Nguyen, Giang D.Mir, Arash2019-05-162019-05-162017http://hdl.handle.net/2440/119024Recent advances in computational mechanics and numerical simulation techniques enable more efficient and realistic geotechnical and mining designs and analyses. A successful numerical simulation requires a robust and rigorous constitutive model, which is capable of predicting the most fundamental features of material behaviour. In conjunction with numerical simulations, the complex behaviour observed in geomaterials also encourages the development of more capable and realistic constitutive models. The key aspects of developing constitutive models for rocks are to capture the essential features of rock deformation and failure, observed in experimental studies or in the field. These features include brittle behaviour, which refers to a sudden post-peak strain softening, ductile behaviour which is interpreted as the capacity for undergoing substantial inelastic deformation without gross fracturing and the transitional state between these two regimes of behaviour. Another important behavioural feature of rocks and also other geomaterials is the localisation of deformation within a narrow band. Upon the onset of localisation, the homogeneity of stress and strain fields is lost and any macroscopic definition of stress and strain is no longer physically meaningful. It is also essential for any constitutive model to be thermodynamically admissible. The focus of this study is on the development of thermodynamically consistent constitutive models for rocks. The development of the constitutive models is carried out within the framework of generalised thermodynamics to ensure the thermodynamic admissibility of the models. The key feature of the generalised thermodynamic framework is that the entire constitutive relations can be derived by explicitly defining two scalar functions, namely, an energy potential and a dissipation function. In this study, it is demonstrated that how the most fundamental mechanisms of deformation and energy dissipation can be incorporated into the model formulation by enriching the two thermodynamic functions with extra kinematic constraint equations. The theories of plasticity and continuum damage mechanics are also used to describe the mechanisms of energy dissipation and deformation. By adopting the thermodynamic approach, the coupling between damage and plasticity is specified in the formulation of the dissipation function, which is subsequently transformed (using a degenerate Legendre transformation) to a single generalised yield function. This method for coupling damage and plasticity facilitates the numerical implementation of the models as a single yield function controls the simultaneous evolution of damage and plastic strains. An important aspect of the coupled-damage plasticity models developed in this study is that, in accordance with experimental observations, the initial yield surface is transformed to a final failure envelope due to the evolution of the internal variables of the models. Owing to this feature of the models, rock mechanical behaviour under various stress states can be captured without any need for separately introducing hardening/softening rules into the model formulation. The constitutive models developed in this study are examined against experimental data from drained triaxial tests on rock specimens available in the literature. It should be noted that the localisation of deformation and the subsequent inhomogeneity of the kinematic field and stress redistribution give rise to the deterministic size effect problem. It is, therefore, inferred that experimental data from rock specimens are not merely representative of intrinsic rock material behaviour but are also influenced by the specimen size. Finite element (FE) simulations of cylindrical rock specimens are, therefore, carried out to study the specimen size effect on its overall mechanical response. Classical constitutive models are developed for a homogeneous representative volume element (RVE) without considering the features of localised failure and deterministic size effect. After the completion of model formulation, regularisation techniques, such as non-local or gradient enhancements, are employed to eliminate the numerical instabilities and ill-posedness of the boundary value problems (BVPs) caused by the localisation of deformation. These approaches, however, may lead to computational inefficiency, particularly, in large scale modelling applications. In this study, a thermodynamic approach is developed to model the localised deformation and failure of geomaterials in a rigorous and consistent manner. To this end, the underlying mechanisms of localised failure are described at the material level for a non-homogeneous RVE (an RVE containing a localisation band). Hence, the kinematic dependency between the two material phases beyond the onset of localisation is described by means of some kinematic constraint equations. Due to the direct incorporation of the essential mechanisms of localised failure in the constitutive equations, calibration and identification of model parameters can be carried out in a more consistent and physically meaningful manner. Additionally, introducing the features of localised failure at the material level can significantly reduce the cost of computation in large scale modelling applications in geotechnical and mining engineering.enThesis