Percolation conditions in fractured hard rocks: A numerical approach using the three-dimensional binary fractal fracture network (3D-BFFN) model

We numerically investigate fracture connectivity and percolation conditions in fractured hard rocks using a three-dimensional binary fractal fracture network (3D-BFFN) model based on three fractal geometric parameters: the fractal dimensions (D-2) of the spatial distribution of fractures, the exponent of the power-law cumulative fracture length distribution (a), and the maximum fracture length (l(max)) normalized by the domain length (L), l(max)/L. Numerical results clarify that the percolation threshold in 3D-BFFN models is strongly controlled by fractal geometric parameters and is independent of any anisotropy in the orientations Theta. In addition, when a < 1.8 and l(max)/L < 1.0, percolation seldom occurs independently of D2 and Theta. In the current study the analytical solution of percolation probability (P) is presented as a function of the three fractal parameters within the 3D-BFFN model. Application of the 3D-BFFN model to seismogenic fractures determined from the earthquake catalogue in an offshore volcanic region between Miyake-jima Island (MI) and Kozu-shima Island (KI) off the Izu Peninsula, Japan, suggests that P is mainly affected by the error involved in determining a during actual surveys. Otherwise, P provides a useful index for determining whether a three-dimensional domain percolates in fracture networks in fractured hard rocks. The basis of this approach is the observation from fracture network connections that domains with P > 0.55 are percolated domains. The zone of percolation within seismogenic fracture networks between MI and KI reveals that the networks formed from seismic-swarm-related seismogenic fractures over a 7-week period related to the intrusion of a dyke, inferred previously from seismicity and deformation data.