Numerical modeling of saturated soils, based on Smoothed Particle Hydrodynamics (SPH) - Part 1: Seepage analysis

Smoothed particle hydrodynamics (SPH) is a mesh-free numerical method originally developed in the 1970s for astrophysical analysis. In the recent decades, it has been applied to a wide range of research fields, including fluid and solid mechanics, hydrodynamics and coastal and geotechnical engineering. This paper presents an application of SPH to the problem of interaction between the soil skeleton and the pore water in saturated soils. The formulation of the equations of conservation in SPH has been modified so that a drag force due to seepage is introduced and calculated using Darcy's law. Two test cases are considered for the analysis: a basic drainage of a vertical sand column due to gravity and seepage through a vertical dam (also known as the Muskat problem). Both simulations show very good agreement with the analytical solutions. The results prove the potential of SPH.