Adaptation of granular solid hydrodynamics for modeling sand behavior

Abstract

The development of constitutive models that can realistically represent the effective stress-strain-strength of the soil properties is essential for making accurate predictions using finite element analysis. Currently, most of the existing constitutive models are based on the framework of incrementally-linearized elasto-plasticity. However, most of these models do not typically consider energy conservation and are also phenomenological. This means that they can only be used to predict the behavior/ loading conditions for which they have been developed and that they often employ artificial mathematical formulations. This research proposes an improved constitutive model for sands based on the framework of Granular Solid Hydrodynamics [GSHJ. The GSH framework considers energy and momentum conservation simultaneously and, by combining them with thermodynamic considerations, develops constitutive relations for a given energy expression.

This thesis offers a detailed study of the element level behavior of the Tsinghua-Thermosoil model [TTSI (Zhang and Cheng, 2016) based on the GSH. Through this study, we identify and propose a series of modifications to the original formulation in order to improve predictions of well-established soil behavior. The proposed formulation, MIT-GH, introduces a new expression of the free energy and modifies the evolution laws and the steady state values for the internal variables. The model can successfully predict phenomena such as a unique compression response at high confining pressures (Limiting Compression Curve [LCC]) and at large shear strain conditions (Critical State Line [CSL]), and a State Boundary Surface [SBS] that limits the peak shear resistance measured in drained shear tests. The LCC and CSL conditions are defined solely from the evolution of elastic strains while the SBS is defined from the free energy expression.

Finally, our work also offers a novel use of the "double" failure mechanism -- inherent in the GSH framework. Using these mechanisms, MIT-GH can model not only Critical State conditions but also localization phenomena. The proposed criterion for the localization is the maximum expected peak friction angle that a specimen can develop at different void ratios and stress levels. This study also includes a detailed parametric analysis of the model and a proposal for the calibration of the model. The proposed MIT-GH model should be considered as a first generation formulation based on the principles of granular solid hydrodynamics and how it ties to classic knowledge of soil behavior and prior elasto-plastic models. Further research is now needed to extend the framework to address more complex features of sand behavior including the cyclic response and liquefaction.