Constitutive modelling of progressive localised failure in porous sandstones under shearing at high confining pressures

Localised failure in porous sandstones under shearing at high confining pressure takes place gradually with a progressive development of discrete compaction bands and corresponding evolutions of degrees of grain crushing in these bands. This complex underlying governing mechanism results in cycles of stress drop and increase corresponding to the activation and deactivation of compaction bands. In this study, we develop a hierarchical constitutive structure that allows the modelling of this progressive localised failure at the material (constitutive) level. This capability is usually missing in classical continuum models, making them unable to track the material behaviour beyond the onset of localisation. The key feature of the development in this study is the enrichment of the constitutive strain fields for post-localisation analysis that distinguishes the responses inside and outside compaction bands. This enrichment creates more rooms for the embedment of localised failure mechanisms, instead of adding more parameters to improve the phenomenological behaviour of a model. As a result, compared to the homogeneous case, the enriched model possesses only an extra length parameter directly related to the width of a compaction band while having predictive capabilities to trace the activation and deactivation of several bands during shearing at high confining pressures.