Equation for the force experienced by a wall overflowed by a granular avalanche: experimental verification

Mean force and fluctuations on a wall immersed in a sheared granular flow

In a sheared and confined granular flow, the mean force and the force fluctuations on a rigid wall are studied by means of numerical simulations based on the discrete element method. An original periodic immersed-wall system is designed to investigate a wide range of confinement pressure and shearing velocity imposed at the top of the flow, considering different obstacle heights. The mean pressure on the wall relative to the confinement pressure is found to be a monotonic function of the boundary macroscopic inertial number which encapsulates the confinement pressure, the shearing velocity, and the thickness of the sheared layer above the wall. The one-to-one relation is slightly affected by the length of the granular system. The force fluctuations on the wall are quantified through the analysis of both the distributions of grain-wall contact forces and the autocorrelation of force time series. The distributions narrow as the boundary macroscopic inertial number decreases, moving from asymmetric log-normal shape to nearly Gaussian-type shape. That evolution of the grain-wall force distributions is accompanied at the lowest inertial numbers by the occurrence of a system memory in terms of the force transmitted to the wall, provided that the system length is not too large. Moreover, the distributions of grain-wall contact forces are unchanged when the inertial number is increased above a critical value. All those results allow to clearly identify the transitions from quasistatic to dense inertial, and from dense inertial to collisional, granular flow regimes.

Dry granular avalanche impact force on a rigid wall: Analytic shock solution versus discrete element simulations

The present paper investigates the mean impact force exerted by a granular mass flowing down an incline and impacting a rigid wall of semi-infinite height. First, this granular flow-wall interaction problem is modeled by numerical simulations based on the discrete element method (DEM). These DEM simulations allow computing the depth-averaged quantities-thickness, velocity, and density-of the incoming flow and the resulting mean force on the rigid wall. Second, that problem is described by a simple analytic solution based on a depth-averaged approach for a traveling compressible shock wave, whose volume is assumed to shrink into a singular surface, and which coexists with a dead zone. It is shown that the dead-zone dynamics and the mean force on the wall computed from DEM can be reproduced reasonably well by the analytic solution proposed over a wide range of slope angle of the incline. These results are obtained by feeding the analytic solution with the thickness, the depth-averaged velocity, and the density averaged over a certain distance along the incline rather than flow quantities taken at a singular section before the jump, thus showing that the assumption of a shock wave volume shrinking into a singular surface is questionable. The finite length of the traveling wave upstream of the grains piling against the wall must be considered. The sensitivity of the model prediction to that sampling length remains complicated, however, which highlights the need of further investigation about the properties and the internal structure of the propagating granular wave.

Drag force on a spherical intruder in a granular bed at low Froude number

The drag force on an object, or "intruder," in a granular material arises from interparticle friction, as well as the cyclic creation and buckling of force chains within the material. In contrast to fluids, for which drag forces are well understood, there is no straightforward relationship between speed and mean drag force in granular materials. We investigate spherical intruder particles of varying radii moving at low speeds through granular beds. The system can be parametrized using the dimensionless Froude number Fr=2v/√[gR], for intruders of radius R moving at a speed v. For frictional systems, we find the drag force obeys a linear relationship with Fr for low Froude numbers above Fr>1. For Fr<1 we observe a deviation from this linear trend. This transition can be explained by considering the characteristic inertial and gravitational granular time scales of the system. We show that a suitably normalized measure of dissipated power obeys a linear relationship with the imposed intruder velocity, independent of the intruder dimensions. This is found to hold even for particles with no friction, identifying a relationship between the imposed motion of the intruder and the resistance of the granular material to purely geometric rearrangements.