YloSo Arm
Coast. Eng Res. ST.

CETA 79-6

Estimation of Wave Transmission
Coefficients for Permeable Breakwaters

by
William N. Seelig

COASTAL ENGINEERING TECHNICAL AID NO. 79-6
OCTOBER 1979

Approved for public release;
distribution unlimited.

U.S. ARMY, CORPS OF ENGINEERS
~ COASTAL ENGINEERING
330 RESEARCH CENTER

Ne Kingman Building
. 49-6 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.

Limited free distribution within the United States of single copies of
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available from:

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Springfield, Virginia 22161

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.

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.

HAAN LUC

0 0301 0089715 3

UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

REPORT DOCUMENTATION PAGE FR Oo es

1. REPORT NUMBER 2. GOVT ACCESSION NO, 3. RECIPIENT'S CATALOG NUMBER
CETA 79-6

4. TITLE (and Subtitle) - TYPE OF REPORT & PERIOD COVERED

ESTIMATION OF WAVE TRANSMISSION COEFFICIENTS Coastal Engineering
FOR PERMEABLE BREAKWATERS Technical Aid

6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)
William N. Seelig

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK
AREA & WORK UNIT NUMBERS
Department of the Army
Coastal Engineering Research Center (CERRE-CS) F31538
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

14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of thie report)

UNCLASSIFIED

15a. DECLASSIFICATION/ DOWNGRADING
SCHEDULE

16. .DISTRIBUTION STATEMENT (of this Report)

Approved for public release; distribution unlimited.

DISTRIBUTION 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)

Permeable breakwaters
Transmission coefficients
Wave transmission

20. ABSTRACT (Continue om reverse side if necessary and identify by block number)
The Madsen and White (1976) analytical model of wave transmission through

permeable breakwaters is combined with a wave transmission by overtopping formula
to provide a method of predicting wave transmission coefficients for permeable
breakwaters. Comparison of this combined prediction technique with physical
model laboratory tests shows that the technique is useful for estimating trans-
mission coefficients for design. A computer program was found the most conven-
lent method of making predictions. The computer program and an example showing
program use are included in an Appendix.

DD ass 1473 Eprtion oF t Nov 6515 OBSOLETE UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

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PREFACE

This report describes methods for predicting wave transmission coef-
ficients for permeable breakwaters using a transmission by overtopping
equation together with the analytical model of Madsen and White (1976).
This technique has been tested with physical model results for nonbreak-
ing and some breaking waves, for monochromatic and irregular wave condi-
tions, and for riprap and some concrete armor unit breakwaters (Seelig,
in preparation, 1979). The technique was found to give useful predic-
tions of transmission coefficients for design. The work was carried out
under the offshore breakwaters for shore stabilization program of the
U.S. Army Coastal Engineering Research Center (CERC).

This 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.

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

CONTENTS

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

I INTRODUCTION .

II WAVE TRANSMISSION BY OVERTOPPING .
IEEE WAVE TRANSMISSION THROUGH PERMEABLE BREAKWATERS
IV EXAMPLE

APPENDIX LISTING OF THE COMPUTER PROGRAM MADSEN .

wn

TABLES
Porosity of various armor units
Kinematic viscosity of water .
Format of input information.
Sample input
Sample output

FIGURES

Definition of terms for wave transmission for permeable
breakwaters

Observed and predicted transmission coefficients for a
rubble-mound breakwater .

Example breakwater .

Information required for (horizontal layer) example breakwater .

Page

10

17

14

16

15

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:

Multiply by To obtain
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 TONS TAD Ome 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!

’ Ifo 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.

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ESTIMATION OF WAVE TRANSMISSION COEFFICIENTS
FOR PERMEABLE BREAKWATERS

by
William N. Seeltg

I. INTRODUCTION

The primary purpose of a breakwater is to reduce wave energy in an
area to be sheltered. One of the important characteristics of a break-
water is the maynitude of the wave transmission coefficient, defined as
the ratio of the transmitted wave height to the incident wave height.

Two basic types of wave transmission are: (a) by overtopping that
occurs when wave runup exceeds the crest elevation of the breakwater,
overtops the breakwater, and generates waves in the lee; and (b) through
a permeable structure that occurs because some of the wave energy is not
dissipated by the breakwater and is transmitted through the breakwater.
The total wave transmission coefficient, Kp, is given by:

Kp =4/(Kro)2 + (Kpe)2 = Hp/Hy (1)
where
Sg = transmission by overtopping coefficient
Kp- = coefficient of transmission through the structure
H; = incident wave height
lp = transmitted wave height

These and other symbols are defined in Figure 1.

Since the prediction method is complex, particularly for transmission
through the structure, a computer program is presented in an Appendix to
this report. The program incorporates the analytical model to determine

Kp~_ by Madsen and White (1976)! and an empirical equation to Cee CHULLNE
Kno developed by Seelig (in preparation, 1979)2.

IMADSEN, O.S., and WHITE, S.M., "Reflection and Transmission Character-
istics of Porous Rubble-Mound Breakwaters,'' MR 76-5, U.S. Army, Corps of
Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., Mar.
1976.

2SEELIG, W.N., "Two-Dimensional Tests of Wave Transmission and Reflec-
tion of Laboratory Breakwaters,"' U.S. Army, Corps of Engineers, Coastal
Engineering Research Center, Fort Belvoir, Va. (in preparation, 1979).

7
Z
Z
a
pea
KR A ~N
eG | KTo
te B R
Hy ——_
LA
Ao
<< Permeable

Kp =/(Ko)2 + (Kpe)2 = Hy/ty

Figure 1. Definition of terms for wave transmission
for permeable breakwaters.

II. WAVE TRANSMISSION BY OVERTOPPING

Wave transmission by overtopping occurs when wave energy is trans-
mitted by flow over the top of a structure. The transmission by over-
topping coefficient can be estimated using (Seelig, in preparation,
1979)?:

Kg = le BYAN) (2)
= 0 for F/R greater than 1.0
where
R = wave runup
F = breakwater freeboard, defined as the structure
height, h, minus the water depth, d.
C = an empirical coefficient
(Kp )max eH lic (0)

Laboratory tests show that the value of C is related to the crest width
of the structure, B:

Gy=FORS1L9= OR By ihe (3)

Thus, a slight decrease in the transmission by overtopping occurs as the
structure crest width increases.

3SEELIG, W.N., op. cit., p. 7.

Wave runup is estimated using the formula (Ahrens and McCartney,
1975)":

Reree, ag
Hy ~ 1 + be (%)

where a = 0.692 and b = 0.504 are recommended for rubble-mound break-
waters and a = 0.988 and b = 0.703 are recommended for a breakwater
armored with two layers of dolos. &€ is the surf parameter given by

tan _ 0 (5)

where 9 is the angle of the seaward face of the breakwater, and Lp is
the deepwater wavelength obtained from linear wave theory. Calculations
of wave transmission by overtopping are performed automatically in the
program MADSEN (see App.).

III. WAVE TRANSMISSION THROUGH PERMEABLE BREAKWATERS

The coefficient of wave transmission through permeable breakwaters,
Kpe, is estimated using the analytical model of Madsen and White
(1976)5. In this model the transmission coefficient is related to a
complex function of the size and porosity of the materials used in
building the breakwater (Table 1), the breakwater geometry, the seaward

Table 1. Porosity of various armor units (after U.S.
Army, Corps of Engineers, Coastal Engineer-
ing Research Center, 1977)§.

ee haces
layers__|_Placement__| _ Po.

Armor unit

Quarrystone(smooth) 2 random 0

Quarrystone (rough) 2 random 0.37
Quarrystone (rough) 3 random 0.40
Cube (modified) 2 random 0.47
Tetrapod 2 random 0.50
Quadripod 2 random 0.49
Hexapod 2 random 0.47
Tribar 2 random 0.54
Dolos 2 random 0.63
Tribar il uniform 0.

Quarrystone random 0.

4 AHRENS, J., and McCARTNEY, B.L., "Wave Period Effect on the Stability of
Riprap,' Proceedings of Civil Engineering in the Oceans/III, June 1975, pp.
1019-1034 (also Reprint 76-2, U.S. Army, Corps of Engineers, Coastal Engi-
neering Research Center, Fort Belvoir, Va., June 1976, NTIS A029 739.

SMADSIEN, OS, einch Weirme, Seles Os Cilio, Do 75

6U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER,
Shore Protection Manual, 3d ed., Vols. I, II, and III, Stock No. 008-022-
00077-1, U.S. Government Printing Office, Washington, D.C., 1977.

slope of the structure, water depth, wave height and period, and the
kinematic viscosity of water (Table 2). To use this method, waves
should have

d We AS
L <a (6)

VHy cot2 6
where L is local wavelength.

Table 2. Kinematic viscosity of water.
Water temperature Kinematic viscosity of water

(2C) Gels)
0° 0.0000018
10° 0.000001
20° 0.0000010
30° 0.0000008

The Madsen and White model was tested against laboratory data for
permeable breakwaters (Seelig, in preparation, 1979)7 and was shown to
give useful estimates for both monochromatic and irregular waves. For
irregular wave conditions, the wave input to the program should be the
mean wave height and period of peak energy density. A few tests with
breaking waves suggest that the prediction method can also be used with
breaking waves. The Madsen and White model appears to effectively
account for breaking wave energy losses, although it does not explicitly
include breaking. Tests of breakwaters armored with dolos units suggest
that the program can also be used for artificial armor units. Compari-
son with laboratory data shows that the model gives the best predictions
for shallow-water waves. Predictions of transmission coefficients tend
to be conservative for transitional or deepwater waves. Refer to Seelig
(in preparation, 1979)7 or Madsen and White (1976)5 for more information.
Figure 2 shows a comparison between wave transmission coefficients ob-
served in a laboratory model and predicted using the methods described
iil Els CVA,

IV. EXAMPLE

Use of the computer program (MADSEN) in the Appendix can best be
illustrated by an example. The format of required input information is
given in Table 3. Any number of breakwater geometries, water depths or
wave conditions can be analyzed in a single run. The first 53 cards are
a standard deck of look-up (input) tables (see Table A-1); card type 1
provides the number of breakwater configurations or water depths to
analyze. Card types 2 to 6 give required input information for each
breakwater of interest; however, a separate set of these card types is
required when the breakwater geometry or water depth is changed.

7SEEDLGH NENG RODE Cleanup ery.
“MADSEN, 0.S., and WHITE, S.M., op. cit., p. 7.

10

0.0065< a <0.055

| 3 ft
Auge) 5 0.00009< +~-<o0.014
7 b gt?

B/h = 0.43

|.00

Observed = Predicted

0.80

0.60

0.40

7 (predicted using this CETA )

K
O
ho
(e)

O 0.20 0.40 0.60 0.80 1.00
K+ (observed in the laboratory)

Figure 2. Observed and predicted transmission coer-
ficients for a rubble-mound breakwater.

Ik

Table 3. Format of input information.

Description

53 standard input cards

Number of breakwater configura-
tions or water depths to test
20A4 Title card
312,4X, 7F10.5 Number of wave conditions to test

Number of materials
Number of horizontal layers
Structure height (m)

Water depth (m)

Kinematic viscosity (m2/s)
Width of top of breakwater (m)

Front slope of breakwater = tan
(8)

Wave runup parameter a

0.692
Wave runup parameter b = 0.504

10x, 2F10.5
(1 card per material)

Material diameter (m) (armor ist)
Material porosity

10x,7F10.5
(1 card per hori-
zontal layer)

Layer thickness (m)

Mean length of each material type
in the layer (put in consecutive
order; e.g., material 1 (armor)
Ist, etc.)

2F10.5
(wave condition card;
one card per wave
condition)

Wave period (s)

Wave heights (m)

Repeat card types 2 to 6 for each water depth or breakwater configura-
tion to be tested.

Card type 3 gives the number of wave conditions to analyze and sum-
Marizes general input information (Table 3). For the example breakwater
(Fig. 3), 18 wave conditions with periods of 5, 10, and 20 seconds and
with heights that range from 0.1 to 2.0 meters, are analyzed.

Card type 4 gives material characteristics, one card per material
and the first card should describe the armor material. The example
gives three materials (armor, underlayer, and core); diameter and poros-

ity of the materials are shown in Figure 3.

7

Card type 5 is used to input the mean horizontal length of various
materials in various horizontal layers of the breakwater. A new hori-
zontal layer occurs when there is a change vertically in material type
or slope and the layer next to the seabed should be designated as "layer

number 1."'

In the case of the example breakwater, three horizontal layers

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13

are shown in Figure 4. Sample horizontal length calculations are also
included. Note that when determining horizontal lengths of the armor
material, the outer layer of the armor on the seaward side of the break-
water should be "removed'' first because dissipation of the seaward face
is determined in a separate part of the computer program.

Table 4 gives the computer program input information required for the
example; Table 5 is the resulting program output. The output shows that
predicted transmitted wave height for this example is a complex function
of incident wave height and period.

Table 4. Sample input.

{
EXAMPLE PROBLEM

U3) 3 B 609 4.6 00090093 2,%$2 0,667 020692 02504
MAT { 00729 0.37
MAT 2 00338 0.37
MAT 3% 02092 0.37
LAY 1 3.55 4.93 3,80 6040
LAY 2 @o7A 4.23 2.654 0.0
LAY 3 6.47 5,25 0.0 020
D050) Ool

560 005

5.9 1.0

AG) 425

560 eur5

5.0 2.0

10,9 ‘Oven!

10,0 065

10.0 1.0

10,0 105

19,0 ov

10,0 220

20,0 Oel

20,9 029

20,0 1.0

20,9 7)

20,0 1075

20,9 220

V. SUMMARY

A computer program is presented for estimation of wave transmission
coefficients for permeable breakwaters. Extensive testing of the program
with laboratory data has shown that the program can be used to estimate
transmission coefficients for monochromatic or irregular waves and for
rubble-mound or other types of permeable breakwaters. A limited amount
of testing suggests that it can also be used for breaking and nonbreaking
waves.

A copy of the card deck and more extensive program documentation for
the computer program MADSEN (CERC Program Number 752X6RICPO) are avail-
able from the ADP Coordinator at CERC. The cost of running the program
on a CDC 6600 computer is only a few cents for each wave condition of
interest.

14

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Table 5. Sample output.

EXAMPLE PROBLEM

COMPUTATIONS OF WAVE TRANSMISSION THROUGH A POROUS BREAKWATER

NUM OF wAVE CONDITIONS 18
NUM OF MAYTERTALSS 3
NUM QF HORIZONTIAL LAYERS=s a}
STRUCTURE HETGHT (M)s 6.000
WATER OEPTR (Mj 4,800
KINEMATIC VISCOSITY (M2/SEC)=E ,000000930
BW TOP wIDTH (M)3 2.520
TANB OF FRONT SLUPES 06670

RUNUP COEFFICIENTS A= (692 BS Su
MATERIAL CHARACTERISTICS (MakK& ARMOR MATERIAL NUMBER 3)

MATERTA4L& 1 OTAMEYER (Hye ,729 PORNSITYS .370
MATERTALS 2 OTAMETER (M9B 33H PORNSITYS ,370
MATERTALS S$ OTAMETER (498 092 POROSITYS .370

RORITZONTIAL LAYER CHARACTERISTICS
(MAKE LaYER NEXT TO SEABED LAYER NUMRER 1)

; MATERTALa =| 2
HORIZONTIAL LAVERS 1 THFCHNESS (M9s 3.550 LENGTHS (M)za 4.5 308
HORJZONTIAL LAYERS 2 THYCHNESS (M)yz 4780 LENGTHS (M)3 4.5 205
RORIZONTIAL LAYERs 3 THYCHNESS (M)z 470 LENGTHS (M)s 503 0.0
HO¢M) T(SEC) H/(GST¥P) H/L D/(GST*Ts) KTT KTO KT
0100 5.90 0000498 000335 00196 391 0.070 591
e500 §.00 0902041 001074 00196 e214 0,000 ell
1.000 §.90 000402 003349 00196 0149 0.000 2149
10500 5.00 0006322 005023 09196 4129 ,036 ,134
107530 5.90 0007143 005866 09196 o324 .0R6 148
22000 5200 60081635 006697 09196 4113 6125 4168
0100 19.00 e000lne 0090154 000489 «64397 0,000 ,397
0500 10.90 0900540 000753 00049) «©4199 0.000 199
1.000 10200 0901090 001507 09049 135 0,000 135
10590 10.40 0001551 202260 00049 2099 3455 yiSe
12730 10200 0901786 002637 00049 088 159 ,182
2,000 10.00 0002041 003013 ©0049 ,080 193 ,209
0190 29200 0000096 oN007TS% 00012 0379 0.000 2379
0500 29.00 00001298 000367 00032 4184 9,070 .184
12000 20200 6009285 009735 OWONG G85" sOd@ —4ieo
10500 20200 e0003A3 o01192 00012 0096 0154 218e
10750 20000 0000446 001286 00012 2086 196 ,e14
2.000 20000 0000540 201476 00012 080 .2A7 24)
© WAVE TRANSMISSION THROUGH THE STRUCTURE
ew WAVE TRANSMISSION BY nNVFRTUPPING COEFFICIENT
2 TOTAL WAVE TRANSMISSION COEFFICIENT
© WAVE REFLECTION COEFFICIENT
© TRANSMITTED WAVE HEIGHT

16

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028
027
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062
064
064
064
093
066
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APPENDIX

LISTING OF THE COMPUTER PROGRAM MADSEN

PROGRAM MANSENCTMPUT, UUTPUT, TAPESSTNPUT) TAPEGSOUTPUT, TAPE 8)
COMMONSMALST SNM NLOVC LID eNC HA) oLL tied ido TH(11)

COMMUN/SSEELSNKL OFS

REAL NEL

DIMENSION THE CZ yo TITLE (CA0) oNtUM(10)

REAL Lodtlgk Te KRoNolt oNQolL Lo KTNeKTT

DATA NUMSJ eee SeYe D0 FT yp Oe FOILS

PI=3.141599

CALL READ)

REAN( 0590) NCOMP

FORMAT $Tee 4X oe 7F 1009)

Ou 20g I1..55 encour

D TNPUT [Mr ORMATTON

REANCS e171) CTITLEC JIM) 0 TIME1, 00)

FORMAT(20AY4)

WRITE (69172) CTITLECIIM) o JUME4 920)

FORMATO IHL 19Xeen Ad)

REAU(5eS9U) NTo MMe NLohSeHUg NU, TOPW, TANR Gg RAGRB

Fek5en(!

TFCRA,LE.0,) RAEN Ade

TFCRB LE.0,) KBs, 504

WRITE (69971) NT ghMohlL eHSeHOohlieTOPwe TANHe RAG RB

FORMAT(/ cL 0xetfUMPUTATIONS OF Wave TRANSMISSTON THROUGH «a PORONS
BREAKWATER @//fedkKe INUM OF HAVE CUNDITIUNS eo feXel se /05Xo
eR UNUM OF MATERIAL Sze) TreT3e4eSXo

* tNUM MF HORTZUNTIAL LAYERSS!eAXoTSe/e5Xe' STRUCTURE HETGHT (™)
Hole heb MDa eo SX_g MATER NE PIH (Mysto AXKok 100 50/99XKe

BUKINEMATIC vTSCoslty (Mes5FC)s!oF 11 o%e 7o5XetBw TOP WIDTH (M)yety
HLOXeF 1M Se/oSKel TANG UF FRONT SLOPES Te Pot Be4oseSXe!RUNUP COEFF ICI
WENTS S854 eFO, $0! B10 6,3)

00 99 J=io11

NO 98 Jetoid

LLCIsJI=E0-

CONTINUE

WRITE (50283)

FORMAT( SX, (MATERTAL CHARACTERISTICS (MAKE ARMOR MATERTAL NIIMBER 14)
B1e/)

OO 6 1S1eN™¥

READ(507) NCJ) eNC1)

FORMAT( LOX. TFIN,S)

WRITE (60177) Tel ( IT) eN(7)

FORMAT(SXe MATERIALS! oT Se! DIAMETER (M)ZIoF 6530! POROSTTY=E! ef 603)

CONTI Ue

WRITE COePBU) CNUMC IM) o PAE) Oo NM)

FORMATO/S/o Ske (HORT ZUNT TAL LAYER CHARACTERISTICS! o/05Xo

wICMAKE LAYER NEXT TU SFAREFNM LAYER NUMBER J) toe

& Sexo MATERTALS VeTl TVG SX)osob3xnebl1es4xdo/)

00 38 JeseNt

REAU(5¢7) THE J) ce (LLCTo yo eTElon™)

WRITE (G01 7TA) JeTHC J) o (th Cleod)o*&4_Nh)

FORMAT(SX¢ IHORIZONTIAL LAVERSt91%_,! THICHNESS (M)B'_y F630! LENGTH

IL

33

Qua

22

#S (Male Ge lle 7esOXeTF eat)

CONTINUE

NMONMe |

NONM) SNC 1)

N(NM)=0,01

NLENLe1

THEINL)S1M90N0000,

LLONM oe ML ISR, #901)

WRITE (6094?)

FORMAT(/7/¢ oxe'H(M) TOSEG) HACGHTET) HAL D/(GETET/) KTT
KTO KT KR hTehyty

NN 199 TKsyeNnT

REAIX(S5¢8) Tot

FURMAT(C2F 10,5)

ASHE .S

MREDC{) FOS

TF CAL TeX eNVHO1) GO TL {ng

TECTANK, LEO.) GO TO 37

CALL PEFL(AGHSe DET) eo HUSTANBgT RIT,» RUeL)

AJ=RII¥A

DHT=2,#KURA

TFL aG=0

C ASSUME DMEEDHT aN) ITERATE ON THE FQUITLIVANT BW

10

37

9B,
1009
199

ICNOUNTE0

DHE SDH T

TCOUNTHICOUNTSHS

CALL EX bBACNHE DHT oLE oH Ne HS oe TANReNReDRe TUPW)
CALL INTER(VRe Ty LE OHO eal eNUGDROTIGRItLo lFLAG)
TFCTFLAG EQ, 1) NREDRED 45

TRIOURINEIG GEAR ne Ginn Ole)

DHES(y,tRLyeRT Twa

IFC ICOUNT.LIT,4) GO 10 40

KRoRTEk TT

KTTsTye¥kT1

TFCTANB LE LOL) CALL INTERCN( 4) op Ty TOP MH Ag NUGN(1) KTVT eKRol oe IFLAG)
TEC IFLAG,EN,1) DREDK*0.S

IFC IFLAG,EQ,1) GA TU 37

SURFSTANB/SURTCHs/CL SoweT*T))
RHERAASURF/( 4, +RKRESURE Y

RSkeRH

FR=F/R

CE0,51 "0e11*TOPW/HS

KTOSCK(1.eFR)

TF OCCTOP WHS) (GT MBB AND GE LT 0.) KTUSCH(L mFRIRM (1 HO, FC) FER
TECK OR GT eM M=

IFCFR,GI1,1,0) KTNSN,

HGT2=A*2,/(9, 89" THT)

HL =2,#4/L

NGT25HOs(9,4O* THT)

FLAG= 5+

KT=SQRT(KTT##204KTUFEO)

TRCKT,G1,1,0) KT=1,0)

Hy] ene T

WRITE (66984) He ToHGTP oth (NGT2AgKTT KIO KT eKRo HT
FURMATC SKeFh a deh IV eCVF IDG OeF IL OeSeF 10 oy SFO, Ser Once 743)
CONTINUE

CONTINUE

WRITE (60201)

18

204 FORMATO //o2xKetKTT © WAVE THANSMISSTON THROUGH THE STRUCTURE I O74
B2XetKTO = WAVE TRANS“ISSTON RY OVERTOPPING COEFFICIENT! o So
& 2XeIKT = TOTAL WAVE TRANSMISSION COEFFICIENT Ie soens
k YKR © wAVE REFLECTION COEFFICIENT! 0
O/e2XetHT © TRANSMITTED WAVE HEIGHT!)
200 CONTINUE
STOP
END
SUBROUTINE REFILL C Ae MSel’g te TANBo Te @TLoRilol )
COMMONSEADSZEST(Q0NS) PRUT(COet {I oRTCL of Lat KC 9910) RX (9910)
DIMENSTUN ESSCV1)oKUS(II)okSC41)
REAL tetSleLlS
C och & MODEL CURRECTION FACTUR TO ACCOUNT FOR MODFL SLOPE EFFECTS
CFSpeeB=0e57AFTANB
JECTANR LT C,H) CREEL e0A
TFC TANE,GI 0,68) CFE0 AW
C FIND WAVE LENGTH L
HOLOEHOs OL SAST#ET)
CALL LESGTCHOL Oe KUL)
LE4U/HROL
LSSHO/sTANH
IF (HS LT.) LSSHS/IANR
LSLELSSL
TRCLSt eb T29,8) GO TO 1nd
TMINSSORT (A, PASE(LS/008)/(% AF TANH( GeeRS#HO/S(LS/0,8))))
WRITE (6Oe10$) TYIN
104 FURMATOS// 61 Xe 'WARNINGSTHE MINTIUM #AVE PERIOD TO BE ANALYZED RY T
KHIS PROGRAM TStekOece! SEC FOUR THIS CONDITION!)
LSL=E9,799
19s TECLSL FIN +1.)
C INTERPOLATE ITVPUT TARLE FUR THIS LSL VALUE
TIELSL¥CO +1,
NO 3 Jetted
FSSC J)SFST (Ted tC STC late J oF STC e JI IFILSLe(C191)*0,1)709,1
RUS(CJYERUTC Ee Jt CRUTCT ole J eRUTCT JI IFCLSLECT=1)*F0,.11/0,3

3 RSCJIVERTCI Te J @CRICT 14g s J) eRICTI eS) RC LSU CL IES1) 02.05) /0.05

C GUESS PHI AND TTFRATE
PHI=5,0
Men

6 JaPHI
FACECALOG(PHT ed ,)eALUG(J41 6.) )/CAl OG (JH20)eALOG(JH1.))
FS=FSS(Je1)¢ FACHE(FSSCI42)eF SSCJ41))
RUSKUS(J+1)¢ FAC#(RIS(CJ42) eRUISCI+HL))

RITERS( Its ye (RSC Jee )erRsS( Jel) FF AC
ARGED CUE(N/HO) FHV eCH (RIK GFAS(CHMHTANB) 440, 5¢FS
PHINZ0 eS *FATAN( ANG) 57699578
MsM¢ 4
DELSABS(PHINePH])
TF(M.G1T,2e0) GO In 9
PHJSPHIN
TFCPHY.LT.9,01) PHI=0,01
TF CPHY].GT.9,99) PHILE9,99
TE(DELe&T.20.95) GU T0 4
9 RYTsRyYTscr
RETURN
END
SURRONTINE REANT
COMMON/JAALSSEST(Q011) oRUT(CFONF)VORTCL Tell) 9 TXC F910) REC S010)

LY)

177 FORMAT(3Kef7F4ee)
NO 1 MEielt

1 READ(Se177) (ESTO NOM) ONS1 99)
OO 2 MEiel)4

2 READ(Se177) (RUTOCNOM) NEI 99)
DO 3 MBle}1

3 READ(50177) (RTICN6™) oNehofd7)
DU 4 MEfetd

7) READC5e177) CTX(NOM) o%e1 09)
00 5 ME{edo

5 READ(S0177) ORX(Ne MN) oN2de 9)
RE TURAN
END

SUBROUTINE LENGT( DLOenk)
REAL LLelLUNEwel on
LOZ, e0/VLU
LONE. O/NLO
Noi
PJ3$.44159
i ARGS? ,0*PI1/LO
LUNE 4SLON* TANR(C ARG)
NoN¢l
DIFFSARS(CLONFWePLDN)
TF(N#200) 3e4ed
3 IFCOIFFE0ennns) aeedd
5 LDE(LONE StL DIs2A.6 |
GU 10 |
4 DLEe1e0/L DEW
WRITE( 60100) DLO,VL
JO9 FURMAT (Gur SUBROUTINE LENGTH DTD NOT CONVERGE» D/LO = oF 10059
1 BRIDAL S oF10.5)
e DLEy,0/7LONEw
RETURN
END
SURROUTINE EGKBH(DHE PONTO LE CHO HS e TANR eG NRoDRe TOPHW)
COMMONSJHADSISNM ONL SUCL II ONO 14) 0 LOtdotieTH(11)
DIMENSION RETACT IS) 904(41)
REAL NeLeoLFaNr
NRE0.U35
BETARZ2e7TO1 ANY SONKAK SER)
one) el Joterm
ei BETACTIR2Z67FC} eMC TII/ONCT) *¥3*D07))
THIS0,
THPeSN,
DO 4 J=ile%L
THISTHI+TH( J)
NYL=J
DHCJJSTH( J) /H0
IF CTH ebT eH) D(C JIE Che THe) SHO
TF C144 .67T. HG} GO 10 S
4 THPSTHO+TH(J)
SUMA=0,
00 16 J=tsNYL
SUM{=EAN.
O00 17 Tate
17 SUMJFSSUMIFRETACT)SSETARFL (1 9J)

w

Ds)
=)

16 SUM2ESUMN2ONHE J) sOC99RT(CSUMy))
LESL eC SUNPEHEO)ENHE /DMT
RETURN
END
SUBROUTINE INTER Ne Toby MO Ag Ntle Mo TToRIoMLo IFLAG)
COMMON/SFEL JNKL oF S
COMMAN/MADSSEST (OTL CRUT(Fe tH ORTICI ToS 1) 9 TX09910) oRK( 9910)
MIMENSTUN THC{O) eKS(10)
REAL NKLeoLeNUgKOeLAMHVDA ON
SSS(N/0,45)¥%#0
KSA es ,18ISDsSHL
NKLSNaKO@L
BETASP,7E( 1 gan) S( NFR S5FH)
LAMBDA 15
P=),
RC=1706¢
Ics
rd FNSE
TC=1C4l
WEAESURTI CO, BOSHOYS (19+) AMBIA)
ROSUFH/NU
FENs(KOSL)ECSURTC Det (1. t¢ROSRD) (1G, FRE TARARL/( $,%3,14159*HN)))=1,)
LAMBDASKUSL F702, #1)
YECIC,GT.219) GO TO 5
TECCABRSCE NSE YF) oT eee) GO TN 2
) TIEde/(10%l AMHDA)
RI=LANBDAS CL +L ANKDA)
FSSF/SS
C WRITE (60597) FoF SoVeRD
397 FORMAT( COX IF oF Se UokKNS1o4E13,5)
TECNKL 667.9,9) IFLAG=}
TE CNKL oe bT.9,9) RETURN
TEFONKL LT. ,1) RETURN
TECES,GT.35,) FSE5%e
JahkKLe10,
Naira)
C INTERPOLATE MANSEN CURVES 39 ANN 3%
NO J MElo10
RSCMIERKC Te Mye (RKC IHL OMI eRX CSM) HENKEL =O e1#II/NGI
1 TS(MISTXC Te MVE CT XC StL emyeT XC Se MI VFCNML ON 1 KII0G 1
TECHS bt e1,9) TIZETS(V)sALUGIOCFSI*(TS(19)-TSCI))
TFCES bb e1. 0) RISRSCI)FALOGIO(C ES) #€CRSC 10) 2RST1))
TE CFS GE 6100.) TISTS(I0V F055 ,.2FS) S256
IF CFS, GE,19,) RIEKSCI0VECL H@RSCIO) FCF S910—) 7256
TECFS LE eL OUR SES. GE 19,0) RETURN
RISRS(T)+¢C RSC Ty eROCT I) ECALOGCES) <AlLUGCTSt ,)) s(ALOGC 144.) 2ALOG(I*
*1,)) ;
TIZSTS(IIFCTSELTH1IETSCL)) &CALNGCFS)MALOG(T 41) ISCALOG(I HL e)eALUG(I*
*1.))
RETURN
END

Dk

OmMrADOWEwWwNM~

Table A-1.

085 83
085 .A3
085 283
28S 83
26S 83
285 ,&3
085 ,A3
o@5 88
eoAS 83
085 2&5
085 -A3

40091209
12001209
10001600
42091200
400010209
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1000 99
1009 099
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780 .66
267 299
058 QU!
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e485 . 30
041 o26
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033 22!
e511 15
029 417
ec5 240
235 652
e044 4,60
050 267
oe of!
Ato 67/8
063 0676
066 78
206A ,B0

Standard look-up tables t
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subroutine REDI. ee

0991259206192 0533,233,44h

ST ALG one T ORE ose ores
0901 89 ol hle29S,1N3,2AZ.70
090147201 ML e2eL, 945,973 ,40
0991 462 eNS2.142, 742,893,000
£991,451 ,9R2,032.502,502,60
1901.001,891,922.282,222,20
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15001 .2426032,492,6930283. $53,704.00
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10094 52?16852.1 6265120562 .632.732.80
10001 02010762.03261 420282322, 349,36
1000401916791 690169R2,042.042,021.97
10000019} 0611.78] e821 0821 .791.734 668
1.001 e1R 10541 .6810h714651 581,494.38
eNNL oI Ay oHAl -S7foS41 e471 373 271018
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1090101610371, 5hle 311018! .05 y
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