Element Free Galerkin Mesh-Less Method for Fully Coupled Analysis of a Consolidation Process

Abstract. A formulation of the Element Free Galerkin (EFG)، one of the mesh-less methods، is developed for solving coupled problems and its validity for application to soil-water problems is examined through numerical analysis. The numerical approach is constructed to solve two governing partial di erential equations of equilibrium and the continuity of pore water، simultaneously. Spatial variables in a weak form، the displacement increment and excess pore water pressure increment، are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used to create the discretization of the time domain. Implementation of essential boundary conditions is based on penalty method. Examples are studied and the obtained results are compared with closed-form or nite element method solutions to demonstrate the capability of the developed model. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well، both soil deformation and the variation of pore water pressure، over time. Keywords: Mesh-less; EFG; Penalty method; Soil-water coupled problem; Consolidation process.