The deformation and failure properties of granular soils largely affect the stability of upper structures built on or in such soils. Owing to its discrete nature as well as the randomness of particle shape and inter-particle connectivity, the internal structure of a granular material usually exhibits a certain level of anisotropy. In addition, the microstructure of a granular material evolves following certain patterns, which are influenced by the initial fabric, void ratio, stress level, as well as the stress or deformation history. It has been a major challenge to properly describe the deformation of anisotropic granular materials in constitutive models especially when the materials are subjected to cyclic loading. The existing constitutive models usually have limited capabilities in describing the behaviour of granular materials subjected to repeated loading with principal stress rotation. How to quantify the microstructure change and how to consider the changing microstructure in constitutive models have been two missing links for building a comprehensive model framework.
This research aimed at developing a constitutive model that can properly describe the deformation of granular soils under repeated multi-directional loading. To achieve this goal, a systematic study was performed, including a comprehensive experimental study and a theoretical development of a stress-strain model with proper consideration of the influence of fabric. The developed model was verified with experimental results and then implemented into a finite element code to solve boundary-valued problems.
In the first part of this study, a comprehensive experimental study was carried out to investigate the behaviours of granular materials under both monotonic and cyclic loading to investigate the influence of the intermediate principal stress and the major principal stress direction on soil responses. The results of monotonic loading tests showed that both the strength and dilatancy of sand decreased notably with an increase of either the intermediate principal stress or the inclination angle of the major principal stress direction relative to the major principal fabric direction. The stress states at failure from the tests suggested that the benchmarked Matsuoka-Nakai and Lade-Duncan failure criteria are only valid under certain conditions. From the cyclic loading tests, it was observed that, in addition to the increased intermediate principal stress, varied cyclic loading direction caused a significant increase in accumulative volumetric compaction.
To consider the microstructural dependencies of granular materials, a more general mathematical formulation of stress-dilatancy was developed based on the assumption of the existence of a critical state fabric surface that is expressed as a function of the invariants of the fabric tensor. This assumption was also used to establish the fabric evolution law. The implementation of the resulting stress-dilatancy formulation and the fabric evolution law in elasto-plasticity theory produced interesting modelling results consistent with experimental observations with respect to the microstructural aspects of granular materials. The developed constitutive model was further extended to cyclic loading within the framework of hypo-plasticity with kinematic hardening. The model was capable of describing the behaviour of sand subjected cyclic loading under various conditions including the variation of loading directions.
Finally, the constitutive model was implemented into a commercial software package ABAQUS via the subroutine UMAT. The capacity of the proposed stress-strain model in solving boundary value problems was examined. Six series of elements tests were designed to examine the proposed model under different initial void ratios, degrees of anisotropy, loading directions, and stress paths. Furthermore, a series of simulations were performed for the settlement of footing on sands with different bedding plane orientations. Results from the simulations were found to be consistent with experimental observations. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/22888 |
| Date | January 2018 |
| Creators | Li, Xing |
| Contributors | Guo, Peijun, Civil Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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