Cascade Continuum Micromechanics model for the effective permeability of solids with distributed microcracks: Comparison with numerical homogenization

The effective permeability of microcracked heterogeneous materials such as rocks, ceramics and concrete can be determined using analytical and computational homogenization methods. While in the companion paper (Timothy and Meschke, 2017) a semi-analytical Cascade Continuum Micromechanics (CCM) model is proposed to predict the effective permeability and the percolation threshold for porous materials with microcracks, the focus of this paper is to validate the CCM model by means of direct numerical meso-scale simulations of representative elementary volumes concerned with water flow through porous materials. Algorithms are developed to generate overlapping and non-overlapping microcrack morphologies within the framework of the finite element method to analyse the effective permeability as a function of the microcrack volume fraction. The numerical results confirm the predictions from the CCM model for different scenarios, including a low and high permeable matrix and different microcrack morphologies, both qualitatively as well as quantitatively. It is also shown, that in computational homogenization procedures, the effective permeability around the percolation threshold is strongly dependent on the discretization of the numerical REV.