Effective Elasticity of Rocks with Irregularly Shaped and Intersecting Cracks

A circle is the basic fracture shape adopted by conventional effective media theories to<br>describe the overall elasticity of cracked solids. As fractures in rocks do not resemble circles, it is important to find out to what extent the available theoretical results are applicable 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<br>partially closed and might intersect each other.<br><br>Despite profound deviations of our fracture geometries from circles, we find that the theoretical results originally developed for penny-shaped cracks remain valid for a wide variety of irregular planar fractures. Based on a series of finite element computations, we show the following: <br>(1) As far as the effective elasticity is concerned, fractures with random in-plane irregularities are accurately represented by the circular ones.<br>(2) Approximate effective elliptical orthotropy established for multiple sets of dry,<br>non-intersecting, penny-shaped cracks embedded in otherwise isotropic host rock also<br>holds for irregular, possibly intersecting fractures.<br><br>In essence, our findings show that the theories developed for penny-shaped fractures can be applied with confidence to cracks in real rocks.<br>