Identification of rotational failure mechanisms in cohesive media using discontinuity layout optimisation

Discontinuity layout optimisation (DLO) is a generally applicable numerical limit analysis procedure that can be used to identify critical plastic collapse mechanisms in geotechnical problems. Previous research has focused on using plane-strain DLO to identify mechanisms that are purely translational, or which involve rotations only along predefined boundaries. In this paper a more general formulation, capable of identifying mechanisms that can involve arbitrary rotations and/or translations in cohesive media, is presented. The formulation is then verified through investigation of the yield surface and evolution of the collapse mechanism associated with a footing under combined vertical and moment (V, M) loading, and through study of the well-known anchor uplift problem. It is shown that results of very high accuracy can be obtained, in terms of the collapse load and of the predicted failure mechanism. In the light of the new results, the Bransby design formula for combined vertical and moment loading has been modified to improve its accuracy. Additionally, the more general DLO formulation presented is shown to have several inherent advantages compared with existing numerical limit analysis approaches.