Average Property in Random Two‐State Medium

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1、AVERAGEPROPERTYINRANDOMTWO-STATEMEDIUMByWilsonH.Tang,1Member,ASCE,IndraSidi,2andRobertB.Gilbert3ABSTRACT:Aone-dimensionalmediumconsistingoftwoalternatingmaterialstatesisstudied.Theoccurrencesofthestatesaswellastheirrespectivedurationsareassumedrandomaccordingtoarenewalprocess.Thepro

2、pertiesassociatedwiththetwomaterialscouldbedrasticallydifferent;theyarealsosubjecttouncertain•tiesandspatialvariation.Satisfactoryperformanceofasystemassociatedwithsuchmediumcoulddependonthespatialaverageoversomedomainwithinthemedium.Thedomainmayconsistofarandomnumberofnonoverlappin

3、gsegmentsofthetwomaterials.Basedontheproposedmodel,statisticsofthedomainaveragepropertyarederived.Thesestatisticsmayserveasinputstoreliabilityevaluation,includingthedeterminationofexceedanceprobabilityofagiventhresholdbysomelocalspatialaverageproperty.Extensivesensitivityanalysisrev

4、ealstheimplicationofprobablepresenceofanothermaterialwithinanotherwisestatisticallyhomo•geneousmedium.Besidesapplicationtogeotechnicalproblems,resultscouldbealsousefultoanyprobleminvolvingarandomtwo-statemedium.INTRODUCTIONRandomfieldhasbeenused(e.g.,Vanmarcke1977)tomodelthespatialv

5、ariationofsoilpropertieswithinahomogeneousstratum.Itprovidesananalyticalbasisforincorporatingthespatialcorrelationcharacteristicsofsoilpropertiesinareliabilityevaluation.Inparticular,itcanrelatethestatisticsofsoilpropertyatapoint,resemblingthatasdeterminedfromatypicalsoilsample,toth

6、estatisticsoftherelevantvariablesgoverningsatisfactorygeo•technicalperformance.Geotechnicalperformancegenerallyinvolvesspatialaveragesoilpropertyoversomedomain;forinstance,theaverageundrainedshearstrengthoveragivenslipsurfaceorsomelocalregion(forinitiatingprogressivefailure)inslopes

7、tabilityanalysis,theaveragefrictionalresis•tancealongapile,ortheaveragefractionofbouldervolumealongagivenlengthoftunnelexcavation.However,asoilmediumordinarilyconsistsofmorethanonesoiltype—evenasupposedlyhomogeneoussoilstratummayembodygeologicalanomalies.Propertiesbetweendifferentso

8、iltypescanexhibitsu