Multi-scale modeling of time-dependent behavior of claystones with a viscoplastic compressible porous matrix

• A micro–macro viscoplastic model is developed for clayey rocks.
• A two-step homogenization method is proposed.
• The model takes into account effects of pores and mineral inclusions at different scales.
• The model is able to describe the main features of short and long term behaviors of clayey rocks.
• The proposed can also be applied to other heterogeneous geomaterials.

This paper is devoted to multi-scale modeling of time-dependent behavior of claystones using a two-step homogenization procedure. Two materials scales are considered. At the mesoscopic scale, the material is constituted by a clay matrix and embedded mineral grains. At the microscopic scale, the clay matrix is a porous medium composed of a solid phase and spherical pores. The macroscopic plastic criterion of the clay matrix is first determined by a modified secant method (Maghous et al., 2009) considering a pressure sensitive yield function for the solid phase. This criterion is then used as the loading function for the description of viscoplastic deformation of the clay matrix, together with a non-associated viscoplastic potential. At the second step of homogenization, the macroscopic behavior of the claystone is determined by taking into account the effect of mineral grains (quartz and calcite). For this purpose, we propose an extension of the incremental approach initially proposed by (Hill, 1965) to modeling of time-dependent behavior. Therefore, the micromechanical model is able to explicitly account for the effects of pores and mineral grains at two different scales. The numerical algorithm for numerical implementation of the micromechanical model is also presented. The proposed model is finally verified through comparisons between numerical results and experimental data in triaxial compression tests with constant strain rate and in triaxial creep tests.