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Bulldozing of granular material

Published online by Cambridge University Press:  28 April 2014

A. Sauret ,
N. J. Balmforth ,
C. P. Caulfield  and
J. N. McElwaine
A. Sauret*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
N. J. Balmforth
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
C. P. Caulfield
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
J. N. McElwaine
Affiliation:
Department of Earth Sciences, University of Durham, Durham, DH1 3LE, UK WSL Institute for Snow and Avalanche Research SLF, Flüelastrasse 11, Davos, Switzerland
*
†Email address for correspondence: asauret@princeton.edu
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Abstract

We investigate the bulldozing motion of a granular sandpile driven forwards by a vertical plate. The problem is set up in the laboratory by emplacing the pile on a table rotating underneath a stationary plate; the continual circulation of the bulldozed material allows the dynamics to be explored over relatively long times, and the variation of the velocity with radius permits one to explore the dependence on bulldozing speed within a single experiment. We measure the time-dependent surface shape of the dune for a range of rotation rates, initial volumes and radial positions, for four granular materials, ranging from glass spheres to irregularly shaped sand. The evolution of the dune can be separated into two phases: a rapid initial adjustment to a state of quasi-steady avalanching perpendicular to the blade, followed by a much slower phase of lateral spreading and radial migration. The quasi-steady avalanching sets up a well-defined perpendicular profile with a nearly constant slope. This profile can be scaled by the depth against the bulldozer to collapse data from different times, radial positions and experiments onto common ‘master curves’ that are characteristic of the granular material and depend on the local Froude number. The lateral profile of the dune along the face of the bulldozer varies more gradually with radial position, and evolves by slow lateral spreading. The spreading is asymmetrical, with the inward progress of the dune eventually arrested and its bulk migrating to larger radii. A one-dimensional depth-averaged model recovers the nearly linear perpendicular profile of the dune, but does not capture the finer nonlinear details of the master curves. A two-dimensional version of the model leads to an advection–diffusion equation that reproduces the lateral spreading and radial migration. Simulations using the discrete element method reproduce in more quantitative detail many of the experimental findings and furnish further insight into the flow dynamics.

JFM classification

Complex Fluids: Complex Fluids Granular media: Granular media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 748 , 10 June 2014 , pp. 143 - 174
Copyright
© 2014 Cambridge University Press 

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Sauret et al. supplementary movie

Movie of an experiment showing the bulldozed dune from a front view for r0=25 cm, Ω=0.05 rad s-1 and m=1000 g. The red laser line highlights the topography of the dune at the location y0.

Download Sauret et al. supplementary movie(Video)
Video 9.4 MB

Sauret et al. supplementary movie

Movie of an experiment showing the bulldozed dune from a side view for r0=25 cm, Ω=0.05 rad s-1 and m=1000 g. The red laser line highlights the topography of the dune at the location y0.

Download Sauret et al. supplementary movie(Video)
Video 6.4 MB

Sauret et al. supplementary movie

Movie of a DEM simulation showing the initial transient during the bulldozing of the granular material. The particles become distributed so that they build up a wedge of depth H against the blade.

Download Sauret et al. supplementary movie(Video)
Video 9.9 MB

Sauret et al. supplementary movie

Movie of a lateral spreading simulation with an underlying layer and |Ub|=1. The particles are coloured according to their initial height.

Download Sauret et al. supplementary movie(Video)
Video 2.2 MB

Sauret et al. supplementary movie

Movie of the front view of a lateral spreading simulation with an underlying layer and |Ub|=1. The particles are coloured according to their initial height.

Download Sauret et al. supplementary movie(Video)
Video 6.5 MB

Sauret et al. supplementary movie

Movie of the side view (at y=0) of a lateral spreading simulation with an underlying layer and |Ub|=1. The particles are coloured according to their initial height.

Download Sauret et al. supplementary movie(Video)
Video 9 MB