Erosion and deposition processes on an inclined granular bed
Résumé
We investigate experimentally erosion and deposition processes on a titled granular bed. For this, we have designed an experimental set-up that permits to release a finite mass of granular material on an inclined granular bed. For small angle of inclination, accretion surpasses erosion, while for higher angle, erosion exceeds accretion. The equilibrium situation occurs at a critical angle, termed “neutral angle” [1], when erosion of the granular bed is exactly balanced by deposition. At the neutral angle, an avalanche leaves the slope of the granular bed unchanged.We have characterized the bed erosion as a function of the inclination angle varying several parameters such as the mass of the released material and the bed length. Interesting features are drawn from the experiments. First, experimental data show that the neutral angle of the granular bed is almost invariant with the bed length but slightly varies with the mass of the released avalanche. The neutral angle actually decreases with increasing mass. Second, the net bed erosion for inclination angles that departs from the neutral angle increases linearly with the angular deviation from the neutral angle. The increasing rate is found to be independent from the released mass but drastically augments with increasing bed length.We also compared our experimental results with the predictions of the “erosion/deposition” model introduced by Bouchaud, Cates, Ravi Prakash and Edwards (BCRE). In the original BCRE model, the local exchange rate between the mobile grains and the granular bed is assumed to be linear with the angular departure from the neutral angle and proportional to the thickness R of the mobile layer. The latter does not predict correctly the experimental results. In contrast, the predictions of the modified version of the BCRE model proposed by Boutreux and De Gennes, in which the exchange rate is independent of the flow thickness, are in remarkable agreement with the experimental results.As a conclusion, our experiments strongly suggest that the modified version of the BCRE model is a good continuum framework for describing erosion and deposition processes on a tilted granular bed.