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

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.