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Effectiveness of recurved wave return wall

Effectivenessof recurved
wave returnwalls

MWOwenandAAJSteele

ReportSR 261
February1991 RevisedApril 1993

lltul
io I

HR Wallingford


Contract
Thisreportdescribes
workcarriedoutby membersof the CoastalEngineering
14Afundedby lhe Ministry
Groupof Hydraulics
ResearchunderCommission
officerMr A Allison.At thetime

of Agriculture,
Fisheries
and Food,nominated
of repodingthis project,HydraulicsResearch's
nominatedprojectofficerwas
Dr S W Huntington.
of Agriculture,
Fisheries
and
Thisreportis published
on behalfof the Ministry
Food, but any opinionsexpressedare lhose of the authorsonly, and not
necessarily
thoseof the ministry.

Prepared by

(name)

(job title)

Approvedby

f-l^+^
UATY

@

Crown Copyright1991

Publishedby permissionof the Controllerof Her Majesty's StationeryOffice,
and on behalfof the Depadmentof the Environment.

sFr 261 C8,/04/93


Summary
Effectivenessof recurvedwave return walls
MWOwenandAAJSteele
Repod SR 261
February1991 RevisedApril 1993
Model studies have been carried out at a scale of 1:15 lo measure the
overtopping discharges for recurved wave return walls located on top of
smooth, plain sloping seawalls. The measured discharges were compared
with the expectedvalues if the wave return walls had been absent, to derive
a discharge factor representingthe effectivenessof the return wall. These
expecteddischargeswere estimatedfrom dimensionlessexpressionsderived
from many tests reportedelsewhere.
The model tests were for a fixed recurveprofile,and for seawall slopes of 1:2
and 1:4. A range of return wall heights, seawall elevations,return wall
positions, and wave conditions was examined. Based on analysis of the
results a design method has been proposed to enable the ovefiopping
dischargefor wave return walls to be estimated.
This study forms part of a continuing programme of research into the
behaviourof seawalls,being carried out at HR Wallingfordwith suppofi from
the Ministryof Agriculture,Fisheriesand Food underCommission144, Marine
Flood Protection,Sea Defence Structures.
For further information about this study please contact the authors or
Dr D M Herbeftin the CoastalGroup of HR Wallingford.

sR 261 08i04/S3


Notation
A,B

4

cw
Df
g
Hs
OBAR
Q"

QSOBAR
Q*b
Q"*

Rc
R",n
R*"
R**
S
SWL
Tm

wh
W"
X*

Empiricalcoefficientsdefining the dischargecurve for a
given Seawall profile
Adjustmentfactor
Width of crest berm (m)
Dischargereductionfactor - Q-u./Q-u
Gravitationalacceleration
Significantwaveheight
Mean overtoppingdischarge Us/mor m3/s/m
DimensionlessdischargeaBAR/(Tg Hr)
Standarddeviationof discharge
dischargeat the base of the recurve
Dimensionless
dischargeover the returnwall
Dimensionless
Freeboardat the top of the seaward slope
Freeboardat the top of the wave return wall
Dimensionlessslope freeboard - RJ(T* (g Hr).f)
Dimensionlesswallfreeboard- Rc/Om tg HJ':)
Sea steepness. In deep water S = 2n HJgT^'
Still water level
Mean wave period
Heightof wave returnwallfrom base to top
Dimensionlesswall heightWh/Rc
Adjusted dimensionlessfreeboard R"c X At

sF 261 0ev04/93


Contents
Page
Titlepage
Contract
Summary
Notation
Contents

lntroduction....

1

Test variables . .
2.1
Returnwallprofile
2.2
Returnwallposition
2.3
Seawardslope
2.4
Bermgeometry
2.5
Crestelevation

1
1
2
2
2
2
2

2.6

Wave conditions

Modeldescription
Wave measurements. .
Overtoppingmeasuremenls. .

2
2
3
3

Method of analysis
4.1
Dimensionless
freeboard
discharge
4.2
Dimensionless
4.3
wall height
Dimensionless
4.4
Returnwall effectiveness
4.5
Base overtoppingdischarge . .

3
3
4
4
4
5

Testresults....
5.1
Data presentation
5.2
Effectsof crest elevationand wall height
5.3
Effect of seawallslope .
5.4
Effect of crest width

5
5

Test measurements
3.1
3.2
3.3

o
o

6

Design method
6.1
Designgraph
6.2
Exampleproblem
6.3
Applicationto other seawalls
6.4
Rock revetmenls.

7
7
8
I
10

Discussion

11
11
11

7.1
7.2
7.3

Crest raisingversusreturnwalls . . . . .
Dimensionlessovertoppingexpressions
Recurvedwall orofile

t1

Conclusions
References

sF 261 0€vO4/93


Contents continued

Table
Table1

Adjustmentfactors

Figures
Figure1
Figure2
Figure3
Figure4
Figure5
Figure6
Figure7
Figure8
Figure9
Figure10
Figure11
Figure12
Figure13
Figure14

Basic form of recurvedwall profile
Configurationfor model tests
'l:2 gradient crest width 0m
Resuftslor
Resuftsfor 1:2 gradient crest width 4m
Resuftstor 1:2 gradient crestwidth 8m
Resultstor 1:4 gradient crestwidth 0m
Resultsfor 1:4 gradient crest width 4m
Resultsfor 1:4 gradient crest width 8m
Finaldesigngraph
Rock revetmentreturn wall
Rock slopeovertoppingcurves
Rock slopecomparedwilh 1:2, 0m berm
Rock slopecomparedwith 1:2, 4m berm
Effect of raisingthe crest

Appendices
Appendix
A
AppendixB
AppendixC

Ovedoppingmeasuremenl
Physicalmodel test facility
Spectralanalysisand wave countingprograms

sR 261 08V04/93


Introduction
By far the most common type of seawall in the UK, in terms of the length of
coastlineprotected,is the simple earth embankment,consistingof a sloping
seawardface, a horizonialcrest just a few metres wide and possibly a rear
slope. These embankmentsare pafiicularlyfrequentin rural areas, where the
seawardface is often protected either by grass or pitched stone. In urban
areas howeverthe seawall frequentlyincorporatesa wave return wall at its
crest. This wall can be locatedeither at the top of the seaward slope, or else
it can be sited a few metres back allowinq the crest berm to be used as a
promenade.
In the late 1970's the then HydraulicsResearch Station carried out an
extensiveresearch programmelo determine the overtoppingdischargesfor
embankmenttype seawalls,culminatingin the productionof designguidelines
'1,
and softwarefor the predictionof ovedopping(References 2, 3 and 4).
However virtually no information has been available to quantify the
effectivenessof wave returnwalls in reducingovertoppingdischarge. As pafl
of HydraulicsResearch'scontinuedinterest in the design of seawalls,model
tests have now been carried out to measure the overtoppingdischargesof a
rangeof recurvedwave returnwalls,for differentseawallslopes,water levels,
and wave conditions. This report describesthe tests carried out (Section2),
the measurements
made (Section3), the analysismethodsemployed(Section
4), and the resultsobtained(Section5). Finallythe resultsare usedto derive
a methodfor estimatingthe effectivenessof recurvedwave returnwalls during
the design of seawalls (Section 6). Section 7 summarises the main
for the design of
conclusionsof the study, and makes recommendations
seawallsincorporatingwave return walls.

2

Iesf variables

For the most part, the test conditionsused in this presentstudy have been
based on those used for the earlierstudies on embankmenttype seawalls
(Reterence1),and on a parallelresearchprogrammeto measurewave run-up
and overloppingon seawalls with rough and/or porous seaward faces. This
has enableddirect comparisonof the results obtainedwith wave return walls
with those obtainedseparatelyfor flat-crestedseawalls.

2.1 Returnwall profile
Wave returnwalls with a very wide range of profileshave been constructedat
differentlocationsaround the UK coastline. For this study, only the basic
profileoriginallysuggestedby Berkley-Thorne
and Roberts(Reference5) and
cited by Owen (Reference3) has been used. This basic form is shown in
Figure1 which also includessome typicaldimensions.The majorfeatureof
this profile is the very shallow angle (above the horizontal)at which the
returningwave exits from the top of the recurvedwall. This means that the
returningwave is much less susceptibleto being carriedover the seawallby
strongonshorewinds,in contrastwith a near vefiicalwave returnwall. During
this study,returnwall heightshave been used which representthe most likeiv
rangein practice.

sFt 261 08/O4l93


2.2 Returnwall position
At some localions,the wave returnwall is positioneddirectlyat the top of the
seawardslope of the seawall,with the foot of the recurvejoinedtangentially
to the slope. Howeverin many coastalresoflsthe returnwall is a few melres
backfrom the top of the seawardslope:in this situationthe crestberm is used
as a promenadeduringcalm weather. For this studythe distancebetweenthe
top of the seaward slope and the foot of the return wall was set at either 0, 4
or 8 metres. Figure2 shows the generalconfigurationfor the modeltests.

2.3 Seawardslope
The seawardslope of the main seawallwhich forms the base for the return
walfwas set at either1:2 or 1:4. Duringthe earliertests on embankmenttype
seawallsslopesof 1:1, 1:2 and 1:4 were tested. Howeverthe overtopping
dischargesfor 1:1 seawallswere found to be very similar to those for 1:2
slopes,and the 1:1 slope was thereforeomittedfrom these tests.

2.4 Berm geometry
Throughoutthese tests the seaward face of the seawall was a plain slope
withoutany berm betweenthe toe and the crest.

2.5 Crest elevation
For each of the seawall slopes tested, crest elevationsof 0.5, 1.0 and 1.5
metresabovestillwaterlevel (SWL)were tested. In the modelthiswas in fact
accomplisfred
by changingthe water level by the requiredamount.

2.6 Waveconditions
For each combinationof seawalland wave returnwall, up to 5 wave heights
weretested,givingsignificant
of 1.25,1.75,2.25,2.5
heightsat the structures
and 2.75m respectively.For all wave conditionsa constantsea steepnessof
0.045 was used (basedon the mean deepwaterwave lengthgf ^2lZnit.

3

Test measurements

3.1 Modeldescription
The modeltests were carriedout at a scale of 1: 15 in a randomwave flume
measuring
50m longwitha nominalworkingdepthof 0.61 metres.The overall
widthof the flumeis 1.22m,whrchwas dividedintotwo channels.The working
channelwas 0.75mwide, and containedthe seawallstructureto be tested.
The workingchannelwas separatedfrom the secondchannelby a perlorated
wall, with the porosityincreasingtowardsthe wave generator. By this means
wave reflectionsfrom the seawall during the tests were dissipatedin the
secondchannelbeforereachingthe wave generator.All the testswerecarried
out underdeepwaterwave conditions,with a horizontalbed extendingfromthe
wave generationsectionto the model seawall(see AppendixB).
The seawalland the wave returnwall were both constructedmainlvrn !'!'oa.
with their paintedsurfacesgivinga smoothf inisi:


3.2 Wavemeasurements
Random waves were generated by a wedge-typewave paddle driven by a
double-acting hydraulic ram, and controlled by micro-computer. Using
softwaredevelopedat HR, this system is capableof producingrandomwaves
with any desiredenergy spectrumand for a wide range of sequence lengths,
but with repeatablesequencesto allow the performanceof differentstructures
to be comparedunder identicalwave conditionswithoutstatisticaluncertainty.
For this study the JONSWAPform of the wave energy spectrumwas used for
all tests, and a very long sequence length was employed (typically3000
waves). The wave conditionsduring the tests were measured by hvin wire
wave probes locatedin the second channel of the flume, well away from the
wave generatorand a few metres off a shallowsloping shingle beach. At this
locationthe measuredwaves were free of any reflectioneffects. The wave
probeswere connectedto a micro-computer,and the signals were processed
to give significantwave height and mean zero crossing wave period. During
the initialcalibrationof the model the signalswere also processedto give the
wave energyspeclrumfor comparisonwith ihe requiredJONSWAPspectrum.

3.3 Overtoppingmeasurements
For each test condition,five overtoppingmeasurementswere taken to enable
the mean and the standard deviation of discharge to be calculated. Each
measurementconsisted of collecting all the water which overtopped the
seawallduringa periodof 100 waves (definedas 100 times the nominalmean
wave period). The resultingdepth of water in the collectingtanks was
measured,and using previouslyderived calibrationdata the total volumeof
water was calculated. Furtherdetails of these overtoppingmeasurementsare
given in AppendixA.

4 Method of analysis
4.1 Dimensionless
freeboard
The freeboardof a seawall is the differencebetween the crest elevationand
the still waterline. For seawallswith a returnwall some confusioncan arise
over the definitionof the "crest",especiallyif the returnwall is set back some
distancefrom the top of the seaward slope of the seawall. In this study two
definitionswere used for freeboard
-

Rc,the freeboardat the top of the seaward slope,
R"*, the freeboardat the top of the wave return wall.

From allthe previousresearchat HR on a wide range of seawallsit has been
found usefulto expressthe freeboard in dimensionlessterms, defined as
R." = R./T, (g Hr)"
and R-,n= R.u/T, (g H.)"
where T, and H" are the measured mean zero crossing wave periodand the
measuredsignificantwave height respectively. The physical significanceof
groupingcan perhapsbe appreciatedbetterbv notingthat
this dimensionless
in deep waler an identicaldefinitronis
R.. = (R"rH.)x t2nlSl'

sR 261 0&04/93


where S is the sea steepness.

4.2 Dimensionless
discharge
From the test measurements,each ovedopping discharge was calculatedby
dividing the volume of water collected by the actual duration of the
measurement (nominally 100 x Trn). Each measured value therefore
represeniedthe averageover 100 waves. Furtherto this, each measuremenl
was taken 5 times : from these measurements the mean overtopping
discharge,OBAR,and the standarddeviation,OSDBAR, were calculated,both
expressedin terms of cubic metres per second per metre length of seawall
(prototypeunits).
In similarfashionto the freeboard,a dimensionlessdischargecan be defined
AS

Q,w=QBAR/T*gH.
where Q,* is the dimensionlessdischargeovertoppingthe wave returnwall.
All measuredovertoppingdischargeresults were converted to dimensionless
valuesusingthis definition.

4.3 Dimensionless
wall height
Duringthe courseof the analysisof the results it became clear that one factor
govemingthe effectivenessof the wave return wall was the height of the wall
relativeto its positionabovethe stillwater line. Accordinglythe dimensionless
height of the return wall was defined as

W. = Wn/R"
whereWn is the heightof the wave returnwall from its base to its top, and R"
is the freeboard between the top of the seaward slope (which was at an
identicalelevationto the base of the returnwall) and the still water line.

4.4 Returnwall effectiveness
There are many possible ways of defining the effectivenessof wave return
walls. Two optionswould be
-

the ratio of lhe measuredovertoppingdischarge to the dischargewhich
would have occurred if the return wall had been removed, and the
seawardslope had been extendedup to the same elevationas the top
of the relurnwall. This was the definitionused by Allsop and Bradbury
(Reference6).

-

the ratio of the measuredoverloppingdischarge to the dischargewhich
would have occurred if the return wall had been absent. In most cases
this is equivalentto the ratio of the dischargewhich overtopsthe return
wallto the dischargewhich arrivesat its base.

For the presentstudythis seconddefinitionhas been used, since it seems a
more direct indicatorof the per{ormanceof the return wall, and also hopefully
ii shouldbe much less dependenton the geometryof the seawallon which it
is based.

sFt26r o8vo4/93


4.5 Baseovertoppingdischarge
Using the above definitionof the effeclivenessof the wave relurn wall, it is
necessaryto know the ovedopping discharge which would have resulted
during the tests if the wave return wall had been absent, for identical wave
conditions, water level and seawall geometry. Measurements of these
discharges were not made specifically for this study, but extensive
measuremenlsunder similar conditions had been made during the earlier
researchprogramrne(Reference1), and these measurementshad also been
repeatedand extendedduringa researchprogrammerunning in parallel with
this study,to determineovertoppingdischargesfor seawallswith rough and/or
porousseawardslopes. From allthese measurementsit had been found that
for a given seawall geometrythe overtoppingdischarge could be predicted
from the expression
Q. = A exp (-B R.)
where A and B are dimensionlesscoefficientswhose values depend on the
seawallgeometry.For plain slopingseawallswith 1:2 and 1:4 gradients,as
used in this study, the coefficientshave the followingvalues

Slope

1:2

1:4

A

9.39x 10-3

1 . 1 6x 1 0 - 2

B

21.6

41.O

Thesevaluesare slightlydifferentfromthosepublishedin Reference1, having
been revisedto includethe resultsfrom all the latest tests.
For each test in the presentstudy,the overtoppingdischargelo be expected
withoutthe wave returnwall was calculatedfrom the above expression,with
the appropriatevalues of the coefficients,and using lhe measured significant
wave heightsand mean wave period. The measureddischargeovertopping
the wave returnwall,expressedin dimensionless
terms as Q"* could then be
comparedwith this dimensionless
base dischargeQ,6to derivethe discharge
reductionfactor
Dt = Q.*/Q.b

5 lesf resurts
5.1 Datapresentation
ln choosingthe methodof presentingthe data, considerationwas given to the
way in which a designercould use the informationto calculatethe discharge
overtoppinga wave returnwall. Figure3 shows the form of presentationwhich
was finallyselected,in this case for a seawallwith a 1:2 seawardslope,and
with the wave returnwall placeddirectlyat the top of the slope (ie C* = O;.
ln this graphthe abscissais the dimensionlesscrest berm freeboardR.", as
definedin Section4.1, which can be calculatedfrom the aclual freeboard and
the wave height and period. Each line on the graph representsa constant
valueof the dimensionless
wavereturnwall heightW. (Section4.3),whichcan
be determinedfrom the actualwall heightand the actualfreeboardto the top
of the seawardslope of the seawall. Knowingthe values of dimensionless
freeboardand dimensionless
wallheiqht.the discharqefactorcan thereforebe

sR 261 0€v04/93


read from the graph. The overloppingdischargeat the base of the return wall
can be calculatedfrom the freeboard and the wave conditions (Section4.5),
and the dischargeovertoppingthe wave return wall is then obtained simply by
multiplyingthe dischargefactor.

5.2 Effectsof crest elevationand wall height
crest
factorincreasesas the dimensionless
Figure3 showsthatthedischarge
elevationdecreases:
in otherwordsthe wave returnis more effectivewhen
thereis lesswaterarrivingat ils base. Whenvery largequantitiesof water
and hasvery littleeffecton the
arriveat the returnwallit becomes"drowned",
the very strongeffectof
overtopping
discharge.Figure3 also demonstrates
the returnwallheighton the dischargefactor,whichis to be expected.At first
the wall height
it was expectedthat the best way of non-dimensionalising
wouldbe by divisionby the waveheight. Howeverthis did not produceany
consistentpatternin the results. Dividingby the crest freeboardis in fact
displayingthe messagethat return walls which are low in relationto the
quantityof water which reachesthem are less effectiveat reducingthe
overtopping
discharge.

5.3 Effectof seawallslope
Figure3 is for a 1:2 seawallslope,with the returnwall at the top of the slope.
Figures 4 and 5 show the results plotted in the same form for return walls
placed 4 and 8m respectivelyfrom the top of slope. Figures 6-8 show the
resultsfor a 1:4 seawallslope for the three different crest widths tested. On
each graphthe linesjoiningresultsfor constantdimensionlesswall heighthave
been fitted using the methodof least squares.
Compadsonof Figures3 and 6 shows the effect of seawall slope. For lhe
same dimensionlessfreeboardand dimensionlessreturn wall height a return
wall based on top of a 1:4 seawall appears to be more effeclive than one on
a 1:2 seawall. For example,taking a dimensionlesscresl elevationof 0.04
and a dimensionless
wall heightof 1.0, the dischargefactor for a returnwall
on a 1:2 slope is about 0.1: on a 1:4 slope it is about 0.025. Similar
reductionsin dischargefactors also occur for the other crest widths. This
increased effeclivenessis explained in pad by the fact that for a given
dimensionless
crest heightthe overtoppingdischargefor a 1:4 slope is less
than for a 1:2 slope,and as mentionedpreviouslya wave return wall is more
effectiveat low discharges. This suggests that replotting Figures 3 and 6
'l:2
and 1:4 data
using Q. as the abscissainsteadof R. might collapsethe
onto the same line. Howeverreplottingin this fashion,while it broughtthe
data closer together,still indicatedthat wave relurn walls are more effective
when basedon top of a 1:4 seawall.

5.4 Effect of crest width
Comparisonof Figures3, 4 and 5 shows the effect of moving the wave return
'l:2
wall backfrom the top of the seawardslopefor a
seawall,and Figures6,
7 and 8 show the same for a 1:4 seawall. For a 1:2 slope there is a
noticeableimprovement(reduction)in the discharge factor when lhe wave
returnwall is retardedby 4m, with very littlefurther reductionat 8m. For the
same dimensionlesscresl elevation and dimensionless wall height as
exampledpreviously,the dischargefactors are about 0.07 for both crest berm
widths,comparedwith about 0.1 for a return wail directlv at the top of the
seawardslope.

sB 251 0&04/93


For a 1:4 slope, there is much less consistency in the effects of the crest
widths on the dischargefactor. For low values of dimensionlesswall height
(Wh/Rc= 0.3 and 0.5) a return wall placed 4m back from the top of the
seaward slope is more effective,but for larger values of dimensionlesswall
height there appearsto be a slightworseningof the dischargefactor. When
the crest width is increasedto 8m, the discharge factor improves (reduces)
significantlyfor the lower dimensionlesswall heights, and also improves
noticeablyfor larger wall heights. This compares with the 1:2 slope tests
where there was very little differencebetween the 4m and 8m wide crest
results.

6 Design method
Figures 3 to 8 can be used directly in the design of a wave return wall,
knowingthe dimensionsof the return wall and the wave conditions,and
providedthat the crest width and the seawall slope are equal to one of those
combinationstested. Howevera single design graph would be preferable,
together with some means of estimating the overtopping discharge for
conditions not specificallytested. This section of the repofl attempts to
addressthese questions.

6.1 Designgraph
Examinationof Figures3 to 8 showed that for a given dimensionlessreturn
wall height the slopes of the lines were almost constant irrespectiveof the
crest width or lhe seawallslope. Giventhe scatterof the results,and the fact
that fewer than the ideal number of tests were carried out, it was decided to
investigatewhethera standardslope could be fitted to all lines having the
samedimensionless
wall height.Clearlythe interceptsof the lineson the axes
would be differentaccordingto the crest width and seawall slope.
In concept,the methodof determiningthe slopesand the displacementsof the
lineswas as follows.Firstly,the resultsobtainedfor a 1:2seawardslope were
taken as the baselineconditions.The equivalentgraph for the 1:4 slope was
then overlaidonto the standardgraph: by displacingthe overlay to the right,
both groups of data tended to form single groups of data for each
dimensionless
wall height. The methodthen is lo move the 1:4 data by an
amounlx alongthe 8." axis,and calculatethe best fit lineto the combined1:2
and 1:4 data usingthe methodof least squares. This was then repeatedfor
displacements
x +/- Ax untilthe highestoverallcoefficientof correlationwas
found for the data groups. This overallcorrelationwas taken as the average
of all the coefficients of correlation of all the data groups for different
dimensionlesswall heights. The lineardisplacementnecessaryto achievethis
best fit was noted:becausethe x-axis is logarithmic,this displacementcan be
expressedas a factor to be applied to the dimensionlesscresl elevation to
derivethe adjusteddimensionless
freeboardX.,
where

X, = R.cx At

and

A, is the adiustmentfactor

The pairsof Figures3 and 6, 4 and 7,5 and 8 were each treatedin this way,
to giveadjustmentfactorsto combinethe 1:4 slope resultswithlhe 1:2 results
for crestwidthsof 0, 4 and 8m. A simiiarprocesswas then used to combine
allthe 8m crestwidthresultswiththe 4m results FinallVall the 4m and 8m
sR 261 08,/0{193


results were adjusted to the 0m crest width results. Here however it was
found that there were significant differences in the adjustment factors
necessaryto obtain high correlationsfor all the different dimensionlesswall
heights. Two differentadjustmentfactors were thereforeadopted dependent
uponthe value of the dimensionless
wall height.
Using these methods, a single graph was produced, and this is shown in
Figure 9. For each value of dimensionlesswall height there are now
approximately
20 data points,throughwhich a straightline (using logarithmic
scales)has been fittedby the methodof least squares. For most wall heights
there seems to be a good fit to the data, althoughsome wall heights suggest
a slight curyature,with the dischargefactor reducing more rapidly for higher
values of adjusted freeboard. Figure 9 should be used in conjunction with
Table 1, which gives the values of adjustment factor to be used for any
pafiicularcombinationof seawallslope and crest width.

6.2 Exampleproblem
Given

Seawallslope 1:4
Crest elevation5.0m OD
Crest width 8.0m
Returnwall height0.8m

Find

Overtoppingdischargewhen:Still water level 4.2m OD
Significantwave height1.2m
Mean wave period3.64s

Solution

Dimensionless
crest elevation
R'" = R/Tr (gH")* = 0.8/3.64(9.81x 1.2)h = 9.964
Dimensionless
base discharoe
Q.b = A exp (-B R.")

FromSection4.5, the valuesof A and B for a simpleseawallwith a 1:4 slope
are givenas 1.16x 10-2and 41.0 respectively.
.'. Q.6 = (1.16x tO'2)exp (-41.0x 0.064)= 8.41 x 10-a
Hencethe dimensionalovertopping
dischargeat the base of the returnwall is
Qu = Q.uTr g H. = 8.41x 104 x 3.64 x 9.81 x 1.2 = 0.036m3/s/m.run
This is a rather high overtoppingdischarge (36 litres/s/*rl which would
probablynot be toleratedif pedestriansregularlywalked behind the seawall,
hencethe need for a wave returnwall. For the relurnwall, the dimensionless
wall heightis
w. = wn/Rc= 0.9/0.9= 1.0
With an 8m wide cresl, and a 1:4 seawall slope. Table i shows a cresi
elevationadjustmentfactorof 1.33,for dimensionlesswall heiqhts> 73

Thereforethe adjusteodimensioniess
freebcar,--r
::,

sF 261 0A/04/93


X. = R-cX 41 = 0'064 x 1.33= 0.085
From Figure9, the dischargefactorDr for X. = 0.085,W. = 1.0 is read off as
3.7 x 10-3. The actual overtoppingdischargeover the wave relum wall is
therefore
OBAR

= D fX Q u = 3 . 7 x 1 0 - 3 x 0 . 0 3 6
= 1.33x '10-4m3/s/m.run

which is very large reduction.
Because the location of the return wall and the slope of the seawall are
standardvalues which were actuallytested,the dischargefactor could in this
case have been read directly from Figure 8, using the un-adjusted
dimensionlessfreeboardR.c = 0.064. The slightlydifferentvalue obtained(Dt
= 3.3 x 1O-3)arisesfrom the ditferentnumberof data pointsused in the linear
regression.
For the examplegiven,the dimensionlesswall heightcorrespondsexactlywith
a tested condition:some interpolationbetweenlineswill usuallybe necessary.
ln many cases it may also be necessaryto extrapolatethe lines to higher
values of X.: this shouldbe done with extremecaution,althoughit is likelythat
the resulting estimate of overtopping discharge will be too high, ie
conservative. lt was not possibleto extendthe range of results in the model
study because the overtopping discharges became too low to measure
accurately. lf accurateestimatesof overtoppingdischargeare requiredfor this
situation,then considerationshouldbe givento carryingout model tests for the
specific seawall design, with special measures to record the very low
'1000
instead
discharges(eg collectingthe oveftoppingwater for a period of
of 100 waves).

6.3 Applicationto other seawalls
The modeltests describedhere were carriedout only for simple seawallswith
smooth seawardslopesof 1:2 and 1:4. Testingof additionalseawallswas not
will
possible within the research budget. Some interpolation/extrapolation
thereforebe necessaryfor the applicationof the resultsto other seawalls. For
simpfe seawalls with seaward slopes between 1:1 and about 1:21/2,lhe
ovedoppingdischargesat the baseof the wave returnwall will be very similar
for the range of dimensionlesscresl elevationsused in the tests, and therefore
it seems reasonablelo use the same dischargefactorsas for the 1:2 slope.
For sfopes betweenabout 1:2Yzand 1:4 the overtoppingdischargedecreases
almost finearly,and linearinterpolationbetweenthe dischargefactors tor 1:2Yz
(takenequalto 1:2)and for 1:4 wouldthereforebe appropriate.
None of the tests in this study involvedseawallswith a berm located partway
betweenthe toe and the crest of the seawardslope. Thereforethere must be
some uncertaintyaboutthe way in whichtheseresultscould be used for that
situation.The most logicalway wouldbe to convertthe bermedslope intoan
equivalentplain slope (whichwill alwaysbe flatter),whichfor the same wave
conditions,water level and crest level would give the same ovedopping
discharge. The dischargefactorsappropriateto this equivalentplain slope
would then be used for designingthe wave returnwall Often howeverthe
equivalentplainslopewillturnout to be flatterthan .i:.1the mostshallowslope
which has been used in thesetests.

sR 261 0ryO4/93


For seawalls which are rough but impervious,the most logical method to
proceedwould again be to conveftthe rough slope into an equivalentplain
smooth slope, giving the same ovenopping discharge, and using the
appropriatedischargefactor.
From the above discussion,it will be seen that lhere are likelyto be occasions
when the only accuratemethod of determiningthe overtoppingdischargefor
a bermed or a rough seawallwill be lo commissionspecific model studies.

6.4 Rock revetments
All the tests in this presentstudy werefor plain smooth and imperviousslopes.
Howevertests had been carriedout by Allsopand Bradburyin an earlierstudy
(Reference6) in which measurementshad been made of the overtopping
dischargesfor crown walls mountedon top of rock revetmenlsor breakwaters.
In all cases the tests were carried out only for a seaward slope of 1:2, and
most of the crown walls had a vertical faces on their seaward side. A few
tests had a recurved face, albeit of different profile to the present sttidy,
illustrated in Figure 10. No tests were carried out with the crown walls
completelyremoved.
To make use of the results obtained in that eadier study, Allsop and
Bradbury'sexperimentalequipmentwas reinstatedfor this study,and a series
of measurementsmade for a plain rock slope only, without any crown wall
present. The resultsobtainedare plottedin dimensionless
form in Figure11.
Unlike a smoothimpermeableseawallit is impossibleto measureovedopping
dischargedirectlyat the top of a rough porous slope. For the stabilityof the
slope a crest width of a least two rock diametershas to be allowed, in this
case equivalentto a cresl width of 2.2 metres,and the overtoppingdischarges
were thereforemeasuredat this distancebackfrom the top of the slope. Even
so the significantscatter in the results shown in Figure 11 indicatesthe
difficuhy of measuring overtopping discharges for rock slopes, and also
indicatesthe variabilityin ovedoppingdue to the differenl degrees of energy
absorption on the slope and of drainage into the crest for different wave
conditionsand water levels. The resultsare plottedin Figures12 and 13,
where they are comparedwith a 1:2 plain smooth slope for crest widths of 0
and 4 metres respectively.
Figures12 and 13 show that the dischargefactorsfor a returnwall mounted
on top of a rock slope are very much better (lower)than for a smooth slope.
The recurvedprofileshown in Figure10 would be expectedto be less effective
than that given in Figure '1, and the reductionin dischargefactor must
thereforebe due to the effectsof the rock slope. The probableexplanationis
as follows. As the wave runs up the slope and onto the crest, its forward
progress is arrestedby the return wall, increasingthe depth of water on the
crest. For an impermeableslope the remainderof the wave run-upto some
extent rides over this cushionof water and a fractionovertopsthe wave return
wall. On a permeableslope the increaseddepth of water on the cresi causes
a greaterhead differencefrom the crest to the bottom of the slope, increasing
the reversedrainagedown throughlhe armourlayer and,.to a lesserextent,
the underlayer. The remainderof the wave run-up thereforefinds it rnore
difiicultto ovefiop lhe wave return wall.

IU

sF 261 08/04/93


7

Discussion

7.1 Crestraisingversusreturnwalls
The resuftsof the tests have shown that recurvedwave returnwalls can have
a very dramatic effect on the overtoppingdischargesof seawalls. For some
test conditionsthe dischargewas reducedby almostthree ordersof magnitude
compared to the expected situationwithout the return wall. Of course some
reductionwould have been obtainedsimplyby raisingthe basic seawallby the
same amountas the heightof the returnwall. Howevercalculalionsshowed
that, for the same tests conditions,the reductionachievableby this method is
only about one order of magnitude. This point is well illustratedby the two
exampfesshownin Figure14 (Reference7). For eithera 1'.2or a 1:4 seawall,
the figure shows a plot of the overloppingdischargeagainstthe total heightof
the seawall, for a pafticularwave conditionand water level. Stading from a
crest elevationof 1.0m with no wave returnwall. the solid lines show the
reductionin dischargewhich is obtainedby addinga returnwall of gradually
increasingheight. The dottedlineshowsthe reductionobtainedby raisingthe
crest height,withoutany wave relurn wall. For a grventotal heightof seawall,
the incorporationof a wave return wall greatly reduces the overtopping
discharge comparedto simply raisingthe crest.

7.2 Dimensionless
overtoppingexpressions
To calculate the effectiveness of the wave return walls, the measured
overtoppingdischargeshave been comparedwith the expecteddischargesif
lhe returnwall had been absent. The estimationof these expecteddischarges
was based on the use of the dimensionless
ovedoppingexpressions.
Q. = A exp (- BR,)
where the coefficientA and B dependon the seawallgeometry. In this study
the values of A and B used for the smooth '1:2and 1:4 plain slopes differ
slightlyfrom lhose quoted in earlierrepodsand software(eg References1 and
4). This is because a large number of extra tests have been per{ormedand
these results have been combined with the earlier ones to produce revised
estimatesof the coefficients. Exlra tests have also been carriedout for many
of the bermed seawalls,and all these revisedvalues will be publishedin a
separate report,and will no doubt be incorporatedinto the next versionof the
software when it is produced.

7.3 Recurvedwall profile

/'

ifr^/**
l,

I

4

-1|

llll

J"f*J ffi

Almost all the tests in this study were carriedout for a fixed type of recurved
wave returnwall. Underconditionswhenthe relurnwall is almostdrownedout
(ie when it is least effective)the exact shape of the recuryeprobably makes
very littledifference. Underthose conditionsFigure9 could thereforeprobably
be used whaleverthe design profile. Howeverfor high wave returnwalls on
top of a seawall with large freeboard the recuruedprofile is very important,
since it defines the trajectoryof the returnedwater jet. The profile shown in
Figure 1 is probably one of the most effective,since the waler is returned
seawardat a very shallowangle above the horizontal. Verticalwave return
walls are probablyvery much less effective

n4/%12

11

sB 261 0UO4/93


I

Conclusions
A series of model tests has been carried out at a scale of 1:15 to
measureovertoppingdischargesfor a standarddesignof recurvedwave
returnwall, mountedon top of a plain slopingseawall. The tests covered
two seawallslopes('1:2and 1:4),and a rangeof seawallheights,return
wall heightsand positions,and wave conditions.
The measuredovertoppingdischargeswere comparedwith the expected
dischargesif the wave returnwall had been absent,to derivea discharge
factor which expressedthe effectivenessof the return wall in reducing
oveilopping.
The expected discharges were calculated using
dimensionlessexpressionsderivedfrom many tests performedearlier.
The resultsshowedthat the effectivenessof a wave returnwalldepended
stronglyon its dimensionlessheight, and also on the dimensionless
freeboard of the seawall itself. As would be expected, the lowest
dischargefactor was obtainedwhen a high retum wall was mounted on
top of a seawall with large freeboardand flatter slope. For some of the
tests the overtoppingdischargewas reduced by almost three orders of
magnitude by the presence of the return wall (dischargefactor about
1 . +x t o - 3 ) .
Purely in terms of reducingthe overtoppingdischarges,it is much more
effectiveto add a wave returnwall of given heighton top of an existing
embankment-type
seawallthan lo.raise the crest of the seawallby an
equalamounl.
Previouslyreportedtests to measureovertoppingdischargesfor crown
walls on top of rock revetmenlsor breakwaterswere extendedduringthis
studyto measureovertoppingwithoutany crownwall. Comparisonswere
made of the results for the recurvedcrown wall, with the results of the
present study. Although the recurves had a different profile, the
comparisonshowed that wave returnwalls on top of rough,porous rock
revetmentsare even more effectiveat reducingovertoppingdischarge.
Basedon analysisof all the resullsobtainedfor the smoothseawalltests
a designmethodhas been producedto enableengineersto estimatethe
ovefioppingdischargesfor any wave return wall wilhin the range of
variablestested. Some guidancehas also been given on suitable
methodsof interpolation/extrapolation
to obtainapproximateovertopping
dischargesfor othertypes of seawalls. Howeverthere will continueto be
many seawall designs for which accurate predictionsof overtopping
dischargecan onlybe obtainedby speciallycommissioned
modelstudies.

tz.

sF 261 0€v04/93


9

References

1.

Designof seawallsallowingfor wave ovefiopping,HydraulicsResearch
Station. EX 924,June 1980.

2.

Overtoppingof sea defences. Proc. of Conf. on HydraulicModellingof
Civil EngineeringStructures,BHFIA;Coventry,1982.

3.

Hydraulic design of seawall profiles. Proc. of Conf. on Shoreline
Protection. lCE, Southampton,1982.

4.

SWALLOW- a seawalldesignpackagefor microcomputers.Distributed
by HR Wallingford.

5.

Sea defence and coast protection works. R Berkley-Thorn and
A C Roberts. Publishedby ThomasTelfordLtd, 1981.

6.

Hydraulicpedormanceof breakwatercrown walls. HydraulicsResearch
'1988.
Limited. ReportNo SR 146, March

7.

Research on beaches and coastal structures. Proc. of Conf. in Coastal
Management.lCE, Bournemouth,
1989.

IJ

sB 261 0&O4l93



Tables

SH 261 0€Y04/'93



Table 1

Adjustment factors

wh/Rc>%

> /L

1:2slope,
1:2slope,
1:2slope,

0m crest
4m cresl
8m crest

1:4 slope ,
1:4 slope ,

4m crest
8m cresl
:.1

'1.00
1.O7
1. 1 0 '

^.

Wn/R"s1zz
1:2 slope ,
1:2 slope ,
1:2 slope ,
1:4 slope ,
1:4 slope ,
1:4 slope ,

0m
4m
8m
0m
4m
8m

crest
crest
crest
crest
crest
cresl

1.00
1.34

l.,sa
1.27
1.53
1.67

sF 261 0€r/04/93



AppendixA

Oveilopping measurement

sR 261 0&O4l93


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