Percolation properties of stochastic fracture networks in 2D and outcrop fracture maps

Percolation theory is widely used to analyze connectivity of fracture networks. The quantities commonly used to characterize fracture networks are the total excluded area, total self-determined area, and number of intersections per fracture. These three quantities are percolation parameters for the constant-length fracture networks, but no one has investigated them in complex fracture networks. We investigate variability of these three quantities in three types of fracture networks, in which fracture lengths follow a power-law distribution, fracture orientations follow a uniform distribution, and fracture center positions follow either a uniform distribution (type 1 and 2) or a fractal spatial density distribution (type 3). We show that in type 1 and type 2 fracture networks, these three quantities are percolation parameters only when the power-law exponent is larger than 3.5. In type 3 fracture networks, none of the three quantities are percolation parameters. We also investigate 16 outcrop fracture maps and find that these maps are closest to type 3 fracture networks. The outcrop fractures cluster and have lengths that follow power law distribution with the exponent ranging from 2 to 3.