An efficient fully Crouzeix-Raviart finite element model for coupled hydro-mechanical processes in variably saturated porous media

Abstract

Coupled hydro-mechanical processes in variably saturated porous media can be encountered in several applications in geosciences and soil mechanics. They are ruled by highly nonlinear and strongly coupled equations of fluid flow in unsaturated porous media and quasi-static mechanical deformation. In this work, we develop an efficient and robust numerical scheme for unsaturated poroelasticity that allows for balancing computational requirements and accuracy. The spatial discretization is based on the Crouzeix-Raviart (CR) finite element method for both the displacement field and the hydraulic head. The CR method is locally mass conservative and uses low-order approximation, which alleviates the computational burden. The time discretization of the coupled nonlinear hydraulic mechanical equations is performed using high order time integration methods and efficient time stepping schemes via the method of lines (MOL).Four test cases are investigated to highlight the efficiency and accuracy of the developed numerical scheme. The first test case deals with the settlement induced by gravity in the case of saturated and unsaturated soils. A new semi-analytical solution is developed for the settlement in the unsaturated case and used for the validation of the numerical scheme. The second test case is the Cantilever bracket problem, extended here to variably saturated media and studied to investigate the nonphysical oscillations of the pressure variable with different numerical schemes. The results are compared to finite element solutions obtained with COMSOL with either linear or quadratic approximation of the displacement field. The third test case deals with the deformation of an unsaturated soil under partial infiltration and surface load. This test case is simulated to investigate the accuracy and efficiency of the CR scheme for the challenging problem of infiltration into dry soils. The last test case is simulated to show the applicability of the developed model to a realistic problem dealing with the stability of a hillslope under intense rainfall periods.Results of the numerical experiments show that the CR scheme coupled with high order time integration methods allows for significant gain in both computational requirements and accuracy.