Percolation conditions in binary fractal fracture networks: Applications to rock fractures and active and seismogenic faults

Abstract

The fracture network patterns in crystalline rock are treated using a binary fractal model described by three fractal geometric parameters: the fractal dimension D of the spatial distribution of fractures, the fractal dimension a of the fracture length distribution, and the maximum fracture length (lmax) normalized by the domain length (L), lmax/L. We present a percolation threshold relationship describing the boundary between percolating and nonpercolating conditions in random binary fractal fracture networks (RBFFNs) and apply this to observations of natural fractures. Our results indicate that the three fractal parameters identified indeed control the connectivity of fracture networks, and hence the migration of fluids through rock fractures, and active and seismogenic faults. Moreover, our numerical approach may be applied in the future to investigating fluid migration associated with seismicity based on fractal parameters determined from earthquake catalog data.