A micro–macro model for clayey rocks with a plastic compressible porous matrix

Abstract

This paper is devoted to mesomechanical modeling of plastic deformation in a clayey rock. The material contains linear-elastic mineral grains embedded in a porous clay matrix at mesoscale. The clay matrix itself is composed of a solid phase containing spherical micropores. A two-step homogenization procedure, from micro to meso and from meso to macro, is proposed to estimate the macroscopic elastoplastic behavior of the clayey rock. The meso–macro upscaling is performed considering the incremental approach initially proposed by Hill (1965) which allows to account for the effects of mineral inclusions. For the micro–meso transition, the pressure sensitive behavior of the solid phase of clay matrix is described using a Drucker–Prager yield criterion and an associate flow rule. The effects associated with the presence of micropores are taken into account using a limit analysis-based homogenization approach. It is shown that, although the macroscopic model based on an associated plastic solid phase correctly predicts the non linear response and failure stress of the clayey rock under conventional triaxial compression tests, it fails to quantitatively reproduce volumetric deformation. By considering a non-associated flow rule for the solid phase, the agreement with experimental data is significantly improved. Comparisons between the numerical results and experimental data show that the proposed micro–macro model is able to capture the main features of mechanical behavior of heterogeneous clayey rocks.