Skip to main content Accessibility help
×
Home

Granular column collapses down rough, inclined channels

  • GERT LUBE (a1), HERBERT E. HUPPERT (a2), R. STEPHEN J. SPARKS (a3) and ARMIN FREUNDT (a4)

Abstract

We present experimental results for the collapse of rectangular columns of sand down rough, inclined, parallel-walled channels. Results for basal inclination θ varying between 4.2° and 25° are compared with previous results for horizontal channels. Shallow-water theory can be usefully combined with scaling relationships obtained by dimensional analysis to yield analytical functions of the maximum runout distance, the maximum deposit height and the time to reach the maximum runout. While the theory excellently predicts the maximum lengths of the deposit it generally overestimates the runout time. The inertial flows are characterized by a moving internal interface separating upper flowing and lower static regions of material. In an initial free-fall phase of collapse the deposited area (= volume per unit width) below the internal interface varies with the square-root of time, independent of the initial height of the column and channel inclination. In the subsequent, lateral spreading phase the deposition rate decreases with increasing basal inclination or with decreasing initial height. The local deposition rate at any fixed distance is a constant, dependent on the column aspect ratio, the channel inclination and the longitudinal position, but invariant with flow velocity and depth. In the lateral spreading phase, vertical velocity profile in the flowing layer take a universal form and are independent of flow depth and velocity. They can be characterized by a shear rate as a function of channel inclination and a length scale describing the fraction of the column involved in flow.

Copyright

Corresponding author

Email address for correspondence: heh1@esc.cam.ac.uk

References

Hide All
Balmforth, N. J. & Kerswell, R. R. 2005 Granular collapses in two dimensions. J. Fluid Mech. 538, 399428.
Dalziel, S. B. 2005 DigiFlow User Guide. Available at: http://www.damtp.cam.ac.uk/lab/digiflow/.
Doyle, E. E., Huppert, H. E., Lube, G., Mader, H. M. & Sparks, R. S. J. 2007 Static and flowing regions in granular column collapses down channels: insights from a sedimenting shallow water model. Phys. Fluids 19, 106601, 116.
Midi, G.D.R. 2004 On dense granular flows. Eur. Phys. J. E 14, 341.
Gauer, P., Rammer, L, Kern, M., Lied, K., Kristensen, K. & Schreiber, H. 2006 On pulsed Doppler radar measurements of avalanches and their implication to avalanche dynamics. Geophys. Res. Abstracts 8, 04683.
Huppert, H. E., Hallworth, M. A., Lube, G. & Sparks, R. S. J. 2003 Granular column collapses. Bull. Am. Phys. Soc. 48, 68.
Huppert, H. E., Lube, G., Sparks, R. S. J. & Hallworth, M. A. 2004 In Granular Column Collapse. ICTAM Proceedings. Kluwer.
Hutter, K., Koch, T., Pluss, C. & Savage, S. B. 1995 The dynamics of avalanches of granular materials from initiation to runout. Part II. Experiments. Acta Mech. 109, 127.
Kerswell, R. R. 2005 Dam break with Coulomb friction: a model for granular slumping? Phys. Fluids 17, 057101, 116.
Lajeunesse, E., Mangeney-Castelnau, A. & Vilotte, J. P. 2004 Spreading of a granular mass on a horizontal plane. Phys. Fluids 16, 23712381.
Lajeunesse, E., Monnier, J. B. & Homsy, G. M. 2005 Granular slumping on a horizontal surface. Phys. Fluids 17, 103302.
Larrieu, E., Staron, L. & Hinch, E. J. 2006 Raining into shallow water as a description of the collapse of a column of grains. J. Fluid Mech. 554, 259270.
Lube, G., Huppert, H. E., Sparks, R. S. J. & Freundt, A. 2005 Collapses of two-dimensional granular columns. Phys. Rev. E 72, 041301, 110.
Lube, G., Huppert, H. E., Sparks, R. S. J. & Freundt, A. 2007 Static and flowing regions in granular column collapses down channels. Phys. Fluids 19, 043301, 19.
Lube, G., Huppert, H. E., Sparks, R. S. J. & Hallworth, M. A. 2004 Axisymmetric collapses of granular columns. J. Fluid Mech. 508, 175199.
Mangeney, A., Heinrich, P. & Roche, R. 2000 Analytical solution for testing debris avalanche numerical models. Pure Appl. Geophys. 157, 10811096.
Mangeney-Castelnau, A., Bouchut, B., Vilotte, J. P., Lajeunesse, E., Aubertin, A., & Pirulli, M. 2005 On the use of Saint–Venant equations for simulating the spreading of a granular mass. J. Geophys. Res. 110, B09103, 117.
Pouliquen, O. 1999 Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11, 542.
Pouliquen, O. & Forterre, Y. 2002 Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane. J. Fluid Mech. 453, 131.
Savage, S.B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177.
Siavoshi, S. & Kudrolli, A. 2005 Failure of a granular step. Phys. Rev. E 71, 051302, 16.
Staron, L. & Hinch, E. J. 2005 Study of the collapse of granular columns using 2D discrete grains simulation. J. Fluid Mech. 545, 127.
Thompson, E. L. & Huppert, H. E. 2007 Granular column collapses: further experimental results. J. Fluid Mech. 575, 177186.
Zenit, R. 2005 Computer simulations of the collapse of a granular column. Phys. Fluids 17, 031703, 14.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Granular column collapses down rough, inclined channels

  • GERT LUBE (a1), HERBERT E. HUPPERT (a2), R. STEPHEN J. SPARKS (a3) and ARMIN FREUNDT (a4)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.