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 P 22 B 22 connections per line C L and connections per branch C B 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 B 22C 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.