Modelling erosion and deposition in geophysical granular mass flows

During hazardous geophysical mass flows, such as rock or snow avalanches, debris flows and volcanic pyroclastic flows, a continuous exchange of material can occur between the slide and the bed. The net balance between erosion and deposition of particles can drastically influence the behaviour of these flows. Recent advances in describing the non-monotonic effective basal friction and the internal granular rheology in depth averaged theories have enabled small scale laboratory experiments (see fig. 1) to be quantitatively reproduced and can also be implemented in large scale models to improve hazard mitigation.

The effect of boundary roughness on dense granular flows

In the field of granular rheology, an important open question is to understand the influence of boundary conditions on granular flows. We perform experiments in a quasi-2D annular shear cell subject to 6 different boundaries with controlled roughness/compliance. We characterize the granular slip at the boundaries to investigate which aspects of a dense granular flow can be controlled by the choice of boundary condition. Photoelastic techniques are implemented to measure the stress fields P(r) and τ(r) throughout the material. A full inverse-analysis of the fringes within each disk provides the vector force at each contact. This allows us to measure the continuum stress field by coarse-graining internal forces. We have observed that boundary roughness and compliance strongly controls the flow profile v(r) and shear rate profile γ˙(r). We also observed that boundary roughness and compliance play a significant role in the pressure profile P(r) and shear stress profile τ(r).

The granular Blasius problem

We consider the steady flow of a granular current over a uniformly sloped surface that is smooth upstream (allowing slip for $x<0$) but rough downstream (imposing a no-slip condition on $x>0$), with a sharp transition at $x=0$. This problem is similar to the classical Blasius problem, which considers the growth of a boundary layer over a flat plate in a Newtonian fluid that is subject to a similar step change in boundary conditions. Our discrete particle model simulations show that a comparable boundary-layer phenomenon occurs for the granular problem: the effects of basal roughness are initially localised at the base but gradually spread throughout the depth of the current. A rheological model can be used to investigate the changing internal velocity profile. The boundary layer is a region of high shear rate and therefore high inertial number $I$; its dynamics is governed by the asymptotic behaviour of the granular rheology for high values of the inertial number. The $\unicode[STIX]{x1D707}(I)$ rheology (Jop et al., Nature, vol. 441 (7094), 2006, pp. 727–730) asserts that $\text{d}\unicode[STIX]{x1D707}/\text{d}I=O(1/I^{2})$ as $I\rightarrow \infty$, but current experimental evidence is insufficient to confirm this. We show that this rheology does not admit a self-similar boundary layer, but that there exist generalisations of the $\unicode[STIX]{x1D707}(I)$ rheology, with different dependencies of $\unicode[STIX]{x1D707}(I)$ on $I$, for which such self-similar solutions do exist. These solutions show good quantitative agreement with the results of our discrete particle model simulations.

Granular surface avalanching induced by drainage from a narrow silo

Using theory and experiments, we investigate granular surface avalanching due to material outflow from a narrow silo. The assumed silo geometry is a deep rectangular box, of moderate spanwise width and small gap thickness between smooth front and back walls. A small orifice deep below the free surface lets grains drain out at a constant rate. The resulting granular flows can therefore be assumed quasi-two-dimensional and quasi-steady over most of the surface descent history. To model these flows, we couple a kinematic model of deep granular flow with a dynamic model of shallow surface avalanching. We then compare the calculated flow fields with detailed particle tracking measurements, letting the silo ascend relative to the high-speed camera to increase spatial resolution. The results show that the avalanching surface shape and near-surface flow are controlled by the spanwise gradient in subsidence velocity, and how this gradient is in turn controlled by the height above orifice and the gap thickness. Whereas the deep flow pattern is rate independent, shallow avalanching is paced by the granular rheology.