考虑非线性渗流的渗流-应力耦合分析

J.H.SHIN建国大学校土木工学科GeosystemLaboratory考虑非线性渗流的渗流-应力耦合分析Numericalanalysisofstructuralandhydraulicinteractionconsideringnonlinearpermeability22.NonlinearPermeabilityModels1.Introduction3.StiffnessCompatiblePermeability4.NumericalImplementationandValidation6.ConcludingRemarks5.ApplicationtoTunnelProblemsContents31.Introduction4SignificanceofPermeabilityPermeabilityisoneofthemostdifficultparameterstoevaluate-distributionrange:10−4~10−12m/secAninaccurateevaluationofpermeabilitymayresultin-over-sizedhydraulicstructuresor,-alackofhydrauliccapacityExcessivehydrauliccapacityincreasesconstructioncost,whileinsufficiencymaycauseoperationalproblems.22lnsoookhqhrEg,Goodmanetal.(1965)r0ksQ0,Ql(Qlt)pl=γwhlhho1.Introduction5ShamensubseatunnelinChinamajorsumpAnExample:1.Introduction6Drainagesysteminsubseatunnel(Channeltunnel)1.Introduction7IssueDefinition•Appropriatenonlinearpermeabilitymodel•Compatibilitybetweendeformationbehavior&flowbehaviorThus,themodelingrequiresconsideringthestructuralandhydraulicinteraction•Deformationcausesvolumechange.•Permeabilityisdependentonvolumechange.Permeabilitycharacteristics1.Introduction8StiffnessnonlinearityPermeabilitynonlinearityNonlinearstiffness-permeabilitycompatibility1.Introduction9IssuesonNonlinearStiffness1.Introduction10BenderElements1.Introduction11Δσ'Δσ'deformationbehaviorflowbehaviorflowratevBpwuppkppkukiq)()(vfkΔqΔqCompatibilitybetweendeformationbehavior&flowbehavior1.Introduction12RelativestiffnessvsRelativepermeability10.10.010.0010.00010102030405060708090100Normalizedpore-waterpressurepl/p0ⅹ100(%)Shinetal.,2005Shinetal.,2007■●representativecurve■■■■■■Permeabilityratio,kl/ks●●●●●●●●●impermeableprimaryliningdrainagelayersecondaryliningsteelribpermeabilityks:ground,kl:primaryliningkf:drainagelayerwaterpressureflowrigidfootingflexiblefootingcontactpressuresettlementstripfootingwallloadRelativestiffnessvsRelativepermeability1.Introduction13ResearchNeedsFewresearchonnonlinearpermeabilityNostudyonstiffness-permeabilitycompatibilityNow,Issuestobesought:Generalizednonlinear/anisotropicpermeabilitymodelStiffness-permeabilitycompatibilityImplementationtostructuralandhydraulicinteractionproblemApplicationtonumericalanalysisofactualproblemsCurrentProblems1.Introduction142.NonlinearPermeabilityModels154.03.02.01.010-1010-910-810-710-610-510-410-310-210-11251617237418196623119242181215302613292714102228520부분불투수매우낮음낮음중간높음간극비,e투수계수(cm/sec)범례1Compactedcaliche2Compactedcaliche3Siltysand4Sandyclay5Beachsand6CompactedBostonblueclay7Vicksburg8Sandyclay9Silty-Boston10Ottawasand19Leanclay11Sand-GaspeePoint20Sand-UnionFalls12Sand-FranklinFalls21Silt-NorthCarolina13Sand-Scituate22Sandfromdike14Sand-PlumIsland23Sodium-Bostonblueclay15Sand-FortPeck24Calciumkaolinite16Silt-Boston25Sodiummontmorillonite26-30Sand(damfilter)18Loess17Silt-BostonNaturalIn-situSoils𝐥𝐨𝐠𝒌=𝒂+𝒃𝒆𝑎and𝑏areconstants,and𝑒isthevoidratio2.NonlinearPermeabilityModels16∆𝑒=𝐴∆log𝑘DeformingSoilsLogarithmiclawbasedontheassumptionthat𝑚𝑣isconstant,𝑘=𝑘0exp(−𝐵𝜎′)𝑘=𝑘0𝜎′−𝐵′Powerlawbasedontheassumptionthat𝐶𝑐remainsconstant.ExperimentalfindingsNonlinearityinpermeabilityvs𝐥𝐨𝐠𝒌=𝒂+𝒃𝒆Nonlinearpermeabilitymodel(Vaughan,1989)Lackoflogicalbackground;Nogeneralizedexpression2.NonlinearPermeabilityModels17ProfP.R.Vaughan,1997,Iresland2.NonlinearPermeabilityModels18Anisotropyinpermeability𝑘ℎ𝑘𝑣=𝛽2.01.81.61.41.21.00.80.60.30.40.50.60.70.80.91.0eminemaxStaticcompactionDynamiccompactionIsotropyAnisotropyratio(rk=kh/kv)Voidratio(e)•sedimentarySoils•compactedSoilsCrossisotropicproblemsGenerally,𝜷1.02.NonlinearPermeabilityModels19−𝑘𝜕ℎ2𝜕2𝑥𝑖+𝜕𝜀𝑣𝜕𝑡=0ℎisthetotalhydraulichead,𝜀𝑣isthevolumetricstrain,tisthetime,and𝑥𝑖isthecoordinateinxdirection.𝒌=𝒇∆𝒆=𝒇(∆𝒗)=𝒇(𝜺𝒗)and∆𝒑′=𝑩∆𝜺𝒗(whereBisthebulkmodulus),𝒌=𝒇𝒑′.CoupleddeformationandflowbehaviorNonlinearPermeabilityModel𝑝′=𝜎𝑣′+2𝜎ℎ′3,𝑣=1+𝑒2.NonlinearPermeabilityModels20bλ1νlnp'lnklnp'λ11N1lnk01κν-lnp'lnp'-lnk∆𝑒=𝐴∆log𝑘∆𝑣=𝐴∆log𝑘Criticalstateparameters𝑣=1+𝑒2.NonlinearPermeabilityModels21Derivationofnon-linearpermeabilitymodel𝒆=𝑵−𝟏−𝟐.𝟑𝝀𝐥𝐨𝐠𝒑′𝟐.𝟑𝐥𝐨𝐠𝒌=𝒂+𝒃(𝑵−𝟏)−𝟐.𝟑𝒃𝝀𝐥𝐨𝐠𝒑′𝑘0isthepermeabilityat𝑝′=1𝒌=𝒌𝟎𝒑′−𝜶𝐥𝐨𝐠𝒌=𝐥𝐨𝐠𝒌𝟎−𝜶𝐥𝐨𝐠𝒑′α(=bλ)isdefinedastheslopeinlog𝑘−log𝑝′relation𝐥𝐨𝐠𝒌=𝒂+𝒃𝒆2.NonlinearPermeabilityModels22𝒌𝒉𝒌𝒗=𝜷=𝒌𝟎𝒉𝒌𝟎𝒗𝒑′(𝜶𝒗−𝜶𝒉)=𝜼𝟎𝒑′−𝝌where,𝜂𝑜=𝑘0ℎ/𝑘0𝑣,χ=𝛼ℎ−𝛼𝑣Derivationofanisotropicpermeabilitymodel𝒌𝒗=𝒌𝟎𝒗𝒑′−𝜶𝒗𝒌𝒉=𝒌𝟎𝒉𝒑′−𝜶𝒉ForcrossisotropicproblemsPermeabilityanisotropy2.NonlinearPermeabilityModels23onmixedcompactedsoilsModelValidationRoweCellTestEquip.2.NonlinearPermeabilityModels24samplemandrelguidebushformandrelcirculartemplatetofitoncellflangeRowecellbodylocationofholefordrainagewellTestingmethods•verticaldraintests•horizontaldraintests2.NonlinearPermeabilityModels25grainsize(mm)passingpercent(%)1008060402000.0010.010.11100.00010102030400204060watercontent,w(%)percentageofdryclayweight,C(%)dominantcohesivebehavio