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1、AnalysisofReinforcedandUn-reinforcedSoilSlopesusingAbaqus3OverburdenpressuremodelAnun-reinforcedsoi1slopeinclinedat79degreesandwithverticalheightof25misconsidered.Thehorizontaldistancebetweenthetopandthebottomoftheslopeis5in.Thesoi1isconsideredtobedry,andthesoildensityis1800kgm3.linearDrucker-Prager
2、plasticitymodelisemployedwithfrictionanddiIationanglesof30degrees.Materialcohesionis100kPa.Damageinitiatesinthesoi1atanequivalentfracturestrainof0.01atastresstriaxial-ityof0.01.DamageisconsideredtoevolvethroughadiSplaceinent-baseddamageevolutioncriterion.Themodelissubjectedtogravitationalforces.Addi
3、tion-ally,thetopportionoftheslopedsoi1massisloadedbyanoverburdenpressureloadof1MBadistributedoverarectangularpatchasshowninFigure3.AnalysisThereinforcedsoilanalysisisperformedusingAbaqusZStandardthroughaseriesofsteps.Inthefirststepgeostaticequilibriumisobtainedbyapplyingthegravityload.Inthesecondste
4、ptheregionoverlayingthetopoftheslope(theyellowregioninFigure1)isremovedsothatagroundslopeof10degreesisobtained.Inthethirdstepasecondexcavationisperformedandthere-giondepictedingreeninFigure1isremoved.The55-degreeslopeisthenexposed.Thereinforcingnailsinanailedsoilslopecontributetosoi1stabilityonlyaft
5、erthesurroundingsoilhasfailedandappreciablydisplaced,whichresultsinthegenerationoftensileforcesinthenails.Inorderforthenailstosignifi-cantlycontributetowardsresistingthefailureofthesoilwithoutanyassociatedappreciabledisplacementinthesoil,thenaiIsneedtobepre-stressed.Intheseanalysesatensilepre-stress
6、isappliedtothereinforcingnails.sthesoi1materialpropertiesarenottemperaturede-pendent,thepre-stressisinducedinthenailsthroughtheuseofthermalcontractions.Amaximumtensileforceof4MNisassumedineachnai1whenthedisplacementsattheirendsarerestricted.Abaqus/Explicithasbeenusedtoanalyzethemodelin-voIvingthefai
7、lureofaslopeduetogravityandoverbur-denpressure.Thisanalysisisrunintwosteps.Inthefirststepthegravityloadisappliedthroughasmoothstepamplitudedefinition.Theoverburdenpressureisappliedinthesecondstep.sthepressureloadisapplied,thesoilmaterialintheinterioroftheslopedomainfailsinshear,andisconsideredtobeda
8、maged.ThedamagedelementsareautomaticalIydeleted;acontactinteractionzoneisnew1ycreatedbetweenthedislodgedsoilandtheintactsoilregions,andtheanalysisprogressesfurther.ResultsFigures4,5,and6showthedeformedconfigurationsduringtheexcavationoftheslopeanalyzedusingFigure3:Abaqus/Explicitslopefailureanalysis
9、model.baqusStandard.InFigure4,themodelisshownattheendofthefirststep.Figure5showsthedeformedcon-figurationafterthesecondstep,thatis,aftertheremovalofthesoi1intheyellowcoloredregion.Figure6showsthefinaldeformedconfigurationofthesoilmass,thatis,aftertheremovalofthesoi1inthegreencoloredregion.Figure4:Th
10、efiniteelementmeshattheendofthegcostaticstepandshowingthethreesoi1regionsFigure5:DeformedsoilmeshafterthefirstexcavationFigure6:Deformedsoi1meshafterthesecondexcavation,exposingthe55-degreeslope4Astheoverlayingsoilisremoved,theunderlyingsoildis-placesverticallyupwardsduetotheremovaloftheasso-ciatedw
11、eightoftheoverlay.InFigure7,thedisplacc-mcntsattheendofthethirdstep,relativetothoseattheendofthesecondstep,areshowninasymbolplot.Thearrowsindicatethemagnitudeanddirectionofthedis-placements.Theverticaldisplacementsattheleftmostregionofthelowerflatportionofthesoi1arelargerthanthosealongtheinclinedreg
12、ionduetoalargerreductionintheoverburdenweight.Slopefailurescanoccurwhencontiguousregionsofthesoilmassyieldsimultaneouslyinshear.Theequivalentplasticstrainmeasureavailableasanoutputvariable(PEEQ)inbaquscanbeusedtoassesstheaccumula-tionofplasticstraininthesoi1region.Figures8,9,10,and11showcontoursofth
13、eequivalentplasticstrainfortheun-reinforcedand,one,three,andsevennailcases,respectively.Itisseenthatasthenumberofnailsin-creases,thesizeoftheregionoverwhichtheequivalentplasticstrainislargedecreases.Figure7:Deformedsoi1meshafterthesecondexcavationFigure8:Equivalentplasticstrainfortheun-reinforcedslo
14、peFigure9:Equivalentplasticstrainfortheonenai1caseFigure10:EquivalentplasticstrainforthethreenailcaseFigure11:Equivalentplasticstrainforthesevennai1caseFortheun-reinforcedcase,continuousbandsofhighequivalentplasticstrainextendtoabouthalftheslopeheight.Suchlargebandsareexpected,astheslopeconfiguratio
15、nisjuststable.However,withincreasingnumberofreinforcingnailstheextentofthesebandsreduces,andforthecasewithsevennailsnosuchcontigu-ousbandsareseen,indicatingamuchhigherdegreeofstability.Thepropensityforinstabilityataparticularpointinasoi1masscanalsobeassessedbyexaminingtheproximityofthedeviatoricorsh
16、earstressvaluesatthatpointtothemaximumshearstrengththatcanbegeneratedatthatpoint,whichinturndependsonthepressureexistingatthatpoint.Inordertoexpressthispropensityquantita-lively,weconsidertherat100ftheMisesstressatthatpointtothemaximumMisesstressthatcanbegeneratedattheexistingpressure.Pythonscriptha
17、sbeenwrittentoobtainvaluesofsuchratios,whichwetermastheDPYieldFactorsatthesoilmaterialpoints.TheDPYieldFactorwillbe1whenthematerialpointundergoesyield-ing,andiszerowhentheMisesstressiszero.Figures12,13,14,and15depictcontourplotsoftheDPYieldFactorfortheun-reinforcedand,one,three,andsevennai1cases,respectively,attheendoftheanalyses.Whenthesoi1massisun-reinforced,theDPYieldFactoriscloseto1overalargerportionoftheinteriorregion.However,inthepresenceofanincreasingnumberofreinforcingnailstheextentoftheinteriorregionexperi-encingahighDPYieldFactorgetsreduced,indicating
