The discrete technique combined with the upper bound approach is applied to analyze the stability of soil slopes with multiple layers in this paper. Based on the geometrical relationship derived from the normality requirement, an algorithm is proposed to determine the coordinates of discrete points on the failure surface. Specifically, these points are generated from the initial point to the terminal point. After completion of the discrete sliding surface, the sliding block is sliced by the vertical slice technique. Equations with integral form for rates of internal energy dissipation and external work are then derived. The scheme for calculation of the safety factor is presented by means of the strength reduction method and the optimization algorithm. Comparison analysis based on four examples under various conditions demonstrates the validity of the proposed method in addressing stability problem of slopes with multiple layers.

本文将离散技术结合上界法应用于多层土边坡稳定性分析。基于由正态性要求导出的几何关系，提出了一种确定失效面上离散点坐标的算法。具体来说，这些点是从起点到终点生成的。完成离散滑动面后，通过垂直切片技术对滑块进行切片。然后推导出具有积分形式的内部能量耗散率和外部功的方程。结合强度折减法和优化算法，提出了安全系数的计算方案。