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

Abstract

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 (D2) of the spatial distribution of fractures, the exponent of the power‐law cumulative fracture length distribution (a), and the maximum fracture length (lmax) normalized by the domain length (L), lmax/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 Θ. In addition, when a < 1.8 and lmax/L < 1.0, percolation seldom occurs independently of D2 and Θ. 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.