Mesoscale Forces and Grain Motion in Granular Media Exhibiting Stick-Slip Dynamics: Effects of Friction and Grain Shape
An important challenge in the physics of granular materials is understanding how the properties of single grains, such as grain shape and friction, influence the mechanical strength and dynamical response of the bulk granular material. While spherical grains are often used to study granular materials in experiments and simulations, the interactions among grains, and in many cases the flow and stability of granular packings, change when grain shape is modified. In this dissertation, we explore the influence of friction and grain shape on grain-scale dynamics, properties of mesoscale force chains, and macroscopic stick-slip dynamics of granular materials through novel experiments. In one set of experiments, an intruder is pushed by a spring through an annular cell filled with a quasi-2D monolayer of photoelastic grains that either contact a glass substrate or float on water. We characterize the effects of basal friction between the substrate and grains, intergrain friction, intruder size, and grain shape on the dynamics of the intruder, the flow of grains during slip events, and spatial distribution of stresses within the granular material in stable sticking periods. In another set of experiments, a slider is pulled by a spring across a quasi-2D monolayer of gravity-packed grains set between two glass plates. We observe the influence of grain angularity on statistical properties characterizing the stick-slip dynamics of the slider as well as grain-scale dynamics and stresses.
We first compare the dynamics of the intruder driven through packings of disks that either contact the glass base -- having basal friction -- or float on water -- having no basal friction. At high packing fractions, we find that the intruder exhibits stick-slip dynamics when basal friction acts on the grains, but the intruder instead flows freely through the granular material, with only occasional sticking periods (called intermittent flow or clogging-like dynamics, quantified by the average time between sticking periods), when basal friction is removed. We also observe when basal friction is present that the intruder's dynamics transition from stick-slip to intermittent flow with decreasing packing fraction; this transition occurs at a higher packing fraction with lower intergrain friction. Lastly, in simulations that model this experimental system, we vary static and dynamic basal friction coefficients and show that dynamic basal friction, rather than static basal friction, determines whether the intruder exhibits stick-slip or intermittent flow at high packing fractions.
We next vary the size of the intruder and, at several different packing fractions for each intruder size, compute statistics of the waiting time between sticking periods, duration of sticking periods, energy released in slip events, and force of grains acting on the intruder. We show that each statistical measure for all intruder sizes collapses to a single curve when packing fraction is rescaled by the packing fraction below which the intruder carves out a completely open channel in the granular material. With a geometrical model, we relate the packing fraction of open channel formation to a characteristic packing fraction of the material and the ratio of the intruder's diameter and the width of the annular cell, and we confirm the prediction of this model.
We thirdly compare the dynamics of the intruder and grains with packings of disks and pentagons. We observe that the packing of pentagons exerts comparable forces on the intruder as the packing of disks, though at significantly lower packing fractions. We also find from the average flow fields of grains during slip events that disks circulate around the intruder and rotate about their centers of mass significantly more than pentagons, which tend to flow forward from the intruder. Lastly, using photoelasticimetry, for the packing of disks we measure a significantly larger spatial extent of stresses around the annular cell, and a significantly larger fraction of events that feature back-bending force chains, compared with the packing of pentagons.
In the last set of experiments, we vary grain angularity of a vertical (gravity-packed) granular material sheared by a slider. We observe that the average shearing force required to initiate slip events increases with angularity. As a result, sticking periods last longer and slip events release more energy in packings with more angular grains. We also observe differences in the flow fields of disks and angular grains in slip events; disks tend to form a pile in front of the slider, while other grains do not. Moreover angular grains are able to form local column-like structures at the surface of the bed that prop up the slider during sticking periods, while disks do not. We lastly show that the depth of the shear band and the depth of stress fluctuations between sticking periods are unaffected by grain angularity.
Overall, these novel observations from each experiment demonstrate that friction and grain shape are important factors determining properties of macroscopic stick-slip dynamics of granular materials, stress transmission in stable granular materials, and grain-scale dynamics during slip events. Our observations also serve as motivation for more robust modeling and theoretical descriptions of granular stability and flow more generally by considering the influences of basal friction and changes in grain shape.
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