EFG mesh-less method for coupled hydro-mechanical analysis of unsaturated porous media

Numerical modeling of the fully coupled phenomena of solid deformation-fluid flow in partially saturated porous media is of great interest in many branches of science and engineering. In this study, a new formulation based on one of the famous mesh-less methods, called Element-Free Galerkin (EFG), is developed to simulate the water and air movement through variably saturated soils. For this purpose, the governing partial differential equations including the equilibrium equation and mass conservation laws for each fluid phase are discretized in space using the same EFG shape functions. To enforce the essential boundary conditions, penalty method is employed. Temporal discretization is performed by utilizing the finite difference technique and adopting a fully implicit scheme to avoid spurious ripple effects. The performance of the developed computer program is examined via some numerical analyses and comparing the results to the semi-analytical or finite element solutions. According to the obtained results, the newly presented mesh-free computational algorithm can well handle the complexities involved in the hydro-mechanical behavior of unsaturated soils.