Computer simulations of the collapse of columns formed by elongated grains

A numerical investigation of the collapse of granular columns has been conducted. In particular, we address the effect of the grain shape on the properties of the collapse. We show that the final runout and height of the deposits scale as a power law of the initial aspect ratio of the column, $a$, independently of the elongation of the grains used. We describe this process in terms of an energy balance, and construct an “inertial number” that can be used to describe the flow in terms of a recently proposed granular rheology. We argue that an effective friction that results from this dimensionless quantity explains why the shape of the grains is irrelevant for the final properties of the collapse.

Figure 1

Final runout (filled symbols) and height (empty symbols) as a function of the column's initial aspect ratio $a$ for columns made of long grains of type $N_1$ (circle), $N_3$ (square), $N_5$ (diamond), and $N_8$ (triangle). The dashed lines correspond to the fit that gives the scaling exponent of Table .

Figure 2

Snapshots of the column collapse process for a column aspect ratio $a\approx 4$. Each row shows a snapshot taken at the dimensionless time $\tau \approx 0.0,0.3,0.6,1.5$, and $3.0$ (from top to bottom) as indicated in Fig. 3. Light gray (blue online) shading to dark gray (red online) shading colors indicate increasing grain speed. Note that only the right side of the collapses are shown as they are very symmetric.

Figure 3

Dimensionless energies as a function of time for columns with initial aspect ratio of $a\approx 4$. Symbols are the same as in Fig. 1 for grains of type $N_3$ (square), $N_5$ (diamond), and $N_8$ (triangle). The vertical lines indicate the times at which the snapshots of Fig. 2 where taken. Black curves show $E_p^{*}$, blue $E_k^{*}$, and red $E_{\mathrm{dis}}^{*}$.

Figure 4

Time evolution of the inertial number $I$ from Eq. (2) during collapse for the columns of Fig. 2. Symbols and vertical lines are the same as in Fig. 3.