Application of smoothed point interpolation methods to numerical modelling of saturated and unsaturated porous media

Abstract

This study aims to develop an efficient computational framework for a rigorous coupled flow and deformation analysis of saturated and unsaturated porous media. The governing equations are derived based on equations of equilibrium, and conservation equations of mass and momentum for each phase. For numerical solution of the governing equations, the edge-based smoothed point interpolation method (ESPIM) is employed due to its numerous advantages over the classical techniques. The ESPIM was originally introduced for problems in single phase media. The extension of the technique to multiphase media is not trivial, and therefore as the first development step, ESPIM is extended for the solution of the coupled hydro-mechanical problems in saturated porous media through a novel approach for evaluation of the coupling matrix. Verification of the proposed ESPIM formulation is performed using several benchmark numerical examples. Subsequently, the method of manufactured solutions (MMS) is introduced, for the first time in geomechanics, for a systematic and more rigorous verification of the computational scheme. The proposed numerical framework is then extended to include material nonlinearity. For this purpose, a non-associative Mohr-Coulomb constitutive model is adopted and an algorithm is developed based on the modified Newton-Raphson technique to address the nonlinearities arisen from the elasto-plastic constitutive model. Stress integration is performed using the substepping method. The computational framework is then further extended to include the problems in unsaturated soil mechanics, taking account of coupling among different phases, and the hydraulic hysteresis observed in the behaviour of unsaturated soils. A framework based on the effective stress principle is followed in the formulation and a hysteretic water retention model is taken into account which includes the evolution of water retention curve (WRC) with changes of void ratio. An elasto-plastic constitutive model is employed within the context of bounding surface plasticity theory for predicting the nonlinear behaviour of soil skeleton in saturated and unsaturated porous media. The model is validated by comparing the numerical predictions with experimental or numerical data from the literature for fully and partially saturated soils. The results demonstrate the capability of the proposed numerical framework to predict essential characteristics of variably saturated soils.