Gravity-driven free surface flow of granular avalanches over complex basal topography

A two-dimensional depth-integrated theory is derived for the gravity-driven free surface flow of cohesionless granular avalanches over complex shallow basal topography. This is an important extension of the one-dimensional Savage-Hutter theory. A simple curvilinear coordinate system is adopted, whic...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 1999-05, Vol.455 (1985), p.1841-1874
Main Authors: Gray, J. M. N. T., Wieland, M., Hutter, K.
Format: Article
Language:English
Subjects:
Avalanches
Coordinate systems
Coulomb Behaviour
Depth-Integrated Equations
Friction
Granular materials
Gravity Flow
Hyperbolic Equations
Mohr
Momentum
Rapid Granular Flow
Research Article
Spherical coordinates
Tensors
Topography
Transition zones
Velocity
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Summary:A two-dimensional depth-integrated theory is derived for the gravity-driven free surface flow of cohesionless granular avalanches over complex shallow basal topography. This is an important extension of the one-dimensional Savage-Hutter theory. A simple curvilinear coordinate system is adopted, which is fitted to the 'mean' downslope chute topography. This defines a quasi-two-dimensional reference surface on top of which shallow three-dimensional basal topography is superposed. The governing equations are expressed in the curvilinear coordinate system and the mass- and momentum-balance equations are integrated through the avalanche depth. An ordering argument and a Mohr-Coulomb closure model are used to obtain a simple reduced system of equations. Laboratory experiments have been performed on a partly confined chute to validate the theory. An avalanche is released on a section inclined at 40 degrees to the horizontal, on which there is a concave parabolic cross-slope profile, and runs out through a smooth transition zone onto a horizontal plane. A comparison of the experiment with numerical solutions shows that the avalanche tail speed is under-predicted. A modification to the bed-friction angle is proposed, which brings theory and experiment into very good agreement. The partly confined chute channel the flow and results in significantly longer maximum run-out distances than on an unconfined chute. A simple shallow-water avalanche model is also derived and tested against the experimental results.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.1999.0383