Directional strengthening and weakening in hydrodynamically sheared granular beds

Granular beds driven by overlying shear flows begin to erode when the stress delivered to the bed by the fluid exceeds a critical value. Previous studies have shown that this critical stress depends on the stress history of the bed, and that beds will strengthen when subjected to subcritical stresses. By measuring the behavior of erodible beds in a laboratory flume, we confirm this strengthening effect, but also find that it is strongly directional. We find that preconditioned granular beds are indeed more resistant to erosion when driven in the direction of the conditioning flow, but that this strengthening is accompanied by a weakening when driven in other directions. Preconditioned beds are in fact more susceptible to erosion by flows in the direction opposite to that of the conditioning flow than freshly settled beds are. Our results show that the strength of a natural erodible bed with a stress history is likely to be highly anisotropic, with significant implications for predictions of sediment transport.

Figure 1

Diagram of the test section of the apparatus. The measurement region is indicated by the position of the overhead camera (for measurements of the grain motion) or laser (for measurements of the flow).

Figure 2

Example velocity profiles measured for freshly settled beds for four different flow speeds. The solid curves are fits to the particle-tracking data (see text for details).

Figure 3

Mean grain velocity $\langle u_g\rangle$ averaged over all identified grains as a function of Shields number $\mathrm{\Theta }$. The grain velocities are scaled by $u\left(D\right)$, the fluid velocity one grain diameter above the bed. Data are shown for several cases. Different symbols indicate different durations of the conditioning flow: 0 s (that is, freshly settled beds; black circles), 360 s (red squares), 776 s (green triangles), 1671 s (blue inverted triangles), and 3600 s (cyan diamonds). Solid lines indicate measurements made with the flow in the same direction as the conditioning flow, and dashed lines indicate that the flow was in the opposite direction. Error bars show the standard error computed over three trials.

Figure 4

Grain velocity PDFs for $\mathrm{\Theta }=0.012$ (blue), 0.019 (red), 0.022 (green), and 0.025 (black) for freshly settled beds. The dashed lines are fits to the mixture model described in the text.

Figure 5

The fraction of mobilized grains $B$ as determined from fits to the mixture model in Eq. (2) as a function of the Shields number $\mathrm{\Theta }$. Symbols, line styles, and error bars have the same meanings as in Fig. 3.

Figure 6

The typical velocity of mobilized grains $u_g^{*}$ as determined from fits to the mixture model in Eq. (2) as a function of the Shields number $\mathrm{\Theta }$. $u_g^{*}$ is scaled by $u\left(D\right)$, the fluid velocity one grain diameter above the bed. Symbols, line styles, and error bars have the same meanings as in Fig. 3.