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AD-A250 876 (AD-A2 0 876MISCELLANEOUS PAPER CERC-92-3
OVERTOPPING RATES FOR SEAWALLS
by
Donald L. Ward, John P. Ahrens
Coastal Engineering Research Center
- DEPARTMENT OF THE ARMYWaterways Experiment Station, Corps of Engineers
3909 Halls Ferry Road, Vicksburg, Mississippi 39180-6199
JUN 0 2 1992
Cantft racin 4 Configuration S
C, 4 igratton 6 ConLI ration
April 1992Final Report
Approved For Public Release; Distribution Is Unlimited
92-14363F, lN l iii ll
92 6 o4
Prepared for DEPARTMENT OF THE ARMYUS Army Corps of Engineers
Washington, DC 20314-1000
Destroy this report when no longer needed. Do not returnit to the originator.
The findings in this report are not to be construed as an officialDepartment of the Army position unless so designated
by other authorized documents.
The contents of this report are not to be used foradvertising, publication, or promotional purposes.Citation of trade names does not constitute anofficial endorsement or approval of the use of
such commercial products.
Form ApprovedREPORT DOCUMENTATION PAGE OMB No. o7o4-01
gatmeng ndmamitmfl~g*4 at E~d.~ndmpetlg ndreve -n I, mletn of gnformation. sjeni ommnts ed gthbudneinaetanoheaecofhnchuo,,n ,of 0Inlmatmon. in udw*n wursthon for dingthis b ~ith . to WaNngto II edqruae rSeS iwmvsLc w w or wge= Opeartoom a 'nd
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Oesighway. sute 104. Ai ot-- f0.4 . e td ie O c of anagmn and de.a oetw70 1) wh . DC Z053
1. AGENCY USE ONLY (Leave bimnk) 12. REPORT DATE 3. REPORT TYPE AND DATES COVERED
[_April 1992 IFinal report4. TITLE AND SUBTITLE S. FUNDING NUMBERS
Overtopping Rates for Seawalls
6. AUTHOR(S)
Donald L. Ward and John P. Ahrens WU No. 32432
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
USAE Waterways Experiment Station, Coastal Engineering REPORT NUMBER
Research Center, 3909 Halls Ferry Road, Vicksburg, Miscellaneous PaperMS 39180-6199 CERC-92-3
9. SPONSORING/ MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/ MONITORINGAGENCY REPORT NUMBER
US Army rps of Engineers, Washington, DC 20314-1000
11. SUPPLEMENTARY NOTES
Available from National Technical Information Service, 5285 Port Royal Road,Springfield, VA 22161
12a. DISTRIBUTION I AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
Approved for public release; distribution is unlimited.
13. ABSTRACT (Maximum 200 words)
Regression analysis is used to develop equations that are easy to use butreasonably accurate in calculating overtopping rates for seawalls. Data aretaken from physical model studies and include a wide range of seawall types andwave conditions. The seawalls are divided into seven basic groups, and re-gression coefficients are determined for each group.
The basic regression model estimates dimensional overtopping and providesa simple means of comparing performance of different seawall designs. Animproved model also is developed that provides improved correlation between adimensionless overtopping variable and the collected data.
14. SUBJECT TERMS IS. NUMBER OF PAGES
Coastal flooding Seawalls 66
Irregular wave overtopping 16. PRICE CODEOvertoDnina
17. SECURITY CLASSIFICATION 11S. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT
UNCLASSIFIED UNCLASSIFIED I I _j
NSN 7540-01-280-5500 Standard Form 298 (Rev 2-89)Prelcbe by ANSI Std 10.1S
210-102
PREFACE
The investigation described in this report was authorized as a part of
the Civil Works Research and Development Program by Headquarters, US Army
Corps of Engineers (HQUSACE). Work was performed under Work Unit 32432,
"Design of Revetments and Seawalls," at the Coastal Engineering Research
Center (CERC), US Army Engineer Waterways Experiment Station (WES).
Messrs. John H. Lockhart, Jr., and John G. Housley were HQUSACE Technical
Monitors. Dr. C. Linwood Vincent was CERC Program Manager.
The study was conducted by personnel of CERC under the general direction
of Dr. James R. Houston, Director, CERC, and Mr. Charles C. Calhoun, Jr.,
Assistant Director, CERC. Direct supervision was provided by Messrs. C. E.
Chatham, Chief, Wave Dynamics Division (WDD), and D. Donald Davidson, Chief,
Wave Research Branch (WRB), WDD. This report was prepared by
Messrs. Donald L. Ward, Principal Investigator, WRB, and John P. Ahrens,
Research Oceanographer, WRB. The models were operated by Messrs. Willie G.
Dubose, Engineering Technician, WRB, and John M. Heggins, Computer Technician,
WRB. This report was typed by Ms. Myra E. Willis, WRB, and edited by
Ms. Janean C. Shirley, Information Technology Laboratory, WES.
At the time of publication of this report, Director of WES was
Dr. Robert W. Whalin. Commander and Deputy Director was COL Leonard G.
Hassell, EN.
Acession ?or
U r S G A & ?
_~,ncedDTIC TA
Uhianno,).fledJuzti1ficztlo
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ailablitY Codes
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!I
CONTENTS
Page
PREFACE ............ .............................. .1
CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENT. . 3
PART I: INTRODUCTION ........ ...... ...................... 4
Background ......... ...... ......................... 4The Problem .......... ..... ......................... 5Purpose of Report ........ ...... ...................... 5
PART II: THE MODELS ........ ...... ....................... 7
Wave Flume ........ ........ ......................... 7Design of Models .......... .... ....................... 10Description of Seawall Configurations ... ............ .11Test Conditions and Collected Data .... .............. ... 16
PART III: DISCUSSION ........ ....................... .38
Basic Overtopping Equation ...... .................. .. 38Effect of Revetments in Front of Seawall .. .......... 40Effect of Recurve on Seawalls ..... ................ .. 50Improved Model ......... ....................... 52
PART IV: CONCLUSIONS ........ ....................... ... 62
REFERENCES ........... ............................ 63
APPENDIX A: NOTATION .............. ....................... Al
2rm i
CONVERSION FACTORS, NON-SI TO SI (METRIC)UNITS OF MEASUREMENT
Non-SI units of measurement used in this report can be converted to SI
(metric) units as follows:
Multiply By To Obtain
cubic feet 0.02831685 cubic metres
feet 0.3048 metres
pounds (mass) per 16.01846 kilograms percubic foot cubic metre
3
OVERTOPPING RATES FOR SEAWALLS
PART I: INTRODUCTION
Background
1. Seawalls are in common use along the coasts in many parts of the
country to protect property from erosion and/or inundation by the seas.
BecaLs.e of continuing coastal development and increasing property values, and
possibly from rising sea levels, use of seawalls is likely to continue and
expand.
2. Design of a seawall is critically tied to overtopping rate. A
structure designed to prevent all overtopping under severe storm conditions
will likely be too expensive to build. If occasional overtopping is per-
mitted, rate of overtopping must be calculated to determine expected damages
and design of drainage systems. Higher initial cost associated with increased
protection must be balanced against greater damages associated with less
protection.
3. Local requirements and aesthetics also may affect design of a
seawall, and overtopping rates are necessary to assess compromises involved
in satisfying these constraints. For example, at Roughan's Point,
Massachusetts (Ahrens, Heimbaugh, and Davidson 1986) and Virginia Beach,
Virginia (Heimbaugh et al. 1988), standard seawalls of sufficient height to
protect against wave action would block the ocean view and were considered
unacceptable. Alternative seawall configurations, coupled with improved
drainage systems, were designed based on overtopping rates determined through
physical model testing.
4. An extensive series of physical model tests has been conducted at
the US Army Engineer Waterways Experiment Station's Coastal Engineering
Research Center (CERC) to study performance of various seawall configurations.
The study was initiated by serious coastal flooding that occurred at Roughan's
Point and Revere, MA in February, 1978 (Hardy and Crawford 1986), and has
:ontinued due to the widespread problem of coastal flooding in the United
States.
4
The Problem
5. Design of seawalls is commonly based on data in the Shore Protection
Manual (SPM) (US Army Corps of Engineers 1984). These data were collected
from a series of laboratory tests using monochromatic waves and then plotted
in a series of graphs presented Ln the SPM. A serious problem with this
method is that ocean waves are not monochromatic; therefore, the data do not
reflect prototype conditions. Also, overtopping coefficients used with the
graphs have only been determined for a limited number of cases and interpola-
tion between values is difficult and inaccurate. Studies have indicated that
under certain conditions the SPM method will under-predict (Douglass 1986) or
over-predict (Gadd, Machemehl, and Maniban 1985) overtopping rates, but it is
not clear under which conditions overtopping will be under- or over-predicted.
6. Diversity in seawall designs greatly complicates determination of
overtopping rates. Although equations have been developed for simple desigis,
such as a straight vertical seawall, physical model tests are typically re-
quired for more complex geometries. Optimizing a design for a given location
then may become a very costly endeavor because of many configurations that may
be considered, such as variations in recurve, revetment height and width, and
design of caps or parapets.
Purpose of Report
7. The purpose of this report is to present methods for calculating
overtopping rates for common seawall types. A series of physical model
studies has been conducted using irregular waves and several seawall configu-
rations. Data from 13 configurations tested have been arranged into seven
groups with similar configurations within each group. Using regression
analysis, equations have been developed for each group to predict overtopping
rates. Configurations tested include vertical, stepped, and recurved sea-
walls, vertical seawalls with recurved parapets, and seawalls fronted by a
riprap revetment. In each case, an equation will be presented to quickly
estimate overtopping rates. Physical model studies still are required to
accurately determine overtopping rates for a given configuration exposed to a
specific set of storm conditions. However, the equations presented here will
prove useful in preliminary studips and for selecting among alternative
5
seawall designs, thereby reducing the extent of the physical model study.
8. Final selection of a seawall design will be based on numerous
additional factors, such as degree and frequency of wave exposure, foundation
conditions, beach use and access, aesthetics, and cost. These factors are
beyond the scope of this report.
6
PART II: THE MODELS
Wave Flume
9. With the exception of the stepped seawall tests, model studies were
conducted in CERC's 3.0-ft*-wide by 3.0-ft-deep by 150.0-ft-long wave flume
(Figure 1). The test section of the flume was divided into two channels, each
1.5 ft wide, with the model located in one channel and wave absorber material
placed in the other channel. Use of the wave absorber reduced reflected wave
energy and helped insure an incident wave spectrum with a minimum of contami-
nation. Irregular waves representing Joint North Sea Wave Project spectra
(Hasselman et al. 1973) were generated by a hydraulically actuated piston-type
wave maker controlled by a computer-generated signal. Wave data were
collected for each run using two arrays each consisting of three elec-
tronically driven resistance-type wave gages. One array was placed in the
channel with the model to record nearshore wave spectra, the other array was
located in front of the wave board to record the generated signal. Recorded
signals were separated into incident and reflected spectra by the method of
Goda and Suzuki (1976).
10. Tests for the model stepped seawall were conducted in CERC's 11.0-
ft-wide by 250-ft-long wave flume (Figure 2). A wave absorber comprised of
rock "ith a 1:6 slope was placed in the end of the flume away from the wave
generator. The width of the flume in the vicinity of the model was divided
into two 3.0-ft-wide outside channels and two 2.5-ft-wide center channels.
The center channels were empty and nIlowed wave energy to pass to the wave
absorber at the end of the flume. One of the outside channels was divided
into two 1.5-ft-wide channels. The model seawall was placed in one of the
1.5-ft-wide channels and three wave gages were placed in an array in the
channel to record water level fluctuations (waves). A single gage was placed
across from the model in the second 1.5-ft-wide channel, and a three-gage
array was placed across from the model in the other 3-ft-wide channel.
Irregular waves representing Texel-Marsen Arsloe (TMA) shallow-water spectra
(Hughes 1984) were generated by a hydraulically actuated piston-type wave
maker controlled by a computer-generated signal.
* A table of factors for converting non-SI units of measurement to SI
(metric) units is presented on page 3.
7
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Design of Models
11. Recent seawall studies at CERC have included a vertical seawall
with parapet at Roughan's Point, MA (Ahrens, Heimbaugh, and Davidson 1986), a
recurved seawall at Cape Hatteras, NC (Grace and Carver 1985), and a stepped
seawall with recurve at Virginia Beach, VA (Heimbaugh et al. 1988). These
seawall types were retested for this study at a 1:16 linear scale except for
the stepped seawall, which was tested at a 1:19 linear scale. Based on
Froude's model law (Stevens et al. 1942), the following model-to-prototype
relations were derived in terms of length (L) and time (T):
Model-to-Prototype Model-to-PrototypeCharacteristic Dimension Scale Relations (1:16) Scale Relations (1:19)
Length L Lr - 1:16 Lr = 1:19
Area L2 A, = 1:256 Ar = 1:361
Volume L3 Vr = 1:4,096 Vr = 1:6,859
Time T Tr = 1:4 Tr = 1:4.36
12. Using these relations, the following transference equation may be
derived to determine the scale size of armor units used in the studies.
(Wa) P (Ya)p ( Lp [ (Sa)p - 1
where
subscripts m,p = model and prototype values, respectively
W. = weight of an individual stone, pounds
7. = specific weight of an individual stone, pounds per cubicfoot
L,/Lp - linear scale of the model
S. - sipecific gravity of an individual stone relative to thewater in which the breakwater is constructed, i.e.,Sa = 7a/Yw
7w - specific weight of water, pounds per cubic foot
Scaling in the models assumed specific weights of 62.4 lb/ft3 for fresh water
used in the wave flume, 64.0 lb/ft3 for sea water at the prototype, and
165 lb/ft 3 for stone used in the model.
13. A calibrated container was placed behind the models to collect
water overtopping the structure. Water surface elevation in the overtopping
10
container was measured with a point gage before and after each test to deter-
mine total quantity of overtopping. Total quantity was divided by length of
test run to determine overtopping rates.
Description of Seawall Configurations
14. Seawall configurations tested have been divided into seven groups
that share similar characteristics. Each group is described and illustrated
below.
15. Group 1 seawalls are vertical walls with a recurved parapet and no
revetment (Figure 3). Design for this group was taken from configuration 1 in
the Roughan's Point, MA, study (Ahrens, Heimbaugh, and Davidson 1986).
Configuration I modeled the existing eastern seawall at Roughan's Point, which
has a crest height of 17.6 ft National Geodetic Vertical Datum (NGVD), with
the 1:100 slope beach intersecting the seawall at -0.48 ft NGVD. Water depths
at the toe ranged from 8.9 ft to 11.7 ft.
24 3
i76'NGVD
16-
U) 0 -
w 0-Lii 0
- 04>BEACH LINE Z M
0 (L0
0 ,
0
>0 0
-16 - 0 >
-241I-II27 26 25 24 23 22 21 20 19
DISTANCE ALONG TANK FLOOR, FT
Figure 3. Cross section of group 1 seawalls
16. Group 2 seawalls are vertical walls with a recurved parapet fronted
by a high revetment, or without the parapet if the revetment extends to the
top of the seawall (Figure 4). Designs for this group were taken from config-
urations 2, 3, and 10 in the Roughan's Point study (Ahrens, Heimbaugh, and
Davidson 1986). Configuration 2 modeled the existing eastern seawall at
Roughan's Point but added a three-layer riprap revetment with a 1:3 slope from
-3.5 ft NGVD to +14.0 ft NGVD and a 5-ft crest width. Configuration 3
11
16- 0
6 . -2
C- >I5.g A-G
0
DISTANCE ALONG TANK FLOOR,FT
a. Roughan's Point configuration 2
0
-2z
0C
V4
4.z
DISTANCE ALONG TANK FLOOR, FT
b. Roughan's Point configuration 3
1 02 4z
Wa 30'
00 >-55'NGVD4
AIG .4,
I I I I
DISTANCE ALONG TANK FLOOR, F7
LEGENDSYMBOL STORE WEIGHTS
Wo 2551 LIBWI 347 LB
W2 45 LB
c. Roughan's Point configuration 10
Figure 4. Cross sections of group 2 seawalls
12
modified the revetment to include a 6.5-ft-wide berm at 0.0 ft NGVD, and ex-
tended the revetment slope to intersect the seawall at +15.6 ft NGVD.
Configuration 10 replaced the Roughan's Point seawall with a vertical sheet-
pile seawall with a crest height of +17.0 ft NGVD. A three-layer, 1:3 riprap
revetment extended from -3.5 ft NGVD to the crest of the seawall with a 6.5-ft
crest width in front of the seawall.
17. Group 3 seawalls are vertical seawalls with a recurved parapet, a
fronting revetment with one or two berms, and may have a cap on the parapet
(Figure 5). Designs for this group were taken from configurations 4, 5, 6, 7,
and 8 in the Roughan's Point study (Ahrens, Heimbaugh, and Davidson 1986).
Configuration 4 had a 1:3, three-layer rubble revetment from -3.5 ft NGVD to
+8.0 ft NGVD, with a 25.5-ft-wide berm in front of the seawall. The berm in
the armor layer extended well past the horizontal portion of the two under-
layers, resulting in an armor layer up to 9.0 ft thick. Configuration 7 was
the same as configuration 4, but a 1-ft-high cap was added to the parapet in
configuration 7. Configuration 6 was similar to configurations 4 and 7 (in-
cluded the 1-ft-high cap on the parapet) but the revetment extended to a
height of +10.0 ft NGVD, which reduced the berm width to 23.5 ft. Configura-
tion 5 placed a three-layer revetment at a 1:3 slope from -4.0 ft NGVD to +6.0
ft NGVD, followed by a 20-ft-wide berm, a 1:2 slope from +6.0 ft NGVD to +10
ft NGVD, and an 18-ft-wide berm.
3
-z4 .17 I, I I
Q0
0 0
0
W o
wE 45
a. Rouha ' oin Iofguaio t
DISTANCE ALONG TANK FLOOR, FT
LEEND1
SYMBOL STONE WEIGNT,105 0
2551 LB
347 Le
W2 45 LB
a. Roughan's Point configuration 4
Figure 5. Cross sections of group 3 seawalls (Sheet 1 of 3)
13
>00 a - PD2
0 0
4IT0C ALONG TAK0LR~
2 7 2~~~5 LBS3 22 21 2
b. ~ ISAC ALugan G PoiN cLonfigrto
LEGEND
24 o27~~~A 26 2 4 23 2 1 2
IITAf ALN AKF0-F
LEGENDSSUBI. SONE EGM,4 5
z25s1'LB
-33 ~ 34 LB /j-
214
0o to
02 a
'24 0
27 26 25 2 23 22 21 20 19
DISTANCE ALONG TANK FLOOR, FT
LEEND
SYMBOL STONE WEIGNT.W5 0
W, 2551 LBWa 34? LB
VIZ 45 LB
d. Roughan's Point configuration 7
24- 3
-2
0253 LU5
-115
18. Group 4 (Figure 6) and group 5 (Figure 7) seawalls are recurved
seawalls with revetments. Models of these seawalls were originally used in
the Cape Hatteras study (Grace and Carver 1985) as configurations R4S3 and
R4S2, respectively. Because the Cape Hatteras study used monochromatic waves
and did not include overtopping, the models were retested in a flume with
spectral capabilities, and measurements were made of overtopping rates.
Results of these tests are reported in Ahrens (1988) as Gape Hatteras seawall
configurations 1 and 2, respectively. A riprap revetment in front of a
prestressed concrete sheet-pile cutoff wall extended to an elevation of +8.0
ft. The concrete recurved seawall was an additional 11.2 ft high for
configuration 1 and 10.9 ft high for configuration 2. Both seawalls have the
same recurved section, but configuration 1 has a 1.3-ft seaward extension to
the overhang at the crest, and the extension increased the crest height of the
seawall by 0.3 ft.
19. Group 6 seawalls are vertical walls with a revetment (Figure 8).
This configuration was tested in the Cape Hatteras study (Grace and Carver
1985) as configuration R4SI, and retested with spectral waves and measured
overtopping in Ahrens (1988) as Cape Hatteras seawall configuration 3. The
model used the same revetment and prestressed concrete sheet-pile cutoff wall
that was used for seawall groups 4 and 5, but a vertical wall extending
11.2 ft above the cutoff wall was used in place of the recurved seawall.
20. Group 7 seawalls are stepped seawalls with a recurved parapet and a
fronting revetment (Figure 9). This configuration was tested in Phase II of
the Virginia Beach study (Heimbaugh et al. 1988) for hurricane and northeaster
storm conditions (long wave periods), then retested for this report to provide
a wider range of wave conditions.
Test Conditions and Collected Data
21. Tables 1 through 7 list test conditions and collected overtopping
rates for seawall groups 1 through 7, respectively.
16
E1.2
U :3 -~SIMLATED C T-OF$ WALL
Figure 6. Cross section of group 4 seawalls
2717
MATERIAL CHARACTERISTICS
MODE L PROTOTYPE
W, @21.LESIAFOOSATI(?CPCF ", oM-lO#NSIAPOOSAT ITCCF
O02-71-1,1STOMEIAT IS5PCIF W m- 1.4-TON TONE AT I6SVCF
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CH4 E 1. -9 2
C45 EL .7 EL1
CI46EL 62ftI
Figure 9. Cross section of group 7 seawalls
18
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37
PART III: DISCUSSION
Basic Overtopping Equation
22. Using a simplified theoretical analysis, Jensen and Juhl (1987)
determined that a reasonable conceptual model for wave overtopping rate Q
and dimensionless freeboard F' for breakwaters could be described by a simple
exponential relationship of the form
Q = Q, exp(C F) (1)
where Q0 and C1 are determined from regression analysis, and dimensionless
freeboard is defined as
F' = F/H s (2)
where F is freeboard (vertical distance from still-water level (SWL) to top
of structure), and H. is incident significant wave height.
23. Although the analysis in Jensen and Juhl (1987) was based on
laboratory data for breakwaters, the data included breakwaters with crown-
walls, which are hydraulically similar to seawalls with revetments. It is
interesting that Owen (1980, 1982a, 1982b) used a nondimensional equation of
the same basic form as Equation 1, and Jensen reported overtopping rates in
nondimensional form in an earlier paper (Jensen 1984). However, Jensen and
Juhl (1987) were unable to determine a nondimensional form that worked well
for all configurations tested, and therefore used a dimensional overtopping
rate. Similarly, Ahrens and Heimbaugh (1988) were unable to normalize Q to
improve correlation over use of a dimensional Q for all seawall configura-
tions tested with Equation 1.
24. One advantage of using a dimensional overtopping rate is that it
allows easy correlation with potentials for flooding or structural damage such
as those tabulated in Fukuda, Uno, and Irie (1974) or Goda (1985). Fukuda,
Uno, and Irie measured and filmed waves overtopping coastal structures during
severe storms. The films then were shown to a panel of coastal experts who
determined the degree of danger posed by the overtopping to a person, a car,
or a house located 10 ft behind the structure. Averaging the results of the
panel, it was determined that overtopping rates greater than 0.002 cfs/ft were
dangerous for a walking person, greater than 0.0002 cfs/ft would prohibit a
38
vehicle from driving past at high speed, and damage to a house could be ex-
pected at overtopping rates greater than 0.0007 cfs/ft. These rates could be
increased by a factor of 10 for a location 30 ft behind the structure. Goda
studied storm damage to coastal structures and found that overtopping rates in
excess of 0.5 cfs/ft were dangerous to structures with concrete sides and
crest.
25. Ahrens and Heimbaugh (1988) defined dimensionless freeboard as
F2 = F1/(HmLp)1'3 (3)
where Hm. is zeroth moment wave height measured near the toe (groups 1
through 6) or at the toe (group 7), and L is local wavelength at the toe of
the structure calculated from linear wave theory using depth of water at the
toe (d.) and incident wave period of peak energy (TP). For all data groups
except stepped seawalls (group 7), incident TP was an assumed period based
on the known peak period generated at the wave board, which was assumed con-
stant in the wave flume. In the stepped seawall tests, incident TP was
determined from the three-gage array located across from the structure. F' is
seen to be a ratio of structure freeboard to a form of wave severity.
26. Equation 3 is an efficient definition of relative freeboard because
it includes information about water level, structure height, and wave condi-
tions in just one term. An interesting and useful consequence of this defini-
tion is that it provides an easy reference to inundation of the structure.
Observations made during the test runs indicated that as wave conditions be-
came more severe for a given freeboard, the structure would become flooded and
changes in structure geometry had little effect on overtopping rates. This
inundation effect was observed with dimensionless freeboards less than 0.3.
27. Equation 1 was linearized for the regression analysis by taking the
natural logarithm of each side, which tends to decrease the relative impor-
tance of tests with high overtopping rates. Also, measurements of overtopping
volume have a greater percert error for low overtopping rates. A weight func-
tion was therefore employe( o reflect the greater importance of tests which
produced high overtopping rates. The weight function is defined as
weight function = f (Q x 100) + 1 (4)
39
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49-
(group 1), a vertical seawall with a high revetment (group 2), and a vertical
seawall with a berm revetment (group 3). The seawalls were all topped with a
recurved parapet with the exception of one configuration in group 2 in which
the revetment extended Ir the top of the seawall.
31. Dissipation of wave energy by a rubble revetment is very difficult
to predict quantitatively due to the turbulent flow regime, nonlinear wave
forms, and complicated boundary conditions. Several qualitative effects
should be noted, however. As a wave runs up a revetment, the water penetrates
into the rubble mound. Damping of -ave energy occurs within the rubble due to
friction with the rock surfaces, and expansion, contraction, and eddy diffus-
ion losses due to irregularities in the interstices. Energy losses also occur
along the surface of the rubble both from surface friction and the increase in
turbulence caused by surface roughness. After the rubble has filled with
water, a "ramp effect" occurs whereby succeeding wave bores may more readily
flow up the revetment (Goda 1985) although mixing within the rubble continues
due to penetration of wave energy into the rubble.
32. In Figure 18, it is clear that revetments aid in the dissipation of
wave energy, as expected. Less obvious, however, are the comparative effects
of a wide bermed revetment versus a higher revetment without a berm. While
both revetments may contain similar quantities of stone, the bermed revetment
was found in these tests to reduce overtopping more effectively than the high
revetment. Clearly, runup reaching the top of the high revetment flowed over
the seawall, as the revetment extended to the top of the seawall. The berm
revetment was lower and more water reached the top of the revetment, but over-
topping was impeded by the portion of the seawall extending higher than the
revetment.
Effect of Recurve on Seawalls
33. Figure 19 illustrates overtopping rates based on Equation 1 for the
three configurations of the Cape Hatteras study (Grace and Carver 1985; Ahrens
1988) reported herein as groups 4, 5, and 6, and the stepped seawall with
recurve used in the Virginia Beach study (Heimbaugh et al. 1988) and reported
herein as group 7. The revetment fronting the Cape Hatteras seawalls was the
same for each group, but group 4 had a recurved seawall with overhang, group 5
had the same recurved seawall but without the overhang, and group 6 was just a
50
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Ifl I~jLo
Lo -4
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It W
ul 0/ -i~
IT 0
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51I
vertical wall. The group 7 seawall was similar to group 4 (with the over-
hang), but used a smaller revetment and added a series of steps between the
revetment and the recurve.
34. The improvement in use of a recurved seawall over a vertical wall
is obvious in Figure 19. The addition of the overhang on group 4 also sub-
stantially reduced the quantity of overtopping. Both the recurve and the
overhang were effective at impeding the horizontal, shoreward progression of
wave energy by redirecting the energy vertically and/or seaward.
35. Figure 19 also compares the effectiveness of the large revetment in
group 4 to the small revetment and steps in group 7. Although it is difficult
to make direct comparisons due to differences in configuration of the
recurves, it appears that the larger revetment is more effective at dissi-
pating wave energy than the stepped seawall. A stepped seawall is intended to
dissipate energy by disrupting the runup and increasing losses due to
turbulence. Observations made during testing of the stepped seawall indicated
the steps may have been too small to effectively disrupt the flow, therefore
the stepped seawall may have compared more favorably if larger steps had been
tested. Revetments have an advantage over steps in that the stones not only
disrupt flow along the surface of the revetment, but wave energy is also
damped within the rubble mound.
Improved Model
36. Equation 1 is recommended for its ease of use and ready correlation
to tabulated values of inundation and damage. However, improved regression
correlation was obtained by using an equation of the form
Q1 =Q exp(C F + C2 X) (5)
where Qo' and C2 are dimensionless regression coefficients, X may be any
of several dimensionless variables which improve the predictive ability of the
model, and Q' is a dimensionless overtopping rate defined as
Q, = QI_(g*H.3) (6)
where g is gravitational acceleration, and other terms were defined for
Equation 1. Many different terms were tried for X and the terms that
offered the best correlation coefficients are listed in Table 9. By comparing
52
Table 9
Regression Coefficients, Secondary Variables, and Correlation
Coefficients for Seawall Groups 1 Through 7
Correlation
Group No. X __ C, C, Coefficient
1 F/d, 0.338 - 7.385 - 2.178 0.923
2 (H=o/Lo)112 0.308 -10.732 - 6.629 0.794
3 (Hue/to) I 2 1.000 -14.371 -11.411 0.841
4 WB/L P 1.000 -12.690 -20.870 0.943
5 (HIL/Lo) I O.S41 -11.702 - 5.771 0.947
6 H.m/DB 1.000 - 7.558 - 1.366 0.918
7 (H.o/L) 11 2 1.000 -11.174 -10.664 0.948
the correlation coefficients in Table 9 for the improved model to the
correlation coefficients in Table 8 for the basic model, the improvement
offered by this model is evident. Only data sets 2 and 3 have correlation
coefficients less than 0.9, which is reasonable considering the range of
structure configurations included in these two groups.
37. In four of the data sets, a wave steepness parameter was chosen for
the secondary variable, defined by
X = (7)
where L, is deepwater Airy wavelength based on the wave period of peak
energy. The influence of wave steepness indicates that surf conditions play
an important role in the runup and overtopping of these structures. For two
of the data sets (4 and 6), the rubble berm plays an important role, as
indicated by the secondary variables. For data sets 4 and 6, the secondary
variables that best improved the correlation between observed and predicted
values were WB/LP and H.o/d B , respectively, where WB is berm width and
dB is water depth over the berm. It was found that if water depth over the
berm was small, then changes in water depth were quite important (data set 6),
but for deeper water the berm width was more critical (data set 4).
38. Figures 20 through 26 illustrate dimensionless overtopping rates
for a range of freeboards for each of the seven data groups. The three curves
53
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shown on each figure illustrate a range of values of the secondary variables.
It is important to note that several of the curves are extended beyond the
range of the test data. This is only for illustrative purposes to demonstrate
the effects of the secondary variable. In practice, the regression curves
presented herein should not be used beyond the range of the test data from
which the equations were obtained.
61
PART IV: CONCLUSIONS
39. A conceptually simple yet efficient equation has been developed
which incorporates information on wave conditions, structure height, and water
level in the determination of overtopping rates. This equation has been used
with regression analysis to determine overtopping rates for a variety of sea-
wall types over a wide range of sea conditions with reasonable accuracy.
Although physical model testing is still recommended for final stages in the
design of a structure, these equations are sufficient for preliminary stages
in the design process and for comparing the effects of different structure
types.
40. An improved model also is presented which provides a somewhat
better correlation with the data. Although the secondary variable in the
improved equation makes it difficult to compare results from different struc-
ture types, this equation may be used to provide an improved estimate of
overtopping rates for a specific structural design and a given set of sea
conditions.
41. Although the test conditions employed in this analysis cover a widerange of sea conditions, it must be emphasized that the equations should not
be used outside the ranges tested unless physical model tests are used to
confirm the results.
62
REFERENCES
Ahrens, J. P. 1988. "Methods to Reduce Wave Runup and Overtopping of Exist-ing Structures," Technical Report REMR-CO-7, US Army Engineer WaterwaysExperiment Station, Vicksburg, MS.
Ahrens, J. P., and Heimbaugh, M. S. 1988. "Seawall Overtopping Model,"Proceedings. 21st Coastal Engineering Conference, Malaga, Spain.
Ahrens, J. P., Heimbaugh, M. S., and Davidson, D. D. 1986. "Irregular WaveRunup and Overtopping of Seawall/Revetment Configurations, Roughans Point,Massachusetts," Technical Report CERC-86-7, US Army Engineer WaterwaysExperiment Station, Vicksburg, MS.
Douglass, S. L. 1986. "Review and Comparison of Methods for EstimatingIrregular Wave Overtopping Rates," Technical Report CERC-86-12, US ArmyEngineer Waterways Experiment Station, Vicksburg, MS.
Fukuda, N., Uno, T., and Irie, I. 1974. "Field Observations of Wave Over-topping of Wave Absorbing Revetment," Coastal Engineering in Japan, Vol 17.
Gadd, P. E., Machemehl, J. L., and Maniban, V. 1985. "Comparison of WaveOvertopping Prediction to Measurements from Large-Scale Model Tests,"Proceedings of Arctic '85, San Francisco, CA.
Goda, T., and Suzuki, Y. 1976. "Estimation of Incident and Reflected Wavesin Random Wave Experiments," Proceedings of the 15th Coastal EngineeringConference, Honolulu, HI, pp 828-845.
Goda, Y. 1985. Random Seas and the Design of Maritime Structures, Universityof Tokyo Press, Tokyo, Japan.
Grace, P. J., and Carver, R. D. 1985. "Seawall and Revetment StabilityStudy, Cape Hatteras Lighthouse, North Carolina," Technical Report CERC-85-12,US Army Engineer Waterways Experiment Station, Vicksburg, MS.
Hardy, T. A., and Crawford, P. L. "Frequency of Coastal Flooding at RoughansPoint, Broad Sound, Lynn Harbor, and the Saugus-Pines River System," inpreparation, US Army Engineer Waterways Experiment Station, Vicksburg, MS.
Hasselmann, L., et al. 1973. "Measurements of Wind-Wave Growth and SwellDecay During the Joint North Sea Wave Project (JONSWAP)," DeutschesHydrogrephisches Institute, Hamburg, Germany.
Heimbaugh, M. S., Grace, P. J., Ahrens, J. P., and Davidson, D. D. 1988."Coastal Engineering Studies in Support of Virginia Beach, Virginia, BeachErosion Control and Hurricane Protection Project, Report I: Physical ModelTests of Irregular Wave Overtopping and Pressure Measurements," TechnicalReport CERC-88-1, US Army Engineer Waterways Experiment Station, Vicksburg,MS.
63
Hughes, S. A. 1984 (Dec). "The TMA Shallow-Water Spectrum Description and
Applications," Technical Report CERC-84-7, US Army Engineer Waterways
Experiment Station, Vicksburg, MS.
Jensen, 0. J. 1984. "A Monograph on Rubble Mound Breakwaters," Danish
Hydraulic Institute, Denmark.
Jensen, 0. J., and Juhl, J. 1987. "Wave Overtopping on Breakwaters and SeaDikes," Proceedings. International Conference on Coastal and Port Engineeringin Developing Countries, Beijing, China.
Owen, M. W. 1980. "Design of Seawalls Allowing for Overtopping," ReportNo. EX 924, Hydraulics Research Station, Wallingford, England.
1982a. "The Hydraulic Design of Sea-Wall Profiles,"Proceedings. International Coastal Engineering Conference, University ofSouthhampton, England.
1982b. "Overtopping of Sea Defenses," Proceedings of Inter-national Conference on Hydraulic Modeling of Engineering Structures, Coventry,England.
Shore Protection Manual. 1984. 4th ed., 2 vols, US Army Engineer WaterwaysExperiwent Station, Coascal Engineering Research Center, US GovernmentPrinting Office, Washington, DC.
Stevens, J. C., Bardsley, C. E., Lane, E. W., and Straub, L. G. 1942."Hydraulic Models," Manuals on Engineering Practice No. 25, American Societyof Civil Engineers, New York, NY.
64
Appendix A: NOTATION
C2 Regression coefficient 'I
C2 Regression coefficient
dB Water depth over berm
d. Depth at the structure toe
F Dimensional freeboard
F' Dimensionless freeboard
g Gravitational acceleration
H., Wave height of the zeroth moment
HS Significant wave height
L/L- . Linear scale of the model
L. Deepwater Airy wavelength
LLocal wavelength at the structure toe
Q Dimensional overtopping rate per unit length of seawall
QV Dimensionless overtopping rate
Qo Regression coefficient
SA Specific gravity of an individual stone relative to the water in
which the breakwater is constructed
TP Wave period of peak energy density
W ?A Weight of an individual stone, lb
WB Width of berm
X Secondary variable
Specific weight of an individual stone, pcf
Specific weight of water, pcf
fIndicates quantity in parentheses is a truncated integer
Al
