POROELASTIC BEHAVIOR OF CRACKED ROCKS AS HOMOGENIZED MEDIA

The formulation of macroscopic poroelastic behavior of a cracked rock is investigated within the framework of a micro-macro approach. The micro-cracks are modeled as interfaces and their behavior is modeled by means of generalized poroelastic state equations. Starting from Hills lemma extended for a medium with cracks and extending the concept of strain concentration to relate the crack displacement jump to macroscopic strain, the overall poroelastic constitutive equations for the cracked 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 cracks are required for the macroscopic drained stiffness to entirely define the poroelastic behavior. This is achieved, for instance, if the crack network is characterized by a unique Biot coefficient. Extension of the analysis to non-linear poroelasticity is also outlined. Finally, the theoretical formulation is applied to a particular case of cracked rock for which explicit expressions of the overall poroelastic parameters are derived.