英语翻译-植被模型对边坡稳定性的影响

河北工程大学本科毕业设计英语翻译译文题目：ModellingtheEffectsofVegetationonStabilityofSlopes植被模型对边坡稳定性的影响姓名：专业：勘查技术与工程班级学号：指导老师：指导教师职称：教授2013年6月12日ModellingtheEffectsofVegetationonStabilityofSlopesSummary:Itiswellunderstoodthatvegetationinfluencesslopestabilityintwoways:throughhydrologicaleffectsandmechanicaleffects.Hydrologicaleffectsinvolvetheremovalofsoilwaterbyevapotranspirationthroughvegetation,whichleadtoanincreaseinsoilsuctionorareductioninpore-waterpressure,hence,anincreaseinthesoilshearstrength.Theshearstrengthofthesoilisalsoincreasedthroughthemechanicaleffectsoftheplantrootmatrixsystem.Thedensityoftherootswithinthesoilmassandtheroottensilestrengthcontributetotheabilityofthesoilstoresistshearstress.Theeffectsofsoilsuctionandrootreinforcementhasbeenquantifiedasanincreaseinapparentsoilcohesion.Thispaperinvestigatestheeffectsofvegetationonthestabilityofslopesusingthefiniteelementmethod.Twokeyvegetation-dependentparametershavebeenincorporatedinthefiniteelementslopestabilityanalysis,namely,apparentrootcohesion(CR)anddepthofrootzone(hR).Parametricstudieswereperformedtoassessthesensitivityofthestabilityofaslopetothevariationinthekeyvegetationandsoilparameters.Resultsshowthatvegetationplaysanimportantroleinstabilizingshallow-seatedfailureofslopes,andsignificantlyaffectsstability.INTRODUCTIONSlopeinstabilityisoneofthemajorproblemsingeotechnicalengineeringwheredisasters,likelossoflifeandproperty,dooccur.Themajorityoftheseslopefailuresareofvegetatedorforestednaturalslopes.Anaturalslopeisdifferentfromanembankmentoraman-madeslopeinthattheeffectsofvegetationandsoilvariabilityplayanimportantroleintheirstability.Theeffectsofvegetationonthestabilityofslopesarewellrecognized.Vegetationaffectsslopestabilitythroughmodificationofthesoilwaterregime,whichinturncausesavariationinsoilsuctionorporepressure.Vegetationcanalsoenhancethestabilityofaslopebyrootreinforcement.Wuetal.(1979)investigatedthestabilityofslopesbeforeandafterremovalofforestcoverandconcludedthattheshearstrengthcontributedbytreerootsisimportanttothestabilityofslopes.Thestudyindicatedthatvegetationcouldcontributeshearstrengthtotheslopesthroughrootreinforcement.Wuetal.(1979)showedthatslopefailurewouldhaveoccurrediftheeffectsofvegetationwerenottakenintoaccountinslopestabilityanalyses.Naturalslopesaresubjectedtoinherentvariabilitybothinthesoilandthevegetation.Itisunlikelythattheunderlyingsoilprofilesofnaturalslopesarecompletelyuniformorhomogenous.Evenwithinahomogenoussoillayer,soilpropertiestendtovaryfrompointtopoint(Vanmarcke,1977).Thegrowthofvegetationissensitivetoenvironmentalconditionsandchanges.Typicallydifferenttypesofvegetationgrowonanaturalslope,suchasamixtureofgrasses,herbs,scrubsandtrees.Theirdifferencesinsizeandphysicalpropertieswillaffecttheslopestabilityindifferentways.Therefore,theuseofasingleinputvalueforthevegetation-dependentparametersinanalysesisbestviewedasafirstapproximationofthefieldconditions.Thispaperinvestigatestheeffectsofvegetationonthestabilityofslopesusingthefiniteelementmethod.Thefiniteelementmethodallowstheextentofthevegetationeffectstobedefinedbytheuserduetothenatureofthemethodwhereslopegeometryisdicretisedintosmallelements.Tolimitthescopeofthispaper,onlytheeffectsofrootreinforcementareincorporatedintheslopestabilityanalysis.Thevariabilityinthevegetationandsoilpropertiesarenotconsideredinthispaper.A2:1homogenousslope(angleofinclination26.57°)isusedtoinvestigatetheeffectsofvegetationonslopestability.Twokeyvegetation-dependentparametersareincorporatedinthefiniteelementslopestabilityanalysis,namely,apparentrootcohesion(cR)anddepthofrootzone(hR).Parametricstudieswereperformedtoassessthesensitivityofthestabilityoftheslopetothevariationinthekeyvegetationandsoilparameters.PREVIOUSANALYSESOFTHEEFFECTSOFVEGETATIONONSLOPESTABILITYModelofRootReinforcementForthepastthreedecades,researchhasfocusedonutilizingplantrootreinforcementtostabilizeslopes.Theabilityofplantrootstostrengthenasoilmassiswellknown.Theinclusionofplantrootswithhightensilestrengthincreasestheconfiningstressinthesoilmassbyitscloselyspacedrootmatrixsystem.Thesoilmassisboundtogetherbytheplantrootsandtheshearstrengthisincreasedbythiseffect.Thecontributionofrootreinforcementtoshearstrengthisconsideredtohavethecharacteristicsofcohesion(Wuetal.,1979).Wuetal.(1979)proposedasimplifiedperpendicularrootmodeltoquantifytheincreasedshearstrengthofsoilduetorootreinforcement.Theincreaseinshearstrengthofthesoil,Sr,wasexpressedbythefollowingrelationship:Sr=tR(cosθtanφ′+sinθ)(1)whereSr=shearstrengthincreasefromrootreinforcement,tR=averagetensilestrengthofrootperunitareaofsoil,θ=angleofshearrotation,andφ′=frictionangle.Sincethemechanicaleffectofplantrootsistoincreasethecohesivenessofthesoilmass,Srcanbeconsideredasequivalenttoanapparentcohesionofthesoil,knownasapparentrootcohesion(cR).Typicalvaluesofapparentrootcohesion(cR)rangefrom1kPato17.5kPa(CoppinandRichards,1990).Thesevalueswereobtainedfromthestudiesofseveralinvestigatorsusingdifferenttechniquesincludingbackanalysis,directsheartests,rootdensityinformationcombinedwithverticalrootmodelequations,andbackanalysiscombinedwithrootdensityinformation.Thevaluesofapparentrootcohesion(cR)aredependentonthetypeofvegetationandin-situsoilconditions.PreviousSlopeStabilityAnalysesWuetal.(1979)incorporatedtheeffectsofvegetationinslopestabilityanalysisbyusingconventionallimitequilibriummethod.Inlimitequilibriummethods,theshearstrengthofthesoilalongapotentialslipsurfaceisassumedtobefullymobilizedatthepointoffailure.TheMohr-Coulombequationisusedtodescribetheshearstrengthofthesoil:τ=c′+(σ-u)tanφ′(2)Byincorporatingtheeffectofrootreinforcement,Equation(2)becomes:τ=(c′+cR)+(σ-u)tanφ′(3)Wuetal.(1979)incorporatedtheapparentrootcohesion(cR)intheirinfiniteslopeanalysisandfoundanincreaseinthefactorofsafety(FOS)forsomeslopes.Theresultsindicatedthattreerootsimprovedthestabilityofforestedslopes.Therehavebeennopublishedstudiesusingnumericalformulationstoanalyzerootreinforcementeffects.Thepresentstudyemploysnumericalanalysiswhichallowslimitingtheextentoftherootzone.Byassigningdifferentvaluesofapparentrootcohesion(cR)totherootzone,itssignificanceontheFOSisevaluated.DESCRIPTIONOFNUMERICALSTUDYUSEDTOMODELVEGETATIONEFFECTSInthepresentstudy,theeffectofvegetationonthestabilityofslopeshasbeeninvestigatedusingthefiniteelementmethod.Thediscretisationprocessofthefiniteelementmethodbreaksdowntheslopegeometryintosmallelementsandthisfacilitatestheincorporationoftheeffectsofvegetationintheslopestabilityanalysis.Theeffectsofvegetationaretakenintoaccountintheslopestabilityanalysisbymodifyingthesoilpropertiesoftheindividualsoilelementthatisaffectedbyvegetation.Forexample,thesoilelementsinthetoplayeroftheslopecanhaveahighercohesionvalueduetotheadditionalapparentcohesionfromrootreinforcement.Variationofsoilsuctioncausedbyvegetationcanalsobeincorporatedinthefiniteelementanalysis.Theflexibilityinlocatingthevegetation-affectedelementsmeansthatthevariableandrandomnatureofvegetationcanbemodeledeffectively.Inthispaper,theworkislimitedtotheeffectsofrootreinforcementonthestabilityofslopes.TheFiniteElementModelThefiniteelementmodelinthepresentstudyassumes2-dimensionalplanestrainconditions.TheprogramusedinthisstudywasdevelopedbySmithandGriffiths(1998)andituseseight-noddedquadrilateralelements.Anelasto-plasticmodelwithMohr-Coulombfailurecriterionisassumed.Thisprogramhasbeenusedtoanalyzeseveralslopestabilityproblemsincludingtheinfluenceoflayeringandfreesurfaceonslopeanddamstability(GriffithsandLane,1999).Theprogramcomputesthefactorofsafety(FOS)oftheslopebyusingthenonconvergencesolution,coupledwithasuddenincreaseinnodaldisplacementsasanindicationoffailureconditions(GriffithsandLane,1999).Inthisstudy,a2:1homogenousslope(26.57°)withaheightof10metresisusedtoinvestigatetheeffectsofvegetationonthestabilityofaslope,asshowninFigure1.Thesoilpropertiesareasfollows:φ′=25°c′=0γ=20kN/m3Twoadditionalvegetation-dependentparametersusedintheslopestabilityanalysisareapparentrootcohesion(cR)anddepthofrootzone(hR).Apparentrootcohesion(cR)istheapparentsoilcohesioncausedbytheplantrootmatrixsystem.Thedepthoftherootzone(hR)isdefinedastheeffectivedistancebeyondwhichplantrootscauselittleornoeffectsonthesoilshearstrength.Twoscenariosareconsidered:(1)vegetationconfinedtotheslopesurfaceonly;and(2)vegetationextendingovertheentiregroundsurface.Parametricstudiesareperformedtoassessthesensitivityofthestabilityoftheslopetothevariationinkeyvegetation-dependentparameters.Figure1.Meshfora2:1HomogenousSlopewithaSlopeAngleof26.57°,φ′=25°,c′=0.RESULTSOFANALYSESSlopewithoutVegetationEffects(c′=0,cR=0)Thestabilityofthe2:1homogenousslopewithoutvegetationwasanalysedusingboththefiniteelementmethodandthelimitequilibriummethod.ThelimitequilibriummethodwasperformedusingtheGGU-Stabilityprogram(Buß,1999)whereBishop’ssimplifiedmethodofsliceswasadopted.TheresultsoftheanalysesaresummarisedinTable1.Table1.FactorofSafetyfortheSlopeUsingDifferentMethods.METHODFOSFiniteElementMethod0.95LimitEquilibriumMethod0.93TheresultsinTable1showthatbothmethodsgivecomparableresults,althoughthelimitequilibriummethodgivesaslightlylowervaluecomparedtothefiniteelementmethod.Figure2showsthedeformedfiniteelementmeshoftheslopeatfailure,andthecorrespondingFOS=0.95.Itcanbeobservedthatthefailuremechanismisashallowplanarfailure.Thefailureoccurswithinthefirsttwolayersoftheelements,extendingto2metersbelowtheslopesurface.Figure2.DeformedMeshatFailurefortheSlopewithc′=0.SlopewithVegetationEffects(c′=0,cR=5kPa,hR=1m)Case1–VegetationConfinedtotheSlopeSurfaceOnlyThefirstcaseinvolvesascenariowherevegetationgrowsontheslopesurfaceonly.Thehorizontalgroundsurfaces,ontheslopeitselfaswellasbeyondtheslopetoe,arenotcoveredbyvegetation.Theeffectofrootreinforcementisconsideredbyusingapparentrootcohesion(cR)of5kPa.Thedepthofrootzone(hR)isconsideredtobe1metre.Accordingly,thezonemodelledwiththeadditionalrootstrengthisconfinedtothefirstlayerofthefiniteelementsbeneaththeslopesurface.Thus,thefirstlayerofelementsinthefiniteelementmodel,shownasshadedinFigure3,hasahighervalueofsoilcohesioncomparedtoallotherelementsinthefiniteelementmesh.TheslopestabilityanalysisgavearesultofFOS=0.97.ThedeformedmeshoftheslopeatfailureisshowninFigure3.Sincetheslopeisprotectedbyvegetationontheslopesurfaceonly,failurewas,inthiscase,initiatedfromtheslopetoe(elementT).Afailureslipsurfacethendevelopedalongthesoillayerbeneaththerootzone,asthissoillayeristhetopoftheweakzoneintheslopeafterintroducingarootzone.AlthoughtheincrementintheFOSissmall,itcanbenotedfromFigure3thatthecriticalslipsurfacehasbeenshifteddeeperbelowthegroundsurface,beinglocatedbetweenthesecondandthirdlayersofthefiniteelements.Theshallowplanarfailureattheslopesurfaceisnolongercritical,becauseofthepresentoftherootzone.Whentheslopetoeelement(elementTinFigure3)istreatedasavegetatedsoilelement(assignedhigherapparentcohesion),theFOSfortheslopeincreasesto1.02.Thisshowsthattoefailureisthecriticalfailuremechanismforthecasewherevegetationisconfinedtotheslopesurfaceonly.TheincreaseintheFOSisnotsignificantiftheslopetoeisnotvegetated.Therefore,theextentoftherootzonetotheslopetoeregionisanimportantfactortobeconsideredwhenvegetationisusedtoimprovethestabilityofaslope.Figure3.DeformedMeshatFailurefortheSlopewithVegetationonSlopeSurfaceOnly(c′=0,cR=5kPa,hR=1m).Case2–VegetationExtendingOvertheEntireGroundSurfaceAmorecommonscenarioinnaturalslopesisthecasewherevegetationgrowseverywhereonthegroundsurface,whichextendsfromtheuppersloperegiontotheslopetoe.Similarly,anapparentrootcohesionof5kPaanddepthofrootzoneof1metrewereadopted.Inthiscase,therootreinforcementeffectextendseverywhereonthegroundsurfaceinthefiniteelementmodel,asshowninFigure4.ThefiniteelementanalysisyieldedaFOS=1.03,showingasignificantincreaseduetothepresenceoftherootzonelocatedeverywhereonthegroundsurface.Theslopethatwasinitiallyunsafe(FOS=0.95)isnowmarginallysafe(FOS>1)duetotherootreinforcementeffects.ThedeformedmeshoftheslopeisshowninFigure4.Itisnotedthatthecriticalslipsurfaceisnolongerplanarbutiscircular.Figure4.DeformedMeshfortheSlopewithVegetationExtendingOvertheEntireGroundSurface(c′=0,cR=5kPa,hR=1m).Theaboveexampleshaveshownthatrootreinforcementcanimprovethestabilityofaslope.Byincorporatingtheapparentrootcohesionintherootzoneoftheslope,theFOSoftheslopeisincreased.Thecontributionofrootreinforcementtothestabilityofslopeissignificant.Referringtothe2:1homogenousslopeintheaboveexamples,thisslopewouldbeunstableiftheeffectofvegetationisnottakenintoaccount.Inreality,therearemanyslopesthatwouldfail,basedonthestabilityanalysisusingthefieldorlaboratorysoildata,butremainintactforalongperiodoftime.AcaseinpointistheThredbolandslide(Hand,2000).Thepresenceofvegetationonsuchslopesisclearlyoneofthemajorcontributionstothestabilityoftheseslopes.PARAMETRICSTUDIESParametricstudieswereperformedforarangeofthevegetationandsoilparameters.Theapparentrootcohesion(cR)wasvariedoverthefollowingrange:0≤cR≤20kPa(4) Threevaluesofdepthofrootzone(hR)wereused,namely:hR∈{1m,2m,3m}(5)Forthesoilproperties,onlytheeffectivecohesion(c′)wasvaried.Thevaluesofeffectivecohesion(c′)consideredwereasfollows:c′∈{1kPa,2kPa,3kPa,4kPa,5kPa}(6)TheresultsoftheparametricstudiesaresummarisedinFigure5to7.Figure5showsthevariationofthevaluesofFOSwiththeapparentrootcohesion(cR)wherec′=0andvegetationisconfinedtotheslopesurfaceonly.Twosetsofresultsarepresentedinthisfigure.Thebrokenlinesrepresenttheresultsforthecasewherevegetationisconfinedtotheslopesurfaceonly,withoutextendingtotheslopetoe.Thesolidlinesaretheresultsforthecasewheretheslopetoeelement(elementTinFigure3)isassumedtobeaffectedbyvegetation.Generally,thevaluesofFOSincreasewhenapparentrootcohesion(cR)increases.Forthecasewheretheslopetoeisnotprotectedbyvegetation,theFOSincreasesslightlyinitially,butdropstoalowervalueafterreachingamaximumvalueofFOS.TheFOSremainsconstantregardlessofanyincreaseintheapparentrootcohesion.Foracohesionlesssoilslope(c’=0),thefailuremechanismisashallowplanarfailure.Thisfailuremechanismispreventedwhenplantrootsarepresent.Astheapparentrootcohesionincreases,thecriticalslipsurfaceshiftsdeeperbelowthegroundsurface.Whenthecriticalslipsurfaceisbeyondtheextentoftherootzone,anyincreasesinapparentrootcohesiondonotleadtoanincreaseinFOSfortheslope.Sincetheslopetoeisnotprotectedbyvegetation,thisregionistheweakzone,andastheapparentrootcohesionintherootzoneincreases,failureisinitiatedfromthisregion.Thiseventuallytriggersfailureduetoadifferentmechanism–toefailure.Whentheslopetoeisprotectedbyvegetation,theFOSincreasesastheapparentrootcohesionincreases.Therefore,theslopetoeappearstobethemostcriticalregionwherevegetationneedstobeconsideredinslopestabilisation.Thus,inordertoensureimprovedstabilityofaslopeusingvegetation,therootzoneneedstoextendbeyondthetoeregion.Figure5.VariationofFOSfortheCasewhereVegetationisConfinedtotheSlopeSurfaceOnly(c′=0).Figure6showsthevariationofthevaluesofFOSwiththerootcohesion(cR)wherec′=0andvegetationextendsentirelyoverthegroundsurface,includingtheupperslope,slopesurfaceandslopetoe.TheFOSincreasesastheapparentrootcohesion(cR)increases.Itisnotedthat,whentheentireslopeisprotectedbyvegetation,theeffectsonFOSaresignificant.Forexample,whenhR=1mtheFOSisincreasedby26%forcR=20kPa.Theincreaseisevenmoresignificantwithadeeperrootzone(higherhR),asshowninFigure6.Figure6.VariationofFOSfortheCasewithVegetationExtendingOvertheEntireGroundSurface(c′=0).Figure7showsthevariationoftheFOSwiththedimensionlessparametercR/c′forthecasewheretheeffectivecohesionofthesoilc′∈{1kPa,2kPa,3kPa,4kPa,5kPa}.TheanalyseswereperformedforthecasewherevegetationextendseverywhereonthegroundsurfaceandhR=1m.TheanalysiswasterminatedatcR=20kPaforeachvalueofc′.ItisworthwhiletonotethattheincreaseintheFOSismoresignificantforaslopewithaloweffectivecohesion(c′=1kPa)comparedwithaslopewithahigheffectivecohesion(c′=5kPa).Examinationofthedeformedmeshesshowedthat,inthecaseofslopeswithhighervaluesofeffectivecohesion(c′),failureoccurredalongadeep-seatedrotationalslipsurface.Thisimpliesthatvegetationhaslessofaneffectondeep-seatedfailureswhenthedepthofrootzone(hR)isshallow.Figure7.VariationofFOSfortheCasewithVegetationExtendingOvertheEntireGroundSurface(c>0,hR=1m).FUTUREWORKByincorporatingtheeffectsofrootreinforcementinslopestabilityanalysis,significantinfluenceonthestabilityofslopeshasbeenobserved.Tomodelanaturalslopemoreaccurately,theinfluenceofsoilsuctionandsoilvariabilityshouldbetakenintoaccount.Thisworkwillbecarriedoutinthisongoingresearchproject,inparticular,toincorporatevariabilityofthevegetationandsoilpropertieswithinthefiniteelementframework.SUMMARYANDCONCLUSIONS Vegetationplaysanimportantroleinthestabilityofslopes.Rootreinforcementhasbeenconsideredasanincreaseinapparentsoilcohesion.Theapparentrootcohesion(cR)hasbeenincorporatedintheslopestabilityanalysisusingthefiniteelementmethod.Theextentofthevegetationeffectshasbeencharacterisedbythedepthofrootzone(hR).Thestabilityofaslopeissensitivetoboththeapparentrootcohesion(cR)anddepthofrootzone(hR).ThestabilityofslopesisimprovedwithanincreaseinthevaluesofcRandhR.Inaddition,resultsshowedthattheimprovementinFOSforaslopewithvegetationcoverovertheentiregroundsurfaceishighercomparedwithvegetationcoverontheslopesurfacealone.Thestudyhasalsoshownthattheeffectsofvegetationaremoresignificantinslopeswithlowvaluesofeffectivecohesionwhereshallowplanarfailuresarelikelytooccur.Correspondingly,vegetationhaslessofaneffectondeep-seatedfailure.植被模型对边坡稳定性的影响摘要：据了解，植被在两个方面影响边坡稳定：水文效应和机械效应。水文效应包括通过植被土壤水分蒸散，从而导致土壤吸力的增加或者孔隙水压力的减少，因此，增加了土的抗剪强度。通过植物的根矩阵系统的力学效应，也增加了土壤的抗剪强度。在土体内根密度和根抗拉强度也有助于增加土壤的抵抗剪切能力。土壤吸力和根钢筋的影响在表现土壤凝聚力方面已经量化。本文利用有限元法分析植被在斜坡稳定性方面的影响。两个关键的植被参数已被纳入有限元边坡稳定分析中，即明显的根凝聚力（CR）和根区的深度（hR）。对由植被和土壤参数变化引起斜坡稳定性的灵敏性进行了参数研究评价，结果表明，植被在斜坡浅层失稳中起着重要作用，并且显著影响其稳定性。引言边坡失稳灾害时岩土工程中的主要问题之一，它的发生也会造成生命和财产的损失。这些失稳的边坡大多数是植被或森林覆盖的天然斜坡。天然斜坡和与河堤或者人工斜坡是不同的，植被和土壤变异在它们的稳定性方面起着重要作用。植被对斜坡稳定性的影响是众所周知的。植被通过改变土壤水分构成的改变来影响斜坡的稳定性，这反过来又导致土壤吸力或空隙压力的变化。植被也可以通过根加固来提高斜坡的稳定性。Wuetal.(1979)对移除植被前后斜坡的稳定性进行调查，得出结论，树根提供的抗剪强度对斜坡的稳定性是至关重要的。研究表明，植被可以通过根钢筋提高坡体的抗剪强度。Wuetal.(1979)表示，如果在边坡稳定性分析中不考虑植被的影响，边坡则可能发生失稳。天然斜坡受制于土壤和植被固有的变异性。这就使得天然斜坡的底层土壤坡面不能完全一致或者同质。即使是在一个相同土质的土层，土壤的性质从点到点也是变化的（Vanmarcke，1977年）。植被的生长对环境状况和变化非常敏感。通常不同类型的植被生长于一种天然的斜坡上，如牧草，药材，灌木和树木等。这些不同植物的大小和物理性的不同都会导致对斜坡稳定有不同的影响。因此使用单一为分析植被参数的输入值最好看作是原始条件下的近似值。本文利用有限元方法对植被影响斜坡稳定性进行调查。有限元法允许用户将斜坡几何分成小分子的方法来确定植被对斜坡稳定性影响的程度。由于本文篇幅的限制，本文只将根钢筋的影响纳入边坡稳定分析，不考虑植被和土壤性质的变化。2:1同质坡（倾角26.57°角）用于研究植被对边坡稳定性的影响。两个关键的植被参数被纳入有限元边坡稳定性分析，即明显的根凝聚力（CR）和根区的深度（hR）。同时对由植被和土壤参数变化引起斜坡稳定性的灵敏性进行了参数研究评价。植被对边坡稳定性影响的前期分析根筋模型在过去的三十年中，研究集中在利用植物根系加固稳定斜坡。植物根系的能力来加强土壤稳固是众所周知的。有高抗拉强度的植物根系能利用其密集的根矩阵系统来提高土体的强度。土体质量与植物根系是紧密联系在一起的，土体抗剪强度就是利用这种影响增加的。根钢筋对抗剪强度的贡献被认为是有凝聚力的特点Wuetal.(1979)。Wuetal.(1979)提出一个由于根加固土作用使土体抗剪强度增加的简化的量化模型。土体的抗剪强度的增加由以下关系表示：Sr=tR(cosθtanφ′+sinθ)(1)其中SR=由根钢筋的加固引起的土体的剪切强度的增加值，tR=平均单位面积土壤根抗拉强度，θ=剪切旋转的角度，φ'=摩擦角。由于植物根系的力学效应可以提高土体的凝聚力，Sr，可视为相当于土壤的凝聚力明显，被称为表观根凝聚力（CR）。表观根凝聚力（CR）范围典型值，从1kPa到17.5kPa（Coppin和Richards，1990）。这些值的获得是根据几个学者利用不同方法的研究，这些研究方法包括反分析、直接剪切试验、结合垂直根模型方程的根密度信息、结合根密度信息的反分析调查研究。表观根凝聚力（CR）的值依赖于植被类型和原始土壤条件的。前期边坡稳定性分析Wuetal.(1979)通过使用传统的极限平衡法分析植被对边坡稳定性的影响。沿着潜在滑动面的土壤抗剪强度极限平衡法，假设失稳点得到充分调动。用来描述土壤抗剪强度的Mohr-Coulomb方程：τ=c′+(σ-u)tanφ′(2)纳入根钢筋加强作用的影响，（2）式变为：τ=(c′+CR)+(σ-u)tanφ′(3)Wuetal.(1979)在他们的无限边坡分析纳入表观根凝聚力（CR），并发现一些斜坡安全系数（FOS）有所增加。结果表明，树根能改善有森林覆盖的斜坡的稳定性。现在还没有发表的利用数值方程分析根加固效果的研究论文。本研究采用数值分析，允许限制根区的程度。通过对根区赋予不同的表观根凝聚力（CR）值，评价其对斜坡安全系数（FOS）的重要意义。模型植被影响的数值研究的说明在本研究中，采用有限元法已展开对植被对斜坡稳定性的影响的调查。有限元方法的离散化过程将边坡几何分解成多个小分子，这有利于在边坡稳定性中分析植被的影响。在边坡稳定性分析中植被的影响是通过修改个别土壤元素的性质来发挥作用的。例如，在顶层的斜坡土壤元素可以有较高的凝聚力由于加上额外的根钢筋的表观根凝聚力（CR）值。植被造成土壤吸力的变化也可以纳入有限元分析。定位植被影响因素的灵活性意味着可以有效地进行建模的变量和随机的自然植被的选取。本文主要是阐述有限的根钢筋加强作用对斜坡稳定性的影响。有限元模型在本研究中的有限元模型假定2维平面应变条件。在这项研究中所使用的程序是由史密斯和格里菲斯（1998）提出的，它使用八面的四边形单元，与莫尔-库仑破坏准则的弹塑性模型假设是一致的。这项计划已被用来分析几个边坡稳定性问题，包括分层的影响和对边坡和大坝稳定的自由表面的影响（Griffiths和Lane，1999年）。程序计算使用的不收敛的解决方案，再加上作为指示故障情况（Griffiths和Lane，1999年）在节点位移突然增加（FOS）的斜坡安全的因素。在这项研究中，2:1同质边坡高度为10米（26.57°），用于研究植被对边坡稳定性的影响，如在图1所示。土壤性质如下：φ′=25°c′=0γ=20kN/m3两个额外的植被在边坡稳定性分析中使用的参数是明显的根凝聚力（CR）和根区的深度（hR）。明显的根凝聚力（CR）是由植物的根矩阵系统造成的土壤表观凝聚力。根区的深度（hR）定义为植物根系造成土的抗剪强度很少或根本没有影响的有效距离之外。考虑有两种情况：（1）植被局限于坡面;（2）整个地面植被延长。参数研究表明边坡稳定关键取决于对植被参数变化的敏感性。 图1网为2:1均质边坡的边坡角26.57°，φ=25°，C'=0结果分析边坡没有植被的影响（c′=0，CR=0）同时利用有限元法和极限平衡法对2:1均匀无植被边坡稳定性进行了分析。极限平衡法使用GGU稳定程序（巴斯，1999年）主教的简化方法进行。分析结果列于表1。表1。使用不同的方法边坡的安全系数。方法FOS有限元法0.95极限平衡法0.93这两种方法提供了类似的结果，尽管极限平衡法给的值比有限元法略小。图2显示了失稳的的斜坡变形有限元网格，相应的FOS=0.95。它可以观察到失稳的机制，是一湾浅浅的平面失稳。问题发生在第一层，延伸到2米以下的坡面。图2C’=0边坡失稳的变形网格边坡植被的影