UDEC/3DECShortCourseItascaSoftwareTrainingCourseTongjiUniversityShanghai,ChinaOctober27-31,2008PeterCundall,YanhuiHan&RogerHartItascaConsultingGroup,Inc..TrainingSchedule

October28,2008(afternoon)02:00-03:15 OverviewofUDEC/3DECFeaturesandCapabilities

-Overviewofcapabilitiesingeo-engineering -NewfeaturesinUDECand3DEC -Theoreticalbasis03:15-03:30Break03:30-05:00 RunningModelsinUDEC -Menu-drivenversuscommand-drivenoperation-Simpletutorial

.UDECisaDEMcodethatallowsthesimulationoftheinteractionofblocks.Thismaybeajointedrockmass,amasonrywall,oranymaterialwherethemodeofdisplacementmayoccuralongpre-existingplanesofweaknessordiscontinuity.Anygeometrycanberepresented,andtheboundaryconditionsarequitegeneral.UDECalsosimulatesthebehavioroftheintactmaterialbetweentheplanesofweaknessasanonlinearcontinuum,usingthegeneralizedfinite-differencemethod(arbitraryelementshapes),knownasthefinitevolumemethod.UDECsolvesthefulldynamicequationsofmotionevenforquasi-staticproblems.Thishasadvantagesforproblemsthatinvolvephysicalinstability,suchascollapse,aswillbeexplainedlater.Tomodelthe“static”responseofasystem,dampingisusedtoabsorbkineticenergy.WhatisUDEC?.UDECDiscontinuousmediummodeledasanassemblage

ofconvexorconcaveblocks;blocksmayberigidordeformable.Discontinuitiestreatedasboundaryconditionsbetweenblocks.Motionalongdiscontinuitiesgovernedbylinearandnon-linearforce-displacementrelationsformovementsinboththenormalandsheardirection.Manybuilt-inblockandjointconstitutivemodelsthatarerepresentativeofgeologic,orsimilar,materials;optionaluser-writtenmodels.Plane-strain,plane-stressandaxisymmetricgeometrymodes.Structuralelementmodelsforrock-structureinteraction–cables,piles,beams,liners,shotcrete,soilreinforcement,etc.Staticanddynamicanalysiscapabilities.Transientandsteadystatefluidflowinjoints.Viscoelasticandviscoplastic(creep)models.Thermalanalysiscapability,withcouplingtosolidandfluid…isbestsuitedtomodelingdiscontinuousmaterials(containingmanyintersectingdiscontinuities)thatexhibitnonlinearbehavior.Inparticular,itfeatures:.3DECsimilartoUDEC,butinthreedimensionscontainsthesamefeaturesaslistedforUDEC

Modelofarchdamusingfinite-elementblocks.NewFeaturesinUDEC4.0

GraphicaluserinterfaceFactor-of-safetycalculationbasedontheshearstrengthreductionmethodUser-definedzoneandjointconstitutivemodelsMixeddiscretizationtoprovidemoreaccuracyforplasticityanalysisTwo-phaseflowinjointsNetworkkeylicenseversionNewFeatureinUDEC4.01ReleasedinOctober2008Improvedandre-structuredgraphicaluserinterface(availableatnoadditionalchargetocurrentVersion4.0owners).PlannedNewFeaturesinUDEC5.0Generic“virtual-model”generationtooltofacilitatemodelcreationSpeedupofdouble-precisionversionbyconvertingtoIntelFortrancompilerMixedDiscretizationschemefortriangularelements“NodalMixedDiscretization”toprovidemoreaccuratesolutionofplasticityproblemsusingtriangulargridsRockboltelementstosimulaterockreinforcementincludingtensilerupture,strain-softeningbehaviorofgroutandeffectofchangingconfiningstressHelpFilecontainingCommandReference,FISHReferenceandExampleApplicationsEstimatedrelease:mid2009.NewFeaturesin3DEC4.1Acceleratedinteractivegraphics(OpenGLbasedplotting)withnewgraphicalstructureNewMixedDiscretizationschemefortetrahedralelements“NodalMixedDiscretization”providesmoreaccuratesolutionofplasticityproblemsusingtetrahedralgrids64-bitversionFactorofSafetycalculationmodeImprovementstouser-definedconstitutivemodelsandadditionofuser-definedjointconstitutivemodelsImprovementstostructuralelementlogicincludinginstallationattunnelintersectionsHelpFilecontainingCommandReference,FISHReferenceandExampleApplicationsNewPGENinterfaceImprovedFISHlanguageReleasedinJanuary2008.TheExplicitDynamicSolutionSchemeandtheDistinctElementMethod

in

UDEC&3DEC.DEMDefinitionsThename“DiscreteElementMethod”(DEM)shouldbeappliedtoamethodonlyifit*:allowsfinitedisplacementsandrotationsofdiscretebodies;includingcompletedetachmentrecognizesnewinteractions(contact)automaticallyasthecalculationprogressesAdiscreteelementcodewillembodyanefficientalgorithmfordetectingandclassifyingcontacts.Itwillmaintainadatastructureandmemoryallocationschemethatcanhandlemanyhundredsorthousandsofdiscontinuitiesorcontacts.Thename“DistinctElementMethod”isusedforaDEMthatusesanexplicitdynamicsolutiontoNewton’slawsofmotion.*Cundall,P.A.,andR.D.Hart.”NumericalModelingofDiscontinua,”EngineeringComputations,9(2),101-113(1992).Finiteelementcodesformodeling“discontinua”areoftenmodifiedcontinuumprograms,whichcannothandlegeneralinteractiongeometry(e.g.manyintersectingjoints).Theirefficiencymaydegeneratedrasticallywhenconnectionsarebrokenrepeatedly..TypesofDiscreteElementMethodsforDiscontinuumAnalysisDistinctElementUseexplicittime-marchingschemetosolveequationsofmotiondirectly.Bodiesmayberigidordeformable,contactsaredeformableModalMethodsSimilartodistinctelementmethodinthecaseofrigidblocks.Fordeformablebodies,modalsuperpositionisusedsonon-linearityisdifficulttoimplementDiscontinuousDeformationAnalysisAssumescontactsarerigidbodiesandbodiesmayberigidordeformable.No-penetrationisachievedbyiterationMomentumExchangeMethodsAssumeboththecontactsandbodiestoberigid.Momentumisexchangedbetweentwocontactingbodiesduringcollision.Canrepresentfrictionsliding..DistinctElementMethodThreeaspects...GeometryContactmechanicsSolidbodymechanics.DistinctElementMethodGeometrySpecificationofshapesin2and3dimensionsInteractionofpairsofcontactingblocksorparticlesIdentificationofcontactcharacterbetween2blocks.DistinctElementMethodSpecificationofshapesin2and3dimensions2&3dimensions–PFC

disks&spheres2dimensions–UDEC arbitrarypolygons–convexandconcave–withroundedcorners3dimensions–3DEC arbitrarypolyhedra–concavebodiesareconstructedofseveralconvexbodiesattachedtogether.DistinctElementMethodInteractionofpairsofcontactingblocksorparticlesIfweattempttoidentifyneighboringblocksbyanexhaustivescan(i.e.eachblocktestedagainsteachother),thenthesearch-timeisproportionaltoN2whereNisthenumberofblocks.Twomethodstoreducesearchtime:Cell-mapping,usedinUDEC&3DECCirculatingdatastructure,thatmimicsthetopologyofthesystemasusedinUDEC.Cell-mapping

Thesolution-spaceiscoveredbyrectangularcells.Eachblockdepositsamarkerinallthecellsthatitoverlaps–thisprocesstakesNproportionaltime.Eachblockcanfindallofitsneighborsbylookinginjustthosecellsthatitoverlaps-thisprocessisalsoNproportional,ifthecellsizeisofasimilarordertotheblocksize..Circulatingdatastructure

Linkedliststhatdescribeblockboundariesalsotraceoutthevoidspacesautomatically.Ablockneedsonlytosearchitslocalvoidspacestofinditsneighbors.Thisschemebreaksdownifmanyblocksbecomedisconnected,butitiswellsuitedtomodelfluidflowinjoints.closeddomaincanrestrictsearchtothecloseddomain–anynewcontactsmustbethere.DistinctElementMethod Identificationofcontactcharacterbetween2blocks

Weneedtoknow: typeofcontact(e.g.corner-to-corner,corner-to-edge,etc.)directionofnormaltoslidingdirectiongapbetweenblocks,orcontactoverlap.Block2Jointun2us2Block1us1un1InitialPositionofblock2xyblockcentroidContactBetweentwoRigidBlocks

Acontactiscreatedateachcornerinteractingwithacorneroredgeofanopposingblock..RoundedCornersinUDECCornerroundingschemewithconstantlengthdrdd=rd>>rrdd =distancetothecorner r=radiusoftheroundedcornerrdd=rdrd>>rCornerroundingschemewithconstantradiusr,showingthatsmallanglesinthecornerleadstolargedistancesd.

DefinitionofcontactnormalRoundedcorner-to-edgecontactRoundedcorner-to-cornercontact.L1L2L3123ElementNodes123Corner-EdgecontactsL1,L2,L3LengthsassociatedtothecontactsContactsandDomainsbetweenTwoDeformableBlocksD1D2D1D2DomainsBLOCK1BLOCK2.InteractionoftwosquaresMaximumnumberoftests124corners4edgescorneredgecorner16edge16corner16edge16.Interactionoftwocubes126faces12edges8cornersface36edge72corner48face48edge96corner64face72edge144corner96Total676facecorneredge.Modesofcontactscorner-corneredge-edgecorner-facecorner-edge.Modesofcontactsface-faceedge-face.“Commonplane”logicAlgorithmexecutedinparallelwithmechanicalcalculation:“maximizethegapbetweenthecommonplane(c-p)andtheclosestvertex”c-p12.“Commonplane”logicIfweassumeac-pcanbefound,blocksareconvex then...testforcontactsiseasytestcornersofbothblocksforcontactwithc-p(16dotproducts)iftestforbothblocksarepositivethenblocksaretouchingdetermininggapiseasysumofmin.distancesfromeachblock’scornertoc-pcontactnormalis...thenormalofthec-pisalwaysdefined.CommonplanelogicWhataboutassumptions?Usethealgorithm“maximizethesmallestgapbetweeneachblock(ofacontact-pair)andtheplane”Constructconcaveblocksfromseveralconvexblocks(the“join”doesnotexist,asfarasphysicsisconcerned)shift,then...rotation.CommonplanelogicModesofcontactcanbefoundeasilywithcontact-planelogic“countthenumberofcornersthattouchthecommonplane”modeofcontactisdeterminedbycounts:e.g.1-4=“corner-face”note:”touch”impliesgap<0BlockA1corner2edge3faceBlockB1corner2edge3face.DistinctElementMethodContactmechanics Allcontactsareassumedtobe“soft”-i.e.contactforcesaredirectlyrelatedtothedeformationsor“overlaps”atcontacts.Forpoint-contact,Hertz/Mindlincontactlawscanbeused.Foredge-to-edgecontact,suchasrockjoints,variousconstitutivelawscanbeused–e.g.,elastic/Coulombslip.

UDEC&3DECalsohavethe”continuouslyyielding”model,whichemployscontinuousfunctionsfortheforcedisplacementrelations.Thereisalsointernaldamageaccumulation..DistinctElementMethodSolidbodymechanics TherearetwoformulationsRigidbodytranslationandrotationDeformablebodymechanics

.Rigidbodytranslationandrotation

Ifmostofthemovementinasystemtakesplaceinadiscontinuousway(e.g.sliding,opening,relativerotation,interlocking),thenthebodiesmaybeassumedtoberigid.DistinctElementMethod.Deformablebodymechanics

Ifthereisappreciabledeformationoftheintactmaterial,comparedtodiscontinuousmotion,thenthebodiesmustbetakenasdeformable.DistinctElementMethod.Deformablebodymechanics

Inordertomodeldeformableblocks,thereareautomaticgenerators–inUDECtodivideabodyintotriangles,andin3DECtodividebodiesintotetrahedra.Thefinite-differenceformulationfortheseinternalelementsisidenticaltothatforFLAC.Severallinearandnon-linearconstitutivemodelscanbeusedintheinternalelements.

DistinctElementMethod.TheExplicitDynamicSolutionScheme

appliedwiththe

DistinctElementMethod

.UDECand3DECsolvethefulldynamicequationsofmotionevenforquasi-staticproblems.Thishasadvantagesforproblemsthatinvolvephysicalinstability,suchascollapse.Tomodelthe“static”responseofasystem,arelaxationschemeisusedinwhichdampingabsorbskineticenergy.Thisapproachcanmodelcollapseproblemsinamorerealisticandefficientmannerthanotherschemes,e.g.,matrix-solutionmethods.BasisoftheSolutionSchememovie.OverviewofDEM&explicit,dynamicsolutionschemeTheformulationisverysimple.Forexample,foraballimpactingawall,massOnetimestep,

unknownsknowns(allcontacts,ingeneral)(allparticles,ingeneral)Fulldynamicequations

(integrationofNewton’s2ndlaw)

Explicit

solutionschemeThreeconsequencesofthisformulationareasfollows…(centraldifference–2ndorderaccurate).1.Treatingeachbodyasdiscrete

(DEM)

allowsdiscontinuousmaterial(suchasarockmass)tobemodeledeasily.2.

Fulldynamicequationsofmotionallowtheevolutionofunstablesystemstobesimulatedrealistically.3.

Explicitsolutionschememakesthetaskofhandlingnonlinearitytrivial.Examplesofnonlinearitiesare:(a)contactmaking&breaking;(b)softeningmaterialbehavior(rock-like);e.g.,forcedisplacementINPUTOUTPUTTheexplicitschemeusesatimestepsosmallthat

informationcannotpropagatebetweenneighborsinonestep.Thus,eachelementisisolatedduringonestep,enablingmtkD<S.ComputationCycleinUDEC&3DECksknFnFsDunDusAllthecontactsCONSTITUTIVE+MxiAtthecentroidALLTHEBLOCKSMOVEMENTzonenodeAttheelementAtthenodeMOVEMENTALLTHEBLOCKSRIGIDBLOCKSDEFORMABLEBLOCKSGoto.TIMESTEPThesolutionschemeusedinDEMisconditionallystable.Alimitingtimestepmustsatisfyboththecalculationforinternalblockdeformationandinter-blockrelativedisplacement.Forstabilityoftheblockdeformationcomputation:wheremiisthemassassociatedwithblocknodei;andkiisthemeasureofstiffnessoftheelementssurroundingthenode.Forcalculationsoftheinter-blockrelativedisplacement,thelimitingtimestepiswhereMministhemassofthesmallestblockinthesystem;andKministhemaximumcontactstiffness.Thecontrollingtimestepis.MECHANICALDAMPINGMechanicaldampingisusedinUDECand3DECforstatic(non-inertial)solutionsandfordynamicsolutions.Forstaticanalysis,theapproachissimilarto“dynamicrelaxation.”Theequationsofmotionaredampedtoreachastaticstateasquicklyaspossibleundertheappliedinitialandboundaryconditions..DYNAMICRELAXATIONIndynamicrelaxationblocks(andgridpoints)aremovedaccordingtoNewton’slawofmotion.TheequationsofmotionaredampedtoreachaforceequilibriumstateasquicklyaspossibleDampingisvelocity-proportional–i.e.,themagnitudeofthedampingforceisproportionaltothevelocityoftheblocks.

Velocity-proportionaldampingintroducesbodyforcesthatcanaffectthesolution.UDECand3DECprovidetwodifferenttypesofdampingtominimizethisproblemforstaticanalysis:adaptiveglobaldamping(DAMPauto)localdamping(DAMPlocal).ADAPTIVEGLOBALDAMPINGAdaptiveglobaldampingisaservo-mechanismusedtoadjustthedampingconstantautomaticallysuchthatthepowerabsorbedbydampingisproportionaltotherateofchangeofkineticenergyinthesystem.Adjustmentoftheviscosityconstantismadebyanumericalservo-mechanismthatseekstokeeptheratio,R,equaltoagivenratio(e.g.,0.5)..LOCALDAMPINGThedampingforce,

Fd

is:

Dampingforcesareintroducedtotheequationsofmotion:whereFi

istheunbalancedforce

InUDECand3DECtheunbalancedforceratio(ratioofunbalancedforce,

Fi

,totheappliedforcemagnitude,Fm)ismonitoredtodeterminethestaticstate.

Bydefault,whenFi

/Fm

<10-5inUDEC(or10-4in3DEC)thenthemodelisconsideredtobeinanequilibriumstate.Thedampingforceatagridpointisproportionaltothemagnitudeoftheunbalancedforcewiththesignsettoensurethatvibrationalmodesaredamped..BASISOFSTATICSOLUTIONSINUDECand3DECTheunbalancedforceratio(ratioofunbalancedforce,Fi

,totheappliedforcemagnitude,Fm)ismonitoredtodeterminethestaticstate.Boththeadaptiveglobaldampingandlocaldampingdynamicsolutionmethodsprovideastaticsolution(withtheeffectofinertialforcesminimized)providedtheunbalancedforceratioreachesasmallvalue.Thisiscomparabletothe“l(fā)evelofresidualerror”or“convergencecriterion”definedformatrixsolutionmethodsusedinmanyfiniteelementprograms.InUDECand3DEC,theleveloferrorisquantifiedbytheunbalancedforceratio.InbothUDEC/3DECandFEsolutions,thestaticsolutionprocessterminateswhentheerrorisbelowadesiredvalue..ComparisonofadaptiveglobaldampingandlocaldampingAsimpleexample:tenblocksslideonaroughbase*Velocityproportionaltoout-of-balanceforcewithproportionalityconstantDynamicrelaxationwithstandardvelocity-proportionaldampingAdaptiveglobaldampingLocaldamping*.MASS(DENSITY)SCALINGForstaticanalysis,materialinertialmassescanbescaledsothatlocalcriticaltimestepsareincreased.Thevalueofinertialmassisirrelevanttomodelingstaticsystems,providedgravityforcesarecorrectlypreserved.(Notethatgravitationalmassesarenotaffected.)Criticaltimestepcanbeincreasedbecauseitisproportionalto.Theprocedure,called“densityscaling,”scalestheinertialdensityofblocksorzonesbasedontheiraverageblock,orzone,mass.DensityscalingisinvokedwiththeMSCALEcommand.Itisturnedonautomaticallywheneverlocaldampingoradaptiveglobaldampingisused..RunningModelsinUDEC.OverviewofUDECoperation(1)-Engineeringsimulationsusuallyconsistofalengthysequenceofoperations.-AUDECdatafilecanbeeasilymodifiedwithatexteditor.Severalfilescanbelinkedtogether.-Thewordorientedinputfilesprovideanexcellentmeansforkeepingadocumentedrecordofanalyses.-Thecommanddrivenstructureallowsthedevelopmentofpre-andpost-processingprogramstomanipulateUDEC

inputoroutputasdesired.UDECisacommand-drivenprogram.COMMAND

keyword

value…<keyword

value>CommandSyntaxExample,new (clearsthememory)

block0,00,1010,1010,0(createsablock)crack0,28,10 (createsasinglefractureinblock)plotblock (drawstheblockonthescreen)Thereareover50commandsand400keywordsinUDEC!!!OverviewofUDECoperation(2).UDECisamenu-drivenprogram-Point-and-clickoperationaccessesallcommandsandfacilitiesinUDEC.-DesignedtoemulateexpectedWindowsfeatures.-Digitizedplotsorgraphicsfilescanbeimportedtoguidemodelgeneration.-Providesaccesstoadatabaseofmaterialproperties.OverviewofUDECoperation(3).TheGIICisaJAVA-basedapplicationthatrunsindependentlyofUDEC;dataa