Constitutive modelling of the elastic–plastic, viscoplastic and damage behaviour of hard porous rocks within the unified theory of inelastic flow
Résumé
This article presents a constitutive model for the elastic-plastic, viscoplastic and damage behaviour of hard porous rocks. The main hypotheses of the model are based on a large set of experimental data which are also presented in the paper. This constitutive model is of the over-stress type and is formulated within the unified theory of inelastic flow. An energy-based failure surface was considered to describe both short- and long-term behaviours within the same formulation. The inelastic yield surface is of static nature while the failure and damage surfaces are of dynamic nature. The kinetic law is written in terms of internal state variables that allow the description of how the frictional and the cohesive internal strengths of the material evolves. The reversible inelastic behaviour is also modelled using the ``under-stress'' concept, and considering that, it depends explicitly on the locked energy during the inelastic flow. In addition, this model is adapted to the porous nature of rocks such as iron ore that exhibit strong volumetric deformations and mean stress dependence. A large fraction of the volumetric straining is explained by damage mechanisms that also allow the accelerated creep to be modelled. Model parameters can easily be identified in the laboratory with commonly used mechanical tests. The constitutive model was implemented in a numerical code, and some qualitative simulations and comparisons with experimental curves showed the suitability of the model to reproduce both short- and long-term behaviours of porous rocks similar to iron ore.