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CETA 80-7

Estimation of Wave Transmission Coefficients
for Overtopping of Impermeable Breakwaters

by
William N. Seelig

COASTAL ENGINEERING TECHNICAL AID NO. 80-7
DECEMBER 1980

WH ot |
DOCUMENT

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distribution unlimited.

U.S. ARMY, CORPS OF ENGINEERS
+c COASTAL ENGINEERING
ae RESEARCH CENTER

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Fort Belvoir, Va. 22060

Reprint or republication of any of this material
shall give appropriate credit to the U.S. Army Coastal
Engineering Research Center.

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Coastal Engineering
Technical Aid

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ESTIMATION OF WAVE TRANSMISSION COEFFICIENTS
FOR OVERTOPPING OF IMPERMEABLE BREAKWATERS

7. AUTHOR(s)

William N. Seelig

9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of the Army

Coastal Engineering Research Center (CERRE-CS)
Kingman Building, Fort Belvoir, Virginia 22060

10. PROGRAM ELEMENT, PROJECT, TASK
AREA & WORK UNIT NUMBERS

F31538

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Department of the Army
Coastal Engineering Research Center

Kingman Building, Fort Belvoir, Virginia 22060
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Approved for public release; distribution unlimited.

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18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary and identify by block number)

Breakwaters Wave runup
Impermeable breakwaters Wave transmission coefficients

Waves

20. ABSTRACT (Continue on reverses side ff necessary and identify by block number)

Methods are presented for estimating coefficients of wave transmission by
overtopping for smooth and rough impermeable breakwaters. These techniques can
be used for monochromatic or irregular wave conditions and for submerged break—
waters. Example problems are worked to illustrate calculations.

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PREFACE

This report describes methods for estimating wave transmission coefficients
for overtopping of impermeable breakwaters. It supplements Section 7.23 of the
Shore Protection Manual (SPM) and replaces the Coastal Design Memorandum No.
76-1 (Seelig, 1976). The methods presented can be used with smooth or rough
impermeable breakwaters and for irregular as well as monochromatic incident
waves. Laboratory tests show that the prediction methods give useful estimates
of transmission coefficients for submerged breakwaters. The work was carried
out under the offshore breakwaters for shore stabilization program of the U.S.
Army Coastal Engineering Research Center (CERC).

The report was prepared by William N. Seelig, Hydraulic Engineer, under
the general supervision of Dr. R.M. Sorensen, Chief, Coastal Processes and
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.

a

ED E. BISHOP
Colonel, Corps of Engineers
Commander and Director

CONTENTS

CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) .....

SNAMOSLO MES) /ANTD), IDISIOIONIEAILOINISS 55 6 6 G6 56 06 0 6 6 Oo oO oo
TUNE NOIDIUCIEIOW 5 56 6 6 6 6 0.0 6 6 6000.0 16 0 6.6'6 06 6 6
ESTIMATION OF TRANSMISSION COEFFICIENTS .......+4.-.
[DSIEIDMVATEIONN, OLY WA INDIO 6 5 6 5 6 600000 oOo
GAME IPNOWIDMNISS, 6 56 6.66 6 6 0606650 60.06.06 615,50 0 6

W GUMWARY 5 oo 6 6 6 0.0 0 6 0 0 6 6 6066100 8 6 6 0 6

TGINU RVING, GING 6 5 60 6 6 0060066000006 60 0
TABLES

Empirical wave runup prediction coefficients for smooth
TiMDeMOADLE SIRES 56 6 0000060000000 00 50066 0

Rough slope empirical runup coefficients for breakwaters with
LEADS: Coe eG So 5° 6 6% oo 6 6 36 6 6 oO ofa. 6S 6 oD 6 6

FIGURES
Wave transmission by overtopping of an impermeable breakwater

Predicted transmitted wave heights for Example 2. ......

Page

10

iL

11

CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) UNITS OF MEASUREMENT

U.S. customary units of-measurement used in this report can be converted to
metric (SI) units as follows:

Te

Multiply by To obtain
SS
inches 25.4 millimeters

2.54 centimeters
square inches 6.452 square centimeters
cubic inches 16.39 cubic centimeters
feet 30.48 centimeters
0.3048 meters
square feet 0.0929 square meters
cubic feet 0.0283 cubic meters
yards 0.9144 meters
square yards 0.836 square meters
cubic yards 0.7646 cubic meters
miles 1.6093 kilometers
square miles 259.0 hectares
knots 1.852 kilometers per hour
acres 0.4047 hectares
foot-pounds 1.3558 newton meters
millibars 1.0197 x 1073 kilograms per square centimeter
ounces 28.35 grams
pounds 453.6 grams
0.4536 kilograms
ton, long 1.0160 metric tons
ton, short 0.9072 metric tons
degrees (angle) 0.01745 radians
Fahrenheit degrees 5/9 Celsius degrees or Kelvins!

mr

1To obtain Celsius (C) temperature readings from Fahrenheit (F) readings,

use formula: C = (5/9) (F -32).

To obtain Kelvin (K) readings, use formula: K = (5/9) (F -32) + 273.15.

SYMBOLS AND DEFINITIONS
empirical coefficients of runup on rough breakwaters
crest width of a breakwater
an empirical wave transmission by overtopping coefficient
empirical smooth slope runup coefficients
water depth at the toe of the structure
breakwater freeboard = h - dg
acceleration due to gravity
incident wave height; use the mean wave height for irregular waves
transmitted wave height
structure height
wave transmission by overtopping coefficient
wavelength
deepwater wavelength
wave runup
wave period; use the period of peak energy density for irregular waves
breakwater seaward face front slope angle

the surf similarity parameter = tan 9/V7H/L,

ESTIMATION OF WAVE TRANSMISSION COEFFICIENTS
FOR OVERTOPPING OF IMPERMEABLE BREAKWATERS

by
Willtam N. Seeltg

I. INTRODUCTION

When a wave strikes an impermeable breakwater, some of the water may over-
top the breakwater and produce regenerated waves. Section 7.233 of the Shore
Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering
Research Center, 1977) and Seelig (1976) give a method for estimating trans-
mission by overtopping coefficients for smooth, vertical-faced breakwaters
overtopped by monochromatic waves. Wave period effects are not considered.
This report presents a more general method of predicting transmission by over-
topping coefficients that includes the influence of structure slope (nonvertical
as well as vertical), crest width, roughness, wave period, and wave type (ir-
regular and monochromatic waves). The method is based on laboratory tests for
d/gT“ < 0.03, where d is the water depth, g is the acceleration due to
gravity, and T is the wave period. Figure 1 shows the case of transmission
for an impermeable breakwater and illustrates some of the terms used. Methods
described in this report apply to breakwaters with an impermeable surface, an
impermeable core, or an impermeable diaphragm to prevent wave transmission
through the structure.

impermeable

Ko. 4

Figure 1. Wave transmission by overtopping of an impermeable breakwater.
II. ESTIMATION OF TRANSMISSION COEFFICIENTS

Laboratory data show that the coefficient of wave transmission by over-
topping for an impermeable breakwater, Kto, can be predicted using (Seelig,

1980).
tae
To pee(2 7) (1)

where F/R is the ratio of the breakwater freeboard to wave runup suggested
by Cross and Sollitt (1971), and C is the empirical given by

y B
= 0.51 - 0.11 h (2)
where B is the structure crest width and h the structure height. Equation
(2) is valid for the range O < B/h < 3.2. Equation (1) slightly underpredicts
the transmission coefficient for submerged breakwaters with a 1 on 15 bottom
slope in front of the breakwater; a revised formula is suggested for those

cases:
F F
repeat une) eatetiemeay | (3)

IIL. ESTIMATION OF WAVE RUNUP

Values of wave runup on the structure are necessary to use equation (1).
If the runup exceeds the breakwater freeboard, transmission by overtopping will
occur. The recommended runup equation for smooth slopes is given by Franzius

(1965)
6G. wEl/al sp C )
L 2 3 (4)
R = AC, (0.123 x)

where

H or H, = incident wave height

L = wavelength

d = water depth

Ci» Co» and C, = empirical coefficients.

Values of the empirical coefficients dare given in Table 1. A linear interpo-
lation of these values is necessary to obtain coefficients for other slopes.

Table 1. Empirical wave runup prediction coefficients
for smooth impermeable slo

Vertical

iVvon 0s 5

on 1.0
on 1.5
on 2.25
on 3.0

The recommended equation for estimating runup on rough slope impermeable
breakwaters is given by Ahrens and McCartney (1975):

af Dye wtans6 (5)
Bs (ie) * = viii

8

where & is the surf parameter, 6 the angle of the seaward face of the break-
water, Lo the deepwater wavelength given from linear theory as

22
T (6)
aly = a

and a and b are empirical coefficients. Suggested values of a and b
are in Table 2.

Table 2. Rough slope empirical runup coefficients
for breakwaters with 1.25 < cot @ < 5.0.

[Armor type |

Peeemmeniaa |

o layers of rubble 6 To obtain
an upper
limit or
conservative
estimate of
runup and Kr

wo layers of dolos

For additional information on wave runup refer to Stoa (1978) and the SPM.

For irregular wave conditions use the mean wave height (approximately 0.63
times the significant wave height; Sec. 3.22 of the SPM) and the period of peak
energy density in equations (4), (5), and (6) (Seelig, 1980).

IV. EXAMPLE PROBLEMS
kK kK kK KK KR KK RK KX & EXAMPLE PROBLEM 1 * * *¥ * *¥ ® ¥ ¥ KK RK KR KK
GIVEN: A rough impermeable breakwater covered with two layers of rubble on a

1 on 3 slope. The structure height is 18 feet (5.49 meters), crest width is
12 feet (3.66 meters), and water depth is 15 feet (4.57 meters).

FIND: The transmitted wave height produced by overtopping for an incident wave
with a height of 9 feet (2.74 meters) and period of 11 seconds.

SOLUTION: From equation (5) the surf parameter is

@ = eee EL ae 083 7G,
VEER) 1S Gere)

Using the recommended rubble runup coefficients of a = 0.692 and b = 0.504
(Table 2), the predicted runup is:
BE / 2036922 - ( 0.692 x 2.77
R me = \ Segre a 7) 9 = 7.2 feet (2.2 meters)
The breakwater freeboard, F, ish = Gla dis} — Sy Sel eecie (GEHL mStar)
From equation (2), C = 0.51 - 0.11 B/h = 0.51 - 0.11 (12/18) = 0.44 and from
equation (1), the transmission coefficient is:

9

a |

07 o(1- ) = 0.44 (2 - 555) = 0.257

The transmitted wave height is:

Ht = Kto Hy = 0.257 (9) = 2.3 feet (0.71 meter)
kkk kK kK RK KK & KK & & EXAMPLE PROBLEM 2 * & ¥ ¥ KK RR KKK KK KK
GIVEN: A vertical, smooth-faced impermeable breakwater with a crest width of
~ 12.0 feet (3.7 meters), a structure height of 16.0 feet (4.9 meters), and a

water depth of 11.2 feet (3.4 meters) as shown in Figure 2(a).

FIND: Transmitted wave height for an incident monochromatic wave with a period
of 12.0 seconds and height of 6.0 feet (1.8 meters).

SOLUTION: From equation (4) the runup is

(0.228 V6/11.2 + 0.0578)
224-1) = 8.1 feet (2.5 meters)

LING 6. 958) (0. 123 -— 1

From equation (2)

12ROR\n
= 0.51 - 0.11 aIGROW La 0.43

and the breakwater freeboard is
F=h -dg = 16.0 - 11.2 = 4.8 feet (1.5 meters)

From equation (1) the transmission by overtopping coefficient is

4 @ (2 z ) SOs G - 48) _ = OM98

and the transmitted wave height is

He = Kjo H = 0.175 x 6.0 = 1.0 foot (0.32 meter)

Figure 2(b) shows how the predicted transmitted wave height varies as a func-
tion of incident wave height and period for this example breakwater.

V. SUMMARY

Methods of predicting transmission coefficients of impermeable breakwaters
show that the magnitude of the transmission coefficients is a function of the
breakwater freeboard, incident wave height and period, water depth, and struc-
ture slope, crest width and roughness. Calculations may be performed manually
or with the FORTRAN computer program OVER (Program No. 752XRICYO) available
from the CERC ADP Coordinator, U.S. Army Coastal Engineering Research Center,
Fort Belvoir, Virginia 22060.

incident waves
<+—

a. Profile view of conditions for Example 2.

0.8

20
12
0.6
4
mi ‘
cay 0.4 T(s
0.2
0
1.0 1.5 2.0 2.5

Hy (m)

b. Predicted transmitted wave heights.

Figure 2. Predicted transmitted wave heights for Example 2.

LITERATURE CITED

AHRENS, J.P., and McCARTNEY, B.L., "Wave Period Effect on the Stability of Rip-
rap,'' Proceedings of Civil Engineering in the Oceans/III, American Society
of Civil Engineers, 1975, pp. 1019-1034 (also Reprint 76-2, U.S. Army, Corps
of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., NTIS
A029 726).

CROSS, R.H., and SOLLITT, C.K., "Wave Transmission by Overtopping,'' Technical
Note No. 15, Massachusetts Institute of Technology, Ralph M. Parsons Labora-
tory, Cambridge, Mass., July 1971.

FRANZIUS, L., "Wirkung und Wirtschaftlichkeit von Rauhdeckwerken im Hinblick
auf den Wellenauflauf,"' Mitteilungen des Franzius-Iinstituts fur Grund- und
Wasserbau der TH Hannover, Heft 25, 1965, pp. 149-268.

SEELIG, W.N., "A Simplified Method for Determining Vertical Breakwater Crest
Elevation Considering Wave Height Transmitted by Overtopping," CDM 76-1,
U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort
Belvoir, Va., May 1976. :

SEELIG, W.N., "Two Dimensional Tests of Wave Transmission and Reflection
Characteristics of Laboratory Breakwaters,'’ TR 80-1, U.S. Army, Corps of

Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., June
1980.

STOA, P.N., “Reanalysis of Wave Runup on Structures and Beaches," TP 78-2, U.S.
Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir,
WElog Mewes IG)7isc

U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Pro-
teetton Manual, 3d ed., Vols. I, II, and III, Stock No. 008-022-00113-1,
Government Printing Office, Washington, D.C., 1977, 1,262 pp.

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