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1、ProbabilisticAnalysisofFoundationSettlementbyGordonA.Fenton1,G.M.Paice2,andD.V.Grif®ths3AbstractItisatleastintuitivelyevidentthatvariabilityinsoilpropertieswillhaveasigni®canteffectontotalanddifferentialsettlementofstructuralfoundations.Bymodelingsoilsasspatiallyr
2、andommedia,whosepropertiesfollowcertaindistributionsandspatialcorrelationstructures,estimatesofthereliabilityoffoundationsagainstserviceabilitylimitstatefailure,intheformofexcessivedifferentialsettlements,caninprinciplebemade.Thesoil'spropertyofinterestisit'selast
3、icmodulus, ,whichisrepresentedhereusingalognormalmarginaldistributionandanisotropiccorrelationstructure.Predictionofsettlementbelowafoundationcanthenbemadeusingthe®niteelementmethodgivenarealizationoftheelasticmodulus®eldunderlyingthefoundation.Bygeneratingandanal
4、yzingmultiplerealizations,thestatisticsanddensityfunctionsoftotalanddifferentialsettlementscanbeestimated.Thispaperestimatesprobabilisticmeasuresoftotalsettlementunderasinglespreadfootingandofdifferentialsettlementunderapairofspreadfootingsusingatwo-dimensionalmod
5、elcombinedwithaMonteCarlosimulation.Forthecasesconsidered,totalsettlementisfoundtobewellrepresentedbyalognormaldistributionandsimplerelationshipsareproposedallowingtheapproximationofthesettlementdistributionparametersforafootingfoundedonaspatiallyrandomsoilofconst
6、antdepthand®xedPoisson'sratio.Aone-parameterexponentialdistributionis®ttedtodifferentialsettlementsandfoundtogivereasonableprobabilityestimates,particularlytowardsthetailofthedistribution.Amethodofpredictingthesingleparameterisgivenintermsofstatisticsoftheelasticm
7、odulus®eldandlocalaveragesoverthe®eld.Anexampleispresentedtoillustratetheproposedmethodologyforasinglefooting.INTRODUCTIONThesettlementofstructuresfoundedonsoilisasubjectofconsiderableinteresttopracticingengineerssinceexcessivesettlementsoftenleadtoserviceabilityp
8、rob-lems.Inparticular,unlessthetotalsettlementsthemselvesareparticularlylarge,itis1M.ASCE,AssociateProfessor,DepartmentofAppliedMathematics,TechnicalUni
