Interaction between a fracture network and a cubic cavity.

The intersection between a network of polygonal fractures and a cubic cavity is numerically studied. Several probabilities are defined and particular attention is paid to the probabilities of intersection or not of the percolating cluster with the cavity; they depend on the size of the domain, on the fracture density, and on the relative size of the fractures and of the cavity. These probabilities are extrapolated to infinite domains. Analytical approximations are proposed which are in good agreement with the numerical data for sufficiently large densities. Some extensions of practical and theoretical interests are given in the concluding remarks.