Percolation and fracture

Abstract A statistical model of fracture, based on percolation theory, is presented which allows the quantitative evaluation of clustering of cracks in solids. Unlike models of branching processes which are more in accord with Griffith fracture, the concept of percolation lattices (finite and infinite) is used following from a physical model of multiple fracture. Some experimental results on acoustic emission, dilatancy and geophysical precursors of earthquakes can be correlated with the percolation fracture model. The model does not depend on the mechanism of crack formation, critical parameters being the number of elementary events (cracks), the dimensionality of the process and the coordination number for a network of cracks and, in finite systems, their specific size. Fracture prediction is possible from the number of elementary acts, cluster statistics and other characteristic parameters of the model. Possible applications of the percolation model for earthquake prediction are considered.