2D slope stability analysis based on Pan’s maximum principle

Traditional slice methods for slope stability analysis must introduce some assumptions regarding the inter-slice forces and hence lack a rigorous theoretical basis. In this study, a new block method for slope stability analysis is proposed based on Pan’s maximum principle. In this method, the slope is cut into a block system, and the search for the maximum factor of safety is accomplished by a nonlinear mathematical programming method. During the searching process, the magnitude, direction and action point of the inter-block forces are taken as a variable system. The static equilibrium and yield criterion that satisfy the requirement of the statically admissible field of Pan’s maximum principle are used as constraints, and the maximum factor of safety is regarded as the optimization objective. Therefore, the problem of slope stability analysis is transformed into an optimization problem. This method does not introduce any other assumptions except for block rigidity. This approach can compensate for not only the lack of theoretical rigour in the traditional limit equilibrium theory but also the low computing efficiency and the optimization difficulty of the limit analysis finite element method. In this new method, a block system is used to simulate the structural characteristics of a toppling slope and the transfer of the toppling load and moment through the balance of the force and moment. The proposed block method is verified by one case with an analytical solution and two ACDAS test questions; additionally, the proposed method offers a satisfactory result for complex engineering slopes. In addition, both slope sliding and toppling failure can be analysed, and the results determined with the proposed method are close to those determined with the Goodman-Bray method. Because the computing precision of this method is comparable with the limit analysis finite element and its computation cost is as low as that of the limit equilibrium method (LEM), this method demonstrates robust slope stability analysis and has great potential in engineering practice.