Cascade continuum micromechanics model for the effective permeability of solids with distributed microcracks: Self-similar mean-field homogenization and image analysis

The transport and fluid flow in heterogeneous materials such as rocks, ceramics and concrete with a distributed random microcrack network is strongly influenced by the density and the topology (distribution and connectivity) of microcracks. The overall fluid flow characteristics of such microcracked solids can be quantified in terms of an effective permeability. In the paper, a semi-analytical formulation for the effective permeability is proposed within the framework of the mean-field homogenization method using the cascade continuum micromechanics model considering long range and short range interactions. We compare model predictions of the percolation threshold i.e. critical volume fraction of microcracks beyond which a solid with distributed microcracks becomes permeable, using results from numerical simulations. The model reveals a new perspective into the self-similar characteristics of the microcrack morphology near the threshold volume fraction of microcracks at which the microcrack structure changes from multiple disconnected microcracks to a connected self-similar microcracked structure.