Personalize with title, slogan or I/B/P name in master slide Gravitational Collapse of Rectangular Granular Piles M.H. Babaei Ocean, Coastal, and River Engineering, National Research Council of Canada, Ottawa, Canada T. Dabros Natural Resources Canada, CanmetENERGY, Devon, Alberta, Canada S.B. Savage Department of Civil Engineering & Applied Mechanics, McGill University, Montreal, Quebec, Canada 4 Oct. 2012, COMSOL2012, Boston, USA Excerpt from the Proceedings of the 2012 COMSOL Conference in Boston
Transcript
Personalize with title, slogan or I/B/P name in master slide
Gravitational Collapse of
Rectangular Granular Piles
M.H. Babaei Ocean, Coastal, and River Engineering, National Research Council of Canada,
Ottawa, Canada
T. Dabros Natural Resources Canada, CanmetENERGY, Devon, Alberta, Canada
S.B. Savage Department of Civil Engineering & Applied Mechanics, McGill University,
Montreal, Quebec, Canada
4 Oct. 2012, COMSOL2012, Boston, USA
Excerpt from the Proceedings of the 2012 COMSOL Conference in Boston
Personalize with title, slogan or I/B/P name in master slide Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
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Presentation Outline
• Introduction, Motivation & Background
• Constitutive Relations
• Numerical Solution
• Material Properties & Investigated Geometries
• Results
- Evolution of Slump Shapes
- Comparison with Experimental Data
• Summary & Conclusions
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This sample slide shows how you can use
imagery. If you are looking for interesting
images specific to your presentation,
contact: Harry Turner 613-993-4507
Introduction
• Flow & collapse of granular materials:
• Industry:
- Agriculture
- Pharmaceuticals
- Petroleum & Mining
• Geophysical processes:
- Landslides
- Avalanches
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
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• Available Literature
• Experimental
• Geometries (2D Symmetric, 2D dam-break, Semi-
Axisymmetric, Axisymmetric)
• Materials (sand, glass beads, rice, sugar, …)
• Basal conditions (rough and/or smooth bottom)
• Numerical
• Usually depth-averaged equations, shallow-water
approximation
• Collapse of short-thick blocks; NOT tall-thin blocks
Motivation & Background
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
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Constitutive Relations & Governing
Equations
• Modified von Mises yield function
• Isotropic
• Associated flow rule
• Incompressible
• Plane strain
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
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• Stress-strain rate relationship:
• The granular material is a fluid with the dynamic shear
viscosity of:
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
0.5
2/ 3 sin /ij m ij ij kk ij m I
0.5
2sin / 2p I
0.5
2sin / 2p I
Numerical Stability
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Numerical Solution
• COMSOL FE tool (version 4.2a), CFD two-phase laminar
flow module
• The Level-Set method was used to track the interface
between the two phases
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
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Granular Material
• Grit, irregular grain shapes, mean size 1 mm.
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
Grit Surrounding Air
34grit 510air Pa s
32600 /grit kg m 31 /air kg m
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I ( )
H = 25 cm
L = 2 cm
tall thin Case
( )
H = 10 cm
L = 20 cm
short thick Case
H
H
L
L
aspect ratio = 0.5
12aspect ratio = .5
Geometries
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
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Results
• Triangular mesh, element size is approximately 4 mm
2
1
0.075
Pa s
s
0.5
2sin / 2p I
No Slip
Slip
Free
Partial Slip
Partial Slip Slip length = 2 mm
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
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• CASE I, Low Aspect Ratio Pile
Collapse of Rectangular Granular Blocks, Babaei, Dabros, Savage
Evolution of Slump Shapes
incr
easi
ng t
ime
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• CASE II, High Aspect Ratio Pile
Evolution of Slump Shapes
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
increasing time
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• Close prediction of the final runout, final height, and the final
free surface profile
• An increase in the internal angle of friction reduces the runout
Comparison with Available Experiments
Final profiles
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
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Summary & Conclusions
• Mohr-Coulomb based constitutive relations
• Strain-rate and pressure dependent shear viscosity
• Two-phase flow problem
• Partial slip at boundaries in contact with the granular
material
• Stable heaps are captured
• Final free-surface profiles agree with experiments
Gravitational Collapse of Rectangular Granular Piles, Babaei, Dabros, Savage
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