A coupled fluid-solid SPH approach to modelling flow through deformable porous media

Abstract

In this paper, a computational framework based on the mesh-free smoothed particle hydrodynamics (SPH) method is developed to study the coupled behaviour of fluid and solid in a deformable porous medium. The mathematical framework developed herein is derived from the Biot's two-phase mixture theory in which the solid is modelled as an elasto-plastic material and the pore-fluid as an incompressible fluid. The key feature of the proposed numerical framework is that both solid and fluid phases are solved simultaneously in two different Lagrangian discretisations (or two different sets of Lagrangian particles) using their own governing equations that are linked through several laws of physics. The capability of the SPH method to model large deformation of the solid materials enables the framework to account for the permeability change due to the dilatant shear behaviour of the solid phase. To obtain a stable and accurate SPH solution for the pore-fluid, an incompressible SPH (ISPH) approach is adapted to correctly simulate the pore-pressure distribution of the fluid phase inside the porous medium. The proposed coupled SPH framework is firstly validated against analytical and solutions obtained using finite element method (FEM) for a submerged soil medium subjected to a gravitational load and a seepage flow through an elastic embankment, respectively. Then, it is employed for the simulation of flows through rockfill dams and an embankment failure induced by seepage flows. Simulation results predicted by SPH show very good agreements with analytical, FEM and experimental results. This suggests that the proposed two-phase SPH framework is a promising approach for future studies of coupled problems that involve complex water free-surface/seepage flows and large deformation of soils which are difficult to be modelled using traditional FEM-based coupled two-phase flow models.