The influence of crack shape on the effective elasticity of fractured rocks

A circle is the basic fracture shape adopted by conventional effective media theories to describe the overall elasticity of cracked solids. Fractures in rocks do not resemble circles, so it is important to find out to what extent the available theoretical results apply to realistic fracture shapes. To address this issue, we conduct 3D numerical experiments on the so-called digital rocks containing irregular cracks that might be partially closed and might intersect each other. Despite profound deviations of our fracture geometries from circles, we find that basic theoretical results originally developed for penny-shaped cracks remain valid for arbitrary fracture shapes. Based on a series of finite-element computations, we show that as far as the effective elasticity is concerned, flat fractures with random in-plane irregularities are represented accurately by circular ones. We also show that approximate effective elliptical orthotropy established for multiple sets of dry, penny-shaped cracks embedded in isotropic host rock holds with the same accuracy for irregular, possibly intersecting fractures.