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1、ProceedingsofInternationalConferenceonProblematicSoils,25-27May2005,EasternMediterraneanUniversity,Famagusta,N.CyprusUnsaturatedSoilMechanicsasaSeriesofPartialDifferentialEquations12Fredlund,D.G.,GitiranaJr.,G.1ProfessorEmeritus,UniversityofSaskatchewan,Saskatoon,SK,Canada2Ph
2、.D.Student,UniversityofSaskatchewan,Saskatoon,SK,CanadaAbstractUnsaturatedsoilstheorycanbelaidoutasaseriesofgoverningpartialdifferentialequations(PDEs),allowingforthesolutionofcomplexproblems,includingtheanalysisofvolumechangeofexpansiveandcollapsiblesoils,thedesignofsoilcove
3、rsystems,theanalysisoftransientslopestability,tonameonlyafewproblems.ThepracticalrelevanceofdesignapproachesbasedonPDEshasincreasedasaresultofrecentadvancesincomputergeotechnicsandtheriseofproblemsolvingenvironments.ThispaperpresentsanoverviewofPDEsgoverningthebehaviourofunsa
4、turatedsoils.Numerousphenomenawereconsidered,includingairflow,liquidwaterandvapourwaterflow,staticequilibrium,totalvolumechange,yield,heattransfer,andfreeze-thawingprocesses.ThePDEsdescribingunsaturatedsoilbehaviourmayalsobesimplifiedandde-coupled,inordertoneglectprocessestha
5、tareunimportantincertainsituations.Severaldegreesofde-couplingtraditionallyadoptedincommerciallyavailablesoftwarepackagesaredescribedandtheconsequencesofsuchsimplificationsareexplored.Finally,theuseofgeneralPDEsystemsalongwithgeneralpurposepartialdifferentialequationssolversi
6、sshownasthewayforward.Itisenvisagedthatstate-of-the-artproblemsolvingenvironmentscanbeusedastheultimatetoolinunsaturatedsoilmechanicspractice.Keywords:unsaturatedsoils,continuummechanics,partialdifferentialequation,numericalmodelling,soil-watercharacteristiccurve.1Relevanceof
7、partialdifferentialequationstounsaturatedsoilmechanicsContinuummechanicsanddifferentialcalculushavebeentraditionallyusedformodellinggeotechnicalengineeringproblems.Continuummechanicstheoriesareoftenexpressedintheformofpartialdifferentialequations(PDEs)thatgovernthedistributio
8、nofsoilstatevariablesinspaceandtime.Thepartialdifferentialequationsg
