有限土体主动土压力计算

 建立在半无限土体假定基础上的朗肯、库仑土压力理论并不适用于有限土体土压力的计算。根据实际情况，建立有限土体土压力计算模型，基于极限平衡理论及平面滑裂面假定，在考虑土黏聚力及有限土体宽度的基础上，推导有限土体滑裂面剪切破坏角的数学表达式，并建立有限土体主动土压力计算公式。所建立的计算公式表明，有限土体滑裂面剪切破坏角不再是库仑土压力理论给出的定值45°+j/2，而是一个变量，与计算深度、土内摩擦角、土黏聚力及有限土体宽度有密切关系。通过算例分析发现，有限土体滑裂面剪切破坏角随深度增加成非线性增长；而与土黏聚力和有限土体宽度成负相关；随着土内摩擦角的增大，剪切破坏角先是减小，随后增大。最后，将有限土体土压力计算结果与朗肯土压力进行对比，证实了有限土体主动土压力计算公式的合理性。

CALCULATION OF ACTIVE EARTH PRESSURE FOR LIMITED SOILS

With the development of underground engineering in cities，people pay more attention to the calculation of earth pressure for limited soils in foundation supporting projects. However，Rankine¢s and Conclom¢s theories based on semi-infinite space assumption are not suitable for calculating the earth pressure of limited soils. Based on the limit equilibrium theory and the hypothesis of planar sliding plane，a formula for calculating the angle of shear failure in limited soils is deduced with the consideration of cohesion force and the width of limited soils. And then，a formula is proposed to calculate the active earth pressure of limited soils exerted against the supporting system. The formula shows that the angle of shear failure of limited soils is no longer the one in Conclom¢s theory. And the angle of shear failure is no long equal to 45°+j/2，but is a variable related to the width of limited soils，the cohesion of soil，the friction angle of soil and the depth. It is found that the angle of shear failure of limited soils increases nonlinearly with the increase of the depth，and decreases with the increase of the width of limited soils and the cohesion of soil. It is interesting that the angle of shear failure in limited soils decreases firstly with the increase of friction angle of soil，but latterly it will increase with the increase of friction angel of soil when it reaches to a certain degree. Finally the calculated results using the deduced formulas for the angle of shear failure and the active earth pressure of limited soils are analyzed by comparison with those of Rankine¢s theory. It proves the present formulas are reasonable.