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1、原文:Chapter44VERTICALSLOPEINCOHESIVEMATERIALAwellknownandimportantproblemofsoilmechanicsisthecaseofaverticalcutoffinapurelycohesivematerial(),asoccurswhenmakingaverticalexcavation,oraverticalslope,seeFigure44.1.Theproblemtobeconsideredinthischapteristhedeterminationofal
2、owerboundoranupperboundforthemaximumpossibleheightoftheslope,foramaterialhavingaconstantcohesivestrengthc,andaconstantvolumetricweightγ.44.1LowerboundInthiscaseitisessentialthattheweightofthematerialistakenintoaccount.TheequationsofequilibriumnowareAsimpleequilibriumsy
3、stemisshowninFigure44.2,consistingofthreezones.Ontheinterfacesbetweenthezonesthenormalstressesparalleltotheseinterfacesmaybediscontinuous,withoutdisturbingequilibrium,seeChapter40.Theboundary15conditionsforthestressesarethatthenormalstressesandtheshearstressesarezero,a
4、llalongtheuppersurface.TheseconditionsareexactlysatisfiedbythestressfieldsindicatedinFigure44.2.Thisfieldcanbeconstructedbystartingtoassumethatintheentirefieldtheshearstress,becausethisshearstressmustbezeroonthetwohorizontalboundaries,andontheverticalslope.Inordertosatisfy
5、theconditionthatontheverticalslopethehorizontalstress,itfollowsfromtheequationofhorizontalequilibrium,eq.(44.1)thatthisstressmustbezerothroughoutzoneI.Theexpressionsfortheverticalnormalstressfollowimmediatelyfromtheequationofverticalequilibrium(44.2)byputting,andusingt
6、heboundaryconditionsatthetopofthesoil.TheexpressionsforthehorizontalstressinzonesIIandIIIcanbechosenarbitrarily,buttheymustbeconstantinx-direction(tosatisfyhorizontalequilibrium),andpreferablyasclosetoaspossible,tokeepthemaximumshearstressassmallaspossible.Bychoosingth
7、eMohrcircleinzoneII,inthelowerleftpart,reducestoapoint.Thisseemstobeveryattractive,buttheconsequenceisthatinzoneIII,thelowerrightpart,thedifferenceofthestressesandisratherlarge,.Theverticalandhorizontalstressesareprincipalstressesinthiscase,becauseeverywhere.Therefore,
8、theMohr-Coulombcriterionnowis.Asthelargestvalueofoccursinthelowerrightpart,itfollowsthatthecriticalvalueoftheheight.T
