The Effect of Seepage on the Stability of Sea Wall

7/29/2019 The Effect of Seepage on the Stability of Sea Wall

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CHAPTER48 THEFFECTOFEEPAGEONTHETABILITYOFEAW A L L

F.E.Richart, Jr. and. H. SchmertmannDepartmentofCivilEngineering,UniversityofFloridaGainesville, FloridaINTRODUCTION

Verticalbulkheads,retainingwallsoftheheet-pileype,oftenusedaseawallsatlocationsnotubjectedtocontinuousorseverewaveaction.anymilesofthisypeeawallhavebeenconstructedalongheFloridacoastandcoastlineoftheUnitedStatesarhavegivenatisfactoryservice.owever,heailuresfverticalwallswhichcontinueooccurduringmildtormsndicatehattheisignproceduresavailable, oractuallyused,maybenadequate.Thetabilityofverticaleawallsplacedincohesionlessoilpendsupontheelationsbetweenforceswhichtendtooverturntheandthosewhichprovideaestrainingmoment. Staticorcesonthewallareproducedbytheoilandwaterpressurefthebackfillwhitendtooverturnthewall,ywaterandpassiveoilpressuresonth

seawardideofthewall, andbyanchoroads. Dynamicorcesarealsoappliedtohewallbydirectwaveactionandbytheorcesdeveopedintheoilmassesdueoeepagelow. Theoileboundafte-wavempactonthewallincreasesheoilpressureofthebackfillrequireshedevelopmentoftemporarilylargerpassiveoilandanloadsorcontinuedwalltability. Seepageorceseducehepassipressurehatcanbedevelopedontheeawardideofthewallandtherebythreatenwalltability.

Thetabilityofaeawallhusdependsdirectlyuponthecap,ityoftheoiltodevelopufficientpassivepressureatregionsofdesignedestraint. Anyfactorwhichreducesheavailablepassiv*soilesistanceofloadedregionscausesaeductioninthetabilitythewall.

Conditionsuchaswavesovertoppingheeawall, rainwatfallingbehindthewall, orheaccumulationofwaterun-offfromhighergroundmayresultincompleteorpartialaturationofthefillandcauseawatereveldifferentialbetweentheoppositeidesthewall. Thisheaddifferenceesultsn eepagelowthroughtlbackfillandunderhewall. Theverticalcomponentftheattendaseepagepressurescausesachangeneffectiveoildensityandarespondingchangenoilpressures, suchthatthetabilityoftheischangedundereepageconditions.

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TH EFFECTOFEEPAGEONH ETABILITYOFEAWALLSInstabilityofeawallsmayalsodevelopnaprogressiveashiondueoextensivecouratthewallacewiththeesultingdecreasenpassiveearthpressureesistance. Scourmayoccurdueohighwatervelocityalone, ortmayoccuratlowerwatervelocityiftheeffectivedensityofthecohesionlessoilseducedbyupwardeepagelow. A

uniformateofupwardflowinfrontofthewallesultsromeepagethroughthebackfillandunderhewall. Inaddition, atransientupwardseepagelowisdevelopednearhewallacedueodifferentialwaterpressuresontheeabedcausedbywaveaction. Thecombinedeffectofthesewoeepagelowsncreasesheprobabilityofscournearhefaceoftheeawall.

Oneobjectofthispaperwasodeterminequantitativelythenflu-enceofeepagehroughhebackfillontheactorofafetyagainstwallrotationabouttheanchorpoint. Thegraphicallownetprocedurewasusedtocomputeheadditionalloads, causedbyeepagelow,whichactontheheet-pilewalls. Theesultsofthesecomputationswerencor-poratedintodiagramswhichpermitaapidcomputationoftheseaddi-tionalwalloadsandtheesultingchangesntheactorofafetyagainstwallotation. Thesediagramsncludeaufficientangeofthevari-ablesnvolvedtobeusefulasdesignaids.

Theecondobjectofthispaperwasoevaluatehepotentialef-fectsofeepageonthemportantproblemofcournfrontofthewall.Itsdemonstratedinthispaperhatanupwardeepagegradientatthesurfaceoftheoilnfrontofthewallcanbeamajoractornfluencingthepotentialcourofthisone. Suchaverticalgradientsdevelopedwhenbackfilleepageoccurs. Furthermore, thisteadygradientcanbetronglyeinforcedbyaransientgradientdevelopedfromwaveactioninfrontofthewall. Theequationsanddiagramspresentedinthispaperpermitevaluationofthecontributionoftheseeepageeffectstocourattheaceofthewall. Smalldepthsofcourcauseappreci-ablechangesntheactorofafetyagainstwallotationabouttheanchorpoint.

REVIEWOFLOADSACTINGONVERTICAL,SEAWALLSTheuseoftheclassicalearthpressureheoriespermitsaim-plifiedevaluationofthemagnitudeanddistributionofactiveandpassiveiarthpressuresalongheheightofaverticalheet-pilewall. ThesepressuredistributionsarellustratedinFig, 1asheyoccuralong:antileverandanchoredbulkheads.Theclassicalpressuredistributionshavegenerallybeenusedas

hebasisorhedesignofbulkheadsandheet-pilewallsalthoughits.nownhatmportantmodificationsofthepassivepressuredistribution,nparticular, mayresultfromwalllexibility. Methodsorncluding

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THEFFECTOFEEPAGEONTHETABILITYOFEAWALLS theeffectofwalllexibilityintodesxgnprocedureshavebeenpresentedbyTerzaghi1954),asedonheesultsfmodelestsbyRowe1952)andTschebotanoff(1949).ACTIVEEARTHPRESSURE

Whenawallmovesoutwardelativeoheoilmasstconfines,theoilmassproducesactiveearthpressureonthewall. Forcohe-sionlessbackfillsbearingagainsttheearaceofeawalls, theactiveearthpressure, PA atanydepth, z, inoilofeffectiveunitweight Y-isgivenbytheexpression:

f*rK#z (i)inwhichKAlshecoefficientofactiveearthpressure, ascomputedfromCoulomb'sEquation(Taylor, 1948).PASSIVEEARTHPRESSURE

Theexpressionforheimitingpassiveearthpressurewhichcanbedevelopedatanydepth,,sawallsmovedntocohesionlessoilis,

'pKftZ 2)inwhichK pscomputedromheCoulombequationorpassiveearthpressurecoefficientTaylor, 1948). Designproceduresoftenarebasedontheassumptionhattheangleofwallrictionisero, sincehispro-videsaconservativedesign. Table givesvaluesoftheactiveandpas-sivecoefficientsfearthpressure, KAandK p forheconditionscor-respondingozeroangleoffrictionbetweenthebackfillandaverticalwall, andforwhichtheurfaceofthebackfillshorizontal. Terzaghi(1954)hasgivenvaluesofKAandKp baseduponvaluesfanglefwallrictionobtainedfromestdata, whichmayalsoeusedfordesignpurposes.

Passiveearthpressureprovidesdirectestraintoheembeddedportionofcantileverandanchoredheetpileeawalls, andprovidesn-directestraintoheupperendofanchoredeawallshroughtheanchorystem. Figure 1howsheonesofoildevelopingpassivee-sistancesomotionsfthewall.797


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C O A S TA LENGINEERINGTABLE

Angledf CoefficientofoefficientofCohesion- Internal ActiveEarthassiveEarthlessSoil Friction oj Pressure K^_ressureKp

Dense 38 0.24.2Medium 34 0.28.5Loose 30 0.33.0

EFFECTOFSTATICWATERPRESSUREWhenevertaticwaterpressureexistsnoiladjacentoaea

wall, itcausesnncreaseofpressureonhewallbyanamountof64b. pert.2oreachootofwaterepth, andatheameimecausesaeductionofheearthpressureonhewall. Theactiveandpassiveearthpressuresaredecreasedbecauseheubmergedunitweightofhematerialnowcauseshehorizontaloilorcenhewalland'm t V > $\jrmustbeusednEqs. 1and nplaceoftheotalunitweight H^).

Whenhebackfillsplacedhydraulicallybehindheeawall, itpossibleorheotaloadonhewalloexceedhedesignoad. Undetheseconditions, waterpressureoadshewallovertsentireheightadditionoheactivepressureexertedbyheubmergedbackfill. Suaconstructionprocedureamountsooneypeofoverloadestofhestructureandmayconstitutehegreatesttaticoadhewallmustsustain.EFFECTSOFWAVEACTION

Inadditionotaticoads, aseawallmustresistheattackofwavesuringstorms. Verticaleawallshouldnotbeusedatoca-tionsubjectedoviolent,reakingwavesbecauseofheargempacforceswhichmaydevelop, butareoftenusedwheremoderatewaveactionmayoccur. Evenmoderatewaveactioncontributesynamicloadsdirectlyoaeawallandheurroundingoil. Inadditionerrporarilynducedwatermotionnheoilmaycauseignificantchanginearthpressures.

Figure llustratesheactors, describedbyBruun1953)ontributedbywaveaction,whichmayhavemportanteffectsuponhestabilityofverticaleawalls. Wavesactingdirectlyagainsthewalproducepulsationsofhorizontaloadwhichareesistedbyoilorcedevelopedashewallmoves. Occasionalhighwavesovertophewal

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TH EFFECTOFEEPAGEONH ETABILITYOFEAWALLSanddumpwaterontoheurfacefthebackfill. Ifthebackfillmaterialispervious, thiswaterindstswaybacktoealevelbypercolatingthroughthebackfillandunderhebottomoftheeawall. Finally, asthewaveseflectedfromhewall, waterushesdowntheaceofthewallandproducescourofthebottommaterialnearheaceoftheeawall. Theprocessfcournearheacefheeawallsassistedbytheupwardhydraulicgradientdevelopedintheperviousbottommaterialbythewavepressuresonthebottomandbyeepagehroughthebackfill.

Saturationofthebackfillcanalsooccurdueodirectainwater,oraccumulationofrainwaterunoff, aswellasbywaveoversplash.Accumulationofwaterbehindthewallcausesanncreasedoutwardpres-sureandattheameimeeducespassiveoilesistanceasaesultofseepagepressures. A detaileddiscussionofthemethodsorevaluatingtheeffectsofeepagepressuresonthedesignofeawallssgiveninafollowingectionofthepaper.

EVALUATIONOFSEEPAGEEFFECTSTHESEEPAGEFLOWNET

Theconvenientgraphicallownetconstructionforhandlingeep-ageproblemswasdevelopedbyForscheimer1930)andhasbeenusedextensivelyformanyyears. Thelownetsestablishedbytrialketch-ing. Thus, itsanapproximateprocedure;butalownetaccurateenoughforengineeringpurposescanbemadeapidlyafteromeprac-tice. Inadditionohenumericalnformationobtainedfromuchadiagram, thelownetalsogivesanover-allpictureofthelowcondi-tionsntheegionconsidered.

Thelownetepresentsateadytate, twodimensionallowcon-ditioninwhichDarcy'sLawsassumedvalid. Itconsistsoftwoetsoflines, flowlinesandlinesofequaltotalhead. Iftheoilssotropicwithrespecttopermeability, thentheseineseverywherentersecteachotheratightangles. Forketchingandcomputationalconvenience,thelownetsgenerallydrawnwithaquareashebasicelementfthenetandwithanequalateofflowbetweenanytwoadjacentflowlinesnthenet. Withthelownetdrawn, theateofeepagelow , thehydraulicgradient , andthewaterpressure p , maybecomputedatanypointwithinthenet.

Flownetconstructionandanalysiscanbemodifiedtohandlemorecomplicatedconditionsuchascaseswherehepermeabilityoftheoilinthehorizontalandverticaldirectionsarequitedifferent, transientflowproblems, somehree-dimensionallowproblems, andflowys-temshroughlayersofdifferentpermeabilities. Sinceadetaileddiscus-sionofthedevelopmentanduseofflownets, aswellasreatmentsf

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TH EFFECTOFEEPAGEONH ETABILITYOFEAWALLSspecialproblems, wasgivenbyCasagrande1937)andbyTerzaghi(1943),ndisavailablenrecentbooksnoilmechanics,twillnotberepeatedhere,EFFECTSOFSEEPAGEONTHEPRESSUREDISTRIBUTIONAROUNDVERTICALWALLS

AshownbyEqs. 1and, theactiveandpassiveoilpressuresaredirectlyelatedtoheunitweightoftheoil. Theeffectiveunitweightoftheoilchangeswiththedevelopmentofeepagelowandtheassociatedeepagepressuresexertedontheoil. Downwardeepageflowbehindthewallncreasesheeffectiveunitweightoftheoilandthusncreasesheactivepressurepushinghewalleaward. Upwardflowinfrontofthewalldecreasesheunitweightofthisoilandhusreduceshepassiveoilesistanceoanyoutwardmovementoftheoeofthewall.

Theaboveeffectcanbecalculatedfromheormula,

where \S.shechangentheubmergedunitweightoftheoil,)fcy.isheunitweightofwater,

and, isheverticalcomponentofthehydraulicgradient.Thus, inorderoobtainheaveragechangeneffectiveunitweightdueoeepagelow, itisonlynecessarytoobtaintheaverageverticalcomponentofthehydraulicgradientneitherheactiveorpassiveail-urewedges, andtomultiplythisbytheunitweightofwater. UsingheflownetofFig. 3, theaverageverticalcomponentsofhydraulicgradi-enthavebeendeterminedforheactiveandpassiveearthfailurewedgesindicatedinFig. 3. Thesegradientshenchangeheeffectiveunitweightoftheoilbytheollowingamounts:

(4 )**?**,*= (tv fca-0.30(64)*-19 %

Sinceaypicalvalueorheubmergedunitweightofaandis0bs.ft. , itmaybeeenthateepagecancauseappreciableearthpressurechangesnthedirectionofwallnstability.8 01


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C O A S TA LENGINEERINGOntheotherhand,eepagelowalsohasaneffectwhichincrease

thewalltability.hewaterpressurehasamoreavorabledistributicagainstthewallwheneepagelowexistshanthehydrostaticdistribu-tionforheamewaterevels,shownonFig..tmaybeeenthetheeffectisoneofincreasedtabilityofthewalldueoeductionofwaterpressuresontheactiveide,ndadditionalwaterpressureontlpassiveide.Theneteffectoftheimultaneouswochangesnpressuredistributionmustbeevaluatedwhentudyingheeffectsfeepageonthestabilityofawall.igure waspreparedinorderopermitarapidestimateofthechangemhorizontalorcesonaheet-pileypewallwl

thehydrostaticpressureconditionischangedbyeepagelowunderhwall.heeepageorcecorrectionmethodpresentedinFig. isbasontheollowingassumptions:1.hewallsplacedinahomogeneous,isotropic, cohesiclessoilwhichoverliesanimperviousayer.2 .llchangesnoilandwaterpressuresdueoeepageeffectsareassumedtovarylinearlywithdepth, whichpermitsthewopressurechangeeffectsobencorporatedintooneAFcomputation.3.heA"and"P"hartsareonlyvalidwithwallpenet]tionratiosD/D')between.1and.7.ithinthisangethasbeendeterminedthatneglectinghendividualD/D'ationvolveamaximumerroroflesshan0% .

Anyerrorsnvolvedintheusefassumptions and areprobeminorcomparedwiththepotentialerrorsnassumption;oilsplactbymanornaturenhorizontaltrataarenotlikelytobehomogeneouandisotropic.herefore,nmanynstancesheuseoftheeepageforcecorrectionprocedureuggestedhereinmustbeconsideredasapreliminarycomputationtodeterminefthepressurechangesdueopotentialeepagelowareignificantinthewalldesign.SEEPAGERESULTINGFROMWAVEACTION

Surfacewaterwavesoccurringnainitedepthofwaterproducunderwaterpressureswhichcanbemeasured,rmaybeestimateduseofanappropriatewaveheory.hepressureattheeabottombeexpressedas,fr*K^(vt) (5)

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THEFFECTOFEEPAGEONTHETABILITYO FEAWALLS where (x,t)epresentsheelevationofthewaveurfacemeasuredfromhetillwaterevel, J ishedensityofwater, andKrepresentsasub-surfacepressureesponseactor."

Atanyinstantoftimeadifferencenpressureexistsbetweentwopointseparatedbyadistancexalongheeabottom. Ifthebedmaterialspermeablehispressuredifferenceonitsurfacewillcauseseepagelow. Inhistudyofhedampingeffectongravitywavescon-tributedbypermeableeabedmaterial, Putnam1949)consideredthatthiseepagecausedbygravitywavessgovernedbyDarcy'sawforsteadylow. Recently, ReidandKajiura1957), alsonvestigatedtheeffectofapermeableeabedonthedampingofgravitywavesbytreat-ingheproblemasawo-layer, coupledystem. Theyincludedheeffectsfaccelerationofflowinthepermeableayer, butoundtheef-fectsofaccelerationtobenegligibleorpracticalcases.

Inhemmediatevicinityofaeawallheeepagecausedbythedifferentialwavepressuresalonghebottomsconsiderablyaffectedbythepresenceofthewall. Ashewaveunsntoaeawall, thewaterheightathewalleachesatleasttwoimesheunobstructedwaveheightandproducesacorrespondingncreasenpressurenhebot-tom. Ashewaterallsalonghewallodevelopaetreatingwave, atroughisormedadjacenttoheeawall. Figure a)and(b )llus-trateheeepagelowinapermeableeabedresultingrompressuresdevelopedbythesewoconditionsofwavemotionatheeawallace.ThempermeableboundaryformedbypenetrationoftheeawallntothepermeablematerialwillforceeepagelowtobecomeverticalatthewallfaceasndicatednFig. 2b). Forhewavepositionasndi-catednFig. 2b), theupwardeepageorcesnearhewallacedueothewavewilleinforceheupwardeepageorcesdevelopedfromover-splash. AtthepointA, thewaveeepageorcesaredownandinthisregiontheywillendtocounteracttheoversplasheffects.

Inorderoevaluatehemportanceoftheeepagedueowaveactionnearaeawall, ariangulardistributionofpressureonheeabottomwasassumedtoepresenttheransientpressurebeneathae-treatingwave. Byconsideringhispressuredistributionastaticataparticularnstantoftime, theteadytateeepagelowwasestablishedbymeansoftheRelaxation"procedure, andthelownethownnFig.wasobtained. Thehydraulicgradientwhichcausesupwardflowatthefaceoftheeawalldependsdirectlyuponthehydraulicgradientalongtheeabottom," /jftaL- Themaximumvalueofhydraulicgradientattheaceoftheeawallandattheandurfaces, C mMe< &.& "d*/jftLandtheaveragevalueoveranarea.2Ldeepandextending.2Lfromthewallaces, ^awe*0- '"H^L. ^hevaluesfhydraulicgradientatotherpointsbeneaththewavecanbeobtainedfromFig. 5 .

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THEEFFECTOFSEEPAGEONTHESTABILITYOFE AWALLSUpwardforcesnearheeawallaceesultingromwaveeepagepressureseduceheeffectiveunitweightoftheeabedmaterialbyanamountequalto vJju-. Figure permitsanevaluationofthehydraulicgradientntheeabedintermsofthewavepressuregradientontheeabottom, resultingromanygivenurfacewavehape. Thusanestimate

canbeobtainedofthecontributiontowardcouroftheeabedmaterialwhichisproducedbywaveeepagepressures.Theeffectsofaccelerationofflowdueoheimeateofchange

ofpressuredistributionontheurfaceoftheeabedwereneglectedinthistudy. However,tmightbeanticipatedthatheupwardhydraulicgradientsnearheeawallfacewouldbencreasedomewhatbyaccel-erativelow.CHANGESINWALLSTABILITYDUEOSEEPAGE

Inorderoevaluateheeffectofeepageonthetabilityofaverticalheet-pileypeeawall, considerananchoredwallwithfreeearthupportasllustratedinFig. 1a). Theactorofafetywithre-gardtootationofthewallasaigidbodyabouttheanchorpointwillbeusedashecriterionorevaluatinghetabilityofthewall.Inorderoimplifytheequationsorheactorofafety, itwasassumedthattheubmergedunitweightoftheoil, isequaltoheunitweightofwater, ,. Theactorofafetywithandwithouteepage

flowwasdeterminedforaheaddifference,Ah ashownonFig. 1a),assumedtobeequalotsmaximumvalueofH' D. Forheconditionofhydrostaticpressureofoilandwateractingonthewall, theactorofsafetyagainstotationabouttheanchorpointis,

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C O A S T A LENGINEERINGfamiliesofcurveshownonFig. a).husorawallhavingparticulargeometricalratiosD/H"ando C ,heactorofafetywilldependup< theallowablevalueofthecoefficientofpassiveearthpressure,Kp.definition, factorofafetyof1.0orgreatersequiredfortabilityofthewall,onsequentlythecurveshownonFig. a)whichextendbelowF.S. =1.0epresentunstableconditions.

Wheneepageoccurs,tillwithAhmaintainedashemaximumvalueofH1 D, changentheactorofafetyofthewalloccurs,rtheactorofafetyundereepageconditionssgivenasF5 (3-%')[(P/rf)VitPO-%')]

Thenthechangenfactorofafetyasaesultoftheeepagelowcanbedeterminedfrom,

Eq .< o -q .7AFS*,81Figure b )howshepercentchangenfactorfafetydueoeepaflow.hehadedportionsfthediagramsepresenttheportionofpracticalignificance,orwhichthewallstableunderconditionscompletebackfillaturationandnoeepagelow.heneepagelowoccurs,heactorofafetymaybedecreasedorncreased,owevertheeffectisgenerallylesshan0percentdifferentfromhatorheflowcondition.

Fromhisimplifiedtreatmentofthetabilityofsheet-pileyjseawallstisevidentthatfuchawallisdesignedtowithstandfullwaterpressuredifferenceandretainanadequateactorofafetyundtheseconditions,hattheadditionaleffectsofeepagelowwillprodonlymallchangesntheactorofafety.EFFECTSOFCHANGESIND/H'

FromFig. a)tseenthattheactorofafetydependsmaedlyupontheatioD/H',wheno Cn


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THEFFECTOFEEPAGEONTHETABILITYOFEAWALLSFigure 7a)howshedimensionsandoilcharacteristicschosen

toepresentapproximatelyaheet-pileypeeawallwhichfailedduringamildtorm. Whenthebackfillscompletelyaturated, andthewaterlevelontheoutsideofthewallsustattheandurface, theunbal-ancedwaterhead, Zih, is.5'. Forhisconditionandfornoeepageflow, theactorofafetyagainstotationabouttheanchorpoints.62.Wheneepagelowoccursheactorofsafetyiseducedo.57, orareductionofabout percent. Consequently, theeffectofeepagelowalonesnsignificant.

Whenthedepthofembedment, D, isvaried, theeffectonthefactorofafetyisashowninFig. 7b). ThewallbecomesunstablewhenDiseducedjustlightlymorehanoneoot, forheconditionincludingeepagelow, andforlightlylesshan.5'ornolow. Thismagnitudeofcourhasbeenobservedattheaceofeawallshatfailed,andtsprobablehatbackfillaturationandtoecourweremportantfactorsntheailures.

Thehorizontalorcesdevelopedduringeepagelowthusappeartobeofmallmportancecomparedtochangesndepthofembedmentaseachcontributesoaeductionintheactorofafetyofsheet-piletypeeawallswithfreeearthupport.

EFFECTOFSEEPAGEONSCOURATWALLFACEHYDRAULICGRADIENTSA N DSCOURVELOCITY

Theprecedingectionhasllustratedthemportanceofrelativelysmalleductionsnthedepthofwallembedmentupontheactorofsafety. Thedepthofmaterialwhichestrainsheoeofthewallagainstoutwardmotioniseduced-whencouroccursnthisegion;scoursparticularlyimportantwhenitoccursadjacenttohewallace.Thustbecomesnecessaryoestimateheeffectscontributedbyeep-agelowtowardincreasingheprobabilityofcourattheaceofthewall.

Fromaboratorytudies, suchashosepresentedbyIppenandVerma1953), ithasbeenhownthatcoursacomplexphenomena,evennacontrolledlaboratoryflume. Thecouringactionofwavesreflectedfromaverticalwall, withappreciableairandoilcontainedinheurbulentwaterepresentsanevenmorecomplexproblem. How-ever, thecontributionofverticaleepageowardncreasedcourcanbeestimatedbyconsideringonlyitseffectonheunitweightoftheoilparticles.807


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COASTALENGINEERINGFigure howsaurfacecohesionlessoilparticlebeingub-jectedtopotentialcourbywatermovingacrossheparticlewithvelocity V. Theorcesactingonthisparticleareasollows:FQ =dragorce BV3/24BiV2 (IppenandVerma, 1953)FL =iftforce CV2 (IppenandVerma, 1953)W =effectiveweightoftheparticleFf smaximumrictionforce WFjJan;where shefrictionangleandincludesboththeruerictionandparticlenterlockingeffects.

Anupwardhydraulicgradient, iv throughtheoilbedonwhichthesoilparticlesestingeducesheeffectiveweightoftheoilparticlethuseducingherictionforce.

Themaximumnon-scourvelocity, V, isattainedwhenFJJ Ffandiv , andmaybeexpressedas:B,V-(Wl'.0-CV,)t*iw (9)

Whenupwardeepagesoccurring, (iv ) ,Wseducedandthemasmumnon-scourvelocityiseducedtoV. Equation9henbecomes:

Dividingequation0by9, andimplifying, gives:(10)

(11)

TheatioV'/Vepresentsheactorbywhichthehorizontalvelocityhasobeeducedtopreventcourafteranupwardhydraulicgradienhasdeveloped.hisatiowillbecalledthescourvelocityreductiofactor"andbegiventheymbolR.Anypercentreductionintheeffectiveweightofeachoilparticresultsnaimilareductioninthemtergranularpressureswithint

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COASTALENGINEERING soilmass.nexpressionforatioofverticalntergranularpressure,p ndthereforealsoofindividualparticleweight,W,tanydepthinaubmergedoilmass,eforeandafterupwardeepagelows:

(12)iv*o v4*o.z[(fie)ft*"lvft"-] , (i+e\"J Thepecificgravityvalues, G , ofthehreemostcommonandgrainmineralsarequartz 2.66, calcite 2.72, andfeldspar 2.56. A commonrangeofvoidratiovalues, e, foruniformands.5 5o0."Therefore, unlessGandearemateriallydifferentromheabove,equation2maybewrittenwithufficientaccuracyas:

wU*o ./-.-. "> a*0-\.)Fromequations1and2 , onecanobtain:

(14)Or, fromequations1and3onecanobtainthemoreapproximatefo

Equation5hasbeenusedtoprepareagraphoftheelationshjbetweenthecourvelocityreductionfactor, R, plottedagainstthe< ticalhydraulicgradient, iv ThisgraphispresentedinFig. 9. Atinstantoftime, ivepresentsheummationofthegradientsdueosteadyeepageromhebackfillandtheransienteepageconditiontowaveaction.EVALUATIONOFEXITGRADIENTDUEOBACKFILLSEEPAGE

Thelownetsconstructedforhepurposeofevaluatingheoa zontalorcesonthewalldueoeepagealsoprovidevaluesfthehydraulicgradientattheoilurface.orhistudy,lownetsweconstructedforaD/Hangerom.25o.50,ndforaD/D'anof.1o.7. Byexpressingheexitgradientas810


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T H EFFECTOFEEPAGEONH ETABILITYOFEAWALLSleS(^f) 16 )

theextremevaluesofSwereoundobe.21and.2 8orvaluesftheparametersD/D' =0.7, D/H =0.25, andD/D' ., D/H =0.5,respectively. Valuesof"S"obtainedfromdatagivenbyMcNamee1949)forheameangeofgeometricalparameterswereoundobe.22 and.30, respectively. IncomparingheesultsofelevenflownetswithMcNamee'sesults, thedeviationsnindividualvaluesofexithydraulicgradient, ie variedromzeroo percent. Thisndicatesthatthegraphicallownetswereuniformlyaccurate.

SincehevaluesofSwereoundtohaveafairlysmallvariation,itisuggestedhatanaveragevalueof.25beusedinEq. 16, orhattheexithydraulicgradientcausedbyeepagehroughthebackfillbetakenas,

TheuseofS /4nvolvesamaximumerrorof7%orhecasesstudied, buthiserrorsnodoubtmuchsmallerhanthosearisingfromthedifferencesbetweenactualoilconditionsandthehomogeneous, iso-tropic, conditionsassumedasabasisorhelownetconstruction. TheuseofS /4isalightefinementoftheupperimitingvalueofS /3whichwasuggestedbyTerzaghi1954).EXAMPLE

TheexampleofFig. 7a)sherecontinuedtonvestigatehem-portanceofeepagegradientsonpotentialcournfrontofthiswall.Considerhecaseofthiswallduringatorm, whenrainfallandover-splashhavecompletelysaturatedhebackfillandwavesaretrikingandbeingeflectedbyhewall.ForhemaximumvalueofhofH 1 DusedwithEq.7,heexithydraulicgradientdueoeepagehroughthebackfillorheex-ample, Fig. 7a), is

Inadditiontoheteadyeepage,wavepressuresontheurfaceoftheseabedproduceamaximumvalueofverticalhydraulicgradientatthefaceofthewallof,

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COASTALENGINEERINGlMX-.* "9,

andanaveragevalueoveradistance.2Ldeepand.2Lawayfromlwallface, of, l-'0M& 20)Foravalueof$9^firL.*0.4 - } themaximumandaveragevalueofverticalhydraulicgradientdueowavepressuresare,

^mx*0-6+ 21)lave O.Z6Theseemporarygradientsareaddedtoheteadyvaluedueobackfseepageogive

H-~-98OOWAL 0.60

WTAt 22)

WhenenteringFig.withtheaboveesults,tmaybeeenthathecourvelocityreductionfactor,R,salmostzeroorhemaximigradientmmediatelyadjacenttohewall,ndisabout0.6orheavageconditionoverhe.2Ldistanceromhewall.hus,hebackfiseepageandwaveconditionsassumedinthisexamplearecertaintoresultncourmmediatelyadjacenttothewall,ndtheresagreatincreasedlikelihoodofcouroradistancefatleast.2Lromhewall.METHODSOFELIMINATINGO RMINIMIZINGSCOUR

Scourattheaceofaverticalheet-pileypeeawallmaycauamarkedeductioninfactorofafetyofthewall,swasdemonstrainthetudyftheexamplehownonFig..herefore,recautionsshouldbeakentominimizehepossibilitiesfcouratthemostcricalegions.Sinceupwardeepageorcescontributeotheprobabilityofcmethodsfpreventingorcontrollingeepagelowhroughthebackfi]shouldbencorporatedintohedesignofthewall.avingheurfac

ofthebackfillsoneobviousmethodofpreventingwaterromenteri812


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T H EFFECTOFEEPAGEONH ETABILITYOFEAWALLSPAVED SURFACE OF BACKFILL

INVERTED FILTERANDIPRAP DRA IN

Fig.0 Methodsofminimizingeffectsofseepage.

FLOW FLOW NETPig.1Effectofimpermeablebodyonverticalseepageflow.

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C O A S TA LENGINEERINGthebackfillbyoversplashorainrun-off,ndhasbeenfoundeffectiveinincreasingthewalltability.rainsarealsodesirableontercepiwaterwhichleakshroughcracksnthepaving,roequalizeheun-balancedwaterpressuredevelopedduringarapiddrawdownofthemesealevel.yinterceptinghewaterlow,hedrainspreventflowbe-neaththeoeofthewallandonotallowverticalhydraulicgradientsdevelopntheoneofpassiveoilpressure.igure0llustratesaneffectiveocationforadrainystem;hedrainisowenoughthatlargunbalancedwaterheadscannotdevelop.

Upwardeepageorcesontheeabedcanbecounteractedbyprvidmgtaticweightnearhewallface.ipraporargeocksmustbusedascoverorhisoadedegiontomaintaintheoadatthepropeilocation,venduringevereactionbylongshorecurrentsandbreakirwaves.riteriaestablishedforbreakwaterdesign,uchashosegivenbyHedar1953),maybeusedtoelecttheproperizeofcovermaterial.owever,tsnotatisfactorytoplaceargeocksdirectuponbeachmaterial,inceheinermaterialmaybecarriedthrougrthevoidsntheargermaterialbywaterlow.

Figure1llustrateshedisturbanceofverticallowbyanim-permeableobjectrestingontheurfaceofthepermeablebed. Theflowofwatermustdetouraroundtheobstacle, therebycrowdingheflowlinesogetherandincreasingthehydraulicgradientnearheboundaryftheock. Inthisegiontheeffectiveweightofthebedmaterialhasbeeneducedbytheupwardflow. Erosionwilloccur_bjneaththeedgesftheockasaresultfhorizontalwatervelocitiescausedbywavesactingonthebedmaterial. Progressiveunderminioftheedgesftheockwilleventuallycausettoinkintoheandandbecomeneffectiveascourprotection.

Morehanfortyyearsagotwasecognizedthatapermeablesurchargeplacedoverheegionofupwardeepagelowwouldprevitheoccurrencefpiping"beneathstructuresdueoeepagelowthroughpermeableoundations. Terzaghihasmadeextensiveusei suchapermeableurchargeconstructedintheormofan"invertedfilter,"nwhichthelayersfcohesionlessmaterialsncreasedingramizeowardtheop. Healsoestablishedrelationsorhegrasizevariationsofuccessivelayers. TheseulesorgrainizevaationswereatermodifiedlightlyasaesultfextensiveestsbyWaterwaysExperimentStation, Vicksburg,Mississippi, andtheeimendeddesignproceduresareummarizedinthepaperbyPosey1

Filtershouldalsobeplacedaroundcollectorpipesnthebacfilldrainystemopreventthebackfillmaterialfromlowingoutthroughthedrains. Asaturatedcohesionlessbackfillwillloweacthroughelativelymallholesorcracksnaetainingwallandcan

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TH EFFECTOFEEPAGEONH ETABILITYOFEAWALLScauseacave-inofthebackfillurface. Severalcave-intypeailureshavebeenreportedbyGebhard(1949)whichwerecausedbyandflowingthroughsmallholesorcracksnthetructure. Whenacave-intypefailureofaeawallbackfilloccursduringatorm, theoilesistancetowaveorcesseliminatedatthisocationandthewallisknockedover, landward, byrepeatedwavempacts. Thushetabilityoftheseawallagainstthisypeoffailuredependsuponmaintainingcontinuityofth ebackfill.

CONCLUSIONSTheeffectsofeepagelowonthetabilityofverticalheet-pilewallswereconsideredinthistudy. Stabilitywasevaluatedintermsoftheactorofafetyagainstigidbodyrotationofthewallaboutthepoint

ofanchorattachment.Seepagelowthroughhebackfillandunderhewallcauseshori-zontalorcesonthewallasaesultofthechangesnwaterandoilpressuredistributionsromhosecorrespondingohehydrostaticcon-dition. Theneteffectontheactorofafetyproducedbythesechangesinwaterandoilpressureswasoundtobeunimportantforhecasesstudied.Atudyofthemportancefthegeometricalparametersfaeawalldemonstratedthattheactorofafetychangesignificantlywith

smallchangesntheembeddeddepthofthewall. Removalofmaterialattheouteraceofthewallbycourchangesheembeddedlengthoftheseawallandinthiswaycourmaychangeheactorofafetyofthewallappreciably.Oneeffectofeepagehroughthebackfillsoeduceheeffectivedensityofthecohesionlessmaterialnfrontoftheeawall. Thisteadystateeductionnoildensityiseinforcedbyatransienteffectesult-ingromeepagelowinducedbypressuregradientsdevelopedalongheseabottombywaterwaves. Adiagramsncludedwhichillustrateshe

relationbetweentheexithydraulicgradientdueoeepagelow, whichdeterminesheeffectiveoildensity, andtheeductioninvalueofhori-zontalwatervelocityequiredtoproducecour.Abriefdiscussionisalsoincludedofmethodsoreducingoreliminatingcourfmaterialattheaceftheeawall.

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C O A S T A LENGINEERINGREFERENCES

Bruun, P. (1953). BreakwatersorCoastalProtection--HydraulicPrinciplesnDesign: XVIIIInternationalNavigationCongress,Rome, Sll-Q..

Casagrande,A. (1937). SeepageThroughDams: HarvardUniversity,SoilMechanicsSeriesNo. 5 .Forscheimer, P. (1930). Hydraulik: Thirdedition.Gebhard,.C.1949).ave-InsofSandyBackfills:rans.ASCE,Vol. 114 , p. 490.Hedar, P.A. (1953). DesignofRock-FillBreakwaters: Proceeding!

MinnesotaInternationalHydraulicsConvention, Minneapolis,Minnesota.Ippen,A..ndVerma,R..1953).heMotionofDiscretePar-ticlesAlongheBedofaTurbulentStream:roceedingsMinne-sotaInternationalHydraulicsConvention, Minneapolis, MmnesoMcNamee,.1949).eepagentoaSheetedExcavation:eotechnic

Vol. 1,p. 229-241.Posey, C. J. (1957). FloodErosionProtectionforHighwayFills:TransactionsASCE, Vol. 122 ,p. 531-542.Putnam, J. A. (1949). LossfWaveEnergydueoPercolationinaPermeableSeaBottom: Trans.AmericanGeophysicalUnion,

Vol. 30, No. 3, June.Reid,R..ndKajiura, .1957).ntheDampingfGravityWa'overaPermeableSeaBed:rans.AmericanGeophysicalUnicOctober, pp. 662-666.Rowe,.W.1952).nchoredSheet-PileWalls:roc.nst.fCrv Engineers, London, Vol. 1, Part, pp. 27-70.Taylor, .W.1948).undamentalsfSoilMechanics:ohnWile^

andSons,nc., . Y.Terzaghi,K.1943).heoreticalSoilMechanics:ohnWileyand Inc., N. Y.

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THEFFECTFEEPAGEONTHETABILITYOFEAWALLSTerzaghi, K. (1954). AnchoredBulkheads; Trans. ASCE, Vol. 119,pp. 1243-1280.Tschebotanoff, G. P. (1949). FinalReport, LargeScaleEarthPres-sureTestswithModelFlexibleBulkheads: PrincetonUniversity.

APPENDIXLISTOFSYMBOLS

A coefficientusedocalculateAF Ba constantC constantDa depthofpenetrationofheetpilewallft.)D' depthromdredgeevelofirstmperviousoilayerft.)e voidatioofoil

FJJ dragorcedueowaterlowingacrossparturfaceoilparticlelbs.)Ff frictionforceesistingcourmovementofoilparticlelbs.) FT liftorcedueowaterlowingacrossparturfaceoilparticlelbs.)F.S.s factorofafetyAF netchangenorceonactiveidefwall, dueobackfilleep-ageeffectslbs.)4Fp netchangenorceonpassiveidefwall, dueobackfillseepageeffectslbs ) G pecificgravityofoilolidsH heightromipofwallowaterevelnbackfill, butnotoexceedH'ft.)

H' totalheightofwallbackfill, fromembeddedipofheetpiles(ft.)Abiheightdifferencebetweenwaterevelbehindandnrontofwallft.)l hydraulicgradientft./ft.)ieaerticalexitgradient, immediatelyeawardofwall, dueobackfilleepageiv erticalcomponentofhydraulicgradientK sub-surfacepressureesponseactorK coefficientofactiveearthpressure

Kpa coefficientofpassiveearthpressureLa assumeddistancebetweenpointsfmaximumand wavepres-sureonahorizontaleabedf) P oefficientusedocalculate AFpp activeearthpressurelbs.ft.2 )Ppaassiveearthpressurelbs /ft. ) pw waterpressurelbs.ft.*) q ratefeepagelowft.2/sec.)Ra scourvelocityeductionactorV /VS oefficientusedodetermineet timeV maximumwatervelocityacrossopfoilparticle, withoutscourmovementofparticleft.sec.)V alueofVwhenupwardeepagesoccurringft./sec )W ffectiveubmergedweightofndividualoilparticlelbs.)xaistancealongheeabottomft.)zaepthfromoilurfaceft.)taatioofheightoanchorpoint/totalbackfillheightJ fanitweightofoillbs.ft.^) J ubmergedunitweightofoillbs.ft.*)

ftv nitweightofwaterlbs./ft.)0 nglefnternalrictionofoil817

The Effect of Seepage on the Stability of Sea Wall

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