边坡稳定的非线性有限元分析

基于有限元强度折减法，进行了边坡的弹塑性材料非线性及大变形几何非线性分析，并考虑了边坡的三维变形情况。在有限元分析中采用的是莫尔-库仑理想弹塑性模型，大变形分析采用的是更新的拉格朗日法。均质边坡的算例分析表明，有限元法与简化的毕肖普法的安全系数计算结果具有相同的规律，即安全系数都随着黏聚力及内摩擦角的增加而增加，随着重度的增加而减小，但是，各种有限元法的计算结果都比相应的毕肖普法的解要大，亦即毕肖普法偏于安全。各种方法对应的安全系数由大到小的顺序依次是：三维小变形有限元分析、二维大变形有限元分析、二维小变形有限元分析，简化的毕肖普法，前二者能更好地反映实际的边坡变形情况，二者的安全系数值也十分接近，因而是较好的方法。

Nonlinear finite element analysis of slope stability

Based on the strength reduction method of finite element method, the elastoplastic material nonlinearity and large deformation geometrical nonlinearity of the slope are studied; and three dimensional deformation features of the slope are also considered. In the finite element analysis, the realistic elastoplastic model of Mohr-Coulomb is adopted; and the method for describing the large deformation characteristic of the soil is updated Lagrangian method. Through analyzing a homogeneous slope, it’s concluded that there exists the same rule among the results of the finite elements and simplified Bishop method. The rule is that the factor of safety will become large if the cohesion and the internal friction angle become large, and it will become small with the increase of unit weight. However, the results of the finite element methods are always larger than the corresponding value of the simplified Bishop method, which means that the result of simplified Bishop method is inclined to conservative. The decreasing order of the four kinds of results of safety factor is Fs (three dimensional small deformation), Fs (two dimensional large deformation), Fs (two dimensional small deformation) and Fs (simply Bishop Method); among them the first two methods are the best one and their values are very close each other.