FLAC/FLAC3DShortCourseItascaSoftwareTrainingCourseTongjiUniversityShanghai,ChinaOctober27-31,2008PeterCundall,YanhuiHan&RogerHartItascaConsultingGroup,Inc.1TrainingSchedule

October27,2008(afternoon)01:00-02:00 OverviewofFLAC/FLAC3Dfeaturesandcapabilities

–Overviewofcapabilitiesingeo-engineering –Theoreticalbasis –Generaloperationprocedures02:00-03:00GridgenerationforFLACmodels –Newvirtual-gridgenerationtools –Automaticre-meshingcapabilityduringcycling03:00–03:15Break03:15-04:15 Structuralelementtopics

–Connectingstructuralelementstorepresentmultiplesupport –Simulatingpre-tensioning04:15–05:00 Stressinitializationtechniques

–Techniquesforinitializingstressinnon-uniformgrids

2FLACisageneral-purposecodethatcansimulateafullrangeofnonlinearstatic&dynamicmechanicalproblems,withcoupledfluidflow,heatflowandstructuralinteraction.Anygeometrycanberepresented,andtheboundaryconditionsarequitegeneral.FLACsimulatesthebehaviorofnonlinearcontinua(withembeddedinterfaces)bythegeneralizedfinitedifferencemethod(arbitraryelementshapes),alsoknownasthefinitevolumemethod.FLACsolvesthedynamicequationsofmotioninthetimedomainandfollowsanyconstitutiverelationinlargeorsmallstrainmode.EveryfeatureofFLACisaccessiblefromapowerfulGraphicalUserInterface.FLACcontainsanembeddedlanguage,FISH,thatgivestheuseraccesstoallinternalvariables,andallowscustom-writtenfunctions.WhatisFLAC?3FLACLarge-strainorsmall-straincalculationmode.Manybuilt-inconstitutivemodelsthatarerepresentativeofgeologic,orsimilar,materials;optionalC++user-writtenmodels.Interfaceelementstosimulatejointsordistinctplanesofweakness.Plane-strain,plane-stressandaxisymmetricgeometrymodes.Groundwaterandconsolidation(fullycoupled)modelswithautomaticphreaticsurfacecalculation;two-phaseflow.Structuralelementmodelsforsoil-structureinteraction–cables,piles,beams,liners,shotcrete,soilreinforcement,etc.Dynamicanalysiscapability;fullgroundwatercoupling.Creepanalysis,withviscoelasticandviscoplasticmodels.Thermalanalysis,withcouplingtosolid&fluid.…issuitedtomodelingcontinuousmaterials(containing,perhaps,afewdiscontinuities)thatexhibitnonlinearbehavior.Inparticular,itfeatures:Shearstrainratecontours4FLAC3DsimilartoFLAC,butinthreedimensionscontainsthesamefeaturesaslistedforFLACupstreamdownstream

5NewFeaturesinFLACVersion6.0Speedupofdouble-precisionversionbyconvertingtoIntelFortrancompilerAutomaticre-meshingschemeforlarge-strainanalysistoovercomebad-geometryproblems.NewconstitutivemodelforsimulatingfrictionhardeningbehaviorofgranularsoilGenericgridgenerationtooltofacilitategridcreation

ReleasedinSeptember2008example6New

FeaturesinFLAC3DVersion3.1Parallelprocessingonmultiprocessorcomputers(e.g.,dualprocessorsordualcoreprocessor)Newstructuralelementtype“EmbeddedLiner”providesshear/slipandnormalinteractionwiththegridonbothsidesoftheliner(e.g.,tosimulateburiedsheetpilewalls)NewMixedDiscretizationschemefortetrahedralelements“NodalMixedDiscretization”providesmoreaccuratesolutionofplasticityproblemsusingtetrahedralgrids64bitversionofFLAC3DHelpFilecontainingCommandReference,FISHReferenceandExampleApplicationsReleasedinDecember20067PlannedNewFeaturesinFLAC3DVersion4.0NewconstitutivemodelforsimulatingfrictionhardeningbehaviorofgranularsoilAutomaticre-meshingschemeforlarge-strainanalysistoovercomebad-geometryproblems3. ImprovedinterfacelogicFastfluid-flowlogicUpdatedDynamicAnalysisvolumeEstimatedrelease:mid20098ConstitutiveModelsforFLACandFLAC3DBuilt-inModelsUser-definedModels*Elasticitymodels:IsotropicTransverselyisotropicOrthotropicPlasticitymodels:Drucker-PragerMohr-CoulombUbiquitous-jointStrain-hardening/softeningBilinearstrain-hardening/softening/ubiquitous-jointDouble-yieldModifiedCam-clayHoek-BrownCYsoil–frictionhardening,withellipticalcapDynamicLiquefactionmodels:Finn(Martinetal.,1975)modelBryne,1991modelCreepmodels:ViscoelasticBurger’ssubstanceviscoelasticTwo-componentpowerlawReferencecreepformulation(WIPP)Burger-creep/Mohr-CoulombviscoplasticTwo-componentpowerlaw/Mohr-CoulombviscoplasticWIPP-creep/Drucker-PragerviscoplasticCrushed-salt*partiallistofmodelscreatedby(ordevelopedfor)codeusersElasticitymodels:HyperbolicelasticDuncan-Chang,1980Plasticitymodels:NorSandJardineetal.,1986Manzari-Dafalias,1997Kleineetal.,2006ConcretehydrationvonWolffersdorffhypo-plasticDynamicLiquefactionmodels:UBCSANDUBCTOTWang,1990Rothetal.,2001Andrianopoulos,2005Creepmodels:MinkleyviscoplasticHein-crushedsaltSalzercreepLubby2creep9FiniteDifferenceFormulation

ofFLAC&FLAC3D

10BASISOFFLACFLACsolvesthefulldynamicequationsofmotionevenforquasi-staticproblems.Thishasadvantagesforproblemsthatinvolvephysicalinstability,suchascollapse,aswillbeexplainedlater.Tomodelthe“static”responseofasystem,arelaxationschemeisusedinwhichdampingabsorbskineticenergy.Thisapproachcanmodelcollapseproblemsinamorerealisticandefficientmannerthanotherschemes,e.g.,matrix-solutionmethods.11ASIMPLEMECHANICALANALOGmF(t)Newton′sLawofMotion

Foracontinuousbody,thiscanbegeneralizedaswhere=massdensity,xi=coordinatevector(x,y)

ij=componentsofthestresstensor,andgi=gravitation12STRESS-STRAINEQUATIONSInadditiontothelawofmotion,acontinuousmaterialmustobeyaconstitutiverelation-thatis,arelationbetweenstressesandstrains.Foranelasticmaterialthisis:Ingeneral,theformisasfollows:where13AGENERALFINITE-DIFFERENCEFORMULAInthefinitedifferencemethod,eachderivativeinthepreviousequations(motion&stress-strain)isreplacedbyanalgebraicexpressionrelatingvariablesatspecificlocationsinthegrid.Thealgebraicexpressionsarefullyexplicit;allquantitiesontheright-handsideoftheexpressionsareknown.Consequentlyeachelement(zoneorgridpoint)inaFLACgridappearstobephysicallyisolatedfromitsneighborsduringonecalculationaltimestep.Thisisthebasisofthecalculationcycle:(Thetime-stepissufficientlysmallthatinformationcannotpropagatebetweenadjacentelementsduringonestep)14BasicExplicitCalculationCycleEquilibriumEquation(EquationofMotion)Stress-StrainRelation(ConstitutiveEquation)Forallgridpoints(nodes)Forallzones(elements)newstressesnodalforcesGauss′theoremstrainratesvelocitiese.g.,elastic15FLAC’sgridisinternallycomposedoftriangles.Thesearecombinedintoquadrilaterals.Theschemeforderivingdifferenceequationsforapolygonisdescribedasfollows:OverlaidTriangularelementNodalforcevectorElementswithvelocityvectorsThebasicFLACelementisatriangle.16FLAC:Forallgridpoints...Gridpointforcesarederivedfromthetractionsactingonthesidesofeachtriangle,derivedfromthezonestresses.Forexample,Thena“classical”centralfinite-differenceformulaisusedtoobtainnewvelocitiesanddisplacements:(…inlargestrainmode)17FLAC:Forallelements...Gauss’theorem,isusedtoderivedafinitedifferenceformulaforelementsofarbitraryshape.nodalvelocitybanodalvelocitySForapolygontheformulabecomesThisformulaisappliedtocalculatingthestrainincrements,eij,forazone:18Overlay&Mixed-DiscretizationFormulationofFLAC:+/2=Each

isconstant-stress/constant-strain:Volumestrainaveragedover

Deviatoricstrainevaluatedforandseparately(Mixeddiscretizationprocedure)Solutionis“UpdatedLagrangian”(gridmoveswiththematerial),andexplicit(localchangesdonotaffectneighborsinonetimestep)19Methodsofsolutionintimedomaindisplacement

uforce

FxFstress

unumericalgridEXPLICITAllelements:(nonlinearlaw)Allnodes:Repeatforntime-stepsNoiterationswithinstepsInformationcannotphysicallypropagatebetweenelementsduringonetimestepAssume(u)arefixedAssume(F)arefixedCorrectif

p-wavespeedIMPLICITelementglobalSolvecompletesetofequationsforeachtimestepIteratewithintimestepifnonlinearitypresent20MethodscomparedExplicit,time-marchingImplicit,static1.Canfollownonlinearlawswithoutinternaliteration,sincedisplacementsare“frozen”withinconstitutivecalculation.2.SolutiontimeincreasesasN3/2forsimilarproblems.3.Physicalinstabilitydoesnotcausenumericalinstability.4.Largeproblemscanbemodeledwithsmallmemory,sincematrixisnotstored.5.Largestrains,displacementsandrotationsaremodeledwithoutextracomputertime.1.Iterationoftheentireprocessisnecessarytofollownonlinearlaws2.SolutiontimeincreaseswithN2orevenN3.3.Physicalinstabilityisdifficulttomodel.4.Largememoryrequirements,ordiskusage.5.Significantlymoretimeneededforlargestrainmodels.21Strengths&LimitationsTheexplicitsolutionschemeusedinFLACenablesthefollowingproblemstobesolvedmostefficiently:

Stronglynonlinearsystems,withextensiveyieldandlargestrain.Systemsinwhichlocalizationoccurs.Systemsthatembodycomplexinteractions,orwhichneedspecialuser-definedconditionsormaterialmodels.Disadvantagesare:Slowexecution(comparedto–say–finiteelements)forlinear(orwell-behaved)systems.Slowexecutioniftherearegreatcontrastsinmaterialstiffnessesorelementsizes.22DYNAMICRELAXATIONIndynamicrelaxationgridpointsaremovedaccordingtoNewton’slawofmotion.Theaccelerationofagridpointisproportionaltotheout-of-balanceforce.Thissolutionschemedeterminesthesetofdisplacementsthatwillbringthesystemtoequilibrium,orindicatethefailuremode.Therearetwoimportantconsiderationswithdynamicrelaxation:ChoiceoftimestepEffectofdamping23TIMESTEPInordertosatisfynumericalstabilitythetimestepmustsatisfythecondition:whereCpisproportionalto1/mgp.Forstaticanalysis,gridpointmassesarescaledsothatlocalcriticaltimestepsareequal()whichprovidestheoptimumspeedofconvergence.Nodalinertialmassesarethenadjustedtofulfillthestabilitycondition:Notethatgravitationalmassesarenotaffected.24DAMPINGVelocity-proportionaldampingintroducesbodyforcesthatcanaffectthesolution.LocaldampingisusedinFLAC---Thedampingforceatagridpointisproportionaltothemagnitudeoftheunbalancedforcewiththesignsettoensurethatvibrationalmodesaredamped:25LOCALDAMPINGThedampingforce,

Fd

is:

Dampingforcesareintroducedtotheequationsofmotion:whereFi

istheunbalancedforceInFLACtheunbalancedforceratio(ratioofunbalancedforce,

Fi

,totheappliedforcemagnitude,Fm)ismonitoredtodeterminethestaticstate.Bydefault,when

Fi

/Fm

<0.001,thenthemodelisconsideredtobeinanequilibriumstate.26STATICANALYSISFLACisadynamicsolutionmethodthatprovidesastaticsolution(withtheeffectofinertialforcesminimized)providedtheunbalancedforceratioreachesasmallvalue(~0.001orless).Thisiscomparabletothe“levelofresidualerror”or“convergencecriterion”definedformatrixsolutionmethodsusedinmanyfiniteelementprograms.InFLAC,theleveloferrorisquantifiedbytheunbalancedforceratio.InbothFLACandFEsolutions,thestaticsolutionprocessterminateswhentheerrorisbelowadesiredvalue.27OverviewofFLACoperation-Engineeringsimulationsusuallyconsistofalengthysequenceofoperations.-AFLACdatafilecanbeeasilymodifiedwithatexteditor.Severalfilescanbelinkedtogether.-Thewordorientedinputfilesprovideanexcellentmeansforkeepingadocumentedrecordofanalyses.-Thecommanddrivenstructureallowsthedevelopmentofpre-andpost-processingprogramstomanipulateFLAC

inputoroutputasdesired.FLACisacommand-drivenprogram28COMMAND

keyword

value…<keyword

value>CommandSyntaxExample,

new (clearsthememory)

grid5,5 (createsagrid) modelelastic (definesanelasticmodel) plotgrid (drawsthegridonthescreen)Thereareover50commandsand400keywordsinFLAC!!!OverviewofFLACoperation29FLACCOMMANDSUMMARYSpecifyProgramControlSpecifySpecialCalculationModesorAdditionalMemoryInputProblemGeometryDelimitRegionsintheModelAssignConstitutiveModelsandPropertiesAssignInitialConditionsandApplyBoundaryConditionsSpecifyStructuralSupportSpecifyInterfacesSpecifyUser-DefinedVariablesorFunctions(FISH)MonitorModelConditionsduringSolutionProcessSolvetheProblemGenerateModelOutput30FLACisamenu-drivenprogram-Point-and-clickoperationaccessesallcommandsandfacilitiesinFLAC.-DesignedtoemulateexpectedWindowsfeatures.-Includesagridlibrarywithcommontypesofgeo-engineeringgrids.-Digitizedplotsorgraphicsfilescanbeimportedtoguidegridgeneration.-Providesaccesstoadatabaseofmaterialproperties.OverviewofFLACoperation31TheGIICisaJAVA-basedapplicationthatrunsindependentlyofFLAC;dataareexchangeddirectlybetweenFLACandtheGIICsothatyoumaymanipulatemodelresultswithoutinterferingwiththesolutionprocess.FLACwiththeGIICrunsasaWindowsapplication.TheGIICrequiresapproximately40MB(includingtheJavaRuntimeEnvironment).FLACcanstillberunwithouttheGIIC(fordie-hardusers).GraphicalInterfaceforItascaCodes32

TheFLAC-GIICmainwindow33

MODELLING-STAGETABS34Virtual-gridGenerationModeinFLAC6.035

GRIDGENERATIONBuildToolsGenerateToolGeometries36

GRIDLIBRARY37VirtualGridfor“SimpleSlopewithTunnel”GridObject38VirtualToolTabs39BlocksEditStageinEditTool40BoundariesEditStageinEditTool41MeshEditStageinEditTool421.Definemodelboundaries432.Specifyboundaryconditionsandtypes443.Selectzoning454.CreateFLACmodelfrom“virtual”model461.Definemodelboundaries472.Specifyboundaryconditionsandtypes483.Selectzoning494.CreateFLACmodelfrom“virtual”model50*TheNewOrleansHurricaneProtectionSystem:WhatWentWrongandWhyAReportbytheAmericanSocietyofCivilEngineersHurricaneKatrinaExternalReviewPanal,2007Figure4.5TypicalUSACEFloodProtectionStructures*51Figure7.417thStreetCanalFailureMechanism**TheNewOrleansHurricaneProtectionSystem:WhatWentWrongandWhyAReportbytheAmericanSocietyofCivilEngineersHurricaneKatrinaExternalReviewPanel,200752StabilityanalysisofI-wallstructureCreateFLACgridrepresentinggeometryofI-wallstructure.I-wallsimulatedwithbeamelementsconnectedtothegridviainterfaces.Assignmaterialsandpropertiesforclay,sandandfill.(fortotal-stressanalysis,assignundrainedshearstrengthandzerofrictiontoclaymaterial)AssignpropertiesforI-wallstructureandwall/soilinterface.Establishstateofstressbeforefloodlevel.ApplywaterpressurestowallrepresentingfloodlevelCalculatefactorofsafety:Case1–nowater-filledgapatwallCase2–withwater-filledgapatwallAnalysisStages:53I-wallgeometry(-65,-75)(78,-75)(156,-75)(156,-17)(150,-17)(124-15)(-65,-3.5)(10,-3.5)(46,-1)(63,4)(78,-1)(93,-1)(112,-9)(78,6.5)(78,14)(78,-17)54Slidingsurfacewithoutawater-filledgap55Slidingsurfacewithawater-filledgap56Automaticre-meshinglogic

inlargestraincontinuumsimulations

-AnewfeatureinFLACVersion6.0

andFLAC3DVersion4.057Necessitytodevelopre-meshinglogicThemeshhastoberezonedinordertocontinuetherunItmightbedesirabletorezonesomeareaatintermediatestages58Atypicalre-meshingprocessThreeStepsStep1:Triggerre-meshingoperation,e.g.,badgeometryStep2:Generateanew,regularmeshStep3:Transfermodelinformation(stresses,velocities,etc)fromtheold,distortedmeshtothenewmesh59Datatransfer(mapping)formulationsMappinginvolume/area(e.g.,propertiesandzonequantities)Interpolationatpoint(e.g.,grid-pointquantities)60Asimpleslopeexample30x20gridMaterialpropertiesK=2E8PaG=1E8PaC=0density=200061Asimpleslopeexampleconfiggrid3020modelmohrtable1010101020203020gentab1modnullreg120fixxyj=1fixxi=1fixxi=31setgrav10propdens2000bulk2e8sh1e8fric10coh1e20tens1e20solvesaveslope_ini.sav;nore-meshingpropcoh0setlargeSolvesaveslope_norez.sav62AsimpleslopeexampleRe-meshingsteps:Step1:StorethesurfaceoftheoldmeshtoatableStep2:Generateanewblockmesh,removetheupper-leftcornerabovethesurfacetableStep3:InformationtransferbyissuingREZONEcommandOld,distortedmeshNew,regularmesh63Asimpleslopeexampledef_autorezcommandrezsetsepmeth=slopeRezonerezsetsurffrom1,11to31,21tab4rezonecyclecontinueendCommandendsetgeom0.25;triggerbadgeomeventifratioofsub-zoneareatototalzoneareaislessthan0.25setrez_func_autorez;invoke‘_autorez’functionifbadgeometryeventoccursplotgridmovieonfileslope.dcx;makemoviemoviestepon50;samplingevery50stepsstep400064AsimpleslopeexampledefslopeRezone_rezcnt=_rezcnt+1oo=rez_exe('gen000203020300')oo=rez_exe('modmohr')_toltab4oo=rez_exe('gentable4')oo=rez_exe('modnullregion1,20')enddef_toltab4_ts=table_size(4)xtable(4,1)=xtable(4,1)-5.xtable(4,_ts)=xtable(4,_ts)+5.endRemeshingprocess65SummaryMeshgenerationmakesuseofFISH,theembeddedprogramminglanguageinFLAC.Informationtransferisautomatic.Thelogicisstillunderdevelopment,althoughmostmodules/modelsarecovered;itisnotcompletelytestedNotapplicabletomodelswithinterfacesorattachedgridsatthecurrentstage66FLAC3DStructuralElements

JoiningStructuralElements(SELs)andPretensioningCables67FLAC3DCapabilitiesInadditiontomodelingasolidcontinuumwiththemaingrid(zonesandgridpoints),FLAC3Dhasthecapabilitytomodelstructures(cables,beams,piles,shells,geogrids,liners)SELsaretruefiniteelements(elementsandnodes)formulatedtoworkinthefinitedifferenceframeworkofFLAC3DStructurescaninteractwiththemaingridandotherstructures68Nomenclature69WhyUseSELsWecouldmodeleverythingwithzonesZonesarepooratmodelingbending(alargenumbermayberequiredacrossthethickness)Gridgenerationbecomesproblematicwhenmodelingstructureswithzones(geometricproblemsaswellasRAMshortage).Ifwearenotinterestedinsmallscalelocaleffects(e.g.,detailedstressdistributionacrossanoddlyshapedbeamsection)thenSELsareideal70SELLinksSELnodescommunicatewithzonesandothernodesvialinks(alogicalconnection)Twotypesoflinksnode-zoneandnode-nodeLinkshaveattachmentconditions(e.g.springs)Linkscanattachanywheretothemaingrid(SELnodesdonotneedtocoincidewithgridpoints)!71DefaultlinkattachmentWhenyoucreateaSELwithinazonetheSELnodeswillautomaticallylinktothezonewithdefaultattachmentconditions(node-zonelinks)72Node-NodeLinksSELnodeswillneverautomaticallylinktoeachother,eveniftheSELnodescoincidewhentheSELiscreated.Youmustmanuallycreatenode-nodelinkstoallowdifferentSELs(e.g.,beamandcable)tointeractwitheachother.73JoiningSELs2.Createnewnode-nodelinkfromSELAtoSELB1.Deletenode-zonelinkonSELASELnodesconnecttogridorotherSELnodeswithlinks74NO!

FLAC3Ddoesnotsupportchainedrigidconnections75Yes!76Example:Retainingwallwithtiebackcableembeddedliner7778cableembeddedliner;printselnodelinkrangeid79;deletethecablelinkclosesttotheretainingwallseldeletelinkrangeid157;createanode-nodelinkfromthecabletothewallsellink79targetnodetgt_num64;printselnodelinkrangeid79sellinkattachxdirrigidrangeid188sellinkattachydirrigidrangeid188sellinkattachzdirrigidrangeid188sellinkattachxrdirfreerangeid188sellinkattachyrdirfreerangeid188sellinkattachzrdirfreerangeid18879cableembeddedlinerseljoincableid2linerid1printselnodelinkrangeid79printsellinkattachrangeid188sellinkattachxrdirfreerangeid188sellinkattachyrdirfreerangeid188sellinkattachzrdirfreerangeid188printsellinkattachrangeid188easier80PretensioningCablesRemoveasegmentfromtheungroutedportionApplyopposingforcestonodesoneithersideofthebreakandequilibriateClosethegapwithapretensionedsegment81plotselgeomcablecidon;createabreakintheungroutedportionofthecableseldeletecablerangecid10882Applynodalforcesdef_appTieLoadRamp_tloadtot=2e5;totalpretensionforce_imaxramp=5_ndid1=87;nodeononesideofthebreakinthecable_ndid2=88;nodeontheothersideofthebreakinthecableloop_iramp(1,_imaxramp)_tloadapp=_tloadtot*float(_iramp)/float(_imaxramp)_ntload=-_tloadappcommandselnodeapplyremoveforcerangeid_ndid1selnodeapplyremoveforcerangeid_ndid2selnodeapplyforce_tloadapp00systemlocalrangeid_ndid1selnodeapplyforce_ntload00systemlocalrangeid_ndid2solveend_commandendloopend83AxialForceinCableSegmentAdjacenttotheBreakvsStepDuringPretensioning84InserttheMissingCableSegmentselcableselid2nodes8788selcableid2propemod2.05e11gr_coh0.0gr_fric0.0gr_k0.0&ycomp1.0e5ytens15.34e5xcarea5.54e-3rangecid131selcablepretension_tloadtotrangecid131;IMPORTANT85FinalAxialForceinCable86Techniquesforinitializingstressesinnon-uniformgrids87In-situStresses

Presentbeforeanyexcavationorconstruction.

Ideally,in-situstressesshouldbemeasuredinthefieldandinitializedinthemodel.

Ifthisisnotavailable,themodelcanberuntoequilibriumforarangeofpossibleconditions.88PossibleScenarios-deepundergroundexcavations-initializeuniformstress-closetogroundsurface-initializestressgradient

uniformmaterial

iniszzszgrad0,0,vznonuniformmaterial

iniszzszgrad0,0,vzrangezz1z2