A mixed finite element/finite volume formulation for granular bentonite mixtures

Abstract

A mixed finite element/finite volume formulation is presented for characterising the macroscopic behaviour of granular bentonite mixtures. The formulation enables fitting the hydro-mechanical behaviour of a mixture parting from a double porosity numerical model. The granular bentonite mixture is abstracted as a finite set of homogeneous units made with bentonite grains (where microstructure and macrostructure coexist) embedded in megapores. The separate mass balances of macrostructural and microstructural water are solved for each unit using the finite volume method. The water mass balance in the megaporosity is calculated for the entire domain using the finite element method. To solve the equilibrium equation, a displacement-based finite element method is applied after defining a global stiffness matrix that integrates the effect of megaporosity. After implementing these approaches in a double porosity numerical model, satisfactory modelling results were obtained in agreement with the experimental tests. The results of the proposed model effectively fit those of a triple porosity bentonite unit model that uses a contact model for displacement compatibility of the units. This contributes to the qualification of the presented model’s ability to produce compatible strains of the units using the proposed global stiffness.