Application of dynamic programming to locate the critical failure surface in a rainfall induced slope failure problem

In this paper, a dynamic programming method is employed in conjunction with limit-equilibrium techniques to determine the location of the non-circular critical slip surface in the analysis of a slope failure due to a rainfall event. The Spencer method of slope stability analysis was incorporated into dynamic programming to predict the time of a slope failure and shape of the failure surface. A one-Dimensional (1D) sliding block model was used to analyze the motion of the failure mass. Furthermore, during the movement of the sliding mass, the stability of the model slope was analyzed by updating the shape of the model slope according to the new position of the sliding mass. The suction head in the soil pore provides soil shear strength to maintain the stability of the slope. The positive pore water pressure reduces the soil shear strength so that the slip surface beneath the water table will be more unstable. Numerous studies (using non-cohesive soil) have been conducted to locate the critical slip surface in slope stability problems without considering the increase in shear strength due to suction and apparent cohesion. The studies do not clearly illustrate the reasonable boundary conditions to avoid the slip surface alignment totally outside the actual slope. This paper clearly discusses the boundary conditions for such a slope stability problem reasonably. The step-by-step calculation procedure is presented through the flow diagram. Three cases of slope failure obtained from a laboratory flume experiment have been analyzed using the proposed method. The numerical simulation results and the results obtained from experiments are comparable.