Topology, connectivity and percolation in fracture networks

Abstract

The connectivity of a fracture network depends on both its geometry and topology, which may be characterized in terms of the types of nodes and branches in the system. A number of dimensionless parameters (dimensionless intensity (P22, B22), connections per line (CL) and connections per branch (CB), are used to characterize and assess network connectivity based on well-established lattice and continuum percolation models. These models result in networks with only I- and X-nodes, whereas most natural fracture networks have many Y-nodes. A simple scheme to transform IX systems into IYX systems is developed that allows the expected value of dimensionless branch intensity (B22C) at the percolation threshold to be derived for any network topology. The method is used to assess if a network is likely to be connected or not, and demonstrated by analysing the development of a network of desiccation cracks.