Skip to main content Accessibility help
×
Home

Bulbous head formation in bidisperse shallow granular flow over an inclined plane

  • I. F. C. Denissen (a1), T. Weinhart (a1), A. Te Voortwis (a1), S. Luding (a1), J. M. N. T. Gray (a2) and A. R. Thornton (a1)...

Abstract

Rapid shallow granular flows over inclined planes are often seen in nature in the form of avalanches, landslides and pyroclastic flows. In these situations the flow develops an inversely graded (large at the top) particle-size distribution perpendicular to the plane. As the surface velocity of such flows is larger than the mean velocity, the larger material is transported to the flow front. This causes size segregation in the downstream direction, resulting in a flow front composed of large particles. Since the large particles are often more frictional than the small, the mobility of the flow front is reduced, resulting in a so-called bulbous head. This study focuses on the formation and evolution of this bulbous head, which we show to emerge in both a depth-averaged continuum framework and discrete particle simulations. Furthermore, our numerical solutions of the continuum model converge to a travelling wave solution, which allows for a very efficient computation of the long-time behaviour of the flow. We use small-scale periodic discrete particle simulations to calibrate (close) our continuum framework, and validate the simple one-dimensional (1-D) model with full-scale 3-D discrete particle simulations. The comparison shows that there are conditions under which the model works surprisingly well given the strong approximations made; for example, instantaneous vertical segregation.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Bulbous head formation in bidisperse shallow granular flow over an inclined plane
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Bulbous head formation in bidisperse shallow granular flow over an inclined plane
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Bulbous head formation in bidisperse shallow granular flow over an inclined plane
      Available formats
      ×

Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: a.r.thornton@utwente.nl

References

Hide All
Allen, M. P. & Tildesley, D. J. 1989 Computer Simulation of Liquids. Oxford University Press.
Babic, M. 1997 Average balance equations for granular materials. Intl J. Engng Sci. 35 (5), 523548.
Baker, J. L., Johnson, C. G. & Gray, J. M. N. T. 2016 Segregation-induced finger formation in granular free-surface flows. J. Fluid Mech. 809, 168212.
Berzi, D. & Jenkins, J. T. 2009 Steady inclined flows of granular-fluid mixtures. J. Fluid Mech. 641, 359387.
Bokhove, O. & Thornton, A. R. 2012 Shallow granular flows. In Handbook of Environmental Fluid Dynamics (ed. Fernando, H. J.). CRC Press.
Bridgwater, J., Foo, W. S. & Stephens, D. J. 1985 Particle mixing and segregation in failure zones – theory and experiment. Powder Technol. 41 (2), 147158.
Bristeau, M. O. & Coussin, B.2001 Boundary conditions for the shallow water equations solved by kinetic schemes. PhD thesis, INRIA.
Brodu, N., Richard, P. & Delannay, R. 2013 Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices. Phys. Rev. E 87 (2), 022202.
Bunya, S., Kubatko, E. J., Westerink, J. J. & Dawson, C. 2009 A wetting and drying treatment for the Runge–Kutta discontinuous Galerkin solution to the shallow water equations. Comput. Meth. Appl. Mech. Engng 198 (17), 15481562.
Campbell, C. S., Cleary, P. W. & Hopkins, M. 1995 Large-scale landslide simulations: global deformation, velocities and basal friction. J. Geophys. Res. 100 (B5), 82678283.
Cockburn, B. & Shu, C. W. 1989 TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Math. Comput. 52 (186), 411435.
Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Geotechnique 29 (1), 4765.
Dalbey, K., Patra, A. K., Pitman, E. B., Bursik, M. I. & Sheridan, M. F. 2008 Input uncertainty propagation methods and hazard mapping of geophysical mass flows. J. Geophys. Res. 113 (B5), B05203.
Davies, T. R. H. 1990 Debris-flow surges – experimental simulation. J. Hydrol. (New Zealand) 29, 1846.
Delannay, R., Valance, A., Mangeney, A., Roche, O. & Richard, P. 2017 Granular and particle-laden flows: from laboratory experiments to field observations. J. Phys. D 50 (5), 053001.
Dippel, S. & Luding, S. 1995 Simulations on size segregation: geometrical effects in the absence of convection. J. Phys. I France 5, 15271537.
Dunning, S. A. & Armitage, P. J. 2011 The grain-size distribution of rock-avalanche deposits: implications for natural dam stability. In Natural and Artificial Rockslide Dams, pp. 479498. Springer.
Edwards, A. N. & Vriend, N. M. 2016 Size segregation in a granular bore. Phys. Rev. Fluids 1 (6), 064201.
Fan, Y. & Hill, K. M. 2011 Theory for shear-induced segregation of dense granular mixtures. New J. Phys. 13 (9), 095009.
Faug, T., Childs, P., Wyburn, E. & Einav, I. 2015 Standing jumps in shallow granular flows down smooth inclines. Phys. Fluids 27 (7), 073304.
Forterre, Y. & Pouliquen, O. 2003 Long-surface-wave instability in dense granular flows. J. Fluid Mech. 486, 2150.
Gajjar, P., van der Vaart, K., Thornton, A. R., Johnson, C. G., Ancey, C. & Gray, J. M. N. T. 2016 Asymmetric breaking size-segregation waves in dense granular free-surface flows. J. Fluid Mech. 794, 460505.
GDR-MiDi 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341365.
Gillemot, K. A, Somfai, E. & Börzsönyi, T. 2017 Shear-driven segregation of dry granular materials with different friction coefficients. Soft Matt. 13 (2), 415420.
Goldhirsch, I. 2010 Stress, stress asymmetry and couple stress: from discrete particles to continuous fields. Granul. Matt. 12 (3), 239252.
González, S., Windows-Yule, C. R. K., Luding, S., Parker, D. J. & Thornton, A. R. 2015 Forced axial segregation in axially inhomogeneous rotating systems. Phys. Rev. E 92, 022202.
Goujon, C., Dalloz-Dubrujeaud, B. & Thomas, N. 2007 Bidisperse granular avalanches on inclined planes: a rich variety of behaviors. Eur. Phys. J. E 23 (2), 199215.
Gray, J. M. N. T . & Chugunov, V. A. 2006 Particle-size segregation and diffusive remixing in shallow granular avalanches. J. Fluid Mech. 569, 365398.
Gray, J. M. N. T. & Ancey, C. 2009 Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts. J. Fluid Mech. 629, 387423.
Gray, J. M. N. T. & Ancey, C. 2011 Multi-component particle-size segregation in shallow granular avalanches. J. Fluid Mech. 678, 535588.
Gray, J. M. N. T. & Edwards, A. N. 2014 A depth-averaged-rheology for shallow granular free-surface flows. J. Fluid Mech. 755, 503534.
Gray, J. M. N. T. & Kokelaar, B. P. 2010a Large particle segregation, transport and accumulation in granular free-surface flows. J. Fluid Mech. 652, 105137.
Gray, J. M. N. T. & Kokelaar, B. P. 2010b Large particle segregation, transport and accumulation in granular free-surface flows – erratum. J. Fluid Mech. 657, 539539.
Gray, J. M. N. T., Tai, Y.-C. & Noelle, S. 2003 Shock waves, dead zones and particle-free regions in rapid granular free-surface flows. J. Fluid Mech. 491, 161181.
Gray, J. M. N. T. & Thornton, A. R. 2005 A theory for particle size segregation in shallow granular free-surface flows. Proc. R. Soc. Lond. A 461 (2057), 14471473.
Haas, T., Braat, L., Leuven, J. R. F. W., Lokhorst, I. R. & Kleinhans, M. G. 2015 Effects of debris flow composition on runout, depositional mechanisms, and deposit morphology in laboratory experiments. J. Geophys. Res. 120 (9), 19491972.
Harten, A., Lax, P. D. & van Leer, B. 1983 On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25 (1), 3561.
Hill, K. M. & Fan, Y. 2016 Granular temperature and segregation in dense sheared particulate mixtures. KONA Powder Particle J. 33 (0), 150168.
Hogg, A. J. & Pritchard, D. 2004 The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 501, 179212.
Hong, D. C., Quinn, P. V. & Luding, S. 2001 Reverse brazil nut problem: competition between percolation and condensation. Phys. Rev. Lett. 86 (15), 34233426.
Iverson, R. M. 1997 The physics of debris flows. Rev. Geophys. 35 (3), 245296.
Iverson, R. M. 2003 The debris-flow rheology myth. In Debris flow Mechanics and Mitigation Conference, Mills Press, Davos, pp. 303314.
Iverson, R. M. & Lahusen, R. G. 1993 Friction in debris flows: Inferences from large-scale flume experiments. In Hydraulic Engineering (ed. American Society of Civil Engineers), vol. 93. ASCE.
Iverson, R. M., Logan, M., Lahusen, R. G. & Berti, M. 2010 The perfect debris flow? Aggregated results from 28 large-scale experiments. J. Geophys. Res. 115, F03005.
Jenkins, J. T. 1998 Particle segregation in collisional flows of inelastic spheres. In Physics of Dry Granular Media (ed. Herrmann, Hovi & Luding), NATO ASI Series, vol. 350, pp. 645658. Kluwer.
Jenkins, J. T. & Yoon, D. K. 2002 Segregation in binary mixtures under gravity. Phys. Rev. Lett. 88 (19), 1.
Johnson, C. G., Kokelaar, B. P., Iverson, R. M., Logan, M., Lahusen, R. G. & Gray, J. M. N. T. 2012 Grain-size segregation and levee formation in geophysical mass flows. J. Geophys. Res. 117 (F1), F01032.
Jop, P., Forterre, Y. & Pouliquen, O. 2005 Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 541, 167192.
Kesserwani, G., Ghostine, R., Vazquez, J., Ghenaim, A. & Mosé, R. 2008 Application of a second-order Runge–Kutta discontinuous Galerkin scheme for the shallow water equations with source terms. Intl J. Numer. Meth. Fluids 56 (7), 805821.
Khakhar, D. V., McCarthy, J. J. & Ottino, J. M. 1999 Mixing and segregation of granular materials in chute flows. Chaos: An Interdisciplinary J. Nonlin. Sci. 9 (3), 594610.
Kokelaar, B. P., Bahia, R. S., Joy, K. H., Viroulet, S. & Gray, J. M. N. T. 2018 Granular avalanches on the moon: mass-wasting conditions, processes and features. J. Geophys. Res. Planets 122, 18931925.
Kokelaar, B. P., Graham, R. L., Gray, J. M. N. T. & Vallance, J. W. 2014 Fine-grained linings of leveed channels facilitate runout of granular flows. Earth Planet. Sci. Lett. 385, 172180.
Kowalski, J. & McElwaine, J. N. 2013 Shallow two-component gravity-driven flows with vertical variation. J. Fluid Mech. 714, 434462.
Larcher, M. & Jenkins, J. T. 2013 Segregation and mixture profiles in dense, inclined flows of two types of spheres. Phys. Fluids 25 (11), 113301.
Larcher, M. & Jenkins, J. T. 2015 The evolution of segregation in dense inclined flows of binary mixtures of spheres. J. Fluid Mech. 782, 405429.
Leveque, R. J. 2002 Finite Volume Methods for Hyperbolic Problems, vol. 31. Cambridge University Press.
Logan, M. & Iverson, R. M.2013 Video documentation of experiments at the usgs debris-flow flume 2008. US Geological Survey Open-File Rep. 2007–1315 v. 1.3.
Luding, S. 2008 Cohesive, frictional powders: contact models for tension. Granul. Matt. 10 (4), 235246.
Luding, S., Clément, E., Rajchenbach, J. & Duran, J. 1996 Simulations of pattern formation in vibrated granular media. Europhys. Lett. 36 (4), 247.
Marks, B., Rognon, P. & Einav, I. 2012 Grainsize dynamics of polydisperse granular segregation down inclined planes. J. Fluid Mech. 690, 499511.
Middleton, G. V. 1970 Experimental Studies Related to Problems of Flysch Sedimentation, vol. 7. The Geological Association of Canada.
Mobius, M. E., Lauderdale, B. E., Nageland, S. R. & Jaeger, H. M. 2001 Size separation of granular particles. Nature 414, 270.
Mullin, T. 2000 Coarsening of self-organised clusters in binary particle mixtures. Phys. Rev. Lett. 84, 4741.
Nurijanyan, S.2013 Discrete and continuous hamiltonian systems for wave modelling. PhD thesis, University of Twente, Enschede.
Pesch, L., Bell, A., Sollie, W. E. H., Ambati, V. R., Bokhove, O. & van der Vegt, J. J. W. 2007 hpGEM – a software framework for discontinuous Galerkin finite element methods. ACM Trans. Math. Softw. 33 (4), 23.
Pouliquen, O. 1999a On the shape of granular fronts down rough inclined planes. Phys. Fluids 11 (7), 19561958.
Pouliquen, O. 1999b Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11 (3), 542548.
Pouliquen, O. & Vallance, J. W. 1999 Segregation induced instabilities of granular fronts. Chaos 9 (3), 621630.
Press, W. H. 2007 Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press.
Reed, W. H. & Hill, T. R.1973 Triangular mesh methods for the neutron transport equation. Tech. Rep. Los Alamos Scientific Laboratory.
Rognon, P. G., Chevoir, F., Bellot, H., Ousset, F., Naaïm, M. & Coussot, P. 2008 Rheology of dense snow flows: inferences from steady state chute-flow experiments. J. Rheol. 52 (3), 729748.
Saingier, G., Deboeuf, S. & Lagrée, P.-Y. 2016 On the front shape of an inertial granular flow down a rough incline. Phys. Fluids 28 (5), 053302.
Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177215.
Savage, S. B. & Lun, C. K. K. 1988 Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid Mech. 189, 311335.
Schlick, C. P., Isner, A. B., Freireich, B. J, Fan, Y., Umbanhowar, P. B., Ottino, J. M. & Lueptow, R. M. 2016 A continuum approach for predicting segregation in flowing polydisperse granular materials. J. Fluid Mech. 797, 95109.
Shu, C. W. 2013 A brief survey on discontinuous Galerkin methods in computational fluid dynamics. Adv. Mech. v43, 541554.
Silbert, L. E., Ertaş, D., Grest, G. S., Halsey, T. C., Levine, D. & Plimpton, S. J. 2001 Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64 (5), 051302.
Silbert, L. E., Landry, J. W. & Grest, G. S. 2003 Granular flow down a rough inclined plane: transition between thin and thick piles. Phys. Fluids 15 (1), 110.
Staron, L. & Phillips, J. C. 2015a How large grains increase bulk friction in bi-disperse granular chute flows. Comput. Particle Mech. 3, 367372.
Staron, L. & Phillips, J. C. 2015b Stress partition and microstructure in size-segregating granular flows. Phys. Rev. E 92, 022210.
Takahashi, T. 2014 Debris Flow: Mechanics, Prediction and Countermeasures, 2nd edn. CRC Press.
Takahashi, T., Nakagawa, H., Harada, T. & Yamashiki, Y. 1992 Routing debris flows with particle segregation. ASCE J. Hydraul. Engng 118 (11), 14901507.
Thornton, A. R. & Gray, J. M. N. T. 2008 Breaking size segregation waves and particle recirculation in granular avalanches. J. Fluid Mech. 596, 261.
Thornton, A. R., Gray, J. M. N. T. & Hogg, A. J. 2006 A three-phase mixture theory for particle size segregation in shallow granular free-surface flows. J. Fluid Mech. 550, 125.
Thornton, A. R., Krijgsman, D., Te Voortwis, A., Ogarko, V., Luding, S., Fransen, R., Gonzalez, S., Bokhove, O., Imole, O. & Weinhart, T. 2013a A review of recent work on the discrete particle method at the University of Twente: An introduction to the open-source package MercuryDPM. In Proceedings of the 6th International Conference on Discrete Element Methods and Related Techniques, pp. 5056. Colorado School of Mines.
Thornton, A. R., Krijsgman, D., Fransen, R., Gonzalez, S., Tunuguntla, D. R., te Voortwis, A., Luding, S., Bokhove, O. & Weinhart, T. 2013b MercuryDPM: fast particle simulations in complex geometries. News. Enginsoft 10, 4853.
Thornton, A. R., Weinhart, T., Luding, S. & Bokhove, O. 2012a Frictional dependence of shallow-granular flows from discrete particle simulations. Eur. Phys. J. E 35 (12), 18.
Thornton, A. R., Weinhart, T., Luding, S. & Bokhove, O. 2012b Modeling of particle size segregation: calibration using the discrete particle method. Intl J. Modern Phys. C 23 (08), 1240014.
Toro, E. F. 2013 Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer Science & Business Media.
Tripathi, A. & Khakhar, D. V. 2011 Rheology of binary granular mixtures in the dense flow regime. Phys. Fluids 23 (11), 113302.
Tunuguntla, D. R., Bokhove, O. & Thornton, A. R. 2014 A mixture theory for size and density segregation in shallow granular free-surface flows. J. Fluid Mech. 749, 99112.
Tunuguntla, D. R., Thornton, A. R. & Weinhart, T. 2016a From discrete elements to continuum fields: extension to bidisperse systems. Comput. Particle Mech. 3 (3), 349365.
Tunuguntla, D. R., Weinhart, T. & Thornton, A. R. 2016b Comparing and contrasting size-based particle segregation models. Comput. Particle Mech. 4, 119.
van der Vaart, K., van Schrojenstein Lantman, M. P., Weinhart, T., Luding, S., Ancey, C. & Thornton, A. R.2017 Segregation of large particles in dense granular flows: a granular Saffman effect? Preprint, arXiv:1705.06803.
van der Vaart, K., Thornton, A. R., Johnson, C. G., Weinhart, T., Jing, L., Gajjar, P., Gray, J. M. N. T. & Ancey, C. 2018 Breaking size-segregation waves and mobility feedback in dense granular avalanches. Granul. Matt. 20 (3), 46.
Vallance, J. W. & Savage, S. B. 2000 Particle segregation in granular flows down chutes. In IUTAM Symposium on Segregation in Granular Flows, pp. 3151. Springer.
Voortwis, A. Te2013 Closure laws for granular, shallow-layer, bi-disperse flows down an inclined chute. Master’s thesis, MSM Group, Univ. Twente, the Netherlands.
Weinhart, T., Hartkamp, R., Thornton, A. R. & Luding, S. 2013 Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface. Phys. Fluids 25 (7), 070605.
Weinhart, T., Thornton, A. R., Luding, S. & Bokhove, O. 2012 Closure relations for shallow granular flows from particle simulations. Granul. Matt. 14 (4), 531552.
Weinhart, T., Tunuguntla, D. R., van Schrojenstein-Lantman, M. P., van der Horn, A. J., Denissen, I. F. C., Windows-Yule, C. R., de Jong, A. C. & Thornton, A. R. 2017 MercuryDPM: A Fast and Flexible Particle Solver Part A: Technical Advances. pp. 13531360. Springer.
Wiederseiner, S., Andreini, N., Épely-Chauvin, G., Moser, G., Monnereau, M., Gray, J. M. N. T. & Ancey, C. 2011 Experimental investigation into segregating granular flows down chutes. Phys. Fluids 23 (1), 013301.
Windows-Yule, C. R. K., Scheper, B. J., van der Horn, A. J., Hainsworth, N., Saunders, J., Parker, D. J. & Thornton, A. R. 2016 Understanding and exploiting competing segregation mechanisms in horizontally rotated granular media. New J. Phys. 18 (2), 023013.
Woodhouse, M. J., Thornton, A. R., Johnson, C. G., Kokelaar, B. P. & Gray, J. M. N. T. 2012 Segregation-induced fingering instabilities in granular free-surface flows. J. Fluid Mech. 709, 543580.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Type Description Title
VIDEO
Movie

Denissen et al. supplementary movie
Height- and small particle height profiles provided by discontinuous Galerkin simulations of the bulbous head formation, starting from an empty chute.

 Video (1.1 MB)
1.1 MB

Bulbous head formation in bidisperse shallow granular flow over an inclined plane

  • I. F. C. Denissen (a1), T. Weinhart (a1), A. Te Voortwis (a1), S. Luding (a1), J. M. N. T. Gray (a2) and A. R. Thornton (a1)...

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