Modelling Slope Failure Using a Quasi-static MPM with a Non-local Strain Softening Approach

The Material Point Method (MPM), which can be thought of as a mesh-free technique, has been shown to be very efficient in avoiding the mesh distortion problem in large deformation analyses. However, for the widely used explicit dynamic MPM formulation, the time step must inevitably be very small in order to guarantee convergence, especially in the case of quasi-static problems. In this paper, an incremental updated Lagrangian quasi-static MPM formulation is developed, which requires less computation effort by using much larger time steps. Issues pertaining to the implementation of the present MPM formulation are discussed. Strain softening, which may potentially lead to localisation phenomena, is also considered in the constitutive model. Scale effects and mesh size dependency in the solution are accounted for by applying a spatial averaging approach to the strains using a weighting function defined by an internal length scale characterising the non-local deformation. A progressive failure of a slope is simulated in order to demonstrate the efficiency and good performance of the proposed formulation.