A closed-form three scale model for ductile rocks with a plastically compressible porous matrix

The present paper is devoted to a micro–macro model of plastic deformation in Callovo Oxfordian argillite. This material is composed of a porous clay matrix which is reinforced by linear elastic mineral grains. The clay matrix is itself constituted of a solid phase containing a distribution of pores. The solid phase of clay matrix is described by a pressure sensitive plastic model. By means of a two step homogenization procedure, a macroscopic plastic criterion is formulated to estimate the nonlinear behavior of the clayey rock taking into account influences of pores and of mineral inclusions. Both associated and non-associated macroscopic plastic flow rules depending if the solid phase is associated or not. The mechanical behavior of the clayey rock in conventional triaxial compression tests is studied with the proposed micro–macro model. It is shown that the non-associated plastic flow rule of the solid phase is an essential mechanism for the description of the macroscopic plastic deformation of the clayey rock. Comparisons between the predicted results and experimental data show that the proposed model is able to capture the main features of the mechanical behavior of the studied material.

► A closed-form three-scale model is proposed for ductile rocks.
► Matrix porosity and rigid inclusions are taken into account at different scales.
► Closed-form macroscopic plastic criterion and potential are obtained.
► Validation of the model is presented by comparing numerical results and experimental data.