岩土边坡稳定性的刚体有限元上限分析法

刚体有限元法与极限分析相结合为求解边坡稳定性问题提供了新的方法。采用刚体有限单元离散边坡计算区域，同时构造运动许可速度场，在满足屈服条件、流动法则、虚功方程以及相应的边界条件的基础上，引入非线性数学规划方法求解最小安全系数。几个算例说明了该方法的正确性和可行性。

UPPER LIMIT ANALYSIS OF STABILITY OF ROCK AND SOIL SLOPES USING RIGID FINITE ELEMENTS

In this paper,the development and application of a new upper limit method for 2D and 3D slope stability problems are presented. Rigid finite elements are used to construct a kinematically admissible velocity field. The proposed method formulates the slope stability problems as an optimisation problem based on the upper bound theorem. The objective function for determination of the minimum value of the safety factor has some unknowns, which are subject to a set of linear and non-linear equality constraints derived from an energy-work balance equation,the Mohr-Coulomb failure (yield) criterion,an associated flow rule and a number of boundary conditions. The objective function with constraints leads to a non-linear programming problem, which can be solved by a sequential quadratic algorithm. Four typical 2D and 3D slope stability problems selected from the literature are analysed with the presented method. The results of the presented limit analysis are compared with those produced by other approaches reported in the literature.