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CHAPTER 5 9

SEAWALLOVERTOPPING MODEL

JohnP .Ahrens,Aff.M .1andMarthaS .Heimbaugh,A.M.,2ASCEABSTRACT

Resultsfromanextensiveseriesoflaboratorytestsofirregularwaveovertoppingforanumberofseawallandseawall/revetmentconfig-urationsi spresented.atafor1 3configurationshasbeencollectedandgroupedinto7datasetsrepresentingrelativelysimilargeo-metricalcharacteristics.lldatasetsshowedanapproximatelyex-ponentialrelationshipbetweenth eovertoppingrateandadimension-lessfreeboardparameterwhichi sth eratioofth eseawallfreeboardtothelocalwaveseverity.hisfindinglogicallyledtoth edevelopmentofthreeprogressivelymorecomplexovertoppingmodels.Themodelsprovidearelativelysimplewaytoestimateovertoppingratesandanobjectivewaytoevaluateth ehydraulicperformanceofseawalls/revetments.dvantagesanddisadvantagesofthemodelsarediscussedandtheirabilitytopredictovertoppingratesi scompared.INTRODUCTION

Waverunupandovertoppingaretwoofth emostimportantfactorsinfluencingthedesignofcoastalstructures.urrentmethodstopre-dictovertoppingrates,suchasgiveninth eShoreProtectionManual(SPM,198^),relyonadatabasecomposedoflaboratorytestsusingmonochromaticwaves.naddition,problemsarisei nusingth eSPMmethodbecauseofuncertaintyi nchoosingproperovertoppingcoeffic-ientsandtreatingwaverunupasanindependentvariable.tudieshavebeenconductedwhichindicatethattheSPMmethodcan,forsomecircumstances,underpredictovertoppingrates(Douglass,1986)andforothercircumstancesgreatlyoverpredictstheratesGadd,etal .1985).hentheseoverestimatesorunderestimatesofovertoppingratesmightbeexpectedi sunclear.ecentlaboratoryworkusingirregularwaveshasproducedanalternativetotheSPMmethodofcalculatingovertoppingrates.

Datafor1 3differentseawallandseawall/revetmentconfigura-tionshasbeencollectedandcollatedinto7representativedatasets.Examinationofthesedatasetsrevealedthatallhadthecommonprop-ertythattheovertoppingratecouldbeexpressedasanexponentialfunctionofadimensionlessfreeboardparameter.hischaracteristicOceanographer,CoastalEngineeringResearchCenter,U.S.ArmyEngineerWaterwaysExperimentStation,P.O.Box631,Vicksburg,MS

39180pCivilEngineer,CoastalEngineeringResearchCenter,U.S.ArmyEngineerWaterwaysExperimentStation,P.O.Box631,Vicksburg,MS39180

7 9 5

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796OASTALENGINEERING1988heldregardlessofwhethertheovertoppingratewa sexpressedasadi-mensionalordimensionlessvariable.imilarfindingshavebeenre-portedbyOwen(1982)andJensenandJuhl(1987). Thispaperwillde-velopthreeexponentialovertoppingmodelswhichrepresentalogicalextensionofthegeneralrelation.achmodelhascharacteristicswhichareusefulandtheadvantagesanddisadvantagesofeachmodelwillbediscussed.criteriaforcomparingthemodelswillbepre-sentedandtheirabilitytopredictovertoppingrateswillbecompared.DATACOLLECTION

Laboratorytestswereconductedi ntheCoastalEngineeringRe-searchCenter's(CERC)45.73mlong,0.91mwide,and0.91mdeepwavetankandthe76.20mlong,3 . 3 5mwide,and1.83mdeepwavetank.lltestsusedirregularwavesgeneratedbycomputercontrolled,hydrau-licallyactuated,pistontypewaveboards.

DatasetswerecompiledfromthreeseparateCERCstudies.nestudytestedthreeseawall/revetmentconfigurationswhichhavebeenproposedtoprotectthehistoriclighthouseatCapeHatteras,NorthCarolina(GraceandCarver1985).secondstudytestedanumberofseawall/revetmentconfigurationsproposedtoimprovetheperformanceofexistingseawallsatRoughansPoint,Massachusetts,(Ahrens,etal.1986).hethirdstudytestedaseawallproposedtoprotectVirginiaBeach,Virginia,(Heimbaugh,etal.1988).esearchfundswereusedtoextendtherangeofconditionstestedtoallowthedevelopmentofmoregeneralrelationships.

Eachtestconsistedofapproximately3 0minutesofirregularwavegenerationduringwhichwaveconditionsweremeasuredusingresistancetypewavegages.ncidentandreflectedwavespectrawereresolvedusingthemethodofGodaandSuzuki(1976).aterwasallowedtopassovertheseawallsandcollectedinacalibratedcontainer.levationsi nth econtainerweremeasuredwithapointgagebeforeandaftereachtest.igure1showssimpleprofilesofeachseawall/revetmentcon-figurationusedtocompilethesevendatasets,andTable1summarizestestconditionsforeachdataset.oredetaileddescriptionsoftestconditionsandtestingprocedurescanbefoundinreferencescitedabove.METHODOFANALYSISANDFINDINGS

Oneofthemostimportantfindingstodatei sthedevelopmentofaneffectivedimensionlessfreeboardparameter,denoted'.'canconsolidatealloftheovertoppingdataforsimilarstructureconfigu-rationsintoasingle,welldefinedtrend.' i sdefined

y r n oiwhere,thefreeboard,is.theaverageverticaldistancefromth emeanlocalwaterleveltothecrestoftheseawall,mostheenergybasedzero-momentwaveheighteithermeasurednearth estruc-ture(datasets1through6 )andassumedtoberepresentativeofHm0tthetoeoftheseawall/revetment,ormeasuredatthetoe(dataset7)..stheAirywavelengthcalculatedusingthenominal (datasets1through6 )andthewaterdepthatthe

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SEAWALLOVERTOPPINGMODEL 797

DATASET

DATASET2

DATASET4

DATASET 3

DATASET5

I L DATASET6 DATASET7

Figure. Simpleeometricrofilessednachataet

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798 COASTALENGINEERING1988

Q.)

< M ,H Z t.

O E -H

O C L- c+> a.J. C(0 P E a)e 1) (0 3 < D

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SEAWALLOVERTOPPINGMODEL99structuretoe,s orthemeasured (dataset7),where i stheperiodofpeakenergydensityofthewavespectrum.henominalTsedi ndatasets1through6wasanassumedperiodbasedontheknownpeakperiodgenerateda tthewaveboardand fordataset7wasth emeasuredpeakperiodusingathreegageGodaarray.

Therelativefreeboard,' i stheratioofthefreeboardtotheseverityofthelocalwaveconditions.orenergybasedwavecon-ditionstheseverityseemstobebettercharacterizedbyvariablescontaining thanbyjustmoAhrens1987).heovertoppingparameter' i sefficientsinceitcontainsinoneterminformationaboutthewaterlevel,structureheight,andwaveconditions.uringatestseriesonaseawall/revetmentconfiguration,aswaveconditionsbecomemoresevere,apointi sreachedwheredetailsofthestruc-ture'sgeometeryseemtohavelittleinfluenceontheovertoppingrate. Thispointoccurswhenacombinationofahighwaterlevelandlargewavescausesthestructuretobevirtuallyswampedorinundatedbywaveaction.nundationoccurswhen'

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8 0 0 COASTALENGINEERING 1 9 8 8

6. 0 r- +5.36n2-0 u li0 B E A C HU N E -_e5-2.0S" 4. 0 ~700 H I 51 6.0 1 1 1 1

Eachofthemodelshascertainadvantagesanddisadvantageswhichwillbeillustratedusingdataset (Table1 )asanexample.ig-ure2showsadetailedprofileoftheseawallconfigurationfordataset1 .heseawallisbasicallyaverticalwallwithoutafrontingrevetmentandasmallrecurveatth ecrest(seeAhrens,etal.1986

0.91

a o fh . 3 0SE!!

o8.2 8.0 7.8 7.6 7.4 7.2 7.0 6.8 6.6 6.4 6.2 6.0 5.8

D I S T A N C E L O N GT A N KLOOR.M Figure2 .ataset seawallconfiguration

forfurtherdetails).igures3athrough3ccomparepredictedversusobservedovertoppingratesusing Models through3forpredictedvalues,respectively.igures4athrough4 cshowtheobservedandpredictedvaluesof r'safunctionof'orModelsthrough3 ,respectively.nFigure4cahorizontallineindicatesanovertoppingrateof0.05nr/m-secwhichrepresentstheapproximateupperlimitofovertoppingforstructuresafety,Goda(1987).ig-ure4cillustratesanadvantageofModel1 ,overtoppingi sgivenindimensionalunitswhichcanbedirectlyrelatedtopotentialflooding,levelsofdamage,orlevelsofdanger,suchasdiscussedbyFukudaetal.(1974)andtabulatedi nOwen(1982).

ByintercomparingFigures3 a ,3 b ,and3 c ,i tcanbeseenthatModel3i sbestatpredicting hesameconclusioni sreachedusingthecorrelationcoefficientsfordataset giveninTable2 .ThisfindingwouldbeexpectedsinceModel3hasthesecondvari-able,2 whichimprovesthepredictionbasedonjustF ' able2showsthatth esecondaryvariablefordataset i s/ds.Consid-erabletrialanderroreffortwentintotheselectionofthesecondaryvariableforeachdataset.nTable2thesecondaryvariablewhichworkedbestwith'npredicting' i slistedbydataset.nfourofthesevendatasetsth emostimportantsecondindependentvariabletousewith' i sthewavesteepnessparameter,

H 1 / 2

where,H E

2TTTheinfluenceofsteepnessinpredicting' indicatesthatsurf

conditionsandtheiraffectonpotentialrunuparequiteimportanttotheovertoppingprocessonsomestructures.ordatasets4and6theinfluenceoftherubbleberminfrontofthewalli simportantandthesecondaryvariablesreflectthisfact.hesecondaryvariableswhichimprovethepredictionof'ordatasets4and6areB/L_ndHdgespectively,wheregsthewidthofthebermandBsthewaterdepthovertheberm.eviewofth edataandtestconditionssuggestthatwhenthewaterdepthoverthebermi ssmallthebermdepthi squiteimportant,e.g.dataset6 ,butarelativelymodest

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SEAWALLOVERTOPPINGMODEL 80 10.20 ' 1 1 !/*-

QUJ PREDICTED= OBSERVED- yt .16Q ill ' 0.12 m " " /^ -dU IJ 2 ..0 8

5- 0 4 n

'ml

MODEL3 R=0.923 -

1 ,

( a )

0.20omt0.16 Q1 1 1 E 0.122-0.08

0.04

_ 1 I /^ _- PREDICTED=OBSERVED^ -- " y

m y' ~ - y - _ * - MODEL2 -- R=0.900 -- up -7,I.I,1 (b )

0.20 -1

PREDICTED 1 i '

-ain& 0.16 - -Q1 1 1 E 0.12 - a 0.08 m a V aa MODEL -n ^ a" ,a a R=0.889 s_- 0.04 __-' a O

n 1 i I

(c )

0.04.0 8.1 2.1 6 .2 0 Q,M7M.SEC,OBSERVEDFigure. Predictedersusbservedvertoppingates,odels-3

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802 COASTALENGINEERING1988

(5 |.016 .014w0.012O m 0.01 J0.0080.006z^0.004?-0.002

O Z .016 a.O .014 W0.0122 0 . 0 1 C O y0.008Q .006 w .004 Q_0.002

O $ 0.20 "g.1 6 if3 l .12C5z8:.0 8

i0.04 Od

1!MODEL3 Q'=0.338exp(-7.385F-2.178^-)a.

VLEGEND

IBSERVEDREDICTED(a)

- . -1 I i -- \ /-MODEL2\S Q'=0.212exp(-10.526F) --

-

- V -- I ~~*fr|fro m ,. l -

(b )

_ ! " I i -- i -MODELy O=6.684exp(-13.586F) --*%'

_ - -

(c)

0.2 0.4.6 F\RELATIVEFREEBOARD 0 . 8Figure1 . Observedandpredictedvaluesof nd'safunctionof'

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SEAWALLOVERTOPPINGMODEL03Table2

SeawallRevetmentSummaryChart*DataSetNo.1

Model1

RegressionCoefficient

71.952- 13. 5 86

OvertoppingVariables

FY

No.of Observations

89

CorrelationCoefficient( Qpred.vsQobs.)

0.889AQ

2 0.212-10.526 Q 'oF '0.90 0.0008561

3 0 .3 3 8-7.385-2.178Q9Fv

F/d30.923

2 1 32.357-13.091 Q9FY

11 8 0.777

2 0.1172-11 .1 3 8 3 * 0.789 0.00016773 0.308

-10.732-6.629 < Hmo

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8 0 4OASTAL ENGINEERING 1 9 8 8increasei nwaterdepthcauses t h e widtho f t h e berm t o b e t h e moreimportantcharacteristic,e . g .d a t a s e t 4 .n s o m einstancesi t w a sn o t c l e a r w h y o n e choice o f asecondaryvariable w a s betterthananother c h o i c e .ince t h e secondaryvariables a r e partlydependent o nt h e conditionstested t h e model3approachshouldn o t b e regardeda sproducing a n overlygeneralf o r m u l a .

I n Table 2 acorrelationcoefficienti sgiven f o r eachmodelf o reachdata s e t .hiscoefficienti s t h e correlationbetween t h e p r e - dicted a n d observeddimensionalovertopping r a t e s .singthiscorre-lationcoefficientprovides a f a i r way t o compare t h e effectiveness o ft h et h r e e m o d e l s .o rs o m e data s e t sModel 2has a l o w e rcorrelationcoefficientthanModel1 ,whichsuggestthat t h e method o f normaliz-i n g a s n o toptimum f o rthat d a t a s e t .no n e c a s e ,data s e t 5 ,Model even h a d ahighercorrelationcoefficientthanmodel3 . I ti sassumed t h a t normalizing nterferedwith t h esurprisinglyhighcorrelationbetween n d' f c o u r s e ,i t w a s necessary t onormalize h es a m e way f o r a l ldata s e t si n o r d e rt o makecompari-s o n s .u i t e a f e w differentways t o normalize ere t r i e d .Ideallyi twould b e advantageoust o normalize singwaveconditionvariablesm0 LD,a n d Tn d u s e characteristics o f t h e geometeryo f t h eseawall/revetment a n d waterdepth t o formulate t h e dimension-l e s sindependentvariables.ttemptst o develop a neffectiveover-toppingpredictionmethodbased o n separatingwave a n d structurevari-ables w a s unsuccessful.xperiencefromt h i ss t u d yindicatesthatthere d o e s n o t seem t o b e aconspicuouslysuperior w a y t o normalizeQ t h i sfindingi sconsistentwiththoseofJensen a n d J u h l( 1 9 8 7 ) .

Inspection o f Table 2indicatest h a t Model3does asubstantiallybetter j o b predictingovertoppingratesf o rdata s e t s1 ,4 ,5 ,6 ,a n d7thanf o rdata s e t s 2 a n d 3 .ata s e t s 2 a n d 3were t h e onlyoneswith t h e correlationbetweenpredicted a n d observedovertoppingratesl e s st h a n 0 . 9 0 .ata s e t s 2and 3 werealso t h e only d a t a s e t s wheret e s t s o fseawall/revetmentconfigurationswithslightlydifferent g e o -metrieswerelumped t o g e t h e r .na l lo ft h e o t h e rdata s e t s t h e waveh e i g h t s , wave p e r i o d s ,a n d waterdepthswerevaried b u t thereweren o changesi n t h e geometry o f t h e s t r u c t u r e .h e conclusioni st h a ts m a l lchangesi ngeometryo f aseawall/revetmentconfiguration c a nhave a nimportantinfluence o n t h e overtoppingrate b u ti sdifficultt o properlyaccount f o r t h echangei n asimpleovertoppingm o d e l .This findingi sconsistentwithOwen( 1 9 8 0 )whotabulatesdifferentovertoppingcoefficients f o reachdifferentprofiletestedofembank-ment t y p e s e a w a l l s ,Jensen a n d J u h l( 1 9 8 7 )whoshowdifferentover-toppingcurves f o r eachbreakwatera n d s e a d i k e t e s t e d ,a n d Bradburya n d Allsop( 1 9 8 8 )whotabulatedifferentovertoppingcoefficientsf o reachbreakwatercrownwallconfiguration t e s t e d .

O n e o f t h e usefulcharacteristics o f model 2i st h a ti t c a n b eeasilyused t o generate a hydraulicinefficiencycoefficient,'f o r aseawall/revetmentconfiguration.'sdefined a st h e areaunder t h e c u r v e ,sucha s showni n Figure 4 b ,between F '=0.30 a n di n f i n i t y .h el o w e rl i m i t o fintegration h a s been s e t a t t h e approxi-matevalue o f F 'wherewaveinundationo f t h e structurebecomes t h edominantmodeofovertopping.ymbolically w e haveio o

A = Q' /e x p( C . F * )d F '=- - - e x p( 0 . 3 0C . )q .30 1

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SEAWALLOVERTOPPINGMODEL05 Valuesof'regiveni nTable2 .enerallyth erankingofthestructuresusing'seemslogicalwithsomesmallsurprises.hesteppedseawallwithamoderaterecurve,dataset7 ,seemstoperformbelowexpectations.henthedatasetsbasedonseawallswithre-curvedparapetsareexamined,datasets4 ,5 ,and7 ,th everticalscaleoftherecurvesfordatasets4and5arelargerinrelationtoth eincidentmohantherecurvefordataset7 .tmaybethattherecurvesusedfordatasets3and4aremoreeffectivethantheoneusedfordataset7 ,partlybecausetheyrepresentalargerdis-continuitytotherunupflow,eventhoughtheyarepartlysubmergedathighwaterlevels.able3summarizestherelaventinformationondiscontinuityeffectsforrecurvedparapetsonseawallsforheavyovertoppingconditionsandlongperiodwaves. Rankingseawallsonth ebasisof'aluesalsoindicatesthatthesmallcurveatthecrestofthewalltestedfordataset i seffectivedespiteitssmallsize.Table3 .iscontinuityeffectsforrecurvedparapetsonseawallsfor

heavyovertoppingconditions,F '=0.30,andlongwaves,T =3.0sec

Vertical Hmotardsfora Heightof HeavyData HighWaterLevel Freeboard Recurved Overtop Discontinuity/Hmoet cm cm cm cm4 23.1 13.5 21.3 14.3 1.495 23.1 12.9 20.8 13.1 1.557 11.0 9.6 9 . 1 9.7 0.94

SUMMARYANDCONCLUSIONResultsfromanextensiveseriesoflaboratorytestsofirregularwaveovertoppingofanumberofseawallandseawall/revetmentconfig-urationsarepresented.vertoppingrateswerefoundtobestrongly

dependentonadimensionlessfreeboardparameter,' whichi stheratioofthefreeboardtoameasureofthelocalwaveseverity,Equa-tion1 .herei sanapproximatelyexponentialrelationbetweenQandF 'whichlogicallyleadstoth edevelopmentofthreeprogressivelymorecomplexovertoppingmodels,Equations2 ,3 ,and4 .heprimarypurposeofthemodelsi stopredictovertoppingratesbuttheyarealsousefulforevaluatingvariousstrategiestoreduceovertoppingandrankingth ehydraulicperformanceofthestructures.odel3i sthemostcomplexandusuallymakesthebestestimatesofovertoppingrates,however,nocompletelysatisfactoryapproachhasbeendevelopedwhichwillprovideagoodgeneralizedovertoppingmodelforavarietyofseawallandseawall/revetmentconfigurations.ACKNOWLEDGEMENTS

ThesupportoftheOffice,ChiefofEngineers,CivilWorksResearchandDevelopmentProgramforgrantingpermissiontopublishthispaperi sgreatlyappreciated.REFERENCESAhrens,J .P . ,Heimbaugh,M .S. ,andDavidson,D .D ."IrregularWaveOvertoppingofSeawall/RevetmentConfigurations,RoughansPoint,Massachusetts,WaterwaysExperimentStation,CorpsofEngineers,TechnicalReportCERC-86-7,Vicksburg,MS,Sep.1986.

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806OASTALENGINEERING1988Ahrens,J .P . ,"CharacteristicsofReefBreakwaters,"TechnicalReportCERC-87-17,U.S.ArmyEngineerWaterwaysExperimentStation,Vicksburg,MS.ec.1987.Bradbury,A .P. ,andAllsop,N.W.H.,"HydraulicEffectsofBreakwaterCrownWalls,"3rdInternationalConference,ICE,Eastbourne,England,May1988.Douglass,S .L. ,"ReviewandComparisonofMethodsforEstimatingIrregularWaveOvertoppingRates,"TechnicalReportCERC-86-12,U.S.ArmyEngineerWaterwaysExperimentStation,Vicksburg,MS.,Dec1986.Fukuda,N.,Uno,T . ,andIrei,I . ,"FieldObservationsofWaveOvertoppingofWaveAbsorbingRevetment,"CoastalEngineeringinJapan,Vol1 7 ,1974.Gadd,P .E . ,Machemehl,J .L . ,andManiban,V. ,"ComparisonofWaveOvertoppingPredictiontoMeasurementsfromLarge-ScaleModelTests,"ProceedingsofArtie' 8 5 ,SanFrancisco,California,April1985.Goda,Y .andSuzuki,Y. ,"EstimationofIncidentandReflectedWavesinRandom WaveExperiments,"Proceedings15thCoastalEngineeringConference,Honoulu,Hawaii,1976.Goda,Y.,"RandomSeasandDesignofMaritimeStructures,"UniversityofTokyoPress1985.Grace,P .J .andCarver,R .D. ,"SeawallandRevetmentStabilityStudy,CapeHatterasLighthouse,NorthCarolina,"TechnicalReportCERC-85-12,U.S.ArmyEngineerWaterwaysExperimentStation,Vicksburg,MS. 1985.Heimbaugh,M .S. ,Grace,P .J . ,Ahrens,J .P . ,andDavidson,D .D. ,"CoastalEngineeringStudiesinSupportofVirginiaBeach,Virginia,BeachErosionControlandHurricaneProtectionProject,"WaterwaysExperimentStation,CorpsofEngineers,TechnicalReportCERC-88-1,Vicksburg,MS.,March1988.Jensen,0 .J .andJuhl,J. ,"WaveOvertoppingonBreakwatersandSeaDikes,"InternationalConferenceonCoastalandPortEngineeringinDevelopingCountries,Beijing,China,Sept.1987.Owen,M .W.,"DesignofSeawallsAllowingforWaveOvertopping,"ReportNo.EX924,HydraulicsResearchStation,Wallingford,England,June1980.Owen,M .W. ,"TheHydraulicDesignofSeawallProfiles,"ProceedingsICEConferenceonShorelineProtection,Southampton,Sept.1982alsoPublishedThomasTelfordLtd,London,1983.ShoreProtection Manual ,4thEd.,U.S.ArmyEngineerWaterwaysExperimentStation,CoastalEngineeringResearchCenter,U.S.GovernmentPrintingOffice,Washington,D.C. 1984.