Granular materials, such as sand, are systems consisting of huge numbers of particles that interact with each other through inter-particle contacts. Different from continuum materials, a granular material displays distinctive features due to the discrete nature of the microstructure, characterized by a spatial arrangement of inter-particle connection as well as a force-chain network. With a consideration of the contact force, the overall contact network is divided into a strong sub-network and a weak sub-network that carry contacts with normal contact forces larger and lower than the average normal contact force, respectively. Thus, the fabric anisotropy for different contact networks, are employed to characterize the microstructure of the granular material.
In this research, the behavior of granular materials subjected to quasi-static shear was extensively investigated in terms of the fabric evolution including the magnitude and direction of anisotropy for different contact networks. Both statistical and micromechanical approaches were adopted to obtain the macroscopic properties, such as the fabric tensor, Cauchy stress tensor and the second-order work, in terms of the micro-scale variables. The discrete element method (DEM) was employed to simulate laboratory tests along fixed loading paths; for example, 2D tests along proportional strain paths, 2D simple shear tests and 3D tests along radial stress paths on the π-plane.
Results demonstrated that the induced fabric anisotropy for the overall contact network can be related to the deviatoric stress ratio for both two-dimensional and three-dimensional conditions. The relation was found to be not unique, depending on the loading paths as well as the stress state. Nevertheless, a unique linear fabric-stress relation was presented between the stress tensor and fabric tensor for the strong sub-network. Specifically, the obliquity of this linear relation was found to be a function of the mean stress. This description held true for initially isotropic specimens subjected to proportional and non-proportional loading paths. On the other hand, for the initially anisotropic specimen, this correspondence only worked at the critical stress state.
According to Nicot and Darve (2006), the macro second-order work cannot be interpreted as a summation of the local second-order work from the contact plane. The second-order work induced by the fabric evolution and the volumetric change must also be taken into account. The second-order work induced by the fabric evolution cannot be neglected in 2D analysis along proportional strain paths. Moreover, the vanishing of the second-order work is related to the fabric anisotropy in contact sub-networks that the decrease of fabric anisotropy for the weak sub-network or the degradation of weak sub-network was observed to be an indicator of deformation instability even though the strong sub-network dominants the shear resistance. The degradation of strong sub-network was a necessary but not a sufficient condition of instability.
The direction of the fabric anisotropy for the strong sub-network was observed to be coaxial with the orientation of the principal stress. The principal direction of fabric anisotropy for the weak sub-network was always perpendicular to that of the strong sub-network, regardless of whether the principal stress rotated or not. For the overall contact network, however, the direction of the fabric anisotropy was not necessarily in line with the major principal stress direction, even for an initial isotropic granular assembly. Therefore, the finding by Radjaï et al.(1998) that the direction of the fabric anisotropy for the weak sub-network is perpendicular to that for the overall contact network only held true for the loadings in which the critical stress could be approached no matter if the principal stress orientation rotated or not. Under this circumstance, the fabric anisotropy for the overall contact network could be interpreted as a function of sub-networks’ anisotropy weighted by the ratio of contact number in each sub-network over the total number of contacts.
At critical state, both the strong sub-network and the overall contact network developed high fabric anisotropy with the weak sub-network being mostly isotropic. When plotted on the π-plane, both the fabric anisotropy for the strong sub-network and the fabric anisotropy for the overall contact network depended on the stress paths but were independent of the mean stress level. The response surface of the former could be expressed as a Lade’s surface. The response envelope of the latter was an inverted Lade’s surface. / Dissertation / Doctor of Philosophy (PhD) / In civil engineering, granular materials are ubiquitous, such as sand, gravel, rock, and concrete. Due to the discrete nature of microstructure, this type of material usually displays exceedingly complicated behaviours under shear, for example, dilatancy, non-coaxiality, critical state, instability, and anisotropy. These mechanical responses are notoriously difficult to model and most existing models are phenomenological and lack a clear physical meaning. To provide a clear physical meaning for the constitutive model of granular material, the current study explored the evolution of the microstructure within the granular material subjected to quasi-static shear and the micromechanical origins of those macroscopic behaviours such as critical state, non-coaxiality, and instability. Both micromechanical analysis and discrete element method were applied. Results showed that the evolution of the whole microstructure depended on the loading condition. However, the evolution of the microstructure joined by the ‘strong contacts’ was independent of the loading path. At critical state, the microstructure was highly anisotropic, not unique and depended on the stress paths. The rearrangement of the microstructure helped to maintain the stability of a granular material. The instability of the granular material was triggered by the failure of the microstructure joined by the ‘weak contacts’.
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/23382 |
| Date | January 2018 |
| Creators | Shi, Jingshan |
| Contributors | Guo, Peijun, Civil Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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