Pipeline Protection in the Surfzone

7/30/2019 Pipeline Protection in the Surfzone

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CHAPTER327 PIPELINEPROTECTION IN THESURFZONE

GerritJ.Schiereck,HenriL.Fontijn 1

ABSTRACT Stabilityrelations forrockonamildslopein breakingwaveswereinvestigated,bothexperimentallyandtheoretically.Assumptionsweremade forth einfluenceof turbulencein breakingwavesonth eloadexertedbyth ewavemotion.tappearsthatwiththeseasssumptions,th emechanismisreasonablydescribedin aqualitativeway.For design purposesth emethodisnotaccurateenough.Thisis possiblyduetoth eneglectionof th e(vertical)velocity fieldnearth ebottomin a breakingwave ,givinganunderestimationof th edifferencein stabilityin spilling or plungingbreakers.Theexperimentalresultsseemconsistentandcanbeusedprovisionallyfordesign purposes.Aninteresting poin tisthattheyalsoarein linewithexistingrelations forstabilityonsteepslopes.ACKNOWLEDGEMENT Theauthorsthankprof. dr.MarcelStiveofDelftHydraulicsforhispermissionto useth ewavemodelENDEC.ACZMarineContractorsisthankedfortheirinitiativeonth estudyonpipelineprotectionandth econtinuousinterestinth eprogress.1.INTRODUCTIONPipelinesonth eseabottomareusuallyprotectedinorderto preventdamagebyanchorsorerosion.Whereapipelinecrossesabeach,itoftenlaysinadredgedtrench,seeFigure1 ,andiscoveredwithstones.Forth edesignofsuchaprotection,whichcanbeseenasanarmourlayeronamildslope,aprovisionaldesignrulewasestablished,seeSchierecketal. ,1994,basedontheoreticalconsiderationsandexperiments.Fornon-breakingwavesonamildslope,th e

lDelftUniversityofTechnology,FacultyofCivilEngineering,P.O.Box5046 ,2600G A Delft,TheNetherlands4228


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PIPELINEPROTECTION 229

TOPLAYERFILTER LAYER 5\

Figure1Outfallprotection resultwasreasonablysatisfying.Forth estabilityinbreakingwavesnotheoreticalconceptwasavailableandth enumberof experimentswasnotsufficienttogivereliableresults.Inaddition,newexperimentswerecarriedout,inwhichth eslope,th estonedensityandth estonesizewerevaried.Also,anattemptwasmadetoderiveatheoreticalrelationshipfo rth estabilityofstonesin breakingwaves.Thepurposeofthisattemptwastwofold.First,experimentalresultsthatcanbeexplainedfromtheoryarebetterunderstood,decreasingth edangerofmisusingempiricalrelations,while,viceversa,heoriesthatcanbeverifiedbyexperimentsgetmorepracticalvaluein hydraulicengineering.Thesecondreasoncomesfromdidactics.Hydraulicengineeringisstillheavilybasedonempiricalrelations.Presentingalltheserelationswithoutalinktoth etheoryonfluidmotionisconsideredaweakpointinacademicalengineeringeducation.2 .APPROACH Experimentsareindispensabletoestablishdesignrulesinhydraulicengineering,so,laboratorytestsareth ebasisofth eresearchinthispaper.But,asalreadystatedinth eintroduction,th eexperimentalresultsshouldbeconnectedwithth ephysicalbackgroundofforcesduetomovingwater.Thecreationo falink betweenth efluidmotionandexperimentalresultsistriedwithasimple,butcompletedescriptiono fth ephenomenainvolved.Thestabilityofstonesona slopeisgovernedbyth erelationbetweenloadandstrength.Thestrengthis usuallysatisfactorilydescribedwithth eeffectiveweightandth efrictiono fth estones.Theloadismuchmorecomplex.Themovingwaterin abreakingwavewillexertforcesonastone.Eveninabreakingwave,th eorbitalvelocitieswillplayaroleinth evelocityfield.Also,th ebreakingwillcauseturbulenteddies,withtheirownvelocityfield.Thewholeoforbitalandturbulentvelocityfieldis responsibleforth eloadingonastone.Anothercomplicatingfactoristhatwavesinnatureareirregular.Therefore,omestatistaldescriptionofth ewavesisnecessary.Inth ecomputationsth eloadwillbecomposedofforcescausedbyth eorbitalmotion,incombinationwithturbulentvelocitiesduetobreaking.Forth estability,existingrelationsbetweenth eloadandstrengthof astonelayerinanoscillatingwatermotionwillbeused.


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4230 OASTAL ENGINEERING 99 6

3.BASICEQUATIONS Orbitalmotion Theoscillatoryflownearth ebottomisapproachedwithth elinearwavetheory:

*2 i n h J f c A TurbulentvelocitiesForth eturbulentvelocities,anapproachasgivenbyBattjes,1975and Battjes ,1987isused.Battjescoupledth erateofproductionofturbulenceenergytoth erateo fdissipationofwaveenergydueto breaking:q tfVPJ,/3 2)

inwhichqisth eturbulentvelocityscale(q 2=U j U j ) .Figure2showsacomparisonbetweenmeasuredandcomputedturbulentvelocityscale.Inthispaperth eexpressionforq ,equation(2) ,willbeusedasameasurefo rth eturbulentvelocity." ( D / P ^ q l m s ' J

0 1 2

0 .)

/(O/P)1/3/K ySy' \/ \V

^. *~* \\\S_L0 0>xm]

Figure2ComparisonofcomputedandmeasuredturbulentvelocityscaleThedissipationo fwaveenergyisderivedfromth eanalogybetweenaboreandabreakingwave,seeBattjesandJansen,1978:D B wgH2u 3 )

in whichQ Bisth efractionofth e(irregular)wavesthatarebroken,derived


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PIPELINEPROTECTION 2 31

from:ln(?s, (4 )

andwhereHMisth emaximum waveheight,givenby:

Formoredetails,eeBattjes& Janssen,1978.Severalmodelsareavailablein whichthisconceptisimplemented,e.g.th e2-dimensionalDUTmodelHISWA,seeHolthuijsenetal,989.Inthisstudyth e1-dimensionalmodelENDEC(DelftHydraulics ,eeBattjes&Stive, 1985)wasusedtocomputeth evariouswaveparametersalongth edifferentslopes,sinceinthismodelth ewaveset-upisexplicitelycomputed,whichpossiblycouldbeimportant.Waveheightdistribution Asabasisforth ewaveheightdistributionth eRayleighdistributionistaken.ThisdistributionisalsousedinBattjesandJanssen,1978.Inshallowwater,th ewaveheightdistributiondeviatesfromth eRayleighdistribution.H 1%inshallow water,whichplaysanimportantroleinth estabilitycalculations,isgivenby,accordingtoStive,seeCUR/CIRIA,991:

(l*Hs/h)1 '3 l+HJh)1'3J7~%-Rayleigh _r\"l%-shallowLoad-strengthrelationsAsimplerelationtoexpressth estabilityofstonesinoscillatingflowisbasedonexperimentsinanoscillatingwatertunnelbyRaneeandWarren,1968(seealsoSchierecketal . ,1994): a -1 =0.025[-5-]3 7> T2Ag50 AnotherapproachisgivenbySleath,1978.Analogousto th eShieldsapproachin uniformf low,Sleathgivesarelationbetweenth eshearstress(whichisnotnecessarilyth edominantload)andth estoneweight,partlybasedonth eexperimentaldatabyRanee&Warren(1968).Therelationfo rstonesreads:

xd=0.056.{p,-pw).g.d 8 ) disth eequivalentsphericaldiameter,inthispaperapproximatedbyd50 ,th e


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mediansievediameter,whichiseasilyavailableanddiffersonlyafew percentfromth esphericaldiameter.Theshearstressduetoorbitalvelocitiescanbeexpressedby:

*-fPw/.-ia 9 )withfwandubdependingonth ewaveheight,H,andth eperiod,T.Thecircumflexoveraparameterdenotes"amplitudeof.Givenacertainwaveheight,th elongerth eperiodis ,th elargerth eorbitalvelocityatth ebottom,ub.Forfw ,th efrictioncoefficient,th eoppositeholds:th eshorterth eperiod,th elargerth efrictioncoefficient.InCUR/CIRIA(1991)anexpressionbySwartis given,basedonJonsson(1966),wherefwisgivenasafunctionofth eorbitalstrokeatth ebottom,relatedtoth ebottomroughness:f xp [-6+ 5.2 A] (fwBM 0.3) 1 0 ) Computa t ionsThecombinationof orbitalvelocities,turbulentvelocities,waveheightdistributionandload-strengthrelationsintoadesignprocedurecanbedonein variousways.Insection5,thisisfurtherelaborated.4.EXPERIMENTS Experimentsweredoneinawavetank(length40m,width0.8m,depth0.9m)atth eLaboratoryofFluidMechanics,DelftUniversityofTechnology(DUT),seeYe, 1996.Theslopeangleswere1 : 10and :25.Themassdensitiesof th estoneswere2550and2850kg/m 3whileth enominaldiameters,dn50,varied between and .5cm .Thewidthofth esievecurvesofth estones(d85/d 15)usedinth eexperimentswasabout1.5.3to4layersofstonewereused,inorderto ascertainaproperroughnessbetweenstonesandslope.Thedifferencewithth egeometryofarealpipelinecover,whichhasafilterlayerunderth eto player,isassumedtobenegligiblewithrespecttoth estabilityofth eto player.Thestoneswerelaidincolouredstripsof 0.25m(measuredinth ewavedirection)overth efullwidthofth eflume.Thetotalnumberofstonesdisplacedaftereverytest,n,dividedbyth enumberofstonesinth ewidthofth eflume,wasusedasth etotaldamageS:S nd /w ID

inwhichwisth ewidthof th eflume.Anarbitrarydamagelevelof2waschosen forincipientmotion.


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Irregularwavesweregeneratedaccordingto aJONSWAP-spectrum;th enumberofwavestestedperspectrumwas2000.Thewaveheightsandspectraweredeterminedatth eto eofth eslope.Thewaterdepthatthatlocationwas0.6m.Figure3showsth eresultsofth eexperiments.ThestabilityisexpressedasHs/Ad,inwhichH sisth esignificantwaveheightatth eto eof th eslope.Thestabilityisplottedagainstth ebreakerparameter,,th eslopeanglerelative to th ewavesteepness.

13n 1211 1 0987 6 543 21 0

c


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5 .COMPARISONOFCOMPUTATIONSAND EXPERIMENTS Inorderto compareth ecomputationalresults,obtainedwithth eapproach describedinsection2 ,withth eexperimentalresults,atfirstth ewaveparameters alongth eslopewerecomputedwithENDEC,usingth emeasured wavecharacteristicsatth eto eofth eslopeatth ethresholdofmotion.From previousinvestigations(seeSchiereck etal. ,1994)it appearedthatinirregularwaves,th ehigherwavesareresponsibleforth eincipientmotion,in particularth ewaveheightthatisexceededby % of th ewaves.Thiswaveheightis computedwithequation(6 )forvariouslocationsalongth eslope.Theorbitalvelocitiesatth ebottom inthesewaveswerecomputedwithequation(1) .Ranee&Warren

Experim enta lresultsd-1m ,A-1.55vs .13 com puta tiona lresultsRanee & Warren 12-11- \ Experimentalr e s u l t s 10 - \S^Computation 1 9-8- \ omputationF-2

0 .6 o i 9 \

Figure4Compar i sonofexperimentswithcomputat ionaccordingtoRanee& WarrenThenecessarystonediameterisfirstcomputedwithth erelationofRanee& Warren.Withub=u*a b ,equation(7 )isrewrittenas:

*50 2.56* 4'5

(12)

Thisequationisvalidfo rahorizontalbottom.Thediameterinthisformulais


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th emediansievediameter,d50.Inordertocompareth ecomputationalresultswithth eexperiments,th enominaldiameter(dn 5 Q )isrequired,whichis approximately0.84*d50 .Theturbulentvelocity,fromequation(2) ,issimplyaddedtoth eorbitalvelocityfromequation(1 ) .Togetherwithacorrectionforth einfluenceofth eslopeangleonth estability,th eequationfinallybecomes:dn 0.84* 2.56* (fib+ F * q ) - 5 s i n < | > 50

]/TP*^8) . 5 sin ($-a)(13)

inwhichFisacalibrationfactorand j > isth eangleofreposeofth estones,heretakenas45.q ,asdefinedinequation(2),istakenasth eturbulentvelocity.Withthisequationth enecessarydiameteralongth eslopeiscomputed.Themaximumcomputeddiameterisused,whichisequivalenttoth euseofatotal-damageconceptinth eexperiments,regardlessofth elocationofth edamage.Forcomparison,th eresultsofth eexperimentswithps=2550kg/m 3anddn50=cmarebeingused.Figure4showsth eresultsforF= andF=2 .Theinfluenceofth eslopeangle,asseeninth eexperiments,isalsofoundinth ecomputations,butth einfluenceofth ewavesteepnessisnotreproducedcorrectly.Jonsson/SleathTherelationshipasfoundfromth eresultsofRanee& Warren(equation(7),expressesth erelationbetweenth estrokeofth eorbitalmotionandth enecessarydiameterto preventth eincipientmovementofth estones.Thisimplicitelyindicatesth einfluenceofth einertiaofth eorbitalmotiononth estonestability.Thesimpleadditionofaturbulentvelocitytoth eorbitalvelocity,asdoneinequation(13) ,attributesth esameinfluencetoth eturbulentvelocity,whichisnotlogic.Anotherapproachisth efollowing.Considerth eforcesonagraininaflowfield,seeFigure5.Theshearforceisexertedbyth eorbitalmovement ,describedwithequations(9),(1 )and(10).Equation(8)givesth erelationbetweenshearstressandstonesizeforincipientmotion.Thisequationisnowrewrittenforth eequilibriumofforces,whereth eturbulentvelocityisassumedtogeneratealiftforce,reducingth eeffectiveweightofth estone.Inthisway,th einfluenceofturbulenceistreatedseparatelyfromth eorbitalmotionwithitsspecificrelationforth efrictionfactor,equation(10).

Figure5Flowforcesonagrain

Theequilibriumofforcesthenleadstoth efollowingproportionality:


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4236 COASTAL ENGINEERING 99 6

-P w/u\\(p ,-p Jg V --PwC ?2 ( 14 )inwhichAhisarepresentativehorizontalarea,bothforshearandlift.V isth evolumeofastoneandCLth eliftcoefficient.Usingequation(8),thisleadsto :|Pw/w =0.056(ps-Pw)gd-pwCLq> (15)

givingfinally:

dn 2inq) (16 )50 0.056A g s i n ( < t > -a)inwhichCLisreplacedbyF,acalibrationfactorinwhichbothth eliftcoefficientandth etransferfromwaveenergydissipationintoturbulenceis included.

13121 1 10 9 8-j

" ( B 1-143 2 1 0

Experimentalresultsd-1cm,A-1.55vs.computationalresults Jonsson/Sleath ExperimentalresultsComputationF-0.1 omputationF-0 .5

1:25

1:10~ b v i o ' . z o i3 04 o ! 5 o l6 o ! 7 o ' . e 6^ ]

Figure6xperimentalesultsomparedithomputationsccordingoJonsson/SleathFigure6showsth eresultsfo rF=0.1andF=0.5.Theagreementissomewhatbetterthanwithth erelationshipofRanee& Warren.Theinfluenceof


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th eslopeangleisrepresentedjustasgoodasforth eRanee& Warrenrelation,whileth etendencyofth einfluenceofth ewavesteepnessisqualitativelycorrect.Thedifferenceinstabilitybetweenlowandhighvaluesof,however ,foronevalueofth eslopeangle,isto osmallinth ecomputations.Variablefriction factorinENDEC Untilnow,inENDEConlyonefrictionfactorhasbeenused,viz.0.05,whichis arelativelyhighvalueduetoth eroughbottom.Equation(10)leadstohigherfrictionfactorsfo rsteeperwaves.Usingdifferentfrictionfactorsfo rdifferentwavesteepness,f w=0.05,0.04,0.03fo rs=0.05,0.03,0.01,respectively)is justified,becauseofequation(10).Forth ecalibrationfactorFinth ecomputations0.25isused,beingavalueinbetweenth etw ovaluesofFigure6.


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unfavourableinfluenceonth estonestability,whichisnotdescribedinth emodelsusedhere.Thisdifference willonlyappearwhenusinga2-dimensionalwavemodelforth ewavemotiononaslope.Theagreementso faris encouragingenoughtotryto coupleth eexperimentalresultsto th ewatermotion,usingabetterwave-velocitymodel.6.EVALUATION

Figure8Plunging jet

o.Thetrendfo rbothsituationsisth esame,whichencouragesfurtherresearchinthisfield.Togetherwitha2 -dimensionalmodel,describingth ewavemotiononaslopeinmoredetailthanth emodelsusedinthispaper,itshouldbepossibleinth efuturetogiveasatisfactorilyaccuratedescriptionofstonestabilityin(breaking)wavesonslopes.Forth etimebeing,th eexperimentalresultsaspresentedinthispapercanbeusedasafirstapproximationforstonestabilityonmildslopes.


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7 .CONCLUSIONS 1 - Thecomputationalresultsgiveadescriptionthatfollowth etrendsof

experimentalresultsreasonablywellinaqualitativeway,whenincludingth efollowingelementsfromth ephysicalprocessof th estabilityofstonesin breakingwavesonamildslope:orbitalmovement(fromlinearwavetheory,equation1 ) waveshearstress(accordingto Jonssson,equation0andusingequation9)Rayleighdistribution(withshallow-watercorrectionbyStive,equation6)wavebreakingandenergydissipation(accordingto Battjes/Janssen,equations3 ,4and5)turbulentvelocities(accordingtoBattjes,equation2)stonestability(accordingtoSleath,equation8)

Thecomputedrelationbetweenstonestability(Hs/Ad)andbreakerparameter(=tanA/(H s/L 0),isquantitativelyinsufficient.Probablyth efactthatth everticalvelocitiesnearth ebottominaplungingbreakerwerenottakenintoaccount,isth emainreasonfo rthis.Otherweakpointsarepossiblyth eturbulencemodelusedandth einfluenceofturbulenceonth estabilityofasinglestone.Theexperimentalresultsseemconsistentandarealsoinlinewithth e(empirical)vanderMeerrelationforstabilityofstonesonsteepslopes.Thisressemblancecanbeusedasabasisforfutureresearchonstonestabilityinbreakingwavesonslopesingeneral.Theexperimentalresultsinthispapercanbeusedfo rth edesignof aprotectiverocklayeronamildslope.


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SYMBOLSa , ,rbitalstrokeatbottomd^oediannominaldiametero fmaterialdn5o=(M50/pJ0'33) m d50ediansievediametero fmaterialD Bnergydissipationduetobreakingo fwavesm/s/m 2 fwrictioncoefficientinwavesFuningfactorgccelerationdueto gravity /s 2 HaveheightHMaximum waveheightH significantwaveheighthaterdepthkavenumber k=2ir/L)/m k quivalentsandroughnessk,=dJ0)L 0eep-waterwavelengthLQ=gT P2/2ir)Mass gnumberof displacedstonesqurbulentvelocityscaleinbreakingwaves /s QBercentageo fbrokenwavesSamagesavesteepness s=H/Lo)T Peakwaveperiodofspectrumf ibmplitudeof orbitalvelocityatbottom /s widthoff lumealopeangleo fstructureAelativemassdensityo fmaterialA=p,-pw)/p w)< / >ngleo freposeo fstonespsas sdensityo fmaterial g/m 3 pwassdensityofwater g/m 3 reakerparameter =tanaf/(WL0 ) -%mplitudeof bottomshearstress /m 2 6 )ngularfrequency u=2x /T )/s


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REFERENCESBattjes,J.A.,1975Modellingofturbulencein th esurf zoneSymposiumonmodelingtechniques,ASCE,SanFranciscoBattjes,J.A.,1987SurfzoneturbulenceSeminaronHydrodynamicsof wavesin coastalareas,IAHR,Moscow Battjes,J .A .and Janssen,J .P .F .M. ,1978Energylossand set-updueto breakinginrandomwaves ,Proc.6thInt.Conf.onCoastalEng.,ASCE,New York Battjes,J .A .andStive,M.J.F . ,1985Calibrationandverificationofadissipationmodel forrandombreakingwaves,Jrnl.ofGeophys.Research,90CUR/CIRIA,9 9 1Manualonth euseofrockincoastalandshorelineengineering,CURReport154/CIRIASpecialPublication83 ,Balkema,Rotterdam,pp.97 ,216 ,2 1 7 ,298Holthuijsen,L.A. ,Booij,N .and Herbers,T.H.C. ,1989 A predictionmodelforstationary,short-crestedwavesinshallowwaterwithambientcurrents,CoastalEngineering,3,pp23-54Jonsson,I.G.,1966Waveboundarylayersand friction fac torsProc.0thConf.onCoastalEngineering,Tokyo,pp.27-148Meer,J .W.vander,1988RockSlopesandGravelBeachesunderWaveAttackDelftHydraulics ,Publicationno.396,TheNetherlandsRanee,P.J. ,andWarren,N.F . ,1968 ,Thethresholdofmovementofcoarsematerialinoscillatory flowProc.1 thConf.onCoastalEngineering,London,pp.487-491 Schiereck,G.J. ,Fontyn ,H.L. ,Grote,W .andSistermans,P.G.J. ,1 9 94 Stabilityofrockonbeaches,Proceedings21 thInt.Conf.onCoastalEng.ASCE,KobeSleath,J.F.A.,1978MeasurementsofbedloadinoscillatoryflowJournalofth eWaterway,Port,CoastalandOceanDivision,ASCE,Vol .104no.WW4,pp.291-307 Y e,Lei,9 9 6StabilityofrockonbeachesMSc-thesis,DelftUniversityof Technology

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Pipeline Protection in the Surfzone