Percolation on anisotropic media, the Bethe lattice revisited. Application to fracture networks

Abstract. A bond-percolation model based on the Bethe Lattice is presented. This model handles anisotropic and multiscale situations where, typically, the bond probability is non unique and depends on the sites it connects. The model is governed by a set of non-linear equations which are solved numerically. As a result, the structure of the network is obtained: strengths of the backbone, dead-end roads and finite clusters. Percolation thresholds and cluster sizes are also obtained. Application to fissured media is presented and random simulations of 3D distributions of fractures show the good accuracy of the model.