Granular friction, Coulomb failure, and the fluid-solid transition for horizontally shaken granular materials

We present the results of an extensive series of experiments, molecular dynamics simulations, and models that address horizontal shaking of a layer of granular material. The goal of this work was to better understand the transition between the “fluid” and “solid” states of granular materials. In the experiments, the material—consisting of glass spheres, smooth and rough sand—was contained in a container of rectangular cross section, and subjected to horizontal shaking of the form [formula presented] The base of the container was porous, so that it was possible to reduce the effective weight of the sample by means of a vertical gas flow. The acceleration of the shaking could be precisely controlled by means of an accelerometer mounted onboard the shaker, plus feedback control and lockin detection. The relevant control parameter for this system was the dimensionless acceleration, [formula presented] where g was the acceleration of gravity. As [formula presented] was varied, the layer underwent a backward bifurcation between a solidlike state that was stationary in the frame of the shaker and a fluidlike state that typically consisted of a sloshing layer of maximum depth H riding on top of a solid layer. That is, with increasing [formula presented] the solid state made a transition to the fluid state at [formula presented] and once the system was in the fluid state, a decrease in [formula presented] left the system in the fluidized state until [formula presented] reached [formula presented] In the fluidized state, the flow consisted of back and forth sloshing at the shaker frequency, plus a slower convective flow along the shaking direction and additionally in the horizontal direction transverse to the shaking direction. Molecular dynamics simulations show that the last of these flows is associated with shear and dilation at the vertical sidewalls. For [formula presented] and in the solid state, there was a “gas” of free particles sliding on the surface of the material. These constituted much less than one layer’s worth of particles in all cases. If these “sliders” were suppressed by placing a thin strip of plastic on the surface, the hysteresis was removed, and the transition to fluidization occurred at a slightly lower value than [formula presented] for the free surface case. The hysteresis was also suppressed if a vertical gas flow from the base was sufficient to support roughly [formula presented] of the weight of the sample. Both the transition to the fluid state from the solid and the reverse transition from the fluid to the solid were characterized by similar divergent time scales. If [formula presented] was increased above [formula presented] by a fractional amount [formula presented] where [formula presented] was small, there was a characteristic time [formula presented] for the transition from solid to fluid to occur, where [formula presented] is [formula presented] Similarly, if [formula presented] was decreased below [formula presented] in the fluidized state by an amount [formula presented] there was also a transient time [formula presented] where [formula presented] is again indistinguishable from [formula presented] In addition, the amplitudes A and B are essentially identical. By placing a small “impurity” on top of the layer, consisting of a heavier particle, we found that the exponent [formula presented] varied as the impurity mass squared and changed by a factor of 3. A simple Coulomb friction model with friction coefficients [formula presented] for the fluid and solid states predicts a reversible rather than hysteretic transition to the fluid state, similar to what we observe with the addition of the small overload from a plastic strip. In an improved model, we provide a relaxational mechanism that allows the friction coefficient to change continuously between the low and high values. This model produces the hysteresis seen in experiments.