土石坝的坝坡稳定是影响土石坝安全的重要因素，传统的土石坝坝坡稳定采用的是瑞典圆弧法或者毕肖普法，其计算结果既不是下限解也不是上限解。在Sloan的工作基础上，基于有效应力的方式, 用有限单元思想离散结构物，建立满足平衡条件、间断条件、应力边界条件以及屈服条件的极限分析下限法的非线性规划模型，并且编制了相应的程序，应用到土石坝坝坡稳定性的计算中。考虑了地震荷载和渗流作用，采用迭代算法对土石坝进行非线性强度指标的坝坡稳定计算。最后，以几个典型土坡和具体的土石坝工程为算例，与多种方法的分析结果比较，表明了该方法的可行性。

The slope stability is an important factor affecting the safety of earth-rockfill dam. Sweden arc and simplified Bishop methods are usually used to calculate the slope stability of earth-rockfill dam, although the calculation results are not the lower or upper solutions. On the basis of Sloan’s work, a finite element method is used to discretize the mechanism. The effective statically admissible stress fields can satisfy the conditions of equilibrium, stress boundary, yielding and stress discontinuity, the earthquake action and the seepage action. They are taken into account. Using the idea of nonlinear programming, a lower bound limit analysis model of mathematical programming for the slope stability of earth-rockfill dam is established. The model can evaluate the slope stability factor of earth-rockfill dam and get the stress field of lower bound. The nonlinear strength indexes and iterative algorithm are also used for the stability calculation and the corresponding program is compiled. Finally, the stability of some typical soil slopes and specific earth-rockfill dams is calculated. The results are compared among the results of many other methods. They indicate the correctness of the method and the program.