An Algorithm for Generating Rock Fracture Patterns: Mathematical Analysis

A statistical, rule-based algorithm for generating fracture patterns similar to those observed in Limestone is presented. For each fracture set, initial seed points are randomly positioned within the modelled domain with the same density as the fractures observed in the field. An orientation is associated with each point by sampling from the distribution of orientations for the corresponding fracture set. Fractures are then allowed to grow from the seed points in both directions with this orientation until they meet other fractures whereupon they continue or terminate according to a fixed probability. A mathematical analysis of this method is presented for the case in which fractures within a set are assumed to be parallel. Approximations to the distribution of semi-trace lengths are derived which are shown to be in good agreement with simulation results. Fracture spacing distributions are also derived for this case.