Three-dimensional simulation of fully coupled hydro-mechanical behavior of saturated porous media using Element Free Galerkin (EFG) method

Meshless methods are a relatively new type of numerical methods that have attracted the attention of many researchers over the past years. So far, a number of meshless methods have been developed and applied to solve problems in various fields of engineering, including solid mechanics and geotechnical problems. The Element-Free Galerkin (EFG) method is adopted in this study for solving the governing partial differential equations of equilibrium and continuity of pore fluid flow for numerical simulation of coupled hydro-mechanical problems. For this purpose, the weak form of the governing equations is derived by applying the weighted residual method and Galerkin technique. The penalty method is used for imposition of essential boundary conditions. The spatial discretization of the resulting constrained Galerkin weak forms is based on using the same EFG shape functions for displacements and pore water pressures, and a fully implicit scheme is used for discretization in the time domain. The performance of the developed EFG-based code is evaluated by comparing the results of the model with analytical solutions. After verification, the developed code is utilized for analyzing two- and three-dimensional consolidation problems considering different drainage and loading conditions. The numerical results indicate that the robust 3D mesh-free code developed in this paper is capable of simulating fully coupled hydro-mechanical problems without spurious oscillations if numerical parameters of the EFG approach are properly selected.