Permeability of Microcracked Solids with Random Crack Networks: Role of Connectivity and Opening Aperture

Abstract

This paper investigates the permeability of microcracked porous solids containing 2D random crack networks. The past works on permeability of crack networks are firstly reviewed. The geometry analysis is performed on numerical samples of crack networks with different crack length distributions, crack densities, domain size ratios and clustering degrees. The parameters from continuum percolation theory are used to characterize the geometry of random networks including the percolation threshold, the scaling exponents for percolation probability and correlation length of crack clusters, and the fractal dimension of spanning clusters. The crack density is used as the basic percolation variable, and a new connectivity factor is proposed for the cluster spanning in finite domain. Then the effective permeability of porous matrix containing 2D random crack networks is analyzed on numerical samples via finite element method. A scaling law for effective permeability is established near the percolation threshold taking into account the matrix permeability, crack opening aperture, crack connectivity and tortuosity. The results from geometry analysis and permeability analysis show that: (1) The new connectivity factor is proved pertinent to network percolation, related to both crack density and crack clustering degree; (2) the percolation parameters of uncorrelated crack networks are rather near to the universal values from the continuum percolation theory, but their values change with the clustering degree of crack networks; (3) the numerical results confirm the scaling law proposed for effective permeability, and the permeability is found to scale with the crack opening through a power law.