第六章 土压力 Chapter6EarthPressureInthislecture,welllearnCoefficientsofearthpressure(土压力系数)Relationship between wall movement & earthpressure(墙体移动与土压力的关系)Earthpressureat-rest(静止土压力)Rankinesearthpressuretheory(朗肯土压力理论)6.1Earthretainingstructures(挡土结构物)Soilnailedwallforacutslope(土钉墙)Bridgeabutment(桥台)Quaywallforcontainerterminal(码头的岸墙)Deepexcavationdiaphragmwall(深基坑 地下连续墙)Deepexcavationsheet-pilewall(深基坑 板式挡土墙)6.2CoefficientofEarthPressure(土压力系数)isunitweightofsoilandzisdepthofsoilH地面Mhv土压力竖向有效应力AACBBCBackfill(填土)Earth Pressure At-Rest (静静止土止土压压力力)whenawalldoesnotmoveatall,i.e.itis“atrest”AA(墙体没有位移墙体没有位移)Active Earth Pressure (主主动动土土压压力力)when a wall moves away from backfill AAtoBB(墙体墙体离开离开填土方向填土方向)Passive Earth Pressure (被被动动土土压压力力)when a wall is pushed against backfill AAtoCC(墙体墙体向填土方向挤压向填土方向挤压)1. Wall Movement (墙体的移动墙体的移动)Howtoevaluatethecoefficientsofearthpressure?怎样计算土压力糸数土压力糸数?Assumptions(假定):-nogroundwatertable(没有地下水)-nomovementofwall(墙体没有位移)Lateral earth pressure (土压力) hactingonthewallis:whereisunitweightofsoil,Hisdepthof soil and Ko is coefficient of earthpressureatrest(静止土压力糸数). v h6.3 Earth Pressure at Rest (静静止土止土压压力力)Jaky(1944)proposedfollowingempiricalexpressiontoestimateKofornormallyconsolidatedsoil(估计正常固结土的Ko的经验公式):whereiseffectiveangleofinternalfriction(有效內摩擦角)Lateral earth pressure hincreases linearly with depthandtotallateralforce(总合力)Poexertedonthewallis:Followingassumptions(假定)aremadetodevelopRankinesearthpressuretheory.Wallisrigid,vertical,frictionlessandextendstoaninfinitedepth(墙背竖直和光滑)Backfillisadry,homogeneous,isotropicandcohesionlesssoil(填土是无粘性土,干,均质和各向同性)Soilsurfaceishorizontal(水平表面)andtherearenoshearstresses on horizontal and vertical planes, i.e. horizontalandverticalstressesareprincipalstresses(水平和竖直方向为主应力方向)6.4.RankinesEarthPressureTheory(朗肯土压力理论)In figure on the right, red circlerepresents initial stress state or KoconditionofelementA(右图的红圆代表土单元A的初始或静止状态)WallismovedawayfromelementAtoB(墙体从土单元A方向离开) h will reduce but v will remainconstant( h减少,但 v不变)Mohrs circle will expand untiltouching Coulomb failure surfacerepresented by blue circle. This iscalledactivefailure.(莫尔圆增大与库伦强度包线相切时为主动破坏,见右图的蓝圆) vf hf库伦强度包线1 .Active Failure (主动破坏主动破坏)Majorprincipalplaneishorizontalsurface(水平面为最大主应力面)Slipplanesforactivefailureareinclinedat45+/2withrespecttohorizontal(主动破坏面与水平面的夹角为45+/2) vf f 1f 3f fc f 1f 1f 3f 3f f f f Mohr-Coulombfailurecriteria莫尔-库伦破坏准则Rearrangingtheequationinthepreviousslide,followingexpressionforactiveearthpressurecoefficient(主动土压力糸数)Kaisobtained:c=03f=hf&1f=vfLateralearthpressurehincreaseslinearlywithdepthandtotalactiveforce(总主动土压力)Paexertedonthewallis:In figure on the right, red circlerepresents initial stress state or KoconditionofelementB(右图的红圆代表土单元B的初始或静止状态)WallisispushedagainstelementB (墙体向土单元B方向挤压) hwillincreasebut vwillremainconstant( h增加,但 v不变)MohrscirclewillfirstcontractandthenexpanduntiltouchingCoulombfailure surface represented by bluecircle.Thisiscalledpassivefailure.(莫尔圆先减小後增大,与库伦强度包线相切时为被动破坏,见右图的蓝圆) hf vf h2 。Passive Failure (被被动破坏动破坏)Majorprincipalplaneisverticalsurface(竖直面为最大主应力面)Slipplanesforpassivefailureareinclinedat45-/2withrespecttohorizontal(被动破坏面与水平面的夹角为45-/2) vf f 1f 3f fc f 1f 1f 3f 3f f f f Mohr-Coulombfailurecriteria莫尔-库伦破坏准则Rearrangingtheequationinthepreviousslide,followingexpressionforpassiveearthpressurecoefficient(被动土压力糸数)Kpisobtained:c=03f=vf&1f=hfLateralearthpressurehincreaseslinearlywithdepthandtotalpassiveforce(总被动土压力)Ppexertedonthewallis:Thelateralearthpressureexertedonthewalldependsonthewallmovement(土压力的大小与墙体位移有关)Only small movement of wall away from soil is required tomobilisefullactiveearthpressureinsoilmassbutsubstantialwallmovementtowardssoilisrequiredtomobilisefullpassiveearthpressureinsoilmass(相对於主动破坏,墙体需要较大位移才能达到被动破坏)Wallmovement(墙体移动)3。 Relationship between wall movement & earth pressure (墙体移动与墙体移动与土土压压力的关系力的关系 )What will be the earth pressures if ground water table exists behind the wall and the backfill is a cohesive soil?当墙背有地下水和填土是粘性土时,怎样计算土压力糸数?Ifgroundwaterispresent,porewaterpressuremustbeconsideredinadditiontolateralearthpressure.DONOTmultiplyporewaterpressurewithcoefficientofearthpressure.4 。 Effect of ground water (地下水作用地下水作用) IfgroundwatertableislocatedataheightH2frombottomofwall,hydrostaticporewaterpressureatbaseofwalliswH2.Total imposed lateral force (Pw) due to pore water pressure iswH22.Belowgroundwatertable,submergedunitweight()isusedtoevaluatelateralearthpressure.Ifbackfillofretainingwalliscohesivesoil,cohesion(c)isnotzero.Atadepthzfromtopofwall,active(pa)andpassive(pp)lateralpressureareasfollows:5 。Effect of Cohesive backfill 粘性粘性填填土土作用作用Foractivefailure,atensile zone (拉拉力力区区)ofdepthzoexistsfromtopofwall.Questions:Whatwillbetheearthpressuresifawallcarriesuniformsurchargeandthebackfillisnothomogeneous?当墙体承受均布荷载和填土是 不 均 质 土 时 ,怎 样 计 算 土 压 力 糸 数 ?Effectofsurchargeandnon-homogeneousbackfill均布荷载不均质填土Example1(例题一)Calculate(i)thetotalactiveforceonaverticalwall5mhighretainingasandofunitweight17kN/m3forwhich=35:thesurfaceofthesandishorizontalandthewatertableisbelowthebottomofthewall,(ii)thethetotalforceonthewallif the water table rises to a level 2 m below the surface of the sand. Thesaturatedunitweightofthesandis17kN/m3.一个高5m的垂直挡土墙,墙后填土是砂土:重度()=17kN/m3,有效内摩擦角()=35,填土表面是水平面.计算墙背上的(i)总主动土压力(ii)总合力当地下水位低于填土表面2m.砂土的饱和重度(sat)=20kN/m35m=17kN/m3=35sat=20kN/m3Example1(例题一)5m=17kN/m3=35sat=20kN/m3(i)NowatertableExample1(例题一)5m=17kN/m3=35sat=20kN/m3=10.2kN/m3(ii)Watertablebelow2mofgroundsurface2mExample2(例题二)5m=18kN/m3=38The soil conditions adjacent to a sheet pile wall are given in the followingfigure.Calculatethetotalactiveforcebehindthewallandthetotalpassiveforceinfrontofthewall.计算板桩墙上总主动土压力和总被动土压力.5msat=20kN/m3c=10kN/m2=28AExample2(例题二)5mAssumethewallrotatesatitsbottom(i.e.pointA).Thus,activeearthpressureactsbehindthewallandpassivepressureactsinfrontofthewall.假没板桩墙上端向外移动但下端不动,墙背产生主动破坏,墙前产生被动破坏.5mAPaPpExample2(例题二)(i)Behindthewall(墙背)Soil15m5mPaPpSoil2Example2(例题二)(ii)Infrontofthewallthewall(墙前)5m5mPaPpSoil2Example2(例题二)5m=18kN/m3=38The soil conditions adjacent to a sheet pile wall are given in the followingfigure.Calculatethetotalactiveforcebehindthewallandthetotalpassiveforceinfrontofthewall.计算板桩墙上总主动土压力和总被动土压力.5msat=20kN/m3c=10kN/m2=28AExample2(例题二)Assumethewallrotatesatitsbottom(i.e.pointA).Thus,activeearthpressureactsbehindthewallandpassivepressureactsinfrontofthewall.假没板桩墙上端向外移动但下端不动,墙背产生主动破坏,墙前产生被动破坏.5m5mPaPpExample2(例题二)(i)Behindthewall(墙背)Soil15m5mPaPpSoil2Example2(例题二)(ii)Infrontofthewallthewall(墙前)5m5mPaPpSoil26.5 Coulombs earth pressure theory(库伦土压力理论)Coulomb (1776) proposed that a condition of limitequilibriumexistsinasoilwedgebetweenaretainingwallandatrialslipplane.(库伦土压力理论假设一个滑动面,整个滑动土体处于极限平衡状态)Theforcebetweenthewedgeandthewallisdeterminedbyconsideringtheequilibriumofforcesactingonthewedge.(利用整个滑动土体上力的平衡条件来确定土压力)Amongthetrialslipplanes,thecriticalslipplaneistheonewhichgivesthemaximumlateralpressureonthewall.(在假定滑动面中,临界滑动面产生最大的土压力)Poncelet(1840)usedCoulombslimitequilibriumapproach to obtain the active andpassive earth pressure coefficients for caseswherebackfillisdry,homogenousandcohesionlesssoilwithanangleofinternalfriction(填土是干,均质和无粘性土)backfill is sloping at an angle to thehorizontal(填土表面与水平面夹角为)wallfrictionoispresent(墙背与填土之间的摩擦角为o)wall face inclined at an angle to thevertical(墙背面与竖直线的夹角为).H1。 Poncelets Assumptions 假设假设Foractivefailure,thewallmovesawayfromthesoilmass(墙体离开填土方向,产生主动破坏)SoilwedgeABCwillslidedown(土体ABC向下滑动)HBACWRPao2。 Active failure (主动破坏主动破坏 )TheforcesactingonsoilwedgeABCisunderequilibrium:itsweight(W),thereactionsontheslipplaneAC(R)andthewallAB(Pa)(土体ABC的重量W,滑动面AC上的反力R与墙背AB上的反力Pa达至静力平衡)PaandRactbelowthenormalofABandBC,respectively.(Pa与R的方向向上)HBACWRPao3.Active failure (主动破坏主动破坏 )Considertheforcetriangleontherighthandsideandfromsinerule(力矢三角形如右图,通过正弦定律可得):WRPa-90-o-TheweightofsoilwedgeABC(土体ABC的重量)ExpressPaasafunctionofDifferentiatePaw.r.t.anditsmaximumvaluecorrespondsto(将Pa对求导数,并令其等於零)whereIfthewallisvertical(=0),thereisnofrictionbetweenthewallandthesoil(o=0)andthesurfaceofthebackfillishorizontal(=0),theexpressionofKabecomesForpassivefailure,thewallispushedagainstthesoilmass(墙体向填土方向挤压,产生被动破坏)SoilwedgeABCwillslideup(土体ABC向上滑动)PpandRactabovethenormalofABandBC,respectively.Ca ae e HBAWRPpoConsidertheforcetriangleontherighthandsideandfromsinerule(力矢三角形如右图,通过正弦定律可得):WeightofsoilwedgeABCExpressPpasfunctionofWRPp+90+o-4. Passive failure (被动破坏被动破坏 )whereDifferentiatePpw.r.t.anditsmaximumvaluecorrespondsto(将Pp对求导数,并令其等於零)Ifthewallisvertical(=0),thereisnofrictionbetweenthewallandthesoil(o=0)andthesurfaceofthebackfillishorizontal(=0),theexpressionofKpbecomesHow to evaluate the earth pressures fromCoulombsmethodifthesoilsurfaceisuneven,thewall carries surcharge, ground water table existsbehind the wall, the backfill is a cohesive soil?怎样利用库伦理论计算土压力当填土表面不是平面,有荷载,填土是粘性土与墙後有地下水?1.Rankinestheoryisbasedonthestressequilibriumofasoilelement.(朗肯理论基于土单元体的应力平衡条件来建立)2.Rankineassumedthatthewallisvertical,frictionlessandthesoilsurfaceishorizontal.(朗肯理论假定墙背面竖直与光滑,填土面为水平)3.Ingeneral,Rankinestheoryover-estimatestheactivepressurebutunder-estimatesthepassivepressure.(朗肯理论高估主动土压力与低估被动土压力)5. Comparisons between Rankines and Coulombs Theories (朗肯与朗肯与库伦库伦理理论的比较论的比较)4. Coulombstheoryisbasedonlimitingequilibriumofforceswithinasoilwedgeforagivenslipsurface.(库伦理论基于滑动块体的静力平衡条件来建立)5. Coulombassumedthefailuresurfaceisaplane.(库伦理论假定滑动面为平面)6. In general, Coulombs theory under-estimates theactive pressure and over-estimates the passivepressure.(库伦理论低估主动土压力与高估被动土压力)