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 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 Test variables 2.1 Returnwallprofile 2.2 Returnwallposition 2.3 Seawardslope 2.4 Bermgeometry 2.5 Crestelevation 1 2 2 2.6 Wave conditions Modeldescription Wave measurements Overtoppingmeasuremenls 2 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 4 Testresults 5.1 Data presentation 5.2 Effectsof crest elevationand wall height 5.3 Effect of seawallslope 5.4 Effect of crest width 5 Test measurements 3.1 3.2 3.3 o o Design method 6.1 Designgraph 6.2 Exampleproblem 6.3 Applicationto other seawalls 6.4 Rock revetmenls 7 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, 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 summarises the main for the design of conclusionsof the study, and makes recommendations seawallsincorporatingwave return walls 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, or 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 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 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 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 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 periodTBAR Resultsfor this balch are then outputand the data discarded before moving onto lhe next batch At the end of samplingthe arithmeticmeanand standarddeviationof H.,r,and TBAR overall the batchesis calculatedand printedout lt is thesetwo values which are then used to representthe wave conditionsof the test The value of Hrr is defined as being the average height of the one third highest waves and is generallyquite close to the spectral analysis equivalentof H,''o SimilarlyTBAR and T,; are also consideredto be comparable This data is followed by two histog'ramsbased on wave height giving wave height class and the number of waves in that class One histogram is accumulated throughoutthe batch and its totals are added into the other histogramwhich is accumulatedover all batches Since they are loo lengthy to be output duringsamplingonly the histogramfor the final batch is outputat the end All the above informationapplies to each of the wave probes being monilored during the test References Wave spectrumsynthesizers E&ME Tech Memo 111572,Hydraulics ResearchStation,June 1972 Twin wire wave probe modules Tech Memo 311974,Hydraulics ResearchStation,October1974 The fast Fouriertransformwith applicationsto spectraland cross spectral anafysis.HydraulicsResearchStation,Int Report100, December1972 sq 261 0&04/93 H A B c D E F H A B C D E F Figure 0.61 0.53 0.38 0.33 0.31 0.15 0.10 33 30.5 22.7 19 16.3 I 0.91 0.79 0.50 0.42 0.52 0.23 0.10 66.7 56.7 35.3 30.7 38.7 o./ ro.J 1.22 1.05 0.61 0.52 0.75 0.30 o.11 100 87.3 47.7 40 64.7 25 7.3 1.52 1.33 o.72 0.60 0.99 0.38 0.11 '1.83 1.63 0.84 0.67 1.24 0.46 0.11 AfterBerkleyThorn & Robefts M odel( m m ) Basic form of recurvedwall profile (metres) cl +I ol :-l o-YI q.(l ul- ! at7 2e va, l-= +a- cro cr$ =3- ;o r-r= -t lJJ J = vl IJ tll E o ou4 F 7A }E o z cL o- e = + ro o Figure2 Configurationfor model tests co -i /o ,t dr ;t /: 't r' ET ,t ' ' f::\ t t2 '/ -,r'1'- ro / A / o / c rlc / / / * E \f,n Oi / ! + = q) -,2 tL /' * r' U) c o C 76 o co >{zu vl AJ o, L O U1 o E U) o +/ Z N.9 O(/} ;vcc J i5 /o a.r / uQ c.t / -i JollDJ Figure3 aDroq )stc Resultsfor 1:2 gradient Crest width 0m A @ O l+ Nr') i LtE {: t/ fo/i' (o A A t U t slc o oo * = _o a) +- L tL F o C (u m o (, a c) o L O (n a CJ c N.9 ^' -(cn O{) U) c : C i5 O O o rol)Dj Figure4 a6Joq )slc Resultsfor 1:2 gradient Crest width 4m O O o -i ,,6 ll tta ro o < o -* o o -o Q/ q) L o o c o tL oo E O/ O/ Xtn o / L / C) co 0/ a o oP s ">)' - - J a o a-z >i (_) -: 0-) (t f, N >.6 q .-,oo o c{., oo o fl U) a q) C a D qJ tC] r'|l l-T-rrT%r.r O O o O o rol)ol Figure Final design graph a6roq)src O LN tn LN e O f, \o E (U 'g o E = a C 'o a C ot E E E E o LN (_ o E c- -)r' tJ O (Y Figure 10 Rock revetmentreturnwall d @ @ o (o o + E rTn OI -(J ! + q) q., = LL c C a c m q) a q) o O a u't o) c NO UI C : o'6 - O q O O O O O Jo])ol a6Joq )slc Figure 11 Rock slope overtoppingcurves o-) i- Ert w & Sdl of l ) (ilA n{ d /1"^ CLUTrn/ ,J; "7r" +-1 2r" ! I t/) tk4JL L t-, I u I f+ {t @ ilo' c; aK\l U + E oY -io -o CJ c) + = tL c o m d UI U U'' o L o o o a (l', c : c!o o'6 A - cc) i5 O o rol)oJ Figure 12 Rock slope comparedwith 1:2,0m berm I O O O d q o O ,- + (o q * E t{- n OY -o -o * = OJ a) tL tr u', o () co L U o q, L O o a a a) c : q.) C NO v( A - oc F ic! m o o O rol)oJ abtoq:srg Figure13 Rock slope comparedwith 1:2,4m berm I '100 \ \ -\_ S e a w a lst l e l:2 t/t OJ Ctl L JO \ tr'10 Se a va l [ s l o p e 1:1 g o - V a r y l n gc r e s t h e l g h t V a r y l n gv a t t h e l g h f Slgnlflcan wta v eh e l g h tl ? m M e a nv a v e p e r l o d5 s Plalnsloplngseavatts Z e r oc r e s t y l d t h 1.0 1:5 2.0 v e r a t h[ e i g h tt m S W L ] Figure 14 Effectof raisingthe crest 2.5 ... 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. .. estimatingthe effectivenessof recurvedwave returnwalls during the design of seawalls (Section 6) Section summarises the main for the design of conclusionsof the study, and makes recommendations seawallsincorporatingwave... 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