三维块体元塑性极限分析下限法

基于块体元离散思想，将三维边坡离散为块体-结构面组成的块体系统，假定块体为刚体，以结构面上的应力为未知量；从下限定理出发，构造满足平衡条件、边界条件和屈服条件的静力许可场，平衡方程严格满足3方向力平衡及绕3个主轴方向的力矩平衡条件，为避免非线性规划，对屈服条件进行线性化处理；最后，建立了下限法数学规划模型，通过线性及非线性规划获得边坡稳定严格的下限解。用几个典型算例验证了文中方法的正确性及可行性。

Three-dimensional block elements plastic lower bound limit analysis method for slope stability

By using the discrete means of the block element method, the 3D slope is partitioned into a proper number of block elements conjoined with the structural planes. It assumes block elements are rigid, stresses only existed in structural planes. Base on the lower bound limit theorem, and regarding the stresses of structural plane as unknown variables, the statically admissible stress fields that satisfy the equilibrium, boundary conditions and yield criterions are constructed. A linearization yield criterion is used for avoiding nonlinear mathematical programming. Finally, the lower bound limit analysis model of linear and nonlinear mathematical programming for 3D slope stability is established; four examples are used and the results agreed well with those from the rigid limit equilibrium and upper bound method.