Continuum modeling of the effect of surface area growth due to crushing and damage on the permeability of granular rocks

This paper discusses a continuum approach to track the evolution of permeability in granular rocks by accounting for the combined effect of porosity changes, grain breakage and cement bond damage. To account for such a broad range of microscopic processes under general loading paths, the Breakage Mechanics theory is used and the computed mechanical response is linked with the Kozeny equation, i.e. a permeability model able to evaluate the reduction of the hydraulic conductivity resulting from the simultaneous loss of porosity and growth of surface area. In particular, the evolution of the internal variables of the model has been linked to idealized geometric schemes at particle scale, with the goal to distinguish the contribution of the fines generated by the disaggregation of the cement matrix from that of the broken fragments resulting from the crushing of the skeleton. Compression/flow experiments available in the literature for different granular rocks are used to validate the proposed methodology. The analyses illustrate that the drop of the permeability of damaged rocks would be severely underestimated without an accurate computation of the growth of surface area, as well as that the distributed fragmentation of skeleton particles tends to have stronger implications than the generation of cement fines. These findings, along with the satisfactory agreement between model predictions and experiments, stress the benefits of adopting microstructure-based constitutive laws for the analysis of coupled hydro-mechanical problems.