Branching of Cracks That Spread in Rocks

Abstract

We study dynamics of cracks that appear in rocks under hydraulic fracturing. Usually, such cracks are modeled as spreading two-dimensional surfaces. However, many reasons e.g. presence of pre-cracks may cause bifurcations of cracks, namely their branching. This phenomenon completely changes the dynamics of fracturing. It is extremely important in modeling extraction of petroleum and caused ecological consequences. To create the mathematical model of such branching, we combine recently developed methods of Dynamical Systems with classical methods of Fracture Mechanics. We demonstrate possible applications of obtained results in modeling dynamics of ecological systems.