Cascade lattice micromechanics model for the effective permeability of materials with microcracks

Within the framework of mean-field homogenization methods, a lattice version of the cascade micromechanics model for the estimation of the effective permeability of microcracked materials with a physically consistent percolation threshold is proposed. Also, a link is investigated between the cascade scheme, self-similarity, and critical phenomena. The cascade lattice micromechanics model is compared with the dilute, the Mori-Tanaka and the self-consistent lattice schemes and validated by means of numerical experiments using a computational lattice microcrack-pore network model. Different scenarios of the microcrack probability and the permeability contrast between the pore channels and the microcracks are investigated.