Column collapse of granular rods

We investigate the collapse of granular rodpiles as a function of particle (length/diameter) and pile (height/radius) aspect ratio. We find that, for all particle aspect ratios below 24, there exists a critical height $H_l$ below which the pile never collapses, maintaining its initial shape as a solid, and a second height $H_u$ above which the pile always collapses. Intermediate heights between $H_l$ and $H_u$ collapse with a probability that increases linearly with increasing height. The linear increase in probability is independent of particle length, width, or aspect ratio. When piles collapse, the runoff scales as a piecewise power law with pile height, with $r_f\sim {\tilde{H}}^{1.2\pm 0.1}$ for pile heights below ${\tilde{H}}_c\approx 0.74$ and $r_f\approx H^{0.6\pm 0.1}$ for taller piles.

Figure 1

Rodlike piles of moderate height may collapse (left), but may also retain their original, cylindrical shape (right). Shown are results from two experiments on aspect ratio $\alpha =16$ particles with identical initial heights. We find the probability of collapse increases linearly with pile height. Particles in both figures are 5 cm in length.

Figure 2

(Color online) The runoff distance $\tilde{r}$ of a collapsed granular pile shows a power-law dependence on initial height $\tilde{H}$, with a transition between linear and square-root scaling. Both radius and pile height $\tilde{H}$ are made dimensionless by the initial pile radius $r_0$. For $\tilde{H}<\approx 1.1$ the runoff increases linearly with $\tilde{H}$, whereas for larger piles the runoff increases as ${\tilde{H}}^{1/2}$ (solid lines are power law fits). Both scaling behaviors, as well as the transition point, arise from conservation of volume arguments that assume all material outside an internal, stable cone collapses.

Figure 3

The critical heights that determine whether a pile acts as a solid or granular material, scaled by particle length, are independent of aspect ratio. The solid and granular regions are separated by a transition region in which the pile has a probability of collapsing, although there are no visible differences between piles that collapse and those that do not.

Figure 4

The probability of collapse within the transition region increases linearly with pile height scaled by the critical heights. This behavior is independent of particle length, width, and aspect ratio. The normalization by critical heights is done so that the origin is the lower transition point and (1,1) is the higher transition point.