一种基于Morgenstern-Price法假定的三维边坡稳定性分析法

 通过侧向剪力系数和侧向剪力分布函数对条间力进行假定，提出所有条柱满足3个力的平衡、滑坡体满足3个力矩平衡的三维边坡极限平衡分析法，可看作是二维Morgenstern-Price法的三维扩展。利用滑体力的平衡条件和边界条件分别得到条柱各行和各列的安全系数，再利用滑体整体力矩平衡条件确定侧向剪力系数?1，?2，?3，?4。该法考虑了所有条间剪力对安全系数的影响，采用直接迭代法求解，提高计算效率。算例分析表明，对于对称边坡，侧向剪力系数?1，?3，?4对安全系数影响不大；对于非对称边坡，?4对安全系数影响也不大，且获得的安全系数均与已有文献结果接近。非对称复合滑动面算例还表明，简化方法给出的安全系数不一定偏于安全。

A LIMIT EQUILIBRIUM METHOD BASED ON MORGENSTERN-PRICE METHOD FOR 3D SLOPE STABILITY ANALYSIS

A limit equilibrium method that satisfies the three force equilibrium conditions of all columns and three moment equilibrium conditions of total failure mass is proposed，in which the interslice forces are assumed by proposed lateral shear factors and lateral shear distribution functions. The present formulation can be treated as an extension of the 2D Morgenstern-Price? technique. The factor of safety of each row(column) is obtained by solving the force equilibrium equations and the boundary conditions of total failure；then the lateral shear factors are determined by solving the torque-equilibrium equations for total failure mass. All intercolumn forces are taken into account in calculating factor of safety. The direct iterative algorithm is implemented in the program developed by the authors to improve the computational efficiency markedly. The analysis results for two examples indicate that the given ?1，?3，?4 have a small effect on the factor of safety for symmetrical slope and the given ?4 also has a slight effect on the factor of safety for asymmetric slope；and these factors of safety obtained in the new formulation are similar to those in previous studies. It is not necessarily true for some composite slip surfaces that a more simplified formulation will give a lower factor of safety.