A thermomechanical approach to constitutive modeling of geomaterials

Abstract

Modeling of the mechanical behavior of geomaterials is a fundamental yet very

difficult problem in geotechnical engineering. The difficulty lies in that the

engineering behavior of geomaterials is strongly nonlinear and anisotropic,

depending on confining pressure, void ratio, stress history, and drainage conditions.

A traditional approach to the modeling of geomaterials is to formulate empirical

equations to fit experimental data. Generally, this approach is not able to provide

physical insights into the diverse responses observed in the soil mechanics

laboratories. Another conventional approach is to make use of the classical

plasticity theory, established mainly for metals, to develop constitutive models for

geomaterials. While this approach is capable of shedding light on the mechanisms

involved, it has been recognized that such models may violate the basic laws of

physics.

The objective of this thesis is to apply a new approach to constructing constitutive

models for geomaterials, by making use of thermomechanical principles. The

essence of the new approach is that the constitutive behavior of geomaterials can be

completely determined once two thermomechanical potentials, i.e. the free energy

and dissipation rate functions, are specified. The yield function and flow rule in the

classical plasticity theory can be established from the two potentials, and the

models so derived satisfy the basic laws of physics automatically. In this thesis, the

theoretical framework for constructing thermomechanical models is introduced.

Several concepts in relation to plastic work, dissipated and stored energy are

discussed. Both the isotropic and anisotropic models are formulated and realized in

this framework and the generated predictions are compared with the test data of a

series of triaxial compression tests on sand. To address the important density- and

pressure-dependent behaviors of sand in the framework, a state-dependent

thermomechanical model is developed, by introducing the state parameter into the

dissipation rate function such that a unique set of model parameters is able to

predict the behaviors of sand for a wide variation of densities and pressures. Finally,

a thermomechanical model for predicting the complex unloading and reloading

behaviors of sand is developed by modifying the hardening laws, and the

performance of this model is investigated.