Effect of crack density and connectivity on the permeability of microcracked solids

Abstract

In composite theory microcracks in solid are usually treated as degenerated inclusions separately embedded in matrix. For heterogeneous engineering composites like concrete and rock, the real cracking patterns are more complicate and quite different from this assumption due to the natural clustering and inter-connection of microcracks. This paper investigates the permeability of solids containing a crack network with finite connectivity following both theoretical and numerical approaches. Firstly, no connectivity is assumed for cracks and the interaction direct derivative (IDD) method is employed to obtain the crack-altered permeability of solids. Then the amplification of permeability by crack connectivity is quantified for parallel crack cases and for general crack patterns. This amplification effect is modeled by a crack length augmentation factor. In this way the IDD method is extended to evaluate the permeability of cracked solids for a finite crack connectivity before total percolation of cracks. Afterwards, by a carefully designed Monte-Carlo algorithm, the representative volume element (RVE) is built numerically for cracked solids with cracks having random spatial locations and random lengths. The permeability of 2D cracked solids is solved by finite element method (FEM). Through this numerical tool, the effect of both crack density and connectivity on the permeability is solved, and especially the relation between crack connectivity and the geometrical coefficient of crack clustering is put into evidence. From this study it is showed that the extended IDD method can be adapted to a microcracked solid with finite connectivity and can provide good estimates for the permeability.