A Constitutive Theory for Sand and Its Application

The objective of the research is to examine the deformation mechanisms of sand, to study the changes, both isotropic and anisotropic, in the mechanical properties of sand associated with any stress history, which includes consolidation history where large deformation is involved, and to describe the effects of these changes in mechanical properties on the response of sand to any loading along any perceivable stress path. A constitutive theory, with its emphasis to reveal the principles of anisotropy of soil, is proposed. The theory predicts existence of critical states--- ultimate states of perfect plasticity. A philosophical model and a practical engineering model are derived from the basic constitutive theory. Both models are built up in stress and strain tensor spaces in order to model soil behaviour under completely general stress and strain conditions from the interpretation of the results of conventional testing, to reflect the development of anisotropy, and to be capable of describing soil behaviour under all imaginable stress paths. The philosophical model is verified qualitatively and quantitatively. The capabilities of the model are demonstrated by predicting commonly observed soil characteristics, especially those greatly influenced by deformation and stress history. Comparisons between the predictions and experimental results are made and analysed; the model is evaluated based on these comparisons. The engineering model has also been formulated. This dissertation is divided into the following four parts. In part I -Review of Constitutive Modelling of Soil - , previous research work in both experiment and theory is discussed and achievements in both research areas are reviewed. Mechanical properties of soil are revealed from experimental data, and deficiencies of the theoretical modelling of soil behaviour are discussed. With the development of new testing methods and the wide area of engineering operation, consistent formulations of a philosophical model and a practical engineering model are increasingly necessary. In part II - A Critical State Constitutive Theory for Sand - , a constitutive theory is proposed. There are three basic assumptions: (1) Sand is assumed to be an isotropic material, but can be in anisotropic state. The deviation of the current state from isotropic reference states results in anisotropic properties of sand. (2) Deformation of sand is associated with the change of stress state and is attributed to two factors: the effect of stress level change and the effect of stress ratio change. (3) Both isotropic and anisotropic properties of sand depend on stress history: i. e. a change in stress state generally induces changes in mechanical properties. The concept of limit surface, which is influenced by anisotropy and state parameter, is introduced. Both peak strength and critical state strength are dependent on the limit surface. The two typical patterns of sand behaviour, i. e. the behaviour of dense sand and that of loose sand, and their transition are dependent on the stability condition of the limit surface. The forms of the yield surface and the subsequent yielding boundary, which govern the behaviour of soil under stress ratio yielding, are distinguished and investigated in a modified five dimensional deviatoric stress vector space. The formation and development of induced anisotropy are studied based on the two concepts; and three different types of deformation mechanisms are identified and associated with the variation of the yield surface and the boundary. A general flow law is theoretically formulated whih incorporates the different principles governing volumetric strain and distortional strain and describes the influence of induced anisotropy and inherent anisotropy. In part III -A Philosophical Model -, the philosophical model is theoretically formulated from the proposed constitutive theory with experimental observations. Some of the basic features of the model are illustrated. Parameters required by the model are analysed, and all parameters can be determined from conventional triaxial tests on samples specially prepared. The extraction of the parameters from conventional tests is described. Predictions made using the proposed model for tests performed by various researchers with different apparatuses, probing soil behaviour in different parts of the stress tensor space with and without rotation of the principal axes, are carried out. Analysis of the predictions is given in detail, and the performance of the model is evaluated. The achievements of the philosophical model are summarized and further research is suggested. In part IV ---An Engineering Model--- (Appendix A), a practical engineering model is deduced from the basic postulates of the constitutive theory and the performance of the philosophical model. There are seven parameters for the engineering model and all the parameters can be determined from conventional triaxial tests. The procedure for the selection of numerical values for these parameters is illustrated