三维边坡稳定问题的基本方程与分析方法

基于空间一点应力分析，进行了空间曲面上一点的应力分析，得出了曲面上一点的法向应力、剪应力与应力分量、曲面一阶偏导数的关系。建立了曲面至边坡表面土柱上力的微分平衡方程、力的平衡方程、力矩平衡方程。和库仑屈服条件一起，构成了边坡稳定问题普遍适用的基本方程。采用与二维问题的简化Bishop法类似假定，得出了一种三维边坡稳定性分析的计算方法。算例表明，本文方法计算结果是合理的，具有广泛的应用意义。

Fundamental equations and analytic methods of three-dimensional slope stability

Based on the stress analysis of a point in space, the stress analysis of a point on a surface is performed, then the relationship among the normal stress, the shear stress, the stress component of a point on a surface and the first order partial derivative of the surface equation is deduced. Equilibrium equations of soil columns between the sliding surface and the top surface of the slope are established, which include differential equilibrium equation of force, equilibrium equation of force, and equilibrium equation of moment. These equilibrium equations and Coulomb yield condition can form the fundamental equations of three-dimensional slope stability analysis. Applying the supposition similar to that applied in the simplified Bishop method, a kind of three-dimensional slope analysis method can be obtained. An example is presented to show that the computation method is reasonable and applicable.