review of rock mechanics and rock engineering

InternationalJournalofRockMechanics&MiningSciences40(2003)283–353JournalReviewArticleAreviewoftechniques,advancesandoutstandingissuesinnumericalmodellingforrockmechanicsandrockengineering$L.Jing*DivisionofEngineeringGeology,RoyalInstituteofTechnology,Technikenringen72,StockholmS-10044,SwedenAccepted20January2003AbstractThepurposeofthisreviewpaperistopresentthetechniques,advances,problemsandlikelyfuturedevelopmentsinnumericalmodellingforrockmechanics.Suchmodellingisessentialforstudyingthefundamentalprocessesoccurringinrocksandforrockengineeringdesign.Thereviewbeginsbyexplainingthespecialnatureofrockmassesandtheconsequentialdifficultieswhenattemptingtomodeltheirinherentcharacteristicsofdiscontinuousness,anisotropy,inhomogeneityandinelasticity.Therockengineeringdesignbackdroptothereviewisalsopresented.ThedifferenttypesofnumericalmodelsareoutlinedinSection2,togetherwithadiscussiononhowtoobtainthenecessaryparametersforthemodels.Thereisalsodiscussiononthevaluethatisobtainedfromthemodelling,especiallytheenhancedunderstandingofthosemechanismsinitiatedbyengineeringperturbations.InSection3,thelargestsection,states-of-the-artandadvancesassociatedwiththemainmethodsarepresentedindetail.Inmanycases,forthemodeltoadequatelyrepresenttherockreality,itisnecessarytoincorporatecouplingsbetweenthethermal,hydraulicandmechanicalprocesses.ThephysicalprocessesandtheequationscharacterizingthecoupledbehaviourareincludedinSection4,withanillustrativeexampleanddiscussiononthelikelyfuturedevelopmentofcoupledmodels.Finally,inSection5,theadvancesandoutstandingissuesinthesubjectarelistedandinSection6therearespecificrecommendationsconcerningqualitycontrol,enhancingconfidenceinthemodels,andthepotentialfuturedevelopments.r2003ElsevierScienceLtd.Allrightsreserved.Keywords:Review;Rockmechanics;Numericalmodelling;Design;Coupledprocesses;OutstandingissuesContents1.Introduction................................................2841.1.Specialnatureofrockmasses....................................2851.2.Rockmechanicsmodellingforrockengineeringdesignandconstruction..............2861.3.Scopeofthisreview.........................................2872.Numericalmethodsinrockmechanics...................................2872.1.Numericalmethodsformodellingcontinuousanddiscontinuousrockmasses...........2872.2.Characterizationofrockmassesfornumericalmethods.......................2912.3.Enhancedunderstandingprovidedbynumericalmethods......................2913.Numericaltechniquesforrockmechanics:states-of-the-art........................2933.1.FiniteDifferenceMethods......................................2933.1.1.Basicconcepts........................................293$ThisisthesecondofaseriesofJournalReviewArticlescommissionedbytheEditor.Theseriesconsistsofarticlesreviewingsignificantortopicalsubjects,orsubjectsrequiringexpertexplanation.ThisReviewisasignificantlyexpandedversionofthe‘‘NumericalMethodsinRockMechanics’’CivilZoneReviewpaperwhichwaspublishedinVol.39,No.4,June2002,pp.409–427,andislongerthanusualpapersinordertodojusticetothesubject.Also,anenhancedreferencingsystemhasbeenusedherewiththereferencesbeingprovidedintwoways:firstly,byauthoranddate,sothatthisinformationiscontaineddirectlyinthetext;and,secondly,bybrackettednumbers,followingthestandardJournalformat.*Tel.:[phone];fax:[phone].E-mailaddresses:[e-mail](L.Jing).1365-1609/03/$-seefrontmatterr2003ElsevierScienceLtd.Allrightsreserved.doi:10.1016/S1365-1609(03)00013-31.IntroductionThepurposeofthisJournalReviewArticleistopresentthetechniques,advances,problemsandlikelyfuturedevelopmentsinnumericalmodellingforrockmechanics.InthisSection,thereviewisprefacedbynotingthespecialnatureandidiosyncraciesofrockmasses—andhencesomeofthedifficultiesassociatedwithcapturingtherockrealityinthenumericalmodels.Theutilityofnumericalmodellinginproviding3.1.2.FinitevolumeapproachofFDManditsapplicationtostressanalysis...........2943.1.3.Fractureandnon-linearanalyseswithFDM/FVM.....................2943.2.FiniteElementMethodandrelatedmethods.............................2953.2.1.Basicconcepts........................................2953.2.2.FractureanalysiswiththeFEM...............................2963.2.3.Meshless(meshfree)methods................................2983.3.BoundaryElementMethods.....................................3013.3.1.Basicconcepts........................................3013.3.2.FractureanalysiswithBEM.................................3033.3.3.AlternativeformulationsassociatedwithBEM.......................3043.4.BasicfeaturesoftheDiscreteElementMethod(DEM).......................3073.4.1.ExplicitDEM—DistinctElementMethod:blocksystems..................3083.4.2.ImplicitDEM—DiscontinuousDeformationAnalysismethod:blocksystems.......3123.4.3.KeyBlocktheory......................................3143.4.4.DEMformulationsforparticlesystems...........................3143.4.5.Dynamiclatticenetworkmodels...............................3143.5.DiscreteFractureNetworkmethod.................................3153.5.1.DFN-thebasicconc