A multi-layer SPH method for generic water–soil dynamic coupling problems. Part I: Revisit, theory, and validation

Abstract

In this work, a three-dimensional multi-layer SPH method is presented for generic water–soil dynamic coupling problems. Based on the mixture theory, two mathematical models using the apparent and intrinsic fluid densities are formulated. Compared with models from literature, our models correctly consider the spatial and temporal change of soil porosity. For numerical discretization, two overlapping layers of SPH particles are used to represent the two phases independently. The water phase is modeled as weakly-compressible Newtonian fluid, and the soil phase is modeled using an elastoplastic constitutive model. A corrected Shepard filter is proposed to achieve C1 particle consistency. A new method is proposed to realize the free-slip boundary condition. Some other issues in numerical implementation such as interface treatment, and simulation initialization are discussed. Through three validation cases, it is demonstrated that both models provide accurate simulations well corroborated by analytical results. Moreover, the intrinsic density-based formulation (IDF) gives more accurate numerical results and more stable simulations. Finally, a submerged landslide is simulated to demonstrate the capability of the proposed SPH model in solving the dynamic soil–water coupling problems.