Interfacial Instability during Granular Erosion

Gautier Lefebvre (1) , Aymeric Merceron (1) , Pierre Jop (1)

1 SVI - Surface du Verre et Interfaces

The complex interplay between the topography and the erosion and deposition phenomena is a key feature to model granular flows such as landslides. Here, we investigated the instability that develops during the erosion of a wet granular pile by a dry dense granular flow. The morphology and the propagation of the generated steps are analyzed in relation to the specific erosion mechanism. The selected flowing angle of the confined flow on a dry heap appears to play an important role both in the final state of the experiment, and for the shape of the structures. We show that the development of the instability is governed by the inertia of the flow through the Froude number. We model this instability and predict growth rates that are in agreement with the experiment results. Understanding sediment transport in Nature is essential to model landscape evolution, such as the transport processes in rivers and their formation [1, 2]. Patterns are known to spontaneously develop at the bottom of the river bed depending on the coupling between the flow and the bed geometry through the erosion/transport laws [3, 4]. Granular flows such as landslides can also alter the underlying ground. However, contrary to the fluid case, the erosion mechanisms are less clear when the granular material is dense. Thus recent studies have focused on the evolution of the interface between an erodible layer and a granular flow [5–7], especially to model the entrain-ment rates, the velocities and the runout distances. Understanding such processes can also give insights on past and present climates for example [8–10]. Moreover, although the instabilities of riverbeds have been extensively characterized [11], the studies of instabilities in granular flows were generally focused on the flowing layer, thus describing avalanche fronts, roll waves, upward traveling waves [12–15], providing a better understanding of gran-ular flows. As a result, little attention has been paid to the evolution of a granular bed under a solid mechanical load [16, 17]. Finally, while previous studies on the erosion rate of a cohesive media by a granular flow focused on the physical properties of the cohesive materials (liquid bridges, tensile strength, elastic modulus) [7, 18, 19], the coupling between the erosion mechanism and the interface morphology with the granular flow is still an open question. In this Letter, we explore the coupling between a flow of dry granular material and a cohesive granular bed. Our experiment exhibits an instability, as a train of steps appears along the initially flat interface. Although this instability shares similarities with the erosion of a dense cohesive bed by fluid flow [3], we show that this system presents unique features linked to the specific properties of granular matter. Using a granular rheology and an erosion law, we can model the phenomenon. The threshold and growth rates of the initial instabilities are in good agreement with the theory, providing insights into the erosion mechanism itself.

Domaines: Science des matériaux [cond-mat.mtrl-sci]

Gautier Lefebvre, Aymeric Merceron, Pierre Jop. Interfacial Instability during Granular Erosion. Physical Review Letters, 2016, 116 (6), pp.068002 ⟨10.1103/PhysRevLett.116.068002⟩. ⟨hal-01274966⟩