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1、RolesofFORM,System-FORM,SORM,andRSMingeotechnicalreliabilityanalysisB.K.LowSchoolofCivilandEnvironmentalEngineering,NanyangTechnologicalUniversity,N1-1B-40,50NanyangAvenue,Singapore639798E-mail:bklow@alum.mit.eduThispaperexaminesthecomplementaryrolesandin
2、terconnectionsamongthefirst-orderreliabilitymethod(FORM)forsinglefailuremodes,thesystemFORMforcorrelatedmultiplefailuremodes,thesecond-orderreliabilitymethod(SORM)forcurvedlimitstatesurfaces,andtheresponsesurfacemethodsasalinkbetweenreliabilitymethodsands
3、tand-alonenumericalpackages.Geotechnicalexamplesofreliability-baseddesignandanalysiswillbeprovidedtoillustratetheprinciples,meritsandlimitationsofeach,andtoexplaintheconnectionsandevolutionaryrelationshipsamongFORM,system-FORMandSORM.Comparisonswillbemade
4、withotherprobabilisticmethodsinrecentgeotechnicalliterature.Apartfromelucidatingefficientandpracticalproceduresforreliability-baseddesignandanalysiswiththehopeofengagingmorepractitionerstoconsidertheprobabilisticapproach,thepaperalsoaimstoprovidesomediscu
5、ssionsandamorebalancedperspectiveofotherprobabilisticapproaches(differentfromFORM,system-FORM,SORM,RSM)publishedbyvariousresearchersinrecentgeotechnicalpapers.Keywords:Reliabilityindex,FORM,SORM,responsesurface,failureprobability.1IntroductionThematrixfor
6、mulation(Veneziano1974,Ditlevsen1981)oftheHasofer-Lind(1974)indexβforcorrelatednormalrandomvariableswithmeanvaluesμandstandarddeviationsσis:()()T−1β=minx−ȝCx−ȝ(1a)x∈FInsteadofthecovariancematrixC,thefollowingequivalentformulationintermsofcorrelationmatrix
7、RwasusedinLowandTang(1997):T»xi−μiº−1»xi−μiº(1b)β=min…»R…»x∈Fσσ¬i¼¬i¼TheFORMisanextensionoftheHasofer-Lindmethodintotherealmofcorrelatednonnormalrandomvariables.Theclassicalcomputationalprocedureisdoneintherotateduspace,asdescribedinAngandTang(1984),Halda
8、randMahadevan(1999),Melchers(1999),andBaecherandChristian(2003),forexample.InFORM,onecanrewriteEq.(1b)asfollows(LowandTang(2004)),andregardthecomputationofβasthatoffindingthesmallestequivalenthyperellipsoid(centreda
