动态规划法求解边坡安全系数最小上限解

The least upper-bound solution for safety factor of slope by dynamic programming

基于Sarma法的基本假设,将滑体划分为若干斜条块,由条块力的平衡条件得到条块间推力递推方程。根据推力最大原理,将寻求安全系数最小问题转化为寻求剩余推力最大问题。采用动态规划方法,将斜条块划分问题转化为多阶段决策问题。给出了基于条间推力递推方程的最优决策方法和步骤,对边坡斜条块划分组合进行了优化,找到剩余推力最大的划分组合。由于Sarma法本身是上限解,因此优化得到安全系数本质上是最小上限解。计算结果表明:利用动态规划方法搜索的最优斜条块划分组合,可以充分接近塑性力学解,安全系数一般大于并接近基于垂直条块的严格极限平衡条分法的安全系数。

Based on the basic assumptions used in the Sarma method, the sliding body was divided into a series of oblique slices and the recursive equation of interslice forces were derived according to the force equilibrium conditions of slices. In consistence with the principle of maximum thrust force, the problem of searching the minimum factor of safety was transformed into that of searching the maximum residual thrust force. By using the dynamic programming, the problem of dividing the oblique slices was transformed into that of multi-stage decision. The procedure and steps of the optimal decision strategy was given based on the recursive equation of thrust force, with which the combination of oblique slices was optimized resulting in the maximum residual thrust force. Since the solution of the Sarma method was the upper-bound in nature, the safety factor thus obtained was the least upper-bound solution of slope stability. It was shown that the optimal combination of oblique slices obtained by the dynamic programming agreed well with the theoretical solution of the mechanics of plasticity, and the factor of safety obtained was slightly bigger than that of the rigorous limit equilibrium method of slices with the vertical slices.