MPM dynamic simulation of a seismically induced sliding mass

Abstract

In some geotechnical applications, material can undergo large displacement combined with excessive deformation; e.g. the sliding mass problem. Owing to the limitations of classical Lagrangian and Eulerian finite element methods to model these problems, the Material Point Method (MPM) has been developed about two decades ago to cope with the large deformation. In MPM, the continuum field is represented by Lagrangian material points (particles), which can move through a fixed background of a computational mesh. Therefore, it can be seen as a mesh-based method formulated in arbitrary Lagrangian-Eulerian description. Although MPM represents the continuum by material points, solution is performed on the computational mesh. Thus, imposing boundary conditions is not aligned with the material representation. In this paper, a non-zero kinematic condition is introduced where an additional set of particles is incorporated, which tracks the moving boundary by carrying the time- dependent boundary evolution. Furthermore, the material point method has been adopted to simulate the progressive failure of a sliding granular slope triggered by a seismic excitation. In order to represent the topographical bottom of the sliding mass, on which the seismic motion is applied, a rigid boundary is implemented by introducing an additional set of particles. A frictional contact algorithm is defined between the boundary and the descending mass, which allows sliding and rolling with friction. The traction due to contact is incorporated into the discretised momentum equation as an external force where the solution of this equation is performed separately for each body in contact. Defining the local coordinate system accurately in this algorithm is essential to avoid interpenetration. Thus, a two-dimensional triangular discretisation is utilised within the three-dimensional tetrahedral elements to track the surface progression of each body in contact. Complying with other continuum models findings performed on granular materials, the present model overpredicts the lateral deformations. Therefore, a local damping proportional to the out-of-balance nodal forces is included. In spite of the simple Mohr- Coulomb failure criteria being used, the results of the present numerical model are comparative to another continuum based model.