Classification of fracture patterns by heterogeneity and topology

Fracture patterns arise abundantly in natural and engineered systems, and their geometries depend on material properties and on the ways in which the material is deformed or forces act on it. Two-dimensional fracture patterns can be characterized by their network topology (how fractures connect to each other) and their heterogeneity (whether fractures appear clustered or uniformly distributed in space). We propose a generic model in which the topology can be adjusted by controlling the ratio between the number of dead ends and the number of junctions in the fracture network, and heterogeneity can be adjusted by biasing fracture nucleation to occur near or away from existing fractures. Based on this model we propose a characterization scheme for natural fracture systems and provide and demonstrate an algorithm for recovering model parameters from fracture pattern images.