The thermomechanical framework applied to the development of constitutive models for clays : the novel TARC model

Abstract

The development of constitutive relations for clays has been one of the major focus of geotechnical engineers for over half a century. During this time, major developments in both the understanding and the modelling of clays have taken place. Probably the most commonly used and most important framework for understanding the behaviour of clays is the Critical State Soil Mechanics framework (CSSM), which laid the grounds for the development of the Cambridge models. However, important aspects observed for clays as experimental technological advances occurred made it clear that those models needed to be modified, which resulted in the presentation of numerous often complex models with many ad hoc expressions. The vast majority of these models are however known to violate the laws of thermodynamics. On the other hand, thermochemical-based models are far less popular in the research community and even more so among practitioner engineers. The research undertaken here aims to cover that gap by developing a thermomechanical-based model which not only satisfies laws of thermodynamics, covers advanced clays features, but also remains simple and most importantly its parameters are easily calibrated from commonly used experimental tests. During this development, two approaches under the thermomechanical framework have been studied and it was concluded that although the Cambridge models, and by extension all the models developed after them, initiated with some energy consideration. However, they omitted the stored energy, omission which becomes relevant when developing hardening models, as it is shown during the development of an anisotropic hardening model. Besides, the energy equations needed for development of the model, Free energy and Dissipation function, are not simply postulated but rather systematically developed. The study of stiffness non-linearity led to the development of the elastic component of the Free energy which introduces a simple stiffness matrix. This stiffness matrix considers a well-established shear stiffness–mean effective stress relation and implies the existence of stress-induced effects of the shear stiffness. The novel introduced model is termed the Thermomechanical-based anisotropic model for reconstituted clays (TARC) and has the capacity to connect the volumetric response with the evolution of anisotropy while keeping a volumetric dissipation function. Other features of the model are its ability to simulate anisotropic consolidation loads such as K0 consolidation, most clays natural loading history, to avoid dilative responses for normally consolidated states, to induce stress softening during undrained tests for normally consolidated states, and to reproduce the mean effective dependence of the elastic stiffness. Further, the model contains six commonly used parameters and introduces four new parameters, their calibration procedure is simple and is detailed in full. The model is compared to experiments conducted on Lower Cromer Till, a silty clay from the United Kingdom, and its strength and limitations are highlighted. Finally, based on the limitations of the model’s performance possible future developments are recommended.