[1] Grain crushing and pore collapse are the principal micromechanisms controlling the physics of compaction bands in porous rocks. Several constitutive models have been previously used to predict the formation and propagation of these bands. However, they do not account directly for the physical processes of grain crushing and pore collapse. The parameters of these previous models were mostly tuned to match the predictions of compaction localization; this was usually done without validating whether the assigned parameters agree with the full constitutive behavior of the material. In this study a micromechanics-based constitutive model capable of tracking the evolving grain size distribution due to grain crushing is formulated and used for a theoretical analysis of compaction band formation in porous rocks. Linkage of the internal variables to grain crushing enables us to capture both the material behavior and the evolving grain size distribution. On this basis, we show that the model correctly predicts the formation and orientation of compaction bands experimentally observed in typical high-porosity sandstones. Furthermore, the connections between the internal variables and their underlying micromechanisms allow us to illustrate the significance of the grain size distribution and pore collapse on the formation of compaction bands.

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This paper explains why the critical state of sand is non-unique when expressed in terms of stress and void ratio only. For this purpose, a thermodynamically consistent, micromechanically inspired constitutive modelling framework with competing grain crushing and dilation is developed. While grain crushing is described through the theory of breakage mechanics, dilation is modelled in a novel way by acknowledging its negative contribution to the overall positive rate of dissipation. The competition between dilation and grain crushing underpinned by this framework yields a unique critical state in a space of stress, void ratio and breakage, in agreement with recent experiments. As an example, a simple constitutive model with only five mechanical parameters is proposed, which not only predicts the critical state but also quantitatively connects the full constitutive behaviour to key index properties related to grading- and breakage-dependent minimum and maximum densities.

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[1] We analyze the propagation of compaction bands in high porosity sandstones using a constitutive model based on breakage mechanics theory. This analysis follows the work by Das et al. [2011] on the initiation of compaction bands employing the same theory. In both studies, the theory exploits the links between the stresses and strains, and the micromechanics of grain crushing and pore collapse, giving the derived constitutive models advantages over previous models. In the current post localization analysis, the bifurcation instability of the continuum model is suppressed by the use of a rate-dependent regularization. This allows us to perform a series of finite element analyses of drained triaxial tests on porous sandstone specimens. The obtained numerical results compare well with experimental counterparts, in terms of both the initiation and propagation of compaction bands, besides the macroscopic stress-strain responses. On this basis, a parametric study is carried out to explore the effects of loading rate, degree of structural imperfections, and confining pressure on the propagation of compaction bands.