Analyses of simulated plane shear flows of cohesionless and cohesive granular materials

Granular materials behave differently depending on whether they are in rapid flow or are slowly deforming. Most notably, a constitutive model exists for rapid flows that allows their behavior to be predicted based on particle properties, whereas no such model exists for slow, quasi-static flows. The work detailed in this thesis was performed to investigate the important characteristics of quasi-static shear flows of granular materials, both to obtain a better understanding of such flows and to lay the groundwork for the future formulation of a constitutive model. Particular interest was paid to cohesive materials as their behaviors during flow have not been thoroughly analyzed up until now and they generally only exist in quasi-static flows.;To accomplish this task, simulations of assemblies of cohesive and non-cohesive, monodisperse, spherical particles under shear were performed. In these simulations, cohesion arose from the van der Waals force acting between particles. Three main types of shear were simulated: steady shear at constant volume, steady shear under a constant applied stress, and unsteady shear at constant volume. A number of statistics were gathered from these simulations to quantify the assemblies' behaviors, including their stress, solid volume fraction (when it was not held constant) and microstructure information. A variety of system and particle properties were sampled and the dependencies of the flow characteristics on these properties were found. Based on this analysis, the steady-state properties of cohesive materials were determined and the responses of cohesionless and cohesive systems to unsteady quasi-static flow were identified.;The steady-state behaviors of both cohesionless and cohesive materials are shown to not actually depend on whether shear occurs at constant volume or under a constant applied stress. A significant result from the simulations is that the effect cohesion has on the time-averaged behavior of granular assemblies increases as the systems become less dense. At the highest volume fractions, cohesionless materials exist in the quasi-static regime, where for a given volume fraction the steady-state stress is independent of shear rate. If cohesion is added to these systems, they continue to exist in the quasi-static regime and the mean stress is virtually unchanged. At lower volume fractions, cohesionless materials tend to exist in the inertial (rapid flow) regime, where the stress scales with the square of the shear rate. On the other hand, cohesive materials at these volume fractions tend to exist in the quasi-static regime, but unlike the quasi-static regime at higher volume fractions, the stress here scales with the strength of cohesion. Furthermore, at these lower volume fractions the shear rate required to escape the quasi-static regime increases with cohesive strength and decreasing solid volume fraction.;Another significant result is that the apparent coefficient of friction, i.e. the ratio of the shear stress to the normal stress, proves to have a systematic dependence on the volume fraction and is a strong function of volume fraction when the particles are cohesive, contrary to the usual assumption used in continuum models that it is independent of volume fraction.;Analyses of the fluctuations in stress and volume observed during shear are also presented. Whether shear is performed at constant volume or under constant applied stress naturally affects these fluctuations during shear, but cohesion is shown to also have a strong influence. The normal stress fluctuations for systems sheared at constant volume can be quite large, whereas the volume fluctuations during shear under constant applied stress are observed to be very small. Furthermore, the shear stress fluctuations are smaller when shear occurs under a constant applied stress. However, regardless of the type of shear, cohesion reduces the relative sizes of the shear stress fluctuations.;Finally, the behavior of granular assemblies subjected to unsteady shear is described. The controlling factors behind a system's response are shown to be whether or not shear is reversed and the microstructure, as measured by the fabric tensor. When shear does not reverse direction, the response is virtually instantaneous. On the other hand, when shear reverses direction, the mean particle contact orientation must rotate by 90°, resulting in the stress evolution to last a strain on the order of unity. The exact strain required for the stress to evolve is governed by the microstructure at the moment shear reverses direction and is rate-independent. As such, it is suggested that the constitutive model for quasi-static flows needs to incorporate the microstructure in some manner and to predict rate-independent behavior.