Modeling some elastoplastic aspects of failure in granular materials using a discrete element approach
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2007
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Abstract
In this dissertation, the discrete element method is used to examine some fundamental issues in the failure of granular materials. First, the discrete element model is 'calibrated' and the influences of various micro-parameters on the macroscopic constitutive behaviors of granular materials are discussed. Typical shearing tests in geotechnical engineering, such as drained compression, undrained shearing, and imposed strain path tests are numerically conducted to verify the predictive capability of the discrete element method. Stress dilatancy is an important phenomenon which is a major driver in characterizing granular material behavior. In this thesis, the discrete element model was 'calibrated' to capture the dilatancy phenomenon and the ensuing micro-parameters were used to verify a modified stress dilatancy model based on continuum and elastoplasticity theories. True triaxial shearing tests are numerically conducted to construct various failure contour levels in the deviatoric (1r) plane, and as such Lade-Duncan (1975) failure criterion was recovered. In the classic elastoplasticity theory, it is postulated that the direction of incremental plastic strains developed during plastic deformations depends only on the stress state, and not on the loading direction, which refers to a so-called regular flow rule in the mathematical sense. In this research, discrete element simulations involving directional loadings in the form of spherical probes in the principal stress space demon rate that such a regular flow rule exists only in 2D configurations. In general 3D stress and strain conditions, the postulate of regular flow fails, given that the incremental plastic strain response depends not only on the stress state, but also on loading directions. Stability is another important notion that is ubiquitously used in the realm of soil mechanics and by geotechnical engineers, but unfortunately not in the proper mechanical sense as its interpretation is in fact a misnomer. Instability or stability here refers to a material phenomenon as a result a wide range of bifurcations, namely homogeneous (diffuse failure such as in liquefaction) and non-homogeneous (localized failure in the form of shear, compaction and dilation bands) types. It has been found for a long time that the instability associated with diffuse failure can occur within the Mohr-Coulomb failure surface, thus questioning the very definition of failure. In this research, Hill's stability criterion which transcends Lyapunov's early works was used to examine the material stability issue in granular material behavior. Circular stress probes in the Rendulic plane have been used to investigate the range of loading directions for which the material behavior is unstable, as signalled by a negative second order work. While the topics addressed herein may seem to be theoretical in nature and their treatment futile, the clarification of various failure notions through the use of discrete element simulations goes a long way toward enhancing the predictive capabilities of different classes of elastoplastic theories in modeling the incremental nonlinear behavior of granular materials where the particulate aspect is of paramount issue. In fact, many geomechanics processes inextricably implicate a particulate system in which particles are being lost or gained by either way of fluid flow or mechanical loading.
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Bibliography: p. 157-168
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Li, Q. (2007). Modeling some elastoplastic aspects of failure in granular materials using a discrete element approach (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/1368