OVERTOPPING RATE, Q, CFS/FT RELATIVE FREEBOARD, F’ Figure 17. Comparison of overtopping trend curves for the Roughans Point seawall with no revetment (configuration RP-1) and the Cape Hatteras vertical seawall (configuration CH-3) Storm wave action against a revetment at Nesh Bay, Washington, Nov 1948 Figure 18. 27 1 — apecenlae | | | a LEGEND 1.0 } = Eee | O OBSERVED DATA | ( sCOBSERVED DATA, LOWEST 0.9 WATER LEVEL DATA TREND 07 aja) | 06 See [ee 2 re | Neog | | ‘amiga ener ple inner OVERTOPPING RATE, Q, CFS/FT 0.4 -- —O ‘s B la Oo 03 : Ar oN a es i) a ih oO 8) . So ee = . ae beets etre Oo a : ee i p 7 aay AS Ya ra 7 NE. 5 a si oy Rh A “ { Ds un rn Vy EET Pt ie Oe FN ae ait " so ened Ey = aya wan oh ft Dt) Ut ene iy Maan a AY y es 5 > A on Y i { i 4 APPENDIX A: NOTATION Cross-sectional area of breakwater (ft) Water depth at toe of breakwater (ft) (Weo/m) 3 » typical dimension of the median stone (ft) Crest height of reef breakwater Zero-moment transmitted wave height (ft) Incident zero-moment wave height Airy wave length calculated using a and ae Ge) Wave period of peak energy density of spectrum (sec) Unit weight of stone (1b/£t>) Median stone weight, subscript indicates percent of total weight of gra- dation contributed by stones of lesser weight (1b) (h, - d,), freeboard of structure which for reef can be either positive or negative (ft) nd, » width of reef crest (ft) Crest width factor Zero-crossing wave period (sec) Significant wave height, average of the highest one-third of the waves (ft) Dimensionless freeboard, defined by Equation 1 Acceleration of gravity, 32.16 ft/see- Overtopping rate (cfs/ft) Overtopping coefficient (cfs/ft) Dimensionless overtopping coefficient Hydraulic rank parameter for seawall/revetment configurations (cfs/ft) Al ok i” et re ey Smeal? Sy ; Bie, Tae ” me y ay ae fu ie a My + oT Mage Lana ey nk " (ig He i Contd eas DE eRe IR ve Ay a hs pme 2 tok A av oa : Pr i mA oe } as Fe a ‘Ie ‘a ree): ‘ae i) at yee : KSEE Ne. WN i 7 e, Aas, Chal i> patie cts ay, en us *'9 AW Adie ee iJ wat, i Vy i chia a peg ony i pen nes 'g ae 438 oa ro. tty a a. e A art Not i nen ieee a ft id Pi. eee @. ce 4 yl ‘a : aA ane ape pet, bs ag ee a hs 7 4s ghee BP a are Sal : Lc ais aes Fr hi cei z es, . Tr i< rie i zs iC i = cre af A er i, ae furs a) if hl i Fs . wth A iM ay Mi (7 aX _ ee ’ ' Hh om: \ 5 id uP s , A ma Cn § —_. {Y¥. 4 | ue ale oa a