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1、8.5 Rankines earth pressure theoryBasic principle of Rankines earth pressure theoryThe Rankines earth pressure theorywas proposed by the British scholarRankine in 1857,and was used tocalculate the active or passive earthpressureofthesoilactingontheretaining wall.This theory is still widelyused due t
2、o its clear concept and simplemethod.William John MaquornRankine(1820-1872)土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoBasic assumptions：1.The back of the retaining wall is vertical and smooth.2.The surface of the backfill behind the retaining wall is horizontal.3.The deformation of
3、the rigid wall is neglected.Basic assumptions 土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoSemi-infinite soilBasic principlexx土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoSoil in semi-infinite spaceRankinesearthpressuretheoryconsiders that any soil element M insemi-infi
4、nite space changes from theelastic to the limit equilibrium stateundertheactionofself-weightstress.Moreover,whenthesoilbehind the wall reaches the limitequilibrium state,any soil elementin contact with the back of the wallis in the state of limit equilibrium.xMxxx土力学土力学Soil MechanicsSoil MechanicsPr
5、of.Prof.H.J.LiaoH.J.LiaoThe vertical self-weight stress at depth z below the surface zzz1The horizontal self-weight stress xKzx03Semi-infinite soilEarth-fillEarth-fillActive statePassive state土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoSemi-infinite soil13311331The vertical stress 1i
6、s not changed.The horizontal principal stress3will be gradually decreased to reach the Rankines active limitequilibrium state,i.e.,Rankines active earth pressure state.Active statePassive stateIf the earth-fill pushes the wall forward土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoSemi-i
7、nfinite soil13311331Active statePassive stateThe principal stress 1of the soil element behind the wall is not changed.Thehorizontal principal stress 3is gradually increased with the increase of walldisplacement,until horizontal principal stress turns to the maximumprincipal stress and the Rankines p
8、assive limit equilibrium state will beyielded,i.e.,the Rankines passive earth pressure state.If the wall moves to the earth-filling under the action of external force土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoRankines active earth pressure stateActive earth pressure1331Maximum princ
9、ipal stress plane土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoRankines passive earth pressure stateActive earth pressure3113Maximum principal stress plane土力学土力学Soil MechanicsSoil MechanicsProf.Prof.H.J.LiaoH.J.LiaoStatementStatement:Thanks for some pictures and materials fromthe Internet used in this courseware only for teaching.