Onset of erosion and avalanche for an inclined granular bed sheared by a continuous laminar flow

Abstract

The transport inception of immersed grains is studied experimentally with laminar flow conditions in a Hele-Shaw cell when varying the tilt angle of the cell and the water flow rate. Varying these two parameters, grains are either motionless, rolling on the bed surface, or avalanching downwards. This paper focuses on the determination of the onset for grain motion either by erosion or by avalanche. For a horizontal interface, onset for erosion corresponds to a constant critical Shields number θc=0.14 at small particle Reynolds number (Red<1) but decreases as Red−1 at larger particle Reynolds number (Red>1). For tilted bed, the onset of erosion increases when the flow is opposed to gravity. Both results are compared to a standard model based on a balance of the forces acting on a single grain lying on a tilted plane. When tilt angles are large, avalanches occur. The maximum angle of stability is modified by the flow and increases slightly when the flow acts against gravity. This behavior is compared to a continuous model where a few layers of grains are about to slide.

Relaxation dynamics of water-immersed granular avalanches

“…The shear stress exerted by the fluid on the granular interface can finally be inferred from the relation τ xz 3.26ηU f /b (cf. the appendix of Loiseleux et al 2005).…”

“…The water flow rate is chosen below the threshold corresponding to the onset of bed-load motion. Loiseleux et al (2005) apparent weight. When both avalanche and counter-erosion processes take place simultaneously, Loiseleux et al (2005) also mentioned that nonlinear structures grow quickly.…”

“…Loiseleux et al (2005) apparent weight. When both avalanche and counter-erosion processes take place simultaneously, Loiseleux et al (2005) also mentioned that nonlinear structures grow quickly. In all the present experiments, the θ value will thus be kept below the critical value 0.1 to avoid any bed-load motion and formation of structures that would drastically modify the avalanche flow.…”

“…In all the present experiments, the θ value will thus be kept below the critical value 0.1 to avoid any bed-load motion and formation of structures that would drastically modify the avalanche flow. We also restrict our study to water counterflow as it is difficult to distinguish between erosion and avalanche granular motions for water co-current flows (Loiseleux et al 2005).…”

“…They successfully analysed their results within the local rheology framework µ(I ) developed initially in the dry case but adapted for the liquid-immersed configuration: the falling time scale that enters the definition of the inertial number I is here the viscous falling time already suggested by Courrech du Pont et al (2003a). Finally, Loiseleux et al (2005) studied the influence of a superficial water flow on the onset of granular avalanches: an upward water flow tends to increase the pile stability while a downward water flow decreases it.…”