Accounting for grain crushing and pore collapse for strain localization in rocks

Abstract

We present a model for crushable granular rocks by embedding breakage mechanics in the Cosserat continuum. This model features a dependence on an enriched set of state variables (the elastic strains and curvatures, the density, the solid fraction, and the breakage state variable), demonstrates a dependence of the yield surface on the Lode angle, breakage and solid fraction, and evolution laws that tightly couple the competing processes. We then outline the notion of linear stability analysis and how we use this technique to obtain both the thickness and orientation of any shear bands that may form in the system. The model is then calibrated from data available in the literature on Fontainebleau sandstone and other similar granular rocks. We compare the model predictions with experimental measures of both the stress-strain response, and the width and angle of shear bands, and find good agreement with the results that have been previously reported