Effective elasticity of rocks with closely spaced and intersecting cracks

Abstract

The noninteraction approximation (NIA) is the simplest effective media theory that describes the overall elasticity of fractured rocks. If the NIA is used for fracture characterization, its accuracy and the range of applicability must be estimated. We do it by performing a series of 3D finite element simulations of effective elasticity for models that contain several sets of fractures embedded in otherwise isotropic host rock. We intentionally place the cracks close to each other to create strong interactions in their local stress fields. In addition, we allow the cracks to intersect in such a way that they do not break a rock specimen apart. Perhaps surprisingly, we find that fracture interactions and intersections have little influence on the effective elasticity, and the NIA performs well in all cases. While it has a tendency to slightly underestimate the effective stiffnesses, the incurred errors are small; their typical magnitudes are just a few percent in the entire range of the crack densities expected in naturally fractured formations. In our view, this makes the noninteraction approximation the method of choice for fracture characterization.