华科高等土力学consolidation

ConsolidationtheoryandanalysisFlowinasoilmassWaterheadandhydraulicgradientHereweonlyfocusonflowofwaterinsaturatedsoilFlowinasoilmassalsohastofollowthefundamentalprinciplesofFluidMechanicsFromFluidMechanics,itisknownthatthetotalheadataspecificpositioninaflowcanbedescribedbyBernoulli’sEquation:Velocity

headPressure

headElevation

headh=totalheadu=waterpressurevw=waterflowvelocityrw=unitweightofwaterg=accelerationduetogravityForwaterflowinasoilmass,thewatervelocityisusually

small,sothetermofvelocityheadcanbeneglected:ThisisalsothemeasurablewaterheadbypiezometersThelossofheadbetweenPointAandPointB:Thehydraulicgradient:Darcy’slawIn1856,inhisexperimentDarcy’sfoundthatthedischargevelocityofwaterflowthroughasaturatedsoilmassisproportionaltothehydraulicgradient:v=dischargevelocity,thequantityofwaterflowinginunittimethroughaunit

grosscross-sectionalareaofsoilatrightanglestothedirectionofflowk=hydraulicconductivity(or,coefficientofpermeability)Importantnote:thedischargevelocityisNOTtheactualvelocityvwofwaterin

thesoilpores.Itisbasedonthegrosscross-sectionalarea

ofthesoil.ItisSMALLERthantheactualvelocityvw.Areaofwater-filledporesAvAreaofsoilATheirrelationship?SoilpermeabilityThehydraulicconductivityofsaturatedsoilisaffectedbyTheintrinsiccharacteristicsofsoilThecharacteristicsofporewaterTheintrinsiccharacteristicsofsoilGrain-sizedistributionPore-sizedistributionVoidratioRoughnessofmineralparticlesSoilfabricandstructureSaturatedhydraulicconductivitykCleangravel(102~100cm/s)>Coursesand(100~10-2cm/s)>Finesand(10-2~10-3cm/s)>Siltyclay(10-3~10-5cm/s)>Clay(<10-5cm/s)ThecharacteristicsofporewaterViscosityUnitweightLaplace’sequationofcontinuityConsidera2-Dproblemofsteadyflow.AnRepresentativeVolume

Element(RVE)ofdv=dx*dz*1istakenfromthesoilmassThewaterflowintotheRVE:ThewaterflowoutoftheRVE:Sincewatercanbeassumedtobeincompressible,theconditionofcontinuity

statesthatHence:SoNow,thehydraulicgradients:AndSotheequationofcontinuitybecomesIfthesoilisisotropicwithrespecttopermeability,theLaplace’sequationofcontinuity

becomes:BecauseFundamentalsofconsolidationRecallthedefinitionofeffectivestressExternalloadappliedonasaturatedsoilstrataWhowouldcarrytheload?Theporewater,thesoilskeleton,orboth?Theportionofloadcarriedbytheporewaterisknownastheexcessporepressure

ueTheportioncarriedbythesoilskeletonistheincreaseintheeffectivestress

’Theincreaseinthesoilskeletonwillresultinthedecreaseofthesoilvolume,i.e,thedecreaseofthevoidratioTheporewaterwillbeexpulsedfromthesoilmass(watercanbeconsideredtobeincompressible)pTotalstress:z=pEx.porepress.:

u=z=pEffectivestress:z=0Spring-cylinderanalogymodelforsoilconsolidationTotalstress:σz=pEx.porepress.:

u<pEffectivestress:σz>0Spring-cylinderanalogymodelforsoilconsolidationTotalstress:σz=pEx.porepress.:

u=0Effectivestress:σz=pSpring-cylinderanalogymodelforsoilconsolidationImpervious

layerSaturated

cohesivesoilσz=pp0zH:u=pz=0:u=0z=H:uz

0zH:u=0zChangeofexcessporepressureuduringconsolidationImportantissuesinsoilconsolidationCoefficientofpermeability(“sizeofvalve”)CompressibilityofsoilskeletonTimeDistanceofdissipation(消散)GravelorsandLargecoefficientofpermeabilityExcessporepressurecanbedissipatedmomentarilyThedeformationcouldbeconsideredasimmediatedeformationClaySmallcoefficientofpermeabilityExcessporepressuredissipatesslowlySettlementincreasesgraduallyImmediatesettlementandconsolidationsettlementSilt?One-dimensionalcompressiontestOne-dimensionalcompressiontest(侧限压缩试验)andtime-deformationplotApparatus:Oedometer(一维固结仪)DialgageSpecimenPorousstoneRingTime-deformationplotInitialcompression(初始瞬时压缩)Primaryconsolidation(主固结)Secondaryconsolidation(次固结)CompressioncurveFromoedometertestSelectseveralpressurelevelsDeterminetheinitialvoidratioe0ofthesaturatedsoilspecimenStartingfromthesmallestpressure,readthedeformationH1whenit

stabilizes(endofprimaryconsolidation)Increasethepressurestepbystep,readthecorrespondingdeformation

HiCalculatethevoidratioeiateachpressurelevelCompressioncurve:eWhysmallerslope?Compressioncurveofanaturalsoilspecimenobtainedfromthefield(Logscale)(压缩指数)ExpansioncurveThesmallerslopeisduetothepre-consolidationpressureappliedonthe

onthesoilspecimeninitshistory!Ifunloadedduringcompressione’(log)dUnloadingandreloading:

expansioncurve(回弹指数)IsotropiccompressiontestApparatus:triaxialcompressiondeviceNoaxialloadisneededStressstateTime-deformationplotInitialcompression(初始瞬时压缩)Primaryconsolidation(主固结)Secondaryconsolidation(次固结)Compressioncurve:eCompressioncurveofanaturalsoilspecimenobtainedfromthefield(Logscale)Twopre-consolidationpressures1Dstressstate:Themaximumverticaleffectivestresseverexperiencedby

thesoilinitshistory!Hydrostaticstressstate:Themaximummeaneffectivestresseverexperiencedby

thesoilinitshistory!NormallyconsolidatedclayandoverconsolidatedclayNormallyconsolidated,theeffectivepressureisthemaximumpressureinthesoil’shistoryOverconsolidated,theeffectivepressureislessthanthatwhichthesoilexperiencedinthepast,i.e.,Theoverconsolidationratio(超固结比):Therearetwodefinitionsofoverconsolidationratio!Terzaghi’stheoryof1DconsolidationThebasicassumptionsoftheTerzaghiconsolidationtheoryThesoilishomogeneous;Thesoilisfullysaturated;Theporewaterisassumedtobeincompressible;Porewateronlyflowinthedirectionofcompression;Darcy’slawisvalid.Theseassumptionsaregenerallyvalidformostsoilsunderone-dimensional

consolidation.ConsiderasaturatedsoilelementTherateofwaterflowintotheelement:Therateofwaterflowoutofit:Thechangeinthewatervolumeintheelement,

whichisalsothechangeofthesoilvolume:V=volumeofthesoilelementvz=flowvelocityinzdirectionSo,NowaccordingtoDarcy’slawofflow,h=porewaterheadue=excessporewaterpressureK=coefficientofpermeabilityTerzaghi’s1-DconsolidationtheoryNowweknowthatWealsoknowthatthevolumeofthesolidparticlesofthesoilVsdoesnotchangeTherefore,Butthevoidvolumecanberelatedtothevolumeofthesoilsolidsandtheinitial

volumeofthesoilelementasHence,Finally,thepartialdifferentialequationbecomesThechangeofthevoidratiocanberelatedtothechangeintheeffectivestress

throughaparameter,namelycoefficientofcompressibilityofsoilav::thechangeintheeffectivestress,sincethetotalstress=constant,Thecoefficientofcompressibilityforasoilcanbeconsideredconstantfor

anarrowrangeofpressurechangeNowthepartialdifferentialequationbecomesmv:coefficientofvolumecompressibility=Or,cv:coefficientofconsolidation=Forthe1-Dconsolidationequation:IfThesolutionyieldsWedefinethedegreeofconsolidation(固结度)atadepthzasDegreeofconsolidationue=0zue=0dd(时间因数)FreedrainageseepagezFreeDrainagedTv=0Tv=0.05Tv=0.2Tv=0.7Tv=∞u0=pFreedrainageonjustoneside?dseepageTheaveragedegreeofconsolidationcanbeintegratedfromthedegreeof

consolidationateachpoint,forexample,fortheproblemaboveRelationshipbetweenUandthetimefactorTv:Summaryof1DconsolidationBasicequations:Stressstrainrelationship:Massbalanceoffluid:Darcy’slaw:Inessence:couplingofsoildeformationandseepage!ExampleQ:Whatisthedrivingforceof

settlement?A:Increaseofeffectivestress

duetowaterpumping.Q:Whatistheincreaseofeffective

stress?Thefinalsettlementoftheclaylayer:Theincreaseofeffectivestressatthecenteroftheclay

layer.Thesettlementwithtime:VerticaldrainsThedegreeofconsolidationislargelydeterminedbythelengthof

drainagepath.Verticaldrainscanbeinstalledinthickclaylayertointroducehorizontal

drainage,expeditingtheconsolidatio