外文翻译不确定性和灵敏性在混凝土时间中所受影响的分析.docx
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外文翻译不确定性和灵敏性在混凝土时间中所受影响的分析.docx
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外文翻译不确定性和灵敏性在混凝土时间中所受影响的分析
外文原文一
Uncertaintyandsensitivityanalysisoftime-dependenteffectsin
concretestructures
InHwanYang
DaelimIndustrialCo.,Ltd,TechnicalResearchInstitute,146-12,Susong-dong,Jongro-ku,Seoul110-732,RepublicofKorea
Received21March2006;receivedinrevisedform18July2006;accepted18July2006
Availableonline10October2006
Abstract:
Thepurposeofthispaperistoproposethemethodofuncertaintyandsensitivityanalysisoftime-dependenteffectsduetocreepandshrinkageofconcreteinconcretestructures.TheuncertaintyandsensitivityanalysesareperformedusingtheLatinHypercubesamplingmethod.Foreachsample,atime-dependentstructuralanalysisisperformedtoproduceresponsedata,whicharethenanalyzedstatistically.Twomeasuresareexaminedtoquantifythesensitivityoftheoutputstoeachoftheinputvariables.Thesearepartialrankcorrelationcoefficient(PRCC)andstandardizedrankregressioncoefficient(SRRC)computedfromtheranksoftheobservations.Threepossiblesourcesoftheuncertaintiesofthestructuralresponsehavebeentakenintoaccount—creepandshrinkagemodeluncertainty,variationofmaterialpropertiesandenvironmentalconditions.Theproposedtheoryisappliedtotheuncertaintyandsensitivityoftime-dependentaxialshorteningandtime-dependentprestressforcesinanactualconcretegirderbridge.Thenumericalresultsindicatethatthecreepmodeluncertaintyfactorandrelativehumidityappeartobethemostdominantfactorswithregardtothemodeloutputuncertainty.Themethodprovidesarealisticmethodofdeterminingtheuncertaintyanalysisofconcretestructuresandidentifiesthemostimportantfactorsinthelong-termpredictionoftime-dependenteffectsinthosestructures.
Keywords:
Uncertainty;Sensitivity;Concretestructures;Creep;Shrinkage
1.Introduction
Time-dependenteffectsofconcretestructuresresultfromcreepandshrinkageofconcrete.Creepandshrinkageareimportantfactorsinthedesignofconcretestructures.Forexample,theyaffectthesettingofbearingsofconcretebridgesincludingthesizeofslidingplatesorlaminatedbearingpads.Theyalsoaffectthesizingandsettingofexpansionjointsduetotime-dependentaxialshorteningarisingfromcreepandshrinkageeffectsofprestressforceandtherebyalsoaffectthesecondarymomentsinprestressedconcretebridges.Thecreepandshrinkagemodelswhicharecapableofpredictinglong-termstructuralresponsearespecifiedindesigncodessuchasACI209-92,CEB-FIPModelCode90,etc.
However,theapplicationofcurrentcodeformulationsmayresultinconsiderablepredictionerrorsstemmingfromseveralsourcesofuncertainty.Theypredictonlymeanvaluesandcannotpredictthestatisticalvariation.Therefore,amethodtodealwiththeuncertaintyinvolvedinthepredictionofcreepandshrinkageeffectsofconcreteisnecessary.
Creepandshrinkageinconcretestructuresareverycomplexphenomenainwhichvariousuncertaintiesexistwithregardtoinherentmaterialvariationsaswellasmodellinguncertainties.Thestudyontheuncertaintiesincreepandshrinkageeffectshasbeencontinuouslyanareaofsignificantefforts.Particularattentionhasgiventotheproblemofcreepandshrinkagewithuncertaintymodellingandwiththevariabilityinexternalloads.Thevariationofcreepandshrinkagepropertiesiscausedbyvariousfactorscommonlyclassifiedasinternalandexternalfactors.Thechangeofenvironmentalconditions,suchashumidity,maybeconsideredasanexternalfactor.Theinternalfactorsincludethevariationofthequalityandthemixcompositionofthematerialsusedinconcreteandthevariationduetointernalmechanismofcreepandshrinkage.
Inthepredictionformulasofcreepandshrinkageofconcrete,variouskindsofparametersareinvolvedtoexpressthecharacteristicsofconcreteunderconsideration,i.e.themixproportionofconcrete,theshapeofthestructure,relativehumidity,etc.Sinceitisnotpossibletoremovethestatisticalvariationinvolvedintheparameters,itmaybenecessarytoestimatehowmuchthevariationofeachparameterinfluencesthepredictedvalues.Severaldifferentapproachesofsensitivityanalysishavebeendevelopedasnumericaltoolsforreliabilityassessmentofstructures.Also,areviewofdifferentmethodsforthissensitivityanalysishasbeenprovidedbyNov´aketal..AnotherexampleforsensitivityanalysisisshownbyTsubaki.
Theaimofthepresentstudyistoproposeananalyticalapproachfortheuncertaintyandsensitivityanalysesofcreepandshrinkageeffectsinconcretestructuresutilizingthemodelsinthedesigncodes.Thepresentstudydealswiththeuncertaintiesinthelong-termpredictionofcreepandshrinkageeffects,takingintoaccountthestatisticalvariationofbothinternalandexternalfactorsaswellastheuncertaintyofthemodelitself.Thesensitivityanalysisisperformedtoshowtherelativeimportanceofindividualrandomvariablesemployedinthecreepandshrinkagemodels.Thetime-dependentaxialshorteningofaprestressedconcretegirderbridgeisanalyzedtoshowtheapplicationofproposedmethod.
2.Methodofuncertaintyanalysis
Simulationistheprocessofreplicatingtherealworldbasedonasetofassumptionsandconceivedmodelsofreality.Itmaybeperformedtheoreticallyorexperimentally.Forengineeringpurposessimulationmaybeappliedtopredictorstudytheperformanceand/orresponseofasystemorstructure.Withaprescribedsetofvaluesforthesystemparameter(ordesignvariable),thesimulationprocessyieldsaspecificmeasureofperformanceorresponse.AconventionalapproachtothisprocessistheMonteCarlosimulationtechnique.However,inpractice,MonteCarlosimulationsmaybelimitedbyconstraints,computercapabilityandthesignificantexpenseofcomputerrunsintime-dependentstructuralanalysisofconcretebridges.Analternativeapproachistouseaconstrainedsamplingscheme.Onesuchscheme,developedbyImanandco-workers,isLatinHypercubesampling(LHS)method.Bysamplingfromtheassumedprobabilitydensityfunctionofthe_andevaluatingYforeachsample,thedistributionofY,itsmean,standarddeviationandpercentilesetc.,canbeestimated.
TherepresentativevalueineachintervalisusedjustonceduringthesimulationprocedureandsothereareNobservationsoneachoftheKinputvariables.TheyareorderedinthetableofrandompermutationsofranknumberswhichhaveNrowsandKcolumns.Eachrowofatableisusedontheithcomputerrun.ForsuchasampleonecanevaluatethecorrespondingvalueYnoftheoutputvariable.FromNsimulationsonecanobtainasetofstatisticaldata{Y}=[Y1,Y2,...,YN]T.Thissetisstatisticallyassessedandthustheestimationsofsomestatisticalparameters,suchasthemeanvalueandthevarianceoftheresponse,areobtained.InterestedreadersarereferredtoNov´aketal.foramoredetaileddiscussionofthissamplingmethod.
3.Methodofsensitivityanalysis
TheresultsoftheLatinHypercubesimulationscanbeusedtodeterminewhichofthemodelparametersaremostsignificantinaffectingtheuncertaintyofthedesign.Twocloselyrelated,butdifferent,measureswillbeexaminedinthisstudy.Thesearepartialrankcorrelationcoefficient(PRCC)andstandardizedrankregressioncoefficient(SRRC)computedontheranksoftheobservations.Thismethodisparticularlyusefulwhentherearealargenumberofinputsandseveraloutputshavinganassociatedtimehistory.
Sensitivityanalysisinconjunctionwithsamplingiscloselyrelatedtotheconstructionofregressionmodelswhichapproximatethebehaviourcalculatedbythecomputerruns.Theconstantb0andtheordinaryregressioncoefficientbjareobtainedbytheusualmethodsofleastsquares.Theordinaryregressioncoefficientsarethepartialderivativesoftheregressionmodelwithrespecttotheinputvariables.However,theseordinaryregressioncoefficientsareeasilyinfluencedbytheunitsinwhichthevariablesaremeasured.
Thecoefficientofb_jinstandardizedmodelsiscalledthestandardizedregressioncoefficient.Itisaunitfreemeasurement;suchcoefficientsareusefulsincetheycanprovideadirectmeasureoftherelativeimportanceoftheinputvariables.AftermakingNrunsofthemodelwithvaryinginput,acorrelationmatrixbetweentheinputandoutputiscomputedforagivenstepintheoutputtimehistory.Letthecorrelationmatrixberepresentedasfollows:
ThePCCandSRCmeasurethelinearassociationbetweenvariables.Whennonlinearrelationshipsareinvolved,itisoftenmorerevealingtocalculatetheSRCsandPCCsonvariableintegerranksthanontheactualvaluesforthevariables.SuchcoefficientsaretheSRRCsandPRCCs.
4.Applicationtolong-termpredictionofaxialshortening
andprestressforceinconcretebridges
4.1.Descriptionofstructureandfiniteelementmodeling
Thebridgedeckconsistsofsevencontinuousspansandeachspanis50mlong.The50minteriorspanofthe7-continuousspanbridgesystemisshowninFig.2.ItisaprecastsegmentalprestressedconcretegirderbridgewhosetypicalcrosssectionisalsoshowninFig.2.Theinteriorspanoftheboxgirderhasninesegmentspercantilever(i.e.perhalfspan).Thesegmentsareplacedsymmetricallyonbothsidesofthespan.Thecantileversarejoinedatmidspan.Thecantilevertendons(topslabtendons)anchoredineachsegmentarestressedatthetimeoferectionofthatsegment,whilethecontinuitytendons(bottomslabtendons)arestressedaftermidspanjoiningasshowninFig.2.
Thefiniteelementanalysismethodinthisstudyisbasedontheproceduredevelopedoriginal
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