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AD-A266 371 Technical Report RENIH-CO17!I ' 'II I~I 111 '11 II 11 April 1993
Ub Army Corpsof Engineers 7cWaterways Experiment
Station
Repair, Evaluation, Maintenance, and Rehabilitation Research Program
Use of a Rubble Berm for ReducingRunup, Overtopping, and Damageon a 1V to 2H Riprap Slope
Experimental Model Investigation
by Donald L. Ward, John P. AhrensCoastal Engineering Research Center
DT1CApproved For Public Release; Distribution Is Unlimited UL 0 199
93-14987
Prepared for Headquarters, U.S. Army Corps of Engineers
The following two letters used as part of the number designating technical reports of research publishedunder the Repair, Evaluation, Maintenance, and rehabilitation (REMR) Research Program identify thcproblem area under which the report was prepared:
Problem Area Problem Area
CS Concrete and Steel Structures EM Electrical and MechanicalGT Geotechnical El Environmental ImpactsHY Hydraulics OM Operations ManagementCO Coastal
The contents of this report are not to be used for advertising,publication, or promotional purposes. Citation of tradenames does not constitute an official endorsement or approval ofthe use of such commercial products.
W PRNTED ON RECYCLED PAPER
Repair, Evaluation, Maintenance, and Technical Report REMR-CO-17Rehabilitation Research Program April 1993
Use of a Rubble Berm for ReducingRunup, Overtopping, and Damageon a 1V to 2H Riprap Slope
Experimental Model Investigation
by Donald L. Ward, John P. AhrensCoastal Engineering Research Center Acce-,ion For
U.S. Army Corps of Engineers NTWi CRA&iWaterways Experiment Station DlTIC IAB'/k3909 Halls Ferry Road U:am iou icedVicksburg, MS 39180-6199 Justification
ByDis;ti ib,,:tion I
Availability Codes
Final reportApproved for public release; distribution is unlimited
Prepared for U.S. Army Corps of Engineers
Washington, DC 20314-1000
Under Work Unit 32415
/-
US Army Corpsof Engineers NWaterways Experiment •o ,• -• 'Station
ifllWt /"4SIi~~i • 1 II• /ll
•'VII•NENTJJ.PIJUUC AFFAIRS oFr•"CER yU S. ARMY ENGINEER
WATERWAYS EXPERIMENT STATLNH909 HALLS FERRY ROAD
YICIKSDURG, MIS.SISSPPI 29160-4199
' PIOE ;(601)634-25•02
MAIN. LAORT RESE•ARCH .C •M
Waterways Experiment Station Cataloging-in-Publication Data
Ward, Donald L.Use of a rubble berm for reducing runup, overtopping, and damage on
a lV to 2H riprap slope: experimental morsel investigation / by Donald L.Ward, John P. Ahrens, Coastal Engineering Research Center; preparedfor U.S. Army Corps of Engineers.
69 p.: ill.; 28 cm. -- (Technical report; REMR-CO-17)Includes bibliographical references.1. Embankments -- Models -- Testing. 2. Hydraulic models. 3. Shore
protection. 4. Ocean waves. I. Ahrens, John P. Il. United States.Army. Corps of Engineers. Ill. Coastal Engineering Research Center(U.S.) IV. U.S. Army Engineer Waterways Experiment Station. V. Re-pair, Evaluation, Maintenance, and Rehabilitation Research Program.VI. Title. VII. Series: Technical report (U.S. Army Engineer WaterwaysExperiment Station); REMR-CO-17.
PREFACE
The work described in this report was authorized by Headquarters,
US Army Corps of Engineers (HQUSACE), as part of the Coastal Problem Area of
the Repair, Evaluation, Maintenance, and Rehabilitation (REMR) Research
Program. The work was performed under Work Unit 32415, "Experimental Testing
of Methods for Reducing Wave Runup and Overtopping on Structures," for which
Mr. John P. Ahrens was Principal Investigator. Mr. John H. Lockhart, Jr.
(CECW-EH), was the REMR Technical Monitor for this work.
Mr. William N. Rushing (CERD-C) was the REMR Coordinator at the Direc-
torate of Research and Development, HQUSACE; Mr. James E. Crews (CECW-O) and
Dr. Tony C. Liu (CECW-EG) served as the REMR Overview Committee;
Mr. William F. McCleese, US Army Engineer Waterways Experiment Station (WES),
was the REMR Program Manager. Mr. D. D. Davidson, Wave Dynamics Divi-
sion (WDD), Coastal Engineering Research Center (CERC), WES, was the Problem
Area Leader.
The work was performed at WES, and this report was prepared by
Mr. Donald L. Ward and Mr. Ahrens, WDD, CERC, under the general supervision of
Dr. James R. Houston, Director, CERC, and Mr. Charles C. Calhoun, Jr.,
Assistant Director, CERC; and under the direct supervision of Mr. C. E.
Chatham, Chief, WDD, and Mr. Davidson, Chief, Wave Research Branch, WDD. The
models were operated by Mr. Robert L. Tingle, Jr., Laboratory Technician, WDD.
During publication of this report, Dr. Robert W. Whalin was Director of
WES. COL Leonard G. Hassell, EN, was Commander.
CONTENTS
Pap-e
PREFACE .......................... ................................. 1
CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENT ... ..... 3
PART I: INTRODUCTION ......................... .......................... 4
Background ........................... ............................ 4Purpose .......................... ........................... 4
PART II: DEFINITION OF TEST lkRAMETERS .......................... 5
PART III: THE MODEL ................... .......................... 11
Test Facility .................... ........................... 11Test Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Sounding Equipment ................. ........................ 16Signal Generation .................. ......................... .. 16
PART IV: TEST PROCEDURES AND TEST RESULTS ......... ............... .. 18
Selection of Test Conditions ........... ................... 18Test Procedures .................. .......................... .. 18Test Results ..................... ........................... 19
PART V: DISCUSSION AND ANALYSIS ............. .................... 21
Runup ........................ ............................... 21Damage Level ..................... ........................... 27
PART VI: CONCLUSIONS AND RECOMMENDATIONS ........ ................ .. 42
REFERENCES ......................... ............................... 44
APPENDIX A: DATA TABLES ...................... ......................... Al
APPENDIX B: EXAMPLE PROBLEMS ................. ....................... Bi
APPENDIX C: NOTATION ........................... Cl
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
inches 2.54 centimetres
pounds (mass) 0.4535924 kilograms
pounds (mass) per 16.01846 kilograms percubic foot cubic metre
square inches 6.4516 square centimetres
3
USE OF A RUBBLE BERM FOR REDUCING RUNUP. OVERTOPPING.
AND DAMAGE ON A 1V TO 2H RIPRAP SLOPE
Experimental Model Investigation
PART I: INTRODUCTION
Background
1. Erosion of exposed soil embankments by waves and currents is a
serious problem along coastal and inland shores. A protective revetment of
graded quarry stone or "riprap" is commonly used to provide shore protection
because of its relatively low cost, durability, and availability, and because
the roughness and porosity of the stone is effective in dissipating wave
energy and runup.
2. Rising water levels, larger boat wakes, and increasing values of
land protected by revetments may necessitate improvements to a revetment to
increase the prctection provided. One method of improving the performance of
a revetment is to add an attached berm in front of the revetment. Unfortu-
nately, there is very little design guidance on the use of revetments with
fronting berms.
Purpose
3. The purpose of this investigation was to develop design guidance on
methods of reducing runup and overtopping of revetments based on data col-
lected from laboratory tests of wave runup and overtopping on riprap revet-
ments with a slope of 1:2 (lV to 2H). Tests were conducted in a wave flume
with spectral capabilities at the Coastal Engineering Research Center (CERC)
of the US Army Engineers Waterways Experiment Station (WES) in Vicksburg, MS.
4
PART II: DEFINITION OF TEST PARAMETERS
4. Inconsistencies among authors in notations, definitions of
parameters, and the methods by which a value for a parameter is obtained
greatly complicate the task of comparing results from different studies. In
this report, notations will follow guidelines published by the International
Association for Hydraulic Research in its "List of Sea State Parameters"
(1986). Additional parameters, definitions, and method used to determine the
value of certain parameters, are given below.
5. Wave heights used in this report are the heights of the zeroth
moment (H.o) and are obtained as four times the square root of the zeroth
moment of the potential energy spectrum. The H.o's of the incident spectra
are separated from the H1 o's of the reflected spectra by the method of Goda
and Suzuki (1976), using a three-gage array. Two arrays are used, one to
measure the Hmo's near the wave board (Array 1) and one near the structure
toe (Array 2).
6. Peak period (TP) is the wave period associated with the highest
energy density of the spectrum. This TP was obtained by dividing the
spectrum into 256 bands and taking the reciprocal of the midpoint frequency
causing the highest energy density over 11 adjacent bandwidths.
7. Wave heights and periods are frequently reported in other investiga-
tions in terms of significant wave height (H.) and average wave period (Tz),
where H. is the average of the one-third highest waves. Both P, and T.
are included in the data in this report to simpiiry comparison to other inves-
tigations. Average wave periods in this report were determined as
Tz= (1)
where mo and m2 are the zeroth and second moments of the potential energy
spectrum, respectively.
8. The spectral width or peakedness determined from the wave record is
given as QP , defined by Goda (1970) as
* For convenience, symbols and abbreviations are listed in the Notation
(Appendix C).
5
2 )2 f f[S(f)12 df (2)
where f is frequency and S(f) is the wave spectral density function for
the given frequency.
9. The surf parameter, the ratio of structure slope to square root of
wave steepness, is frequently used as an indicator of wave conditions at the
structure (Battjes 1974) and as a means of nondimensionalizing the wave
period. The surf parameter is defined as
tan a2 7rI/2 3
or, equivalently,
tan a
(H)1/2 (4)LO]
where
- surf parameter
tan a - tangent of the angle of the revetment to the horizontal
g = acceleration of gravity
L, - deepwater wavelength determined from the wave period, T
The wave height (H) and period used to determine ý in this report are H.L
and TP . The physical rationale for this parameter is discussed in Battjes
(1974).
10. The reflection coefficient is commonly defined •s the ratio of
reflected wave height to incident wave height. This definition is clearly
inappropriate when reflected and incident wave neights are dcscribed by
different spectra. Reflection coefficients were therefore determined by the
energy of the respective spectra, following the method of Goda and Suzuki
(1976).
Kr 65)
where Kr is the reflection coefficient and ER and El are the energy of
the reflected and incident spectra, respectively.
11. Reflected wav- aeight is obtained as the product of the reflection
coefficient and the i,-ident wave height.
Hr = KI HMo (6)
where 19 is the reflected wave height.
12. Runup (RP..) is defined as the vertical distance above the still-
water level (swl) that a wave surges up the revetment, or the upper limit of
"green" water since it does not include spash or spray. The elevation of
maximum runup was determined visually and then measured with a point gage.
13. The berm in front of the revetment is described by its height and
width. Berm width (WB) is defined as the distance along the horizontal top of
the berm. Height of the berm (hE) is defined as the vertical distance from
the toe of the revetment without the berm to the top of the berm.
14. Figure 1 illustrates a typical damage profile on a riprap slope.
An area of erosion (A2 ) is seen near the still-water level, with the stones
displaced from the area of erosion being deposited on the lower slope (A3 ) or,
particularly on very flat slopes, on the upper slope (A,). Damage to the
revetment was determined based on the area of erosion.
15. To obtain the respective areas, the six sounding points on each of
the horizontal sounding lines (paragraph 23) were averaged to give a single
cross-sectional profile of the slope. The points on the profile then were
connected by cubic splines, and the before- and after-testing profiles
compared. The area of erosion was determined as the area between the two
curves where the after-testing curve lay below the before-testing curve. The
area was calculated by integrating between the two lines. The damage profile
from TP - 2.25-sec, Hno - 0.50 ft wave conditions is shown in Figure 2.
16. Damage to the revetment was defined by two methods: maximum per-
pendiculat penetration of the erosion into the armor layer (emax) and S2
damage.
S A2 (7)
7
cc EN wU
\c
LLJ
-4
(IJ
w
cc 4
CE
N N 0
N~ zN N
Nl m
N. N. N -- a:
(ELI
N N 0co p o t T N ) a N NJu q c) \
0 0icCL
(4 Hl3 N:~o
9 i
where (D,) 5 0 is the nominal diameter of the median armor stone size, defined
as
(Dý o50 ! ()
where W50 is the median armor stone weight and w, is the unit weight of
the armor stone.
10
PART III: THE MODEL
Test Facility
17. All tests were conducted in a 3.0-ft-wide* by 150-ft-long by 3.0-
ft-deep wave flume (Figure 3). A 1:20 slope was installed in the bottom of
the flume starting 36.5 ft from the wave board and extending for 10 ft,
followed by a 1:100 slope extending to the test structure.
18. The flume was divided lengthwise into two 1.5-ft-wide channels
starting 100 ft from the wave board and extending past the structure. A wave
absorber was placed in one channel while the structure was placed in the otner
channel (113 ft from the wave board) thus minimizing the amount of reflection
in the flume. An array of three wave gages was centered 21.5 ft in front of
the wave board to monitor the generated signal. A similar array was placed in
the side of the flume with the test structure, centered 104.5 ft from the wave
board, to be used in separating the incident and reflected wave trains. Wire
resistance staff gages were read at 10 Hz to monitor the water surface
elevation.
19. The wave flume was equipped with a piston-type wave generator
powered by an electro-hydraulic pump and controlled by a computer-generated
signal.
Test Structure
20. The test structure modeled a 1:2 slope of an impervious substratum
protected by a filter layer and a layer of riprap (Figure 4). Sand was glued
to a plywood board to provide the necessary roughness, and the board installed
in the flume to represent the existing slope. A 0.07-ft-thick layer of
crushed stone averaging 0.04 oz/stone was used for the filter layer. The
armor layer was 0.26-ft-thick and constructed of a crushed limestone with a
specific gravity of 2.70, blocky to angular shape, and gradation of
A table of factors for converting non-SI units of measurement to SI
(metric) units is presented on page 3.
11
0 0
LI-.
14-4
I 0
>1
I .
LU -J
,22 LU-o 0~ C)z LU (L
I- U)
a 0- F
C)C
>W 0
<n ,
c12
-J 4J
UU -
z Q)0.0
0 0
0cr
wr
a:o U)
w (D CA
0 0
o 41(00
0j Or Cc 0n
U) UJ
um
U) CL
13,
D85 = 1.79 (9)DIS
where D85 and D1 5 are the 85- and 15-percentile diameters, respectively, on
a grain size distribution curve, with all armor stones falling within the
range
1 (0-W 5 0 < W <4 W50 (10)
where W is the weight of an individual stone. Gradation of the armor stone
used in this test series is shown in Figure 5.
21. Riprap is commonly sized by either the W50 or the nominal
diameter, (Dn) 50 . The armor layer used in these tests had a W50 of 0.22 lb
and a (Dn) 50 of 0.11 ft. These dimensions correspond to a design section
based on Hudson's equation (Hudson and Jackson 1962) for a design wave height
of 0.30 ft. Hudson's equation is given as
W, H 3W50 =oý-K (SR-i) cotO
where
H - monochromatic wave height
KRR - stability coefficient
Sr - relative specific gravity defined as specific gravity of armorstone divided by specific gravity of water
cot 8 - is the cotangent of the revetment slope
The stability coefficient for graded angular quarrystone for breaking waves is
taken from the Shore Protection Manual (SPM) (1984) as 2.2. For irregular
wave tests, design is based on the average of the highest 10 percent of waves
(H1 0 ). The design H10 of 0.3 ft corresponds to a H.. of about 0.24 ft.
22. The filter and armor stone layers were placed by dumping from a
small shovel in a manner to simulate prototype construction with a bucket
loader. The toe of the structure was 113 ft from the wave board.
14
CD~CD
CDC
00
CD41
CD
0)41V)LC
a,
CUU
- -4
0L 0
0)
(sql)W1 6 C8
1CD
Sounding Equipment
23. After placement, the filter and armor layers were surveyed by
sounding. The sounding apparatus consisted of a row of six vertical rods
spaced across the half of the flume width containing the test structure, with
the outer rods located 0.36 ft from the edge of the flume section and the
center rods spaced at 0.15-ft intervals. Each of the rods had a flat circular
foot, 0.10 ft in diameter, attached to the rod by a ball and socket joint.
The rods were used to take a row of soundings across the test structure. A
row of soundings was taken at horizontal intervals of 0.10 ft down the entire
slope of the revetment. Soundings were taken before and after each test.
Signal Generation
24. Software was developed at CERC to generate a spectral signal to
control the wave board. A signal was generated to simulate a JONSWAP (JOint
North Sea WAve Project) spectrum for each peak period using high- and low-
frequency cutoffs of 3.0 percent of the energy spectrum, high-side decay
factor of 0.09, low-side decay factor of 0.07, peak enhancement factor of 3.3,
and a wave height (H.) at least as large as the largest H., in the test
series. Different H.o's for the tests were obtained by varying the gain to
the electro-hydraulic pump controlling the wave board. Computer limitations
dictated that 30 min was the maximum signal length that could be stored;
therefore a separate signal was generated for each 30 min of a test run, using
a different random seed for each signal. The design spectrum is compared with
the generated spectrum in Figure 6 for the first 30 min period of the Tp -
2.25-sec test series.
16
36.0BOARD SPECTRUM 20.0 WATER SPECTRUM
SSIMULATED - SIMULATED32.0 DESIGN 18.0 - DESIGN
-% 28.0 '• 16.0
24.0 14.0
20.01 9 12.0
16.0 10.0
12.0
8.0 4.0
4.0 2.0
0.0 0.00.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
Frequency (Hz) Frequency (Hz)
WINDOW MODE - 1 (COSINE SQUARED) WINDOW FRACION - 0.10DETREND MODE - I (MEAN REMOVED) BANDS AVERAGED 10WAia..R DETREND FUNCTION - (0.2005E-03) + ( O.OOOOE+OO)*T + (O.OOOOE+00)e*(T*2)BOARD DETREND FUNCTION - (0.2325E-03) + ( O.OOOOE+OO)*T + (o.oooOE+00).C",,2)
UNIDIRECTIONAL WAVE TANK PISTON-TYPE GENERATOR DIGITAL DRIVER FiLE HEADER
OUTPUT FILE - OT2T225H6.DATGENERATOR TYPE - PISTONTRANSFER FUNCTION JOHN AHRENS CORRECTION - NOSPECTRUM - JONSWAP SPECTRUM 24.000 (INCHES) WATER DEPTH AT BOARD
2.250 (SEC) DESIGN PEAK PERIOD 0.030 XIOOPCT MO LOW FREQ. CUTOFF6.000 (INCHES) DESIGN HMO 0.970'XIOOPCT MO HIGH FREQ. CUTOFF3.30 GAMMA 1800 (SEC) TIME SERIES LENGTH
0.0700 SIGMA-LOW 10 (STEPS/SEC) UPDATE RATE0.0900 SIGMA-HIGH 256 UNES IN SOURCE SPECTRUM
0.00319 COMPUTED ALPHA 1989 - RAND. NO. GEN. SEED7.489 INCHES MAX. POS. BOARD STROKE 16.64 - (IN..2/HZ) DES. H20 SMAX
-8.228 INCHES MAX. NEG. BOARD STROKE 0.4444 - (HZ) DES. PEAK FREQ.0.3544 (HZ) LOW FREQ. CUTOFF1.0096 (HZ) HIGH FREQ. CUTOFF
Figure 6. Design and simulated spectra for first
30 min of 2.25-sec wave period tests
17
PART IV: TEST PROCEDURES AND TEST RESULTS
Selection of Test Conditions
25. Tests were conducted for water depths at the toe of the revetment
of 0.66, 0.76, and 0.86 ft, with offshore water depths of 2.00, 2.10, and
2.20 ft, respectively. Peak wave periods tested included 1.25-, 2.25-, 3.0-,
and 3.5-sec waves, and wave heights of the zeroth moment for each period
included 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, and 0.66 ft.
26. The length of each test run was 3,500 times the peak period of the
test, or until failure occurred, whichever came first. Failure was defined as
having the filter layer exposed. If failure was observed, tests with that
period were suspended and larger H.L's were not tested. All tests were con-
ducted with a JONSWAP spectrum (Hasselman et al. 1973).
Test Procedures
27. Each test was run in cycles of approximately 30 min each. For
example, the tests with a 2.25-sec peak wave period were run for 7,875 sec
(3,500 times 2.25 sec), or 131.25 min, in four cycles of about 30 min each
plus one short cycle to obtain the total time required. Wave data were
collected for approximately 500 waves near the beginning and end of each test.
A test was terminated if failure occurred.
28. Wave runup was observed for 256 sec near the middle of a test run.
The elevation of the maximum runup observed then was measured with reference
to a specified datum by use of a point gage.
29. Soundings were taken before and after each test, and the structure
was completely rebuilt whenever significant damage was observed. The pro-
cedure used for the tests is given below.
a. Place and survey the filter stone.
b. Place and survey the armor stone (including the berm, ifused).
c. Generate waves for 3,500 times the design peak period.
(1) Collect wave data for 500 waves near the start of thetest.
18
(2) Measure the runup.
(3) Collect wave data for 500 waves near the end of the test.If failure is expected, collect data for 500 waves priorto the expected failure.
d. Survey the riprap layer and berm.
e. Measure the water in the overtopping catch basin.
f. Rebuild the structure.
30. If the damage was slight, only the riprap layer and berm were re-
built, and the procedure for testing the next wave height was begun at step b,
above. The structure was always torn down and rebuilt from the plywood board
before the next series of tests with a new wave period was conducted.
Test Results
31. Test results are given in Appendix A as Tables Al, A2, A3, A4, and
A5. Tables Al and A2 list data from the tests of the revetment without berm;
Tables A3 and A4 list the results from the revetment with berm, and Table A5
lists damage to the structure as determined by the soundings.
32. As discussed in paragraph 27, multiple cycles were required for
each test run. Each cycle was labeled consecutively a, b, c, etc., and data
were collected during the first and last cycle. For example, tests with a
2.25-sec peak wave period, which required four cycles, had data collected
during cycles a and d. The letter following the run number in Tables Al
through A4 refers to the cycle during which the data were collected. The
structure was surveyed only after the end of the test run. Therefore the
damage information in Table A5 refers only to the run number and does not
include the cycles. Because damage to the berm was not considered as damage
to the revetment, only damage values for the upper part of the revetment
(above the level of the berm) are used in this report and are referred to
simply as S2
33. Scale effects in hydraulic model investigations are an important
consideration, but one that is difficult to address due to conflicting results
from different studies. For the range of tests presented here, Hudson and
Davidson (1975) indicate that stability numbers in the model tests will be
conservative by about 10 percent compared with prototype results, Burcharth
and Frigaard (1988) report that scale effects will be negligible, and
19
Broderick and Ahrens (1982) show that scale effects in the filter layer may
cause the runup values in the model tests to be greater than would be found at
prototype scales. Although scale effects are probably present in this data
set, it seems reasonable to assume that they are either negligible or
conservative.
20
PART V: DISCUSSION AND ANALYSIS
34. Wave runup and overtopping data were collected from a typical
revetment design subjected to spectral wave attack. As a means of reducing
the runup and overtopping of the revetment, a berm has been added in front of
the revetment. Comparisons of results of the tests with and without the berm
will be used to develop design guidance for use by the field to reduce runup
and overtopping of rubble revetments. Structural stability and reflection
characteristics also are being documented.
Wave Runup
35. Ahrens and McCartney (1975) documented the influence of surf
conditions on runup, and an empirical model using the surf parameter to
predict maximum runup has been developed by Ahrens and Heimbaugh (1988). The
empirical model is given by
Rma __a (12)
HMO I.0 + b
where R. is maximum wave runup and a and b are dimensionless runup
coefficients determined from regression analysis. Values of a and b were
determined as 1.022 and 0.247, respectively.
36. Analysis of the data collected in this study indicates that two
additional terms are needed to account for the influence of a berm. These
additional terms account for the height and width of the berm. Through data
analysis, it was found that the most effective variables were relative berm
width, W,/(H•L,)'2 , and relative berm height, h8 /d, . Multivariable analysis
was used to determine the following equation to predict the relative runup,
R__/H.
em x[ + +C (HmoLo) 1/2 * I (13)
where C0 , C, , and C2 are dimensionless regression coefficients given by
21
CO - 0. 669
C, = -10.4
C2 - -0.152
37. Equation 13 shows little or no systematic error in predicting R1,,
as shown by error analysis in Figures 7, 8, and 9. Figure 7 gives the ratio
of the predicted P,,ax to the observed Rmax as a function of the relative
berm width. Figure 8 has the same ordinate as Figure 7 plotted versus the
relative berm height. Figure 9 is an enlargement of the portion of Figure 8
for tests with berms so that the data point symbols can be more readily
identified. In Figures 7, 8, and 9, all data points are denoted by an integer
based on the relative wave size, Hmo/(Dn)50 . Since deterioration of the berm
increases with increasing wave size relative to the stone size, the purpose of
using the relative wave si7e in the figures is to see if berm derioration
affects che prediction of Rkax . Figures 7, 8, and 9 indicate there is
little systematic error in predicting Rmax for tests with a berm.
38. Figure 10 shows relative runup versus wave steepness, Hm./Lo , for
tests without a berm. On a planar riprap slope without a berm, wave steepness
is the most important variable influencing relative runup. Also shown in
Figure 10 is the portion of Equation 13 without the berm effects correction
factor, i.e.,
Rax = exp [Co + C1( ](14)
where C. and C, are the same as given with Equation 13. For tests without
berms, the berm effects term in Equation 13 drops out to leave Equation 14.
In Figure 10, it can be seen that the data scatter around Equation 14 appears
random, indicating a lack of systemic error associated with wave steepness
Figure 10 also shows the runup equation developed by Ahrens and Heimbaugh
(1988) for plane riprap slopes (Equation 12). In Figure 10 it can be seen
that Equation 12 overpredicts the relative runup but follows the data trend
well. It is believed that this difference is caused by systematic differences
in the visual readings of R.,, between ob--rvers.
39. The portion of Equation 13 containing the berm characteristics camT
be thought of as a runup reduction factor that can be defined by
22
r r)
E
4-4
C~j 0
o
E
m -i -0 o
wm
-M (0 0)
N ~ N ~ w4.
-0
144
C~ 0~
'-4
(Pemuesqo)xuwu/(pe)')pejd)x~sw8
23
0
t.'
-<f) (IM NC14 C)C'JN 4w cV)
4.4
0)
0
0 ~0
L4)
I>
cr 0w>
0
wa: 4j0
'44.0
0
-4041)
(0T f)cV) ('a - 01) OD t~-
(paAiesqo)xewH/(pejospe)d)x~w~u 'dflNf
24
C)
-vw r) c)- C)Cw)@a<\
-4"4u
0
0,it 4-)
0Y)
ob
.-.
a) r=
LI-4.
(o 0
4.4
ci
C~j Cr~l M qT CTC* V( J
() C0 c
o -
(pe~~sqoXeWI(Peojped~xwb 'n~n
25)
0 uU
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00
0 0 0
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(4
4)
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26
r = ex C2( ( ) 1/2 *bd-15
Figure 11 shows lines of constant r as a function of the relative berm width
and relative berm height over the range of data collected in this study based
on the value of C2 - -0.152 . Figure 11 helps to visualize the joint
influence of berm width and berm height in reducing wave runup and also
demonstrates that Equation 15 has a logical functional form.
40. To further generalize the findings from this study, Equations 12
and 13 were combined in the following manner
-=a r Z (16)HMO I + bý
The "a" runup coefficient was dropped from Equation 12 since it is very
close to 1.0 and replaced with r , which has a limiting value of 1.0 for
plane slope revetments. Figure 12 is a scatter plot of R.. predicted using
Equation 16 versus observed R. . It is clear from Figure 12 that
Equation 16 follows the trend of the data well but provides conservative
estimates of R. . As noted in paragraph 38, systemic differences between
runup observations in this study and those in Ahrens and Heimbaugh (1988) may
account for the differences in observed and predicted runup in Figure 12.
Damage Level
41. In addition to reducing wave runup and overtopping, the rubble berm
also reduced damage levels on the revetment slope above the berm. Figures 13a
through 13d show the progressive deterioration of the berm with increasing
wave heights. The protection furnished to the revetment is obvious, as seen
when these figures are compared with Figures 14a through 14d. Figures 14a
through 14d show the progressive deterioration of a revetment without a berm
after being subjected to the same wave conditions used in Figures 13a through
13d.
42. Quantification of the improvement can be presented in a manner
similar to the method used for wave runup in Figure 11, i.e., by using a
reduction factor. Damage to the structure above the berm can be quantified
27
coi
-j-
0Z0
o-.40 41)
(D 4
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C4c 41)
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-,D
00
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1 4)
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N)O Hid3C]!DNI3Nflos
31
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N 0N
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32
w
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LL I.- C.)
a::
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~~~~~~~~~r co U-1 u,~~~ 0 ~ ~ t) M N~ \J~
(14) Hl~d30 ONIINflos
33
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a)
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(1:4) Hld3G E)NI]Nflos
34
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'K.
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LL I- (nLLI LL
0 <-
00
~C1
r-c U )CYJ . 0 M~ CO t- to) Lo 1; (n) CJ 0
(4) H-L~dBO ENIGNflQs
35
a:
-, LU 0 4
LuN o
a::NW
NN r-
00ZcD K-N N
~ Z N W(I) ~ N4
Wej) N>.W 5
ul wt K' rýW I- 0 Z
('14)~ ~ Hi3 NN~o
LU >~ 36-
LIJ
U-
cc
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0)
N0 0C-4,
C(0 0
2('2 Hi~d3C]!NI(aNnos
37
either by defining the S2 damage for the region above the berm, or by the
depth of erosion into the armor layer, e... The following equations were
developed using multivariable analysis to predict damage levels.
S 2 = 1.0 (N,)C- expC4 W 3 B 2 h ) (17)
eaxt = CS (N.) 4 exp ( WH B 2 *h) (18)
taC-((H=L,)' 1 da
where N, is the stability number, defined below, t, is the armor layer
thickness, and C3 through C7 are dimensionless regression coefficients
given by
C3 - 2.96
C4 - -3.56
C5 - 0.104
C6 - 2.08
C7 - -2.73
The stability number is defined as
W1/3
NS = i (19)-s 3 (s• - 1)
43. Equations 17 and 18 were developed to show how the reduction factor
concept introduced for runup can also be applied to damage levels and are not
necessarily recommended for prediction purposes since data scatter is very
high in the damage variables. However, all terms in the equations are highly
significant and the equations seem to reflect the trends in the data.
44. Damage can be defined as follows:
is e C4( ( o 1/2 * )] (20)
(H-•oL) 1/
r. efC 7 ( WE * )1 (21)
38
where r. and r. are the reduction factors for S 2 damage and emax
damage, respectively. Figures 15 and 16 show curves of constant reduction as
functions of relative berm width and relative berm height based on
Equations 20 and 21. These figures help visualize the influence of a berm in
reducing damage to a revetment.
39
0
Ojf-) 0 lt)O0c
< (0-~0)
41C\!
00
E 04
CR E
00
CD.
* a:00
V:)
C))
0 r0
400
0C\J
-4
42)
4-4.
0
'44
$4.
to
4-4
0
0 ) A
0
o 0o
41-
PART VI: CONCLUSIONS AND RECOMMENDATIONS
45. This study developed an equation (Equation 16) to predict the upper
limit of irregular wave runup on planar riprap revetments or on riprap revet-
ments fronted by a rubble berm. The equation considers both the height and
width of the berm and provides a way to estimate the effectiveness of a berm
in reducing wave runup. Although the berm was only tested with a 1:2 slope,
the reduction factor is believed to be applicable to other slopes when used in
Equation 16. Since Equation 16 can be used to calculate the runup on both
bermed and plane riprap revetments, it is superior to the method proposed in
Repair, Evaluation, Maintenance, and Rehabilitation Research (REMR) Program
Technical Note CO-RR-l.3, Supplement 3, which provided only a reduction factor
for runup due to the influence of a berm. In addition, Equation 16 is based
on a larger data set and subsequent analysis beyond that given in REMR
Technical Note CO-RR-I.3. An updated version of REMR Technical Note CO-RR-l.3
will be available in Supplement 6 to reflect these changes.
46. A rubble berm not only reduces wave runup but also increases the
stability of the revetment. The berm's influence on stability is considerably
greater, as a percent, than the reduction in runup; i.e. a modest reduction in
runup corresponds to a substantial improvement in stability. Typical reduc-
tions in runup due to a berm observed during this study were in the range of 5
to 15 percent. It is also believed that a modest reduction in runup will
translate into a large reduction in overtopping rates. These intuitive con-
cepts can be supported by making a few logical assumptions and calculating the
consequences.
47. The reduction in overtopping can be estimated by using the method
shown in the SPM and discussed further by Weggel (1976). Assume that R.m -
1.15 * F; i.e. the potential maximum runup is 15 percent greater than the
freeboard of a plane slope riprap revetment. To reduce the overtopping rate,
a berm is added to the revetment that reduces the maximum runup 10 percent or
R. - (1.15 * 0.90) * F - 1.035 * F, where F is the structure freeboard.
This rather modest reduction in runup causes a reduction in the overtopping
volume by a factor of about 8.8 if a value of Weggel's overtopping parameter
alpha - 0.07 is used (see Example I, Appendix B). These reductions are in the
volume of water per unit length of structure for the maximum potential runup.
The average overtopping rates could be expected to be reduced more than the
42
maximum rates since the berm would allow fewer waves to overtop. Values of
alpha selected are reasonable for a riprap revetment based on estimating over-
topping rates using the potential runup approach given by Weggel and the SPM.
48. Reductions in damage for modest reductions in runup are equally
impressive as the reductions in overtopping rates. Compare the reduction
factors for iunup and S, damnge gie-n by Equations 15 and 19 for a berm pro-
ducing a 10-percent reduction in runup. The S2 damage reduction factor cor-
responding to r - 0.90 is r, - 0.085 (see Example 2, Appendix B). This
comparison indicates that a 10-percent reduction in runup will reduce S2
damage by a factor of almost 12.
49. Although comparable reductions in runup and overtopping may be
obtained with a smaller volume by increasing the crest height of the revetment
rather than adding a berm, the use of a berm should prove of value in loca-
tions where an increased crest height is not possible or undesirable. The
advantages of increased protection provided by the berm should also be
considered.
50. Maximum runup elevations from this study are based on visual
observations. These observations appear to be consistently lower than similar
observations made during other studies (Ahrens and Heimbaugh 1988). For this
reason, data analysis was biased towards a conservative interpretation of the
findings from this study. Because of the difficulty in achieving consistent
results among different observers of maximum runup elevations, it is recom-
mended that an electronic runup gage be developed. A runup gage would not
only give consistent results from study to study, but could also provide more
information about irregular wave runup elevations on rough and porous slopes.
With a gage, it is anticipated that statistically stabler runup parameters
could be computed that would yield better insight into the ability of a berm
to improve the performance of a rubble structure. Using a maximum value
contributed to the considerable data scatter in this study and the difficulty
in interpreting results.
43
REFERENCES
Ahrens, J. P., and Heimbaugh, M. S. 1986. "Irregular Wave Overtopping ofSeawalls," Conference Proceedings, IEEE Oceans '86, Washington DC, pp 96-103.
. 1988. "Approximate Upper Limit of Irregular Wave Runup on Rip-rap," Technical Report CERC-88-5, US Army Engineer Waterways Experiment Sta-tion, Coastal Engineering Research Center, Vicksburg, MS.
Ahrens, J. P., and McCartney, B. L. 1975. "Wave Period Effect on the Stabil-ity of Riprap," Proceedings Civil Engineering in the Oceans III, Newark, DE,pp 1019-1034.
Battjes, J. A. 1974. "Wave Runup and Overtopping," Report to the TechnicalAdvisory Committee on Protection Against Inundation, Rijkswaterstaat, TheHague, The Netherlands.
Broderick, L. L., and Ahrens, John P. 1982. "Riprap Stability ScaleEffects," Technical Paper TP 82-3, US Army Engineer Waterways Experiment Sta-tion, Coastal Engineering Research Center, Vicksburg, MS.
Burcharth, H. F., and Frigaard, P. 1988. "On 3-Dimensional Stability ofReshaping Breakwaters," Proceedings of the 21st International Conference onCoastal EngineerinD. Malawga, Spain, 20-25 June 1988, pp 2284-2298.
Goda, Y. 1970. "Numerical Experiments with Wave Statistics," Report of thePort and Harbor Research Institute, Ministry of Transportation, Japan, Vol 9,No. 3.
Goda, Y., and Suzuki, Y. 1976. "Estimation of Incident and Reflected Wavesin Random Wave Experiments," Proceedings of the 15th Coastal EngineeringConference, Honolulu, Hawaii, Vol I, pp 828-845.
Hasselmann, K., Barnett, T. P., Bouws, E., Carlso, H., Cartwright, D. C.,Enke, K., Ewing, J., Gienapp, H., Hasselmann, D. E., Sell, W., and Walden, H.1973. "Measurements of Wind-Wave Growth and Swell Decay During the Joint SeaWave Project (JONSWAP)," Deutshes Hydrographisches Institut, Hamburg.
Hudson, Y. H., and Davidson, D. D. 1975. "Reliability of Rubble-Mound Break-water Stability Models," in Symposium on Modeling Techniques, Symposium of theWaterways, Harbors and Coastal Engineering Division of American Society ofCivil Engineers, San Francisco, CA, 3-5 September 1975, pp 1603-1622.
Hudson, R. Y., and Jackson, R. A. 1962 "Design of Riprap Cover Layers forRailroad Relocation Fills, Ice Harbor and John Day Lock and Dam Projects;Hydraulic Model Investigation," Miscellaneous Paper 2-465, US Army EngineerWaterways Experiment Station, Vicksburg, MS.
International Association for Hydraulic Research. 1986. "List of Sea StateParameters," Supplement to Bulletin No. 52.
44
L
Shore Protection Manual. 1984. 4th ed., 2 vols, US Army Engineer WaterwaysExperiment Station, Coastal Engineering ResearcL. Center, US GovernmentPrinting Office, Washington, DC.
Wegel, J. R. 1976. "Wave Overtopping Equation," Proceedings of the 15tbCoastal Engineering Conference. Honolulu. Hawaii, pp 2737-2755.
45
APPENDIX A: DATA TABLES
a 0= NI a 0 'r Nn NMMM M' t oNM * l A-i n t.tIA0 CD cm o nMM-
99 CL Q C a 0 000 0 0 CD ý 0ý 00 00 0 00 0 0 0 0 0 0 0 0 0 00 0. 0)
cc .. w .0 0. . . . . ." !. :l - ý
~ C 0 -- N i i 4- 4-tIAI 0 ON N) M n a M4 N LN in4 0 - M M M'T -*4
of >.- I.-
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,4 :- LU em --- Cr- - -- -Ne e e N Ny - n err (Meeeeeeee i
-~~~~~~~~~ .. . .00 - 4t.~~ .U~0 .00 . . . . . .
LU( err 0.ee e e e e e e eMMrr r rNW N ND N It NN Neeeeeeeeeeeeeeeeeee
Z - ='C r- !A AA Mt M0 M ttI- M Ny. NM ~ ~ M0
gw >> ch = S
Zc=LU - ~00 N M N N O N M*.O e N M .t.
wu - t
NI-j ce 1 -- ;0 . M^' WMO t0 vM0 .
o0 o
00 -C 4 w
- - -. -ee -N N N N NM M ~ M -c r-- -r - ---
Cu C
(A Z UJ >
SN N N% N% N% N% N% N% N! N N% N% NN N N N% N% N! Ný N% N% Nr IA r% C% afl Vm mý N NNNN
2 .- =.(A z I.- C0
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4u tl. .=ý
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Table 5
Damage Sustained by the Revetment During Test Runs
MAXIMUM MAXIMUMPERPEN- PERPEN-UPPER DICULAR UPPER DICULARS2 ARMOR S2 ARMORRUN # DAMAGE EROSION RUN # DAMAGE EROSION1 0.560 0.010 37 0.189 0.0062 0.883 0.024 38 16.858 0.1943 0.558 0.013 40 0.257 0.0084 1.323 0.053 42 0.495 0.0145 2.161 0.049 44 0.927 0.0186 6.517 0.112 47 0.244 0.0087 11.473 0.121 48 4.881 0.0768 0.514 0.008 49 2.479 0.0489 1.252 0.036 50 0.301 0.00410 5.538 0.090 51 6.491 0.08811 11.219 0.157 52 1.758 0.05812 21.797 0.215 53 0.283 0.00617 0.458 0.006 55 0.209 0.00418 0.458 0.006 57 0.086 0.00419 0.770 0.036 59 1.946 0.03620 1.220 0.030 60 6.944 0.12921 3.637 0.085 61 9.695 0.12522 9.358 0.126 63 0.624 0.01023 8.765 0.158 64 0.693 0.01524 0.338 0.007 65 1.510 0.04125 1.523 0.037 67 0.973 0.03626 12.590 0.137 68 1.306 0.05427 25.188 0.191 69 6.841 0.12328 0.486 0.017 70 9.876 0.10429 2.442 0.044 71 17.981 0.17530 12.220 0.171 85 2.152 0.04432 3.258 0.097 86 1.171 0.03033 12.191 0.146 88 0.890 0.02134 17.883 0.195 89 0.730 0.01735 1.240 0.030 90 0.538 0.01636 37.603 0.286 91 1.610 0.047
A12
APPENDIX B: EXAMPLE PROBLEMS
BI
EXAMPLE 1
GIVEN: Potential runup on a revetment is 15 percent higher than thefreeboard.
FIND: Reduction in overtopping rate if a berm reduces the runup by 10 percent.
SOLUTION: The current method given in the Shore Protection Manual (SPM)(1984)* to calculate overtopping rates is
Q (g0.1085 [R h + d - d s (BI)
where
Q - overtopping rate per unit structure lengthQt and a - empirically determined coefficients based on incident wave
conditions and structure geometry
H' - equivalent deep water wave height
R - maximum potential runup
h - height of structure crest along the bottom
ds - depth at the structure toe
This may be rewritten as (Ahrens and Heimbaugh 1986)
Q -((g Q* H;3)11 •2 R - F) 0.1085 (B2)
where F is the freeboard of the structure.
Given that the potential runup without a berm is 15 percent greater than
the freeboard, then
RNo Berm- 1.150F
If a berm reduces the runup by 10 percent, then
RBerm - 1.150F * 0.90 - 1.035F
The effect of the berm on the overtopping rate is given by
3cH') 1/2 .150F - F 0.1085QNo Berm- 0 o / tl50.150F +F)
3) H91/2 (1.035F - F~ 0.1085~Berm 0* (1.035F+ )o035Fj + (B3)
* See References at the end of the main text.
B2
or,
0.1085ft .150F)QNoBerm - (2.150F (B4)
QBerm 0. 035F( 2. 035F-
For a - 0.07, the berm has reduced the overtopping rate by a factor of 8.8.
EXAMPLE 2
GIVEN: A given berm produces a 10-percent reduction in wave runup, i.e.
r - 0.90.
FIND: What is the damage reduction factor (rs)?
SOLUTION:
r = 0.90 = ex C2* (15 bis*)=
4~W (H ,LO) ,z ds)
I = ? = ex C C (H. Lo) 1/2 . --d j (20 bis**)
Since WB , HB , HMO, Lo , and d. are equal and C2 - -0.152 (pp 25 of
text) and C4 - -3.56 (pp 36 of text), the above reduces to:
I•_ =r eXP c2l (B6)
or
in 0.90 -0.152
In (1') -3.56
-0.105 -0.152in (r.) -3.56
* See p 27 in the main text.•** See p 38 in the main text.
B3
in r = -2.459
= 0.085
B4
APPENDIX C: NOTATION
Cl
a Regression coefficient
A, Area of accretion above the still water level
A2 Area of erosion
A3 Area of accretion below the still water level
alpha Overtopping parameter
b Regression coefficient
Co Regression coefficient
CI Regression coefficient
C2 Regression coefficient
C3 Regression coefficient
C4 Regression coefficient
C5 Regression coefficient
C6 Regression coefficient
C7 Regression coefficient
D15 15-percentile diameter on a grain size distribution curve
085 85-percentile diameter on a grain size distribution curve
(Dn)50 Nominal diameter of the median stone size
ds Depth at structure toe
E1 Energy of the incident wave spectrum
emax Maximum perpendicular penetration of erosion into armor layer
ER Energy of the reflected wave spectrum
f Wave frequency
F Structure freeboard
g Gravitational acceleration
H Wave height
hB Berm height
Hmo Wave height of the zeroth moment
Hr Reflected wave height
HS Average wave height of the one-third highest waves
Kr Reflection coefficient
Krr Stability coefficient
Lo Deepwater wavelength
mo zeroth moment of the potential energy spectrum
C2
m2 Second moment of the potential energy spectrum
Ns Stability number
Qp Spectral width or peakedness
r Runup reduction factor
re Erosion reduction factor
rs S2 damage reduction factor
Rmax Maximum vertical height above still water level of wave runup
S2 Damage relative to size of armor unitS(f) Spectral density function
Sr Relative specific gravity
T Wave period
Tp Wave period associated with the peak energy density
Tz Average wave period
W Weight of an individual armor unit
W50 Median armor stone weight
WB Berm width
wr Unit weight of armor stone
c Angle of the slope with the horizontal
Surf parameter
7r 3.141592654
C3
REPORT DOCUMENTATION PAGE [ ormo Approved
Pu~~cr~pn~q brd fl or this cotiedllon, of inflormtion m estimated to srerage I hourf or, 'ei)nor',e n ud'ng I" Ine for rewwn ntIr on.wrctrign C.T.r"r dat s1*gaterngandinrttd~'.lgthe data. needed. and Oinp)IeIE1g and f.ewni-rg the C041t(1.O4 Of Mfri'ai~nhIOf S.end cormients ~inrqrrg tthsi burden estimateC or an other &MW1o f C th-
collectwo of ,nlOritiatIto. lncd dng ,ge t'onto reducing tirs burden, to Washington 04eaciouartefs Sermrces, Oireitorte ifornormation Ovierations and Aeprmns $2 IS jeffter*orOan, .hwway suite 1204. Arhngto. VA 2220243 . .d to the OflIce of Maflbsgerni t and fludget, Paperwork Aed•,ton Pro t e" (0704411M). WashingtOn. DC 2001
1. AGENCY USE ONLY (Leave blank) 12. REPORT DATE 3. REPORT TYPE AND DATES COVERED
April 1993 Final report4. TITLE AND SUBTITLE S. FUNDING NUMBERS
Use of a Rubble Berm for Reducing Runup, Overtopping, W
and Damage on a 1V to 2H Riprap Slope; ExperimentalModel Investigation
6. AUTHOR(S)
Donald L. WardJohn P. Ahrens
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) S. PERFORMING ORGANIZATIONREPORT NUMBER
USAE Waterways Experiment Station
Coastal Engineering Research Center Technical Report3909 Halls Ferry Road REMR-CO-17
Vicksburg, MS 39180-6199
9. SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING /MONITORINGAGENCY REPORT NUMBER
US Army Corps of EngineersWashington, DC 20314-1000
11. SUPPLEMENTARY NOTES
A report of the Coastal Problem Area of the Repair, Evaluation, Maintenance, andRehabilitation (REMR) Research Program. Available from National Technical
Information Service, 5285 Port Royal Road, Springfield, VA 2216112a. DISTRIBUTION / AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
Approved for public release.; distribution is unlimited
13. ABSTRACT (Maximum 200 words)
Laboratory tests with irregular waves to determine wave runup character-
istics and armor stability of riprap revetments are discussed. Tests includeconventional, plane, 1 on 2 slope revetments, and conventional revetmentsfronted by rubble berms. Rubble berms tested reduced the maximum runup byrather modest amounts, typically around 10 percent, but produced substantial
improvement in the armor stability. These effects are discussed and quantified.
"This study demonstrates the need for a reliable irregular wave run-up gage forlaboratory studies of rough, porous coastal structures.
14. SUBJECT TERMS 15. NUMBER OF PAGES
Berm Revetment 69
Damage Riprap stability 16. PRICE CODE
Overtopping Runup
17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION Of ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT
UNCLASSIFIED UNCLASSIFIED
NSN 7540-01-280-5500 Standard Form 298 (Rev 2-89)1`1-11,beOO h AN%. ý0a ji 'I
