Universal scaling solution for the connectivity of discrete fracture networks

Abstract

The connectivity of fracture networks is critical to the physical characterisation of rock masses and rock engineering, e.g. for the assessment of the performance of rock reservoirs. One way to predict the connectivity is to use the scaling solution of continuum percolation theory based on the renormalisation group. In this study, we create a large amount of discrete fracture networks (DFNs), based on various size distributions, in order to have a significant amount of data to evaluate universal relations. The Fisher distribution is also introduced to consider the orientational anisotropy. By appropriately defining the percolation parameter (i.e. dimensionless density), connectivity and characteristic length scale, we find that the critical quantities are fixed for different DFNs, and the scaling for connectivity of DFNs is universal. Additionally, the definition of characteristic length scale is altered and leads to better scalings, comparing with the classical definition in previous studies. The finding of this study shows great potential in applying the scaling solution to real fracture systems in the future.