Micromechanical Approach to Poroelastic Properties of Cracked Rocks

Abstract

The formulation of macroscopic poroelastic behavior of a jointed rock is investigated within the framework of a micro-macro approach. Particular emphasis is given to the situation of small joints (i.e., cracks) with pressurized saturating fluid. The joints are modeled as interfaces and their behavior is modeled by means of generalized poroelastic state equations. Starting from Hill's lemma extended for a jointed medium and extending the concept of strain concentration to relate the joint displacement jump to macroscopic strain, the overall poroelastic constitutive equations for the jointed rock are formulated. The analysis emphasizes the main differences and similarities of the resulting behavior with respect to that characterizing ordinary porous media. It is shown that, unlike ordinary porous media, conditions on the poroelastic parameters of joints are required for the macroscopic drained stiffness to entirely define the poroelastic behavior. This is achieved, for instance, if the joint network is characterized by a unique Biot coefficient. A micromechanical scheme is then applied to derive analytically the homogenized poroelastic properties in two particular situations: a rock with a network of parallel cracks and the situation of isotropically distributed cracks and Extension of the analysis to non-linear poroelasticity is finally outlined. Validation of the model is made by comparison with finite element solutions based on the cohesive model for the joints.