design of vertical wall caisson breakwaters

8/12/2019 Design of Vertical Wall Caisson Breakwaters

1/14

DesignofVerticalWallCaissonBreakwatersUsingPartialSafetyFactors

HansF.Burcharth*andJohnDalsgaardS0rensen**1 , Abstract

Thepaperpresentsanew system forimplementationoftargetreliabilityincaissonbreakwaterdesignsbymeansofpartialsafety factors.Thedevelopmentofth esystem isexplained,andtablesofpartialsafetyfactorsa re presentedforimportantoverallstabilityfailuremodesrelatedtocaissonstructuresplacedonbeddinglayersandhighrubblemound foundationswithunderlayingsandandclaysubsoils.2 .IntroductionGiventh estochasticnatureofwaveloadsitisimportanttodealwiththeinvolveduncertaintiesinarationalayhenesigningreakwaters.pplicationfheartialafetyactoronceptsgenerallyacceptedasarationalsolutiontoimplementationofsafetyindesigns,andisadoptedin manynationalcodesaswellasintheEUROCODE.Thepartialsafetyfactorsareinexistingcodescalibratedgainstxperiencewithheerformancefumerousivilngineeringtructuresnwhichwayitisassuredthataconventionalstructure,suchasahouse,willbtaintheusualsafety whenesignedsingherescribedafetyactors.owever,hectualafetynermsfprobabilityfacertainamagewithincertainpanofyearssnknown.orbreakwatersthisseemsotoeuitableonceptecausextensivexperiencewithxistingtructuressotavailable.Moreover,tseciableonowhectualafetyfesignlsoecauseationalcomparisonsflternativeesignsaveoeerformednheasisfqualafetyevels.Reliabilityanalysis,f.ex.usingalevel2FirstOrderReliabilityMethod(FORM),canofcoursebedoneornytructureymeansofcomputerrograms.However,tsegardedelpohedesignerstomakea partialsafetyfactorsystemavailablewhichinaneasywaymakesitpossibleto designabreakwatertoanytargetreliabilitylevel.SuchasystemwasintroducedanddevelopedbythePIANCPTCIIWorkingGroup2onRubbleMoundBreakwatersBurcharth991nd993)ndasoweenurtherevelopedoovercaissonbreakwatersbythePIANCPTCIIWorkingGroup2 8onVerticalWallBreakwaters. Thepartialsafetyfactorsystemisdevelopedonth ebasisofthevalidityoftheGoda(1985)waveloadformula.Thisformulaisnotvalidfo rdesigncaseswherefrequentwavebreakingdirectlyon thecaissonwalltakesplace.Thiscausesverylargeshort-durationimpulsiveloadsfo rwhichdesigntoolsarehardlydeveloped.Steepseabedslopesorsemi-highrubbleslopesinfrontofthestructurecantriggersuchunfavorablewaveconditions.Goda(1985pp32-138)providesadviceashowto avoidsuchexcessiveimpactloadings.

*Prof.Dr.Teehn.HydraulicsandCoastalEngineeringLaboratory,Inst.of CivilEng.,AalborgUniversity"Associateprof.Ph.D.Inst.ofBuildingTechnologyandStructuralEngineering,AalborgUniversity2138


2/14

COASTALENGINEERING1998 2139

Theoverallrocedureindevelopmentofthepartialafetyfactorsystemcomprisesth efollowing steps:dentificationoffailuremodesormulationoflimitstateequationsfo rthefailuremodesodellingofuncertaintiesrelatedtoloads(waves),strengths(soils,concrete)andlimitstateequationselectionofformatfo rth epartialsafetyfactorsystem alibrationofth epartialsafetyfactorserification

3.FailuremodesAllossibleailuremodesmusteonsiderednheesign.TheresentaperealswithheoveralltabilityfailuremodesillustratedinFig.l.AmorecompletediscussionoffailuremodesisgiveninBurcharth(1998).

Shorewardliding Overturningroundeel

Crushing

Slipailuren subsoilandettlement

Slipurface'

Slipailuresandubsoil rubbleoundation

Slip surfaces

Erosion ofubbleoundation,foreward tiltndettlement Scourn seabed, forwardtiltndettlement

Erosion* \

_ nI

Scourv'1J..--. A,,'U,

Breakage andisplacement ofarmournitsArmournits

Fig.l . Importantoverallstabilityfailuremodes.


3/14

2140 COASTALENGINEERING1 9 9 8

4 WavemodellingForcalibrationofpartialsafetyfactorshemaximumsignificantwaveheightinTyearsisdenotedHgandismodelledbytheextremeWeibulldistributionfunction:

Hj M=[l e*p(-( ) )] (1)Wavedatarom4quitedifferentgeographicalocationsareelected,eeablewheresshewaterepth,Nsumberofamplesnd sheumberofobservationsperyear.

N A a P h3Bilbao 50 4.17 1 .39 1.06 4.9 2 9 Sines 15 1.25 1.78 2.53 7.1 35

Tripoli 15 0.75 1.83 3.24 2.9 27Follonica 46 5.94 1.14 0.58 2.69 1 0

Table.WavedatafromdifferentlocationsfittedoaWeibulldistribution.3,Hsndhsreinmeters.ThewavedataromBilbao,inesndTripoliorrespondodeepwaterwaveswhilehewavedataromFollonicacorrespondohallowwaterwaves.nordertomodelhestatisticaluncertaintyaand?aremodelledasNormaldistributedvariables.Themodeluncertaintyelatedohequalityofhemeasuredwavedatasmo-delledbyamultiplicativestochasticvariableZHSwhichisassumedtobenormaldistributedwithexpectedvalueandstandarddeviationa zoodandpoorwavedatacouldberepresentedbya z0.05and0.2,correspondingtoaccele-rometerbouyandfetchdiagramestimates,espectively.5.oilstrengthmodellingTheundrainedsheartrengthofclaysmodelledbyaog-Gaussiandistributedstochasticieldcu(x,z)}whereandxareverticalandhorisontalcoordinates,respectively.heexpectedvalueunctionE[cu(x,z)]ndhecovariancefunctionCov[cu(xi,zi),cu(x2,z)}swritten

E[cu(x,z)}=E[cu(z)]Cov[cu(xi,z1),cu(x2,z)]=Cov[cu(x1-X,Zi-z2) 23

where(xi,Zi)and(x2,z2)aretwopointsinthesoil.[cu(x,z)\givestheexpectedvalueindepthzoftheundrainedshearstrengthofclay. ov[cu(xi,i),cu(x2, r 2)]giveshecovariancebetweenutosition(xi,zi)ndutositionx2,z2).Var[cu(xi,zi)]=Cov[cu(xi,zi),cu(xi,zi)]isthevarianceofcMatposition(xi,i).Itseenhatheexpectedvaluedependsonhedepthandhecovariancede-pendsonheverticalandhorisontaldistances.enerallyhecorrelationengthsinhorisontalandverticaldirectionwillbedifferentdueoheoilstratification.


4/14

COASTALENGINEERING998 141 Themeanvaluefunctionandcovariancefunctionareassumedobemodelledby

E[cu(x,z)) o+cnlzCov[cu(x1,z),cu(x2,z)]=ofoexp -|a( -z)|Jexpf-(/3(x1-z2))J

whereu0andKlmodelheexpectedvalue,aCushestandarddeviationandaand3modelhecorrelation.Sincehebreakwateroundationsmadeofrictionmaterialandtsssumedthatoundationfailuremodescandevelopebothintherubblemoundandinsandsubsoil,statisticalmodelsorheeffectiverictionangleandheangleofdilationareneededfortherubblematerialandthesandsubsoil.TheseanglesaremodelledbyLognormalstochasticvariables.6.stimationofpartialafetyactorsoroneailuremodeIncodecalibrationbasedonfirstorderreliabilitymethodsFORM)itsassumedthatheimitstatefunctioncanbewritten

ff x,z = 4where =xi,...,xn)s ealizationfX Xi,...,Xn).xternaloads(e.g.wave),strengthparametersandmodeluncertaintyvariablesareexamplesofuncertainquantities,=z-[,.. ,ZN)reNdesignvariableswhichareusedodesigntheactualstructure.ealizationsxofXwhereg(x,z)correspondsoafestates.IfthenumberofdesignvariablesisN=henthedesignmodelledbyz)canbedeterminedfromhedesignequation

G(xV,7>0 5)xc=(x\,...,xcn)arecharacteristicvaluescorrespondingtothestochastic variablesX. =(71,...,7m)arempartialafetyactors.hepartialafetyactors7areusuallydenneduchhatji>,i=1,...,m.nhemostimplecasem=n.Thedesignequationscloselyconnectedoheimittateunction4).nmostcasesheonlydifferenceishathevariablesxareexchangedbydesignvaluesxrfobtainedromhecharacteristicvaluesxcandhepartialsafetyactors7.Thecharacteristicvaluesareforvariableloadvariablesusuallythe98fractileofthedistributionfunctionofthestochasticvariables.orthesignificantwaveheightthecharacteristicvalueHSLschosenasthecentral estimateofthesignificantwaveheightwhichnaveragesexceededonceeveryTLears.hedesignvaluesorloadvariablesarehenobtainedfrom

xf=xc, ~ f i 6)Thecharacteristicvaluesareforstrengthvariablesusuallythe5%or50 fractilesofhedistributionunctionofhetochasticvariables.Herehe50ractiles


5/14

2142 COASTALENGINEERING1998

usedinordertoobtainpartialsafetyfactorslargerthanorequalto.hedesignvaluesarehenobtainedfrom

7Theimittate esignequationsreormulatedeithers orcebalanceor,inasefoundationailuremodes,sworkequationssinghepperoundtheoryofplasticityelatedokinematicallyadmissibleupturefailures.igureillustrateswoypicalcases.

Horizontalliding Foundationailu

To beariedtodentifymin. stability

Figure.Illustrationoffailuremodesorormulationoflimittatedesignequa-tions.Forslidingfailureheimitstateunctioncanbewritten

g=FGZFvFu(ZHsHD))f-ZFHFH{ZHD)whereFGeducedweightofcaissonunderwaterFuaveinducedupliftorceFHorisontalwaveforceHDesignwaveheightZHSodeluncertaintyrelatedoheignificantwaveheightHspcensityofthecaissonZpHodeluncertaintyonhorisontalwaveloadZpvodeluncertaintyonverticalwaveoad/rictioncoefficientThedesignequationcorrespondingto8)swrittenG=(FG-0.77F[r)fc-0.9(LFwhere 89


6/14


fceanofbasefrictioncoefficientjzartialafetyactoronfcFQeanvalueofreducedweightofcaissonunderwaterF[jandFavenducedpliftorcendorisontalwaveorcealculatedyGodaformulaeusingynHDLswaveheight,whereJHshepartial

safetyactorndHDLshexpectedmaximumwaveheightnstormwithY-yearseturnperiodoftenakens.8HSL).hefactorsZF0.77andZF0.90compensatesorhebiassafety)implementednheGodaormulae.

Forfoundationailureheimitstateunctioncanbewritteng=FS+FG-ZFvFu(ZHaHD))u>v~ZFHF(ZHSHDUH10)whereFsoyancyeducedgravitationalforceonhelidingoilelementu > Visplacementvector,oy=in(tpHisplacementvector,JH=os{^pj,9)/cos(pc iTheeducedeffectiveangleoffrictionscalculatedrom

sintp'rcos/vta,inpd sin< p 'rsinr j )r

wherep' rsheeffectiveangleoffrictionand/vshedilation.Thedesignequationiswritten

G={Fc +F{,-0.77.FX-0.90-F^ 11)whereFJshemeanvalueofFs-ovanduj,areobtainedusinghehedesignvalueoftanipc determinedfrom

72tanv=r.e 2 where7^shepartialafetyfactoronanyj.Theapplicationareaforhecodeisdescribedbyanumber,Lofdifferentypicalstructures.heartialafetyactors7arealibrateduchhatheeliabilityindicesorrespondingohe tructuresareasloseasossibleoheargetreliabilityndex3t=$~1(Pj),wherePjsheargetrobabilityofailure.Thissformulatedbyhefollowingoptimizationproblem

min W(7)=2>y( 7)-ft)2 13)


7/14

2144 OASTALENGINEERING1998

whereWj,j=1,...LareweightingfactorsXw=iwi=1)ndicatingtherelativefrequencyofappearanceofthedifferentdesignsituations.3j(j)sheeliabilityindexorstructureno.7.ormatorpartialsafetyfactorsPartialafetyactorsarecalibratedwithheollowingcodeentries:

hedesignlifetimeTL=20,50or100years)heacceptableprobabilityoffailurePf=0.01,0.05,0.10,0.20or0,40)

correspondingoheargeteliabilityndices3T=2.33,1.65,1.28,0.84or0.25)

hecoefficientofvariationaz =0.05and0.20).Deeporhallowwaterconditions.Hydraulicmodelestornot.

Thepartialafetyactorsare:-aloadpartialsafetyactorfp= obemultipliedtohepermanentoad.-aoadpartialafetyactor7 obemultipliedoHSLthecentralestimateoftheignificantwaveheightwhichnaveragesexceededonceeveryTLears).ThedesignwaveheightsobeakenasamultiplumofHSL.

-aafetyactorjzobeusedwithrictionmaterialsnubblemoundand/orsubsoiltangentohemeanvalueoftherictionangleisdividedbyyz)-

-asafetyfactorjcobeusedwiththeundrainedshearstrengthofclaymaterialsintheubsoil(themeanvalueoftheundrainedshearstrengthisdividedby7c).

8.imitstatefunctionsanddesignequationsForcalibrationofthepartialsafetyactorsheparametersforhestochasticvari-ablesshownintable2areused.hecorrelationcoefficientbetweenZFHndZMHandbetweenZpvndZMVreestimatedoughlyo0.9.nableDdenotesadeterministicvariable,N(jU,a)denotesanormaldistributionwithexpectedvalueftandstandarddeviationaandLN(/J,)denotesalognormaldistribution.Thetidalelevationfismodelledasastochasticvariablewithdistributionfunction-Fc(C)=\arccos( -jwhere(0shemaximumidalheight.0 .75msused.


8/14


distribution referencePc N(2.1,0.1075) Burcharth1992)

ZFH N(0.90,0.25) Bruining1994)ZFV N(0.77,0.25) Bruining(1994)ZM N(0.81,0.40) Bruining1994)ZMV N(0.72,0.37) Bruining1994)V v LN(0.43,0.043)V'r LN(0.61,0.061)Ips LN(0.35,0.035)f . LN(0.52,0.052)U cn N(0,)Cu 150kPaCul 0acu D(37.5kPa)a D(0.33)0 D(0.033)Z N(l,0.1)f N(0.636,0.0954) Takayama1992)

seeeq.14) Takayama1992)Hs exWeibullZHS N(1,^J

Table.tatisticalparametersforcalibrationofpartialafetyfactorsforfounda-tionfailurewithsandubsoil.Ifmodeltestshavebeenperformedtoestimatehewaveforcesthemodeluncert-aintieshownintable3canbeused.

distribution referenceZF N(0.90,0.05) VanderMeeretal.1994)ZFV N(0.77,0.05) VanderMeeretal.1994)ZMH N(0.81,0.10) VanderMeeretal.1994)ZMV N(0.72,0.10) VanderMeeretal.1994)

Table.Statisticalparametersormodeluncertaintieswhenwaveorcesarede-terminedonhebasisofmodelests.8.1HorizontallidingEquationsaregivenin .section68.2ScourfailureforcircularroundheadsonsandThedesignequationswritten,eeSumeretal.1996)noubblefoundation)

G=Vz ~ '5(1"eM~0-mKC(7HH^)-1wherepshewavesteepnessand

KC=vm.J-p u KZHSHSTT smh.(2Txh ILp


9/14

2146 COASTALENGINEERING1998

(T) Slidingetweentructurendeddings)ailurenubblemound" layer/rubbleoundation(3) Failuren rubble andliding betweenrubblendlay/sand 0

Clay,androckFailuren rubblemound

Clay,androck(5JFailurenubblendand

ft 6) ailurenubblendandft

(7) Failurenubblendlayrotation)ft

6J Failurenubblendlaycircular)ft

Figure3.oundationfailuremodes.

T=p ZHSHS7 T sP 9andthewavelengthLpsdeterminedfrom

Lp=gtaBh(2nh JLp)


10/14

COASTALENGINEERING998 21478.3HydraulicnstabilityoffoundationubblemoundarmourlayerThedesignequationswritten,eeMadrigaletal.1995)

hG Ac (5.8- 0.60)iVo7 7HH?

8.4FoundationfailuremodesFigurehowshenvestigatedoundationailuremodes.hecompleteetsofdesignequationscanbefoundinBurcharth(1998)andJ.D.S0rensenetal.1998).9 .artialSafetyFactorsBelowishowntheresultsoftheprobabilisticcalibrationofpartialsafetyfactors.Indeterministicdesignofthebreakwaterheollowingbiasvaluesorheorcesandmomentsaretobeused:

value

ZMH

0.900.770.810.72

Table4.Valuesofmodeluncertaintiestobeusedindeterministicdesign.Foundationailure sandsubsoil:

HS =0.05 a =0.2P .HM 1H 7Z 1H 7Z0.01 1 .4 1 .4 1 .4 1 .4 0.05 1 .3 1 .3 1 .3 1.40.10 1 .2 1 .3 1.2 1 .3 0.20 1 .1 1.2 1 .1 1 .2 0.40 1 .1 1 .1 1 .1 1 .1

Table5.artialsafetyfactorsforfoundationfailure andsubsoil-eepwater-nomodeltestsperformed.

=0.05 ZH =0.2Pf 1H 7Z 1H lz0.01 1 .3 1 .3 1 .4 1 .3 0.05 1 .3 1.2 1.4 1.20.10 1 .2 1 .2 1 .3 1 .2 0.20 1 .1 1.2 1 .1 1 .2 0.40 1 .1 1 .1 1 .1 1 .1

Table. Partialafetyactorsorfoundationfailureperformed. adubsoil eepwatermodelests


11/14

2148 COASTALENGINEERING1 9 98

azxK 0 05 0 2Pf 1H TZ 1H TZ0 01 1 5 1 4 1 3 1 50 05 1 4 1 3 1 3 1 40 10 1 3 1 2 1 2 1 30 20 1 2 1 1 1 1 1 30 40 1 1 1 0 1 1 1 1

Table. Partialafetyactorsorfoundationfailuretestsperformed. ubsoil hallowwater omodelaZK 0 05 zns 0 2

P . 1H Tz 1H Tz0 01 1 3 1 3 1 4 1 30 05 1 3 1 3 1 4 1 30 10 1 2 1 2 1 3 1 20 20 1 1 1 1 1 1 1 10 40 1 1 1 1 1 1 1 1

Table8.artialsafetyfactorsforfoundationfailureperformed. sandsubsoil-hallowwater-modeltestsFoundationfailure-layubsoil:


12/14

COASTALENGINEERING998 2149aL =0.05 a =0.2

Pj IH iz 1c IH IZ 1c0.01 1 .2 1 .5 1 .4 1 .3 1.5 1 .4 0.05 1 .1 1.4 1 .3 1 .2 1.4 1 .3 0.10 1 .1 1.3 1.3 1 .1 1.3 1.30.20 1 .0 1.2 1.2 1 .1 1 .2 1 .2 0.40 1.0 1 .1 1 .1 1 .1 1 .1 1 .1

Table2 .artialsafetyfactorsforfoundationfailure-laysubsoil-hallowwater-modeltestsperformed.Slidingailure:


13/14

2150 COASTALENGINEERING99 8Scourailure:

=0.05 =0.2Pf 7/7 7Z 7H 7z0.01 2.0 2.4 2.0 2.4

0.05 2.0 2.0 2.0 2.00.10 2.0 1.8 2.0 1.80.20 2.0 1.5 2.0 1.50.40 2.0 1.2 2.0 1.2

Table7.artialsafetyfactorsforcourfailureforircularroundheads-eepwater.=0.05 z=0.2

Pf 7H z 7H 7Z0.01 2.0 2.4 2.0 2.40.05 2.0 2.0 2.0 2.00.10 2.0 1.8 2.0 1.80.20 2.0 1.5 2.0 1.50.40 2.0 1.2 2.0 1.2

Table8.artialsafetyfactorsforcourfailureforircularroundheads-hallowwater.Armourayerailure:

=0.05 7 =0.2Pf ~ I z 1H z0.01 1.6 1.3 1.7 1.3

0.05 1.4 1.2 1.5 1.20.10 1.3 1.2 1.4 1.20.20 1.2 1.1 1.3 1.10.40 1.1 1.0 1.2 1.0

Table9 .artialsafetyfactorsforarmourayerfailureeepwater.aZHR =0.05 aZH


14/14


BurcharthH.F.:evelopmentfapartialoefficientystemorheesignofrubblemoundbreakwaters.IANCPTCIWorkingGroup12,Subgroup-F,finalreport,December1991.ublishedbyPIANCn1993).BruiningJ.W.Waveforcesonvertical breakwaters.Reliability ofdesignformula.DelftHydraulicsReportH1903,MASTIcontractMAS2-CT92-0047,1994).BurcharthH.F.:dentificationofdesignoolsorverticalwallbreakwaters.I-ANCPTCIWorkingGroup28,ReportbySub-GroupA.1998).MadrigalB.G.nd.M.Valds:esultsontabilityestsorubbleoundationofacompositeverticalbreakwater.ASTI/MCS,CEPYC-CEDEX,Madrid,(1995).SumerB.M.&J.Freds0e courattheheadofavertical-wallbreakwater.CoastalEngineering,1996).S0rensenJ.D.andBurcharthH.F.:mplementationofsafetyinthedesign.IANCPTCIWorkingGroup28,ReportbySub-GroupD.1998).TakayamaT.:stimationofslidingfailureprobabilityof presentbreakwatersforprobabilisticdesign.eportofPortandHarbourResearchnstitute,Yokosuka,Japan,Vol.1,No.,1992).VanderMeer.,K.d'Angremondand.uhl:robabilisticcalculationsofwaveforcesonverticaltructures.roc.oatalEngineering,Kobe,apan,pp.754-17671994).

design of vertical wall caisson breakwaters

Documents