Double-scale FEM modelling applied to clay rocks

A number of natural materials involved in geotechnical and geological applications present heterogeneities over a wide range of scales. How the microstructural characteristics of such materials can be taken into account in models of their macroscale deformation is a question that has received considerable interest in recent years. Here, the clay rock that constitutes the bedrock of boring sites is studied. Clay rocks are a mixture of quartz, pyrite and carbonates inclusions embedded in a permeable clay matrix. They are therefore heterogeneous from the millimetric to the macroscale, which impacts their mechanical response when constrained. A double-scale Finite Element approach is taken to model numerically this response that represents the micro-structure of clay rocks over a representative element. This microstructure is formed of solid, deformable grains and permeable interfaces. In such model, no constitutive law is prescribed at the macro-scale, but is instead obtained from numerical homogenization of the microscale solution, thereby allowing to infer the effect of microstructural heterogeneity on larger scales. Two-dimensional, coupled hydro-mechanical simulations of the compression of pre-constrained clay rock samples are conducted in which microstructures of different mineralogy (i.e., several different representative elements) are combined to induce some heterogeneity at the macroscale, which represents parts of the rock with different proportions of mineral inclusions. This macroscopic heterogeneity is introduced both in a random and in a structured manner to represent the absence or present of some stratification of the bedrock. Its effect on the localization of the deformation and rock permeability is investigated.