Mean granular force on a wall overflowed by free-surface gravity-driven flows in steady and unsteady states
Force granulaire moyenne sur un mur débordé par un écoulement gravitaire à surface libre en régimes permanent et transitoire
Résumé
Free-surface gravity-driven flows of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the bottom are investigated for both steady and unsteady incoming flow conditions. 2D hard-particle discrete numerical simulations using a linear damped spring law between particles with a Coulomb failure criterion have been carried out. Our focus is on the mean force exerted by the flow on the obstacle for varying values of the incoming inertial number that measures the ratio between a macroscopic deformation timescale and an inertial timescale. The results show transitions between different flow regimes in steady and unsteady states. At high inertial numbers, the force is close to a purely dynamic force which characterizes a rapid dilute regime. At low inertial numbers, a dense regime appears and the force scales as a hydrostatic force but with a value several times greater than a purely hydrostatic force. A stagnant zone, inside which high frequency force chains with high amplitude, is formed upstream of the wall and contributes to largely increase the force on the wall in this dense regime. When the inertial number tends towards zero in the quasi-static regime, this stagnant zone propagates indefinitely upwards. A simple hydrodynamic model based on momentum conservation is proposed for steady flows. This model predicts fairly well the numerical data and allows us to quantify the force contributions due to the weight of the stagnant zone and the friction of this latter with the bottom. These two contributions are shown to become very large compared with both hydrostatic and dynamic forces when the inertial number decreases. Beyond these discrete numerical simulations and the hydrodynamic model proposed, this work is of interest in connection with the large pressures on obstacles measured from full-scale snow avalanches and debris flows at low Froude numbers.