中文摘要：

基于极限分析上限法基本原理和强度折减技术，根据滑坡体处于极限状态时两功率相等（虚功率方程）条件，推导了带台阶的多级边坡整体失稳和可能出现的局部失稳安全系数计算公式。并以3级边坡为例，编制优化程序，采用序列二次规划迭代算法计算确定最危险滑动面的位置：即对多个可能的滑动面进行搜索，获得安全系数最小（也即稳定性最差）的面作为潜在最危险滑裂面。采用具体算例，对比分析了3级边坡的整体稳定性和可能出现的局部稳定性问题，并由此开展了参数分析。对比分析表明：获得的安全系数较已有方法略小，得到的最危险滑动面与已有结果颇为接近，可以验证其有效性和可行性；参数分析表明：对均质多级边坡，当某级边坡坡角过大时，边坡更易发生局部失稳；高边坡增设边坡台阶可以有效提高边坡稳定性并降低施工难度。

英文摘要：

Based on the theory of upper bound method in limit analysis and the strength reduction technics, according to the condition of the power of the internal force equals to that of the external force （ virtual power equation） when landslide body is in ultimate state, the formula of safety factor of multi-stage slope with steps which occurs overall instability and potential local instability is derived. Taking a 3-stage slope for example, the location of the most dangerous sliding surface is determined by using prepared optimization procedure and sequential quadratic plan iterative algorithm： which means searching a potential plurality of sliding surface to find the sliding surface whose safety factor is the least （whose stability is the worst） as the most potential dangerous one. The overall stability and potential local stability of 3-stage slope are comparatively analysed by analyzing example and parameters. The result of comparative analysis shows that （ 1 ） the obtained safety factor is slightly smaller, and the obtained most dangerous sliding surface is also quite close to the existing results, which can verify the effectiveness and viability of this method. The result of parametric analysis shows that （1） to homogeneous multi-stage slope, local instability is easily happened when slope angle of a stage becomes larger; （2） the stability of high slope can be improved and the difficulty of construction can be reduced by adding steps.