Micromechanical Approach to Nonlinear Poroelasticity: Application to Cracked Rocks
Résumé
This paper considers a saturated porous medium in which the matrix is a cracked solid. Progressive crack closure is responsible for an overall nonlinear poroelastic behavior. The state equations of nonlinear poroelasticity are derived in a differential form within a micromechanical framework. When a hydraulic connection exists between the cracks and the pores of the porous space, the tangent drained stiffness tensor as well as the tangent Biot tensor and modulus are shown to depend on Terzaghi effective stress. Estimates for these coefficients as functions of Terzaghi effective stress are then derived with the tools of homogenization for disordered media. They are based on a crack closure criterion giving the condition for a crack to be closed under a given macroscopic stress state, depending on its aspect ratio. In the case of an isotropic orientation of cracks, it is shown that the influence of cracks on the overall poroelastic properties is governed by the crack density parameter which characterizes the distribution of aspect ratios. Conversely, an experimental methodology for the determination of the distribution of aspect ratios from the measurement of the macroscopic compliance is proposed.