Explicit finite element analysis of slope stability by strength reduction

The construction of stable slopes and vertical cuts is an important step in many geotechnical projects. Limit equilibrium methods (LEMs) are well-accepted procedures to compute factors of safety (FoS); however, they fail to provide any information about the distribution of the field variables within the soil mass because they do not include any stress-strain relationship in their formulation. On the other hand, the iterative finite element method (FEM/I) can estimate the field variables, but in the current study, we show that, for steep slopes and vertical cuts, it underestimates the FoS compared to the LEM. To overcome the obstacles that exist in this method, this study proposes a new approach to define the initiation of instability based on an abrupt change in the kinetic energy of the system. We also suggest a procedure to calculate the minimum FoS based on the explicit finite element method (FEM/E). Comparison of the results obtained from the proposed method, LEM, and FEM/I revealed that the FoS computed by the proposed method is in good agreement with the results of the LEM for a wide range of material parameters, geometries and external loading conditions, while no assumption regarding the critical slip surface needs to be made.