Analysis of Reinforced and Un-reinforced Soil Slopes using Abaqus_0.docx

AnalysisofReinforcedandUn-reinforcedSoilSlopesusingAbaqus3OverburdenpressuremodelAnun-reinforcedsoi1slopeinclinedat79degreesandwithverticalheightof25misconsidered.Thehorizontaldistancebetweenthetopandthebottomoftheslopeis5in.Thesoi1isconsideredtobedry,andthesoildensityis1800kgm3.linearDrucker-PragerplasticitymodelisemployedwithfrictionanddiIationanglesof30degrees.Materialcohesionis100kPa.Damageinitiatesinthesoi1atanequivalentfracturestrainof0.01atastresstriaxial-ityof0.01.DamageisconsideredtoevolvethroughadiSplaceinent-baseddamageevolutioncriterion.Themodelissubjectedtogravitationalforces.Addition-ally,thetopportionoftheslopedsoi1massisloadedbyanoverburdenpressureloadof1MBadistributedoverarectangularpatchasshowninFigure3.AnalysisThereinforcedsoilanalysisisperformedusingAbaqusZStandardthroughaseriesofsteps.Inthefirststepgeostaticequilibriumisobtainedbyapplyingthegravityload.Inthesecondsteptheregionoverlayingthetopoftheslope(theyellowregioninFigure1)isremovedsothatagroundslopeof10degreesisobtained.Inthethirdstepasecondexcavationisperformedandthere-giondepictedingreeninFigure1isremoved.The55-degreeslopeisthenexposed.Thereinforcingnailsinanailedsoilslopecontributetosoi1stabilityonlyafterthesurroundingsoilhasfailedandappreciablydisplaced,whichresultsinthegenerationoftensileforcesinthenails.Inorderforthenailstosignifi-cantlycontributetowardsresistingthefailureofthesoilwithoutanyassociatedappreciabledisplacementinthesoil,thenaiIsneedtobepre-stressed.Intheseanalysesatensilepre-stressisappliedtothereinforcingnails.sthesoi1materialpropertiesarenottemperaturede-pendent,thepre-stressisinducedinthenailsthroughtheuseofthermalcontractions.Amaximumtensileforceof4MNisassumedineachnai1whenthedisplacementsattheirendsarerestricted.Abaqus/Explicithasbeenusedtoanalyzethemodelin-voIvingthefailureofaslopeduetogravityandoverbur-denpressure.Thisanalysisisrunintwosteps.Inthefirststepthegravityloadisappliedthroughasmoothstepamplitudedefinition.Theoverburdenpressureisappliedinthesecondstep.sthepressureloadisapplied,thesoilmaterialintheinterioroftheslopedomainfailsinshear,andisconsideredtobedamaged.ThedamagedelementsareautomaticalIydeleted;acontactinteractionzoneisnew1ycreatedbetweenthedislodgedsoilandtheintactsoilregions,andtheanalysisprogressesfurther.ResultsFigures4,5,and6showthedeformedconfigurationsduringtheexcavationoftheslopeanalyzedusingFigure3:Abaqus/Explicitslopefailureanalysismodel.baqusStandard.InFigure4,themodelisshownattheendofthefirststep.Figure5showsthedeformedcon-figurationafterthesecondstep,thatis,aftertheremovalofthesoi1intheyellowcoloredregion.Figure6showsthefinaldeformedconfigurationofthesoilmass,thatis,aftertheremovalofthesoi1inthegreencoloredregion.Figure4:Thefiniteelementmeshattheendofthegcostaticstepandshowingthethreesoi1regionsFigure5:DeformedsoilmeshafterthefirstexcavationFigure6:Deformedsoi1meshafterthesecondexcavation,exposingthe55-degreeslope4Astheoverlayingsoilisremoved,theunderlyingsoildis-placesverticallyupwardsduetotheremovaloftheasso-ciatedweightoftheoverlay.InFigure7,thedisplacc-mcntsattheendofthethirdstep,relativetothoseattheendofthesecondstep,areshowninasymbolplot.Thearrowsindicatethemagnitudeanddirectionofthedis-placements.Theverticaldisplacementsattheleftmostregionofthelowerflatportionofthesoi1arelargerthanthosealongtheinclinedregionduetoalargerreductionintheoverburdenweight.Slopefailurescanoccurwhencontiguousregionsofthesoilmassyieldsimultaneouslyinshear.Theequivalentplasticstrainmeasureavailableasanoutputvariable(PEEQ)inbaquscanbeusedtoassesstheaccumula-tionofplasticstraininthesoi1region.Figures8,9,10,and11showcontoursoftheequivalentplasticstrainfortheun-reinforcedand,one,three,andsevennailcases,respectively.Itisseenthatasthenumberofnailsin-creases,thesizeoftheregionoverwhichtheequivalentplasticstrainislargedecreases.Figure7:Deformedsoi1meshafterthesecondexcavationFigure8:Equivalentplasticstrainfortheun-reinforcedslopeFigure9:Equivalentplasticstrainfortheonenai1caseFigure10:EquivalentplasticstrainforthethreenailcaseFigure11:Equivalentplasticstrainforthesevennai1caseFortheun-reinforcedcase,continuousbandsofhighequivalentplasticstrainextendtoabouthalftheslopeheight.Suchlargebandsareexpected,astheslopeconfigurationisjuststable.However,withincreasingnumberofreinforcingnailstheextentofthesebandsreduces,andforthecasewithsevennailsnosuchcontigu-ousbandsareseen,indicatingamuchhigherdegreeofstability.Thepropensityforinstabilityataparticularpointinasoi1masscanalsobeassessedbyexaminingtheproximityofthedeviatoricorshearstressvaluesatthatpointtothemaximumshearstrengththatcanbegeneratedatthatpoint,whichinturndependsonthepressureexistingatthatpoint.Inordertoexpressthispropensityquantita-lively,weconsidertherat100ftheMisesstressatthatpointtothemaximumMisesstressthatcanbegeneratedattheexistingpressure.Pythonscripthasbeenwrittentoobtainvaluesofsuchratios,whichwetermastheDPYieldFactorsatthesoilmaterialpoints.TheDPYieldFactorwillbe1whenthematerialpointundergoesyield-ing,andiszerowhentheMisesstre