U.S. Arey Coast. Ging Res. Ctr CDM 76-1 A Simplified Method for Determining Vertical Breakwater Crest Elevation Considering Wave Height Transmitted by Overtopping by William N. Seelig COASTAL DESIGN MEMORANDUM NO. 76-1 MAY 1976 ‘Doc SUMENY \ COLLECTION Approved for public release; distribution unlimited. U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING et RESEARCH CENTER 555 Kingman Building ,5SH Fort Belvoir, Va. 22060 1976 Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: National Technical Information Service ATTN: Operations Division 5285 Port Royal Road Springfield, Virginia 22151 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. INN 0 i q iii QO 030) ANN UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE BEROREICONDE EE 1. REPORT NUMBER 2. GOVT ACCESSION NO] 3. RECIPIENT'S CATALOG NUMBER CDM 76-1 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED A SIMPLIFIED METHOD FOR DETERMINING VERTICAL Coastal Design Memorandum BREAKWATER CREST ELEVATION CONSIDERING WAVE HEIGHT TRANSMITTED BY OVERTOPPING 7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s) 6. PERFORMING ORG. REPORT NUMBER William N. Seelig 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. RO Ga EN AEM eaes TASK Department of the Army Coastal Engineering Research Center (CERRE-CS) E 31229 Kingman Building, Fort Belvoir, Virginia 22060 11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Coastal Engineering Research Center 13. NUMBER OF PAGES Kingman Building, Fort Belvoir, Virginia 22060 16 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report) UNCLASSTFIED 15a, DECL ASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. - BISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) . SUPPLEMENTARY NOTES - KEY WORDS (Continue on reverse side if necessary and identify by block number) Crest elevation Wave regeneration Vertical breakwater design Wave transmission Wave overtopping ABSTRACT (Continue on reverse side if necesaary and identify by block number) A method is presented for the design of vertical-faced breakwaters for wave transmission by overtopping based on laboratory experiments of Goda, Takeda, and Moriya (1967) and Goda (1969). A step-by-step procedure is outlined, design curves are presented, and examples worked to illustrate the procedure. DD , tes 1473 EDITION OF | NOV 65S OBSOLETE UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) PREFACE This memorandum describes a method for determining the crest height of vertical-faced breakwaters considering allowable wave regeneration by overtopping. It is based on laboratory work and data analysis reported by Goda, Takeda, and Moriya (1967) and Goda (1969). The work was carried out under the coastal structures program of the U.S. Army Coastal Engi- neering Research Center (CERC). The technical guidelines presented in this memorandum are intended to augment the procedures described in the ''Shore Protection Manual" (SPM), Section 7.23, 'Wave Transmission" (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1975); the discussion in the SPM is limited to thin and wide submerged impermeable breakwaters and broad-crested, permeable rubble-mound breakwaters. The memorandum was prepared by William N. Seelig, Research Hydraulic Engineer, Coastal Structures Branch, under the general supervision of Dr. R.M. Sorensen, Chief, Coastal Structures Branch. Comments on this publication are invited. Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963. JAMES L. TRAYE Colonel, Corps of Engineers Commander and Director CONTENTS SYMBOLS AND DEFINITIONS . INTRODUCTION BREAKWATER CREST HEIGHTS SAMPLE DESIGN PROBLEMS SUMMARY . FIGURES Definition of terms and symbols Freeboard for vertical-wall and vertical thin-wall breakwaters (dimensionless) Freeboard for composite breakwaters (dimensionless) Freeboard for vertical thin-wall breakwaters. Freeboard for vertical-wall breakwaters Freeboard for composite breakwaters Freeboard for composite breakwaters Freeboard for composite breakwaters Page 16 SYMBOLS AND DEFINITIONS crest width water depth (feet) water depth at the base of the vertical face of a composite structure incident wave height (feet) transmitted wave height (feet) freeboard (total height of structure - stillwater depth) (feet) incident wavelength (feet) wave period (seconds) dimensionless parameter dimensionless parameter A SIMPLIFIED METHOD FOR DETERMINING VERTICAL BREAKWATER CREST ELEVATION CONSIDERING WAVE HEIGHT TRANSMITTED BY OVERTOPPING by William N. Seelig I. INTRODUCTION The function of a breakwater is to lower wave heights in an area to be protected, where the final design depends on the incident wave condi- tions, protection criteria, cost, and environmental considerations. Wave energy can be transmitted to the lee of a structure by regeneration of waves by wave overtopping of the structure, propagation through the structure if sufficiently porous, and diffraction through openings in the breakwater. This design memorandum discussed wave regeneration by overtopping for three types of vertical-faced impermeable breakwaters: vertical thin-wall breakwaters, vertical-wall breakwaters, and composite breakwaters (see Section 7.23 of the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1975)! for discussion of wave transmission). II. BREAKWATER CREST HEIGHTS Goda, Takeda, and Moriya (1967) 2 and Goda (1969) 3 performed extensive wave transmission by overtopping laboratory tests for a variety of struc- tures. They found that wave regeneration by overtupping for vertical- faced breakwaters is given by: Ht = 0.5 Hy a - sin sie + e)| } ; (1) where Hz is the average transmitted height (which will have different wave height and period characteristics than the incident wave), H; is the incident wave height (assumed to approach the structure normally), and (h - dg) is the breakwater crest height or freeboard above the local water level. 1y.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Protection Manual, 2d ed., Vols. I, II, and III, Stock No. 008-022- 00077, U.S. Government Printing Office, Washington, D.C., 1975, 1,160 pp. 2GODA, Y., TAKEDA, H., and MORIYA, Y., "Laboratory Investigation of Wave Transmission over Breakwaters,'' Report of the Port and Harbour Research Institute, No. 13, Apr. 1967. S@ODA, Mos "Reanalysis of Laboratory Data on Wave Transmission over Breakwaters,"' Report of the Port and Harbour Research Institute, Vol. 18, No. 3, Sept. 1969. The empirical coefficients, a and £8, are determined from labora- tory experiments for the three breakwater types for water depth to wave- length (d/L) ratios of 0.14 < d/L < 0.5. The definition of terms and symbols is shown in Figure 1. Note that the crest width, B, is approx- imately zero for the thin-wall breakwater, and B is approximately equal to the water depth for the other breakwaters. In most design situations the general incident wind-wave conditions are known and the desired wave conditions in the protected area are established; therefore the height of a structure of given form can be calculated. Rearranging equation (1) gives: (ni 2d) 2\ne E ee coin (a Se )| (2) which has been used to develop the design curves. Figures 2 and 3 are dimensionless plots of (h - d,)/H; versus H;/H;; Figures 4 to 8 are plots of equation (2) in English units. These curves can be used in several ways. If the incident height and transmitted height are given, the crest height can be determined. If the crest height is given and the incident height is known, transmitted height can be approximated. III. SAMPLE DESIGN PROBLEMS The following examples demonstrate the use of the techniques presented. Refer to the SPM (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1975)! for useful information in a total design problem (e.g., wave theory, a discussion of tides, storm surges, wave breaking). Bet Es Ea tat Mea es ote) ea eae a TOE ANY PPLE!) JONES MLA IN JL) eae, Sule ea Neel eR Ry ee See eee a GIVEN: Sie —Son0) teete ily — 4a Siseconds and Glens 1240) \skOOe. FIND: The freeboard, (h - d,), of a vertical thin-wall breakwater with Hei ele oe be cite SOLUTION: The design techniques in this memorandum apply to waves of 0.14 < d/L < 0.5; first, check the value of d/L as explained in the SPM, Section 2.231, and using the tables in Volume III (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, WS) + In this problem: GWibo = I2LO/(Sot2 8 QsSye)) SONNE 1y.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Oe Cilies g\ [io Ae Vertical Thin-Wall! Breakwater a=1.8 B=0.1 B=o Vertical-Wall Breakwater a=22 B=0.4 a5]. Betis | Composite Breakwater B~ds dwds=0.3 @=2.2 B=0.1 a Me iN >| Beds [|e dwds=0.5 a=2.2 B=0.25 dwds=O.7 a@=2.2) B=035 Patouase le Definition of terms and symbols. (h-ds) 3.50 3.00 2250 2.00 0.00 = {leS0) = 2109) Ac) 0) =), of OO), OFZO. O}SOPNOAOV 1550, OL6O8 (OFKONOLSOF OLS ORMIFOC Ht/ Hj; Figure 2. Freeboard for vertical-wall and vertical thin-wall breakwaters (dimensionless). Composite Breakwater B=ds aio dwg 3 a=2.2 B=0.| d d -!.50 - 2.00 -3.00 0.00 O10 Falounr eyes): S , 70.5 a=2.2 B=0.25 W=Oi7 Ja=22)15=0.35 0.20 030 040 050 060 070 080 O90 Hy/H; Freeboard for composite breakwaters (dimensionless). "(1°0 = 9 “8° = ») StoqeMYeOTG T[EM-UTY} TBITILOA IOF pIeOgeery ‘p oansty (4) HH 000! 00'6 00'8 OO0'L 00'9 00'S 00'v OO'E O00? 00"! 00'0 ClO G 000 00? OO0'8 OOO! 10 00°01 Ss p/p) siozemyeoig a3tsodwod Toy pireoqessy (4) 'H ‘Qg omnsTy 002 00'8 Ooo0! 12 o 4 oO a \)° © + p 'd 72) a. = oO e) (e) 1) : . Ay . fe) a4 a0) 5 aN ee ° na) WN o o a) an Oo : oO ™ — o) Na =) te¥)) “d jag or oO 12) or si or CW = OfuSay\s therefore, the technique applies. Second, check that the wave has not broken, or that H;/L < 0.143 tanh 2 1 d/L. In this problem: H/L = 5.0/77.56 < 0.143 (0.7497) 0.0644 < 0.1072 ; therefore, the incident wave has not broken before reaching the structure. Using Figure 2 (curve 1) or Figure 4 the freeboard, (h - d,), is determined as 1.75 feet. Go te CP CR Ca EP EP EP EP TENGAMIDIR JDO BIASING SSP SS a ED a Ra, ES es a ta te SP) Es GIVEN: H = 5.0 feet, T = 4.5 seconds, and dg = 12.0 feet. FIND: The freeboard of a vertical breakwater which has a crest width approximately equal to the water depth (B = dg) with H¢ = 0.5 foot. SOLUTION: The d/L and H/L conditions of this problem fall into the required ranges (see problem 1). From Figure 2 (curve 2) or Figure 5 the freeboard is determined as 4.3 feet. G3) Sg CR EE ES eee SS ee es TON IDIGIS | UNOS! SS RR Rete Ke RO RG ES he So ES td ed kd kg GIVEN na oi10 feet hi- 4h) seconds), -andide ys TZ 0p tect R FIND: The transmitted wave height, H;, of a vertical breakwater (B with the crest height at the water level, (h - dg) = 0. d,) SOLUTION: From Figures 2 (curve 2) and 5 the transmitted height is deter- mined as 2.3 feet. cD Go eb SER LF RH a RP ER EP ee ee TENOR ILI: IPI ONEN BIN! Ul Se co tol eS SO re eo ee ee eo Ed Eo tS GIVEN: The conditions in problem 2. FIND: The freeboard for a composite breakwater, (h - ds), for dy/dg = 0.5, with H¢ = 0.5 foot. SOLUTION: The d/L and H/L conditions of this problem fall into the required ranges (see problem 1). From Figure 2 (curve 4) or Figure 7 Ene On = Ge) =] SoS weSres * *e * Kk * kK KK * * * *F KF EXAMPLE PROBLEM 5 * * * * * * * *¥ & *® * * K GIVEN: The conditions in problem 2. FIND: The transmitted height for a submerged thin-wall breakwater with (h - dg) = -1.0 foot. SOLUTION: Figure 2 (curve 1) or Figure 4 are used to find H; = 2.8 feet. Co) Sk Ton Bor EPS CeCe CH tS Se eS Ee PES CAEP OE ES So SP EF EP EP ee EP SS IV. SUMMARY The results of Goda, Takeda, and Moriya (1967) 2 and Goda (1969) 3 are used to design breakwaters for wave transmission by overtopping. To illustrate the transmission by different types of breakwaters, consider the case where the freeboard is equal to one-half the incident wave height: (h - ds)/Hij = 0.5. The predicted dimensionless transmitted height is: BREAKWATER TYPE He/Hi Vertical thin wall 0.25 Vertical By=id- 0.20 Composite dy/dg = 0.3 0.30 Composite d,,/dg = 0.5 0.25 Composite d,,/d, = 0.7 0.21 For this condition, the vertical breakwater with a width approximately equal to the depth gives the smallest transmitted wave height; a composite structure gives the largest predicted transmitted wave. 2GODA, TAKEDA, and MORIYA, op. cit., p. 5. 3GODA, op. cit, p. 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