[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.

A theoretical framework is defined that allows plasticity and damage models of inelastic behaviour to be combined within a consistent approach. Much emphasis is placed on the fact that, within this framework, the entire constitutive response is specified through two potential functions, with no additional assumptions or evolution equations being necessary. Both plastic strain and damage parameter have roles as internal variables within the theory. Two classes of models are derived: involving respectively uncoupled and coupled plasticity and damage. Examples of application of the theory are presented. Crown

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SUMMARYThe development of a coupled damage-plasticity constitutive model for concrete is presented. Emphasis is put on thermodynamic admissibility, rigour and consistency both in the formulation of the model, and in the identification of model parameters based on experimental tests. The key feature of the thermodynamic framework used in this study is that all behaviour of the model can be derived from two specified energy potentials, following procedures established beforehand. Based on this framework, a constitutive model featuring full coupling between damage and plasticity in both tension and compression is developed. Tensile and compressive responses of the material are captured using two separate damage criteria, and a yield criterion with a multiple hardening rule. A crucial part of this study is the identification of model parameters, with these all being shown to be identifiable and computable based on standard tests on concrete. Behaviour of the model is assessed against experimental data on concrete.

We develop a constitutive model for rocks that are constituted from brittle particles, based on the theory of breakage mechanics. The model connects between the energetics and the micromechanics that drive the process of confined comminution. Given this ability, our model not only describes the entire stress-strain response of the material, but also connects this response to predicting the evolution of the grain size distribution. The latter fact enables us to quantify how the permeability reduces within cataclasite zones, in relation to aspects of grain crushing. Finally, our paper focuses on setting a framework for quantifying how the energy budget of earthquakes is expensed in relation to dissipation events in cataclasis. We specifically distinguish between the dissipation directly from the creation of new surface area, which causes further breakage dissipation from the redistribution of locked-in stored energy from surrounding particles, dissipations from friction and from the configurational reorganisation of particles.

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A new formula is proposed for the end-bearing capacity of piles penetrating into crushable soils. The formula is based on a breakage mechanics model that accounts for the evolution of the grain size distribution (GSD) due to grain crushing with only physically meaningful parameters. The model is integrated using the finite-element method to study the penetration problem. Predictions of GSDs surrounding piles and pile end-bearing capacities are validated against experiments. Next, a parametric study is carried out to quantify the effects of grain crushing on the bearing capacity, and then to establish the formula. The predictive capability of the new formula is highlighted against predictions by previous formulae, which highlights its superior origins.

Localised failure of geomaterials involves deformation at two scales: a narrow localisation zone and the surrounding bulk. The behaviour associated with both scales should be properly taken into account in the development of constitutive models. This article presents a general constitutive modelling framework to connect these two scales, each of which is associated with a different stage of the material behaviour. It is demonstrated how this approach can be applied to any geomaterial model and how it could help obtain solutions independent of the spatial discretisation in numerical analysis.