Wick-drain

GEO-SLOPEInternationalLtd,Calgary,Alberta,Canada:Wickdrain.doc(pdf)(gsz)Page1of9WickDrain1IntroductionThisexampleisaboutmodelingthebehaviorofawickdrain.Theprimarypurposehereistoillustratehowinterfaceelementscanconvenientlybeusedtoincludetheeffectsofawickdrain,andtodiscusssomeoftheanalysisissuesrelevanttowickdrains.2ConfigurationandsetupForillustrativepurposeshere,onlyonewickdraincellisanalyzed,asshowninFigure1.Thedrainspacingis4mandthedrainlengthis6m.Theexcesspore-pressureisinducedbyasurfacepressureequalto100kPa.Distance-m-0.50.00.51.01.52.02.53.03.54.04.55.0Elevation-m-0.50.00.51.01.52.02.53.03.54.04.55.05.56.06.57.07.58.08.59.09.510.0Figure1ConfigurationofwickdraincellThistypeofstudyrequiresafullycoupledtypeofanalysis,whichinessencemeansitisnecessarytospecifyalltheusualSIGMA/WmaterialpropertiesandboundaryconditionsaswellasalltheSEEP/Wones,suchashydraulicmaterialpropertiesandboundaryconditions.2.1Stress-deformationpropertiesThesoilistreatedasaLinear-Elasticmaterialwitheffectivesstressparameters.TheE-modulusis5000kPaandν=0.334(1/3).GEO-SLOPEInternationalLtd,Calgary,Alberta,Canada:Wickdrain.doc(pdf)(gsz)Page2of9Thesurfacepressureisappliedwiththestep-functioninFigure2.Thefirsttimestep(Δt)is1day.Theincrementchangeinpressurefromt=0tot=1is100.Forallothertimesteps,theincrementalchangeiszero.Physically,theloadcanonlybeappliedonce.Usingtheboundaryfunctionachievesthis.SurfacepressureNormalBoundaryStress(kPa)Time(day)020406080100012345Figure2Boundaryfunction.Fromastructuralpointofview,thedrainsoilisassignedthesamepropertiesasthesurroundingclay,inferringthatthedrainitselfhasnoeffectonthecompressionbehaviorofthesoil.2.2HydraulicpropertiesThesoilanddrainwillatalltimesremainsaturatedandbeunderpositivepore-pressures.ThismeansthattheVolumetricWaterContentfunctionandhydraulicconductivityfunctionareactuallyonlyrequiredforpositivepore-pressureconditions.ThismeansthatonlymvandKsatarerequired.Foracoupledanalysis,functionsarenonethelessrequired,eveniftheyaresimpleestimates.Figure3showstheVolumetricWaterContentfunctionusedforboththeclayandthedrain.ClayVol.WaterContent(m³/m³)MatricSuction(kPa)0.10.20.30.40.5110ClayVol.WaterContent(m³/m³)Pore-WaterPressure(kPa)0.10.20.30.40.5-2-3-4-5-6-7-8-9-10-1Figure3VolumetricWaterContentfunctionThesoilwillbesaturatedatalltimes,sotheconductivityKcanbespecifiedbyafunctionliketheoneinFigure4.ThismeansKisinessenceaconstant,ornotafunctionofthepore-pressureasforunsaturatedconditions.Kisequalto1x10-4m/day.GEO-SLOPEInternationalLtd,Calgary,Alberta,Canada:Wickdrain.doc(pdf)(gsz)Page3of9ClayKX-Conductivity(m/day)MatricSuction(kPa)0.000010.0010.0001110Figure4HydraulicconductivityfunctionfortheclayTheconductivityofthedraincanalsobespecifiedbyaK-functiontogetherwithananisotropyratio.ThesameK-functionusedfortheclayisusedforthetransverseconductivityofthedrain.AconductivityfunctioninGeoStudiodefinestheconductivityinthex-directionorthex΄-direction.Theconductivityintheorthogonaldirection(yinthiscase)isthex-conductivitytimesthespecifiedratio.Thespecifiedratiois1000.Thismeansthattheconductivityinthelongitudinaldirectionis1000x1e-4=0.1m/day;thatis,Klis1000timesgreaterthanKt.Thehydraulicboundaryconditiononthegroundsurfaceissettozeropressure,inferringthatthewatertableisatthegroundsurfaceandanywateroutflowwillnotchangethepositionofthewatertable.3InitialgroundconditionsTheinitialinsitugroundconditionsareignoredinthisanalysis,sinceonlytheexcesspore-pressuresareofinterest,andsinceweareusingLinear-Elasticproperties.IfweweretouseanElastic-PlasticorCam-Clayeffectivestressmodel,thenwe’dhavetoalsodealwiththeinitialinsituconditions.4Results4.1PressuresinthedrainFigure5showsthepressuredistributioninthedrainwithtime.Initiallythereissomeexcesspressureinthedrain,butthenitdissipatesandeventuallybecomeshydrostatic.Thefactthatthepressureisnothydrostaticimmediatelymeansthedrainisofferingsomeresistancetoflowintheverticalorlongitudinaldirection.Aneasyandconvenientwayofmodelingaperfectlyfree-flowingdrainistodefineaHead-typeboundaryconditionalongthecenterofthedrain.Inthiscase,aboundaryconditionofH=10mwouldensurethatthepressureinthedrainishydrostaticatalltimes.GEO-SLOPEInternationalLtd,Calgary,Alberta,Canada:Wickdrain.doc(pdf)(gsz)Page4of9DrainpressureY(m)Pore-WaterPressure(kPa)45678910020406080100120Figure5Pressuredistributionsinthedrain4.2PressuredistributionThefollowingdiagramsshowthepore-pressuredistributionsatDay1andatDay6.41618121416181Figure6Pore-pressuredistributionsonDay1andDay6Anotherwayofinspectingthechangesistolookatasectionacrossthecell.Figure6showsthechangeswithtimealongacrosssectionatElevation7m.GEO-SLOPEInternationalLtd,Calgary,Alberta,Canada:Wickdrain.doc(pdf)(gsz)Page5of9Pressureat7mExcessPWP(kPa)X(m)02040608010001234Figure7PressurechangesatEl.7m5EquivalentplanestrainWickdrainsareusuallyonlyabout100mmwideandareinstalledonasquareortriangularpattern.Th