• TABLE OF CONTENTS
HIDE
 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 List of symbols
 Introduction
 Experimental approach
 Analyses and results
 Design and program
 Summary and recommendations
 References
 Appendix A. Design aid program
 Appendix B. Experimental data
 Appendix C. Report abstracts






Group Title: UFL/COEL (University of Florida. Coastal and Oceanographic Engineering Laboratory) ; 88/004
Title: Performance and stability of low-crested breakwaters
CITATION PDF VIEWER PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00076142/00001
 Material Information
Title: Performance and stability of low-crested breakwaters
Series Title: UFLCOEL
Physical Description: vii, 76 p., ca.150 leaves : ; 28 cm.
Language: English
Creator: Sheppard, D. M
Hearn, J. K
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal and Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1989
 Subjects
Subject: Breakwaters   ( lcsh )
Coastal and Oceanographic Engineering thesis M.S
Coastal and Oceanographic Engineering -- Dissertations, Academic -- UF
Genre: non-fiction   ( marcgt )
 Notes
Bibliography: Includes bibliographical references.
Statement of Responsibility: by D.M. Sheppard, J.K. Hearn.
General Note: "February 1989."
General Note: Cover title.
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
 Record Information
Bibliographic ID: UF00076142
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: oclc - 20349070

Downloads

This item has the following downloads:

UF00076142 ( PDF )


Table of Contents
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement
    Table of Contents
        Table of Contents 1
        Table of Contents 2
    List of Tables
        List of Tables
    List of Figures
        List of Figures 1
        List of Figures 2
    List of symbols
        Unnumbered ( 8 )
        Unnumbered ( 9 )
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
    Experimental approach
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
    Analyses and results
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
    Design and program
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
    Summary and recommendations
        Page 72
        Page 73
        Page 74
    References
        Page 75
        Page 76
    Appendix A. Design aid program
        A 1
        A 2
        A 3
        A 4
        A 5
        A 6
        A 7
        A 8
        A 9
        A 10
        A 11
        A 12
        A 13
        A 14
        A 15
        A 16
        A 17
        A 18
        A 19
        A 20
        A 21
        A 22
        A 23
        A 24
        A 25
        A 26
        A 27
    Appendix B. Experimental data
        B 1
        B 2
        B 3
        B 4
        B 5
        B 6
        B 7
    Appendix C. Report abstracts
        C 1
        C 2
        C 3
        C 4
        C 5
        C 6
        C 7
        C 8
        C 9
        C 10
        C 11
        C 12
        C 13
        C 14
        C 15
        C 16
        C 17
        C 18
        C 19
        C 20
        C 21
        C 22
        C 23
        C 24
        C 25
        C 26
        C 27
        C 28
        C 29
        C 30
        C 31
        C 32
        C 33
        C 34
        C 35
        C 36
        C 37
        C 38
        C 39
        C 40
        C 41
        C 42
        C 43
        C 44
        C 45
        C 46
        C 47
        C 48
        C 49
        C 50
        C 51
        C 52
        C 53
        C 54
        C 55
        C 56
        C 57
        C 58
        C 59
        C 60
        C 61
        C 62
        C 63
        C 64
        C 65
        C 66
        C 67
        C 68
        C 69
        C 70
        C 71
        C 72
        C 73
        C 74
        C 75
        C 76
        C 77
        C 78
        C 79
        C 80
        C 81
        C 82
        C 83
        C 84
        C 85
Full Text


UFL/COEL 88/004


PERFORMANCE AND STABILITY OF LOW-
CRESTED BREAKWATERS







BY

D.M. SHEPPARD


J.K. HEARN


FEBRUARY 1989











ACKNOWLEDGEMENTS



A portion of this work was supported by Mr. John P. Ahrens of the U.S.

Army Corps of Engineers Coastal Engineering Research Center, Wave Dynamics

Division, Wave Research Branch in Vicksburg, Mississippi.








TABLE OF CONTENTS


Page

LIST OF TABLES iii

LIST OF FIGURES iv

LIST OF SYMBOLS vi

CHAPTER 1 -- INTRODUCTION 1

1.1 BACKGROUND 1

1.2 BRIEF SUMMARY OF PREVIOUS WORK 2

1.3 PURPOSE AND ORGANIZATION OF THIS REPORT 3

CHAPTER 2 -- EXPERIMENTAL APPROACH 5

2.1 DESCRIPTION OF EXPERIMENTS 5

2.2 BRIEF SUMMARY OF AHRENS' ANALYSES AND RESULTS 11

CHAPTER 3 -- ANALYSES AND RESULTS 23

3.1 STRUCTURAL STABILITY 24

3.1.1 Volumetric Changes 27
3.1.2 Crest Height Changes 29

3.2 WAVE FIELD MODIFICAITON DUE TO THE BREAKWATER 30

3.2.1 Comparison of Transmission Gages 32
3.2.1(a) Wave height 32
3.2.1(b) Goda's spectral peakedness parameter 34

3.2.2 Energy Transmission 35
3.2.2(a) Variation of Kt within a test 35
3.2.2(b) Prediction of Kt 37
3.2.2(c) Comparison of data with predictive approaches
of other researchers 45

3.2.3 Energy Reflection 48

3.2.4 Changes in Wave Period and Spectral Peakedness 52
3.2.4(a) Change in T 52
3.2.4(b) Change in Ts and T 52
3.2.4(c) Change in Qp 57

CHAPTER 4 -- DESIGN AID PROGRAM 60










CHAPTER 5 -- SUMMARY AND RECOMMENDATIONS 72

REFERENCES 75

APPENDICES

A DESIGN AID PROGRAM

B EXPERIMENTAL DATA

C REPORT ABSTRACTS










LIST OF TABLES


Table Page

2.1 Summary of incident wave conditions for low-crested
breakwater test. 8

2.2 Summary of structural and incident wave conditions for
type 1 (stability) tests 9

2.3 Summary of structural and incident wave conditions for
type 2 (previously damaged) tests 10

3.1 Summary of slopes and y-intercepts for design curves in
Figure 3.3(b) 31












LIST OF FIGURES

Figure Page

2.1 Details of Experimental Setup (after Ahrens 1984). 7

2.2 Damage parameters as a function of the Hudson stability
number and the spectral stability number for subset 1. 12

2.3 Damage parameters as a function of the Hudson stability
number and the spectral stability number for subset 3. 13

2.4 Damage parameters as a function of the Hudson stability
number and the spectral stability number for subset 5. 14

2.5 Damage parameters as a function of the Hudson stability
number and the spectral stability number for subset 7. 15

2.6 Damage parameters as a function of the Hudson stability
number and the spectral stability number for subset 9. 16

2.7 Comparison of the measured and calibrated incident wave
heights. 19

2.8 General trend for transmission coefficient vs. relative
freeboard (after Ahrens 1984). 21

2.9 General relationship between energy reflection, trans-
mission and dissipation as a function of relative free-
board (after Ahrens 1984). 22

3.1 Relationship between initial structure height and total
cross-sectional area. 26

3.2 Dimensionless damage as a function of the modified spectral
stability number. 28

3.3 Relationship between final relative height and spectral
stability number -- (a) data from type 1 tests; (b) design
curves based on subsets 1, 3, and 5. 30

3.4 Comparison of transmitted wave heights measured at gages 4
and 5. 33

3.5 Comparison of spectral peakedness parameters (Q ) measured
at gages 4 and 5. 36

3.6 Change in transmission coefficient from the beginning to
the end of damage tests. 38

3.7 Transmission coefficient as a function of relative freeboard. 39










Figure Page

3.8 Transmission coefficient as a function of P for relative
freeboards greater than 1.0 41

3.9 Transmission coefficient as a function of relative free-
board, R, for R < 1.0. Data are separated by both peak
incident wave period (a) and subset (b). 42

3.10 Design curves for the prediction of transmission coefficient
as a function of relative freeboard and P. 44

3.11 Definition sketch of idealized dmaaged structure. 46

3.12 Comparison of measured transmission coefficients with those
predicted by the approaches of Seeling (a, b) and Madsen and
White (c, d). Seelig (1980) accounts for transmission by
overtopping only. Madsen and White (1975) consider both
overtopping and transmission through the structure. 50

3.13 Transmission coefficients predicted by the approaches of
Seelig (a, b) and Madsen and White (c, d) as a function of
relative freeboard. Seelig (1980) accounts for transmission
by overtopping only. Madsen and White (1975) consider both
overtopping and transmission through the structure. 49

3.14 Design curves for the prediction of reflection coefficient
as a function of relative freeboard and relative depth. 51


3.15 Ratio of incident to transmitted peak period as a function
of relative freeboard. 53

3.16 Ratio of transmitted to incident significant wave period
as a function of relative freeboard. 54

3.17 Ratio of transmitted to incident significant wave period as
a function of relative freeboard. The limits used in the
design program (Chapter 4) to determine the upper and lower
bounds on the ratio are shown. 55

3.18 Ratio of transmitted to incident average wave period as a
function of relative freeboard. 56

3.19 Ratio of transmitted to incident spectral peakedness parameter
as a function of relative freeboard for each of the four wave
files. 58

3.20 Ratio of transmitted to incident spectral peakedness parameter
as a function of relative freeboard. The limits used in design
program (Chapter 4) to determine the upper and lower bounds on
the ratio as shown. 59












LIST OF SYMBOLS



a 0.5926 (Equations 3-10, 11, 4-9, 12, 18, 21, 22, 23, 25)

aj wave amplitude of frequency band in Equation 3.4

Ad area of original breakwater that displaced during test

At total cross-sectional area of structure

B breakwater crest width

d water depth
Ad
D.D. dimensionless damage = 2
(D50)
w
D50 median stone diameter = w-)
r
f wave frequency in Equation 3.4

F freeboard, h d, in Seelig's formula for Kt (Equation 3-12)

h structure crest height in Seelig's formula for Kt (Equation 3-12)

hf maximum damaged crest height

hf average final crest height

hi initial structure crest height

hf/d final relative crest height

Hc incident zero-moment wave height used in the calculation of Kt

Hs incident zero-moment wave height

Ht transmitted significant wave height calculated as average of two
transmission gages H3

K Hudson's dimensionless stability coefficient =
D (- 1) cot a
Kd energy dissipation coefficient D50 w

Kr energy reflection coefficient

Kt energy transmission coefficient










Lp wave length corresponding to T
h 1.5
i\l*J
M modified spectral stability number = N (s


H
N Hudson's stability number =

w


(H2 L )1/3
N spectral stability number = --
s w

A H
P 2w--
D p
50


Q Goda's spectral peakedness parameter defined by Equations 3-3
and 3-4
h -d
R relative freeboard =
H
S(f) value of energy density spectrum (Equation 3-3)

T average wave period of spectrum

T peak wave period of spectrum

Ts significant wave period of spectrum

w50 median stone mass

wr mass density of stone

ww mass density of water

Af frequency band width (Equation 3-4)

Ah change in crest height = hi hf

a slope of structure face










CHAPTER 1 INTRODUCTION


1.1 BACKGROUND

Traditional ideas about shore protection works embrace the philosophy

that damage to a structure is to be avoided for all but catastrophic

conditions. In the case of offshore breakwaters, this usually means

specifying the crest elevation such that little to no overtopping occurs,

since the volume of water overtopping the crest has been found to be an

important parameter in determining rear slope stability (Graveson et al.,

1980). This approach often results in cost-prohibitive shore protection,

because structure cost is integrally related to the volume of material

required for construction and maintenance. Thus, any reduction in crest

height results in a cost savings and an increase in project feasibility.

Recent field observations and subsequent laboratory studies indicate

that adequate shore protection can be achieved in some instances through

the use of low-crested and/or "sacrificial" breakwaters. In 1976, com-

bined wave and surge action due to Cyclone David caused severe damage to a

breakwater at Rosslyn Bay in Australia. Despite the fact that its crest

was battered to below mean water level, the breakwater continued to func-

tion effectively for two and a half years until the structure was repaired

(Bremner et al. 1980). The unexpected success of this failed breakwater

prompted the concept of a "sacrificial" offshore structure which is used

to protect an inner breakwater or revetment and is designed to fail under

extreme wave conditions. Model tests on such a structure proposed for

Townsville Harbor, Australia were conducted, and it was shown that this

approach would save 40 percent over a conventional design (Bremner et al.

1980). Interestingly, these tests also suggested that the wave

transmission may not be very dependent upon the amount of structural










damage, because the increased energy transmission resulting from a lower

crest is balanced by the increased energy dissipation resulting from a

wider crest. Thus, the design parameters associated with these structures

are the prediction of damage levels and the subsequent performance of the

"failed" breakwater. Additional research is required in order to better

understand the influence of structural and wave parameters on these

criteria.


1.2 BRIEF SUMMARY OF PREVIOUS WORK

Ahrens (1984) investigated the stability and to some extent the per-

formance of low-crested breakwaters, with regard to certain structure

parameter and incident wave conditions. His data and findings are the

basis for this report and are discussed in greater detail in Chapter 2. A

brief summary of recent studies on the low-crested design concept consti-

tutes the remainder of this section. A more comprehensive list and

annotated bibliography of research on submerged and low-crested structures

and related topics is included in Appendix A.

Foster and Haradasa (1977) conducted model tests on the original

Rosslyn Bay breakwater and on a proposed modification. Irregular incident

wave conditions were simulated using monochromatic waves with the same

height and period as the significant wave height and peak period of the

prototype spectrum. The tests closely reproduced the mode of damage seen

in the prototype structure, except that the initiation of damage occurred

earlier and the rate of damage after initiation was slower in the model

than in the prototype.

Foster and Khan (1984) studied overtopped structures in an attempt to

determine the variables most influencing their stability. They conclude

that the relationships between the parameters governing stability of an










overtopped structure are more complex than for a non-overtopped structure.

They recommended that rigorous physical model testing with the full range

of expected wave conditions and water depths be conducted prior to proto-

type construction.

Seelig (1979) studied wave transmission by overtopping of regular and

irregular waves for subaerial and submerged smooth, impermeable, trape-

zoidal structures. Seelig found that the dimensionless parameter, free-

board divided by the incident significant wave height, is an important

factor governing energy transmission by overtopping. In a later investi-

gation, tests were extended to include rubble mound and dolos armored

structures (Seelig 1980). An empirical method for determining wave trans-

mission by overtopping that includes the effects of structure width and

wave runup, in addition to freeboard and wave height, was developed.

Allsop (1983) studied transmission, overtopping, and damage to low-

crested, multi-layered trapezoidal structures. He found that wave trans-

mission, which was largely due to overtopping, is a function of wave

steepness. Although he did not find a similar period dependence in the

damage data, he notes that since stability is closely related to overtop-

ping, it is possible that stability of overtopped structures is a function

of the wave period.


1.3 PURPOSE AND ORGANIZATION OF THIS REPORT

The purposes of this investigation were to provide additional

insights into the stability and wave transmission data from studies of

homogeneous, low-crested breakwaters conducted at the Coastal Engineering

Research Center (Ahrens 1984), and to develop an interactive computer

program to assist in the design of these structures. In addition, an

extensive literature search was conducted. Pertinent papers and reports










are summarized in a series of abstracts which are presented in Appendix C

of this report.

Chapter 2 of this report outlines the experimental approach and

analytical techniques used by Ahrens (1984). Chapter 3 describes the

analyses used here and presents the results which are the basis for the

design program summarized in Chapter 4. Summary, conclusions and recom-

mendations for future work are given in Chapter 5. Contained in the three

appendices are: the design aid program, the experimental data analyzed in

this report and the abstracts of related reports and technical papers.










CHAPTER 2 EXPERIMENTAL APPROACH


2.1 DESCRIPTION OF EXPERIMENTS

Laboratory experiments on the performance of low-crested breakwaters

were conducted (by Ahrens) in the wave flume at the U.S. Army Corps of

Engineers Waterways Experiment Station in Vicksburg, Mississippi (Ahrens

1984). Structures were tested in a 61-cm wide channel within a 1.2 m by

4.6 m by 42.7 m tank. Signals for the generation of irregular waves were

stored on magnetic tape and transferred to the wave paddle using a data

acquisition computer system (DAS). Four files with periods of peak energy

density ranging from 1.45 to 3.60 sec were used. A total of five wire-

resistance wave gages recorded wave conditions in front of and behind the

structure. Records from three unequally spaced gages in front of the

structure were used to resolve the incident and reflected wave fields

using the method of Goda and Suzuki (1976). Two gages behind the struc-

ture recorded the transmitted wave conditions. The DAS sampled the gages

sixteen times per second for 256 seconds.

A ten-turn potentiometer in a voltage divider network was used to

regulate the signal amplitude to the wave blade. The signal amplitude is

related to the wave heights that are generated. An undamped signal pro-

duced the depth-limited energy spectrum as described by Vincent (1981,

1982). The theoretical basis for this spectrum is taken from the work of

Phillips (1958) who proposed an expression for the upper bound on energy

density for deep water waves based on wave steepness. Phillips' limit is

proportional to f-5 where f is wave frequency. Using Phillips' expression

as a starting point, Kitaigordoskii et al. (1975) derived an equation for

the depth-controlled maximum energy density. The depth-dependent limit on

energy density is proportional for f-. Other characteristics of these
energy density is proportional for f .Other characteristics of these










spectra are a sharp drop in energy density at frequencies below the peak,

and, in the shallow water limit, wave heights that are proportional to the

square root of depth.

To ensure the most severe wave conditions possible at the structure,

waves were shoaled on a 1:15 slope from a water depth 25 cm greater than

the depth at the breakwater. Incident significant wave heights ranged from

one to eighteen centimeters. Details of the test setup are shown in

Figure 2.1. Incident wave conditions are summarized in Table 2.1.

Two types of tests were performed. The purpose of the first type was

to determine expected levels of damage under different wave conditions,

both mild and severe. The second type sought to evaluate the performance

of the damaged breakwaters under more typical, less severe wave attack.

Wave action for Type 1 tests lasted between 1.5 hr for File 1 spectra to

3.5 hr for File 4 spectra. Wave data were collected several times during

each run. Tests on the previously damaged structures lasted about

30 minutes and data were collected two to three times.

Structures were built with homogeneous stone. Two different stone

sizes were tested. Specific gravity and median mass were 2.63 and

17 grams, respectively, for the smaller stone, and 2.83 and 71 grams for

the larger stone. The undamaged structures were trapezoidal with front and

rear slopes of 1 on 1.5. The initial profile for a Type 2 test was the

same as the final profile of the proceeding test. Starting crest heights

ranged from 24.11 to 36.09 cm in a water depth of 25 cm and from 31.55 to

32.06 cm in a depth of 30 cm. Using test type, initial structure height,

stone size, and water depth as criteria, the 205 experiments were divided

into ten subsets. A summary of pertinent parameters for each subset is

given in Tables 2.2 and 2.3.















SCALE
0 1 2 3 4 5 Iml

o DENOTES WAVE GAGE LOCATION
WALL OF WAVE TANK


TO WAVE
GENERATOR
19 m

TRAINING
WALLS


GRAVEL WAVE ABSORBER GRAVEL WAVE ABSORBER BEACH
1 ON IS BEACH PONOING RELIEF CHANNEL WAVE
61 cm SCALING SLOPE oo o o o ABSORBER
REEF- ONOING LIEF CHANNEL MATERIAL
BREAKWATER ---
GRAVEL WAVE ABSORBER BEACH GRAVEL WAVE
AUXILIARY CHANNEL ABSORBER BEACH
6 GRAVEL WAVE ABSORBER BEACH


WALL OF WAVE TANK
PLAN VIEW


Figure 2.1 Details of Experimental Setup (after Ahrens 1984).


WAAA


r\rru











Table 2.1. Summary of incident wave conditions for low-crested breakwater test.


Water Approx Range of Incident
File No. Depth (cm) Peak Period Wave Height (cm)
(Sec)


1 25 1.45 1.09 11.47
30 1.45 5.76 12.63

2 25 2.25 1.16 13.43
30 2.25 2.58 14.46

3 25 2.86 1.62 15.78
30 2.86 8.20 18.17

4 25 3.60 2.25 16.10
30 3.60 5.22 17.60











Table 2.2. Summary of structural and incident wave conditions for type 1 (Stability) Tests


Range of Range of
Subset No. of Median Stone Water Cross-Sect onal File Incident Initial Crest
No. Tests Diameter (cm) Depth (cm) Area (cm ) No. Wave Height (cm) Height (cm)


1 27 1.86 25 1170 1 2.87 11.45 24.11 25.39
2 2.91 13.43 24.41 25.48
3 3.89 15.78 24.44 25.73
4 5.46 16.10 24.14 25.12
----------------------------------------------------------------------------------------

3 29 1.86 25 1560 1 2.82 11.36 29.02 30.48
2 2.89 13.38 29.29 29.81
3 3.68 15.63 28.74 29.84
4 2.59 15.84 28.86 30.08
----------------------------------------------------------------------------------------

5 41 1.86 25 2190 1 2.75 11.35 34.38 35.57
2 4.03 13.02 34.41 36.06
3 1.81 15.61 34.93 36.09
4 2.56 15.99 34.59 36.03
-------------------------------------------------------------------------------------------------

7 38 2.93 25 1900 1 2.60 11.44 31.36 32.00
2 2.72 13.11 31.49 32.34
3 1.65 15.66 31.24 32.52
4 2.35 16.04 31.39 32.80
-------- --- -------------------------------------------------------------------------------------

9 13 2.93 30 1900 1 5.76 12.63 31.55 31.82
2 5.80 14.46 31.58 31.67
3 8.20 18.17 31.61 32.06
4 5.22 17.60 31.61 32.13
----------------- --------------------------------------------------------------------------------



















Table 2.3. Summary of Structural and Incident Wave Conditions for Type 2 (Previously Damaged) Tests


Range of Range of
Subset No. of Median Stone Water Cross-Sectional File Incident Initial Crest
No. Tests Diameter (cm) Depth (cm) Area (cm ) No. Wave Height (cm) Height (cm)


2 3 1.86 25 1170 1 N/A N/A
2 5.87 5.95 15.88 19.99

4 12 1.86 25 1560 1 3.17 11.19 17.56 18.01
2 2.72 13.27 17.80 19.45

6 11 1.86 25 2190 1 2.84 11.47 19.54 19.81
2 2.49 12.88 19.78 19.96

8 26 2.92 25 1900 1 1.09 11.03 28.19 28.35
2 1.16 13.31 28.16 28.29
3 1.62 13.32 27.58 28.01
4 2.25 12.26 27.55 28.01

10 5 2.92 30 1900 1 N/A N/A
2 2.58 14.41 24.96 25.21










2.2 BRIEF SUMMARY OF AHRENS' ANALYSES AND RESULTS

Structural stability is defined by Ahrens (1984) in terms of both the

volumetric damage and the change in crest height. Volumetric damage is

described by a dimensionless damage parameter,


Ad A
D. D. = = d (2-1)
w50 2/3 ( 2
50) (Ds50
r
where

Ad = cross-sectional area of the portion of the original break-

water that was displaced;

w50 = median mass of the stone;

wr = mass density of the stone; and

D50 = the median stone effective diameter.

The change in crest height is represented by the final relative crest

height or ratio of final crest height to the water depth. Final crest

height is measured at the highest point on the structure.

Hudson's stability number defined as,


H
N s (2.2)
D 50( 1)
w

where

Hs = incident significant wave height; and

w, = mass density of water,

was initially used by Ahrens as a means of predicting the stability of the

structure. Plots of final relative crest height and dimensionless damage

as a function of Ns are presented in Figures 2.2 2.6(a,b) for the Type 1

tests. The expected trends are obvious; larger values of stability number

































00 L
o o0 o-
Jo o a h"
: oee Ronge of .
a eg d
0

0 00
0
1 0




.o00 2'00 u.00 6'.00 8'.00
HUDSON STABILITY NUMBER
(a)



0









Shz
Range of -



o -

J 0 0

'0 0
0
0


b.oo .0oo 8.00 12.00 16.00
SPECTRAL STABILITY NUMBER
(C)


0.


).ootb.oo





o
0
0
0..


-I 1
20.00 o. oo


2'.00 .00 6.00 '.00
HUDSON STRBILITT NUMBER
(b)


4.00 8.00 12.00
SPECTRAL STABILITY
(d)


16.00 20.00
NUMBER


Figure 2.2 Damage parameters as a function of the Hudson stability
number and the spectral stability number for subset 1.


I00 ;
oo
---
CI.O
01a


00 0

08
0a


r


__ ? *' l- u .1 .1 .. ,1.-



















































W.oo 2'.o .00 o '.O 8.00 10
HUDSON STRBILITT NUMBER
(a)



D





m h
S- -Ronge of


++ +

S+ 44- -
44-

4.-








V I _____________________4 .


.0oo0


0'.oo 8.00 1.oo 16.00
SPECTRRL STRBILITT NUMBER
(c)


0M


.oo0 .oo0


2b.00oob.o


2'.00oo .oo soo 0 800
HUDSON STRBILITT NUMBER
(b)


40oo 8.00 1t.00 16.00
SPECTRAL STRBILITT NUMBER
(d)


1b.00


0.0oo


Figure 2.3 Damage parameters as a function of the Hudson stability

number and the spectral stability number for subset 3.








13


-h,
Range of -'




*



-+ +
+




+4









4*.
+

+
tt


"r
cv:



Uv4-
tnU
LU
+
0 + +

z +
Lii+


'+

0-


+


I


c


2
























6* h7T
S** Ronge of
". o







cr
-o *




0-J
z
a:







.00 2000 4. 6'.00 8'.00 10
b.oo 2'.oo 0 'oo s.oo soo
HUDSON STABILITY NUMBER
(a)



0
V)


2


.oo 8'.00 1 0.o sb.oo0
SPECTRAL STABILITY NUMBER
(c)


0.


.0 .00


2.00 o .00 6.00 s8.00 1
HUDSON STABILITY NUMBER
(b)


.00 8'.oo 12.oo00 Ib. 2
SPECTRAL STABILITY NUMBER
(d)


Figure 2.4 Damage parameters as a function of the Hudson stability
number and the spectral stability number for subset 5.


6
e

*
6
*6
6
*


*
* 6

6
* 6
6


6 -
* hi

Ronge of-
a.. d



*
$3)




0 0
a: *

0


.o
ar !
c)-

CJ
-0

ZC9


i3


'


.oo00


01l


















o__


*1


x "
xx
x.


Ronge of -
d


booo 2'.00oo lao soo e'o io
b.OO 2.00 '1.00 6.00 8.00 1i
HUDSON STABILITY NUMBER
(a)















Range of-


xx


.oo 0 oo 8.00 .0o0 .oo0
SPECTRAL STABILITY NUMBER
(c)


0
0


1.00


b.00 2.00 '.00 6'.00 8.00 It
HUDSON STABILITY NUMBER
(b)



0
0
0 ______ ^ _ - 11 1. .


4.00 8.00 12.00 16.00
SPECTRAL STRBILITT NUMBER
(d)


20o. o.coo


Figure 2.5 Damage parameters as a function of the Hudson stability

number and the spectral stability number for subset 7.


tM

0
0

o


(0.

U,

_J
Zo
00


0.
en"


0


x


o _', x


).00





































0.00


%C.oo


2


,


09 7--


2


I


r












































b.OO 2.00 4'.00 6.00 8.00 I
HUDSON STABILITY NUMBER
(o)


a


0,


b.0oo oo


Y


2.00 4.00 s.00 8.00
HUDSON STABILITY NUMBER


k'.oo .o00 1I.00 b.oo0
SPECTRAL STABILITY NUMBER
(c)


.00oo'.oo


4.:00 8.00 1.00
SPECTRAL STABILITY
(d)


t1.00 20.00
NUMBER


Figure 2.6


Damage parameters as a function of the Hudson stability
number and the spectral stability number for subset 9.


Y y hJ
Y Ronge of -
d
Y


-- '----- ---- ----

y Range of
d
y


b.oo


y
I Y
Iy
00 = YYy


O


D ....


0 I


o










lead to greater damage and lower crest heights. The data, however,

exhibited considerable scatter. Scrutiny of the data with respect to peak

incident wave period suggested that some of the scatter might be elimi-

nated by the inclusion of a term to account for wave period effects.

Graveson et al. (1980) present results of several different rubble mound

stability studies conducted at the Danish Hydraulic Institute (DHI). They

note that the dimensionless stability coefficient defined by


H3
K = s (2-3)
3 w
D50 (-h 1) cot a
where w
w
a = slope angle,

is proportional to wave steepness, H/Lp where L is the wave length

corresponding to the peak period. Thus, Hudson's stability number was

modified to the following:

2 1/3
(H L )
N = sp (2-4)
s w
50 ( 1)
w
w


Using this parameter, Ahrens found that substantial reduction in scatter

could be achieved (Figures 2.2 to 2.6(c,d)). A general trend seen in all

the subsets is that the onset of damage occurs at about Ns* = 6. Expected

damage increases slowly as Ns* approaches 8, and increases rapidly for

Ns* > 8.

The manner in which wave energy is distributed can be described by

the equation


2 2 2
K + K + K = 1 (2-5)
t r d










where


Kt = transmission coefficient;

Kr = reflection coefficient; and

Kd = energy dissipation coefficient.

For these tests, Kr is given as the reflection coefficient measured during

the last period of wave sampling in a test; the Kt value is the average

transmission of all the sampling periods. Traditionally, Kt is defined by

the ratio of the measured transmitted wave height to the measured incident

significant wave height. This approach can lead to artificially low

values of Kt, however, since some energy is lost due to internal and

bottom friction between the wave gauges on the forward side of the break-

water and the wave gages measuring transmission. In order to ascertain

the amount of energy transmission due to the breakwater only, the trans-

mission coefficient was defined as


H
K (2-6)
t H=
c


where

Ht = the average value of significant wave height as measured at

the back gages, and

Hc = the average incident significant wave height at the loca-

tions of the transmitted gages without the structure in

place.

This definition gives a more conservative estimate of Kt than the

traditional approach. Figure 2.7 illustrates the difference between the

incident and calibrated wave heights.










































D.00 4 .00 8 .00 12.00 16.00 20.00
MEASURED INCIDENT WAVE HEIGHT





Figure 2.7 Comparison of the measured and calibrated incident wave
heights.










In agreement with other researchers (Seelig 1979), Ahrens notes that

the relative freeboard defined by


h d
R = (2-7)
s


where

hf = final crest height, and

d = water depth at structure site,

is the primary variable in the determination of Kt for overtopped and sub-

merged structures, i.e., situations in which the dominant mode of trans-

mission is overtopping. As R gets large, however, the dominant mode

shifts from overtopping to transmission through the structure. Ahrens

(1984) suggests that this transmission occurs at about R = 1.5. As the

mode of transmission changes, so do the variables affecting Kt. Wave

steepness, for example, becomes more important as R increases. Figure 2.8

shows the general trend exhibited by the data from these tests. The

dashed line indicates the region in which transmission through the

structure dominates. One should not interpret the dashed line to mean

that wave transmission increases as the freeboard increases--this is

clearly contrary to intuition--but rather that for a constant freeboard,

smaller wave heights give larger transmission coefficients.

Finally, Ahrens (1984) presents a schematic graph of the general

relationship between energy reflection, transmission and dissipation as a

function R (Figure 2.9). One notes that the energy of long waves is not

as easily dissipated as the energy in short waves. The difference is

particularly obvious for wave reflection for larger values of R.

























I
p-- TRANSITION BETWEEN
I TRANSMISSION MODES


a--

a-


I I i 1 I I


-2.0 -1.0 0 1.0
hf-d
RELATIVE FREEBOARD,
Hs


3.0


Figure 2.8


General trend for transmission coefficient vs. relative
freeboard (after Ahrens 1984).


1.0,-


- 0.8


0.6 k


0L
-3


.0











100 u
~//////,/_ /. 1 SHORT
S / WAVES
90 -10
LONG
WA VES--REFLECTED
S. ENERGY 20
w I w
S70 30 >-

,6 40 zr
z i- 60 \ L
S60 ENERGY W
WH DISSIPATED O
> U) >
< 50 50 <

0- o-
W 40 V 60 W

w n TRANSMITTED ww\
a. 30 ENERGY 70 _-
< w
SHORT WAVES LONG
20 WA VES 80


10 90


0 iii100
-4 -3 -2 -1 0 1 2 3
hf d
RELATIVE FREEBOARD,
Hs


Figure 2.9 General relationship between energy reflection, transmission
and dissipation as a function of relative freeboard (after
Ahrens 1984).












CHAPTER 3 ANALYSES AND RESULTS


CERC provided the summarized damage and transmission data on 5 1/4

inch floppy disks in spreadsheet format for use with a personal computer.

In addition, some of the computer printouts from which the summaries were

compiled were supplied. Because it was faster, the spreadsheet files were

transferred to the Coastal and Oceanographic Engineering Department's VAX

750 computer.

The spreadsheet summary includes the following information for each

of the 205 tests.

Subset number (1-10);

Test type (stability or previously damaged);

File number and wave maker signal amplification;

Median stone mass, w50;

Stone mass density, wr;

Cross-sectional area of breakwater, At;

Water depth, d;

Average incident significant wave height, Hs;

Average incident peak period, Tp;

Average transmitted significant wave height, Ht;

Average reflection coefficient, Kr;

Calibrated significant wave height, Hc;

As built structure height, hi;

Damaged structure height, hf;

Area of damage, Ad;

Peak, significant, and average incident and transmitted wave

periods,










Tp, Ts, and T, respectively, for the final sampling period of a

test;

Goda's spectral peakedness parameter, Q for the final sampling

period of a test;

Fraction of displaced stone found seaward of the structure;

Unsubmerged area of the damaged breakwater.

Discussion of the data analyses and results is in two parts. Section

3.1 deals with the mechanisms governing overall structure stability.

Section 3.2 reviews the parameters influencing spectral changes and energy

redistribution due to the breakwater.


3.1 STRUCTURAL STABILITY

Structural stability of overtopped breakwaters is complexly related

to many factors, including stone shape, density, and median mass; incident

wave height and period; ratio of structure height to water depth; storm

hydrograph; and currents. As discussed by Foster and Khan (1984), the

relationship between governing variables and stability is much more

complex for overtopped than for non-overtopped breakwaters, and careful

modeling of proposed structures is still the best way to obtain infor-

mation about an individual structure's behavior. It is, however,

beneficial to be able to predict the general performance of the structure

in order to expedite testing.

Ahrens' data were examined exhaustively in an attempt to enhance

existing understanding of stability of low-crested structures and to

develop a viable preliminary design procedure. Prior to a discussion of

analyses and results, it is enlightening to examine what is meant by

"stability" of low-crested structures and how the expression of stability

is related to structure shape and size. As discussed in Chapter 1, the










design problem associated with stability of a low-crested structure is not

necessarily prevention of damage, but rather prediction of damage for a

given set of incident wave conditions. For maintenance purposes, the

volume of material displaced is needed. For prediction of energy trans-

mission, the reduction in crest height, and, to a lesser degree, final

structure width are important. It is obvious that structures of many

different shapes may have the same total volume of material (cross-

sectional area), but entirely different relationships between that volume

and structural dimensions. For example, a rectangle with a given area has

an infinite number of height to width ratios, and a rectangle and

isosceles triangle with the same area and base dimensions have quite dif-

ferent heights. Similarly the damage area associated with a given reduc-

tion in crest height is a function of the initial structure size and

shape. Thus, the application of results that utilize quantities such as

damage area, total area, and structure height are necessarily restricted

to structures of like shape. The structures used in this study were

trapezoidal with front and back slopes of 1:1.5. The relationship between

the total area and initial structure height was linear (Figure 3.1) and is

described by the equation,



At = m hi + b (3-1)

where

m = 98.7769 cm2/cm; and

b = -1285.44 cm2

Converting to prototype units,

m = S (0.987769) m2/m; and

b = S2(-0.128544) m2















2500




2000-

N


<1500-
E


-
LUJ
1000-


I--
500
500-


I Range of Data


INITIAL HEIGHT (cm)


Figure 3.1


Relationship between initial
cross-sectional area.


structure height and total










and


m = S (3.24067) ft2/ft; and

b = S2(1.38260) ft2

where

S = prototype to model length scale.

Based on Ahrens' observation that Ns* provides better definition of

stability than Ns, the relationship between damage and Ns was not con-

sidered in the analyses. Instead, an extension and hopefully improvement

of the Ahrens (1984) work were sought.


3.1.1 Volumetric Changes

Examination of Figures 2.2 2.6(d) reveals that the rate at which

dimensionless damage increases as Ns* increases is dependent upon the

ratio of initial structure height to water depth, hi/d. Ahrens calls this

the "exposure parameter" (personal communication, 1986). This observation

is a reflection of the fact that the more of the structure that is exposed

to direct wave attack the greater the volume of displaced material will be

for the same Ns*. Often the structure stabilizes once the crest becomes

submerged and the water acts as a protective cushion (Bremner, et al.,

1980). Since dimensionless damage is a function of both Ns* and h /d, a

new relationship is proposed in which dimensionless damage is related to

the product of Ns* and (hi/d)n. It was found that the best correlation,

using a least squares curve-fitting technique, is obtained for n = 1.5

(Figure 3.2). The curve shown is described by the equation,



D.D. = 19.4458 7.4546 m + 0.760505 m2 0.010478 m3, (3-2)





















CD
CC
r:
CC



-J
CI




0


LUJ
CO
0




Q


0 SUBSET 1
+ SUBSET 3
0 SUBSET 5
C X SUBSET 7
Y SUBSET 9


0




o ++




o
+









< ii~r8--------


1.00 8.00
MODIFIED


16.00
SPECTRRL


21L.00
STRBI


I


32.00 40.00
LITT NUMBER


(H Lp)
Ns* = (HL
D ( -w- -1)
5D wg


Figure 3.2


Dimensionless damage as a function of the modified spectral
stability number.


e~










where


M = Ns* (hi/d)1'5

and is valid within the limits 6 < M < 29.


3.1.2 Crest Height Changes

The typical final structure profile was irregular in that the crest

height varied along its length. For the purposes of this study, the final

crest height, hf, was specified by the highest surveyed point on the

crest; hf cannot, therefore, be geometrically related to Ad. For this

reason, an estimation of hf was made independent of Ad. Figures 2.2 -

2.6(c) show that hf varies approximately linearly with N for Ns* > 6,

and constant hi/d. All data from Figures 2.2 2.6(c) are shown on

Figure 3.3(a). In a manner consistent with the observations in the last

section, the rate of decrease of hf/d increases as hi/d increases. The

data from subsets 7 and 9 appear to drop off more rapidly than is expected

based on results from subsets 1, 3, and 5. This does not suggest that the

structures built with larger stone suffered more damage. Rather, it may

be an artificial effect resulting from the difference in stone size, i.e.,

the removal of one large stone shows up as a greater decrease in height

than the removal of several smaller stones. Because the range of Ns*

tested and the number of tests where damage was measured were less for the

large stone structures, the average trend is not as well-defined. It was,

therefore, decided to use only data from subsets 1, 3, and 5 for this

analysis. Based on these data, and a least squares analysis, a set of

design curves is proposed as shown in Figure 3.3(b). Each line is for a

constant value of hi/d; interpolation is required for intermediate values

of hi/d. A summary of slopes and y-intercepts for each line is given in

Table 3.1.


















0-SUBSET
^ -+-SUBSET
*- SUBSET
aX X- SUBSET "
^X^?04) xY-SUBSET !

++ +
+ -
+ +
+ +f 4+









00 +++
Oe.

+ 0

0


I'.00 8'.00 1i.00
SPECTRAL STABILITY
(a)


1.oo0
NUMBER


Figure 3.3


Relationship between final relative height and spectral
stability number (a) data from type 1 tests; (b) design
curves based on subsets 1, 3, and 5.


L-

F..40







'-
LoI





--o


1--
Lu_


--.4.


.00oo


0I


0











Table 3.1. Summary of slopes and y-intercepts for design curves in Figure 3.3(b)


h.
Subset # Range of Slope 102 y-intercept


1 0.9644 1.029 -3.32322 1.21020

3 1.150 1.219 -4.39221 1.44490

5 1.375 1.444 -6.19724 1.80112










3.2. WAVE FIELD MODIFICATION DUE TO THE BREAKWATER

Several types of changes to the wave field due to the presence of the

breakwater were examined. Emphasis was placed on energy transmission, but

attention was also given to energy reflection, shifts in the peak, signi-

ficant, and average wave periods, and changes in the spectral peakedness

parameter, as defined by Goda (1970). In addition, data from the two wave

gages in the lee of the structure, gages 4 and 5, were compared. The data

were also compared to the predictive methods of Seelig (1980) and Madsen

and White (1976).

Calculation of the transmitted Qp and the comparison of gages 4 and 5

are based on data from four runs from subset 3, all of subsets 5, 6, 8 and

9, and all but a few runs in subset 7.


3.2.1 Comparison of Transmission Gages

3.2.1(a) Wave height

Figure 3.4 shows the significant wave heights measured by gages 4 and

5 for each of the four data files. It is clear from these plots that the

magnitude of the discrepancy between the gages is in part a function of

the incident Tp. In general, the measured difference increases as T

increases and within each file as wave height increases. The differences

are probably caused by reflection from the absorbing material at the end

of the wave tank. As the wave period (wave length) increases, so do the

amount of reflection for a given wave height and the difference in wave

heights measured by gages 4 and 5. Little if any difference is seen in

the File 1 data. File 2 data show only small absolute differences--up to

about 3/4 cm--but these can translate into substantial percent

differences, particularly for the smaller waves. Usually, but not always,

the larger Ht was measured by gage 4. The File 3 and 4 data have about




































2A50 S00H
WAVE HEIGHT


7.50 ab.oo
CM (GAGE 4)


'.so s 0'. 7'.50 tb.oo
HAVE HEIGHT IN CM (GAGE q)
(b)


Figure 3.4


Comparison of transmitted wave heights measured at gages 4
and 5.


N.


Wg
Ujo.
9
0"
cr
o
a
X:U
Ur.-


I-o
z



LDW
>. 3=)

0*/
3:



o
0d


File I
Tp =1.45sec








0/^







0o


File 2
Tp=2.25sec




A
A


A


b~ oo


TY


o
c


M -


'..ooD










the same maximum absolute difference (1 1/2- 2 cm); Ht at gage 5 was always

greater than Ht at gage 4. Note also that the absolute difference for

File 3 increases gradually as wave height increases, but the discrepancy

in File 4 data grows rapidly to about Ht = 3 cm and more slowly

thereafter. The result is that the percent differences for File 4 are

greater than for File 3.

It is difficult to assess the error due to reflection that is intro-

duced into the calculated value of Ht because the measured values of Ht

depend upon the location of the wave gages with respect to the partial

standing wave. Goda's resolution procedure should be used in order to

ensure that the most accurate transmitted wave height is obtained.


3.2.1(b) Goda's spectral peakedness parameter

Goda (1970) defines spectral peakedness as



2 f fS(f)2df
0
Q = 2 (3-3)
(I S(f)df)
0



where,

f = frequency; and

S(f) = value of the energy density spectrum.

In differential notation,





2 j fj a,_ (3-4)
Qp A ( aj2) 2










where


fj = frequency at the midpoint of the band; and

Af = spectral band width.

The higher the value of Qp, the more peaked the spectrum.

The Qp values for the wave spectra measured by gages 4 and 5 were

calculated and are presented in Figure 3.5. To maintain consistency for

comparison with the incident Qp, all Qp values were calculated using the

range of frequencies spanned by the incident spectrum. Except for File 1,

the trends observed are generally consistent with the observations of

Section 3.2.1(a). Figure 3.5(a) suggests that the spectral peak at gage 4

is greater than the peak at gage 5, but no corresponding difference in

wave height is observed (Figure 3.4(a)). Plots of the File 1 energy spec-

tra show only small differences in the energy densities measured by the

two gages. Thus it seems that the Qp values are more sensitive than the

wave heights to small differences in energy density.


3.2.2 Energy Transmission

3.2.2(a) Variation of Kt within a test

As discussed in Section 2.2, the Kt value obtained by Ahrens for use

in subsequent analysis was calculated using,



1 m (Kt + K )
K = z (3-5)
t m n= 2



where

m = number of sampling periods;

Kt4 = transmission coefficient obtained using Ht from gage 4; and

Kt5 = the transmission coefficient obtained using Ht from gage 5.

































































Figure 3.5


Comparison of spectral peakedness parameters (Q ) measured
at gages 4 and 5.










This value gives the average Kt that can be expected for the given storm

event, but if Kt changes substantially from the beginning to the end of a

test, it may not be adequate for prediction of the maximum transmission.

Figure 3.6 presents typical examples of Kt vs. sampling period for

one test from each of the four files. The difference between the gages is

due to the difference in the measured Ht (Section 3.2.1(a). Due to the

reduction in freeboard, energy transmission increased as the tests

progressed. The increase is smaller, however, than would be expected if

the crest height had been reduced without the accompanying increase in

structure width. This observation is consistent with those of Bremner, et

al. (1980). The maximum absolute difference in Kt for the four files

ranged from about 0.06 to 0.17, but the percent change was as high as 46

percent. These changes are the same order of magnitude as the difference

between the values of Kt measured by gages 4 and 5. Without resolving the

discrepancy between the gages, it is inappropriate to do a detailed trans-

mission analysis based on the "maximum" Kt. Even greater inaccuracies

could be introduced, because the existing errors may tend to cancel one

another. Figure 3.6 suggests, however, that the increase in Kt should be

addressed in future studies.


3.2.2(b) Prediction of Kt

The relative importance of the parameters governing energy trans-

mission and, therefore, the method used to predict Kt change as the

dominant mode of transmission shifts from overtopping to flow through the

structure. Figure 3.7 presents the average Kt as a function of relative

freeboard, R. The relationship between Kt and R changes at about R = 1.0

because as R increases, transmission by overtopping approaches zero, and

the importance of freeboard in determining Kt is diminished. Ahrens







































S2 P4 6R
SAMPLING PERIOD


Run 88
Tp= 2.84sec








_-u .-X
...-- :.---.-....-.








...................... GAGE 4
----- GAGE 5


SM 4 6
SAMPLING PERIOD


0
0

I--

LU
-4


-4.
U_


U-
LUo


CO
Z
o




ri
8-
z

cc


8
8;


C
c


UJ
Lno


i-
I--
L00





CO
U,

(0
in




z
cc-


cc


j i r I I I I
2 4 6
SAMPLING PERIOD









S.


Run 47
T =3.58 sec


x
/M




. ...N"









...................... GAGE 4
---------- GAGE 5


2 P 6
SAMPLING PERIOD


Figure 3.6 Change in transmission coefficient from the beginning to the
end of damage tests.


RUN 97
Tp 1.33 sec



















...................... GAGE 4
-..... -..- GAGE 5
GAGE 5


.0

1 -*



i-n
z




LU



8-
IL
iL
O








U,
0-
10


.1-
o,
o~v


Run 101
Tp= 2.28 sec











...... .......... .... ."..






...................... GAGE 4
---------- GAGE 5


LO
t-
z




LU







U')
-4.-
LL0
LU
0






1,



z


I-
0
0
0


























0 SUBSET 1
A SUBSET 2
+ SUBSET 3
X SUBSET 4
x SUBSET S
SUBSET 6
X SUBSET 7
x A Z SUBSET B
x x Y SUBSET 9
S X X SUBSET 10





A z
z



+ z x







+ 4 *

< 0 2
.k X
YI? :^ ^
ax ;xx

*^
*+ *a
*


I I


-2.00 0.00
RELATIVE


2'.00 L.00
FREEBORRD


Figure 3.7.


Transmission coefficient as a function of
freeboard.


I-

U

.L-

LJO
LIJ C
C) C;
od


z

zo











*-i
2O


OC



o


o


6.00


relative


;I


.oo0










(personal communication, 1986) found that Kt is a function of the

parameter, P, for R > 1.0, where


H A
P = (3-6)
L (D50)
p 50

(Figure 3.8). Note that, in this formulation, Kt is independent of free-

board for R > 1.0. At values of R < 1.0, Kt depends upon both P and R,

i.e., transmission is by a combination of the two mechanisms. The

relative importance of P decreases as R gets smaller.

The parameter, P incorporates the influences of wave period, stone

size, structure area or width, and Hs all of which can be examined

separately. Figures 3.9(a) and 3.9(b) show the transmission data for

R < 1.0. From Figure 3.9(a), it is clear that the longer waves tend to

produce a higher Kt than the short waves, all else being equal. Unfor-

tunately, there are no long wave data for R less than about -0.6. The

available data indicate, however, that the Kt for Files 3 and 4 and low R

values would be higher than for Files 1 and 2. Figure 3.9(b) shows that

the Kt for subsets 7-10 is consistently higher than the Kt for subset

1-6. The difference is probably due to the larger void spaces resulting

from the use of larger stones in the structures of subsets 7-10. Also, Kt

is generally smaller for subsets with larger cross-sectional areas, all

else being equal, suggesting additional energy dissipation across the

crest and/or through the structure.

The approach used to predict Kt varies depending upon the value

of R. For R < 0.0, Kt is assumed to be a function of R only and is

predicted using an exponential curve of the form

























+ SUBSET 3
SUBSET 5
X SUBSET 7
Z SUBSET 8







z
z
z

z
I
x


x5\

\X
^Y- a
3t~~^X


0

C-

LL-o
LLJCO



Z
1-40
o
cno



C.)

-o

0.



9J.


00


Ib.oo


15.00


2b.00


P= LP D50)


Figure 3.8


Transmission coefficient as a function
freeboards greater than 1.0.


of P for relative


5.00


25.00



































S* 0 1
'x'A+ xX
0 0

2 A +
0 0A


o0 9o


0 ^x






o +


0 FILE I
A FILE 2
+ FILE 3
X FILE 4


x x
x


& x X 3+











* SUSSE *I 4.
A U



SUBSET









+ SUBSET

X SUBSET 1
2 SUBSET |
+ It

+ SUBS

X SUBSET

X SUBSEI 1
X SUISET IS
YZ S V BeSS : I


I I I


-1.80 -1.00 -0.20 0.60
RELATIVE FREEBOARD


1.10


'.1


-.80o -1.0o -b.20o 0o6
RELATIVE FREEBORRD
(b)


Figure 3.9


Transmission
freeboard, R,
incident wave


coefficient as a function of relative
for R < 1.0. Data are separated by both peak
period (a) and subset (b).


LL*-

C.
*-*
U


Oo



C()
CO




cr

zo
1*-


-0
..6


I


C,


- .60


0












Kt = All + A21 eR


where

All = 0.9 and

A21 = -0.358.

For 0.0 < R < 1.0


1.0
K =
t
A12 + A22 R






1.0
A12 = = 1.845 and
All + A21


A22 = (1 A12) + pa

= -0.845 + pa


(3-8)







(3-9)





(3-10)


where


a = 0.5926



For R > 1.0, Kt is a function of P only. The relationship shown in

Figure 3.8 is given by


1
K =
t 1 + pa


(3-11)


(Ahrens, personal communication, 1986). Design curves for different

values of P are shown in Figure 3.10. Details of this development are

discussed in Chapter 4.


where


(3-7)


































x xg
+ x^

x

Iz





z
,


'R2







*

**. *


-2.00 0.00 2. 00 4'.00
RELATIVE FREEBOARD


.1


6.00


L.00 -2.00 0.00 2.00 4
RELATIVE FREEBORRD


S.00


Figure 3.10 Design curves for the prediction of transmission
coefficient as a function of relative freeboard and P.


-1I


1._
I--


u-4

L-o

L.)

o

(ol
z






'-4
C)
1-0
U) =!,






FE-


0 SUBSEI I
SUBSEt S
+ SUBSET $
X SUBSET I
* SUBSET 5
+ SUBSET a
X SUBSET I
Y SU1SEIt
X SUBSET a
x SUsSE 1 1


2


* *4


0
0




F-3
Zc0


-4

LL
L)O


z
Cr)


zo



eLT
acc


P=50


P= 100
P= 15.0


6.0C












3.2.2(c) Comparison of data with predictive approaches of other
researchers

Seelig (1979, 1980) found that the transmission coefficient due to

overtopping for a structure fronted by a 1:15 slope is given by


Kt = C (1 F/U) (1 2C) F/U and (3-12)

C = 0.51 0.11 B/h

where

F = freeboard;

U = Wave runup;

B = crest width; and

h = structure height.

Madsen and White (1976) derived an analytical solution for transmission

through trapezoidal, permeable, multi-layered structures. CERC program,

MADSEN, (presented in Seelig, 1980) calculates the total transmission com-

bining both approaches using



Kt (total)2 = Kt (overtopping)2 + K (through)2. (3-14)



In order to compare these approaches with the data, the width of the

damaged structure had to be estimated. This was done by assuming that the

final structure shape is a trapezoid similar to the initial shape, e.g.,

parallel on top and bottom with side slopes of 1:1.5. The material

removed from the top is redistributed at the front and back sides. The

increased area at the sides is equal to the area of damage, Ad

(Figure 3.11). The total cross-sectional area, At, is the same for both

profiles, so that At is expressed in terms of initial conditions as

45
























----Original Profile


Idealized Damage Profile


Figure 3.11. Definition sketch of idealized damaged structure.


I
hf
I












A = (B-+4) h (3-15)
2


Damage area is given by


W +W
Ad = ( ) Ah (3-16)
2


where

Ah = the change in crest height (hi hf).



The values W1, W2, W3, W4, and B are given by


A
W1 h- 1.5 hi, (3-17)



w2 = W1 + 3hi, (3-18)



W3 = W1 + 3Ah, (3-19)



W4 = B + 3f and (3-20)


A
B = 1.5 hf. (3-21)
hf


All variables in the above equations are known except hf, which represents

the average final crest height of the structure. The measured final

crest height is not used because it is the highest point on the crest and

would give a value for B that is inconsistent with the known values of At

and Ad. To solve for hf, equations 3 and 6 were combined to obtain


1










1.5(Ah)2 + W1Ah Ad = 0 (3-22)


which is a quadratic in Ah. The solution is the positive root of

1
-W1 (W12 + 6 Ad)2
Ah = (3-23)
3

The average final crest height is thus, h = h Ah.

Comparison of the data with the predicted Kt by overtopping (Seelig,

1980) and with the predicted total Kt (Madsen and White, 1976) are shown

in Figures 3.12(a, b) and (c, d), respectively. Predicted Kt is plotted

against R in Figure 3.13. As expected, the predicted Kt due to

overtopping is less than the total measured Kt, with the discrepancy

increasing as Tp increases. Overprediction occurs at low relative

freeboards, and no transmission is accounted for when R > 1.0.

Consideration of transmission through the structure gives some

improvement, especially for cases of R > 1.0, but there is still

considerable scatter in the data. In particular, when the subsets are

considered individually the predicted values are unsatisfactory.

Predicted Kt has much less variation than the measured data show. A

possible explanation is that Seelig's formulation is valid for

0.88 < B/h < 3.2, but the range of B/h for these tests is 0.23 to 5.9.

For larger values of B/h, the relationship may overaccount for structure

width.


3.2.3 Energy Reflection

The reflection coefficient as a function of R is shown in Figure

3.14(a). There is a clear separation of the data into two groups based on

T with the longer waves of Files 2, 3, and 4 having a higher Kr than the

































































Figure 3.12.


0.40 0.60 U.BU I.u" o b. 00 0.20 0.40 0.60 0.80 1.00
MEASURED KT MEASURED KT
(c) (d)



Comparison of measured transmission coefficients with those pre-
dicted by the approaches of Seelig (a, b) and Madsen and White
(c, d). Seelig (1980) accounts for transmission by overtopping
only. Madsen and White (1975) consider both overtopping and
transmission through the structure.


I









































-.00 0.00 2.00 4.00
RELATIVE FREEBOARD
(a)


-.00o 0.00 2.00 4.00
RELATIVE FREEBOARD
(c)


Figure 3.13


6.00


0 FILE I
A FILE 2
+ FILE 3
SX FILE 'I
' c








0

S 4x








x
i* x
t^

?


'' ^ e


g~j
*> y


x 0 SUBSET I
A SUBSET 2
+ SUBSET 3
o f X SUBSET I
** SUBSET S
+o SUBSET B
B X SUBSET 7
e Z SUBSET B
Y SUBSET 9
1 X SUBSET 10




*+ z*

0)

C"
.H
0 4 4


1.00


- n.00 0.00 2.00 4'.00
RELATIVE FREEBOARD
(d)


6.00





































6.00


Transmission coefficients predicted by the approaches of
Seelig (a, b) and Madsen and White (c, d) as a function of
relative freeboard. Seelig (1980) accounts for trans-
mission by overtopping only. Madsen and White (1975)
consider both overtopping and transmission through the
structure.


- 0.00 o oo 2.00 .00 oo
RELATIVE FREEBOARD
(b)


x 0 SUBSET I
A SUBSET 2
+ SUBSET 3
X SUBSET 4
x 0 SUBSET 5
+ SUBSET 6
+ X SUBSET 7
Z SUBSET 8
Y SUBSET 9
X SUBSET 10













zx


SO0 FILE I
A FILE 2
S ,+ FILE 3
o X FILE 4


)x
6
o






xx o
; ~~ ^ x< a


0
9.1


'-l.00


---- --


m


I


I


-


r..




















o O
0 0

0 FILE I
A FILE 2
+ FILE 3
O x FtILE 4
I U



U.- x U0o d/L=0.0455
l.,-C x LL",
LU XC +x +X X + 4 u-
C o d/L= 00625
Sx A x A / d/L= 0.0800

cO* x / d/L=0.1000
O- a d/L=01200
0 ^x\' eo o e 0


o A

o 0


o
00 '

o o

.00 -.00 0'.00 2.00 4.00 6.00 -l1.00 -2.00 0'.00 2.00 4 '.00 6.01
RELATIVE FREEBOARD RELATIVE FREEBORRD
(a) (b)




Figure 3.14 Design curves for the prediction of reflection coefficient
as a function of relative freeboard and relative depth.










short waves in File 1. As R increases, Kr approaches a constant whose

value is a function of Tp only. Kr is predicted by fitting three lines

within the ranges of R < 1.0, 1.0 < R < 3.0, and R > 3.0 (Figure 3.14(b).

The lines were matched at R = 1.0 and R = 3.0 such that the overall good-

ness of fit was as high as possible. The effects of Tp are included in

the linear coefficients which are a function of d/L. A detailed dis-

cussion of the prediction of Kr is given in Chapter 4.


3.2.4 Changes in Wave Period and Spectral Peakedness

3.2.4(a) Change in T

As discussed earlier, Tp is the wave period in the spectrum that

contains the most energy. It is expected that energy will be lost at the

peak and redistributed to higher and lower frequencies, but that, in the

absence of breaking, the frequency at which the peak is located will not

change. This is generally the case for these data. The ratio of the

transmitted to incident Tp as a function of R is shown in Figure 3.15.


3.2.4(b) Change in T. and T

Ts is the average wave period of the one-third highest waves. T is

the average of all waves. Unlike Tp, Ts and T are expected to change

because they are directly related to the wave heights. As higher fre-

quencies are introduced or filtered out, the change should be reflected in

Ts and T. The ratios of transmitted to incident Ts and T vs. R are shown

in Figures 3.16 and 3.18, respectively. The data in Figure 3.16(a-d) are

plotted together in Figure 3.17. There is a distinct pattern to these

data that corresponds to the shift in transmission modes. For R less than

about 1.0, the ratio is less than one. This means that higher harmonics

are being introduced as waves pass over the structure. For R > 1.0, the







































Itoo -D.o o o .00 2.o00 4.00 6.
(a)
0







File I
Tp:1.45 sec

- .00oo -.oo 0o'.oo00 2.00 I.oo 6.
RELATIVE FREEBOARD
(a)


s +



0














Tp = 2.86 sec

S.o -2.o 0.00ooo a'. oo00 '.oo
RELATIVE FREEBOARD
(C)
Cc)


Figure 3.15


C
a
I-
c
0
C

C
a
c


it
a



U
a


00


N
3
C4
o
-C

AA A AA













1.00 Do0 0'.00 2. 00 4.00 S.--C
AI0 A


a
a
J




File 2
i Tp= 2.25 sec

-.o00 -2.00o o.oo 2. 00oo '.oo 6
RELATIVE FREEBOARD
(b)



o





0

0
0







CI
=CD
UJo


a"





File 4
a Tp=3.60 sec
0
1.00 -2.00 0'00 22.00 11.00 .
RELATIVE FREEBOARD
(d)


Ratio of incident to transmitted peak period as a function
of relative freeboard.

















-*1



m O
E"
3



S 0

so







File I
0 Tp= 1.45 sec
.00.o -.0 0 0'.00 2' o '00
RELATIVE FREEBOARD
0 10



r













zo







File 3
.00 Tp= 2.86 sec

-.o1 -0 .oo o'.00 2. 00 7L00 6.
RELATIVE FREEBOARD
(c)
o,




--D



3Lo












RELATIVE FREEBOARD
(0)


Figure 3.16 Ratio of transmitted to incident
function of relative freeboard.


Cfr





a:
0
Oo


e 4
A&

LL.I A



zo


File 2
S= Tp=2.25sec
0
G .00 -2.00 O.00 2.00 t00 6
RELATIVE FREEBOARD
(b)


0
0








X %





2 < X



x



File 4
STp3.60 sec

n -. _nn u' nn a nn


RELATIVE FREEBOARD
(d)


significant wave period as a


w~uu


















































Figure 3.17


4.00 -2.00 0.00 2.00 4.00 6.00
RELATIVE FREEBORRD



Ratio of transmitted to incident significant wave period as
a function of relative freeboard. The limits used in the
design program (Chapter 4) to determine the upper and lower
bounds on the ratio are shown.






























File I
Tp= 1.45 sec
- 00 2.00 I00

RELATIVE FREEBOARD
(a)
(a)


+ + +
+










File 3
STTp = 2.86 sec
S.00o -1.00 0.00 2.00 .o00 6.
RELATIVE FREEBOARD
(c)


Figure 3.18


00


IO
















Fil 2
File 2






I-
J x

File 2
o Tp32.25 sec

-o00 -2.00 0.00 2.00 i.o00 6.
RELATIVE FREEBOARD
(b)


0
D













o





File 4
- .0 I.0


00


RELATIV


E FREEBOARD
(d)


Ratio of transmitted to incident average wave period as a
function of relative freeboard.










ratio is greater than one, indicating that higher frequencies are being

filtered out. This is characteristic of waves passing through a struc-

ture. The magnitude of the change is in part dependent on T Overall,

longer waves experience a greater change in Ts and T.


3.2.4(c) Change in Q

The Q ratios are plotted in Figure 3.19 and 3.20. Changes in the Qp

ratio are attributed to the same factors as the changes in T and T.
S


















(0









-0
o
0
o







0







(a)
-.O O -20 'O '.0 *.0
RErIEFREOR
(a


0




S+
.t +
+ 4+
4.

0 + "







File 3
,Tp= 2.86 sec

-.oo -k.oo o'.oo 2o00 o oo0 6.
RELATIVE FREEBORRD


0
0








A AA











3-.oo 00oo .00 2.00 '.00 6.
RELATIVE FREEBOARD
(b)
(b)


"M

SX XX







x
.0







File 4
o Tp=3.60sec

.00 -D.oo 0'00 2.00 '.00 8.1
RELATIVE FREEBOARD
(d )


Figure 3.19 Ratio of transmitted to incident spectral peakedness parameter
as a function of relative freeboard for each of the four wave
files.


00





















































Figure 3.20


i4.00 -2.00 o0.00 2 .00 u4.00 6.00
RELATIVE FREEBORRD



Ratio of transmitted to incident spectral peakedness
parameter as a function of relative freeboard. The limits
used in design program (Chapter 4) to determine the upper
and lower bounds on the ratio as shown.












CHAPTER 4 DESIGN AID PROGRAM


This chapter describes in detail the computer program, LCBDGN, which

is to be used as an aid in designing low-crested breakwaters. Version 1.0

of this program is based on laboratory data only. Future versions will

incorporate field data as well.

The assumption is made that the designer knows the incident wave

conditions for which the breakwater is to be subjected and the desired

transmitted or reflected significant wave height for specified incident

wave conditions. Two sets of incident wave conditions must be specified

(referred to here as operational and extreme) as well as which of these

conditions are to be used as a basis for design. The program computes the

structure height needed in order product the desired results and the

height to which the structure must be constructed in order to achieve that

final height. The constructed height may or may not be the same as the

final height depending on the specified design conditions and structure

parameters.

Any two sets of incident wave conditions for which the designer would

like stability and performance information is acceptable as long as they

are within the range of the present data. As more and better data are

available the program can be upgraded and extended to include a wider

range of conditions. If sufficient statistical information is known about

the incident wave climate, the "operational" sea state may be taken as the

conditions (significant wave height, peak period, peakedness parameter)

that are not exceeded a high percentage (say 95%) of the time. "Extreme"

conditions refer to what is often called "design conditions" and are the










most severe conditions anticipated during the life of the structure.

LCBDGN computes the performance (i.e., transmitted significant wave

height, peak period, significant period range and peakedness parameter

range and reflected significant wave height) of the breakwater for both

sets of conditions before and after it has been subjected to the extreme

sea state.

Least squares curve fits to laboratory data have been made regarding

the stability and performance of low-crested breakwaters. A description

of how these curves are used to compute structure heights and damage and

transmitted and reflected wave parameters is presented below.

Final Structure Height

The structure height required to produce the desired transmitted or

reflected significant wave height for a specified set of initial condi-

tions is computed using lease squares curve fit equations of the data

shown in Figures 3.10, 3.3(b), and 3.14(b). Figures 3.10 and 3.3(b) are

used when transmitted wave conditions are specified and Figure 3.14(b)

when specific reflected wave conditions are desired.

First consider the case where transmitted waves are specified (refer

to Figure 3.10)

For R < 0.0, the transmission coefficient is given by


K = All + A21 eR (4-1)


All is fixed at 0.9 and A21 is determined using least squares curve fit

techniques



All = 0.9 (4-2)











A21 = (


K = 0.9
t


n R n R
S tiA
E e K -All E e
i=1 t i=l
i


n 2R
iE e
0.358 e
- 0.358 e


) = -0.358


(4-3)


(4-4)


Solving for hf in Equation 4-4 we get


h d 0.9 K
R = = and
s. 0.358

0.9 K
hf =d + H In ( t0 ) .
1 0.358


For 0.0 < R < 1.0, the transmission coefficient is given by



K 1.0
Kt = .
A12 + A22 R


In order to make the Kt vs. R curve continuous at R = 0.0,

expressed as


Al2 1.0
A12 l + A21
All + A21


1.845


(4-5)



(4-6)


(4-7)



A12 is


(4-8)


A22 is chosen so that the Kt vs. R curves will be continuous at

R = 1.0,


A22 = (1 A12) + pa


(4-9)


where, as defined in Chapter 3,


H A
s t

p 50


(4-10)


Thus










and


h
A = hi (-- + b)
tan e


Substituting these expressions into the Kt equation results in


t


A12 + {1 A12 +


H h


H hi
( s
L (---(D50)
p 50


hi can be expressed in terms of

Figure 3.3(b).

For N > 6.0
s

h
f *
= A13 A23 N
d s


h
(-h +b))a} R
tan e


(4-12)


hf by using the curves from


(4-13)


where


h
A13 = A113 + A213(--)
d


h
A23 = A123 + A223 (-)






h h h
= [A113 + A213(-)] + [A123 + A223(- -)]N
d d d


(4-11)


and


(4-14)


(4-15)


(4-16)









Solving for hi we have


hf
d[(---) A113 A123 N* ]
h = ds (4-17)
[A213 + A223 N ]


Substituting this expression into the Kt equation yields




h -k h -k h -d
{k6 + [k5( k3 ( "-k k + k )]a( H + k7) = 0 (4-18)
2 3 2 3 s




where


k. = A113 + A123 N


k2 A213 + A223 N


k3 tan e ,


k b ,


k Hi /Lp(D50)


k6 1.0 A12 (4-19)


k A12 -
7 K A
t

A113 = -0.2338 ,


A213 = 1.436 ,


A123 = 0.03737 and


A223 = -0.06997 .









This transcendental equation can be solved using a Newton-Raphson


scheme, i.e.,


f(hf() )
hf(j+) =hf(j) -f'[h )


where


f(hf)



h k h k hf d
{k6+ [k5 (- k ) k k -)a H + k7) = 0
2 3 2 3 s


d f(hf)
f'(hf d h


hf k1 hf k1
{k6 + [k5( k k k + k4)]a}(1
2 3 2 3 s


hf k hf kk + a-1
+ a[ki(2 k 2 kt+ k4)
S2 3 2 3


hf k1 1.0 k h k hf d
[k 2 T )+ fr k + k k k 4
5 k k k k k k k k 4
2 3 2 3 2 3 2 3 s


(4-20)


(4-21)


(4-22)










For R > 1.0
K 1.0
K =
t 1.0 + pa


where


H h
p = s [h.( e + b)]
S(D 2 50tan

p 50


(4-23)


(4-24)


Substituting this expression for P into the above Kt equation and solving

for hi results in


-b tan 0
h = -
i


(b tan 2
(b tan O) +


where


K* E (1 -
Kt


Next, equate hi in this expression to hi in Equation 4.17.


hf *
[ d A113 (A123) N]
d( d Ns)
(A213 + (A223) Ns)


-b tan 6 1
2 2


(b tan +
(b tan 0) +


4L (D50)2 K* tan 6
(50
H
S


Solving for hf we get


L (D50)2 K* tan 8
H
s


(4-25)


(4-27)










h = A113 (A123) Ns
f s


+ [A213 + (A223)


2 *
-b tan 6 1 2 4Lp(D50) K tan 0
N ][ + -- (b tan 8) + H
s 2d 2d H 4
(4-28)


a = 0.5926


(4-29)


For the case where reflected

Figure 3.14(b) must be used.



For R < 1.0


significant


wave height is specified,


KR = A14 + (A24) R


A14 = A114 + A214


d
(--)
L
p


1.0
A24 = --
A124 + A224 (--)
L
p

K A14
R = 4 and
A24


(K A14)
hf = d + Hs A24
f 5 A24


H {K [A114 +
s lr L


[A124 + A224


A214(d-)]}
L


d
(--)
p


where


(4-30)


(4-31)




(4-32)




(4-33)


hf =d+
f


(4-34)










where


A114 = 0.5085 ,

A214 = -2.018 (4-35)

A124 = 1.019 and

A224 = 137.6 .



For 1.0 < R < 3.0



Kr = A15 + (A25) R (4-36)


d
A15 = All5 + A215(--) (4-37)
P

1.0
A25 = 1 (4-38)
A125 + A225(--)
P

H {Kr -[A114 + A214(-)}
hf = d + 1.0 (4-39)

[A124 + A224( )]
P


where

A115 = 0.7195 ,

A215 = -3.400 (4-40)

A125 = 48.70 and

A225 = 268.1

For R > 3.0

hf(R = 3.0)

= A15 + A25(3.0) (4-41)










Initial Structure Height

Once the final structure crest height has been determined then the

initial or constructed crest height can be obtained from Figure 3.3(b)

(Eq. 4-17).

f *
(--) A113 (A123)N
hi = dS d
(A213 + (A223)N
s

Knowing the initial structure height, the "area of damage" can be

found from the least squares curve fit to the data in Figure 3.2.



Ad = (D50)2[A16 + A26M + A36M2 + A46M3] (4-42)



where



M N )15 (4-43)
s d


and

A16 = 19.45 ,

A26 = -7.455 (444)

A36 = 0.7605 and

A46 = -0.01048 .



With the initial and final structure heights established, the break-

water performance can be computed for the circumstances and conditions of

interest. As stated earlier in this report, the performance parameters for

this version of the program include:










1. Transmitted significant wave height

2. Transmitted significant wave period range

3. Transmitted peakedness parameter range

4. Reflected significant wave height



These parameters are computed for the following circumstances:

1. Operational Incident Waves

a. Previous wave conditions not exceeding operational sea

state.

b. Previous wave conditions reaching but not exceeding

extreme sea state.

2. Extreme Incident Waves

a. Previous wave conditions reaching but not exceeding

extreme sea state.

Transmitted Significant Wave Period

The data for transmitted significant wave period is not sufficient to

allow prediction of specific values. Bounds on the range values for given

set of conditions can, however, be obtained from the data as shown in

Figure 55. The equations for these bounds are as follows:

T
ss 1.0 R < -3.5
= T11 + (T21)R -3.5 < R < 1.0 (4-45)
s T13 + (T23)R 1.0 < R


where

T11 = 0.6320 and

T21 = -0.106 (4-46)










Transmitted Peakedness Parameter

As with transmitted significant wave height, there is not enough data

to predict specific values of the peakedness parameter. Bounds on the

range of values were established by eye and equations fit to these bounds.

These equations are given below:


Pt 1.0 R < -3.5
= Q11 + (Q21)R -3.5 < R < 1.0 (4-47)
Pi 1.28 1.0 < R


where

Qll = 0.67 and

Q21 = -0.095 (4-48)










CHAPTER 5 SUMMARY AND RECOMMENDATIONS


Data from experiments on low-crested breakwaters conducted at the

Coastal Research Engineering Center were analyzed with respect to

structural damage and modifications of the wave field by the breakwater.

The results were incorporated into an interactive breakwater design

program use with a personal computer. In addition, observations from

these analyses were used to develop recommendations for future studies.

Structural damage was assessed in terms of both crest height changes

and volumetric changes. The volumetric change, expressed as dimensionless

damage, was found to be related to a modified spectral stability number

defined by
h 1.5
M = N (-)
=Ns



For values of 6 < M < 29 this relationship is given by a third order

polynomial (Equation 3-2). For M < 6, the damage is effectively zero.

Crest height changes are determined using a linear relationship between
hf i
- and N for a specified value of --. Three design curves are based on
d s d
data from subsets 1, 3, and 5 having values of -- of about 1.0, 1.2,

and 1.4, respectively, see Figure 3.3.

The modification of the wave field due to the breakwater is a complex

function of many variables including wave height, wave period, stone

characteristics, freeboard, and cross-sectional area of the structure.

The relative importance of these paramterrs in the determination of Kt and

Kr depends upon the relative freeboard, R, which also serves to define the

transition from transmission by overtopping to transmission by flow

through the structure. Prediction of Kt is divided into three zones. For










R > 1.0, transmission is predicted using the parameter, P, which is a

function of wave steepness, cross-sectional area of the structure, and

stone diameter, but is independent of R. The region 0 < R < 1 is a

transition zone in which Kt is a function of both P and R. At negative R,

Kt is primarily a function of R. The influences of stone and structure

parameters are less obvious in the reflection data. Below R = 3.0, Kr is

a function of R and incident wave period expressed as the relative depth,

d/L. At higher values of R, Kr depends of d/L only.

The shift in dominant mode of transmission also effects the ratio

between the transmitted and incident wave periods and spectral peakedness

parameters. When transmission is by overtopping (R < 1.0), higher

harmonics are introduced into the transmitted wave and the wave period and

spectral peakedness ratios are less than one. For higher relative

freeboards, high frequency (short period) waves are filtered out and the

ratio is greater than one.

Based on observations from these data and analyses, the following

recommendations for future studies are made:

1) Apply Goda's method for the resolution of reflected and incident

waves behind the structure as well in front of the structure;

2) Examine the increase in Kt as the damage tests progress in order

to determine the relationship between the average Kt and the

maximum Kt that can be expected during an extreme event;

3) Conduct experiments specifically designed to determine the rela-

tionship between transmission at low relative freeeboards and

stone characteristics, structure size, and wave period; and

4) Conduct three-dimensional tests so that a) (structure) end

effects can be examined and (b) non-orthogonal incident waves can

be tested.










A computer program has been written as part of the work reported

here. The program name is Low Crested Breakwater Design, LCBDGN, and its

purpose is to aid in the design of low crested breakwaters. The initial

version (Version 1.00) has certain limitations which need to be pointed

out at this point.

1. The data on which the design equations used in the program are

based are two dimensional wave tank data. There has been no

attempt to account for scale effects in going from the laboratory

to the prototype (field).

2. No attempt has been made to account for 3-dimensional effects,

i.e., refraction and diffraction at the end(s) of the structure.

3. Incident reflected and transmitted waves are assumed to approach

and leave the structure at right angles to the structure (i.e.,

wave crests are assumed to be parallel to the structure).

In spite of the above qualifications, LCBDGN should be helpful to the

engineer designing a low-crested permeable rubble mound breakwater. The

intent is to incorporate scale and other effects in later versions of the

program as field data (and its analysis) becomes available. In the mean-

time, the program can be used as long as the results are used along with

"engineering judgment" and additional information regarding the factors

discussed above.










REFERENCES

Ahrens, J. P. (1983), Reef type breakwaters, Proc. of 19th Coastal
Engineering Conference, August, Houston, Texas, pp. 2648-2662.

Allsop, N. W. H. (1983), Low-crest breakwaters, studies in random waves,
Proc. of Coastal Structures '83, March, Arlington, Virginia, pp. 94-
107.

Bremner, W., D. N. Foster, C. A. Miller, and B. C. Wallace (1980), The
design concept of dual breakwaters and its application to Townsville,
Australia, Proc. of the 17th Coastal Engineering Conference, March 23-
28, Sydney, Australia, Vol.2 pp. 1898-1908.

Foster, D. N. and D. Haradasa (1977), Rosslyn Bay Boat Harbour Breakwater
Model Studies, University of New South Wales Water Research
Laboratory, Technical Report No. 77/6, April, 12 pp. + figures and
tables.

Foster, D. N. and S. P. Khan (1984), Stability of overtopped rock armoured
breakwaters, University of New South Wales Water Research Laboratory,
Report No. 161, February, 38 pp. + figures.

Goda, Y. (1970), Numerical experiments on wave statistics with spectral
simulation, Report of the Port and Harbor Research Institute Ministry
of Transport, Japan, Vol. 9, No. 3, pp. 3-57.

Goda, Y. and Y. Suzuki (1976), Estimation of incident and reflected waves
in random wave experiments, Proc. of 15th Coastal Engineering
Conference, July, Honolulu, Hawaii, pp. 828-845.

Graveson, H., 0. J. Jensen, and T. Sorenson (1980), Stability of rubble
mound breakwaters II, Danish Hydraulic Institute Technical University
of Denmark, 19 pp. (No report number).

Kitaigorodskii, S. A., V. P. Krasitskii, and M. M. Zaslavskii (1975),
Phillips' theory of equilibrium range in the spectra of wind-generated
gravity waves, Jour. of Physical Oceanography, Vol. 5, pp. 410-420.

Madsen, 0. S. and S. M. White (1976), Reflection and transmission charac-
teristics of porous rubble-mounds breakwaters, U.S. Army Corps of
Engineers Coastal Engineering Research Center, Misc. Report No. 76-5,
March, 138 pp.

Phillips, 0. M. (1958), The Equilibrium range in the spectrum of wind-
generated waves, Jour. of Fluid Mechanics, Vol. 4, pp. 426-434.

Seelig, W. N. (1979), Effect of breakwaters on waves: laboratory tests of
wave transmission by overtopping, Proc. of Coastal Structures '79,
March, Alexandria, Virginia, pp. 941-961.

Seelig, W. N. (1980), Two-dimensional tests of wave transmission and
reflection characteristics of laboratory breakwaters, U.S. Army Corps
of Engineers Coastal Engineering Research Center, 187 pp.










Vincent, C. L. (1981), A method for estimating depth-limited wave energy,
U.S. Army Corps of Engineers Coastal Engineering Research Center,
Technical Aid No. 81-16, November, 22 pp.
Vincent, C. L. (1982), Depth-limited significant wave height: A spectral
approach, U.S. Army Corps of Engineers Coastal Engineering Research
Center, Technical Report No. 82-3, 23 pp.































Appendix A








DOCUMENTATION FOR LCBDGN.FOR


"LCBDGN.FOR" is an interactive FORTRAN program the purpose
of which is to aid in the design of low crested breakwaters. Input
data can be entered 1) from the keyboard, 2) from a disk file or
3) by a user modified disk file (i.e. any number of the 18 input
quantities can be changed from within LCBDGN. An input data file
is created each time the program is run under the name LCBIN.DAT.

In order to make changes in the input data file you must
know the "sequence" number of the quantities you wish to change.
These numbers are given below:


SEQUENCE
NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16


QUANTITY


HSO
TSO
TPO
QPO
HSE
TSE
TPE
QPE
BS
WD
WIDTH
SS
WW
WR
W50
IDGNI


IDGN2


HSD


DESCRIPTION


Incident Operational Significant Wave Height (m)
Incident Operational Significant Wave Period (sec)
Incident Operational Peak Period (sec)
Incident Operational Peakedness Parameter
Incident Extreme Significant Wave Height (m)
Incident Extreme Significant Wave Period (sec)
Incident Extreme Peak Period (sec)
Incident Extreme Peakedness Parameter
Bottom Slope at Structure (del z)/(del x)
Water Depth at Structure (m)
Width of Structure Crest (Constructed) (m)
Structure Slope (forward and back) (del z)/del x)
Mass Density of Water (kg/m**3)
Mass Density of Stone (kg/m**3)
Mass of Mean Stone (kg)
Denotes Design Wave Condition
1 Operational Wave Conditions
2 Extreme Wave Conditions
Denotes Design for Transmitted or Reflected Wave
1 Transmitted
2 Reflected
Desired (Transmitted or Reflected) Significant
Wave Height (m)







C----------------------------------------------------------------------C
C PROGRAM LCBDGN (VERSION 1.00) 15 NOVEMBER 1986 C
C LOW CRESTED BREAKWATER DESIGN C
C C
C D.M. SHEPPARD ((904) 392-1570) C
C C
C PURPOSE: C
C The purpose of this interactive FORTRAN program is to aid in C
C the design of Low Crested Breakwaters. The structure of the C
C program is such that new data and information regarding the C
C performance and stability of Low Crested Breakwaters may be C
C added with a minimum of effort. C
C C
C PROGRAM DESCRIPTION C
C The following assumptions are made: C
C 1. OPERATIONAL incident wave conditions are known C
C 2. EXTREME incident wave conditions are known C
C 3. The design is based on a desired transmitted or C
C reflected significant wave height for either C
C OPERATIONAL or EXTREME conditions. C
C C
C PROGRAM OUTPUT C
C 1. Constructed structure height C
C 2. Structure height after structure experiences OPERATIONAL C
C waves C
C 3. Structure height after structure experiences EXTREME C
C waves C
C 4. Transmitted and reflected wave parameters for OPERATIONAL C
C and EXTREME conditions C
C C
C-------------- ---------------------------------------------------------C
C
DIMENSION DATA(18),ANDATA(18)
COMMON HSO,TPO,QPO,HSE,TPE,QPE,WIDTH,SS,WW,WR,W50,
1SSND,WD,WLO,WLE,D50,HCIOOT,HCIOOR,HCIEET,HCIEER
INTEGER ITEM(18)
C
OPEN(I1,FILE='LCBOUT.DAT',STATUS='UNKNOWN')
C
10 WRITE(*,20)
20 FORMAT(3X,'TYPE THE NUMBER IN FRONT OF THE DESIRED OPTION',
1/4X,'l) INPUT DATA FROM KEYBOARD '
2/4X,'2) INPUT DATA FROM DATAFILE LCBIN.DAT AS IS',
2/4X,'3) MODIFY DATA IN DATAFILE LCBIN.DAT',/)
READ(*,*)IOPT
IF(IOPT.EQ.1)GO TO 105
IF(IOPT.EQ.2)GO TO 30
IF(IOPT.EQ.3)GO TO 40
GO TO 10
C
30 OPEN(9,FILE='LCBIN.DAT',STATUS='OLD')
READ(9,*)HSO,TSO,TPO,QPO,HSE,TSE,TPE,QPE,BS,WD,WIDTH,
1SS,WW,WR,W50,IDGNI,IDGN2,HSD
GO TO 280
40 OPEN(9,FILE='LCBIN.DAT',STATUS='OLD')
WRITE(*,50)
50 FORMAT(3X,'REFER TO THE "INPUT DATA LIST" IN THE DOCUMENTATION',
1/1X,'FOR THIS PROGRAM !',//,3X,
2'HOW MANY QUANTITIES WOULD YOU LIKE TO CHANGE ?',/)
READ(*,*)INCNG
DO 70 I=I,INCNG






WRITE(*,60)I
60 FORMAT(3X,'TYPE THE NUMBER IN FRONT OF ITEM',12,IX,
1'TO BE CHANGED',/IX,'FOLLOWED BY THE NEW VALUE OF THE ITEM (SEPARA
2TED BY A COMMA)',/)
READ(*,*)ITEM(I),ANDATA(1)
70 CONTINUE
READ(9,*)(DATA(J),J=1,18)
CLOSE(9,STATUS='DELETE')
DO 90 K=1,INCNG
JK= ITEM(K)
DATA(JK)= ANDATA(K)
90 CONTINUE
OPEN(9,FILE='LCBIN.DAT',STATUS='NEW')
DO 100 L=1,18
WRITE(9,*)DATA(L)
100 CONTINUE
CLOSE (9)
GO TO 30
C
105 WRITE(*,110)
110 FORMAT(3X,'TYPE THE FOLLOWING "OPERATIONAL" INCIDENT WAVE',/IX,
1'INFORMATION SEPARATED BY COMMAS',/4X,
2'1. SIGNIFICANT WAVE HEIGHT (in meters)',/4X,
3'2. SIGNIFICANT WAVE PERIOD (in seconds)',/4X,
4'3. PEAK PERIOD (in seconds)',/4x,
5'4. Qp SPECTRAL PEAKEDNESS (Qp = 2.0 for PIERSON-MOSKOWITZ)',
6//)
READ(*,*)HSO,TSO,TPO,QPO
WRITE(*,120)
120 FORMAT(3X,'TYPE THE FOLLOWING "EXTREME" INCIDENT WAVE',/IX,
INFORMATION SEPARATED BY COMMAS',/4X,
2'1. SIGNIFICANT WAVE HEIGHT (in meters)',/4X,
3'2. SIGNIFICANT WAVE PERIOD (in seconds)',/4X,
4'3. PEAK PERIOD (in seconds)',/4x,
5'4. Qp SPECTRAL PEAKEDNESS (Qp = 2.0 for PIERSON-MOSKOWITZ)',
6//)
READ(*,*)HSE,TSE,TPE,QPE
WRITE(*,130)
130 FORMAT(3X,'TYPE BOTTOM SLOPE AT LOCATION OF STRUCTURE.',/IX,
1'( (DELTA Z)/(DELTA X) )'/)
READ(*,*)BS
IF(BS.GT.0.07)GO TO 135
WRITE(*,133)
133 FORMAT(/3X,'CAUTION! DATA USED IN THIS VERSION OF THIS PROGRAM',
1/1X,'IS BASED ON A BOTTOM SLOPE OF 1(VERT) ON 15(HOR) AT',/IX,
2'THE STRUCTURE')
135 WRITE(*,140)
140 FORMAT(3X,'TYPE WATER DEPTH (in meters) AT THE STRUCTURE SITE',
1/)
READ(*,*)WD
WRITE(*,150)
150 FORMAT(3X,'TYPE WIDTH OF STRUCTURE CREST (in meters)'/)
READ(*,*)WIDTH
WRITE(*,160)
160 FORMAT(3X,'TYPE STRUCTURE SLOPE (DELTA Z)/(DELTA X)',/)
READ(*,*)SS
IF(SS.LT.0.7.AND.SS.GT.O.6)GO TO 165
WRITE(*,163)
163 FORMAT(/3X,'CAUTION! DATA USED IN THIS VERSION OF THIS PROGRAM',
1/1X,'IS BASED ON A STRUCTURE SLOPE OF 1(VERT) ON 1.5(HOR)')


_ __~~ _____ ___ ___






165 WRITE(*,170)
170 FORMAT(/3X,'TYPE WATER DENSITY (in kg/m**3)',/)
READ(*,*)WW
WRITE(*,180)
180 FORMAT(/3X,'TYPE STONE DENSITY (in kg/m**3)',/)
READ(*,*)WR
WRITE(*,190)
190 FORMAT(/3X,'TYPE MEDIAN STONE WEIGHT, W50,(in kg)',/)
READ(*,*)W50
200 WRITE(*,210)
210 FORMAT(3X,'TYPE THE NUMBER IN FRONT OF THE CONDITIONS',
1/3X,'TO BE USED FOR DESIGN ',//4X,
2'1. OPERATIONAL CONDITIONS',/4X,
3'2. EXTREME CONDITIONS',/)
READ(*,*)IDGN1
IF(IDGNI.EQ.1.OR.IDGNI.EQ.2.)GO TO 220
GO TO 200
220 WRITE(*,230)
230 FORMAT(3X,'TYPE THE NUMBER IN FRONT OF THE CONDITIONS',
1/3X,'TO BE USED FOR DESIGN ',//4X,
2'1. TRANSMITTED SIGNIFICANT WAVE HEIGHT, HST,',/4X,
3'2. REFLECTED SIGNIFICANT WAVE HEIGHT, HSR,',/)
READ(*,*)IDGN2
IF(IDGN2.EQ.1.OR.IDGN2.EQ.2.)GO TO 240
GO TO 220
240 GO TO(250,260),IDGN2
250 WRITE(*,255)
255 FORMAT(/3X,'TYPE DESIRED VALUE OF TRANSMITTED',/3X,
1'SIGNIFICANT WAVE HEIGHT (in meters)',/)
READ(*,*)HSD
GO TO 270
260 WRITE(*,265)
265 FORMAT(/3X,'TYPE DESIRED VALUE OF REFLECTED',/3X,
I'SIGNIFICANT WAVE HEIGHT (in meters)',/)
READ(*,*)HSD
270 CONTINUE
C
OPEN(9,FILE='LCBIN.DAT',STATUS='UNKNOWN')
C
C WRITE INPUT DATA TO FILE
C
WRITE(9,*)HSTQTSO,TPO,QPO,HSE,TSE,TPE,QPE,BS,WD,WIDTH,
1SS,WW,WR,W50,IDGNI,IDGN2,HSD
C END INPUT
C------ ----------------------------------------------------------------C
C START COMPUTATION
C------------------------------------------------------------------------ C
C
C COMPUTE DESIRED TRANSMISSION OR REFLECTION COEFFICIENT
C
280 IF(IDGN1.EQ.1)THEN
AK= HSD/HSO
ELSE
AK= HSD/HSE
C IF(AK.GE.0.75)THEN
C WRITE(*,281)AK
C 281 FORMAT(IX,'THE VALUE OF Kt (Kt = ',F8.3,') IS TOO LARGE FOR',
C 1 /IX,'THE RANGE OF VALIDITY OF THIS PROGRAM')
C GO TO 500
C ENDIF


___





ENDIF
C
C COMPUTE OPERATIONAL AND EXTREME WAVE LENGTHS, WLO AND WLE
C
CALL WAVLEN(WD,TPO,WLO)
CALL WAVLEN(WD,TPE,WLE)
050= (W50/WR)**.333333
SSND= D50*((WR/WW)-1.)
SSNO= (((HSO**2)*WLO)**.3333333)/SSND
SSNE= (((HSE**2)*WLE)**.333333)/SSND
C
C COMPUTE STRUCTURE HEIGHT
C
C-----------------------------------------------------------------------C
C IDGN1 = 1 FOR OPERATIONAL DESIGN
C = 2 FOR EXTREME DESIGN
C IDGN2 = 1 DESIGN BASED ON TRANSMITTED HS
C = 2 DESIGN BASED ON REFLECTED HS
C
C ICOND = 1 FOR OPERATIONAL CONDITIONS
C = 2 FOR EXTREME CONDITIONS
C
C IPREV = 1 FOR OPERATIONAL CONDITIONS NOT YET EXCEEDED
C = 2 FOR EXTREME CONDITIONS REACHED
C----------------------------------------------------------------------C
C
C COMPUTE STRUCTURE INITIAL AND FINAL HEIGHTS AND
C AREA OF DAMAGE FOR FOLLOWING SITUATIONS:
C
C TRANSMITTED
C
IFLAG= 0
IF(IDGN2.EQ.2)GO TO 310
C
IF(IDGNI.EQ.2)GO TO 290
C
C 1. DESIGN OPERATIONAL CONDITIONS
C TRANSMITTED HS
C CONDITIONS OPERATIONAL
C
IDGN1= 1
IDGN2= 1
ICOND= 1
CALL STRSTA(IDGN1,IDGN2,ICOND,AK,HSO,WLO,HI,HF,AD,RI,RF,IFLAG)
IF(IFLAG.GT.O)GO TO 500
HCIOOT= HI
HCFOOT= HF
DAMOOT= AD
RIOOT= RI
RFOOT= RF
C
C 2. DESIGN OPERATIONAL CONDITIONS
C TRANSMITTED HS
C CONDITIONS EXTREME
C
IDGNI= 1
IDGN2= 1
ICOND= 2
CALL STRSTA(IDGNI,IDGN2,ICOND,AK,HSE,WLE,HI,HF,AD,RI,RF,IFLAG)
IF(IFLAG.GT.O)GO TO 500






HCIOET= HI
HCFOET= HF
DAMOET= AD
RIOET= RI
RFOET= RF
GO TO 340
C
C 3. DESIGN EXTREME CONDITIONS
C TRANSMITTED HS
C CONDITIONS EXTREME
C
290 IDGNI= 2
IDGN2= 1
ICOND= 2
CALL STRSTA(IDGNI,IDGN2,ICOND,AK,HSE,WLE,HI,HF,AD,RI,RF,IFLAG)
IF(IFLAG.GT.0)GO TO 500
HCIEET= HI
HCFEET= HF
DAMEET= AD
RIEET= RI
RFEET= RF
C
C
C 4. DESIGN EXTREME CONDITIONS
C TRANSMITTED HS
C CONDITIONS OPERATIONAL
C
300 IDGNI= 2
IDGN2= 1
ICOND= 1
CALL STRSTA(IDGN1,IDGN2,ICOND,AK,HSO,WLO,HI,HF,AD,RI,RF,IFLAG)
IF(IFLAG.GT.O)GO TO 500
HCIEOT= HI
HCFEOT= HF
DAMEOT= AD
RIEOT= RI
RFEOT= RF
GO TO 340
C
C
C REFLECTED
C
C 1. DESIGN OPERATIONAL CONDITIONS
C REFLECTED HS
C CONDITIONS OPERATIONAL
C
310 IF(IDGNl.EQ.2)GO TO 320
IDGNI= 1
IDGN2= 2
ICOND= 1
CALL STRSTA(IDGN1,IDGN2,ICOND,AK,HSO,WLO,HI,HF,AD,RI,RF,IFLAG)
IF(IFLAG.GT.O)GO TO 500
HCIOOR= HI
HCFOOR= HF
DAMOOR= AD
RIOOR= RI
RFOOR= RF
C
C 2. DESIGN OPERATIONAL CONDITIONS
C REFLECTED HS


__ ___






C CONDITIONS EXTREME
C
IDGNI= 1
IDGN2= 2
ICOND= 2
CALL STRSTA(IDGNI,IDGN2,ICOND,AK,HSE,WLE,HI,HF,AD,RI,RF,IFLAG)
IF(IFLAG.GT.O)GO TO 500
HCIOER= HI
HCFOER= HF
DAMOER= AD
RIOER= RI
RFOER= RF
GO TO 340
C
C 3. DESIGN EXTREME CONDITIONS
C REFLECTED HS
C CONDITIONS EXTREME
C
320 IDGN1= 2
IDGN2= 2
ICOND= 2
CALL STRSTA(IDGN1,IDGN2,ICOND,AK,HSE,WLE,HI,HF,AD,RI,RF,IFLAG)
IF(IFLAG.GT.O)GO TO 500
HCIEER= HI
HCFEER= HF
DAMEER= AD
RIEER= RI
RFEER= RF
C
C 4. DESIGN EXTREME CONDITIONS
C REFLECTED HS
C CONDITIONS OPERATIONAL
C
330 IDGN1= 2
IDGN2= 2
ICOND= 1
CALL STRSTA(IDGNI,IDGN2,ICOND,AK,HSO,WLO,HI,HF,AD,RI,RF,IFLAG)
IF(IFLAG.GT.O)GO TO 500
HCIEOR= HI
HCFEOR= HF
DAMEOR= AD
RIEOR= RI
RFEOR= RF
C
C-----------------------------------------------------------------------C
C COMPUTE THE PERFORMANCE OF THE BREAKWATER FOR
C THE FOLLOWING SITUATIONS:
C
340 IF(IDGN1.EQ.2)GO TO 350
C
C
C TRANSMITTED
C
C 1. DESIGN OPERATIONAL
C CONDITIONS OPERATIONAL
C PREVIOUS CONDITIONS OPERATIONAL NOT EXCEEDED
C
HSI= HSO
TSI= TSO
QPI= QPO






IF(IDGN2.EQ.1)THEN
HCP= HCFOOT
HCON= HCIOOT
ELSE
HCP= HCFOOR
HCON= HCIOOR
ENDIF
AT= HCON*((HCON/SS)+WIDTH)
ALP= WLO
CALL STRPER(HSI,TSI,QPI,HCP,AT,ALP,HST,TST,QPT,HSR)
IF(IDGN2.EQ.1)THEN
HTTOO=1 HST
TTTOOI= TST
QTTOO1= QPT
HTROO1= HSR
ELSE
HRTOO1= HST
TRTOO1= TST
QRTOO1= QPT
HRROO1= HSR
ENDIF
C
C 2. DESIGN OPERATIONAL
C CONDITIONS OPERATIONAL
C PREVIOUS CONDITIONS EXTREME CONDITIONS REACHED
C
HSI= HSO
TSI= TSO
QPI= QPO
IF(IDGN2.EQ.I)THEN
HCP= HCFOET
HCON= HCIOET
ELSE
HCP= HCFOER
HCON= HCIOER
ENDIF
AT= HCON*((HCON/SS)+WIDTH)
ALP= WLO
CALL STRPER(HSI,TSI,QPI,HCP,AT,ALP,HST,TST,QPT,HSR)
IF(IDGN2.EQ.1)THEN
HTTOO2= HST
TTTOO2= TST
QTTOO2= QPT
HTROO2= HSR
ELSE
HRTOO2= HST
TRTOO2= TST
QRTOO2= QPT
HRRO002= HSR
ENDIF
C
C 3. DESIGN OPERATIONAL
C CONDITIONS EXTREME
C PREVIOUS CONDITIONS EXTREME CONDITIONS REACHED
C
HSI= HSE
TSI= TSE
QPI= QPE
IF(IDGN2.EQ. )THEN
HCP= HCFOET


______ ____ __ __ ______ __ ___~___






HCON= HCIOET
ELSE
HCP= HCFOER
HCON= HCIOER
ENDIF
AT= HCON*((HCON/SS)+WIDTH)
ALP= WLE
CALL STRPER(HSI,TSI,QPI,HCP,AT,ALP,HST,TST,QPT,HSR)
IF(IDGN2.EQ.I)THEN
HTTOE= HST
TTTOE= TST
QTTOE= QPT
HTROE= HSR
ELSE
HRTOE= HST
TRTOE= TST
QRTOE= QPT
HRROE= HSR
ENDIF
GO TO 360
C
C 1. DESIGN EXTREME
C CONDITIONS OPERATIONAL
C PREVIOUS CONDITIONS OPERATIONAL NOT EXCEEDED
C
350 HSI= HSO
TSI= TSO
QPI= QPO
IF(IDGN2.EQ.1)THEN
HCP= HCIEOT
HCON= HCIEET
ELSE
HCP= HCIEOR
HCON= HCIEER
ENDIF
AT= HCON*((HCON/SS)+WIDTH)
ALP= WLO
CALL STRPER(HSI,TSI,QPI,HCP,AT,ALP,HST,TST,QPT,HSR)
IF(IDGN2.EQ.1)THEN
HTTEOI= HST
TTTEO1= TST
QTTEO1= QPT
HTREOI= HSR
ELSE
HRTEO1= HST
TRTEO1= TST
QRTEOI= QPT
HRREO1= HSR
ENDIF
C
C 2. DESIGN EXTREME
C CONDITIONS EXTREME
C PREVIOUS CONDITIONS EXTREME CONDITIONS REACHED
C
HSI= HSE
TSI= TSE
QPI= QPE
IF(IDGN2.EQ.1)THEN
HCP= HCFEET
HCON= HCIEET






ELSE
HCP= HCFEER
HCON= HCIEER
ENDIF
AT= HCON*((HCON/SS)+WIDTH)
ALP= WLE
CALL STRPER(HSI,TSI,QPI,HCP,AT,ALP,HST,TST,QPT,HSR)
IF(IDGN2.EQ.1)THEN
HTTEE= HST
TTTEE= TST
QTTEE= QPT
HTREE= HSR
ELSE
HRTEE= HST
TRTEE= TST
QRTEE= QPT
HRREE= HSR
ENDIF
C
C
C 3. DESIGN EXTREME
C CONDITIONS OPERATIONAL
C PREVIOUS CONDITIONS EXTREME CONDITIONS REACHED
C
HSI= HSO
TSI= TSO
QPI= QPO
IF(IDGN2.EQ. )THEN
HCP= HCFEET
HCON= HCIEET
ELSE
HCP= HCFEER
HCON= HCIEER
ENDIF
AT= HCON*((HCON/SS)+WIDTH)
ALP= WLO
CALL STRPER(HSI,TSI,QPI,HCP,AT,ALP,HST,TST,QPT,HSR)
IF(IDGN2.EQ.1)THEN
HTTEO2= HST
TTTEO2= TST
QTTEO2= QPT
HTRE02= HSR
ELSE
HRTEO2= HST
TRTEO2= TST
QRTEO2= QPT
HRREO2= HSR
ENDIF
C
C----------------------------------------------------------------------C
C OUTPUT
C
C INPUT DATA
C
360 WRITE(11,370)
370 FORMAT(IX,'
1 ',//10X,'DATA INPUT TO PROGRAM',/1X,'
2/)
WRITE(11,380)HSO,TSO,TPO,QPO,HSE,TSE,TPE,QPE,BS,WD,WIDTH,
1SS,WW,WR,W50


__ ___







380 FORMAT(4X,'OPERATIONAL INCIDENT WAVE CONDITIONS',/IX,
I'SIGNIFICANT WAVE HEIGHT (meters) ------------------- ',F7.2,/1X,
2'SIGNIFICANT WAVE PERIOD (seconds) ------------------- ',F6.2,/1X,
3'PEAK PERIOD (seconds) ------------------------------ ',F6.2,/1X,
4'SPECTRICAL PEAKEDNESS PARAMETER (Qp) ----------------
5F6.2,//4X,
6'EXTREME INCIDENT WAVE CONDITIONS',/IX,
7'SIGNIFICANT WAVE HEIGHT (meters) ------------------- ',F7.2,/1X,
8'SIGNIFICANT WAVE PERIOD (seconds) ------------------ ',F6.2,/1X,
9'PEAK PERIOD (seconds) ------------------------------ ',F6.2,/1X,
I'SPECTRICAL PEAKEDNESS PARAMETER (Qp) ----------------
2F6.2,//4X,'GENERAL PARAMETERS',/IX,
3'BOTTOM SLOPE AT STRUCTURE -------------------------
4F6.4,/1X,
5'WATER DEPTH AT STRUCTURE (meters) ------------------ ',F7.1,/1X,
6'INITIAL WIDTH OF STRUCTURE CREST (meters) ---------- ',F6.1,/1X,
7'STRUCTURE SLOPE -------------------------------------
8F6.3,/1X,
9'MASS DENSITY OF WATER (kg/m**3) -------------------- ',F7.1,/1X,
1'MASS DENSITY OF STONE (kg/m**3) ------------------- ',F8.1,/1X,
2'MEDIAN STONE MASS (kg) --------------------------- ',F8.1,/1X,
3' ",//)
C
C OUTPUT DATA
C
WRITE(11,390)
390 FORMAT(4X,'THE COMPUTATIONS MADE IN THIS PROGRAM ARE BASED',/2X,
1'PRIMARILY ON THE RESULTS OF LABORATORY TESTS WITH',/2X,
2'TRAPAZOIDAL STRUCTURES WITH FORWARD AND BACK SLOPES',/2X,
3'OF 1.5 (HORIZONTAL) ON 1 (VERTICAL). IN THIS VERSION ',/2X,
4'OF THE PROGRAM NO ATTEMPT HAS BEEN MADE TO ACCOUNT FOR',/2X,
5'SCALE EFFECTS.',//)
WRITE(11,400)
400 FORMAT(1X,'
1____ ',/1X,'
2 ',//2X,'STRUCTURE DESIGN BASED ON:')
IF(IDGNI.EQ.1)THEN
WRITE(11,410)
410 FORMAT(6X,'1) OPERATIONAL WAVE CONDITIONS')
ELSE
WRITE(11,420)
420 FORMAT(6X,'1) EXTREME WAVE CONDITIONS')
ENDIF
IF(IDGN2.EQ.1)THEN
WRITE(11,430)HSD
430 FORMAT(6X,'2) DESIRED TRANSMITTED SIGNIFICANT WAVE HEIGHT',/IOX,
1 'HST (meters) = ',F6.2)
ELSE
WRITE(11,440)HSD
440 FORMAT(6X,'2) DESIRED REFLECTED SIGNIFICANT WAVE HEIGHT',/1OX,
1 'HSR (meters) = ',F6.2)
ENDIF
C
450 IF(IDGN1.EQ.1.AND.IDGN2.EQ.1)THEN
WRITE(11,460)HSO,TSO,TPO,WLO,QPO,HCIOOT,RIOOT,HCFOOT,RFOOT,AT,
1SSNO,DAMOOT,HTTOO1,TSO,TTTOO1,TPO,QPO,QTTOO1,HTROOI,HCIOET,
2HCFOET,AT,DAMOET,HTT02,TSO,TTTOO2,TPO,QPO,QTTOO2,HTROO2,HSE,
3TSE,TPE,WLE,QPE,HCIOET,HCFOET,RFOET,AT,SSNE,DAMOET,HTTOE,TSE,
4TTTOE,TPE,QPE,QTTOE,HTROE
GO TO 500


_ __






ENDIF
IF(IDGNI.EQ.1.AND.IDGN2.EQ.2)THEN
WRITE(11,460)HS,TSTSO,TPO,WLO,QPO,HCIOOR,RIOOR,HCFOOR,RFOOR,AT,
1SSNO,DAMOOR,HRTOO1,TSO,TRTOO1,TPO,QPO,QRTOO1,HRROO1,HCIOER,
2HCFOER,AT,DAMOER,HRTOO2,TSO,TRT02,TPO,QPO,QRTOO2,HRROO2,HSE,
3TSE,TPE,WLE,QPE,HCIOER,HCFOER,RFOER,AT,SSNE,DAMOER,HRTOE,TSE,
4TRTOE,TPE,QPE,QRTOE,HRROE
GO TO 500
ENDIF
IF(IDGN1.EQ.2.AND.IDGN2.EQ.1)THEN
WRITE(11,460)HSO,TSO,TPO,WLO,QPO,HCIEET,RIEET,HCFEOT,RFEOT,AT,
1SSNO,DAMEOT,HTTEO1,TSO,TTTEO1,TPO,QPO,QTTEO1,HTREO1,HCIEET,
2HCFEET,AT,DAMEET,HTTEO2,TSO,TTTEO2,TPO,QPO,QTTEO2,HTREO2,HSE,
3TSE,TPE,WLE,QPE,HCIEET,HCFEET,RFEET,AT,SSNE,DAMEET,HTTEE,TSE,
4TTTEE,TPE,QPE,QTTEE,HTREE
GO TO 500
ENDIF
IF(IDGN1.EQ.2.AND. IDGN2.EQ.2)THEN
WRITE(11,460)HSOTSO,TSO,TPO,WLO,QPO,HCIEER,RIEER,HCFEOR,RFEOR,AT,
1SSNO,DAMEOR,HRTEO1,TSO,TRTEO1,TPO,QPO,QRTEO1,HRREOI,HCIEER,
2HCFEER,AT,DAMEER,HRTEO2,TSO,TRTEO2,TPO,QPO,QRTEO2,HRREO2,HSE,
3TSE,TPE,WLE,QPE,HCIEER,HCFEER,RFEER,AT,SSNE,DAMEER,HRTEE,TSE,
4TRTEE,TPE,QPE,QRTEE,HRREE
ENDIF
C
C OUTPUT FORMAT
C
460 FORMAT(/1OX,'FOR OPERATIONAL INCIDENT WAVES ',/2X,
I'SIGNIFICANT WAVE HEIGHT (meters) ------------------- ',F6.2,/2X,
2'SIGNIFICANT WAVE PERIOD (seconds) ------------------ ',F5.1,/2X,
3'PEAK PERIOD (seconds) ------------------------------ ',F5.1,/2X,
4'WAVE LENGTH (peak period) (meters)------------------ ',F6.1,/2X,
5'PEAKEDNESS PARAMETER, Qp,---------------------------
6F5.1,///2X,
7'THE FOLLOWING STRUCTURE AND WAVE PARAMETERS ARE FOR',/2X,
8'A STRUCTURE THAT HAS ONLY EXPERIENCED WAVE CONDITIONS',/,2X,
9'NO GREATER THAN OPERATIONAL',//2X,
I'CONSTRUCTED STRUCTURE CREST HEIGHT (meters) --------- ',F5.1,/2X,
2'INITIAL DIMENSIONLESS FREEBOARD, R,----------------- ',F6.2,/2X,
3'STRUCTUE CREST HEIGHT AFTER OPERATIONAL WAVES(meters) ',F5.1,/2X,
4'DIMENSIONLESS FREEBOARD AFTER OPERATIONAL WAVES ,R,- ',F6.2,/2X,
5'TOTAL STRUCTURE CROSS-SECTIONAL AREA (meters**2) -- ',F7.1,/2X,
6'OPERATIONAL SPECTRICAL STABILITY NO. ,Ns*,--------- ',F6.2,/2X,
7'AREA OF DAMAGE (meters**2) ------------------------ ',F7.1,//10X,
8'TRANSMITTED WAVES',/2X,
9'SIGNIFICANT WAVE HEIGHT (meters) ------------------- ',F6.2,/2X,
I'SIGNIFICANT WAVE PERIOD (seconds) --- BETWEEN',F5.1,' AND',
2F5.1,/2X,
3'PEAK PERIOD (seconds) ------------------------------ ',F5.1,/2X,
4'PEAKEDNESS PARAMETER, Qp, ---------- BETWEEN',F5.1,' AND',
5F5.1,//10X,
6'REFLECTED WAVES',/2X,
7'SIGNIFICANT WAVE HEIGHT (meters) ------------------- ',F6.2,/1X,
8'------------------------------------------------------------- -
9///2X,
1'THE FOLLOWING STRUCTURE AND WAVE PARAMETERS ARE FAR',/2X,
2'A STRUCTURE THAT HAS EXPERIENCED EXTREME WAVE CONDITIONS',//2X,
3'CONSTRUCTED STRUCTURE CREST HEIGHT (meters) --------- ',F5.1,/2X,
4'STRUCTUE CREST HEIGHT AFTER EXTREME WAVES(meters) -- ',F5.1,/2X,
5'TOTAL STRUCTURE CROSS-SECTIONAL AREA (meters**2) -- ',F7.1,/2X,


__ __ ___ ___ __ ___






6'AREA OF DAMAGE (meters**2) ------------------------ ',F7.1,//10X,
7'TRANSMITTED WAVES',/2X,
8'SIGNIFICANT WAVE HEIGHT (meters) ------------------ ',F6.2,/2X,
9'SIGNIFICANT WAVE PERIOD (seconds) --- BETWEEN',F5.1,' AND',
1F5.1,/2X,
2'PEAK PERIOD (seconds) ------------------------------ ',F5.1,/2X,
3'PEAKEDNESS PARAMETER, Qp, ---------- BETWEEN',F5.1,' AND',
4F5.1,//1OX,
5'REFLECTED WAVES',/2X,
6'SIGNIFICANT WAVE HEIGHT (meters) ------------------- ',F6.2,//1X,
7'----------------------------------------------------------- -,/ X
8,'------------------------------------------------------------- '
9///,10X,
I'FOR EXTREME INCIDENT WAVES ',/2X,
2'SIGNIFICANT WAVE HEIGHT (meters) ------------------- ',F6.2,/2X,
3'SIGNIFICANT WAVE PERIOD (seconds) ------------------ ',F5.1,/2X,
4'PEAK PERIOD (seconds) ------------------------------ ',F5.1,/2X,
5'WAVE LENGTH (peak period) (meters)------------------ ',F6.1,/2X,
6'PEAKEDNESS PARAMETER, Qp, ---------------------------
7F5.1,///2X,
8'CONSTRUCTED STRUCTURE CREST HEIGHT (meters) --------- ',F5.1,/2X,
9'STRUCTUE CREST HEIGHT AFTER EXTREME WAVES(meters) -- ',F5.1,/2X,
1'DIMENSIONLESS FREEBOARD AFTER EXTREME WAVES,R,------ ',F6.2,/2X,
2'TOTAL STRUCTURE CROSS-SECTIONAL AREA (meters**2) -- ',F7.1,/2X,
3'EXTREME SPECTRICAL STABILITY NO. ,Ns*,------------- ',F6.2,/2X,
4'AREA OF DAMAGE (meters**2) ------------------------ ',F7.1,//1OX,
5'TRANSMITTED WAVES',/2X,
6'SIGNIFICANT WAVE HEIGHT (meters) ------------------- ',F6.2,/2X,
7'SIGNIFICANT WAVE PERIOD (seconds) --- BETWEEN',F5.1,' AND',
8F5.1,/2X,
9'PEAK PERIOD (seconds) ------------------------------ ',F5.1,/2X,
1'PEAKEDNESS PARAMETER, Qp, ----------- BETWEEN',F5.1,' AND',
2F5.1,//O1X,
3'REFLECTED WAVES',/2X,
4'SIGNIFICANT WAVE HEIGHT (meters) ------------------ ',F6.2,//1X,
5'///)
500 STOP
END
C END MAIN *
C**********************************************************************C


--







C
SUBROUTINE WAVLEN(WD,T,L)
C
C----------------------------------------------------------------------
C SUBROUTION WAVLEN C
C WAVE LENGTH C
C C
C PURPOSE: C
C The purpose of this subroutine is to compute the wave length, C
C L, (linear theory) of a wave in water depth, WD, and with a C
C period, T. C
C C
C---------------------------------------------------------------------C
C
REAL L,LN
PI=3.14159
ACC= .001
G= 9.800
10 RTEST= WD/(G*T**2)
IF(RTEST.LT..0025)THEN
L= T*SQRT(G*WD)
GO TO 20
ENDIF
IF(RTEST.GT..08)THEN
L= (G*T**2)/(2.*PI)
GO TO 20
ENDIF
L= (T*SQRT(G*WD)+ (G*T**2)/(2.*PI))/2.
20 A= G*T**2
B= A/(2.*PI)
C= A*WD
E= 2.*PI*WD
DEL= 1.0
30 IF(DEL.GE.ACC)THEN
CL= C/L**2
EL= E/L
SECH2= (1.0/(COSH(EL)))**2
LN= L-((L-B*TANH(EL))/(I.+CL*SECH2))
DEL= ABS((LN-L)/L)
L= LN
GO TO 30
ENDIF
RETURN
END
C END SUBROUTINE WAVLEN *
C***********************************************************************




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs