Limit Equilibrium and Limit Analysis: Comparison of Benchmark Slope Stability Problems

Conventional stability analyses use various limit equilibrium (LE) methods to determine the minimum, critical factor of safety and its associated failure mechanism. These methods generally assume that collapse will follow predefined geometric constraints that are dependent on certain input criteria—an effective approach for simple geotechnical problems, but challenging in consideration of complex problems. An effective solution lies in the use of upper bound limit analysis (LA) in conjunction with a discretization procedure known as discontinuity layout optimization (DLO). Use of DLO-LA can be an effective tool for establishing a critical failure mechanism and its stability without the constraints or assumptions required in LE analyses. This study compares the use of LE (Spencer method with dynamic programming optimization, Morgenstern-Price, Spencer) and LA for several examples that focus on complex geotechnical scenarios to illustrate agreement and differences between the analyses, as well as situations where use of DLO-LA may be more appropriate. It is shown that LA can provide results that are comparable, and sometimes more critical, than rigorous LE while managing to handle complexities without the same assumptions regarding failure surface geometry or entrance/exit points of the slip surface. With the advance of accessible computer processing, engineers are at the point where more computationally intensive analyses like DLO-LA present a viable alternative to analyses that are dependent on potentially nonintuitive assumptions, especially for complex, yet realistic geotechnical problems.