Permeability enhancement due to microcrack dilatancy in the damage regime

Abstract

A three dimensional microscopically based permeability model incorporating inelastic deformation has been developed to account for the modification of transport properties due to fracturing. The basic hypothesis investigated is that permeability enhancement during brittle deformation is caused by the formation of dilatant microcracks which are associated with friction sliding on a preexisting random population of shear cracks. Additional dilatancy, produced as a result of frictional sliding over asperities, is also accounted for by the introduction of a crack roughness parameter. Linear elastic fracture mechanics is used to calculate the evolution of crack length and crack area as a function of applied stress and fluid pressure. After making a geometrical simplification the microcrack parameters derived from the deformation model can be used to calculate the permeability tensor assuming that fluid transport results from Poiseuille flow through a connected distribution of cracks. The model enables investigation of the macroscopic permeability variation as a function of two loading parameters, three constant material parameters, and the crack roughness parameter. Results demonstrate that permeability is a smooth but strongly increasing (near power law) function of the Terzaghi effective stress ratio and is strongly dependent on the initial crack density, Young's modulus, the friction coefficient, and the effective confining pressure. Numerical results are in quantitative agreement with published experimental measurements and display behavior similar to results obtained with a relatively simple analytical model. The model enables calculation of the degree of stress‐induced anisotropy, which is shown is be relatively small (< × 10) for resonable effective stress ratios. The modeling presented provides a quantitative tool with which the effects of microcrack‐induced permeability enhancement can be investigated within the broader context of coupled fluid flow and brittle deformation in the crust.