Time-varying force from dense granular avalanches on a wall

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.

Depth-averaged analytic solutions for free-surface granular flows impacting rigid walls down inclines

In the present paper, flows of granular materials impacting wall-like obstacles down inclines are described by depth-averaged analytic solutions. Particular attention is paid to extending the existing depth-averaged equations initially developed for frictionless and incompressible fluids down a horizontal plane. The effects of the gravitational acceleration along the slope, and of the retarding acceleration caused by friction as well, are systematically taken into account. The analytic solutions are then used to revisit existing data on rigid walls impacted by granular flows. This approach allows establishing a complete phase diagram for granular flow-wall interaction.

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

The present paper deals with the force experienced by a wall overflowed by a granular avalanche. First, we briefly report laboratory tests on dry granular avalanches overflowing a wall down a rough channel. In the first step, the thickness and velocity of the control flows without a wall are measured. In the second step, a wall is mounted to obstruct the flow and the normal force experienced by the wall is measured. Then a set of equations based on depth-averaged momentum conservation, making it possible to derive the time-varying force on the wall, is described. The model was proposed and calibrated in two-dimensional (2D) discrete numerical simulations in an earlier work [Chanut, Faug, and Naaim, Phys. Rev. E 82, 041302 (2010)]. This model takes into account the fact that a quasistatic stagnant zone is established upstream of the wall and coexists with an inertial flowing zone above. For a large range of slopes, the model's prediction is successfully compared to experimental data with a reasonable estimation of the incoming flow density and in spite of some rough assumptions made to describe the dynamics of the dead zone. Finally, the results are analyzed with regard to previous 2D discrete numerical simulations and we discuss future work to be undertaken on the dynamics of the dead zone established upstream of the wall.