A Coupled MPM–SPH Numerical Simulation for Fully Saturated Soil

Abstract

The material point method (MPM) has recently been used to perform soil–water interaction analysis for fully saturated soil in geotechnical engineering. In MPM, to treat fully saturated soil, two types of discretization methods have been mainly used: the single point formulation and the double point formulation. The former discretizes the soil–water mixture with a single set of particles, whereas the latter discretizes the soil phase and the water phase separately by using different sets of particles. In both the discretization methods, the flux boundary condition is imposed on the background mesh nodes, and the prescribed pore water pressure boundary condition is directly applied to the particles. This is the reason behind the complexity involved in the setting of boundary conditions for the coupled MPM. To reduce this complexity, this paper presents a discretization technique that combines MPM with smoothed particle hydrodynamics (SPH). SPH is used for the discretization of the generalized Darcy’s law to impose the flux boundary condition directly on the particles. The proposed formulation is validated through the soil–water interaction benchmark problems: the consolidation problems of Terzaghi and Mandel–Cryer. The numerical results are in good agreement with the analytical solutions, which validates the proposed method.