Thermomechanical modelling of sand

Abstract

The aim of this thesis is to develop a constitutive model of sand behaviour within the theoretical framework of thermodynamics. The main appeal of this modelling approach is that the theoretical basis of thermodynamics is well-established thus internal consistency within the model could be readily achieved. There is also the added advantage that we would be able to develop much deeper insight on the fundamental mechanics from the model outputs. This is in stark contrast with the traditional approach based on the theories of plasticity, which were originally developed to model the behaviour of metals. An exhaustive review carried out as part of this study provides a summary of our current understanding of sand behaviour along with its fundamental mechanics that were established from previous experimental researches. Key findings of this review include the difficulties of establishing the critical state line from experiments, the influence on stress-strain behavior from different sample reconstitution procedures, the distinction between different types of volumetric strain, and the overall frictional nature of sand behaviour. The two major ingredients in the thermodynamical modelling approach are the free energy function and the dissipation function. From the dissipation function we are able to determine a yield function using the so-called dissipative stresses, under which the normal flow rule is always followed. A key assumption in this thesis is that the free energy function is a function of the elastic as well as the plastic strains. The "plastic part" of the free energy is responsible for giving rise to the shift stresses, which when added to the dissipative stresses would give the true stresses. This allows us to express the dissipative yield function in terms of true stresses. A parametric study of the thermodynamical model was carried out and the model outputs were fitted with experimental data on Pakiri sand with satisfactory results. The fittings however show that the material behaviour is dominated by the internal kinematic constraints after the initial stage of the test. It has also been found that the use of a variable frictional parameter produces much more satisfactory model fits.