A simplified relationship between the zero-percolation threshold and fracture set properties

Abstract. Percolation analysis is an efficient way of evaluating the connectivity of discrete fracture networks. Except for very simple cases, it is not feasible to use analytical approaches to find the percolation threshold of a discrete fracture network. The most commonly used percolation threshold corresponds to the occurrence of percolation on average for the set of parameters (p50), which is not adequate for applications in which a high confidence in the percolation threshold is required. This study investigates the direct relationships between the percolation threshold at low probability (p0, referred to as zero-percolation threshold) and the properties of fracture networks with one set of fractures (fractures with similar orientations) in two-dimensional domains. A generalized non-linear multivariate relationship between p0 and fracture network parameters is established based on connectivity assessments of a significant number of numerical simulations of fracture networks. A feature of this relationship is the invariant shape of marginal relationships. A comparison study with an analytical solution and applications in both synthetic and real fracture networks shows that the derived relationship performs well in fracture networks of different sizes and orientations. A significant benefit of this relationship is that, when an analytical solution is not available, it can provide fast and reliable connectivity statistics of fracture networks based only on fracture parameters.