We studied free-surface gravity-driven recirculating flows of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. We performed 2D spherical particle discrete element simulations using a linear damped spring law between particles with a Coulomb failure criterion. High-frequency force fluctuations were observed. This paper focuses on the mean steady force exerted by the flow on the obstacle versus the macroscopic inertial number of the incoming flow, where the inertial number measures the ratio between a macroscopic deformation timescale and an inertial timescale. A triangular stagnant zone is formed upstream of the obstacle and sharply increases the mean force at low incoming inertial numbers. A simple hydrodynamic model based on depth-averaged momentum conservation isproposed. This analytical model predicts the numerical data fairly well and allows us to quantify the different contributions to the mean force on the wall. Beyond this model, our study provides an example of the ability of simple hydrodynamic approaches to describe the macroscopic behavior of an assembly of discrete particles, not only in terms of kinematics, but also in terms of forces.

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.

The shapes of standing jumps formed in shallow granular flows down an inclined smooth-based chute are analysed in detail, by varying both the slope and mass discharge. Laboratory tests and analytic jump solutions highlight two important transitions. First, for dense flows at high mass discharge, we observe a transition between steep jumps and more diffuse jumps. The traditional shallow-water equation offers a valid prediction for the thickness of the steep water-like jumps. Diffuse frictional jumps require a more general equation accounting for the forces acting inside the jump volume. Second, moving from dense to dilute flows produces another transition between incompressible and compressible jumps. The observed jump height decrease may be reproduced for a more dilute incoming flow by including experimentally measured density variation in the jump equation. Finally, we briefly discuss the likely relevance to avalanche protection dam design that currently utilises traditional shock equations for incompressible frictionless fluids.

We studied avalanches of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. This paper focuses on the transient

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This paper revisits a great number of data from previous studies about the macroscopic force experienced by either objects moving at constant speed and depth inside static granular materials or motionless objects subject to steady granular flows. It focuses on extended objects whose immersed height is equal or close to the thickness of the surrounding granular medium. A simple scaling argument allows demarcating quasi-static from speed-squared force contributions for all the data from different geometries over a very broad range of Froude number. However, a wide scatter of the data is observed in the quasi-static regime. In the first step, a mean-field model is proposed to describe the average force. Mass and momentum balances are applied to a control volume, namely the expected volume of grains disturbed by the object, which is assumed to extend across the whole width and the entire height of the granular system. This allows defining an equivalent length scale which is computed by fitting the force predicted by the model to the available force data. In the second step, a circular shape is assumed for the effective mobilized domain and the associated diameter can be directly extracted from the computed equivalent length scale. This effective diameter is found to vary linearly with both the object width and the thickness of the granular layer moving around the extended object or the immersed depth of the object. The scaling highlights the key role played by the geometry which may enhance the force in the quasi-static regime.

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