yi
/ | Ww HO! NS TR 80-1

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\ CO L E CTION y. ‘ ” ;
Two-Dimensional Tests of Wave Transmission
and Reflection Characteristics of

Laboratory Breakwaters

by
William N. Seelig

TECHNICAL REPORT NO. 80-1
JUNE 1980

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

Kingman Building
Fort Belvoir, Va. 22060

o2"3a

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 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.

LNW

O 0301 0090098 1

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REPORT DOCUMENTATION PAGE SaaS Gane ee

1. REPORT NUMBER 2. GOVT ACCESSION NO|| 3. RECIPIENT'S CATALOG NUMBER
TR 80-1

4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED

TWO-DIMENSIONAL TESTS OF WAVE TRANSMISSION
AND REFLECTION CHARACTERISTICS OF
LABORATORY BREAKWATERS

Technical Report

6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(e)

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
CONTROLLING OFFICE NAME AND ADDRESS
Department of the Army

Coastal Engineering Research Center
Kingman Building, Fort Belvoir, Virginia 22060
14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office)

10. PROGRAM ELEMENT, PROSE CMG TASK
AREA & WORK UNIT NUM RS

F31538

12. REPORT DATE
June 1980
NUMBER OF PAGES
187

1S. SECURITY CLASS. (of thie report)

11.

UNCLASSIFIED

1Sa. DECLASSIFICATION/ DOWNGRADING
SCHEDULE

Approved for public release; distribution unlimited.

16. DISTRIBUTION STATEMENT (of this Report)

17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report)

18. SUPPLEMENTARY NOTES

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

Breakwaters Wave transmission
Wave reflection Wave transmission coefficients
Waves

ABSTRACT (Continue an reverse sides if necessary and identify by block number)
Monochromatic and irregular wave transmission and reflection measurements
were made for various subaerial and submerged breakwater cross sections.
These two-dimensional laboratory tests included smooth impermeable breakwaters,
rubble-mound breakwaters, and breakwaters armored with dolos units. Wave
transmission by overtopping was found to be related to breakwater freeboard
wave runup, and breakwater crest width; a method of estimating transmission by
overtopping coefficients is presented. The Madsen and White (1976) numerical
(continued)

20,

FORM
DD Jans 1473. Epition oF 1 Nov 65 1s OBSOLETE

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procedure was found to be an important tool for predicting the amount of trans-
mission through permeable breakwaters. Suggested procedures for estimating
transmission coefficients have been incorporated into the computer programs OVER
and MADSEN (included as appendixes) and these programs may be used to predict

wave transmission coefficients for nonbreaking, breaking, monochromatic, and
irregular wave conditions:

2 UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)

PREFACE

This report presents the results of research conducted to develop methods
for estimating wave transmission past submerged, subaerial, permeable, and
impermeable breakwaters. The final prediction techniques are given in the
form of computer programs, and the laboratory data used to develop and test
the methods are included in appendixes to this report. These methods supple-
ment Section 7.23 of the Shore Protection Manual (SPM). 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. J. Ahrens and M. Titus provided a significant contribu-
tion to this report by their many useful suggestions and valuable laboratory
assistance.

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

III

IV

VI

VII

APPENDIX
A

B

C

D

CONTENTS

Page
CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI). ....... 8
SYMBOLS (AND) DERUNTTTONSH i. (3) saat ieeMiethns Lice. cuacakl + akin aera anne aie 9
INTRODUCTION +4 yeas grade so? wegen AMSA a ee ble: Fabel
LITERATURE) RE ViIE Wey Besse ie; \hideh eittanesl ad | et) ec (Se ep ert Gt en ce
LABORATORY DE SIDING iia pci 2 la ily Me Sou Rene ee Ain aL yall a Teepe a Uti 11.5
Is Laboratory TEStsSCUpy 4 fecis rom lc Cee everett ceca Las ae ae LES
26 WMerelvoxels wore (Gemencetea yer WENES 5 od bilo o o 6 6 6 0 ob 6 6 6 ID
3. Data Collection... PURSUE DS RAN FPS Nest MH LAs Mt tlie Aa ia, alin
4. Data Reduction Methods. pel Nal oan rahe 8 a aaa eli RN ee iytl eS
Si UBReAKWaters TeStEdi. eves. le) el eileen ber Peace Soll tae ae pene Seren 240)
Ge TES MEONATEDON'S 0.62 ey cesses ceellameelb sy Rien Uskaen TN Sametcaiee tas: can 0 te men ec?)
Tra) ROSEMRES ULC S aires: raion celle i itela aero eee) Ieper ihe Sea ees ae eA
ANALYSIS OF TEST RESULTS ... . 3 Welee Mey te 2 12d

1. Wave Transmission and Rotilestion Rom Inperneable
Breakwaters. .. Sh! Shatner 212

2. Wave Transmission aad Replcetion! Rare oameabile.

Breakwatersiaii iy sy ra Ve ae) US es the: Ue AAS ot anne re SO)
MODEL SCALE EFFECTS. ... . stildeing. lie eee Ui SIS)
1. Causes of Physical Model ‘Sexi (BRtoets. Seto ihe a) felt aimee meet os O18

2. Interpreting and Applying Bar aan. Results 30
Prototype Conditions .. . Nit Gat ue hh Oi To fs ee Uae tut O18
EXAMPLE OF ESTIMATING WAVE TRANSMISSION COEFFICIENTS ...... 60
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS. ........... «262
SEN Sheva oO UHH EIS) Dokoumonacw oman aciorictio ors Hawn eads.o (a+ oslo lo.o. 6 oo vloae
BREAKWATER: 'GEOMBTRUES i jot ay jess cee Nolen ele Sime cnlitol ea coull/ay ret) ces AUER rem OY,
MATERDAL: CHARACTERTSEUCS i 4 hk, 25. LIN elena cen Caplets, a a 0
REST RESULES ((SINUSOLDATBEADE MOMLON) I pie ee ee See een O)
TEST RESULTS a (ERRE GUEARSWAVIE'S)) een eee ined tire OS)
WEST RESUIERS Ma (GRAPHIC AT sR ORM) ements re)
DOCUMENTATION OF THE PROGRAM OVER ............. =. ~. 169
DOCUMENTATION OF THE COMPUTER PROGRAM MADSEN ......... . 175

4

14

CONTENTS --Continued
TABLES
Range of conditions tested with monochromatic and irregular waves.

Empirical wave runup prediction coefficients for smooth impermeable
slopes. ape ;

Wave runup prediction coefficients using the Ahrens and McCartney
(1975) method .

Effect of relative depth on prediction of Ky.
Porosity of various armor units.

FIGURES
Plan view of wave tank

Determination of incident and reflected waves using the method of
Goda and Suzuki (1976).

The spectral peakedness, Q» for various spectral shapes
Sample incident laboratory wave spectra.

Sample laboratory wave records showing various levels of wave
grouping.

Percent of incident wave energy at the period of wave generator blade
motion for sinusoidal wave generator blade motion .

Definition of terms for wave transmission by overtopping .

Wave reflection coefficients and fraction of wave energy dissipated
for a 1 on 1.5 smooth slope with no wave transmission .

Wave reflection coefficients for a breakwater with zero freeboard
compared to a similar structure with no overtopping .

Wave transmission and reflection coefficients for a smooth impermeable
breakwater.

Wave runup on riprap

Wave runup prediction for rough structures using the Ahrens and
McCartney (1975) method .

Wave transmission coefficients for smooth impermeable breakwaters
with 1 on 1.5 slopes.

Wave transmission coefficients for vertical, smooth impermeable
breakwaters using Goda's (1969) data. o 6

Page
AM

26

28

44

50

14

15
KY

18

WY)

20

22

23

23

25

Du,

28

29

30

15

16

17

18

19

20

21

22

2S)

24

25

26

27

28

29

30

31

32
33
34

CONTENTS
FIGURES --Continued

The effect of the relative structure width on wave transmission of
impermeable breakwaters

Wave transmission coefficients for BW14.

Wave transmission coefficients for a breakwater tested by Saville
(1963) with B/h = 0.88.

Wave transmission coefficients for a breakwater tested by Saville
(1963) with B/h = 3.2

Observed and predicted coefficients of wave transmission by
overtopping

Percent of wave energy at the forcing wave period for wave
transmission by overtopping of a smooth impermeable structure

Sample incident, reflected, and transmitted wave spectra .

Spectral peakedness of incident, reflected, and transmitted wave
spectra .

Zero up-crossing analysis.

Transmitted versus incident wave height distributions for a
breakwater with d,/h = 0.8.

Transmitted versus incident wave height distributions for a
breakwater with d/h Ss iO.

Sample incident and transmitted joint distributions of wave height
and period.

Definition of terms for wave transmission for permeable breakwaters.

Wave transmission and reflection coefficients for BW3.

Sample observed and predicted reflection coefficients for permeable
subaerial breakwaters .

Wave transmission coefficients for a subaerial and a submerged
breakwater.

Observed and predicted transmission coefficients for BW3 .

Observed and predicted transmission coefficients for BW12.
Observed and predicted transmission coefficients for BW4 .

Observed and predicted transmission coefficients for breaking and
nonbreaking conditions.

Page
Bz

32
33
33
34

34

36

37

37
38
38

39
40

41
41

42
45

45
46

46

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

CONTENTS
FIGURES--Continued

Observed and predicted transmission coefficients for a breakwater
with dolos armor units.

Wave transmission past a siete ree breakwater with tribar
armor units ; oO 6 Oro OO

Observed and predicted transmission coefficients for BW16.

Example of the influence of porosity on the predicted coefficient of
transmission for a rubble-mound breakwater.

The relative importance of transmission by overtopping as a function
of the incident wave height and the water depth-to-structure
height ratio.

Observed and predicted transmission coefficients for submerged
permeable structures assuming Kp, = 0

Percent of wave energy at the forcing period for waves transmitted
past a permeable breakwater

Sample incident, reflected, and transmitted wave spectra for BW16.

Spectral peakedness of transmitted and reflected wave spectra versus
incident spectral peakedness for a permeable breakwater

Comparison between incident and transmitted wave height distribution
for a permeable breakwater.

Autocorrelation of zero up-crossing wave heights for transmitted and
incident wave records for a permeable breakwater.

Sample joint distributions of wave height and period for an
irregular wave condition and a permeable breakwater .

Trapezoidal multilayered breakwater tested by Sollitt and Cross
(1976).

Physical model results and correction factors determined from the
analytical model of Madsen and White (1976)

Breakwater cross sections used in the example for estimating wave
transmission coefficients

Predicted wave transmission coefficients

Predicted transmitted wave height as a function of breakwater crest
height.

Page

47

48

49

Sil

51

52

53

54

54

55

57

57/

59

59

60

61

61

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 1,Oloy % 10-2 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!

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

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

SYMBOLS AND DEFINITIONS
material identifier
spectral coefficients
spectral coefficients
empirical rough-slope runup coefficient
incident wave amplitude at a spectral line
reflected wave amplitude at a spectral line
breakwater top width
spectral coefficients
spectral coefficients
empirical rough-slope runup coefficient
transmission by overtopping coefficient
empirical wave runup on smooth-slope coefficients
empirical wave runup on smooth-slope coefficients

empirical wave runup on smooth-slope coefficients

physical model correction factor = (Kp) prototype/(K74) model

water depth

water depth at toe of a structure
median material diameter
breakwater freeboard = h - d,
wave frequency = 1/T

acceleration due to gravity
incident wave height

reflected wave height
root-mean-square (rms) wave height
Significant wave height
transmitted wave height

mean wave height

a 10-digit identification code (year, month, day, hour, minute)

assigned to each data collection run

spectral line number

SYMBOLS AND DEFINITIONS--Continued

Teflectionscoethicrene
my ctl ne 2 2
transmission coefficient Pe + Kot

wave transmission by overtopping coefficient
coefficient of wave transmission through a permeable breakwater
wave number = 27/L

wavelength

deepwater wavelength

material porosity

probability

spectral-peakedness parameter

incident spectral-peakedness parameter
reflected spectral-peakedness parameter
transmitted spectral-peakedness parameter
wave runup

autocorrelation of wave heights
correlation of wave heights and periods
wave period

period of peak energy density

median weight of material

specific weight

band width

gage spacing

root-mean-square water level

angle of seaward face of a breakwater

kinematic viscosity of water

surf parameter = (tan o/ VH/L, )

autocorrelation of zero up-crossing wave heights
e for incident waves

® for transmitted waves

TWO-DIMENSIONAL TESTS OF WAVE TRANSMISSION AND REFLECTION
CHARACTERISTICS OF LABORATORY BREAKWATERS

by
Willtam WN. Seeltg

I. INTRODUCTION

The primary function of a breakwater is to reduce wave heights in an area
being sheltered. Breakwaters are primarily used to protect harbors from
excessive wave action, to prevent beach erosion, and to trap sediment for
mechanical bypassing at an inlet or harbor entrance. A secondary use of
breakwater design is to reduce the wave reflection from the structure.
Reflected waves combined with incident waves can produce undesirable water
motions that may be a nuisance to navigation or encourage scour at the toe of
a structure.

Since the cost of building breakwaters is generally high, methods are
needed to estimate transmitted and reflected wave heights to enable comparison
of alternative structure designs. This report presents suggested methods for
predicting transmission and reflection characteristics of breakwaters based on
laboratory experiments, including the work of previous investigators. These
methods supplement Section 7.23 of the Shore Protection Manual (SPM) (U.S.
Army, Corps of Engineers, Coastal Engineering Research Center, 1977). The
basic types of breakwaters considered are permeable and impermeable structures
with crest elevations above the stillwater level (subaerial) and below the
stillwater level (submerged). The other factors investigated include wave
height, period, breakwater cross-section design, and material characteristics.
Both monochromatic and irregular waves were tested.

Section II of this report presents a brief review of research conducted
by previous investigators. Section III describes the laboratory setup and
procedures; Sections IV, V, and VI present data analysis methods and definitions.
The conditions tested are summarized in Section VII. Detailed descriptions of
the breakwaters tested and materials used are given in Appendixes A and B;
summary tables and figures of laboratory results are presented in Appendixes
CAD ewandmET.

Laboratory results are used in this study to develop a method for predicting
wave transmission by overtopping coefficients using the ratio of breakwater
freeboard to wave runup (suggested by Cross and Sollitt, 1971) and the break-
water crest width (suggested by Saville, 1963). The wave transmission by
overtopping prediction method is then combined with the model of wave trans-
mission through permeable structures of Madsen and White (1976) and this
combination package is verified with the laboratory results over a wide range
of conditions. Prediction methods are summarized in the computer programs
OVER and MADSEN (Apps. F and G). An example breakwater design is worked with
the aid of the two computer programs to illustrate how the prediction methods
can be used to compare alternative breakwater designs, and to illustrate the
importance of various design parameters.

II. LITERATURE REVIEW

_ Some of the important sources of ideas and data used in preparing this
report are summarized below in chronological order.

11

Saville (1963) tested a large number of similar rough structures with a
1 on 2 front-face slope for a proposed breakwater at Point Loma, California.
Most of Saville's breakwater models had a crest elevation near the stillwater
level, so wave transmission in most of the tests was primarily due to overtop-
ping. Some of the breakwaters tested were first modeled in the large wave tank
at the Coastal Engineering Research Center (CERC), then re-tested at a smaller
scale to examine scale effects. Some tests were repeated with otherwise
identical permeable and impermeable breakwaters to assess the influence of
wave transmission through the permeable breakwaters and wave transmission by
overtopping. The breakwater crest width was also varied over a wide range of
values to determine the influence of width on the wave transmission coefficient.
Since wave reflection coefficients were not measured, the burst method was used
during testing to avoid laboratory effects caused by re-reflection of waves
from the generator blade.

Lamarre (1967) measured wave transmission by overtopping for a structure
with a comparatively narrow crest width and 1 on 1.5 structure slopes. Wave
conditions and the height of the structure were varied.

Goda (1969) tested vertical, smooth impermeable structures for wave
transmission by overtopping. The breakwater crest width was varied and a
wide range of submerged and subaerial structure heights and a number of wave
conditions were tested. Wave reflection coefficients were measured to deter-
mine the incident wave height acting on the structure. A nonlinear empirical
equation was developed for predicting wave transmission coefficients. In this
formula the transmission coefficient is a function of the ratio of the break-
water freeboard to the incident wave height and two empirical coefficients,
where the coefficients are related to structure geometry and the relative
water depth.

Davidson (1969) tested a 1 on 40 scale model of a breakwater proposed for
Monterey Harbor, California. The breakwater had tribar armor units and
experienced a combination of wave transmission over and through the structure.

Cross and Sollitt (1971) developed a semiempirical model for wave trans-
mission by overtopping of subaerial breakwaters. The model was compared to
Lamarre's (1967) data for a smooth impermeable structure with a 1 on 1.5 front-
face slope. Cross and Sollitt's model suggests that wave transmission by
overtopping is a nonlinear function of the ratio of breakwater freeboard to
runup. Examination of Saville's (1963) data suggests that a linear model would
form an upper envelope for wave transmission over rough structures.

Keulegan (1973) measured wave transmission through a number of vertical-
faced permeable breakwaters using a wide variety of materials and wave
conditions. Comparison of results led to development of a method for design-
ing scale models that consider scale effects.

Sollitt and Cross (1976) tested wave transmission through a permeable
rubble-mound breakwater and used this information to develop an analytical-
empirical model.

Bottin, Chatham, and Carver (1976) tested 1 on 22 rubble-mound scale and
concrete armor unit breakwaters proposed for Waianae Harbor, Hawaii. Wave
transmission consisted of a combination of wave transmission by overtopping

2

and wave transmission through the structures. Wave reflection coefficients
were not measured. Wave runup on dolos was observed.

Madsen and White (1976) developed a analytical-empirical model for the
prediction of wave transmission and reflection coefficients for wave trans-
mission through subaerial rubble-mound breakwaters. The model employs the
long wave assumption, so predictions using their model are expected to be
most reliable for shallow-water waves. Comparison of the Madsen and White
model with physical model tests by Keulegan (1973) and Cross and Sollitt (1976)
shows that the wave transmission coefficient can be predicted more reliably
than the reflection coefficient.

The data from independant tests of wave transmission by overtopping con-
ducted in this study, together with the results of Saville (1963), Lamarre
(1967), Goda (1969), and Cross and Sollitt (1971), are used to develop a wave
transmission by overtopping equation similar to one proposed by Cross and
Sollitt (1971). The equation is then combined with the model of wave trans-
mission through permeable breakwaters of Madsen and White (1976) to form a
generalized model of wave transmission for breakwaters. This model is verified
by comparing numerical and physical model results for a wide range of conditions.

III. LABORATORY TESTING

le Laboratory Test Setup.

Laboratory tests were performed at CERC in a wave tank 4.57 meters wide,
42.7 meters long, and 1.22 meters deep. A part of the tank was divided by
four walls to form two interior test flumes, each 61 centimeters wide; the
remaining tank width contained a 1 on 12 absorber beach made of crushed stone
with a median diameter of 2.9 centimeters (Fig. 1). This arrangement allowed
two experiments to be performed simultaneously, and energy reflecting off of
the test structures diffracts out of the test flume to minimize re-reflection
of waves off of the generator blade.

The laboratory breakwaters were located between stations 5 and 10 meters
along the flume and parallel-wire resistance gages were used to measure wave
conditions in the flume. Gages placed at stations 1.40, 2.35, and 2.70 meters
along the test flumes were used to document incident and reflected wave condi-
tions. One or two gages placed landward were used to measure transmitted waves

Gate, abe

A wave absorber consisting of a crushed gravel slope covered with a 0.6-
meter-thick layer of hogshair was placed at the end of the test flume to absorb
a majority of the transmitted wave energy. The test flume was terminated 3
meters before the end of the wave tank to allow water overtopping the test
structure to escape from the flume through the absorber gravel. This arrange-
ment prevented the buildup of water on the landward side of the test structure.

2. Methods of Generating Waves.
Waves in this facility were generated by a programable piston-type generator
with a mean blade position 19 meters seaward of the entrance to the test flumes.

A minicomputer was used to produce monochromatic waves of a specified wave
height and period by moving the blade with a sinusoidal motion. Irregular waves

13

Flume ne Wave Gages Laboratory Wove Gage

Breakwater (one pis)

Transmitted Waves

WAVES
incident ~~~ ———

——___——— reflected

Profile view of the left test flume. Flume open to
allow escape of
overfopping water

@—Denotes Wove Gage 0 IRON 20S: OS: OF ae5!0em
Location [Sea ey a es |
Wall of Wove Tonk

<—_— To Wave Generator, 19m

: Gravel Absorber Beach

Transmission and 5
Overtopping Channel

7
Training
Walls

: 6lcm@ @@ _ Runup Chonnel
tot: Gravel Absorber Beach +
iT ! iT it it wey ay KE 10 efter
(0) \ 2 3 4
Woll of Wave Tonk

Wave Tank Stations (m)

Figure 1. Plan view of wave tank setup.

were produced by using the CERC Data Acquisition System (DAS) to create a signa]
to move the blade. Irregular waves were made by summing 50 components of vary-
ing amplitude, period, and random phase to produce a wide variety of spectral
shapes.

3. Data Collection.

The laboratory data collection scheme was designed after the CERC field
wave data monitoring program. Data collection was performed automatically by
the DAS in the following sequence:

(a) Wave gages were calibrated.

(b) Waves were produced for several minutes to allow tank startup
transient conditions to die out.

(c) Wave gages collected data at a sampling rate of 16 times a
second over a 256-second sampling interval.

(d) The 4,096 data points from each gage were then stored on
magnetic tape for analysis.

(e) A 10-digit identification code consisting of the year, month,

day, hour, and minute of the data run was assigned (e.g., ID 7804260916
is a run made 1978, April, 26th day at 09:16).

14

4. Data Reduction Methods.

Laboratory data sorted on magnetic tape were analyzed on a CDC 6600 compute:
using a variety of data reduction schemes. The mean water level and the least
squares, best-fit linear trend in the data was first removed from each gage
record. A Fourier analysis was then performed on each gage record using a fast
Fourier transform (FFT) routine and cosine bell function that is part of the
CERC wave analysis package.

Incident and reflected waves, which are mixed together in each of the gage
records, were separated using the method of Goda and Suzuki (1976) shown in
Figure 2. This technique gives an estimate of the incident and reflected wave
amplitudes, a; and ap, at each spectral line for each gage pair. Using
three gages in front of the structure gives three estimates of the incident and
reflected wave amplitude spectra. Calculations show that in this study the
three estimates of wave amplitudes seldom differed by more than 5 percent, so
the average incident and reflected wave amplitudes at each spectral line, j,
were taken as representative; 1.e., (ay)j is the average incident wave ampli-
tude at spectral line, j. The wave amplitude at each of the spectral lines
was also determined for transmitted wave conditions; i.e., (ar) 3 is the
average transmitted wave amplitude at spectral line, j.

Incident Waves Reflected Waves
s——— - AL =125¢cm ——
A2:90cm
eriewe SWI Mateos
A2Z=35 cm
Goges Tank Bottom
1 A
ar BI SanuEAE (A, - A, cos kAg - B, sin kAg)* + (B, + A, sin kag - B, cos kAL) 2

1
2|sin kal|

aR (A, - A, cos kAg + B, sin kAl)* + (B, - A, sin kA£ - B, cos kg)?

A,B = spectral coefficients
k = wave number = -

AL = gage spacing

where
A
0.05 < = < 0.45
and
20 L

where g equals acceleration due to gravity; d equals water depth; and
T equals wave period.

Figure 2. Determination of incident and reflected waves using the
method of Goda and Suzuki (1976).

15

Incident, reflected, and transmitted wave heights (H;, Hp, Hp) are defined
as

Ha (1)
Hp = (2)
Hp = (3)

where Hy is the height of the wave moving landward toward the breakwater,
Hp the height of the wave reflecting from the breakwater and moving seaward,
and Hp the height of the wave transmitted past and in the lea of the
breakwater.

Wave reflection and transmission coefficients, Kp and Kp, are defined as

Ke enpadil (4)
sip
and
H
oP
KK 2 == (S)
iy He

Wave transmission by overtopping has a transmission coefficient defined as
K75; wave transmission through porous structures is given by a transmission
coefficient Kp+. The coefficient for total wave transmission over and through

a structure, Kr, is
/ 2 2

In the case of irregular waves the significant wave height, Hg (average
of the highest one-third of the waves), is typically used to describe the wave
conditions. To include the effects of wave reflection from the structure,
significant height is defined as (Goda and Suzuki, 1976)

4 Tym

H, = == (7)
i V1 + Ke

where Nims is the average root-mean-square (mms) water level from the three
seaward gages. The mean wave height, H, is defined as

Bed
sit (8)

H = 0.625 H, = ——==
s
V 1 + KF

The wave period used to describe irregular wave conditions is the period
of peak energy density, T,. The spectral-peakedness parameter, (Goda,
1970), is used to characterize the spectral width for irregular wave conditions,

el
qe er (9)

where j is the band number (11 spectral lines are used to make each band),

f;- the frequency midpoint of the band, and Af the bandwidth frequency. aj
may be the incident, reflected, or transmitted wave amplitude associated with
band, j, so that three values of ® (incident, reflected, and transmitted)
are determined for each irregular wave run. Q, was selected as the parameter
to describe the spectral peakedness because it is an especially stable parameter
not strongly influenced by the spectral techniques used to determine its value
(Rye, 1977). The higher the value of ®» the more peaked a spectrum. For
example, white noise has a Q, value of 1.0, a Pierson-Moskowitz spectrum a
value of 2.0, and JONSWAP values of Q, vary between 3.0 and 9.0 with a value
of 3.15 for the mean JONSWAP spectrum (Fig. 3). Values of Q, associated with
several incident wave spectra used in this study are illustrated in Figure 4.

Description Op

Pierson-Moskowitz 2.0

|
|
\
|
1
I \ van JONSWAP 3.15
!
|

=
ao)
=~

Figure 3. The spectral peakedness, Qo»
for various spectral shapes.

17

125

7803271041 75 7804260916
100 H,=13.3cm H,=12.5cm
Qp=.1.76 Qp=2.33

> 75 fs
os ~
E ‘E
2 £
25
O O
O 0.25 0.50 O75) 1.00 (0) 0.25 0.50 C.75 1.00 1.25
f (Hz) f (Hz)
250 250
7803281500 Run ID Code = 7803281403
Hs =15.5¢em Ho=17.2 cm
i Op = 3.45 oes Qp=5.54
150 = 150
~ ~
~ nw
E E
= A
wy 100 w 100
50 50
O 6)
(0) 0.25 0.50 0.75 100 O 0.25 0.50 0.75 1.00 1.25
f (Hz) f (Hz)

Figure 4. Sample incident laboratory wave spectra.

The zero up-crossing method was also used to analyze wave records. In this
method the height of an individual wave is defined as the difference in extreme
water elevations (maximum level minus minimum level) between two successive
points in time where the water level up-crosses the mean water level. The
period associated with that wave is the time between up-crossings. This type
of analysis is useful for examining wave characteristics such as wave height,
period, or joint wave height-period distributions. Zero up-crossing results
may also be used to describe wave grouping (Rye, 1974). A high level of wave
grouping means that there is a strong probability that a wave of approximately
the same height will follow the previous wave (i.e., large waves are followed
by large waves and small waves are followed by small waves). In this study the
autocorrelation of zero up-crossing wave heights is used to quantify the amount
of wave grouping. The wave gage records seaward of the test structure are
somewhat contaminated by reflected waves, depending on the amount of reflection.
so the autocorrelation of incident wave heights, py, is taken as the average
wave height autocorrelation of the three gage records seaward of the structure.

18

Autocorrelation of transmitted waves, Ops is taken as the average autocorre-
lation of any gage measuring transmitted waves. (Note that p may vary between
1.0 and -1.0.) A large positive value of pe means that waves are strongly
grouped. Values of p near zero mean that there is little relation between
successive wave heights. .A negative value of the autocorrelation implies that
small waves follow large waves and vice versa. Several wave records measured

in this study with various values of p are shown in Figure 5. Note that in
all cases the water levels have been normalized by the significant wave height.

7807251105 P=0.71
Qp= 3.58
Hg: 7.38cm

Strong

7807251055 P=:0.41
Qp = 3.48
Hg =17.95cm

Moderate TL

7807251303 P=0.13
Qp: 2.17
Hg: 12.61¢m

Weak i

7807251341 P=-0.13
Pees

aia r y My fut ih Ly ih

[SS 80 oS |

Figure 5. Sample laboratory wave records showing various
levels of wave grouping.

19

For monochromatic wave tests, wave period, T, is defined as the period
of wave generator blade motion. For most of the monochromatic wave conditions
tested, 90 percent or more of the incident wave energy was found to be in the
spectral band containing the blade frequency (Fig. 6). At a given value of
wave steepness the amount of wave energy at higher harmonics of the blade
frequency increases as the relative depth, d/gT*, decreases. This energy
shift occurs because the waveform becomes more cnoidal and less sinusoidal
in shape as d/gT? decreases and H/d increases.

100
S)5)

90

Energy pct.

BWI ds phe 1.0
85 d/gTt*= 0.0065

80
0.0001 0.00! 0.01

H/gT?

Figure 6. Percent of incident wave energy at the period
of wave generator blade motion for sinusoidal
wave generator blade motion.

5. Breakwaters Tested.

Cross sections for 17 breakwaters were tested for wave transmission and
reflection; the cross-section geometries are illustrated in Appendix A. Each
of the structures was assigned the letters BW and a number to identify the
structure. Breakwaters BW1l to BW12 were built and tested on the flat bottom
of the flume. However, BW13 to BW17 were constructed with a 1 on 15 fronting
slope 25 centimeters high and 3.75 meters long. The fronting slope was used
fo simulate a sloping bottom and allow higher waves to break on the structure
being tested. ;

Most of the breakwaters tested were of rubble-mound construction, because
this is the most common type built. However, BWl and BW14 were smooth and
impermeable. BW2 had an impermeable core, and BW8 and BW9 had dolos armor
units and an impermeable cap. BW3, BW4, and BW15 were tested with and without
a vertical, thin impermeable plate placed in the center of the structure to
prevent transmission through the lower section of the breakwater. The symbol
W is used to indicate tests where the impermeable plate was used; e.g., BW3
tested with a plate is designated as BW3W. Materials used to construct the
breakwaters are described in Appendix B.

6. Test Conditions.
Each breakwater was built with a fixed geometry, then tested at various

water depths and wave periods. A number of wave heights were generally examined
for each wave period. Most of the experiments were run with monochromatic waves

20

produced by sinusoidal motion of the piston-type generator blade. The ranges

of dimensionless water depths (water depth at the toe of the structure divided
by structure height, d,/h) tested with monochromatic waves are given in Table 1.
Major emphasis was placed on d/gT* = 0.016 because laboratory waves at this
value of relative depth are comparatively free from secondary and Benjamin-Fier
waves.

Table 1. Range of conditions tested with
monochromatic and irregular waves.

Monochromatic waves
Irregular wave
testing!

0.
0.
0.
0.
0.
0.
0.
0.
0.

Breakwaters BW16 and BW17 were tested extensively with a wide variety of
irregular wave conditions. A limited number of irregular wave runs were also
made for several other breakwaters (Table 1).

Wo ese Keswbes.
Test results for monochromatic and irregular wave conditions are presented

in tabular form in Appendixes C and D; monochromatic results are presented in
graphical form in Appendix E.

21

IV. ANALYSIS OF TEST RESULTS

This section provides an analysis of the wave transmission and reflection
results of the model tests. Impermeable and permeable breakwaters were
investigated, and a separate discussion is devoted to each type breakwater.

The first part of this section describes observed trends in the values of the
transmission and reflection coefficients as a function of the parameters var-
ied in this study. The second part includes development, description, and
evaluation of methods for predicting wave transmission coefficients. The third
part discusses the effect of a breakwater on other wave characteristics, such
as the wave height distribution and shape of the transmitted wave spectra.
Since good models are not available for predicting wave reflection coefficients
for breakwaters, it is recommended that the model tests be used directly to
estimate breakwater wave reflection coefficients.

1. Wave Transmission and Reflection for Impermeable Breakwaters.

a. Observed Trends in Transmission and Reflection Coefficients. As a wave
approaches an impermeable breakwater some of the wave energy is supplied to
wave runup, some of the energy is dissipated, and the remaining wave energy
moves seaward in the form of a reflected wave. If the runup exceeds the crest
elevation of the breakwater, waves will be regenerated on the landward side of
the structure. Figure 7 shows aspects of this process and defines some of the
terms used in wave transmission by overtopping.

Impermeable

Kr = Hy / Hy

Figure 7. Definition of terms for wave transmission by overtopping.

Madsen and White (1976) found that low reflection coefficients and corre-
spondingly large amounts of wave energy are dissipated on smooth nonovertopping
structures. This observation has been verified using the data of Ahrens (1979)
for breaking and nonbreaking waves. The data show that for the case of no
overtopping the reflection coefficient decreases and a larger fraction of the
wave energy is dissipated as the wave steepness increases (Fig. 8). More than
80 percent of the wave energy is dissipated by the smooth slope of 1 on 1.5 for
the steepest waves tested. Note that the magnitude of the wave reflection
coefficient is approximately the same for monochromatic and irregular waves, for
a given value of wave steepness.

As the height of the breakwater is reduced the magnitude of the wave reflec-
tion coefficient decreases because much of the wave energy is transmitted by
overtopping. For example, with a freeboard of zero (water level at the break-
water crest) BWl has reflection coefficients that are less than 20 percent of
the reflection coefficient for a structure that is not overtopped for the
steeper waves tested (Fig. 9). At values of small wave steepness the size of

(2 (2

2 cavaesse ve 2 re) 6
) r) fo)
Soe fo) (2) ® fo) ps
Dears pe o>, Sea 2
XO x 5 wy i ”
(@) 8 X SF Sot xX 2
“3 R HO xX

K
0.6 ib pe

= KS (fraction of wave

energy
0.4 dissipated) is
ee S [efe) ie)
ag
a WAVE WAVE
02 a TYPE STEEPNESS
= © Sine H/gI?
X Irregular Hg/gTe
°9 0.002 0.004 0.006 0.008 0.010 0.012 0.014

Hi/ilins loc eabtey/cailis

Figure 8. Wave reflection coefficients and fraction of wave
energy dissipated for a 1 on 1.5 smooth slope with
no wave transmission (data from Ahrens, 1979).

Structure Slope =!on!.5

Structure with no Overtopping
(Ahrens, 1979)

Breokwoter with F=0
(ds/h=1.0)

——
Volume of Overtopping Increasing

(0) 0.002 0.004 0.006 0.008 0.010 0.012
H / gt?

Figure 9. Wave reflection coefficients for a breakwater with zero free-
board compared to a similar structure with no overtopping.

20)

the reflection coefficients for the breakwater and smooth impermeable slope
is approximately the same because breakwater overtopping is small.

The wave reflection coefficient decreases as the wave height or steepness
increases for a subaerial breakwater, but shows the opposite trend for a sub-
merged breakwater (Fig. 10). There is a slight increase in the reflection
coefficient as the wave height increases for the conditions tested.

The variation of the wave transmission coefficient for a smooth impermeable
breakwater is the reverse of that found for the reflection coefficient. If the
wave runup is less than the breakwater freeboard there is no wave transmission.
As soon as the runup exceeds the crest of the breakwater, wave transmission by
overtopping occurs. All other factors being fixed, as the wave height increases
the size of the runup and the transmission by overtopping coefficient increase
(Fig. 10); as the ratio of the water depth to structure height, d,/h, ap-
proaches 1.0 the transmission coefficient increases. Even with zero freeboard
(d./h = 1) there is some increase in the wave transmission coefficient as wave
steepness increases (Fig. 10). However, for a submerged breakwater of fixed
geometry the wave transmission coefficient declines as wave height or steepness
increases (Fig. 10).

b. Estimating Wave Transmission by Overtopping Coefficients. Wave trans-

mission by overtopping is closely related to wave runup and overtopping of a
breakwater. Weggel (1976) found that overtopping rates are a function of the
ratio of the structure freeboard, F, to the runup, R, on a similar structure
high enough to prevent overtopping (Fig. 7). Cross and Sollitt (1971) also
recommend the dimensionless parameter, F/R, for predicting wave transmission
by overtopping coefficients.

Several methods are available for estimating wave runup on smooth imperme-
able slopes; some of these methods are summarized in Stoa (1978). The runup
prediction equation developed by Franzius (1965) gives the best estimate of
wave runup for predicting wave transmission coefficients. The runup is given by

c, vH/d+C
R = HC, (0.123 L)\ : 3) (10)

where L is the local wavelength determined from linear theory using

T2
L = pein tanh = (11)
27 L

and C,, Cy), and C3 are empirical coefficients. Franzius suggests values
for the coefficients, but improved coefficients were obtained in this study
using the data of Saville (1955) and Savage (1959) with a nonlinear error
minimization computer routine. The recommended values of the empirical coeffi-
cients are given in Table 2. These values are linearly interpolated to estimate
values of the coefficients for other slopes. An advantage of using equation

(10) is that it includes effects of wave height, structure slope, wave steepness,
and the ratio of water depth to wave height on wave runup.

The runup on rough slopes is also a complex function of many factors (Stoa,
1978). Madsen and White (1976) give an analytical-empirical model for estimating

24

B = 30 cm --—+|
dg/gT?

Smooth Impermeable

1-20

Lica ange

1.07
{ .00
OR93

cee Suboerial

0.73 Breakwater
0.67
0-690

lon 1.5 Slope

lon 1.5 Slope

K<XNXAOX+t+PO

0.6
~ Sbeere ye
g y

0.8 ee ud SS

0)
0.000I| 0.0002 0.0004 0.00! 0.002 0.004 0.01
H/gT2

A

srsce tt ps)
1.07 (u)

0.6 =
ve

0.4

0.2

)

0.000! 0.0002 0.0004 0.001 0002 0.004 0.0!

H/gT 2

Figure 10. Wave transmission and reflection coefficients for a smooth
impermeable breakwater (BW1, d/gT* = 0.016, monochromatic waves).

(35)

Table 2. Empirical wave runup prediction coef-
ficients for smooth impermeable slopes.

Front-face slope

of breakwater Gy Cy ae
Vertical 0.958 0.228 0.0578
on 0.5 1.280 0.390 -0.091
on 1.0 1.469 0.346 -0.105
on 1.5 Lo QQ 0.498 -0.185
Om 2o2s 1.811 0.469 -0.080
on 3.0 1.366 0.

runup on an impermeable rough slope armored with one layer of stune. Ahrens
and McCartney (1975) present an empirical method for estimating the runup on
two layers of riprap overlying a 0.2-meter thick underlayer (Fig. 11). In
their method the runup is predicted as a nonlinear function of the surf param-
eter, &,

IN a& ne tan 0
H 1 + bé (z
Lo

where a and b are empirical coefficients with values of a = 0.956 and
b = 0.398.

(12)

Both the Madsen and White and Ahrens and McCartney prediction methods tend
to give high or conservative estimates of wave runup for predicting wave trans-
mission coefficients. However, Hudson (1958) made numerous observations of
runup over a wide range of breakwater conditions; the Ahrens and McCartney
empirical curve (eq. 1) was fitted to the Hudson data to give the recommended
runup coefficients of a = 0.692 and b = 0.504 (Table 3). These coefficients
gave a lower prediction of runup than that’ given for riprap (Fig. 12). The
equation

Re 0.692 & (13)
H 1 + 0.504 &

is recommended for predicting runup on stable permeable and impermeable stone
breakwaters until a more comprehensive model becomes available. Coefficients
for dolos were also estimated using Bottin, Chatham, and Carper's (1976) data
for breaking and nonbreaking waves (Table 3). Stoa (1978) provides additional
information on runup; runup data for nonbreaking waves on breakwaters are pro-
vided in Jackson (1968).

Runup predictions were made for the conditions tested, and observed wave
transmission by overtopping coefficients, K7o, were plotted as a function of
F/R (Fig. 13). This figure shows the case of breakwaters with a slope of 1 on
1.5. The upper part of Figure 13 shows results from BW1 for tests that had a

26

“($261 AouzTeDjIW pue

susilyy t033e) derdta uo dnunz oAeM “TI oansTy

eV”
ail eS

0)

ado|jS O'G UO] + Gc2O

ado|S GE UO] v

adoiS GZ2u0]| o 0S'0
G20
oo1S

Se

Gel
Os |

G2°|

Out

Table 3. Wave runup prediction coefficients using the Ahrens and McCartney (1975) method.
BE ee

—_+——.

2 2 d H
N 1 2 OT
INTO || No or Permeability a b eT eT Cot 8 Source
unit layers
(range) (range) (range)
hearrerm Rese ERT SM PoRT Oar [ore lRas : Ss een ee ——
Rubble 2 I 0.956} 0.398 | 0.0036 to 0.059 0.0004 to 0.013 | 2.5 to 5.0] Ahrens and McCartney
(1975) 3
(large-scale tests)
Rubble 0 P 0.692 | 0.504 | 0.0088 to 0.08 0.0004 to 0.02 1.25 to 5.0 | Hudson (1958) *
5 6
Rubble 2 I 0.775 | 0.361 | 9 ------------ | 9 ------------ 2.5 Gunbak (1979)
Dolos 2 I 0.988] 0.703 | 0.009 to 0.002 0.0002 to 0.006 2.0 Bottin, Chatham, and
Carver (1976)
wre dee we ee de ee See LoS | (ai 8 a eR I a
Ip = permeable; I = impermeable. 4Means of observations.
2R/H = at/(1+bE); & = tan e/VH/L,. SConditions unknown.
3Revised a and b. 61.2 <& < 4.8.

Riprap (Ahrens and McCartney,1975) -—-——~.

Se

Dolos Armored Breakwater
(Bottin, Chatham,and Carver, 1976)

Rubble-Mound Breakwaters
(Hudson, 1958)

tan @
J H/Lo

Figure 12. Wave runup prediction for rough structures using
the Ahrens and McCartney (1975) method.

28

C:0.42 Bwi
0.006 < d/gT2 < 0.03

Wave Type

Monochromotic
o Irregular

Lomorre (1967)
d/gT* <0.03
0.18 <B/h <0.22

Figure 13. Wave transmission coefficients for smooth
impermeable breakwaters with 1 on 1.5 slopes.

breakwater crest width-to-structure height ratio of B/h = 0.4. The lower part
of the figure gives test results from Lamarre (1967), who tested structures

with smaller values of B/h. Although there is some scatter in these data sets,
it appears that the wave transmission coefficient decreases approximately
linearly as F/R increases and that this linear trend is found for submerged

as well as subaerial breakwaters. Most of the scatter occurs where the crest
elevation is at the stillwater level (F/R = 0) for BW1, with small waves having
significantly lower wave transmission coefficients than are present in the

linear trend. Fortunately, small waves are generally not of interest for design
purposes. The few irregular waves tested with BWl suggest that wave transmission
coefficients for irregular waves follow the same trend as for monochromatic
waves. The mean wave height, taken as 63 percent of the significant wave height,
should be used in equation (12) to determine the effective runup for predicting
wave transmission coefficients for irregular wave conditions.

29

Comparison of the upper and lower parts of Figure 13 suggests that the
structure tested by Lamarre (1967) with a smaller relative crest width has
slightly higher wave transmission coefficients than found for BW1.

Results from laboratory tests by Goda (1969) for breakwaters with vertical
faces (Fig. 14) have the same trends as observed for breakwaters with 1 on 1.5
slopes.

1.0
Goda (1969)

an 0.0047< d/gT?<0.027
B/h & 0.86

0.6

=
0.4
0.2

Goda (1969)
d/gT2 = 0.016
B/h,&~ 0.0

F/R

Figure 14. Wave transmission coefficients for vertical, smooth
impermeable breakwaters using Goda's (1969) data.

The recommended formula for predicting the wave transmission by overtopping
coefficient for the range 0.006 < d/gT* < 0.03 is

Gp = C (: = = (14)

30

where C is an empirical coefficient and the minimum and maximum values of
Kro are 0.0 and 1.0, respectively. The recommended value of C is given by

c=0.51-S7°18 5 ox <3n2 (15)

Eales)

for smooth impermeable structures tested over the range 0 < B/h < 0.86 and

rough impermeable breakwaters tested over the range 0.88 < B/h < 3.2 (Fig. 15).
However, for submerged breakwaters tested with 1 on 15 fronting slopes, equation
(14) underestimates the wave transmission coefficient. For example, equation
(14) underestimates the wave transmission coefficient for BW14 when submerged
and the error increases as the breakwater becomes relatively more submerged
(Fig. 16). The data from BW14 and from Saville (1963) show that for submerged
breakwaters with 0.88 < B/h < 3.2 and with a 1 on 15 fronting slope equation
(14) should be adjusted to

i F ; Pua Oe
Kr = C (1 -F) =) (Gl 20) & 3 yo and 1 on 15 fronting slope (16)

Figures 17 and 18 illustrate the observed and predicted wave transmission
coefficients for two of the rough impermeable breakwaters tested by Saville
(1963) for two values of crest width. Figure 17 shows the case of a structure
with a crest width-to-structure height ratio of 0.88; Figure 18 shows the same
information for a much wider structure with a width-to-height ratio of 3.2. A
scatter plot of observed and predicted transmission coefficients using Saville's
(1963) data indicates the level of ability to predict King (Fig. IG).

The above discussion shows that the breakwater freeboard and wave runup
have a major influence on the magnitude of the wave transmission by overtopping
coefficient. Breakwater crest width has a much smaller effect and only large
changes in breakwater crest width could be used to reduce the size of the
transmission coefficient for a given design situation.

Wave transmission by overtopping coefficients may be predicted for imperme-
able structures using the computer program OVER (App. F) which applies methods
described in this section.

c. Influence of a Breakwater on Other Wave Characteristics. The magnitude
of the wave transmission by overtopping coefficient, Kno» is generally the
most important parameter to determine for the design of an impermeable break-
water used to reduce wave height. However, in addition to reducing the average
wave height, the breakwater may also alter other characteristics of the waves,
such as spectral shape or wave height distributions. Since these additional
wave characteristics may be considered in some design problems, they are briefly
discussed below.

The case of monochromatic waves incident on the structure is the condition
most often used to test wave transmission of laboratory breakwaters in previous
studies. This type of wave is similar to swell wave conditions in the prototype
where the incident wave height and period are approximately constant. Spectral
analysis of water level records for gages landward of the breakwater indicates
that a significant part of the wave energy of transmitted waves may be at
harmonic frequencies of the forcing wave (Saville, 1963; Goda, 1969). The
fraction of wave energy at the forcing period (Fig. 20) shows the same trend

31

Structure (Source)

Smooth Impermeable (this study;

Goda, 1969; Lamarre, 1967 )

Rough Impermeable ( Saville, 1963)

Rough Permeable Submerged ( Saville, 1963)

“(>
Tested with | onI5 Fronting Slopes

CSO Os (3/ fy

Figure 15. The effect of the relative structure width on
wave transmission of impermeable breakwaters.

lon 1.5 ke 8] lonl.5

Not to scale

Rope CUSFINISE Filive
F/R<0,C :0.24

0.4 mene Clo GIR)
I/2 121

0.2
C= 0.38

-1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1.0 1.2

Figure 16. Wave transmission coefficients for BW14.

32

Saville (1963) Structure AA cot @= 2.0
B/h = 0.88

| on 15 Slope Seaward of Breakwater
0.006 < d/gT* <0.015

@ Small-Scale Test
X Large-Scale Test

Submerged

O16" — O15) -OF45 OS O!2 Ol O 0.1 O2° O83 O4 OS. Of
F/R

Figure 17. Wave transmission coefficients for a breakwater
tested by Saville (1963) with B/h = 0.88.

Saville (1963) Structure D cot @=2.0
B/h=3.2

| on 15 Slope Seawoard of Breakwater
0.006 <4/gt?<0.015

@ Small-Scale Test
X Large-Scale Test

—_——_—_
Suboaerial

Predicted C=O.15

Submerged

O
“06 =-@Q9 -O4) =O. -O.2 =O, 0) 0.1 O2 O08 Of) OS O06

Figure 18. Wave transmission coefficients for a breakwater
: tested by Saville (1963) with B/h = 3.2.

=)

Predicted = Observed

0.006 < d/gT? < 0.015
0.6< B/h<32
0.78<ds/h< 1.11

Kz, (predicted)

© Subaerial
A Submerged

02 04 06 08 10
Ky, (observed)

Figure 19. Observed and predicted coefficients of wave transmission
by overtopping (Saville, 1963; impermeable breakwaters).

100

Energy (pct)

d/gT?= 0.016
BW 1

(0)
0.000! 0.0002 0.0004 0.001 0.002 0.004 0.01
H/gT?

Figure 20. Percent of wave energy at the forcing wave period

for wave transmission by overtopping of a smooth
impermeable structure (monochromatic waves).

34

as was found for the transmission coefficient, Kp, (lower half of Fig. 10).
Comparison of Figures 10 and 20 suggests that the amount of wave energy found
at the forcing period will increase as the transmission by overtopping coeffi-

cient increases.

The case of irregular waves is where the incident wave energy is distributed
over a range of wave frequencies (several measured incident laboratory wave
records and computed wave spectra are shown in Figs. 4 and 5). Tests with
irregular waves indicate that the shapes of the incident and reflected wave
spectra are approximately the same (two examples are given in Fig. 21). The
approximately constant spectral shape is shown by the spectral-peakedness
parameter, Q,, where the value for the reflected waves, Qpyn, is approxi-
mately equal 5G the incident spectral peakedness, Qpi (ise 22). bhershape
of the transmitted spectrum may be approximately equal to or sharper than the
incident spectrum (Fig. 22) with the spectral-peakedness parameter of the trans-
mitted waves, Qnt> greater than or equal to Q,; (Fig. 22). Secondary waves
may appear in the transmitted wave spectrum at harmonics of the period of peak

energy density, Tp» (alge 21)

A zero up-crossing analysis (Fig. 23) was performed on the wave records to
allow statistical examination of individual wave heights and periods. Since
reflected waves contaminate the incident wave conditions, an analysis was
performed for the record from each gage, then results averaged to minimize the
influence of reflection. Cumulative height distributions were then prepared
for incident and transmitted waves. The cumulative curves were put into dimen-
sionless form by dividing by the observed rms wave height, Hyg, and the
dimensionless heights at various probability levels, p, determined (p = 0.01,
0.02, 0.05, . . . 0.60). A plot of these dimensionless heights for transmitted
versus incident waves indicates the shape of the transmitted wave height distri-
bution as a function of the incident wave height distribution. For the case
of a breakwater with the water depth at the crest level (d,/h = 1.0 or F = 0)
the transmitted wave height distribution is approximately the same as the
incident height distribution (Fig. 24). If the water level is below the crest
elevation (dg/h = 0.80, positive freeboard), the transmitted wave height distri-
bution is skewed toward larger waves (Fig. 25). This means that the larger
transmitted waves are bigger than predicted by the transmission coefficient,
Kno. For example, at the S-percent level, transmitted waves are 30 percent
larger than expected from the overall transmission coefficient and at the
l-percent level 100 percent larger.

The above observations are consistent with the wave transmission by over-
topping model given by equation (14). At zero freeboard the transmission
coefficient is approximately constant, so all waves in a distribution will
transmit the same amount and the distribution will remain unchanged. However,
for subaerial breakwaters the larger waves will have smaller F/R ratios and
transmit more efficiently than small waves, so that the transmitted wave dis-
tribution is skewed toward large waves.

The joint distributions of wave heights and periods observed in the
laboratory illustrate the same overall trends found in the field. Larger
waves have a mean period approximately equal to the period of peak energy
density in the spectrum, T (Goda, 1978), with the average wave period
decreasing for smaller wave heights (Fig. 26). The correlation between

35

Energy ( pct.)

Energy ( pct.)

20 Run ID Code = 7803270943

He = 16.7 (cm)
REFLECTED
me) : TRANSMITTED Kp = 0.26
9p = 0.36
Qp = 9.82
me)
BWI
: do /h = 10
lie OB NOE OTS Ite 125
§ (kz)
20 Run ID Code = 7803270952
i o REFLECTED . os F otk
x TRANSMITTED IN Me
Ny = ©, S99
10 Qp= 4.37

Figure 21. Sample incident, reflected, and
transmitted wave spectra.

36

BW 1

° dg/h = 1.0

© dg/h = 1.0
e ds/h=08

e dg/h=0.8

Figure 22. Spectral peakedness of incident, reflected, and transmitted
wave spectra.

= qT; =e Ts T4

4
Hy :
Si :

Up - crossing
point

MWL

Figure 23. Zero up-crossing analysis.

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38

2.8 2.8
u T
2.4 2.4
BW1
2.0 dg/h = 1.0 2.0
11 26 P8147
gids 4 1418 20 21 26 wlS 106 1661610
a 1426 4 ae 1016 16/1615 6 6
29 (R72 ES
7 4 2611(10 4 184 4 1029341910155 16 6
4 7 1 3232})17 264 114 34 3439/24 206 24 b
0.8 0.8
7 7 29180 262611114 4 D 20 10 20 6
26187 4 4
0.4 0.4
180 4 ~~ INCIDENT 6 TRANSMITTED
7803270952 7803270952
(9) (0)
(@) 0.4 0.8 1.2 1.6 2.0 (@) 0.4 0.8 1.2 1.6 2.0
T/Tp T/Tp

Figure 26. Sample incident and transmitted joint distributions of wave
height and period.

heights and periods (Goda, 1978) was observed to be 0.13 ¢ r(H,T) £ 0.26 for
the incident wave conditions tested with approximately the same values for
transmitted waves. The major difference between observed and transmitted

joint distributions of height and periods is that the mean period of smaller
waves is lower for the transmitted waves (Fig. 26) than for the incident waves.

2. Wave Transmission and Reflection for Permeable Breakwaters.

a. Observed Trends in Transmission and Reflection Coefficients. As a
wave approaches and interacts with a rough permeable breakwater the sequence
of action is similar to that for an impermeable breakwater, but with important
differences. First, some of the wave energy moves through the permeable break-
water and this flow through the porous medium may dissipate a significant
amount of wave energy. Second, because the breakwater absorbs some of the
wave energy and water, the runup and reflection coefficients on a rough
permeable breakwater are less than for the same wave condition on a similar
smooth impermeable structure. If the runup level exceeds the height of the
structure, wave transmission by both overtopping and transmission through the
structure will contribute to the overall transmission coefficient, Kp (Fig.
21)

39

Figure 27. Definition of terms for wave transmission for permeable breakwaters.

The relative water depth, d/gT*, is one of the most important parameters
controlling the reflection coefficient, Kp (Fig. 28), with the reflection
coefficient increasing as d/gT* decreases. The wave steepness, H/gT2, and
the ratio of water depth to structure height, d,/h, have less influence. In
general, the reflection coefficients for rough permeable breakwaters are much
less than for similar smooth impermeable breakwaters (Fig. 10). Since no
comprehensive model is currently available for predicting reflection coeffi-
cients, laboratory model results should be used to estimate Kp. A rough
estimate of the reflection coefficient for permeable subaerial breakwaters
may be obtained using the method of Madsen and White (1976) (computer program
MADSEN in App. G). Typical comparisons between predictions and laboratory
measurements are shown in Figure 29.

The wave transmission coefficient, Kp, is primarily a function of wave
steepness for a given permeable breakwater design and hydraulic conditions
where there is no transmission by overtopping (Fig. 28). Since the wave steep-
ness increases the amount of energy dissipated on the face and inside the
breakwater increases (Madsen and White, 1976), the transmission coefficient
decreases. However, as soon as the wave runup level exceeds the breakwater
crest, wave transmission by overtopping occurs and the transmission coefficient
increases with increasing steepness. Figure 30 (lower part) shows the case
where no overtopping occurs and Kp decreases (low steepness waves), then Kp
increases with increasing steepness where transmission by overtopping and
transmission through a breakwater occur simultaneously. In the case of a
submerged breakwater the wave transmission coefficient decreases as the wave
steepness increases (upper part of Fig. 30).

b. Estimation of the Coefficient of Wave Transmission Through Permeable

Breakwaters Using the Madsen and White Model. The advantages of the Madsen and
White (1976) model for predicting transmission coefficients are that the model
is completely self-contained and it can be used to predict coefficients over a
wide range of conditions. Parameters that can be varied include the breakwater
height, breakwater width, breakwater slope, the size and relative location of
various layers in the breakwater, and the size and porosity of materials used
in the breakwater. Another advantage of the model is that it can be used to

40

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41

Papen
hs: 66cm

ds/gt?
lon 1.5 Slope o 0-0065
2 0-0131
+ 0-0161
x 0.0226
5 0.0363
i See ee os 0.0555
0 0.5 1.0m
BW3
ae Submerged Breakwater
dg/h =1.14
oS (Go

(0)
0.000I 0.001 0.0I
H/gT?

BW3W

Overtopping Subaerial Breakwater

0.6 No Overtopping ds/h=0.93
wa
0.4
0.2
(0)
0.000I 0.001 0.01
H/gT2

Figure 30. Wave transmission coefficients for a
subaerial and a submerged breakwater.

predict coefficients for any size breakwater, useful when designing or assessing
scale effects in small-scale physical models (see Sec. V).

The Madsen and White model was designed for manual use, but because of the
many calculations and iterations necessary, manual calculation is tedious. The
model was automated as a part of this study in a FORTRAN computer program,
MADSEN (App. G) to simplify use of the model. Advantages of the computer pro-
gram are that only a few input cards are required to model even a breakwater
with complex geometry and the program computer cost is very low. The program
includes all the generality in the original model, and the wave transmission by
overtopping model developed in Section IV,1 is also incorporated. Since the
Madsen and White (1976) technique is complex, reference is made to their publi-
cation for details of the model. A brief summary of the major steps in the
model and computer program is given below; additional information on the com-
puter program is given in Appendix G.

42

(1) Determine the breakwater cross-sectional geometry and material
characteristics of diameter and porosity.

(2) Estimate the energy dissipation on the seaward face of the breakwater
assuming it is rough and impermeable. This is done by solving Madsen and
White's equation (127) implicitly using their Figures 15, 16, and 17 and
applying a correction factor from their Table 2.

(3) Assume as a first approximation that the head across the breakwater
is equal to runup determined from step 2 above.

(4) Transform the trapezoidal breakwater into a hydraulically equivalent
rectangular breakwater (see Sec. 4.2 of Madsen and White).

(S) Estimate the coefficient of transmission through the structure, K7+,
using Madsen and White's Figures 2 and 3 and implicitly solving their equation
GE :

(6) Obtain a revised estimate of the head across the breakwater using
Madsen and White's equation (161). (Repeat steps 4, 5, and 6 until a con-
verged solution is obtained.)

(7) Estimate wave runup on the breakwater using the method of Ahrens and
McCartney (1975) and the coefficients given in Table 3 of this study.

(8) Calculate the transmission by overtopping coefficient, Ko, using
equations (14) and (15) in this study.

(9) Calculate the transmission coefficient, Kp, using Ky¢ from step 5
and Kyo from step 8 and

YD) 2
Mp Unie 1Sig6

Madsen and White compared the model predictions to physical model results
from Keulegan (1973) for rectangular breakwaters composed of one rock type, and
from Sollitt and Cross (1976) for a multilayered trapezoidal breakwater made
of riprap. There was good agreement between analytical and physical model
results for predicting the wave transmission coefficient for long nonbreaking
waves. However, the following questions need to be answered to determine the
range of usefulness of the Madsen and White model:

(1) How useful is the model for predicting transmission coefficients
for relatively short waves?

(2) Can the model be used if waves are breaking?

(3) Can the model be used for breakwaters with concrete armor units?

(4) Can the model be used for irregular waves?

(S) How sensitive is the model to porosity of the materials?
(Porosity is an input parameter and although it probably does not vary

over a very wide range, its value will probably not be known accurately
in a design situation. )

43

Each of these areas is discussed below.

(1) The case of the relative wavelength. In many of the laboratory
tests the wave period was varied to cover the range from shallow-water
long waves to deepwater short waves. Comparison of laboratory data
and MADSEN computer program predictions shows excellent correspondence
for shallow-water waves; e.g., at d/gT? = 0.0065 (Table 4). As the
relative depth becomes larger (the wavelength becomes shorter), the
computer program slightly overpredicts the observed transmission
coefficient (Fig. 31). This means that the prediction method is
conservative. Although the absolute value of the overprediction is
small, the percent overprediction may be large (Table 4).

Table 4. Effect of relative depth on prediction of Kp.

Relative
depth

King
Observed Predicted

Shallow
Transitional

Deep

lon 1.5 Slope

lon 1.5 Slope

SAK

0.5

BWwie

1BW12, dg/h = 0.64, H/gT? ~ 0.0015.

pe oe es Se

The ability of the model to predict wave transmission coefficients
for a breakwater constructed entirely of armor stone is shown in Figure
32; wave transmission coefficients for a breakwater with a front-face
slope of 1 on 2.6 are shown in Figure 33.

(2) The case of waves breaking on the breakwater. It was difficult
in the laboratory to generate long waves that would break on a rough
permeable structure without any overtopping. However, several tests
that met these conditions were run using nonsurging, breaking waves
(Galvin, 1968). These laboratory tests show that for breaking and
nonbreaking waves the coefficient of transmission decreases gradually
as the incident steepness increases (Fig. 34); no difference was
evident between Kp; for breaking and nonbreaking waves. The same
trend is observed in Bottin, Chatham, and Carver's (1976) data for a
breakwater with dolos armor units. Comparison of observed and predicted
coefficients of transmission through the structure shows good agreement
for the few breaking wave conditions tested (Fig. 34). These few tests
suggest that the Madsen and White (1976) model can be used for breaking
as well as nonbreaking waves.

44

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46

(3) The case of breakwaters with concrete armor units. The fric-
tion factor and porous media flow factors for concrete armor units are
unknown, but they are assumed to be similar to the properties of stone
with an effective median diameter, dcos of

1
13
W
50
da (17)

Figure 35 shows observed and predicted transmission coefficients for

a breakwater with two layers of dolos armor units. There is excellent
prediction of transmission coefficients for long shallow-water waves
with the Madsen and White (1976) model overpredicting transmission
coefficients for waves with greater relative depth. This is the same
trend found in prediction of transmission coefficients for rubble-
mound breakwaters.

aaa | 64 <ds/h <0.86
hg: 70cm © Ores = dsAni— Fy
Dolos Armor Units 0.0065 <d/gT* <0.055

on 1.5 Slope 0.000! < H/gT? <0.012
B/h = 0.43, C=0.46
G) S 0.692, b = 0.504

ton !.5 Slope

d/gt* Relative Depth

0.0065 Shallow
0.016 Transitional

0.055 Deep
= 0.6
@
2
204
=
e

°
w

o
iN)

0 0.1 0.2 OS O04) Of% OG O77 Ose
K, (observed)

Figure 35. Observed and predicted transmission coefficients
for a breakwater with dolos armor units (BW9).

47

The model also does a good job of predicting the coefficient of
transmission through a permeable breakwater armored with tribars
tested by Davidson (1969) (Fig. 36). However, the effective trans-
mission by overtopping coefficient, C, is larger than would be
expected from Figure 15 for B/h = 0.30. Fortunately, the observed
transmission coefficient appears to be approaching a value of approxi-
mately 0.48, the limiting value of the overtopping wave transmission
coefficient for this breakwater predicted from equations (14) and (15).
The relatively high porosity of artificial armor units apparently
increases the size of the wave transmission by overtopping coefficient
over a limited range of wave heights for this case where the stillwater
level is above the core and close to the breakwater crest (D. Davidson,
Chief, Wave Research Branch, U.S. Army Waterways Experiment Station,
personal communication, 1979).

Tribors

i ee 1on 1.5 Slope

1.5 SI 2g :
ae Slope A-3 a = 0692
a-5 Zs a b = 0.504
C- Stone _ 4

Ky

B/h = 0.30

dg/h=084 Observed —«>e

/ Limiting Predicted
Ky,

°

d/gT? = 0.0063

0)
0.0004 0.0006 0.001 0.002 0.004
H/gT2

Figure 36. Wave transmission past a heavily overtopped breakwater
with tribar armor units (laboratory data from Davidson, 1969).

48

(4) The case of irregular waves. Laboratory tests with a wide
variety of spectral shapes suggest that there is little difference
in the transmission coefficient from one spectral type to another.
The overall transmission coefficient, Kp, is approximately the
same for a monochromatic test as for an equivalent irregular wave
test with the period of peak energy density, Tp, and mean incident
wave height, H, used to characterize the irregular wave conditions.
Figure 37 shows observed and predicted transmission coefficients for
a rubble-mound breakwater tested with monochromatic and irregular
waves. The ability of the computer program MADSEN to predict trans-
mission coefficients for irregular waves is at the same level as for
monochromatic waves for the conditions tested.

B= 60cm 0.61< dg/he 0.91
hge33em [>] on Stope 0.002 < d/gT2< 0.016

lon 2 Slope
SS aioe 1 oe lon !5 Fronting Slope: O.00004 <H/gT* < 0.013

B/h= 1.82, C=0.3!

SS
) 0.5 1.0m a=0.692, b=0.504
BW 16

Predicted = Observed

K(predicted)
ro) °
a rep)

9°
‘fp

0.3
02 Wave Type
© Monochromatic
4 Irregular
0.1
(@)

(0) 0.1 OZ OS O46 OL OB" TO) 0s} 0.9 1.0
K, (observed)

Figure 37. Observed and predicted transmission coefficients for BW16.

49

(5) The case of porosity of the breakwater. Porosity of each of
the materials must be known in order to use the computer program
MADSEN. However, in many design situations the value of porosity
may be poorly known. Typical values of porosity, P, are given in
Table 5. The recommended method of determining the influence of
porosity on the predicted transmission coefficient is to run the
program MADSEN at various values of porosity keeping all other param-
eters fixed. Figure 38 shows predicted transmission coefficients over
a range of wave steepnesses for three different values of porosity.
For this example, the absolute change in Ky¢ produced by a given
change in P is largest for waves of small steepness. The largest
percent change in Kp for a given change in P occurs for the
steepest waves tested. In general, the same trend will be observed
for any breakwater; the value of Kz will increase as porosity
increases for a given set of conditions. However, the magnitude of
change of Kp is a complex function of all of the parameters in a
design (breakwater geometry, water depth, wave height and period,
etc.). A sensitivity analysis with the use of the program MADSEN,
similar to the analysis shown in Figure 38, is recommended if the
porosity of proposed materials is poorly known.

Table S. Porosity of various armor units (from
U.S. Army, Corps of Engineers, Coastal
Engineering Research Center, 1977).

Armor unit No. of | Placement | Porosity

Quarrystone (smooth) Random

Quarrystone (rough) Random

Quarrystone (rough) Random
Cube (modified) Random

Tetrapod Random

Quadripod Random
Hlexapod Random
Tribar Random
Dolos Random

Tribar Uniform

Quarrystone Random

c. Wave Transmission for Submerged Permeable Breakwaters. The coefficient

of wave transmission over a submerged permeable breakwater, Kr ,, may be esti-
mated by the methods given in Section IV,2. However, no generalized model is
currently available for determining the coefficient of wave transmission through
the structure, Kpz. Saville's (1963) data for similar permeable and impermeable
structures show that the total coefficient, Kz, approaches the transmission by
overtopping coefficient, Kz ,, and transmission through the breakwater becomes
less important as the structure becomes more submerged and the incident wave
height increases (Fig. 39). At d,/h 21.2, the data from breakwaters BW3, BW3W,
BW4, and BW4W show that the coefficients of transmission through the structure
are approximately zero, so that K7o/Kp = 1.0. An upper estimate of the coeffi-
cient of transmission through the structure, K+, for a submerged breakwater

50

Underlayer
ds: 3.56m Core <a
. 0.10m

P= Porosity (assumed to be the same for
the armor, underlayer and core )

0.5

0.4

o Depth Limited
Viuve Height
0.2
ds/h=1.43
0.1 d/gT*: 0.0058
0 on __
0.000! 0.0002 0.0004 0.0006 0.00! 0.002 0.004 0.006

H/gT2

Figure 38. Example of the influence of porosity on the predicted
coefficient of transmission for a rubble-mound breakwater.

SSS
Suboerial | Submerged

0.8 0.9 1.0 1 1.2
ds/h

Figure 39. The relative importance of transmission by overtopping
as a function of the incident wave height and the water
depth-to-structure height ratio (after Saville, 1963).

5]

can be made using the program MADSEN with d,/h = 1.0. As a lower estimate,
Kp¢ = 0.0 can be assumed. Laboratory results from BW13, BW15, BW15W, and
BW16 show that even using K7¢ = 0, methods in Section IV,1,b tend to give

conservative estimates of the transmission coefficient for submerged permeable
breakwaters (Fig. 40).

1.0

0.8

2 06
oO
a)
@
Sa
C04
© Sine Waves
0.2 a Irregular Waves
BW 13,15, 15 W
(0)
(0) 0.2 0.4 0.6 0.8 1.0

K ,(observed) '

K (predicted)

O 0.2 0.4 0.6 0.8 1.0
K, (observed)

Figure 40. Observed and predicted transmission coefficients
for submerged permeable structures assuming Ky = 0.

O12

d. Influence of a Permeable Breakwater on Other Wave Characteristics.
Wave energy shifts to higher harmonics are found in the transmitted wave
records for monochromatic wave tests, as determined for overtopped impermeable
breakwaters (Fig. 41). The energy shift is primarily a function of incident
wave steepness and the ratio of the water depth to structure height. The
largest shifts of energy to higher harmonics occur for steep waves where the
structure crest is near to the stillwater level (Fig. 41).

100 ny as one Be

°

90

80

70

Energy (pct.)

60

d/gT*= 0.016

50 BW4

40
0.0002 0.0004 0.0006 0.00! 0.002 0.004 0.006

H/gT?

Figure 41. Percent of wave energy at the forcing
period for waves transmitted past a
permeable breakwater (monochromatic waves).

In the case of irregular waves the higher frequency parts of the reflected
and transmitted spectra tend to be dampened out, so relatively more wave energy
is found at lower frequencies than in the incident spectrum (Fig. 42). This
means that on the average the spectral peakedness, Q,, of reflected and
transmitted spectra is greater than or equal to the spectral peakedness of
incident spectra (Fig. 43).

A zero up-crossing analysis of wave records shows that on the average the
wave height distribution shape is approximately the same for incident and trans-
mitted waves for the irregular conditions tested for a permeable breakwater
(Fig. 44).

The amount of wave grouping or the tendancy of large waves to follow large
waves and small waves to follow small waves is characterized by the autocorrela-
tion of zero up-crossing wave heights, p (see Sec. III,4). Results from BW16
show that the autocorrelation transmitted waves is less than or equal to that
for incident waves in the case of irregular waves incident on a permeable break-
water (Fig. 45).

The joint distribution of transmitted wave heights and periods for an
irregular wave condition is similar to that found for smooth impermeable break-
waters. There is a tendancy for lower transmitted waves to have average periods
less than found in the incident joint height-period distribution (Fig. 46).

Both the incident and transmitted larger wave heights have average periods
approximately equal to the period of peak energy density.

53

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54

( transmitted )

H/Hrms

5.5)

Curve ID Hy (cm)
1 7TANb61912A12 3,49
2 7hI619120A1 Le)
3. 76090191230 3.41
4 7HNO19190359 3.67
5S 7K0619124B %4e76
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7 77206191305 3,47
B 7H06191314 3eAT
9 7800191326 4.70
10 7806191335 4673
1} 7606191344 174
12 7890191355 1073
13 7400191402 2.25
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1.0 y
ohh
Bisa
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0.5
O
O 0.5 1.0 1.9) 2.0 258)

H/Hrms ( incident )

Figure 44. Comparison between incident and transmitted wave height
distribution for a permeable breakwater (BW16).

595

( transmitted )

H/Hrms

40

Curve ID H (cm)

78061509012
7806150924
7806151010
78061510924
7806131 4,42
7006151183
TAOSISI 246
7806151227
7806151238
7800151324
7806151335
7806151455
25 13 7806151407
0 10 7806160803
15 7806169A15

16 780e1600A2A

17 7806160838

2),0)

wero OV OterWV own

e= = eo

18 780616048
19 7806160a58
7806160909
2.0
O
a
+
x
1,5 °
- 0
x YO
|.
d/h = 1.06
ORS
)
6) ORS 1.0 lao 20) 29)

H/Hrms (incident )

Figure 44. Comparison between incident and transmitted wave height
distribution for a permeable breakwater (BW16) .--Continued

56

Figure 45. Autocorrelation of zero up-crossing wave heights for trans-
mitted and incident wave records for a permeable breakwater.

BWI6
ds/h =0.76 19 45 6
6 135814 ‘ 6 13
6 6 40 26 6 6
6 266 13
4 4
4
INCIDENT TRANSMITTED
7806191239 7806191239
; 1.6 : : 1.6
T/Tp T/Tp

Figure 46. Sample joint distributions of wave height and period for
an irregular wave condition and a permeable breakwater.

a

V. MODEL SCALE EFFECTS

1. Causes of Physical Model Scale Effects.

Wave energy dissipation and resulting reduction of wave height produced by
a breakwater are due to a combination of laminar and turbulent energy loss as
well as wave modification. Little information is available on scale effects
of wave transmission by overtopping, but scale effects are probably small.
This is illustrated by Saville (1963) who tested wave transmission by over-
topping for similar breakwaters that differed by a scale of 10. There was
little systematic difference between the results of tests run at the two scales,
with the small-scale tests being slightly conservative.

Wave transmission through permeable breakwaters is controlled primarily by
laminar and turbulent energy loss of flow through the structure (Wilson and
Cross, 1972; Keulegan, 1973; Madsen and White, 1976). In the protoytpe the
wave height reduction is due largely to turbulent effects, but in a model
laminar and turbulent losses may be important so that a model underpredicts
the coefficient of transmission through a breakwater. The size of the scale
effect is a complex function of model design, water depth, and wave height and
period.

The Interpreting and Applying Laboratory Results to Prototype Conditions.

The recommended method of estimating scale effects of transmission through
permeable breakwaters is to use the computer program MADSEN to predict transmis-
sion coefficients for the model and prototype. The physical model correction
factor, CF, is defined as the expected coefficient of wave transmission
through the structure in the prototype divided by the coefficient of wave trans-
mission through the structure at the model scale. CF is determined by first
running the program MADSEN with prototype conditions to determine Kp, (MADSEN
prototype). The program is then run at the model scale to determine K7+z
(MADSEN scale model). CF is defined as

Kp-~ (MADSEN prototype)

CE = (18)
Ke (MADSEN scale model)

The coefficient for wave transmission through the structure measured in the
physical scale model should then be multiplied by CF to estimate the prototype
coefficient.

For example, assume that the laboratory breakwater tested by Sollitt and
Cross (1976) is a 1 on 10-scale Froude model of a prototype structure (Fig. 47).
There was no transmission by overtopping. The program MADSEN was run at both
model and prototype scales and the results together with the physical model
measurements are shown in Figure 48. The MADSEN program output shows that the
physical model was probably underpredicting the prototype coefficient because
the scale model has proportionally more laminar energy loss than the prototype.
Even in this large 1 on 10-scale Froude physical model, the prototype Kz is
expected to be as much as 20 percent higher than in the scale model over the
range of conditions tested.

58

(0) j 2 3 4m Incident Waves

| Top Width 1.53m

T:7.9s

hg = 4.6m
Woter Depth
3.56 m

Horizontal Layer 1

Figure 47. Trapezoidal multilayered breakwater tested by Sollitt
and Cross (1976) (prototype).

d/h,= 0.77
d/gT*= 0.0058

1.0
0.000! 0.0002 0.0004 0.0006 0.001 0.002
H/gT2

Prototype Scale

Computer Program Prediction

Physi¢al Model (Sollitt and
Cross, 1976)

1on10 Scale Froude Model

Computer Program Prediction

d/gT?= 0.0058

10)
0.000! 0.0002 0.0004 00006 0.0o! 0.002
H/gT?

Figure 48. Physical model results and correction factors determined
from the analytical model of Madsen and White (1976).

59

VI. EXAMPLE OF ESTIMATING WAVE TRANSMISSION COEFFICIENTS

kK ke ek kK Kk kk ke kK kK kK kK K K K * BYAMPILE PROBLEM * * * .* * *% * & * * K K KF * *

GIVEN: T = 7.9 seconds
d, = 3.56 meters
Breakwater top width, B = 1.53 meters

Breakwater seaward slope, tan 8 = 0.667 (1 on 1.5)

FIND: The influence of incident wave height and structure height on the
transmission coefficient for the permeable breakwater shown in the upper
part of Figure 49 (change the structure height by varying the thickness of
horizontal layer 1). Also, compare the predicted transmitted wave heights
to heights for a similar smooth impermeable structure (lower part of Fig. 49).

SOLUTION: The computer program MADSEN (App. G) is used to predict wave
transmission coefficients for the permeable structure and the program OVER
(App. F) is used to predict coefficients for the smooth impermeable break-
water. The transmission coefficient for the permeable structure decreases
as wave steepness increases, until overtopping occurs when the transmission
coefficient increases with steepness (Fig. 50). The transmission coefficient
decreases as structure height increases and the initiation of overtopping
occurs at a larger value of the incident wave height as the structure height
increases. The similar shaped smooth impermeable breakwater has. larger
values of the transmission coefficient for the steeper waves examined (Fig.
50) because the runup is higher on the smooth structure. However, there is
no transmission for the impermeable structure for the small waves where the
runup does not reach the breakwater crest. The predicted transmitted wave
height as a function of breakwater crest height is given in Figure 51 for
two values of the incident wave height.

Material ds o(m) Porosity

| 0.381 0.435
Permeable Breakwater 2 0.190 0.435
3 0.095 0.435

Figure 49. Breakwater cross sections used in the example for estimating wave
transmission coefficients.

60

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61

VII. SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS

The primary conclusions from the tests of wave transmission and reflection
of laboratory breakwaters conducted for this study are:

1. A simple formula for predicting wave transmission by overtopping
coefficients together with the model of Madsen and White (1976) for trans-
mission through permeable structures can be used to obtain estimates of wave
transmission coefficients.

2. Limited tests with breaking waves suggest that the methods can be
used for breaking or nonbreaking conditions.

3. Tests with irregular waves show that the transmission coefficient for
irregular waves iS approximately the same as for a similar monochromatic wave
test. The mean wave height and period of peak energy density are the param-
eters recommended to describe irregular waves.

4. Irregular wave tests indicate that for permeable or submerged break-
waters the incident and transmitted wave height distributiors have similar
Shape. However, smooth impermeable subaerial breakwaters have height distri-
butions biased toward the larger heights for irregular waves because large
waves transmit more efficiently than small waves.

5. Transmitted and reflected spectra for irregular waves generally have
equal or higher spectral peakedness than incident spectra.

6. Joint wave height-period distributions have similar dimensionless
shapes for incident and transmitted wave records.

7. There is a tendancy for wave heights to be less grouped after they
have transmitted past a breakwater.

8. Transmitted wave energy may appear at higher order harmonics of the
incident waves for monochromatic wave tests. However, the tendancy for energy
shifts decreases as the wave transmission coefficient increases.

9. Additional work is necessary to develop generalized models for predict-
ing wave reflection coefficients and wave transmission through the crests of
breakwaters armored with relatively porous materials, such as concrete armor
units.

The recommended steps for design of a breakwater for wave transmission are:

1. Use the computer programs MADSEN and OVER to estimate transmission
coefficients for preliminary breakwater design. Alternative designs can be
tested by varying parameters such as:

(a) structure height

(b) crest width

(c) seaward and landward breakwater slopes

(d) water depth

(e) number, thickness, location, and diameter of materials
(f) porosity

(g) permeability

(h) wave height

(1) wave period

62

2. A sensitivity analysis is recommended on those input parameters that
are poorly known. For example, if there is some uncertainty in the value of
the design water level, predictions should be made over the range of expected
water levels keeping all other factors fixed. Comparison between the predic-
tions at different levels will indicate the importance of water level.

3. Estimate reflection coefficients from model results.

4. If possible, final breakwater design should be made with the use of
physical models. The program MADSEN can be used to assist in designing and
interpreting physical laboratory models and results for permeable breakwaters.

Copies of the program decks for the program MADSEN and OVER described in

Appendixes F and G may be obtained from the Automatic Data Processing Coordina-
tor, Coastal Engineering Research Center, Fort Belvoir, Virginia 22060.

63

LITERATURE CITED

AHRENS, J., and McCARTNEY, B.L., "Wave Period Effect on the Stability of
Riprap,'' 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).

AHRENS, J., "Irregular Wave Runup,"' Proceedings of the Coastal Structures '79
Conference, American Society of Civil Engineers, 1979, pp. 998-1019.

BOTTIN, R., CHATHAM, C., and CARVER, R., "Waianae Small-Boat Harbor, Oahu, g
Hawaii, Design for Wave Protection," TR H-76-8, U.S. Army Engineer Waterways
Experiment Station, Vicksburg, Miss., May 1976.

CROSS, R. and SOLLITT, C., "Wave Transmission by Overtopping,'’ Technical Note
No. 15, Massachusetts Institute of Technology, Ralph M. Parsons Laboratory,
July 1971.

DAVIDSON, D., "Stability and Transmission Tests of Tribar Breakwater Section
Proposed for Monterey Harbor, California,"’ MP H-69-11, U.S. Army Engineer
Waterways Experiment Station, Vicksburg, Miss., Sept. 1969.

FRANZIUS, L., "Wirkung und Wirtschaftlichkeit von Rauhdeckwerden im Hinblick
auf den Wellenauflauf,'" Mitteilungen des Franzius-Instituts fur Grund- und
Wasserbau der TH Hannover, Heft 25, 1965, pp. 149-268 (in German).

GALVIN, C.J., Jr., 'Breaker Type Classification on Three Laboratory Beaches,"
Journal of Geophystcal Research, Vol. 73, No. 12, June 1968, pp. 3651-3659.

GODA, Y., "Reanalysis of Laboratory Data on Wave Transmission Over Breakwaters,"!
Report of the Port and Harbour Research Institute, Vol. 18, No. 3, Sept. 1969.

GODA, Y., "Numerical Experiments on Wave Statistics with Spectral Simulation,"
Report of the Port and Harbour Research Institute, Vol. 9, No. 3, 1970.

GODA, Y., "The Observed Joint Distribution of Periods and Heights of Sea Waves,"
Proceedings of the 16th Conference on Coastal Engineering, 1978.

GODA, Y., and SUZUKI, Y., "Estimation of Incident and Reflected Waves in Random
Wave Experiments," Proceedings of the 15th Coastal Engineering Conference,
Vol. 1, Ch. 48, 1976, pp. 828-845.

GUNBAK, A., "Rubble Mound Breakwaters,'’ Report No. 1, Division of Port and Ocean
Engineering, The University of Trondheim, Trondheim, Norway, 1979.

HUDSON, R., "Design of Quarry-Stone Cover Layers for Rubble-Mound Breakwaters ,"'
Research Report No. 22, U.S. Army Engineer Waterways Experiment Station,
Vicksburg, Miss., July 1958.

JACKSON, R.A., "Design of Cover Layers for Rubble-Mound Breakwaters Subjected

to Nonbreaking Waves,'' Research Report No. 2-11, U.S. Army Engineer Waterways
Experiment Station, Vicksburg, Miss., June 1968.

64

KEULEGAN G.H., "Wave Transmission Through Rock Structures,'' Research Report
No. H-73-1, U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss.,
RED) > MVS.

LAMARRE, P., 'Water-wave Transmission by Overtopping of an Impermeable Break-
water,'' M.S. Thesis, Massachusetts Institute of Technology, Sept. 1967.

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

RYE, H., "Wave Group Formation Among Storm Waves,'' Proceedings of the 12th
Conference on Coastal Engineering, 1974, pp. 164-183.

RYE, H., "The Stability of Some Currently Used Wave Parameters,'' Coastal
Engineering, Vol. 1, 1977, pp. 17-30.

SAVAGE, R.P., "Laboratory Data on Wave Runup on Roughened and Permeable Slopes,"
TM-109, U.S. Army, Corps of Engineers, Beach Erosion Board, Washington, D.C.,
Nebe., IES),

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., "Hydraulic Model Study of Transmission of Wave Energy by
Low-Crested Breakwater: Ship Mooring Study, West Coast of Point Loma, San
Diego, California," unpublished Memorandum for Record, U.S. Army, Corps
of Engineers, Beach Erosion Board, Washington, D.C., Aug. 1963.

SOLLITT, C.K., and CROSS, R.H., "Wave Reflection and Transmission at Permeable
Breakwaters,'' TP 76-8, U.S. Army, Corps of Engineers, Coastal Engineering
Research Center, Fort Belvoir, Va., July 1976.

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, Va., Mar. 1978.

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

WEGGEL, J.R., "Wave Overtopping Equation," Proceedings of the 15th Coastal
Engineering Conference, American Society of Civil Engineers, July 1976, pp.
2737-2755 (also Reprint 77-7, U.S. Army, Corps of Engineers, Coastal Engineer-
ing Research Center, Fort Belvoir, Va., NTIS A042 678).

WILSON, K., and CROSS, R., ''Scale Effects in Rubble-Mound Breakwaters ,"

Proceedings of the 13th Coastal Engineering Conference, American Society of
Ciyall jemivimeeies, WOl, S5 I9/25 joie Mes Wee

65

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APPENDIX A
BREAKWATER GEOMETRIES

Each of the breakwaters tested is assigned an identifying code (e.g., BW1).
This appendix includes a cross-section drawing and a brief description of each
of the breakwaters. Note that breakwaters 1 to 12 (Figs. A-1 to A-14) were
tested on a flat tank bottom; breakwaters 13 to 17 (Figs. A-15 to A-19) had a
1 on 15 fronting slope 3.75 meters long. Materials used in construction of the
structures are identified by a circled letter; material characteristics are
discussed in Appendix B.

67

B=30cm

| | Smooth Impermeable

0 0.5 1.0 m BW!

Figure A-1. Breakwater 1 cross section.

BW1l is a smooth impermeable structure tested for wave transmission by
overtopping and reflection. Note that simultaneous measurements of wave
runup were being made on a smooth 1 on 1.5 slope in an adjacent flume by
Ahrens (1978) while the breakwater tests were underway (see Fig. 1).

Impermeable

0 0.5 1.Om Bwe

Figure A-2. Breakwater 2 cross section.

BW2 is similar to a casson breakwater that has been rehabilitated by
adding rock armor units. The major emphasis of these tests was to examine
the effects of wave period and height on transmission and reflection. Armor
material was randomly placed.

68

B=40cm

party he= 66cm

Qa BW 3
0) 0.5 1.0 m

Figure A-3. Breakwater 3 cross section.

BW3 has an armor two units thick of angular stone. A moderate amount of
fitting was used in placing the armor, especially near the crest. Core material
was placed by dumping.

ro hs= 66cm

54-cm-High Plate

) 0.5 1.0m BW3W

Figure A-4. Breakwater 3W cross section.
BW3W is similar to BW3, except that a 5-millimeter-thick metal plate was

installed in the center of the structure. The caulked plate extended from
the bottom to within one armor unit of the crest (54 centimeters high).

69

| | he= 66cm

BW4

Figure A-5. Breakwater 4 cross section.

BW4 is similar to BW3, except with a 1 on 2.6 front-face slope.

BW4w

Figure A-6. Breakwater 4W cross section.

BW4W is similar to BW4, but includes a 54-centimeter-high impermeable plat
in the center of the structure.

70

O 0.5 1.0m BW5

Figure A-7. Breakwater 5 cross section.
BWS, geometrically similar to the upper part of BW3, is typical of a

breakwater built in relatively shallow water. The armor unit size is large
compared to the structure height and the core size relatively small.

Figure A-8. Breakwater 6 cross section.

BW6 was made of three triangular, fine wire containers filled with core
material.

71

Oo
(S))

a ean A)
0 0.5 form BW

Figure A-9. Breakwater 7 cross section.

BW7 is geometrically similar to the core of BW3. The material was held
in a fine wire structure to prevent motion of the stone.

(Edt Sa ne
0 0.5 LOn BW8

Figure A-10. Breakwater 8 cross section.

BW8 uses dolos artificial units as part of the armor material on both the
front and back of the structure near the crest. Stone was used in the lower
parts of the armor. A moderate amount of fitting was used in placing the
armor units. An impermeable cap was installed toward the seaward side of the
Gresite:

72

B=30cm

aA 2 2c SR
© 0.5 Om BW9
Figure A-11. Breakwater 9 cross section.

BW9 is similar to BW8, except that armor units have been arranged so that
all of the dolos units are on the seaward side of the structure.

[SEER sien S| oe
O OS) 1.0m Bwid

Figure A-12. Breakwater 10 cross section.

BW10 was made with an armor one unit thick of well-fitted rectangular rock.
The material was placed with one surface parallel to the structure face.

“3

BWI

Figure A-13. Breakwater 11 cross section.
BW1l was made of two fine-wire rectangular baskets that enclosed core-type

stone. The primary purpose of this structure was to examine the wave trans-
mission and reflection characteristics of permeable material.

B= 30cm

O 0.5 |.Om BWlie

Figure A-14. Breakwater 12 cross section.

BW12 is a structure with no core similar in geometry to breakwaters 8 and 9.

74

eoreene he= 33cm

lon 15 Fronting Slope,
3.75 m Long

Flat
ee el bn A A Es
O 0.5 1.Om BWI3,15

Figure A-15. Breakwaters 13 and 15 cross section.

BW13 and BW15 were tested with a 1 on 15 fronting slope 3.75 meters. Note
that these structures are the same geometry as BWS (built on a flat tank bottom).

lon 15 Fronting Slope

O OFS 1.0m BWI4

Figure A-16. Breakwater 14 cross section.

BW14, a smooth impermeable structure, has the same outside dimensions as
permeable breakwaters BWS, BW13, and BW15.

USD

B=40cm

hg = 33cm

lon!5 Fronting Slope,
3.75 m Long

22-cm-High Plate

BWISW

Ce ee ee
(@) 0.5 1.0m

Figure A-17. Breakwater 15W cross section.

BW15W has the same dimensions and materials as BW13 and BW15, except that
a 22-centimeter-high metal plate 5 millimeters thick has been installed in the
center of the structure. This plate prevents transmission through the lower
part of the structure.

ton !5 Fronting Slope

1 BWI6

Figure A-18. Breakwater 16 cross section.

BW16 is a one-ninth scale Froude model of a proposed submerged breakwater
for Imperial Beach, California.

1 on 1/5 Fronting Slope

aes Sele esl neces ee

Figure A-19. Breakwater 17 cross section.

BW17 is a vertical permeable structure, similar to BW11, with the rock
retained by a thin wire mesh.

76

APPENDIX B
MATERIAL CHARACTERISTICS

Materials used to construct permeable breakwaters are discussed in this
appendix. Each material is identified by a circled letter and shown on the
breakwaters where it was used in Appendix A. Figure B-1 includes photos of
samples of the various materials (material F, not shown, is similar to A and
B). Some basic parameters, such as weights, diameters, and porosities, are
shown in Table B-1. The weight distribution of each.of the materials is
given in Figure B-2.

at

“sTeTiezeuW UOTONAYSUOD FO so.OUd

WD Ol

uD Of

‘[-q omns ty

UD Ol

78

Table B-l. Material characternlsitics:

rie ; c 1 2 3
Material Description Wes Weg Wis

(g) (g) ‘ (g) (cm)

Angular stone 2,520 S50) 990 8.3
Angular stone 4,680 3,690'| 2,900) 11.1

Angular stone 180 68 31 Bos)
Dolos 405 390 390)
Flat stone 13,200 } 11,200} 8,100] 16.1

Angular stone 7,600 ASIOOWM2ZE SOON (2752

=

IWeight at which 85 percent by weight of the
material is heavier than.

2Weight at which 50 percent by weight of the
material is heavier than.

3Weight at which 15 percent by weight of the
material is heavier than.

4Representative diameter corresponding to Wep.
P Pp g 50

20,000

10,000
8,000

6,000

4,000
2,000

1,000
800

600

400

Weight (q)

20

0.1 '2 5 10 20 40 60 80 9095 9899 999
Pct of the Material Heavier than a Given Weight

Figure B-2. Weight distribution of the construction materials.

is)

10

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5B 32U09SU,
VAos2uiate.
Y8032410550
TAO32U}143,
YBo32u1130.
70032711126
7803241058.
7803243202,
YSo03euyr22,
yRoseryiyas,
7803271129,
7803291325.
TASTY 311.6
9803271256,
YRoO%2N7; 429,
TAv3eT{ U3.
TBO3CAL 132.
YBOS2ALISN,
78032Aypuu,
T8os2A 144,
7803281059,
TAO S2R1S22,
78032A 4307,
PA032R1253,
YBO3S2RLb000
¥805290958,
7803290930.
9803291259,
7803293142,

TILL0211 30,
T711021147,
YT110212116
7711081009.
7711021018.
F7IL10A0902,
PI110A0911,
77110219404,
4711080929,
TYL10R0948,
T711021NS6,
77110212306
7711021238,
V711021252.
TTLL0RL O37.
Y711081054,
FTILLOALY 11.
P7L10A1127,
7711021318,
T7110P1332.6
¥711081445,
TTLL0BL2 016
PTILLOBL 247.6

1712231300,
7712231359,
7712241129,
W711 2231115
7712231447,
W7122351201e
7712231239,
1712231226,
9712231253,
7712230726,

TEST RESULTS (SINUSOIDAL BLADE MOTION)

OCCM) 168) WECM) KF

900
900
90.0
65.
85.
806
80.
BO.
75.
7S.
75.
75.
73,5
156
700
700
7%.
65,
65,5
60+
606
600
O00
00.
oe
606
556
50.0
500
45So
45>

ol.
ble
61.
Ole
Ol».
Ole
ole
Ole
ols
610
Ole
b1o
ble
Ole
ole
ole
ol.
ble
blo
ole
ole
ole

9S,
9s,
V15
Gio
91.
91.
91.
Vie
91.
85,

2,99
2.39
e.39
2.32
@.32
2.25
2.25
(ey ee}
3.42
3.42
2,38
Bo1A
1.14
101A
Rall
Q.1)
fel!
2,03
2.03
3.06
3,06
3.06
1.95
1.98
1.95
1.05
1.05
1.87
408
1.78
2.65
1.69

214
2.18
2.14
1.97
1.97
1.97
1.97
1.97
1.97
1.97
1.97
1.06
1.66
$066
1.3!
1.3)
1.31
1.31
1.06
1.06

0A9

289

Pek)

2.46
2.46
3.77
3.77
2,67
2.40
EY)
@.02
2002
3,05

oAAn
0876
0744
9A
0646
0 AO9
070A
056a
o2hu
o3oy
0251
o4aj
0275
0373
0259
o4aj
04S>d
022A
0468
0016
0202
0 3Ou
001
0193
o4h7
0084
o!2a
e294
0061
0094
0042
006d

o30)
027A
1244
0622
e4BA
o4an
0333
«233
0238
0269
02h6
0474
0349
0244
0293
0228
227
of 4%
01046
09Bt
02th
0154
0134

oApe
2844
Ay
0785
0427
0648
1865
0439
0787
0832

SINE BLADE MOTION

APPENDIX C

KR O/GT2 H/GT2

BREAKWATER 1

28A0
0876
e714
0918
2646
0899
2700
0564
vebd
oBoy
083}
0 G4)
0275
0373
0259
eo GU}
0452
0220
0405
0016
0202
0398
0001
0193
0417
0084
oleae
0234
0003
0018
0012
00624

0016
0016
0016
0016
0016
0016
0046
0046
0007
0007
0046
0016
0055
2055
0016
0016
0016
0016
0016
0007
1907
0007
00)6
0016
0046
0056
0056
0016
0016
0016
0007
0016

20002
20008
00034
20003
20021
00002
20008
00033
20003
00011
20002
20010
00026
00101
20017
00031
20053
00028
00046
20009
20015
00024
00024
00042
00063
00076
00130
20047
00038
20048
00021
20055

BREAKWATER 2

0397
2278
oP40
062e
0480
0420
0333
0a53
0256
2260
02ub
0476
0340
eau
0293
0228
e227
014
0196
008)
e216
0156
ol 34

0013
2013
0016
0016
0016
0016
e016
2036
0016
0016
0025
0025
0023
0036
0036
0036
0936
0056
2056
0079
0079
0079

20009
20020
20037
00003
20007
20010
20014
20027
20024
200U8
2004U9
00009
00017
00036
20018
20032
00056
20088
20069
00151
20050
20066
20106

BREAKWATER §

0826
26uy
0817
o7AS
087
0648
On Jab }
0830
0787
0832

0046
0036
0007
0007
0013
0016
0016
0025
00e3
2007

00014
20028
00001
20006
00018
00031
20035
20029
20053
20001

80

10 O(CM) 768) HICH)

THO32UOAHH.
TB03@40ASA.
7803240942,
TAOYZULOOSe
PBO%24U1 0206
7863241105.
7803241122.
TB03%2TIYI9%®
TBO0%2T1104e
7803241152.
T803241 2126
78032841239,
TAO SSTI1 3b.
TA8032TI335—
TBO¥LTIYI Ae
TAOVETIIOX.e
TAO%2TILUSbe
TBOVeTIU2ho
78c%e71U0S.
7803e81{ 42.
7803281 23A,q
7B0%2B13226
ThOVAALLO7.
VOC VeASi ue
7T80%e81L yuo
78032813006
78032816085
7803281552.
76032909400
TB032913310
78032912405.
7803291 Su

7711021155.
77110212040
T711081000.
T7110810246
7711080A52_
TT110210260
7711080920.
T7T11021035ue
7711080939,
T7149211036
T7T11921223.
T711021 2426
T711021 244.6
7711081029,
T711081 0460
77110831036
77110814196
77110611356
T7102) 316
77110213266
T71108!4S3e
771108120%.5

T7{ 2231347,
77, 2231U0S.e
T712231 1220
T71225143R.
7712231 20AR6
T712¢d311530
17122312156
7T712a312336
T7122333006
7712230733,

90.
90.
65.
45.
65.
60.
60,
15.
75>
75.
v5.
75.
15.
7%.
70.
YO.
65.
65,
65,
60,
60.
60,
60,
60.
60,
60.
55.
$5.
50.
USe
45,
4S,

ol»
61.
ol.
61.
ole
ole
ol.
ble
ole
61.
ole
61.
ble
ole
bl.
el.
ol.
ole
ole
ole
ol,
ble

95.
95.
G1.
91.
Ql.
91.
V1.
91.
91,
65.

2.39
2.39
2.32
2032
2.32
2025
2.25
3.42
3,42
2.18
2.18
2018
1.18
aol
el}
eel
2.03
2.03
2.03
3,06
3.06
1.95
1.95
1.95
1.05
1.05
1.87
1,87
1.78
2.605
1069
1.69

2.18
2014
1.97
1.97
1.97
1.97
1.97
1,97
1.97
1.97
1.66
1.66
1.66
1.3!
1.3)
1o3!
1.3!
1.31
1.06
1.06

289

269

2.46
2.46
3.77
2.67
2040
2040
2.02
2.02
1.60
3.65

N
@enweewn OF

© e@ © © © © © © © © © © © © © © © © © © © © © © © e@ © 2 © © © eo

NOWwWN-FOANECWOwWwOCCT OVO PwC BOM SCEw’EA AH

WMEWWO-NUVNNWOATON LF ON OWVRWONW

CeEewetdowWFn Oen @wcon~x

RH Ke ONY WYNN COOwWC COE WH

Ky

0676
0806
0898
»Ab1
0555
o6U8
o6}1
0240
2332
0168
0315
0543
2369
2089
2349
0478
2073
2328
0452
2.087
331
0001
0988
e4uu
0905
0145
0051
0304
0011
2009
0043
2069

0276
0239
2689
0567
0489
0390
0300
0255
0?36
2233
e469
2349
024)
0356
2256
2ee0
019)
2164
0194
0104
0166
0148

2609
2 85u
0804
2830
0451
05358
2838
A)
0715
0793

KR D/GT2 H/GT@

876
2606
0898
0 6A4
0555
2646
26))
2240
e332
03668
0515
0543
0569
0 0A9
0349
0478
0073
0528
0452
0087
0331
009}
00R8
e444
20003
0145
2051
0304
e011
0009
0043
2089

ae76
0239
26A9
0567
0489
0350
0390
0255
0236
0253
0469
2549
ecu
0536
2256
2220
0191
0164
0194
0104
olb6o
03486

2809
0854
0804
2630
085]
0338
0638
0646
0715
0793

2016
2016
0016
2016
0016
2016
2016
2007
2907
0016
0916
0016
2955
0916
0016
2916
216
2916
2016
,007
2007
0016
0016
2016
2956
2956
0016
2016
0916
2007
20lo
2036

2013
2913
2916
20436
0016
0016
2916
2016
2016
0916
2023
oes
20e3
0056
2936
21056
2036
1036
0056
2096
,079
2079

2016
2016
2007
2013
0016
2016
2023
2023
20036
2007

00004
0017
20002
20910
00046
20004
20016
00001
20005
20001
20003
20021
20059
20012
20023
20040
20021
00036
00054
20012
20018
20017
20033
00061
20055
20115
00032
20060
00043
20019
10081
00036

20020
20936
20002
20005
00007
00014
20020
00027
20037
20049
00009
20017
000456
00013
20025
000354
20049
00108
200862
20157
20095
00079

20020
20040
20003
20006
20005
200284
20015
00041
00096
00002

SINE BLADE FOTION
10 OCCM) VC8) HCCH) KF KR O0/GT2 N/GT2 10 N¢CM) 1¢8) HCC) KT KR DsGT2 H/GT2

BREAKWATER 3

Y712230750. 880 3063 1403 072% 07239 0007 ,0011 T712230A81b60 B50 2058 106 o804 6804 013 ,0002
Y712230808, 830 2058 GoS 892 0802 0013 10007 77122307599» 850 2058 1209 «791 6791 »013 ,0020
Y712230829. 850 BoB2 100 0968 0904 001% 20002 77122308320 B5e 2032 351 1849 2840 016 40006
Y712230839, 650 Pod2 oY o 7B} 0781 FOL 20018 T712230BU5. B50 2032 1305 0766 e766 gOIE 20026
7712230855, 880 2032 19e2e 0733 0738 0S 20036 77172309150 856 1296 269 ,864 ,FHY ,023 ,0008
712230908, 850 $096 807 o83H 0818 1023 .0023 T7172309010 B55 1296 1708 6798 6798 4023 40047
712230922, B50 1084 Peo 0938 0912 0037 20009 77122309290 850 1054 5.8 »A59 2859 4037 ,0025
Y712230941, B50 1054 1702 0735 0733 0037? DOOTY TI1AC2URS Oe Fe 3042 365 093% 0939 4007 40001
7712221436, 750 Je42 Gof 075M 0758 0007 20004 T712221A43, 75, 3e42 12,7 2600 2600 ,907 20011
97122219030 750 BeG2 Bal 0706 0796 0013 20004 T7\ 22218970 755 2042 650 0702 o702 40135 ,0010
Y712221450, 750 2042 1708 e622 0628 0013 .0030 77122219160 750 2018 102 0871 6871 ,016 10003
9712221909, 750 BotB 304 086) e867 .016 .0007 77122239220 755 2618 1060 1.685 .6A5 016 ,0921
9712221929, 750 2olh 1401 0835 063% 0016 0030 77122219UB, 755 J,84 2.8 «829 6629 023 2.0008
9712221942, 750 3.84 8.0 066) 0661 2023 .0024 T7172219560 75e 1eA4 14467 627 5677 .N23 ,0044
9712221954, 750 10643 3.8 oAP® 1829 1036 ,0018 TI 22220015 Me 1045 1005 697 2697 6056 40950
Y712222007, 730 Lo4S 170d o4PH 0896 036 ,0084 T712221012» ble 2006 Sed p46 »U46 ,007 .0006
TI1227180b— Ole 3006 7o7 o39A 0378 4007 ,0008 TTIVP2209S9Ie ble 32.06 1005 136% 2349 ,007 0011
TI1222U952— O10 $e06 1307 ob 0414 2007 40015 T7T422210Ubs O1e 2017 Soh 052% 2579 6013 20003
4712221638, O10 Rol? Geo o39Q 03992 0013 .0010 T7122210310 Ole Aol? Vol e341 0341 ,913 0015
Y712221923_ Ole Bol? 1007 0297 0297 O13 0023 77122210196 Ole 2e17 1505 06337 o337 ,O13 2054
F7122210510 O10 LeMS Jeb 46H 0460 0016 40007 77172210357 e bLe 10695 oh 339 6339 4016 60020
9712221104, O10 1095 11.3 02861 0281 2016 .0030 TI12e211100 Ole 1095 1969 6297 2297 gO16 20043
Y712221117e O10 109S 2lo¥ ofa e312 001% ,0087 TT 22214520 ble 1064 1,43 6518 2518 .123 0005
Y71222114U, Slo $eO4 3.5 oUt 0491 2023 20013 TINA T Sie Olle Ne G4) Seid eS 5Oy 0 SSG) 9 Oecd D120
7712221129, OLo 1064 1005 0259 229% 2023 0040 TIM Pe21{23e S1e 1264 15.8 w276 .276 .N23 20060
9732221158, O10 be30 207 oh13 e813 0037 20016 TI 2e2120Ue Sle $030 Se? 1295 0295 ,OS7 40054
T7122217P105 O1e LodM Bef o25H «ohS50 «037? ,0049 77122212160 Ole $430 1800 w2ee4 peu ,037 .0072
Y712221222, blo Led0 1703 e238 of38 O37 0104 771219133560 450 3051 GeO o 314 e314 ,004 ,0004
Y12191 328. 4So 9051 607 oP7G oBTY 0004 20006 TTY2L9L319%e 4So 3051 G2 4240 .2u0 094 ,0008
TL21913100 4So Sod1 12eh 0241 o211 0004 ,0010 TT12191U250 YSe 2065 See 4309 6399 4007 40005
G712191G07%. Se BobS Yo 0256 0856 0007 10007 TTY2191LULUe G56 2065 669 .209 9219 ,007 ,0010
YIL21913SU, GSe 2o68 1004 of68 e163 0007 .0018 TIV219L BUG. YSe 2065 1563 015% 0139 ,007 20022
9712211020. 450 1688 3.0 oP38 0@38 0013 10010 77122110085 45s 1088 4oF 6193 0193 ,013 ,0014
7712191003, 4So 1588 9,3 913 0134 0013 .0027 T712191U3S3e 4Se 1088 1453 e107 0107 013 20041
T7122110520 4So $069 be e156 0136 0016 20022 77122110480 YSo 1069 Gee o124 o12U 4016 20033
F712241038— YSe 1069 1307 of10A 0100 0016 0049 7712211029. G5 106% 1% 52 6096 4096 4916 40009
Y7122411120 430 teh2 Bed 0089 0089 ,023 0040 T7122111060 4Se 1042 1eol 072 2072 ,023 20061
TIL221165%. YSo te4B $404 of 41 0141 2023 007) TI1221112b6e G5 tol2 1003 2040 040 ,037 ,0064

T712211119%e GSe LolR 1301 06349 0038 0037 20107

BREAKWATER Sw

7711290906, 85, G.B¥ 104 oAG$ o84S p0N4Y .0901 7743290927, B5e 4eB3 YeB 0779 4779 ,00U 40002
7711290987, BS, YoBS 107 o843 0813 ,004 0006 7713290949. B50 3265 58 .AbY 864 ,007 .0001
9711290959, 850 3063 206 oASK 0826 007 ,0002 7711291009. 850 3065 824 0776 0776 4007 50906
Y7L1291021, 850 P88 168 081% o817 0013 40003 7711291029, B50 2.58 Sel .R28 628 ,013 20008
T711291957, 835, 2,358 18.3 oAIV2 oB87a 013 wV022 7711291 04B, B85e 2032 29 ~890 .890 ,016 20902
7711291057, 85. Bo32 207 oAQR 848 2016 0005 TTI11291; 060 ASe 2032 Bee 784 47AU 4016 40016
Y711291120—. 855 1696 100 o9{A 0918 2023 ,0003 TTIAL291133e B5e 1296 2.9 2861 wGAL .N23 .0008
9711291108, 65. $096 8.6 oA3A oB3H 2023 0023 TTI1129115R 5 85s 1596 1606 .AUS 2HU5 ,02$ ,0N4U
9711291208. 85s 1.34 203 oAG{ 1691 2037 20009 T711291 2166 BS. 1054 625 .AU2 wHU2 4057 .002R
Y7I112R0936, Toe 3n42 2ey eo TIA 0778 20007 UCD? T7311 2RU9UT, The $242 624.0 p64e wbue2 ,007 20005
T7112R0951_ 76e S$e42 1408 0529 082% 2007 20014 TUPI eva Wp Cote) Nes pvyBO Ayo SOs GooO!
TT112810160 760 BeG2 Seb 0673 0673 2013S 20009 T713281 0010 T6e 2042 1608 1603 2693 ,013 »0029
PIVLZALO37%, 760 BelB 104 oPfd 0772 0016 20903 T7112B104URe %6e 2018 4e0 0706 07% 216 20009
T71128165%, Toe 2018 1206 0670 0874 0016 ,0027 T7IL12BLL1L26 %6e 2018 1865 e492 4492 ,O1K 40040
YIL12R11S60 Te be84 300 0754 0754 0023 10009 77112511465 The 1084 8.45 «629 y629 .M23 10026
PILIVPAL 1226 760 1e8U 1507 036d 0362 0023 .0047 T7112B12036 760 tedd 208 2823 2425 ,057 29014
VT112B12100 T6e 1648 Bey 0739 0 71% 0037 20039 TT112B3 P2160 760 1045 1502 6545 0515 6057 ,O0TY
I7112B1224— Tbe Lolh 203 0831 0811 1056 20017 7711281359. 76e tot V%eb 6656 «656 4056 00056
TT112R1U0b. 76 $018 1509 ebb? e462 0056 00117 T7\12B1ulu» 76. 9B 265 932 2932 ,081 0027
F7112R1U21_. 76s FB 5a7 o7b2 0762 2081 2006} 7711281u27. 7E, «9A 8.8 686 »686H ,081 20095
F7L1230b350, Ole 3009 3,4 SPA 6378 2007 20004 TT11221UUN, ble 3609 629 2304 230K ,N06 .0007
7711221429. O10 3o0% 120d 0303 oIIA 2000 20013 TILL221U0Rs 615 3609 20.0 2443 4US ,0U6 20901
YILL2S30A3F%. OLe 2olB fod ohH8 040% 0015 20003 TT1;23084H. OLe 2018 2a) 237! 037} OLS 20905
T7112308S4, Ole BolS Yet o2BH o@86 0013S 40909 77412309G2. Ole 2018 9.2 w277 set? 29135 20020
PILLZ309100 Ole RolA 1707 obt1 oh11 0013 0038 T7112309200 61e Le97 202 0357 0357 2015 20056
7711230927, O10 1097 Beo o3ah 0320 0016 ,0008 7711230955. ble Jeo97 Yee 289 .2RO .016 ,ON11
T7LS2309U2, Sle 1697 $e «25H oLS0 r01S 0046 7711230949, 61, 1297 8,3 .228 «226 4015 ,0022
PILL231003, O15 1697 19.0 e272 0872 .016 ,0050 T7112310100 OLe 1097 2604 2356 0356 2016 40069
9741231028. O10 tobo Boo o3A4 e324 .023 ,0011 T7112310360 ble 1066 606 0239 2239 ,023 20024
DUD ROONUEE Ole 2066 1805 1290 0294 oO2S .0057 T71123L09S0 Sle teoSl $00 6383 o3A3 036 ,0006

FLLA]B1102. Ole Led! o¥ 0296 0296 0036 ,0014 T7L12S311200 ble 1031 Fed 184 w1AuU 636 ,004U
P7AL2S31128. Ole Lodi 1701 0234 e234 036 ,0102 T7AL2A311 39% Sle 1606 1568 .233 2233 ,055 20016
YVLL2311 Gb. Ole $006 3.5 017% 0173 0055 0082 T7ILV231153e ble 1006 705 yle7 0127 055 .0068
97112312000 Ole 1006 1507 0157 0157 2055 wO1US TT12191119%9 Y5e 3,51 700 .084 wOAY ,004 ,0006
Y71219110%. YSo Bedi 102 0077 0077 0004 ,0010 T71219113ud~ 45. 2,65 Yel .058 2.058 ,007 2.0910
Y7L21011B7. Se Boos 1503 oASR 2082 0007 10023 T7L219L14 10 Se 2688 %.5 2034 2034 O13 20027

81

1D DCCM) TCS) HOCM)

TAOLIAI430,
TAOLLBaj4,
FOOLIAL35%,
Y8011A1503,
TBo0LL8yuSN,
YROVLALa37,
78031815156
78011911066
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PA0LLO1149,
78012011330
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76011913106
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7801191427,
78012n0959,
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7801201030.
78012012155
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7801201239,
78012013110
7801201323.
7801201 3ud,
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TEOL2; 1421,
7801211828,
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VBOLE11554,
7801211606.
28012116310
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7801211659,
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7801211723,

7801181155.
THOLIB11406
y8orteasyec,
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TECTIB1214.
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7801141259,
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TBOTOTOBILUe
7807070755.
7BCOR151133.—
TAOBISI1L196
78081515056
78070710056
78070709476
TB80707I N30
TBORO207196
780R020735e
78081511456
TB07071129,
78070710470
78070711360
TEOTOSL USA,
TBO7T0S1 Udy.
TECTOS1 ibe
780705133u.6
780705135A6
78070514056
7807051u2u._
78070515150
7TB07T05152Re
T80705154%
78070516010
78070515496
78070516200
78070516326
THOTO71IU37.
78070714530
78070712268
TEO7TOTL815_
78070713006
TBOTOTL3220
TECTO7T133A,
TE8OTOTIG1I9®
78070714040

306
306
306
30.
306
306
30.
30.
255
250
25%
250
256
250
256
256
250
250
20,
20.
200
206
20.
206
200
206
200
206
206
200

50.
50.
50.
506
50.
50,
500
50.
50.
50.
59.
50.
5%.
50.
S06
SO.
50.
50.
50.
50.
S0e
U5e
U5e
4Se
45
45.6
US.
uS,
USo
456
4S,
456
us,
456
456
35.
356
35,5
35.
350
35.
35,
35,
350

2017
2017
1.53
1.53
1.53
1538
1.38
1,36
3.70
3,70
3.70
2262
2.62
2062
1.40
1.40
1.26
1.26
3,51
130534
3.51
3.51
2034
2534
2034
2054
254
1077
1.77
1077

6299
6.99
6.34
6.354
6034
6.34
6,34
5.17
Sel?
4,54
4,54
4,54
3.79
3,70
2,80
1.87
1,87
1.87
1.78
1078
1.59
6.99
6090
4,91
49}
4,91
3091
3,51
2.65
2065
2065
1.68
1.68
1,69
1.69
6.09
6.09
4,33
3010
3.10
2.34
2034
1.49
$249

= rs = —
“~SOO@OuUTDONAOUH WV

SHDK—VNK-MWOWT—- KV STTFKNVNVFTWUWYUK-wWOROFWENWOMUN LG OFN

KR O/GT2 H/GT2

2536.

0434
0656
2530
2213
0377
0298
226}
487
0387
eco
e467
ase
2283
oP hl
o14u
0150
9140
6/\t/
ble
444
0225
24S
o472
0316
2209
0169
2605
0295
2175

692
0559
0934
o67k
0682
256)
9458
e670
9943
2546
as77
0296
0501
2367
2689
24o7
409
e311
2472
e294
2352
2660
2475
pou
247i
2 384
0624
e443
0754
0553
0 381
492
e317
20551
0453
e728
0523
2370
0707
0596
0637
2460
0603
e425

2007

2007

2013

2013
2013
216
0016
2016
2902
2902
2002
290d
290d
2004
2013
2013
2916
0916
2002
6002
2002
2002
6004
20040
2008
2004
2004
2007
2907
7007

20909

00932

20003

20054
60105
00014
70044
20080
20001
20002
00014
20904
00912
00925
20028
00094
00064
eOlle
20000
20001
20002
00013
20002
20007
00033
20025
20039
000048
20018
00040

20001
20002
00900
00003
20001
20002
20004
20001
00002
00001
00l2
20904
e001!
00904
Oe
20028
20055
00919
20975
20053
20001
00003
00901
00005
00906
20902
20910
20000
09009
20027
20016
0096)
00905
e022
00001
20005
20005
20001
20006
20005
20018
20006
00029

10

78032A1383,
YBosy2aiays,
FAOS2RLA3I,
PA0S2RL OSI,
7803250934,
7803270952.
7803241013.
78032710326

F8or19133a,
7801191354,
TAOLI9IL U0,
7T801240A17.
7801240A34,
¥Bo12r1312.
7801211327.
7901211339.
7501211 74%
7801211820.

78011816004.
TEOLLGLOL9®
Y8011910416
7801180945,

9802010809,
7802010912,
7802010935.
7802010957,
TBOP011A21e
TAUPOSLOST,
786131¢957,
7801311023.
TROL3S{10466
7801391109,
TE013111316
7801391154,
7802020832,
7802020847,
7902020904.

7802071316,
7802071332.
P802071 34GB,
FA020h02256
7802060239,
78020811156
723020811346
yRoeoR1154,

1802221444,
7802221341,
9802221357.
2802231026.
7802231055.
Y8vu22u1 403,
790227115465
7TB02271a14,
YROR2R1301.
FA022A1 3226
75022A1 342,

7893060930,
7803060948,
TAC3SOHIA06.,
TAOSOH1O2S.

Acc)

4S_

73.6
606
600
45,
as,
45,

7S,
73.
756
756
75.
75.
600
60.
u50
4Se
US.

736
750
75.0
75.

¥C8) CCM) KT

1.60
1.62
3.32
5.32
1.3a
1.56
3.a8
2.00

2,12
2.03
1.4u
2.23
1,3
2012
2.03
1.44
2.35
1.50

1038
1.82
1.04
4.02

1.88
1.19
2.44
1,45
1,34
1.88
2.64
1.55
1.16
2.04
1.55
1.16
g.12
2.35
1.30

91

1.82 |

1.44
1.30
1.53
2,12
1037
1.30

1.43
2.03
1.44
t.45
3,24
2,00
2.75
1.63
1.66
3.32
3.56

1.54
1.72
2061
2.90

0163
0176
ue
0045
0319
03a)
0253
2356

0343
0495S
oSat
o23t
0193
0229
0233
018A
0113
0071

0654
0165
0786
0551

0769
0846
056

a
0298
Any
1959
0815
0663
080u
oA1S
0682
0798
0685
0740

0677
0643
oAa6
0403
0364
e2BR
0264
0234

o4pA
0433
0390
0393
0555
o4Pt
0134
e136
0 ORI
e167
e147

0408
ofA
2625
0475

APPENDIX D
TEST RESULTS (IRREGULAR WAVES)

TRREGULAR WAVES
KR D/GT2 H/GT2 aP

BREAKWATER 4

0103
o1To
0039
0045
0319
e347
0253
0356

0024
2023
0906
2006
0043
0031
0007
0019

00063
20066
00010
00011
00089
00069
00007
00029

BREAKWATER 4

0343
0d9S
0301
023)
0193
0229
0233
0188
oi13
007}

0017
0018
0036
0012
0026
0044
0015
0029
2008
0027

29030
09040
00072
00031
090065
200033
20042
00972
00030
200075

BREAKWATER Yw

2658
0766
0786
0$51

0045
0026
2042
0074

00093
20052
00975
00161

BREAKWATER 5S

0769
0846
0803
0807
2898
0823
e777
0815
0665
0804
0815
0658
0798
0645.
0710

0022
0054
0043
0936
0043
2022
2009
2025
0045
0009
0025
0045
0010
0008
0027

00044
e01en
00017
20946
09101
00044
e0N1A
20065
00102
00018
20065
00102
000288
20029
00074

BREAKWATER 6

0677
26U3
2840
0403
0 S64
0288
0268
0230

0992

2023:

0037
0036
0026
0040
0024
0027

,0164
20030
00072
00094
00067
00028
206865
00076

BREAKWATER 9

0428
0434
0394
0393
0555
042}
0131
elo
0 0AL
0167
0147

00S!
0039
2037
0036
0007
0919
2008
0023
0017
0004
2004

20090
00040
00070
20078
20007
20028
00021
20066
20080
200013
00013

RREAKWATER 10

0408
0418
0628
07S

2043
2026
eOL!
2019

20091
20059
20010
20028

3,33
404
3,38
2.84
2,78
4,37
3,24
2.85

S11
4,56
7,54
4,98
5.62
3.15
4,37
7,42
3,62
6.53

4,49
8,64
9,85
5.35

2013
2.12
2.54
2.93
6020
2.23
2.15
3,47
1059
2019
3.75
1.63
4,77
3.53
6.51

5, Rb
4,69
6.31
5.38
6.02
4,54
4,85
6.6

5,46
u,46
6,74
6.02
4,53
1.56
2,09
3.37
4,46
2.98
3,03

2.15
4,195
3.67
1.79

89

10

TBO3SAL4O3,_
TBOZ2AIL 4226
7TO032AR1 4416
7B8032A1500.
7B0327094S.—
7803271004,
78032710226
T8032710416

7801191346.
78014191404,
7801 2uy808,
7801240825,
7801{2U0R43,_
78012113200
TB0121112206
780321417356
76012317556
78042118300

78011910046
7801191026,
78011809385

¥802010901.
78020109240
78020;0947.
78020110106
78020110346
7TA0201{11076
78015110116
7TB013110340
7801341058,
7T80131111%
7801311142.
7802020A 320
78020A0840.
78020208576
78020209526

7802071324.
7802071339.
7802060216.
78020602326
7802060246.
78020B11250
7602081144,

7802221333.
7802221359,
78022310166
78022310355
7802240953,
78022U101 36
78022712056
YBOP2A1 24%,
78022813100
78022R13326

7803060939
78030609S7e
78030610166
T80V3061N356

606
60.
60.6
60.
75.6
73.6
756
756

74,
74,
60.6
69.6
60.
60.
60.
U56
USe
US.

6S.
65.
76.

750
756
75.6
WS.
75.6
756
60.6
60.6
60.
60.
60.
4So
4uSe
4S.
450

75.
95.
60.
60.6
60.
45,
4S.

73.6
7150
75.0
7S.
75.
75.
606
U5Se
45.
USe

75.0
75.6
75.6
75.

1046
3.08
2.05
2.02
1.45
3.32
1553
1034

097
1053
@el2
1.38
1044
2.23
1.38
2012
1053
1070

1653
1094
1230

1019
2046
1245
1034
1.26
1288
1226
1.97
2,64
1026
1.97
2012
2.243
1.53

of

1230
1.53
1.62
2.03
1.50
2023
1.53

1.30
10$3
1034
1063
1033
1.34
1046
1260
3012
2.05

1045
2.64
1033
1.34

DCCM) T(S) HCH)

KY

0151
0035
00608
0160
0355
0303
029)
0305

0488
2486
0c26
0237
0187
022A
0209
ofS
0084
0109

0755
1768
05348

efuu
0843
0825
0885
0922
026
0792
oAla
e713
0794
20810
0842
0735
0662
0708

0648
0934
2380
e405
0342
0276
e223

0404
e401
0 36u
0372
0361
0417
0120
0104
ely
2098

e4u7
0552
e405
2458

KR D/GT2 H/GT2 OP

015!
0038
0068
2160
0355
0303
029)
2305

2488
0484
e226
257
2187
2228
0209
o1i3
2084
2109

0755
0768
0518

Aud
0843
2825
0885
e922
2826
0792
0814
e715
0791
2810
0842
07395
2662
2708

0648
0934
2 380
0405
e342
0276
o22s

2404
2403
2364
2372
2361
041?
2120
2104
e2i7
2098

24u7
2552
2405
2458

0929
0006
0015
2015
29356
0007
2043
2043

0980
20032
0014
0032
20930
2012
0932
0010
2020
0016

0037
2023
0046

0054
0013
0036
2043
2048
e02ee
0939
0016
2008
2039
2016
2010
0009
2020
0055

20us
0033
2023
0015
2036
2009
2020

2045
2033
2043
2029
2043
20458
2029
2018
2005
e011

2036
Olt
2043

2ous

00082
00009
00051
20059
000B1
00010
00072
00076

00169
00068
000353
00093
00072
20030
000835
00027
0006S
00N44

00073
00041
00095

00121
00017
00047
e010l
Ce i ie
00044
00102
00045
00017
00103
20045
00028
00030
20065
00999

00097
00076
00054
00045
00091
20033
20063

20096
e0072
20090
00066
20071
00076
20079
20076
20009
20039

20079
20015
20072
20074

5.54
3.97
3.77
3,45
5.82
3.94
2.69
1.76

5,39
6,03
5.14
4,59
7.26
4,82
6022
4,46
8,30
9.99

6,30
u,62
5.24

2,14
2.50
2,03
6031
8.90
2024
2.70

2076

1094
2.65
2074
4,90
4,59
5.71
2,58

5.23
5.29
5.42
u,87
8.01
5,69
5.05

49
5.9%
2olt
3.52
2240
1,45
bell
2.10
2.96
2041

6.25
4,5¢
2.357
1.46

IRREGULAR WAVES
10 DCCM) ¥(5) HOEM) KE KR DO/GT2 H/GT2 OP 10 D(Cm) T(8) H(CM) KT KR L,GT2 H/GT2 OP

BREAKWATER 40

FAOSO31LO0S. Oe 1695 2e4 0381 o5SH8L 0016 20006 9,99 TB0ZOBINSt»® 606 1054
TAOSOZLIN1» O00 L091 1602 0191 of 91 2027 20072 4,44 7BOZ03I11%, 605 1064
79030311200 600 bel2 Fo 0305 030% 0006 ,0008 3,24 7803031129 606 3032

14.6 0229 6229 6026 460063 2656
16.
fle
FBOSO3L13% > O00 old 18202 0196 0190 o047 20096 2o35 “%803031148, 605 3566 Ihe
156
160

6
9 0215 0215 0023 060064 3,64
2 026A 4268 4006 s0{0 3,50
3 0232 .232 1005 00009 2.42
TAOSO3SL1G9 > 600 Bed4 14eU 0886 0296 20006 .001Y 2,69 7O030200215 USe 2e2l 4 609M 4090 900% 00932 2,38
TAUS02IG13Se 450 1036 1408 0062 006@ 0025 ,0087 u,b} 78030214220 US, 1067 1 0082 ,082 ,016 00059 Uo1?
PAOSOPI4S1. 4So Bole 607 0213 e213 0005 20007 2,41 FB03021440—e US, 3o28 100% 0155 6155 2004 00010 4,03
PB030P10S00 YSo 202) 1820S 0008 0098 600% 90026 2050 780302145%. US. 3046 1203 0126 0126 2004 00010 2,64

BREAKWATER 13

7B042I124U7, 600 1095 1768 o PM 0724 gO16 0048 2,50 TBOUAY12565 600 1052 1902 o773 e773 0026 00085 3,98
TAOU21130Se 600 1083 2000 0755 0755 0018 20061 3.46 78042113150 60, 2084 708 o767 0767 2008 o0010 3,23
7804241334, 600 1.82 1400 07§3 e713 0014 0043 2,70 780U2411343— 605 YedO 1608 0608 2608 6003 20009 1576
7BOU211353_ 600 Go34 2004 0666 0606 0003 20011 1,83

BREAKWATER 44

1804260846, 35, 2010 15.6 o36t 030% 2008 0036 2,49 780U26082%» 35e 1055 1606 o261 o26) 015 00071 3o73
TAOU2ZKDBS2» 350 2o8U 608 035) 0337 0004 20009 5Se6Y 7804260904. 3$5e 2078 FoF 0352 9352 0003 0001S 466

78042609166 350 Bel 1205 0266 0266 0008 ,0029 2,33 78042609289 359 Ye20 1400 0330 0330 2002 20008 1,81

78042609405 350 4000 1804 089% 0297 2002 .0012 2,03

BREAKWATER 15

7303010409, SO0e 1623 1663 059 0890 0034 .0110 2,00 78050108306 50» 1045 1702 0652 0652 2024 o0M83 3,93
780501084, S00 1057 1708 0653 0653 0021 20074 3,24 78050312250 355 $055 170k 0370 6370 2015 00075 3,72
7805031237%— 350 1063 1802 o34N 0340 0043 00070 3,25 %80S031P47%. 355 2e81 beh 0510 0510 0005 00008 3006
78050312560 350 2061 % 7 eb7b 0476 0005 o0015 4,19 78050313060 350 2008 1203 0383 0383 0008 00029 2,10
7805031315_5 350 4,49 1205 036) o362% 0002 20006 1537 78050313260 350 old 1703 0361 036) 002 00008 1.99
78050313540 350 BolM 1603 0355 035% 0908 10038 2,29 TBOSOB1115e 200 ao2% 1468 o169 216% 2004 00028 2,26
TBOSORI 4260 200 $040 1603 0154 0154 0010 .0085 Uni YBOSOR1!34, 20.0 1065 1603 0157 0157 e007 c0061 3,89
PHOSORL{43, 200 3012 bot 028M 0270 0002 20007 2,86 7BOS0R1153$e 200 3024 1004 o24M 9240 002 00919 2,94
TBOSOAL3S04. 200 2029-1203 0182 0182 0004 .0N24Y 2,32 TBOSORL215Se 205 $086 le? 0196 0196 y002 10009 1,69

BREAKWATER 15w

7PR0U2ZA0947, 35, B10 1562 o374 0374 4008 ,0035 2,42 78042810030 35. 10645 fool o347 o347 O17 00078 3,74
78042R1014, 350 1658 1702 o3a5 0325 0014 20070 3,13 TBOUZRIN24,s 350 2084 6e3 «48H »48B 004 20008 Se2k
T8042R1H653—, 350 Sa7B Fe 44 0444-0005 20013 4,29 Th0U2ZR1043>e 35— 2010 110% 0356 035% 9008 00027 2021
F8OUZALHS3. 350 4o20 1304 «383 0383 2002 2.0008 1,92 7TB0U2ZB1104— 355 4e00 1609 0323 63235 002 0001! 2,05

BREAKWATER 16

TROGSNOR2BR, 45, 2.03 16.2 0561 od9t ,O1L ,0040 2,44 7806300838e WS, 2c03 1605 5500 0500 ,O11 e004! 2,40
FA06300B847, Se 1055 1203 0547 S17 001% 20073 Ueld 7806300857— US. 10655 1707 0515 0518 001% oO075 3,93
78063009060 45e 1055 1703 0544 051! 0099 20073 4,05 78063009170 US, 1098 1864 c496 6496 4018 00075 3476
78063009270 450 1054 1804 096 0896 0038 20075 3.26 78063009369 US_ 1064 1806 0505 2505 o017 0071 3,29
78063N0948e 4Se 3005 603 05S§ 0655 0005 00007 3,62 7806301001 4Se 30205 603 0651 0651 2005 20007 3,71
78063010106 4Se 3005 603 0654 0654 0005 00007 3,72 7806301020. 45. 2.72 0589 ,589 .006 20014 3,54
7806301029. 450 2075- %o8 0599 0699 0006 0013 3,56 78063010385 45. 2675 0614 »614 ,006 20013 3,73
7806301048— YSo $43 1209 0504 0504 o022 20064 2,34 78063010575 4Se 1043 1 0486 2486 .022 o0066 2,29
TR063011200 450 4e2? 1268 0697 0497 0005 20007 1536 FB06301130—0 USe te72 1 2466 9466 gN16 e062 471
THVO3NT1UOe 450 4o2F% 1300 o5ad 0524 0003 20007 1,32 78063013520 WS. Yee 1 0476 2476 ,003 cON0A 1.35
78665012020 4Se 3o88 1804 0308 0300 0003 .0012 2,63 TAGOSO1211e YS. 3288 1 0491 o4%L 9903 eON12 2,83
PRV63SNY 2216 4Se 4.00 1667 e4MA 049K 2903 ,0012 2,49 7B80U6261248— Uo 2075 1 0419 2419 ,005 e021 2.40
78062613000 Yo 2075 1503 0496 0406 2005 0021 2.355 780626135100 UO. 2075 I e414 e414 ,005 00921 2.26
78062613216 Ye Lo4A 1603 0309 0399 001% .O0T6 4,12 TB0H261330— WOe $240 1 0393 393 ,021 cONhS 3,93
780626133%» YOu Lo4M 160d 0393 0393 oM21 2U0KS 3,99 TB0K2b1349%— UO. 1058 1 0446 e416 M16 20072 3015
780627080% 40e 1638 1709 240) 0407 016 2.0073 3.20 7806270R27%. YO. 2288 0578 «578 .005 060008 3,98
T80627NBUS, Yo 2o48 bee 058% 0$83 2005 .0008 3,92 Y806270854— UOe 20868 0587 .587 .005 o00N8 3.90
TA0627I0904s Ye Seth Vet 0549 051% 0004 20010 5.53 78062709130 UO. Be7S e5$2 052 9005 20013 4eld
78062490922. Ye 2075 9S 0516 0510 0905 0013 4eld 7806270931 e Us 10el4 1 038A ,388 .031 e010! 2.358
78062706900, YOu Lol 1208 o391 o391 0031 10101 2,36 7806270949, UO, Lol 1 038K ,388 ,0$1 00101 2.37
7606270959, 400 Ho20 140i 439 0439 5002 ,0008 1,78 7806271007» Yo Yeed 3 04268 .428 ,002 00008 1479
TROG2]TIN{ be YOo Gold 1402 o4H% eUU$ 002 ,0008 1,97 7806271926_ 40. 4.00 1 040M 400 .003 cON11 2013
7T806271N35e YOu Ye00 1709 o3AA 0388 2003 ,0011 2,12 7806271043_ UN, Ue00 1 0390 2390 005 e011 Aelu
T806271{U1— We 2.75 1403 0420 0420 0005 .0019 2,13 YB06271150—5 Uo 2075 1405 o4l2 gU1e .005 e020 2,99
78062911580 Yo 2olS 1405 044 o412@ 2005 20020 2,09 7806271208 40. 1040 1506 0405 ,405 02! 20081 3,69
TBOH2II 2160 Ye 104M 1506 obhe 0406 0021 cONKL 3,69 TAD0KETIA2]5e UO. 1040 1505 o401 e401 2021 00081 3,73
TAOH2TI23b6e 4Oe $038 1604 obi A e41B 0016 20067 2,97 TB06271245_ Ue 12058 1605 o403 o4OL 0016 00N67 2.94
7806275354, 4a 1658 1668 oh4t o411 0016 60069 3,21 78062713049 4Oo 2069 1He3 050M 6500 2006 20720 4,59
VBOR2F1313—0 Ye 2084 867 050% oS47% 0005 cOM1t Sell 78062713220 Ue 2075 Bed 0547 o54 4005 20011 4ela
TBUG2TL3320 40e B@o32 Seb 0607 0607 2006 20008 4,39 TBVG2TI3S91e Ue 2072 5e6 0608 0608 1006 20008 4,39
7306271 34% 400 2at2 506 +608 0603 0006 10908 4,31 T806271359%> YOo $643 1404 eH1M gU10 o020 e005? 2023
7T8062A0637Te Y0e Leah 1106 0357 0357 0026 0082 2,3} FB062CA004B. Ue told Iho7 o387 9387 9031 20092 A.22
9B062R0115—0 400 305: 1200 0431 0431 0003 20010 1227 TA0V62B0123e Ge Be5!l 1109 e431 9431 40035 00010 1027
15.7
159

eee2 2022828282222 22 8 & &

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78062A01320 400 3051 1200 ohb3H 0430 0003 20010 1227 7B062R80142_ Ue oe? o47H ,U7TKX 4002 20009 14640
TA062R0ADSs 400 ed 1606 eh3H 0436 0002 20009 1.50 YB062R07P15e UNe Yea? e430 2430 ,002 20009 1,42
78062608050 350 4020 1205 0392 o372 2002 .0007 1,92 78062608150 350 Ye20 1204 o371 371 2002 20007 $296
7806260824e 350 4e20 1203 0369 036% c002 20007 1.97 78062608335 350 400 1601 0308 308 002 00010 2.01
75062608426 350 4000 1600 0346 0306 0002 00010 2.090 78U6260A51— 355 4e00 1602 o3S1B 9314 2002 20010 2,00

90

IRREGULAR WAVES
To O(CM) TCS) WOEM) KT KR D/GT2 K/GT2 OP 1D D(EM) TCS) HC(CM) KT KR D/GT2 H/GT2 OP

BREAKWATER 16

78062609000 350 200M 1704 0813 e313 0008 20040 2,31 TEUV62609100 350 1054 170d 0302 0302 60135 000TH 2,29
7A062609186 356 Boll 1703 o34a2 ob1a 0008 .0040 2,32 7806260928. 356 $095 170% 0295 29S 0013 00076 4,08
9806260937. 350 1095 1709 e204 0294 0045 o0076 Uo02 78062609465 350 1053 1709 0297 0297 015 00076 34%
FBr 6261404, 350 1098 1902 029F 0298 6014 0078 3,26 Y806261913— 356 1098 1%.2 0288 2B o014 0078 3018
PRCO2410230 350 208A Yat ob99 0474 6004 .0009 4,95 TB06261032— 355 2o84 Tol 0478 .U78 gCOY 20009 4e86
780626194, 350 ae8d Yor o49H o4V0 0004 10009 4,79 7B0626195%— 355 2eA4 1002 o40F eUOT o004 00013 2697
7O0626155%— 350 2084 1002 oto? ohO7 o004 ,0N13 2,98 FBV6261108% > S5e 2084 1002 e409 40% ,004 o0013 3003
7806261118 350 1085S 1306 0349 031% 0023 20089 2,30 TB062b611260 350 1025 1305 0333 0335 2023 00N8B 2,29
T2G02611350 350 Led 1305 0326 0370 0012 20046 2,50 FBV6261147— 350 Ye20 130% 0384 «384 4002 00008 1645
7806261156. 350 SBA 1400 036A 0368 0002 20008 1,69 ¥B06261206e 355 Yo20 1308 o38U o384 4002 00008 1,545
TROGC1SNO12, 350 2010 150f 0261 oB61 0008 0035 2,41 7B06150924e 356 2010 1501 0270 6279 4008 00035 2,42
DAOSISL ALD. 350 2010 1803 026% o843 2008 10035 2,37 FB06151024— S$5e 2010 1502 0261 o26) 9008 00935 2,40
TBOG1S11U2. 350 $055 1605 oP3% 23% 0015 00079 3,78 FBVG1511930 35. 1055 $606 0235 0235 015 00071 3578
POOLE 2166 356 1055 1605 0229 0229 0015 00070 3,83 78061512276 35_ 1058 1704 242 242 oM14 FONT 3610
780618123%, 350 1093 1703 o2H4 o2H4 5014 ,O0OT1 3,12 TBOH1S1324— $55 1058 $704 0242 pede 2014 00071 3010
TE0O15135Se 350 2094 bo2 0385 0385 0004 20008 UQ47 TBV61S13550 355 2084 bed 0380 2380 6004 60008 4,63
TAOOIS1UI%, 350 2o78 %sU o367 0367 0005 20012 4,08 TB062307198 6 356 2078 Bol o47TU g474 4005 e011 4ol7
7806236728, 350 2e7A Boy otFU e474 0905 40011 4,18 FBUG230757%. 350 2078 Bol o47U o47H 4905 aOM11 Yee}
PROb2TOVUT>e 350 2o7H So 0541 0511 0005 c0007 Ueb63 FA0623075Se 350 2078 505 0510 0510 0005 20007 4e5k
TALESTOADUs $50 2eVA Sot o54U oS14 0005 00007 4n61 7806230914e 355 1033 1006 0336 0336 2020 o0061 2015
FA062YPK226 350 1033 1006 0826 03260 0020 00061 2515 FBV62%08310 355 1025 1006 0331 0331 0023 00069 2015
7806230903. 350 4o57 1008 0384 0380 0002 20005 1.32 PBOK2309320 350 Yee? 1406 035A 0358 4002 00908 155}
WAOOAIOAUL s 350 4o2? $406 0356 0356 0002 00908 1452 780623094%, 355 Yo2? 1406 0300 0360 002 00008 1651
TAOE2INISI, 350 SolM 1501 o93A4 0324 0008 20055 2,26 7806231008» 355 2010 150! 0335 0535 e005 0035 2,38
TA0G2SLALTe 350 SelM 1501 0336 0330 0008 40055 2,38 FBU6231026e 35— 1095 bel 0292 2292 9015 1068 3,87
FAVO2T1AS5, 350 1095 1605 0291 o291 0015 007M 3,77 7BO6231043e 350 1095 1604 0289 9289 .015 «ON70 3.80
YA56231054— 356 1098 1704 0294 0291 0014 00070 3,07 78062311100 350 1058 1702 0293 0293S oO14 00070 3,09
¥B0623141% 350 1058 17e2 0295 0299 0014 00070 3.98 FBOH2311320 356 2084 bel o470 e470 2004 00008 4e68
TAAGATI GUL» 350 2084 603 o46A 0468 2004 20008 U,b} FB06A31150—. 350 2084 bel 0469 9469 ,004 20008 4,72
TB05235159— $50 207A %e¥ oh4S$ 0855 0005 00012 4e15 7806231208. 355 2078 %o3 0459 9459 9005 00012 4e57
780625' 21%, 354 2078 %o3 o4SH 0450 0005 ,0012 4,56 78062312260 350 2078 Fos o453 o4SS 2005 e0N12 Uelu
7806231245, 350 2078 Vo 3 04S4 0454 0005 20012 e117 78062312550 35— 1058 17e@ 29h 9298 C14 00070 3,05
78002313036 350 $58 1700 0827 327 0014 00069 3010 7806251 314e 35_5 1058 1703 0296 2296 e014 oON71 3,09
98062313372 350 to25 1109 0303 0303 0023 00078 2,19 78U6231347e 355 2old 1108 0319 0319 0008 00027 2020
YAnb2313560 350 2e10 110% e314 e311 0008 20028 2017 Y806231408. S55 Yo20 1208 0370 0370 9002 00007 1598
78061608010 350 207A oS Bath 2367 0005 .0013 bold 78061608150 350 2081 FS 0355 0355 0009 00012 Yel?
7806160438. 350 BolD 1200 0259 085% 6008 1.0028 2.20 ¥B06160A848, 35o 2010 1201 «252 o25@ ,008 00028 2,18
780616085%,_ 350 Bolh 120} 0209 0249 6008 002A 2,20 7806160909. 355 Yo2d 1300 0297 0297 4002 00008 2.03
7TB80616091% 350 402M 1209 029A 0298 2002 20007 2,00 7B806160928e 350 Yo20 1300 0290 290 .002 00008 2,02
7R0616093%. 350 4o09 1609 024) o247 o002 .0011 2.04 FAOKLACIU%, 355 Yo 1609 247 oe47 ,002 20011 2006
78051610005 350 4000 1609 «4 0244 2002 oCO11 2.04 TA0H16133520 300 2015 1601 0199 0199 0007 00936 2452
PECHLEL3E2e 300 $0540 17%of 09H 0190 0013 20074 2,46 TAVGL613520 300 1094 17e2 019A 0190 oO1S 20074 2657
PADELE{LUO2e 300 1055 1800 0166 0166 0013 00076 4,25 TAVbE1EL4I2e 300 1055 1806 5166 0160 2015 00079 Soll
TAROKLALU2L» 300 1035 1805 0166 ef6% o013S 0079 417? TBOGLHIL450— 30e 1098 1868 0178 o178 pOl2 00977 3,28
TACOL61E39, $09 2004 1856 0183 0183 0011 20071 3,27 PA0G161448. 305 1058 1807 0180 180 o012 «0076 3,22
FAIO1909S7T, 30, 3,05 Pot o392 2392 .003 ,0008 5,60 FA06191N0R. 305 3005 Tol 0393 0393 2003 00008 563
PADCI9IALT. 300 3005 7oq 0394 0394 0003 .0C0B 5,72 YR0619102%— 305 2084 90% 06337 0337 0004 00013 2.58
TB0O191N37. 300 BeBU 949 0336 0330 0004 60015 2,57 78061919065 30.0 2084 1000 0329 6329 2004 00013 2260
78061910S5S6_ $%0 2513 1207 0f67) e262 2007 20029 P26 TBOGL9IL104, 300 2ol3 1300 0258 0258 4007 20029 2430
TAIOL9IT13> 300 213 1209 026 0260 0007 20029 2,29 TB061911230 306 4e20 1208 0300 0300 ,002 20007 1237
P80O191132%0 300 4e2M 1268 029% 0297 2002 .0007 1434 78061911415 300 4e20 1269 0297 6297 2002 00907 1240
YRIG19L 2120 250 1049 150d o1FS 0175S oOl) 20071 2,32 TA0619L2210 250 1649 1523 0176 0176 011 00070 2036
YAOO191230_ 250 1049 1503 0175 0175 o01) 00070 2,36 FBUVH191239— 25, 1055 1604 of62 162 p11 00070 4ol0
7806i912UK, 250 12655 1605 0159 0159 o041 60070 4,15 78061912560 250 1095 1604 0196 0156 e011 20070 4,20
78061913050 250 2023 17%ef ol7A 0178 0005 00055 2,98 TB0G1L9L314e 255 2e23 1701 0179 oi7% 0005 00035 2091
- 7806191326. 250 2o23 1700 0179 017% 0005 00035 2.90 78061913550 250 3005 607 0326 2320 0003 00007 Seo77
PB0O191 3H. 250 3005 607 o8ah 0326 0003 20007 5,77 78061913930 255 3005 be? o32A 9328 2003 2007 5,79
98061910025 250 3620 %5 228A 2&A0 0002 20009 2071 FB06200TS1 0 250 3020 Fed e274 e274 002 20009 2.78
F8062H0%L2, 250 bed Ved 0273 e&75 2002 20909 2,43 TB062007S2e 255 3020 Ved 0273 02735 2002 20009 2.80
TA0b2COAO2%» 250 Peet 1108 0765 025 0005 20025 eed 78062008115 255 2e2l 1109 0196 0196 0005 20025 2024
TBOLZNOR21, 250 2e21 1200 0196 0196 0005 00925 2.27 78062008350 25. 3076 120k 0219 0219 0002 0009 1559
TB062H0A3%, 250 3o76 S204 o214 o@14 0002 20009 1.59

BREAKWATER 17

7808010845. 5% 1655 180d 0298 0278 0021 .0078 4,63 7B80A010855e— S50 1055 1805 0282 282 021 00079 4,43
FB0B010913e S00 4087 $905 0343 0303 0015S 60057 3.72 78080109220 500 1087 1906 0296 0296 o015 00057 3.59
7808030930. S00 108% 1907 0299 0299 5015 20057 3,66 YB0R0109405 S00 3032 700 0496 2496 4005 00006 2,89
9809010948. S00 3032 Yoo o50a 0502 0005 00006 2.90 7808010958. 50.5 3632 700 0502 9502 005 00006 2,89
TAIBOLIN1 6. S0e 3028 1009 o4dd od44 6005 ,0010 2,60 TBOBOVL224s SO» 3028 1009 e445 gUUd 2005 20010 2.59
78080112365 500 2046 1450 0330 0330 2008 0024 3,00 7TB0R0113000 S0e 1054 1400 0329 0329 2022 00060 3.03
TAOTDEO919, SM— 2e39 1603 o33A 0338 00% 00929 2,A1 TA070H0925e S0_ 1055 1607 030M 2308 o02!1 20N71 4,20
TA07TORDIST. SDe $055 1608 630% 0399 OAL 007! 4,31 TBOVOQKUINT.? S0e 1055 1608 0306 2300 oN2l 2O0N7T) 4y19
TEOTOSI321, 506 1033 1207 0356 0350 0029 20073 2,76 TAO7T0G133$1e S0e e394 1506 0393 0393 028 20NKBO 1,87
7B07061340e S00 Lo34 {Fed 0305 0395 0028 40088 1,95 TBOV0G1L34%. SOe Le34 1507 o39K $94 028 20089 1,91
F8070613S9%. S%0 3276 Alo 0362 0362 0004 0015 2.2} TBOT0I614OTs SO. 3076 200% eo 30H 4368 2004 20015 2,518
PAOR210957, 4Oe @o56 1702 0329 0329 2006 20927 2,48 TAUB211N06> Ue 2056 17%al 0329 2329 2006 20027 3,02
TAOMALL1 UF, YOe FoS6 1605 0339 0337 0006 20026 2,85 TROB211201 0 Ue 1036 170% 0315 0319 2022 2NNDD U,UU
PAOM2N11 2120 Ye 1069 1509 0316 0316 0916 90063 47S TBOR2{17350— UO, 1060 $7e7 o317F e317? 2016 e007! 4.55
TB0R2]5123%—. Ge 1,57 1604 oSat 0327 017? 0076 3,37 TBVR2{17P4%, Ue 1057 1905 e312 e312 oO17 eON81 3,41
FBORL1135A, YOu 1057 1853 e832) 0827 2017? VOTH 3,31 TBURLI1307T» UO, 2284 be 4501 2501 2005 20008 3204
PBORCL1316e YOu 2633 605 a4AA o4AB 6006 ,0010 3,11 TBORZS13250 Ue 2ed$ bebo 2483 QUAS 4000 20011 3ehu
TBOASLAZZU, Ue 2.56 Geb oUBl e4bL 2006 20015 3e13- 7TBCR2AY134S. UO, 2e81 %e3 0455S 2U5D 2005 20012 3419
TECA2413S2. 4Oe 2e81 8.3 oUSS 0455 0005 20012 3,24 TAOR2Z212020 Ue 1097? 1502 e324 234 gOI 20NU0 2,9

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2019
2.07
2.94
3,59
3.59
4,26
2096
2.97
u.37
3.82
eI
4.16
3.46
3,46
2.51
1091
1,89
2.80
Yous
3.34
3439
5.82
4,64
4,26
3266
u4,i9
4.19
u 62
4,65
2.24
2.94
eollk
2.95
3,94
Uol2
6072
2040
1,48
2.95
1.98
2094
1.67
2035
2.335
3.73
2,49
2.92
&,fbo
5.18
4,76
2250
1.45
1,44
1.74
3,97
4,00
2.95
5.67
5.61
5075
1ed2
1.54
2.01
2024
ee29
3070
2.90
2095
3,54
4,64
4.56
1.240
1.72

92

10 D(CM) TCS) HECm)

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over @or-ocece oss @eleoconruyvnweoodc

OW ENE WeHewsoer
2 2 e © © @ © © © © eo
OOOO ewVeKewyvIoc oO

KT

0322
0340
0356
0352
0319
0305
0312
0432
e467
0458
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0367
236A
0320
0320
032)
0296
0446
0382
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0274
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KR O/GT2 H/GT2 GP

see
0340
2356

0011
2002
0005

00040
000190
20022

2,868
2.78
20F6

0352 200% 060936 2,86

0319
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0432
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2287
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2296
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0280
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2 380
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2308
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2408
o4el
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se7g
peT4
235e
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0308
0325
2383

eb77

2437
0352
2326
0290

0044
0015
00135
2005
2005
0005
2009
0009
0909
2002
0005
2005
0013
0008
2005
0907
0014
2014
0011
2004
2004
2004
2007
20007
2002
0007
0007
0014
0907
0007
2004
0004
0014
ee |
0004
2004
0004
2007
007
2008
2002
0002
0014

0004:

0007
2007
2002
2002
2011
0005
2001
0003
2012
012
2012
2003
0003
0905
Ott
203t
0001
200!
2901
009
2009
0009
2002
2002
»002
2006
2004
2004
2004
2009
2009
2004
2002
2002
2002
9004
2001
2004

00058
e006)
©0060
00010
00007
00007
00028
00052
00032
20009
00025
00024
00067
00007
00012
00043
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00007
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20008
20008
20029
00929
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00055
00053
00027
20007
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00005
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3.89
3.44
3.46
4,06
5.09
6.28
2.40
2.02
2,03
2.09
3.0)
2092
3.57
3,73
4o\7
2.98
4,44
Uo45
3.41
4eiu
U,ecs
3.48
2.56
2.48
2006
2.77
2071
3,74
3.35
3.38
4,60
6,42
4.20
3,61
4,05
4eil2
4.66
2022
2019
20%
2,94
2,93
G13
6071
2.59
2.37
1.50
2el2
4 alo
3,02
1.64
2.28
3.90
3.85
2, Fa
u,7A
Sele
5.10
2o>)
2050
1,43
1.72
1,72
G,0j
3.04
2.97
5.26
3,46
3,19
1555
1.99
2,00
20e7
3,94
3,74
2090
3.55
3.75
4,86
2018
1.39
1.70

APPENDIX E
TEST RESULTS (GRAPHICAL FORM)

SYMBOL DS/HS

B=30cm

Smooth Impermeable

M~<XNX29O0X+P0C0

OaO OOO ries
eee 0-00 0
J

[rec a
0.0001 o.001 0.01

WAVE TRANSMISSION AND REFLECTIGN CGEFFICIENTS
BREAKWATER 1 O/C Eu2 =o 0s

93

B=30cm

SYMBOL D/GT2

*+¢X+t+POG

0-0131
0-0161
0 -0227
0 -0364
0-0556
0.0788

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS

BREAKWATER

Z

94

DS/HS=

0.87

es

SYMBSL OS/HS

>+oX+?PO0
OOF RFP re
a [en a e 4
_
b

(ee ee] BW3

a
A
@F: es ©F ©
N +> QM WM
oO
O
O
poary

a ORO

H/C GxTxT }
| 6
Ores
O65

Kel

0.4
Oy

9.0001 0.001

H/C GxTxT )

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER S UAECTZ =O One

SYMBOL D/GT2

0

ox+PG

0
0
0
0

i of)
Dots
0.6
KR
0.4
Bee (tree eet
ORO aH
H/{GeTx*T }
1 6)
0.6 x
KT
0.4
OfeZ
0.0001 0.001

H/(GxTxT }

WAVE TRANSMISSION AND REFLECTIGN CGEFFICIENTS

BREAKWATER S DS/HS= 1.14

96

-0065
-0131
-0161
-0226
-0364

0.01

-Q1

SYMBOL D/GT2

@ 90-0038
A 0 -0066
Or oist
~ g-0162
BK WeO229
00368
1.0
0.8
KR
0.4 &——A sa»
ae ee ee ts Pe
0.001 0.01
H/(GeTxT }
1.0
0.8
0.6
KT
0.4
0.2
+
0.0001 0.001 0.01
H/(GxTx*T )

WAVE TRANSMISSION AND REFLECTIGN COEFFICIENTS
BREAKWATER 3 DS/HS= 90.69

SIG

SYMBOL D/GT2

eoxX+bG
oo0o00°0o

0.0001 0.001 0.01
H/(GxTxT }

WAVE TRANSMISSIGN AND REFLECTIGN COEFFICIENTS
BREAKWATER 3 DEV hSs 16s

98

SYMBOL D/GT2

Lt)
iu}
ok
+
x 0
} 0

oO oO

oO)

-0065
-0130
-0161
-0226
-0366

0.0001 0.001 0.01

H/( GxTx*T )

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 3 BSAHS= Halas

99

SYMBOL D/GT2

oX+PCG
oOoo0o00o
a e e e e

(a)

a

(27)

i)

O.
0.
KR
0 e
0.
0.001 0.01
H/(GxTxT }
il oO
0.8
0.6
KT
0.4
A
Doz
0.0001 0.001 0.01
H/(GxTxT }

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 3 OS/ilss OWoQZ

100

a

a Resiccien SYMBOL DS/HS

SH Os)
ee els
0693
WARS)

fo) 0.5 Om BW3W

0.001
H/(G*TT )

0.0001 G.Q01 0.01
H/(GxTxT}

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 3W D/(GT2)=0-.016

101

SYMBSL D/GT2

a WOE
aA 0.0065
+ 09-0130
x 0-0161
A OeG2z26
+ 0-0366
of)
0.8
0.6
KR
Ore
oZ
—_______¢—___» __—__+
> +
oOo OMe
H/( G*xTx*T )
hic
Ge
Or
KT
Wo
Gye
0.0001 0.001 Omen
H/( GxTxT )

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER 3W HS/nes 1628

102

SYMBOL D/GT2

9 99-0066
a 0.0132
q @eonee
Y) ono223
AOMOSG6
A) 080555
x 0-0805
1-0
0.8 |
0.6 6
0.4 VG ear
pala NS es
62 a nl
iP q-01
H/(GxTx*T )
1.0
0.8 ele
0.6 Gin
+
0.4
0.2
0.0001 0.001 aon

H/(GxTxT)

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 3W WoAbo= | ips

103

SYMBOL D/GT2

0-0065
0-0131
0-0161
0.0226
0 -0363
0-0555

+oxX+PG

O
mn WO OO

O O
yN >

0.001 0.01
H/(GxT xT )
1.0
0.8
0-6
KT

0.4
0.2

0.0001 0.001 0.01

H/(GxT*T )

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 3W eines Wossi

104

SYMBGL D/GT2

o 09-0038 .
A 0 -0066
By) Wkosley,
1518)
0.8
G26 o———_®
KR
God
»———a
OZ i
0.001 0.01
H/{GxTx*T )
It ol}
0.8
0.6
KT
Gp
GieZ
+
0.0001 0.001 Geen
H/( GxT*T )

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER 3W DS/HS= 0.69

B= 40cm SYMBOL DS/HS
1.29

MKNMPOX+RB.G
oOooooco0orFrYrr
5 0 0 ise ORO

(=)

BwW4

ORoOw OMG
H/{GxTxT }

0.0001 0-001 0.01
H/(GeTXT }

WAVE TRANSMISSIGN AND REFLECTIGN COEFFICIENTS
BREAKWATER 4 D/C EI Zve0 o016

106

SYMBOL D/GT2

q 09-0065
a 0.0161
+ 0.0546
io W
0.8
OF.6
KR
Bod
ORZ
0.001 Geol
H/{(GxTxT }
e i ea, e
O}.8 ee
ry
0.6
KT
Ho 2
OjaZ
0.0001 0.001 ORon
H/{(G*xTx*T }

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 4 DSAo=) sieliaZS

107

Qo. 16) ©

Q ©

nD @d oO

SYMBOL D/GT2

® 09-0065
K Oo160
+ 0.0553

0.001 0.01
H/(GxTx*T }

0.0001 0.001 0.01
H/(GxTxT }

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS

BREAKWATER 4 S/S Wo Slo

108

SYMBOL D/GT2

a) Wewtss

A 0.0161

# | (0.0555
1.0
0.8
0.6

KR
0.4
0} 62 Se ae ean eS
3A +
0.001 0.01
H/( GaTx*T }
1.0
0.8
0.6
KT

0.4
0.2

+ +

0.0001 0.001 0.01

H/( GxT xT }

WAVE TRANSMISSIGN AND REFLECTIGN COEFFICIENTS
BREAKWATER 4 Bisnis lates}

109

B=40cm SYMBOL OS/HS

| h,=66cm

54-cm-High Plate

NM?POoOX+ERG
ooocodrTr KEK —
° ee 2) Je) te

co

BW4W

ls
0.
8} e
KT
QO.
O.
0.0001 0.001 0.01
H/{ GxTxT }

WAVE TRANSMISSION AND REFLECTION COEFFICIENTS
BREAKWATER 4W O/C Sl Zie0c0ils

110

SYMBOL D/GT2

@ 09-0065
A 0.0161
+ 0-0546
1610)
Os
BY ois}
KR
GQye4
o
ok —_———— 4 ae
(Tho GiGi ORO
H/(GxTxT )
oe tia a
0.8 es
0.6
KT
0.4
OhiZ
Fa BOG) I Oroa ORO

H/(GxTxT }

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER 4W S/he loZs)

nD OW ©

ea © &

SYMBSL D/GT2

» 99-0066
a 0-0162
+ 90-0553
1 Miers ei
«2
0.001 OeGA
H/(G*TxT )
0
B peice
6 A
+
0.0001 0.001 Oran

H/(GxTxT }

WAVE TRANSMISSIGN AND REFLECTIGN COEFFICIENTS

BREAKWATER 4W DS /nS= » cl old

12

SYNBSL D/GT2

» 09-0065
A 00-0161
+ 0.0555
I off)
Oats}
0.6
KR
Wie:
OZ a
+
OSeehl ORO
H/(G* TXT )
lo}
0.8
OS
Kole
Goat
0.0001 0.001 Gao
H/(GxTx*T )

WAVE TRANSMISSIGN AND REFLECTIGN COEFFICIENTS
BREAKWATER 4W OS /hss 1 oSin

113

B= 40cm SYMBOL DS/HS

ica hs = 33cm eee
15 We
eZ BESET) Sail yee
Su a A eA
0.5 1.0m BW5
1.0
0.8
0.6
KR
0.4
OoZ
0.001 ONG
ile)

.001
H/C GxTxT )

WAVE TRANSMISSION AND REFLECTION COEFFICIENTS
BREAKWATER = 5 D/(GT2)=0.016

H4

SYMBOL D/GT2

BS Weearets
a 0-9161
+ 0-0550
Lo
0.8
Ors
KR
0.4
at een ee
0.001 OPOnT
H/(GxTxT )
1.0 4—____»,—________4_,—*
| a
0.8 SO
0.6
KT
0.4
DJ oZ
0.0001 0.001 GeO

H/( GxTxT )

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER fs) OSes | 2aZ27

KT

eq ©

No + DD WwW OO

SYMBGL D/GT2

we Wictaisla!
A 0.0161
+ 09-0330
x 0-0555
Cm oe
A
0} 6 OO (Che Oil.
H/{( GeTx*T )
oO
a
: agains = 5
oS
4
Z
0.0001 0.001 0.01

H/(G*TxT )

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS

BREAKWATER ) OSs/hSs ios

116

B=30cm

SYMBGL DS/HS
| | hg = 60cm
ates
a 1.09
2 mo) Weys
0, 0.5 1.0m BW6
i) oa}
Oss
0.6
0.4
—————

0.001
H/(GxTxT )

GQ 6 f&

(Ohs
Oy
KT pea ee Me ne
0.4 a oe
WoZ
| Se eee Mee || 005 | Ee, | Dems we (| ee
0.0001 0.001 0.01
H/C GxTxT )

WAVE TRANSMISSION SND REFLECTIGN CGEFFICIENTS
BREGAWATER 6 DACGRA =O Ons

SYMBGL D/GT2

a 0 -0065
A 0.0113
fy 0-0161
2 0.0390
an 0-0549
i} ofa)
0} ote
0.6
KR
OR |= :
G42 one =
——___»—-_—
ORO OH ORO
H/( GxTxT )
1 6G)
gos J ee
i Wey
a8.
KT
Ore
QRZ
Oro woot 0.001 ORO

H/(GxT xT )

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER 3) OS/rss LoZs

118

© O So &

SYMBGL D/GT2

9 09-0065
A 0.0114
+ 6.0161
ve Geo392
® 0.0555

0

8

6

4 AD

~—— tt
- epee
; 0.001 0.01
H/(GxTxT )

0.0001 0.001 0.01
H/( GT xT )

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS

BREAKWATER 6 S/S 1500

112

SYMBOL D/GT2

1u)}
a
+
x
ov

0 -0056
0-0065
0.0171
0-0161
0.0555

0.001 0.01
H/(GxTxT }
Wo}
0.8
QO.6
KT
0.4 a
0.2 da
0.0001 0.001 ORO
H/(GxT xT )

WAVE TRANSMISSIGN AND REFLECTIGN COEFFICIENTS
BREAKWATER 6 OS/nss , Gols

120

SYMBGL DS/HS

B=30cm

0.98
ho = 46cm o 1 -30
oO
15 15 a7 BS
V7 Nh
[er ee
0 05 Lom BW?

Ae
0.8
0.6
KR
0.4
MieyZ pf erates ES
0.001 ORG
H/ (GT xT )
1.0
0.8
Oo
KT
0.4
0.2
0.0001 0.001 0.01
H/(GxTxT )

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 7! D/ACGT 2) =O) 00s

121

SYMBGL D/GT2

@ 0.0065
A 0.0161
+ 09-0550
ier)
0.8
0.6
KR
0.4 = ——__e—_» ___—__®
oe ———— Sir
Ocoan (QS (0/5]
H/(GeTx*T )
i oO
0.8 ee oe ee
(8) 65
KT
0.4
0.7?
0.0001 O.O0n Geil
H/{ GeTxT)

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 7] DS/aSs . I ol&S

ee

SYMBGL D/GT2

® 0.0065
A 0-0161
+ @-0555
le)
0.8
ofS
KR
0.4
eer
OFZ OS ga re ee
Deva Gea
H/(GxTx*T )

0.0001 0.001 0.01
H/(GxTxT )

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 7 DSSS Se

25)

SYMBOL OD/GT2

a Wess
7m OLoter
+ 0-0555

1 60)
G} ois!
Ons
0.4 Y)
DoF eT ee ea eS
ar 0.01
H/(G*TxT )
1 o 8)
Oe
ORG
KT am
0.4 ie
Or
0.0001 ORoCH Aoi
H/( GeTx*T )

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER 7 ss= Oasis

124

hg = 70cm 4 SYMBOL DS/HS

0-64
Q
A 0-86

ORCon ORG
H/( G*xTxT )
lof
G.8
OmG
KT
0.4
OrerZ ee i,
O0-00G1 0.001 ORO

H/C GxTxT

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 8 D/ CGT 2 =0) 016

125

Hevea |p SYMBOL DS/HS
@o WBe
4 0-86
+ iL OT?
MIGROS LOG BwW9
1.0
0.8
0.6
KR
0.4
és 8 8 8
0.2 4
OO ee
0.001 eon
H/(GxTxT )
1.0
0.8
0.6 a
KT ;
0.4
Ora
uy
0.0001 0.001 0.01

H/C GxTx*T)

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER S DAUGTZ) = 006

126

SYMBOL D/GT2

® 0-0065
A 0-0161
a, 0.0550
I o{G)
Orme
DoS
KR So enti
0.4
O62
a————— qo Aw “as
ORGeA Oo GF
H/{(GxTxT }
ilo)
0.8
0.6 Ne
0.4
Doz
0.0001 0.001 OOK
H/{GxTx*T )

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 9 DS AS= vial tCy

127

SYMBOL D/GT2

@ 09-0065
A Waonen
+ 0.0555

il 610)
O-8
0.6
KR == On
0.4
i ae ee
oe a
0.001 OF G1
H/{GxTxT }
1.0
(8) ts)
0.6
KT
0.4
OW o2
0.0001 0.001 ORGA
H/{GxTxT }

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER | S/ns= Boss

128

KR

SYMBOL D/GT2

o 90-0065
Ro aE
+ 0.0555

S| ©
mn Om

Fe ee Tne es Ee

0.001
H/(Gx*TxT }

oO
09)

0.0001 0.001 0.01
H/(GxTxT )

WAVE TRANSMISSIGN ANO REFLECTIGN CGEFFICIENTS
BREAKWATER g DS/HS= 0.64

Is)

Fal : SYMBOL OS/HS
ag orld
Goel
i ONG

isenee iN ty [eee are eee BWIO

SES oa ©
oO)

0.001 ORG
H/(G*Tx*T)
il oO)
Os
ORIG a ee
KT )
ce 7 ee A:
Doz
0.0001 0.001 GeGi
H/( G*TXT )

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BRERKNG CER LO O/C Z eu sis

130

SYMBOL D/GT2

mn 0006S
A 0.0161
*, 09-0550
Io}
Oats)
0.6
0.4
OyeZ A
(a ee
GoGo (G} g(a) 21
H/{GxRTxT }
it oW)
0.8
Ofat
KT
0.4
Doz
0.0001 OPFOOH ORO

H/{ GT*T }

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 10 Sissel

SYMBOL D/GT2

a 0.0065
x 0.0161
a 0.0555
io
0.8
0.6
KR
0.4 ©
62
OROon ORG1
H/(GxTx*T }
ie)
a ots
a66
Ml
aA a0 ee
Doz
ae ere (Gite
0.0001 0.001 ORG
H/{GxT*T )

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER 10 S/nSs Ooi

132

B= 30cm SYNBOL OS/HS

r | hs = 60cm 0 0.75
A Q.51
©
a EE BWI!
fo) 0.5 1.0 m

OQ
@

es

=v)
O oO
~ (oy)

&
|
ic}

0.001
H/(GxTxT )

a a

0.0001 0.001 0-01
H/(Gx*TxT )

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 11 DWACE TZ VSte ag ls

133

SYMBOL D/GT2

By Was
A OOS
+ 0.0555

0.001 0-01
H/C GeTXT }
1 oO
0.8
GAG
KT
0.4 er
0.2
"0.0001 0.001 0-01
H/(GxTxT)

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 11 DS/TiSs ls 7s

134

SYMBOL D/GT2

-0083
-0133
-0157
-0231
-0311

oxX+t+PG
OQOo000

0.001
H/(GxTx*T }

(a) (OOO Teg Oa
H/(GxT*T}

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 11 S/H nis= Bots

135

=4 SYNBOL OS/HS

ag hall
a O88
my | Wad)

0 0.5 1.0m Bwi2

H/CORTET I ae

iL 3

0.8 OC ie ae

0.6

0.4

Dez

0.0001 0.001 Ta Gl

H/C GxT*T )

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 12 D/ LET ZU. 016

136

a

SYMBOL D/GT2

on O-O065:
a 0.0161
A) WLO5SO
i 6
ots
0.6
KR
0.4
Do 2
pa els
Gog ORGn
H/( GxTxT }
Lo)
Oia
ae 2 age
KT
Bloat
oZ
0.0001 Omoon ORO
H/{G*eTxT }

WAVE TRANSMISSIGN OND REFLECTIGN CGEFFICIENTS
BREAKWATER 722 CIS | 1 ol 7

{37

SYMBOL D/GT2

a CRS
A 0-0161
i) (Oe 0555
1 o@)
0.8
oS
KR
God 6
0.2 aa
0.001 OPO
H/(GxTx*T }
1 of
0.8
Bos
KT 5
0.4
A
0.2 ic se
0.0001 0.001 ORO
H/(GxTxT }

WAVE TRANSMISSIGN AND REFLECTIGN COEFFICIENTS
BREAKWATER 12 HS/io= — 0.665

138

SYMBOL D/GT2

@ 09-0065
ee) OL OTEH
+ 0.0555

0.001
H/(GxTxT }

0.0001 0.001 0.01
H/(GxTx*T}

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
INVERSE Elis | dbz VSyinss MO std!

139

B=40cm SYNBOL DOS/HS

Rana he= SCH : 1-92
!on!5 Fronting Slope, & :
ROHS s ae ols
Marat
[ERODE SUNS A een Tae Deere) .
0 29 SS BWI3,15
to 8)
0.8
0.6
KR
0.4
OZ
0.001 0.01
H/{ GxTxT )
Lol)
ap Se
A oO
Oris
KT ;
0.4
0.2
0.0001 0.001 Bo il
H/{GTx*T)

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 13 CVACG2Z)=S0 o Wiis

SYMBGL D/GT2

oy) Geadss
ie 0.0161
+ 0.0555
it 5B
0.8
Gree
KR
Gre4
sz
aA
0.001 ORO
H/(GxTxT }
io
0.8 >
ry
0.6
KT
0.4
eZ
0.0001 . ORO ORO
H/(G*Tx*T }

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS
BREAKWATER 13 BS/s= ele

14]

SYMBGL D/GT2

0 -0042
0-0065
0 -0103
0-0161
0 -0353
0-0555

ju}
a
St
x
ov)
+

0.0001 0.001 0.01
H/(GxT*T }

WAVE TRANSMISSIGN AND REFLECTIGN COEFFICIENTS
BREAKWATER 13 DS7to=nleasio

142

SYMBOL D/GT2

fu)

a
+
x

@ -@
OD @W

KR
re ier pan Te te ig |
fu)

._—————— ssa Fh t#4#Y!—_.
OpeyZ. a

0.001
H/(GxT xT }

Or OOO 0.001
H/{GxTxT }

0 -0038
0 -0094
0-0229
0.0324

WAVE TRANSMISSIGN AND REFLECTION CGEFFICIENTS

BREAKWATER 13 Ss/niss it cUle

143

B= 40cm } SYMBOL OS/HS

oO

NxM? OX+

Or rr rer.

Piette, Ne ee
[ep]

0.0001 0.001 Bio Gi
H/(GxTx*T )

WAVE TRANSMISSIGN AND REFLECTIGN COEFFICIENTS
BREAKWATER 14 D/UEVZ VSO oGis

144

ne, ar

SYMBGL D/GT2

o ) aces
AK 0.0161
% | (ORCS55
i 5
(0) ats:
oS
KR
0.4
OeyZ ean a ae
a
ORO wR eo
H/{(GxTx*T }
1 of A a
a
0.8
Ome
KT
dled
eZ
0.0001 ORG wn OROn
H/( GxTx*T )

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 14 toviho= a 182

145

SYMBOL D/GT2

a Wee
A 0.0161
a OR05SS

cree enor

RERUN UO NZ Neo f

ROO neon
H/C GeT xT)
il of ;
(O) ats} =e
vy
tec Sp
KT Bre
0.4 i
0.2
ee eee | ee eee
0.0001 0.001 Teon

H/( GxTxT }

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 14 vS/hss 1.636

SYMBOL D/GT2

0 -0038
0.0094
0-0161
0-0211

1)
A
+
x

0.001
H/C GT *T }

0.0001 DB} BOA Geli
H/{(GeT*T )

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 14 Sass dais

147

B=40cm SYMBOL DS/HS

ie ee — ho= 33cm

lon 15 Fronting Slope,
3.75 m Long

-?>OoxX+bG
oo °orrr-

BWI3,15 |

0.0001 0.001 0.
H/©GxTxT }

WAVE TRANSMISSION AND REFLECTION COEFFICIENTS
BREAKWATER 15 D/ACER2) =O OG

148

SYMBOL O/GT2

ah) osadsg
A Oeanen
+ 0.0555

a — —h—— am

ORO OH
H/( Ge TT }

Bo OUGs Omaan D} 5 (3h
H/{ GeTxT }

WAVE TRANSMISSION AND REFLECTION COEFFICIENTS
SNA IANA ARM Elxe al) US/iS= eeless

149

SYMBOL O/GT2
a WeWiaZ

A 0.0065
eos
ilo
0.8
0.6
O.4
H/CGRTEE ni
| 6
0.8
0.6
O.4
G02
0.0001 7 sour 0.01
H/( Gx TT } |

WAVE TRANSMITSSTGN ANG KEREEET LEN CGERRIETENTS
BSRICNAN Eieuelis OS/As=e 1oZi

SYMBOL D/GT2

0.0046
i OROOSS
ee SOREN

(a OO OU
H/( Gx TT }
il of
0-8
O68
KT [u) +

0.4

~f
Opaz

0.0001 0.001 ORO

H/(G*TXT }

WAVE TRANSMISSION AND REFLECTIGN COEFFICIENTS
BREAKWATER 15 HS/Ans= “ss

IS |

SYMBOL D/GT2

or SeGass
a 0.0065
A Goan

0.0001 0.001 0.01
H/( G*xTxT }

WAVE TRANSMNISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 15 DSSS Oo9i

fo

SYMBOL OS/HS

B=40cm

h,= 33cm ‘u) 1.92
Ix 1.36
lon!5 Fromting Slope, a oat
3.75 m Long x 1.06
os 0.91
22-cm-High Plate
——————E :
x Ae se BWI5W
ilo)
Os
0.6
KR
0 ° 4
oe x
0.001 ORO
H/( GeT*T }
1 0
0.8 S

rie

0.2
Pe en Ree ae |S A my eo CO
0.000 0.001 0.01
H/( GxTxT }

WAVE TRANSMISSION AND REFLECTION CGEFFICIENTS
BREAKWATER 15W DACGhZ V=O0i'6

LOS)

SYMBOL D/GT2

o 0-0065
a O-O161
A WORSE

lO ar cen = Pe

ORO CH Oe Or
H/(G*xTx*T )
il of}
Oras
Ores
KT
(per
Do
ORO won Ooo ORO
i aatt ae a)

AMS TANS HOS MON FING MERLE C Ih GIN (CGlElFIF IC ENTS
BREAKWATER 15W DSVhS= 1.86

154

SYMBGL D/GT2

o 0.0038
A 0.0094
mR OOS
ve M.O2f

1 oD

0.8

0.6

KR
0.4 a
0.2 fos

Ss ues ie ce
000 0.01
H/(GxTxT )
1.0
0.8
a.

KT Se |
0.4 Sx
0.?

0.0001 0.001 0.01
HAE eee

WAVE TRANSMISSION AND REFLECTIGN CGEFFICIENTS
BREAKWATER 15W USAnS= 1 s06

155

B= 60cm SYMBOL OS/HS
; 1.82

NxH?OX+7RG
OoOoOorrrr
ae oe: Meee

Q.0001 Q.001 0.01
H/0GxTxT?

WAVE TRANSMISSION AND REFLECTIGN COEFFICIENTS
BREAN ER is / CErZ J=0 o016

156

SYMBOL D/GT2

ru} 0.0026

A 0 -0065

re 0-0161

x 0-0555
1.0
0.8
0.6

KR
O git
eZ (u) a
o_o"
0.001 0.01
H/(GxTxT )
1 518)
0.8
0.6
KT

0.4
0.2

0.0001 0.001 0.01

H/(G*xTxT )

WAVE TRANSMISSION AND REFLECTION CGEFFICIENTS
BREAKWATER 16 OSAniSs beter2

IST

SYMBOL D/GT2

fu}

4
+
x

0.001
H/(GxTx*T }

oF 7@' oO =@
>

0.0001 ORO OW
H/( GxTxT )

0.0026
0-0065
0.0160
0-0550

WAVE TRANSMISSIGN AND REFLECTIGN CGEFFICIENTS

BREAKWATER 16 WS/nss — 187

158

SYMBOL O0/GT2

a OeMuAs
A 0.0065
mn 0.0161
iL oO
0.8
0.6
Oi4
Os?
+
0.001 ORO
H/( GeTx*T )
150
ies
ORS
0.4
Oo. 2
Oo OU? 0.001 Oe Gil
H/{GxTx*T }

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 16 S/S] 6 ileaSZ

SYMBOL D/GT2

5 0.0024
i 0.0022
A (yoo
y 0.0065
1.0
0.8
0.6
KR
0.4
0.2 | = ——— ee _» 2
ny
Geom ONOA
H/(GxTxT }
i o(G
(DO) 6183
®
0.6 ss —<
KT
Oras
Oo?
0.0001 0.001 SIN

H/(G*xTx*T }

WAVE TRANSMISSIGN AND MELEE LON COEFF CENTS
BREAKWATER 16 S/S Nese

160

SYMBOL O/GT2

0022
0037
-0065
0131
-O161

e@x+bG
ooo0cMe

O01
H/{(GxTx*T )

(ME Se ee rd ee

0.0001 ORewa ORGT
H/( GeT*T}

WAVE TRANSNISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 16 OSS - ° Wetis

16 |

SYMBOL O/GT2

We Wna
A 0.0037
+ 0-0065
% WONgh
Aa HOKE
io
0.8
Ora6
KR
0.4
aA
OraZ % x
GROCh OMOn
H/( GxTx*T }
1 oG
0.8
0.6
if
0.4
x
O62
0.0001 ORG WE 0.01
H/(GxTx*T)

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 16 BS/rss Os9.

SYMBOL D/GT2

0.0019
0.0037
0.0130
0.0161

x+b>G

Bo Oy
H/( GxT*T }

OOOO OROCH Ou
H/(G*T*T)

WAVE TRANSMISSION AND REFLECTION CGEFFICIENTS
BREAKWATER 16 Wovrises We 7is

163

SYMBOL D/GT2

aq O-MOng
A O00)
+ 0.0065

Oj owas
H/(GxTx*T }

Oo
o0)

0.0001 0.001 Cah
H/( GxTxT }

WAVE TRANSMISSION AND REFLECTIGN CGEFFICIENTS
BREAKWATER 16 HS/ASss Oats

164

Mimnccooren SYMBOL DS/HS
a Mets
A Q.75
A Wom)
| on !5 Fronting Slope
ie
Ane erie | Sea
Q 0.5 1Om BWI7
i o@
Ore
Oras
KR ©
0.4
OloZ
ORO eH ORG
H/( G*TxT }
i o@
0.8
Oras
KT
0.4
Doz
(Fo (OKO) OOO ORon

ha Geaciectin)

WAVE TRANSMNISSIGN AND REFLECTIGN CGEFFICIENTS
BREAKWATER 17 D/ACGTZ) =O) 0nt6

165

SYMBOL D/GT2Z

a ceoona
a 0.0013
R Owois)
~ Waa
Z .00s7
A O.0aes
J) MOlL6
27) \okonet
S| On0e27
1.0
0.8
Qo z
KR) = a
0.4
0.2
0.001 0.01
H/(GeT*T }
1.0
0.8
0.6
KT
0.4
0.2
0.0001 0.001 Geon
Heise)

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
INE Elisa ei eee Lae DSSS - Ootss

166

a

SYMBOL D/GT2

a 0.0010

a Onaants

in 0.0037

vO 20065

S 0.0130

* 0.0161
i, 9B)
0.8
0.6
0.4
0.2

(8), (OO ORG

H/( GxTxT )
168
0.8
Oo
0.4 =

Oo2

0 0001 OR GOR CROn

H/(GxTxT )

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS
BREAKWATER 17) ao/is=s -Os7s

167

a aa ee ae
O.4

0.001
H/{ GxTxT })

0.4 i cS Say

Oo} Voi

0.001

H/( GxTx*T )

SYMBOL D/GT2

oX+bG

0

0
0
0
0)

-0010
-0019
-0037
-0065
-0161

(Sahil

oO

WAVE TRANSMISSIGN AND REFLECTION COEFFICIENTS

BREAKWATER

Ly

168

DSho=

0.58

APPENDIX F
DOCUMENTATION OF THE PROGRAM OVER (752X6RICYO)

1. Purpose. This FORTRAN program estimates wave transmission by over-
topping coefficients and transmitted wave heights for smooth impermeable
breakwaters. The method can be used for subaerial and submerged breakwaters
with structure seaward-face slopes from vertical to 1 on 3. It is recommended
for values of d,/(gT*) < 0.03.

2. Mathematical Method and Procedure. The program uses the methods
developed in this report. The procedure is to estimate wave runup on smooth
impermeable slopes, R, using the equation

C, VH7d+C
R = HC, (oui Ly 2 *Cy )

where CC), C2, and C3 are empirical coefficients related to the structure
slope, H is incident wave height, d is water depth, and L is the local
wavelength. Runup on rough slopes is estimated using

Haé

N= = be)

where a and b are empirical coefficients and €&€ is the surf parameter
given by

tan

one

Lo

where © is the angle of the front face of the breakwater and Lg, is the
deepwater wavelength.

A wave transmission by overtopping coefficient, C, is estimated from

0.11 B
h

where B is the breakwater crest width and h the structure height. The
transmission by overtopping coefficient, Ky, is determined from

F
Sig) = c(1 - &)

where F is the breakwater freeboard. For submerged breakwaters with a
1 on 15 fronting slope the equation

kms c( $ x) - Go = ae) (x)

The transmitted wave height, Hp, is given by

€ = 0.51 -

is used.

Hp = Km H

169

3. Program Variables. A description of all program variables is presented
inehablewr— 1K

4. Input. A description and an example of the imput parameters are given
in Table F-2. Note that all measurements are in metric units.

5. Output. Program output includes a summary table of input information
together with the predicted ratio of the breakwater freeboard to wave runup,
the wave transmission by overtopping coefficient, and the predicted transmitted
wave height. An example output corresponding to the input is shown in Table F-3.

6. Program Listing. A listing of the program is shown in Table F-4. The
subroutine LENGTH finds the value of d/L given d/L, by using linear wave
theory.

Table F-1. Variables used in the program OVER.

Variable Description
AC a; rough-slope runup coefficient
BC b; rough-slope runup coefficient
B breakwater crest width (meter)
BH B/h
Cc transmission by overtopping coefficient = 0.51 - 0.11 B/h

CA, CB, CC runup coefficient lookup tables

Cl, C2, C3 smooth-slope runup coefficients (a function of slope)

R/H = C,(0.123 L/Hy (C2¥tl/a+C,

DGT2 d,/(gT?)

DL d,/L

DLO dg/Lo

DS structure water depth, d,

F breakwater freeboard = h - d,

FR F/R

H incident wave height, H

HGT2: H/(gT?)

HMAX depth-limited maximum wave height = 0.78 d,

HS structure height, h,

HT transmitted wave height

I counter index

IFRONT flag to indicate the presence of a fronting slope (IFRONT = 1
for fronting slope of 1 on 15)

KTO wave transmission by overtopping coefficient

L wave length

N number of wave conditions of interest

P linear interpolation factor to find Cl, C2, C3

R predicted smooth-slope runup

RH R/H

SURF the surf parameter = tan 9/ VH/L

T wave period (second)

TANA lookup table of structure slopes corresponding to CA, CB, CC

TANT tangent of the seaward face of the breakwater = tan 0

170

Table F-2. Input to the program OVER.

Card Format Description
1 12 number of breakwaters
2 12 number of wave conditions of interest

eequals 1 if breakwater has a1 on 15
fronting slope seaward of the structure

4X

F10.5 tangent of breakwater seaward slope
e breakwater crest width (m)
e breakwater structure height (m)
ewater depth at toe of the structure (m)
erough-slope runup parameter, a (a = 0 for
smooth slopes)
erough-slope runup parameter, b

3
(one card per F10.5 wave period (s)
wave condition) @incident wave height (in)

(repeat card types 2 and 3 for each breakwater)

Sample input

14.0 0.667 1.53 4.6 3.56 0. 0.
709) 0.2

7.9 0.4

709) 0.6

78) 0.8

7.9 1.0 B= 1.53 m

109) 1.2

7109) 1.4 0.667
To) 1.6 d

To) 1.8

109) 2.0

7.9 Bod

139 2.4

709 2.6

709) 2.8

17 |

Table F-3. Sample output from the program OVER.

PREDICTION UF wAVE TRANSMISSION COEFFICIENTS FOR
AN TMRERMNEABLE BREAKWATER

NUMBER OF WAVE CONDITIONS & 14
JFRONT = 0

TAN(SLOPE)® 667

BREAKWATER TOP wIONTH(M)& 12530
STRUCTURE HEIGHT (M)s 4u,o00

WATER DEPTAC(M)® 43,560

PREEBOARD(M)® 1,040

COEFFICIENT UP UVENTOPPING Ce 4473

C1=4,9910
Cae .4980
C38e,4AS0

T(SEC) DsGT2 CM) H/GT2 R/H F/R kKTU HT(M)

7.900 .0058 2200 209035 1,594 3,261 9,990 0,000
7.6900 00058 e400 000065 36899 1.369 92.000 02000
70900 00058 0600 200094 2,079 2834 079 047
75900 SO0058 SACO OOS ColOTeaspve clhtS) melo
70900 00058 16009 000164 26278 0456 2257 0257
72900 00058 16200 900196 2,534 371 298 0557
TEGOO eOOSE Medno) s0nee? Coors e513 «Seo ude
72900 e095R 30600 000262 2,594 e272 345 0552
7.90H e005R 15800 200294 2.406 2240 4360 2644
76900 00058 20000 000527 26410 e216 2571 0743
TAOOd AOOSE 25200 4OOSO0 B560u 6i9O pdéBO oor
7.900 20058 20400 e603892 2,399 4141 25856 2951
72900 20058 2.600 ,00425 2,366 ,168 ,594 $,025
70900 00058 26800 0600456 26470 0357 0599 10316

a a

Iv 2

10

15

20

25

30

35

40

45

50

55

Oannnannan

]

Table F-4. Listing of the program OVER.

PRUGRAM OVER( INPUT OQUTPUT 0 TAPESSINPUTo TAPE OBOUTPUT)
REAL Le KTO

DIMENSION TANA(H) 9C4(6) oC B(6) 0 CC (6)

DATA TANA/LOpe2o0l 0006679044490 —33h/

DATA CA/0 995804 2800) 046904 IIL 04 B11 01,5007
DATA CBA 2289 3900 6 $469 04989 04699 op S12/

DATA CO/,057800,094 0%,39990,38500,0800,040/
KEAD( S91) NBw

DO 100 IBwWE1» NAW

REAN(Se1) NoTFRONWT eo TANT eo BeHGoD§o AC, BC
PURMAT(2T200X07F 10.5)

N & NUMBER UF WAVE CONDITIONS

JFRONT & 4 FOR $715 FRONTING SLOPE

TANT 3 TANGENT OF FRONT BREAKWATER SLOPE ANGLE

8 8 STRUCTURE WIDTH AY Tre CREST (m)

HS & STRUCTURE HEIGHT (™)

0S & WATER DEPTH ar TOE OF STRUCTURE (m)

AC & ARRENS ROUGH SLOPE RUNUP COEFFICIENT (#0 POR SMOUTH SLOPES)
BC ® AHRENS ROUGH SLUPE RUNUP COEFFICIENT

@e

co

cB)
14

FPERSeDS

BHER/HS

C£u,510e0,11*BH

WRITE (602) No TFRONTo TANT eGo HSeDS oF oC

FORMAT(YH{92X— (PREDICTION OF WAVE TRANSMISSION COEFFICIENTS FOR(9/
Be2XKe (AN IMPERMEABLE BREAKWATER (0//01X0 (NUMBER OF WAVE CONOIT
SIUNS Slol39 elXeo(TERONT Bloleo/oiXo (TANCSLOPE )8 (oh oeSo/elko (BREAK
BKWATER TOP WIDTH(M) (oF bee /01X0 (STRUCTURE HEIGHT(M)& (oF 6,30 /91%
B® eo [WATER DEPTH(M) 8 (oF oe 30/01Xo (FREEHOARD(M) 8 (oF bode f0iXe
® (COKFFICIENT OF OVERTUPPING CB(F6,30//)

TF CAC LTe00001) GO TY ai

WRITE (6022) AC,AC

FORMAT ($ x9 (RUNUP COEFFICIENTS POR ROUGH SLUPE RUNUP ACB (oF b6ede
% ( BCB (oF 6,2)

GU TU 23

OO F JsieS

TEC TANT SFr eTANACL) OR TANT LT 9 TANACIOL)) GY TO 3
PR(TANA(T)&PTANTYS(CTANA(CT) © TANA(TO4))

CIBCA(CT)@(CACT CAC TOL) )eP

C2ECH(T)@(CA(TyeCA(t¥1))#P

CSECC(I)@(CE(L)eCC( 191) )eP

CONTINUE

IFC TANT, GT.10,) ClLscati)

TFC TANT SGT 0100) CesCb(})

IF(T4NT,GT,10.) C33CC(1)

TFC TANT oLT000333) C1#CAl6)

IFC TANT ob 1.05343) CasCB(o)

TPCTANT LT.0,333) C3BCC(O)

RITE (O07) Clecerl3

FORMAT(1X0 (CIB [oFO,do/91Xe (CCE (oFO4o/oiXo (CSa (aFOpde//)

WRITE (6044)

PORMAT(/91X0( TCSEC? O/GT2 HCM) H/GTe R/H F/R KTQ HT(M) Ce
/)

OO Yu IeteN

READ(505) Tot

FORMAT(2F 10.5)

OLOsyS/(1 ,So* TT)

CALL LENGTR(DLOeDL)

173

Table F-4. Listing of the program OVER.--Continued

La0S/0L

hGTPSH/(9, 88T#7T)

OGT2ENS/(9,84&TaT)

RMECL#(0,1238L/H) *#(C2¥SORTCH/DS)¢C3)

SURFATANT/SORT(H/( 1, 96%T#T) )

TF (AC,GT.N,001) RHBACHSURF /( 3 .eBCHSURF)

RaORHeH

PREF/R

KTOsC%&(] ,@FR)

IF CTFRONT E951 AND Fob T9000) KTOSC#(1,@FR)O(§ po2,#C) BFR

TECFR GY 30) KTO8N,

HTSH*KTO

WRITE (6012) ToAGT2eHeHGT2eRHoFReKTOoHT
1a FORMAT( 1X oF bo So FTodoFboSoh e504 be3)

4 CONYINUE
100 CONTINUE
STUP
ENO

SUBROUTINE LENGTHCOLUeDL)
hEAL LOeLONEWeL O00
LQZ1.0/NLO
LOD33 .9/0LU
NB}
PIley.14159
1 ARGad,O*PI/LD
LONE “SLUDSTANH( ARG)
NSNol
OIF FSARS(LONEWealD)
TIFOCN@200) 3eYou
3 IF (DIFF a0,0U05) 20209
5 LOS(LONEWeLD) 42,0
GO TU 4
4 DLai ,o/LONEW
ARITE (60100) DLOeDL
100 FURMAT(Y4A SUBROUTINE LENGTH DID NOY CONVERGE, O/LO o oF 10050
1 6HD/L 3 oF 1009)
r) OLB1.0/LDNEW
RETURN
END

174

APPENDIX G
DOCUMENTATION OF THE COMPUTER PROGRAM MADSEN

The computer program MADSEN (CERC program number 752X1R1CPO) is used to
predict wave transmission through rubble-mound breakwaters using methods
developed by Madsen and White (1976). (Note: Equations and figures refer-
enced from that publication are identified by the symbol MW.) A wave
transmission by overtopping model is also included as discussed in the text
of this report. The program is organized as shown in Figure G-1. Whenever
possible the variable names used are a close approximation to the symbols
used by Madsen and White (1976). Table G-1 lists important variable names,
corresponding symbols used in Madsen and White, and gives a’description
including references to defining equations in Madsen and White (1976). A
description of each of the program subroutines is given below:

SUBROUTINE READI - This routine reads standard lookup tables corresponding
to MW Figures 2, 3, 15, 16, and 17 from Madsen and White (1976). Lookup tables
with a combination linear and logarithmic interpolation were selected to avoid
having to use Bessel functions with complex arguments. The 53 standard lookup
table cards are given in Table G-2.

SUBROUTINE REFL - This routine determines reflection coefficients from
rough impermeable slopes to account for energy dissipation on the breakwater
face (see-Ch. III of Madsen and White, 1976). MW equation (127) is solved
iteratively and the final result corrected by the corresponding correction
factor from MW Table 2 (a linear fit to these points is used). Lookup tables
from MW Figures 15, 16, and 17 are employed in this routine.

Read standard lookup tables (53 cards), CALL READI

Read number of breakwaters to analyze, NCOMP

Loops
For each NCOMP read breakwater geometry

For each period, NT, read wave heights, Hil
For each wave height loop to 100
Determine dissipation on BW face, CALL REFL

Iterate of AH, and AHp to find fg using MW equations (172) and (161)
Find equivalent breakwater (Sec. IV,2, eq- 158), CALL EQBW

Find internal transmission and reflection coefficients, (Sec. II), CALL INTER

Reestimate AH, from MW equation (161)

Determine transmission and reflection coefficients, Kp, and Kp, from MW
equations (175) and (176)

Find wave transmission by overtopping coefficient, Kyo
Print results
100 CONTINUE

199 CONTINUE

721) COG ONG TELN

STOP
END
SUBROUTINES

53 standard lookup cards
Input cards (see Table G-4)

Figure G-l1. General program organization.

175

Table G-l. Program variables.

Symbo 1 Variables Description
(Madsen and
White, 1976)

ay A incident wave amplitude

RII RII reflection coefficient (Sec. III)

AH DHT head (MW eq. 160)

AHg DHE equivalent head (MW eq. 159)

dy, DR reference diameter

By BETAR reference beta

v NU kinematic viscosity

d D diameter (cm)

ar Al equals RII a; (MW eq. 146)

RI ar internal reflection coefficient (Sec. II)

Ma TI internal transmission coefficient (Sec. II)

iT Kena coefficient of wave transmission for trans-

mission through the structure (MW eq. 175)
KTO transmission by overtopping coefficient
KT total wave transmission coefficient equals
VKTT? + KTO@

R KR reflection coefficient (eq. 176)
N porosity

Sie ss (n/0.45)?

nkok NKL equivalent

Le is equivalent BW width (eq. 158)

ho HO water depth

tT Ww wave period

£/S,. FS

r LAMBDA

ko KO 20/L
TS lookup tables

176

Table G-l. Program variables. --Continued
Symbo 1 Variables Description
(Madsen and
White, 1976)
RS lookup tables
FST lookup tables
RUT lookup tables
RT lookup tables
GSS lookup tables
FUS lookup tables
TX lookup tables
RX lookup tables
Ee FS (Fig. 17)
£., ES slope length
L L wavelength
NM number of materials
(maximum of 10)
NL number of layers
(maximum of 10)
Ah ; TH level thickness
Ah;
== DH relative thickness
ho
NR reference porosity = 0.45
Ah-
med s SUM2
ho ( By Ve
= Le
Py
} ee SUM1
lin
TOPW width of top of structure
Ly LL length of materials in
horizontal layers
F breakwater freeboard
R wave runup

177

-
SCOWOONTMNSCWN

Table G-2. Standard lookup tables to be read by READI.

055 083 0901 .50201922 333.2530 4H 3096

285 oBS 0901 ,492 01920 $05,195,423 690

085 083 oF9OL 492 ef blokIFS,10$,283070

085 083 e901 47eeINeelle,IUZ,073,4N

o&S. oBs F049 462 205C 0142, T2027 805000

285 oh3 FOL U5 Le PAS 52,902 e502 ,40

085 0683 0904.44) 08910922, 282,20 2020

08D ohS eADL HAL oAOl e922 1 0914283

0683 683 6901 ,401,701,08! 791,63) .60

oB®S 683 P01, 561061105201 ,571,5A1,24

06S ohS 0901, 3804 501 e401 ,574 0174000
120001 062%2 00320492 06950283, 3555744000
1000140234 0942, 3223502 2582,97 5,203.0 54
1000122} 08526162 03120962,593207382080
Le09Jc201{ oe b62,032 01 belch e, 52205420356
PoOOLelLIZo701,901 oPA2 C042, 0420024 097
16903 01%$ 061157810821 082) ,7/9$ 0751065
100010143 0541.68} 06710651 ,984 0494 258
1000401810481, 5710541 04 71,3571 0274 018
LoOOL od 71 oA3S1 URL odPloselseit.08 97
PoOOLolSjos 71, 5A1o5110181,05 .93 480
PeOOLe1O{os2l,eMo1FG1e0G 93 680 ob?
1200100010001 .002 60010003 ,001 of M1 2004 ,001 5,001.00) ,001 5001 ,001 ,001,00
1,001.00 ,98 ,96 ,92 ,87 ,87 ,8A ,B87 ,8! ,76 ,78 ,79 ,77 72 ,69 ,19
12,001,000 0698 ,93 83 075 276 078 675 266 06% 56) 466 160 ,54 ,48 48
10903009 e9? ,90 0675 065 .66 069 065 53 046 048 459 ,47 ,38 $2 35
40001000 o97 p87 e6R 255 oh 062 056 .42 034 938 .4O 137 ,27 4c) 24
42001200 095 283 06? 04b ee 095 oA 0353 eed 230 eB) 2e9 »18 ele 218
{2.00 099 oI 2/79 057 e40 2&5 050 obs »eb 218 eed ace eels 213 205 amie
12000 099 093 075 054 034 40 04S o35A el of2 ec -2ch 20 ,08 02 413
1000 099 092 072 eA4 028 36 o42 033 o16 007 917 wee ofA 07 .02 013 {
1.090 29? 491 070 oh Pre) 033 o3A 2 350) rile 095 ot 2cG off a OY »te 013 |
1000 oft) 690 5OV oS Of® 580 68S o@7 of 205) ol? o20) «18 Ol 02 oi3

080 e066 9657 50 o4ub6 242 ,38 436 354

067 250 o At 9 34 059 026 ee 018 ol5

258 ol o3e .e6 off ol? 15 oll 0A

650) 588 020 5% ofG okie oY oVV 50S

045 .30 .2e2 .16 o12 98 ,07 ,04 ,03 .

o41 026 ofS 413 009 097 ,05 203 202

037 023 016 g31 cA 205 03 aV2 202

253 o2i of 3 009 006 204 .3 202 oO

o3t 018 012 ~08 005 005 503 202 oD]

eed ott ell 297 204 293 002 001 PaO |

ee On he rl I a Ie i> Neal 059 658 0656 53

235 052 069 265 666 265 63 562 269

e4 660 568 47} o71 269 267 67 056

5150 oO? 678 570 of of av oVH of/O

68V of of3 67 cv of78 OVS ovS oV8

2060 073 078 478 oF! 076 «76 ath o7h

063 o76 260 19 273 »78 3 UY o77 o/7

poe off off oO off oO oO otD vvY

568 ,80 ,82 84 .80 .80 ,80 ,89 ,80

271 81 .83 ,82 .81 »8) ,#! 81 Al

Za

SUBROUTINE INTER - Internal wave transmission and reflection coefficients
for the equivalent breakwater found in EQBW are solved in this routine. MW
equations (57) and (37) are solved implicitly using R, = 170 and interpolation
of MW Figures 2 and 3, when nkl is greater than 0.1. If nkl is greater
than 0.9 the coefficients cannot be solved, so another equivalent breakwater
with smaller reference diameter stone is determined.

SUBROUTINE EQBW - This routine determines the rectangular breakwater
corresponding to the multilayered trapezoidal breakwater using the methods
described in MW Section IV,2. The initial reference diameter is taken as one-
half the armor diameter and reference porosity is defined as 0.435.

SUBROUTINE LENGTH - Finds the relative depth given the ratio of water depth
to deepwater wavelength.

1. Program Use. The following steps are required to use the program MADSEN:
(a) Assign each of the materials used in the various layers of the

breakwater a consecutive number making the armor ''material number 1."
Determine the diameter of each material from

7]
( )

where Wsg is the median weight and y the specific weight. Also
estimate the material porosity.

&

(b) Divide the breakwater into horizontal layers. A new layer
occurs any time there is a change vertically in any material type of
slope (see Fig. G-2 for an example problem). Make the layer next to
the seabed "layer number 1."" Find the thickness of each layer and
determine the average horizontal length of each material in each layer.
Remove the outer layer of armor from the seaward face of the breakwater
before making length calculations, because energy dissipation on the
front face is determined separately in the program.

(c) Estimate the kinematic viscosity of water as a function of
water temperature (Table G-3).

(d) Estimate breakwater water runup parameters, a and b. At
the present time the values of a = 0.692 and b = 0.504 are recommended
based on the laboratory data of Hudson (1958).

(e) Put the information into the required input format (Table G-4).
Input cards for the example breakwater (Fig. G-2) are shown in Table G-5.

(f) Sample output for the example problem is shown in Table G-6.

2. Computer Program. A listing of the computer program MADSEN is given in
Table G-7.

179

“‘pedinbet uotiews1osut yndut seqyemyeorq etdues °*7-9 oansty

w 20'¢: @ 210941 fa: 7

2 WoIyy SHUN Jowsy 2
€ sh: ee NS
082 €Sb
°9 Op l+ 20¢+ sce JON Og HA)
Ov"! Ka)
p=“ es2-8 ——>| we l )
aes SOADM Se 160 260°0 © (ee
00 S2 20+ 920 2 260 eee 0 @
1G
1€°0 6220 ®
00 00 G2s Lb0 € i Ajisouog «= (W) Jayawoig ]O1J9;0;KW
O2'S2I‘SI‘OI'SO'VO = (4)H oy
© ® oO) O2'OI'S = (S)1 auojsAsionb ybnos joisajow
(w) yibuar (w) Ssaunaiyy 3ah07 SUOI}IQUOD OADM

]0149j0¥y JO,UOZIIOH 4aA07 j02144aA = [Oj 0TZ1I0H

180

Tabie G-3. Kinematic viscosity of water.

Water temperature Kinematic viscosity

0.0000013
0.0000010

Table G-4. Format of input information.

Card type Format Description
eee. nee
standard 53 standard input cards (see Table G-3)

1 12 number of breakwater configurations or

water depths to test

2 20A4 title card

3 S12 aXe RO). number of wave conditions to test
number of materials
number of horizontal layers
structure height (m)
water depth (m)
kinematic viscosity (m/s)
width of top of breakwater (m)
front slope of breakwater = tan (6)
wave runup parameter a = 0.692
wave runup parameter b = 0.504

4 0X, 2F10.5 material diameter (m) (armor lst)
(one card per material)

material porosity

5 10X, 7F10.5 layer thickness (m)
(one card per
horizontal layer)

mean length of each material type in the
layer (put in consecutive order, material
1 (armor Ist), etc.)

6 2F10.5 wave period (s)
(wave condition card;
one card per wave wave heights (m)
condition)

configuration to be tested.

18]

TS?

aver
fi) V3)
wh?

c6y4%u L99°%U c5*2

GL v°02

Gg? uve

net u° 02

ei) v°ve

t°u v°ve2

ne? v°ul

oie o*ut

GO| veut

ued Oe |

get) boul

to v°Ot

mre 0°G

sl*t Veg

GY [| UPC

vet 9°s

get 0°s

pow 0°
as 62° ane £ Avi
7G? e 6G°n ey a) ¢ AW
vue? §6°% 54 °8 , avi
4y°u 260°) s Lvw
Lg 70 woo * 4) @ LVw
AE ow areata \ lyw

gHUUUCOL® aen Oty a & el
wd rlouad Jd ldwyx4

J

"NAISGVW Weasoid 03 yndut ofdues “¢-5 oTgGeL

182

KYT
KTN
KT
KR
HT

Table G-6. Sample output.

EXAMPLE PROBLEM

COMPUTATIONS OF KAYE TRANSMISSION THROUGH A POROUS BREAKWATER

NUM OF wAVE CONDITTUNS 18
NUM OF MATERTALS2 3
NUM OF HORIZONTIAL LAYER Sa 3
STAUCTURE HETGHT (M)a ee 6.900
WATER DEPTR (MM) 4,800
KINEMATIC VISCOSITY (M2/SEC)2 6090900930
Aw TOP WIDTH (M)= 20520
TANK UF FRONT SLOPES 06470

RUNUP COEFFICIENTS A= 7692 Bs 4504
MATERIAL CHARACTERISTICS ¢MAKE ARMMR MATERTAL NUMBER 1)

MATERTALS 1 DYAMETER (M)B 4729 PORMSITY3 , 3470
MATEQTAL= 2 DIAMETER (My3 ,$3a POROSITYS 370
MATERTALS 3$ OLTAMETER (MS 092 POROSITYS 370

HORIZONTIAL LAYER CHARACTERISTICS
(MAKE LAYER NEXT TO SEABFU LAYER NUMBER 1)

MATERIALS 1 2
HORIZONTIAL LAYERS 1 THICKNESS (Mya $5550 LENGTHS (M)e 4.5 paA
HORIZONTIAL LAYERs 2 THTCHNESS (M)= 2780 LENGTHS (Jez 445 205
HORIZONTIAL LAYERS 3 THYCHNESS (M)s 2470 LENGTHS (¢)s 503 940
HOM) T(SEC) H/(GRT*T) HAL DO/(G*T#T/) KTT KTA JKT
0190 5.00 onN04nd 060338 09196 4592 0,000 439?
. 0500 5000 oN020u4 s01o74 DONG 5233 DONO HAUS
$2900 5090 eN040AL 20353549 90190 eiDi Oe0N) 415i
12500 500 oADALA2 395023 BONUS oval AOR aise
10750 §.90 eON7T145S 205860 90190 O82 oBS oi\8V
2.000 5.00 2008143 106697 SMII ohlS ofS pihav
0190 10.90 oA0N1ne 00015] 29049 401 2,009 ,40!
0500 $9.00 200054) 209753 ©9049 202 0.000 ee
1.000 10096 90901629 201507 a0049 6135 e000" 4135
12590 aaa oN01533 20266 580R9 6100 ofS piSe
12750 19390 2001786 200627 09049 2088 2159 182
20050 10.90 endeoal 003013 F049 4020 4195 ,end
0100 20200 0900076 200973 29012 4581 0.000 381
2500 20609 000128 200Sh7 00012 9196 0.090 186
1.000 20.90 2000255 209735 DOWIE 6827 ~oO1O0 of@U
12500 20.00 00003AR$ ecdtina 29012 4098 154 .182
1.750 20000 e0ON4IO 091286 SOG GUE 59 AaIe
2,900 20000 2000540 eV1479 00012 2081 eeey ,24t

WAYE TRANSMESSTON THRAUGH THE STRUCTURE

WAVE TRANE™MTSSION HY nv F STOPPING COEFFICIENT
TOTAL WAVE FRANSMISST OY COEFFICIENT

WAVE REFLECTION COEFF ICTENT

TRANSMITTEQ KWAVE PE TORE

183

40

is

20

30

35

40

45S

50

53

60

63

Table G-7. Listing of the computer program MADSEN.

$90

PROGRAM MADSEN(TNPUTe OUTPUT» TAPESBSINPUT, TAPEGEOUTPUT o TAPES)
COMMONSMADSISNMoNL og DC ILI oONCLL) oLLCLioli dof HC14)
COMMON/SEEL/NKL ofS

REAL NKL_

DIMENSION IBUF(1) oTITLEC20) eNUM(10)

REAL LoNUeKTeKReNoLEgNRoLL oe KTO9KTT

DATA NUM/1 920394059607 980991 0/

Play.14i59

CALt READT

REAR(S5¢590) NCOMP

FORMAT (312, 4X0 7F 10,53)

DO 200 IJ={+NCOMP

€ READ INPUT INFORMATION

{71
172

971

98
99

178

33

9uA

REAN(CSeI171) (TITLECIIM) oJeMBlo20)

FORMAT(20 44)

WRIVE(60172) (TTTLEC JIM) oJIMB1020)

FORMAT({H1e10K, 2044)

REAN( 59590) NT» NMoNLoHSeHOoNUy TOP» TANByRAGRB

FeHgeHt

1F(P4,LE.0,) RAB00692

TF(PB.LE.O,) RB2.504

WRITE (60971) NToNMoNLoHSoHOoNUy TOPWeTANBORAGRA

FORMAT(/ 910X%_ (COMPUTATIONS OF WAVE TRANSMTSSJON THROUGH A POROUS
® BREAKWATERCoss705X%0 (NUM OF WAVE CONDITIONS (ol 2KoTSe/eSXe
® (NUM OF MATERTALSSlol7Xol3So/05Xo
s (NUM OF HORIZONTYAL LAVERSB (o6xX015o/09Xe (STRUCTURE HEIGHT (M)
OB (oO KXoF IO Se/eSK¥0 (WATER DEPTH (M)e (of IK oF 10,39 /05XKe
S(KINEMATIC VISCOSITY (M2/SEC)BloF11,% 405% (BW 70? WIDTH (M)B lo
BLOX FI0e3e/e5Xe (TANB OF FRONT SLOPES (e9x9FS.49/05X_ (RUNUP COEFFICI
SENTS AB[oFOe3e( BE l0F6_3)

DO 969 Iesost

DO 98 Jeio4yl

LL(yeJ)=0,

CONYINUE

wRIVE (00283)

FORMAT(Sxo (MATERIAL CHARACTERISTICS (MAKE ARMOR MATERIAL NUMBER 3)
¥le/)

dO (7 Jef 9Nm

REAN(5e7) ACT) oNCT)

FORMAT({0%,7F 10,5)

WRITECOCS77) TeAC I) oNCT3

FORMAT(Sxe (MATERIALS (02300 NIAMETER (M)e lof 6,30 POROSITYEC0F6,3)
CONTINUE

WRITE (Oe284) (NUMC JM) oJMal oN)

FORMAT(//05X9 (HORIZONTIAL LAYER CHARACTERISTICS lo/_5Xo

S((MAKE LAVER NEXT TO SEABED LAYER NUMBER 1) (ose
" Seye (MATERIALS LoL 9 SX) 04e63xX 9 H(L2—4X) oA)

0O 43 JeieNL

REAN(Se7) THC J) o(LLCLeJ) oTE10NM)

WRIVECO01L78) Je THC JI oCLLGITeJ) oT Bi on™)

FORMAT(5X» ([HORTZONTIAL LAYERS (ol3e( THIGHNESS (M)B8[(o FoeSel LENGTH
35 (M) a lo7FocleoseG0XoTFOe))

CONTINUE

NMaNMe |

OC Nm) S001)

N(NM)20,01

NLENLO4-

THCNLIS10000000,

LUCNMoNLJE3,FN(1)

WRITE (60942)

FORMAT(//e 6X9 (H(M) TCSEC) H/(GeT%T) AL D/CGET*T/) KTT
* KYO KT KR HT(M) C)

DO 499 IKzqoNT

RE AN( 598) Tot

FORMAT (AF 1005)

Az=He0,5

DRENC1) 005

184

Table G-7. Listing of the computer program MADSEN. --Continued

IFC boL1,0.00004) GO TO 106
IFCTANA.LE,0,) AU TO 37
70 CALL REFLCAgGHS M61) OHO TANBy To RIT RU gL)
ATSRIJ*A
22 DHT=2,%RUSA
IFLYG=o0
C ASSUME nHESDHT AND YTERATE ON THE EQUILTVANT Bw
75 ICOuNTSO
ORE SOHT .
10 TCOUuNTSICOUNT#4
CALI. EQRW( DHE eDHToLE eo hOoHSp TANBoNRe ARO TOPW)
CALI INTER(NRe To LE oHOeAToNUyDRo TI] oRJokoTFLAG)
80 IFC TFLAG,EQe1) ARSDR¥0,95
IFC TPLAG,EG.1) GO TN 22
OHXES(1,¢RI)*RITHA
IF(TCOUNT,LT,4) GO TO 10
KRERIT*RIT
85 KTTSTIFRII
37 IF(TANB,LE,0,) CALL INTERC(N( 1) o To TOPWeHOoAONUoD(S) »KTToKRobolPLAG)
IFC TFLAGsEQo!) DREDR¥0,5
IFC TFLAG,EQ.3) GO TO 37
SURESTANB/JSART(H/( 1 SO8THT))
90 RHEPASIIRF/( 1 + RESUME )
RSHeRH
FR=SF/R
CZE0.51 @0.11*TORM/HS
KTOsC¥( 1, eFR)
95 LF ((TOPH/HS) ,GT.0eBBeANDoh L150.) KTOSCH(1eeFR)@(1,92,9C)¥FR
IFCKTO,GT,1,) KTUEI,
IF(FR,GTe1,0) KTUFO,
bHGTac dee, /(9,8OUT*T)
HLSa,4A/L
100 DGT2sHO/(9,80* T#T)
FLAGS3H
KTESQRTCKTT*## 2 ek [O¥¥2)
IFCKT.GT,.1,0) 4751.0
HTSWeKT
105 WRITE (60981) Ho TOHGT20HL oDGT2oKTToKTOOKTOKR HT
981 FORMAT 5x oFOaSsoF 10 ce oF 10s P 10 pS 0F I 00d, SFO, 3 uF bee oF 7035)
foo CONTINUE
199 CONTINUE
WRITE (60204)
110 201 FORMAT(//02X0 kT! © HAVE TRANSMISSINN THROUGH THE STRUETURE le /o
*2XorKTO © WAVE TRANSMISSION BY OVERTOPPING COEFFICIENT lo/o
* 2X,(KT © TOTAL WAVE TRANSMISSION COEFFICIENT [o/0 aXe
* (KR oe WAVE REFLECTION COEFFICIENT ty
S/o2X0 (HT © TRANSMITTED WAVE HEIGHT 0)

115 200 CONTINUE
STOP
ENO
1 SUBROUTINE REFLCAeHSe Dp HOoTANBe ToRIToRUGL)

COMMON/SMANS/EST(FIOL1) oRUTCIeA1) ORTCI7TOLIIOTXC9010) pRXC9010)
OIMENSTON FSSC14) eRUS(CI1)ORSCI1)
REAL telStols é
bs) C CF = MODEL CORRECTION FACTOR TO ACCOUNT FOR MONEL SLOPE EFFECTS
CFhS7.28"0,S578*TANB
IF(F4NB,LT,9,4) CFS1.02
TFC TANB,GT,0,68) CF50,89
C FIND wKAVE LENGTH L
10 HOLQSHO/( 1, S6O*T#T)
CALL LENGT(HOLOsHOL)
LEHO/HOL
LSSHU/TANB
IF CRS,LT,HO) LSsHS/TANB
15 LSLsSlLSyL
IF(LSL,LT.0.8) GO TO 105
TMINSSURT (6 .2839%(LS 40.8) /69, 8 TANH(6,283#HOs(1S/008))))
WRI VE (69101) TMIN
101 FORMAT(///¥1Xe (WARNING@THE MINIMUM WAVE PERTOD TO BE ANALYZED BY Tf

185

20

28

30

35

49

4§

10

19

15

20

Table G-7. Listing of the computer program MADSEN. --Continued

105

¥HTS PROGRAM IS(,F6,29lf SEC FOR THIS CONDITION?)
LSL20,799_
T=(1SL*10e410)

C INTERPOLATE INPUT TaBLE FOR THIS LSL VALUE

)

LIS SL¥20 e410

00 3 JEiol!

FSSCJ)SFST( ToS) oC PSTC It fod oF STC oJ) *CLSLECT=91)%0,1)/003
RUS(JISRUT(To J) e(RUTCT#l oJ ORUT(C Tos) F(LSLO(lel)*0,1)/00!
RSCOIVERTCIToJIGERI(Ilelod wRICILoJyy#(LSlelIloi)*0,05)/0.05

C GUESS PHI AND YITERATE

P}

17
16

PH1=5,0

Ms0

JzPuHI

FACS(ALOGCPHI 64, )PALUG(J41,)) /(ALOG(JF2, PALOG(J+I,))
FSSFSS(Je1)¢ FACe(FSS(J+2 oF Sg(Jt1))
RUSRUS( Jer ye FAC#®(RUS(J+2ymRUS(J%1))

RTLERS(J+1 eC RECI+2@RS(CJO1)) FF AC
ARG=0 29% (D/HN) €#0, 28 (RUF2,BA/(HO*TANB) )¥#0, 34FS
PRINEO ,S*ATAN( ARG) #57,29578

bbe 1

DELSARS(PH]NePRHT)

IF(M,6T,2e0) GO TO 9

PHIePHIN

IFCPRT LT .0001) PHI=0.01

IF (PHT ,.G17,.9.99) PHIE9,99
IF(nEL.6G7,0,05) GO 10 6

kKIITSRII*CF

RETURN

END

SUBROUTINE READY )
COYMUNSMANSZESTEVELL) CRUTCIONS) ORTCH7OL1) OTXC 9910) RXC9010)
FORMAT( 3X04 7F4,2)

DU 4 Mstott

REAN(S50477) CFST(NeM) oNe109)

DO 2 MBi9f4

REAN(Se1 77) CRUTCNoM) oNE109)

NO 3 Metold

REAN(So177) (RICNOM) oNBI017)

bO uy Mzio10

REAN(So177) (TKENOM) oNE199)

DO 5 M=4$ol0

REAN( 59177) (RXCNOM) ONZ109)

RETURN

END

SUBRUIITINE EURWE(DH »OHTe LE, HOoHS» TANBoNRe DR, TOPW)
COMMONSMANSI/NMoNLOOCILIONCL S00 LOG oliyoTH(14)
DIMFNSTON BETACYY) eOHC11)
REAL NoLeolEoNR
NRSA,U35
BETAKS2,7*%(1 ,0eNR)/(NR**34DR)
OO 91 Te40NM
BETACT)S2,7¥* (1 ,oNCIV)ACN(T) &#34D(T) 9
THisu,
TH2s0,
DO a JBtieML
THISTHL¢ TROD)
Ny¥LeJd
DH( J) STHOCJ) JHO
TEC THY «GT ehO) DOHC J) 8(HOeTH2) /HO
IF (7Ht,GT.HO) GN TO S
THe=TH2OTH( J)
SUM2=0,
DO 46 JELeNYL
SUM {=0,
OO 47 Tst9NM
SUMVESUMI*¢BETA(Y)/BETARFL( I 90)
SUAPESUM24¢DH( J) /(SQRTCSUM1))
LES qo/(SUM2¥*2) xDHE /DHT

186

es

10

20

25

39

35

40

4s

10

20

Table G-7. Listing of the computer program MADSEN. --Continued

RETURN

END

SUBRUUTINEG INTER(No Tol pHUoApNUSD eo TI RI oWLeiFLAG)
COMMUNSSERL/NKL FS
COPMUNSMADSSESTC901L1) oRUTC 9911) oRT(C 17011) 07K (9010) 9 RX(9040)
DIMENSION TS(10)0RS(10)

REA) MNKL gl »NUskM ol AMHDAGN

SS=¢N/0,45)#¥*2

KIS 2e*3o141S9I/WL

Nk&LeNeK MeL

BETAEO,7T#E({oPN) S(N#HS*ED)

LAMRVASI,

Feu

Icsyl+j
UZARSURT(9OSBOSHN)/( LoL AMBDA)
Rhsiyy*O/NU
FEW (KOFL) #CSORT(S oC 1,¢RC/RU) 1. $6, *BETASASL/ (3,83, 141598H0)) ole)
LAMRLASKO*L#F/(2,¥*N)
IFC 1C,GT.e10) GO 10 5
TFC (ARSC EN@F) SFY eGT.0002) GO TO 2
5 TIE40/01,*L AMADA)
RTS | AMBMA/( 1 ¢¢LAMBDA)
FS=F/SS
C “RITE (69397) FeFSeUekD
397 FORMAT (PUX, (FoF SoUoRVS (04E13.5)
IFCNAL,GT,0,9) YFLAGSI
TECNKL,GT.0.9) RETURN
IF (AKL LT O03) RETURN
IF(FS,G67T,35,) FS255,
JENKL e104
T=zFs
C INTERPU) ATE MADSEN EURVES 2 AND 3
UC ¢ MSte10
RSOMISRK(TeM)S(RXC TOL OMIPRX (Jom) I#(NKL EN LFS) £00)
{ TS(M)STX (SoM) o(TR(JedoMyolX(U,%))a(NKLeA el FJ) /00!
IF CES LE 01,0) TYETS(LIFALOGIOCFS)#(TS({HIeTS(1))
LFCFS Lb ole9) RIFRSCII¢ALOGIOCES) #(RSCIN)@RS(1))
IF(FS.GFoi0.) TYSTS(10)¥*(35,eFS)/25,
IF CES .GE oI.) RTERS(19)4(1 .e@RS(10))#(FSel00)/256
LFCFS,LE G1 ,9,OR,FS,GE,10,0) RETURN
KITEQS(T) (RSC Tod) eRS( IT) SCALOGCFS)eaLOG(l*) JI /CALOG(I+1,) eALOG(T*
F1.))
TIETS(T)OCTSCLo4)PTSCT)#CALOG(FS)cALOGCIEL, I SCALOG(341,) eALOGCIS
1.)
mE TR
ENO
SUBRUUTINE LENGTC DLOODL)
KE AL LDol.DNEW ,LOD
L934 .9/0L0
L9D21,0/0L0
N={
PI=3,14159
{ ARG=c,0¥*PJ/LD
LONE wSLOD#TANH( ARG)
NSNel
CIFFSA8S(LODNEWeLD)
IF(N*@209) 30404

3 IF(RIFFC0,0005) 20205
5 LOS(LONE WOLD) 42,0
GQ yU 4
4 OL=4e6%/LDNEW
WRIFE (60100) DLAePL
109 FORMAT(44H SURROUTINE LENGTH DID NOY CONVERGE, A/LO 8 oF10.5¢
1 6HO/L = oF 1405)
2 DL&4,.0/LONEW
KE TURN
END

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