Modelling internal erosion using 2D smoothed particle hydrodynamics (SPH)

This paper presents a stabilised multi-phase smoothed particle hydrodynamics (SPH) model applicable to seepage-induced internal erosion and the resulting deformation in soils. Based on the continuum mixture theory, a new single-layer SPH model in the u-w-p formulation is derived for the mathematical description of the erodible porous material. A new modified constitutive model is formulated to account for the influence of erosion on the mechanical behaviour of soils. Extensions of a first-order consistent boundary condition as well as the diffusion algorithm for hydro-mechanical coupling in SPH are also proposed to accommodate the analysis of erosion-transport process. A novel viscous dissipation term is designed to mitigate the numerical instability commonly encountered in coupled problems. In contrast to existing stabilisation terms in the SPH literature, which operate on both the bulk component and shear component, this new stabilisation term offers the possibility to increase the dissipation of unphysical oscillation due to the shear deformation. The proposed method is validated through a series of benchmark tests. The results demonstrate the effectiveness of the proposed approach in addressing the coupled problem in porous materials involving multi-phase flow, phase interaction/transfer, and large deformation with enhanced accuracy, stability, and robustness.