Smoothed Particle Hydrodynamics Simulation of Water-Soil Mixture Flows

A two-phase smoothed particle hydrodynamics (SPH) mixture model to simulate water-soil interactions is presented. In this model, each phase of the mixture satisfies its own conservation equations of mass and momentum. The water is considered as a Newtonian fluid and the soil is modeled as an elastic-perfectly plastic material. Drucker-Prager criterion is employed to test the yielding of the soil and an associated flow rule is adopted to describe the soil behavior after yielding. Interactions between water and soil are modeled by the viscous drag force according to Darcy's law. With this mixture model, it is possible to investigate the temporal and spatial evolutions of the volume fractions of both phases. This study first examines the proposed SPH mixture model for two single-phase flows, i.e.,water dam break and sand column collapse, respectively. The drag force model is also tested using the problem of flow in porous media. Then its application to the problem of soil excavation by high-velocity impinging water jets is illustrated. The flow pattern, profile of excavation hole, evolutions of pressure, volume fraction, and plastic shear strain during the impinging process are obtained and found to be qualitatively good compared with previous experimental observations and numerical simulations. Effects of hydraulic conductivity and initial volume fractions of water and soil on the excavation are revealed. Numerical simulation shows that the proposed method is robust and efficient, and can be applied to water-soil mixture flow problems in hydraulic engineering and geotechniques, especially to those cases where volume fractions play important roles in the mixture dynamics.