Coupled material point method and characteristic finite element method for saturated porous media

The material point method (MPM) is a common approach to analyze the large deformation of the saturated porous media. However, the pore pressure oscillations caused by the weak-compressibility fluid, and the complication to apply the pressure boundary are the main challenges in the conventional explicit MPM. In this study, a novel algorithm, which couples the MPM and characteristic finite element method (FEM) for the saturated porous media with the incompressible fluid, is proposed. Inspired by the characteristic-based split (CBS) method, the characteristic-based procedure is applied to the temporal discretion of the fluid momentum equation to avoid the instability induced by the convective term, and the projection method is introduced to split the velocity and pressure in the solid and fluid phases. Several numerical tests, involving the consolidation of one-dimensional saturated soil column and the wave propagation in two-dimensional elastic foundation, are conducted to examine the performance of the proposed method. The simulated results agree with the reference solutions, which indicates that the new algorithm can greatly overcome the water pressure oscillation of the consolidation problem in comparison with the explicit MPM.