Percolation of three-dimensional fracture networks with power-law size distribution

Abstract

The influence of various parameters such as the domain size, the exponent of the power law, the smallest radius, and the fracture shape on the percolation threshold of fracture networks has been numerically studied. For large domains, the adequate percolation parameter is the dimensionless fracture density normalized by the product of the third moment of fracture radii distribution and of the shape factor; for networks of regular polygons, the dimensionless critical density depends only slightly on the parameters of radii distribution and on the shape of fractures; a model is proposed for the percolation threshold for fractures with elongated shapes. In small domains, percolation is analyzed in terms of the dimensionless fracture density normalized by the sum of two reduced moments of the radii distribution; this provides a general description of the network connectivity properties whatever the dominating percolation mechanism; the fracture shape is taken into account by using excluded volume in the definition of dimensionless fracture density.