Intricacies in three‐dimensional limit analysis of earth slopes

Abstract

SummaryAnalyses of three‐dimensional slope failures can be elaborate because of the complexity owed to the geometry of the failure mechanism that needs to conform to an admissible kinematics of the slope collapse. This admissibility is imposed by the soil limit state condition, the normality plastic flow rule, and the boundary conditions. The kinematic approach of limit analysis is employed, and a rotational 3D slope failure is revisited. The study leads to the conclusion that some geometric constraints used in previous studies limit the range of admissible mechanisms resulting in overestimating stability factors. A set of results is presented that was obtained using an algorithm that allowed eliminating limitations present in previous studies. The largest improvements in the solutions were found for undrained failures of narrow slopes. For a 30° slope limited in width by the width‐to‐height ratio of 0.6, the stability factor calculated in previous studies overestimated the current calculations by nearly 39%. This overestimation is smaller for drained failures, and it drops significantly with an increase in the width of the failure mechanism.