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1、1-146Fluid-MechanicalInteraction1.10MiscellaneousFeaturesandTechniques1.10.1Strain-DependentPorosityorPermeabilityThekeywordportableorpertablemaybeusedinsteadofporosityorpermeability,respectively.Inthiscase,look-uptablesprovidepropertyvaluesasafunctionofaccumulatedvolumes
2、train(notethatvolumestrainenteredinatablemustbenegativeforcompressionandpositivefortension).Sufficientscopemustbeprovidedinthetable,sothatallpossiblevolumeexcursionsareanticipated.Volumestrain,asusedbythetable,maybeprintedwiththePRINTvolstraincommand.Sincebothporosityandpe
3、rmeabilitychangesaffectthecriticaltimestepandelementmatrices(seeSection1.3.5),arecalculationofthesequantitiesisdoneifthetablelook-upisactivebut,forreasonsofeconomy,onlyateverytenthstep.Careshouldbetakentoensurethatpermeabilityandporositydonotchangerapidly.Therecalculation
4、ofgroundwaterquantitiesputsanoverheadonthesolutiontime.Asanexampleintheuseofalook-uptable,weconsiderhowporosity,n,isrelatedtothetotalvolume,V,ofanelement:n=1−Vs/V(1.154)whereVsisthevolumeofsolidmaterialintheelement,whichisassumedtoremainconstant(e.g.,thematerialconsistsof
5、incompressiblegrains).Asimilarrelationexistsfortheinitialporosity,n◦,andinitialelementvolume,V◦:n◦=1−Vs/V◦(1.155)EliminatingVsbetweenEqs.(1.154)and(1.155),weobtainV◦n=1−(1−n◦)(1.156)VInsmall-strainmode,thevolumestrainusedbythelook-uptableisapproximatedasV−V◦ev=(1.157)V◦Su
6、bstitutingtheresultingvalueforV/V◦intoEq.(1.156),weobtain1−n◦n=1−(1.158)1+evFLACVersion5.0FLUID-MECHANICALINTERACTIONSINGLEFLUIDPHASE1-147Example1.20illustratestheuseofEq.(1.158)increatingalook-uptableforporosity.Figure1.53showstheresultingdistributionofporosities,plotted
7、ascontours.Theleft-handpartofthetopsurfaceoftheboxmovesdownasarigidpunch;porositiesarereducedunderthisfooting.Example1.20Footingproblemthatusesaporositylook-uptableconfgwdefmake_tab;Makeatableofporosityversusstrain=-0.2;volumestrain.Onlyvalidforloopn(1,11);absolutevol.str
8、ains<20%xtable(p_tab,n)=strainytable(p_tab,n)=1.0-(1.0-start_n)/(1.0+strain)strain=strain+0.04en
