Granular Matter

, 20:46 | Cite as

Breaking size-segregation waves and mobility feedback in dense granular avalanches

  • K. van der VaartEmail author
  • A. R. Thornton
  • C. G. Johnson
  • T. Weinhart
  • L. Jing
  • P. Gajjar
  • J. M. N. T. Gray
  • C. Ancey
Original Paper


Through experiments and discrete particle method (DPM) simulations we present evidence for the existence of a recirculating structure, that exists near the front of dense granular avalanches, and is known as a breaking size-segregation (BSS) wave. This is achieved through the study of three-dimensional bidisperse granular flows in a moving-bed channel. Particle-size segregation gives rise to the formation of a large-particle-rich front and a small-particle-rich tail with a BSS wave positioned between the tail and front. We experimentally resolve the structure of the BSS wave using refractive-index matched scanning and find that it is qualitatively similar to the structure observed in DPM simulations. Our analysis demonstrates a relation between the concentration of small particles in the flow and the amount of basal slip, in which the structure of the BSS wave plays a key role. This leads to a feedback between the mean bulk flow velocity and the process of particle-size segregation. Ultimately, these findings shed new light on the recirculation of large and small grains near avalanche fronts and the effects of this behaviour on the mobility of the bulk flow.


Avalanches Size-segregation Mobility feedback Basal slip Moving-bed channel 



This study was funded by the Dutch STW VIDI project No. 13472, the Swiss SNF Grant No. 200021-149441, and by NERC grants NE/-E003206/1 and NE/K003011/1 as well as EPSRC grants EP/I019189/1, EP/K00428X/1 and EP/M022447/1. J.M.N.T.G. is a Royal Society Wolfson Research Merit Award holder (WM150058) and an EPSRC Established Career Fellow (EP/M022447/1). The authors are grateful to B. de Graffenried for technical assistance, to M. Teuscher for designing and building the experimental setup, and to J.-L. Pfister for assistance with the experiments and analysis. The authors also thank H. Capart for providing the Voronoï tracking code and the referees for helping to improve this paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Sharp, R.P., Nobles, L.H.: Mudflow of 1941 at wrightwood, Southern california. Geol. Soc. Am. Bull. 64(5), 547–560 (1953)ADSCrossRefGoogle Scholar
  2. 2.
    Bagnold, R.A.: Deposition in the process of hydraulic transport. Sedimentology 10(1), 45–56 (1968)ADSCrossRefGoogle Scholar
  3. 3.
    Takahashi, T.: Debris flow on prismatic open channel. J. Hydraul. Div. ASCE 106(3), 381–396 (1980)Google Scholar
  4. 4.
    Takahashi, T.: Debris flow. Annu. Rev. Fluid Mech. 13, 57–77 (1981)ADSCrossRefGoogle Scholar
  5. 5.
    Johnson, A.M.: Physical Processes in Geology. Freeman, Cooper & Company, San Francisco (1970)Google Scholar
  6. 6.
    Johnson, A.M., Rodine, J.R.: Debris flows. In: Brunsden, D., Prior, D.B. (eds.) Slope Instability. Wiley (1984)Google Scholar
  7. 7.
    Costa, J.E., Williams, G.: Debris flow dynamics. Technical Report 84-606, (videotape) U.S. Geological Survey (1984)Google Scholar
  8. 8.
    Iverson, R.M., Logan, M., LaHusen, R.G., Berti, M.: The perfect debris flow? Aggregated results from 28 large-scale experiments. J. Geophys. Res. 115, F03005 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    Iverson, R.M.: Debris flows: behaviour and hazard assessment. Geol. Today 30(1), 15–20 (2014)CrossRefGoogle Scholar
  10. 10.
    Turnbull, B., Bowman, E.T., McElwaine, J.N.: Debris flows: experiments and modelling. C. R. Phys. 16(1), 86–96 (2015)ADSCrossRefGoogle Scholar
  11. 11.
    Pierson, T.C.: Flow Behavior of Channelized Debris Flows, pp. 269–296. Allen & Unwin, Crows Nest (1986)Google Scholar
  12. 12.
    Pouliquen, O., Delour, J., Savage, S.B.: Fingering in granular flows. Nature 386, 816–817 (1997)ADSCrossRefGoogle Scholar
  13. 13.
    Pouliquen, O., Vallance, J.W.: Segregation induced instabilities of granular fronts. Chaos 9(3), 621–630 (1999)ADSCrossRefzbMATHGoogle Scholar
  14. 14.
    Woodhouse, M.J., Thornton, A.R., Johnson, C.G., Kokelaar, B.P., Gray, J.M.N.T.: Segregation-induced fingering instabilities in granular free-surface flows. J. Fluid Mech. 709, 543–580 (2012)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Baker, J.L., Johnson, C.G., Gray, J.M.N.T.: Segregation-induced finger formation in granular free-surface flows. J. Fluid Mech. 809, 168–212 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Wilson, L., Head, J.W.: Morphology and rheology of pyroclastic flows and their deposits, and guidelines for future observations. US Geol. Surv. Prof. Pap. 1250, 513–524 (1980)Google Scholar
  17. 17.
    Major, J.J., Iverson, R.M.: Debris-flow deposition: effects of pore-fluid pressure and friction concentrated at flow margins. Geol. Soc. Am. Bull. 111(10), 1424–1434 (1999)ADSCrossRefGoogle Scholar
  18. 18.
    Calder, E.S., Sparks, R.S.J., Gardeweg, M.C.: Erosion, transport and segregation of pumice and lithic clasts in pyroclastic flows inferred from ignimbrite at lascar volcano, chile. J. Volcanol. Geotherm. Res. 104(1), 201–235 (2000)ADSCrossRefGoogle Scholar
  19. 19.
    Félix, G., Thomas, N.: Relation between dry granular flow regimes and morphology of deposits: formation of levées in pyroclastic deposits. Earth Planet. Sci. Lett. 221(1), 197–213 (2004)ADSCrossRefGoogle Scholar
  20. 20.
    Bartelt, P., Glover, J., Feistl, T., Bühler, Y., Buser, O.: Formation of levees and en-echelon shear planes during snow avalanche run-out. J. Glaciol. 58(211), 980–992 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    Johnson, C.G., Kokelaar, B.P., Iverson, R.M., Logan, M., LaHusen, R.G., Gray, J.M.N.T.: Grain-size segregation and levee formation in geophysical mass flows. J. Geophys. Res. 117(F1), 013301 (2012)CrossRefGoogle Scholar
  22. 22.
    Thomas, N.: Reverse and intermediate segregation of large beads in dry granular media. Phys. Rev. E 62(1), 961–974 (2000)ADSCrossRefGoogle Scholar
  23. 23.
    Zanuttigh, B., Di Paolo, A.: Experimental analysis of the segregation of dry avalanches and implications for debris flows. J. Hydraul. Res. 44(6), 796–806 (2006)CrossRefGoogle Scholar
  24. 24.
    Goujon, C., Dalloz-Dubrujeaud, B., Thomas, N.: Bidisperse granular avalanches on inclined planes: a rich variety of behaviors. Eur. Phys. J. E Soft Matter Biol. Phys. 23, 199–215 (2007)CrossRefGoogle Scholar
  25. 25.
    Middleton, G.V.: Experimental studies related to problem of flysch sedimentation. In: Middleton, G.V., Bouma, A.H. (eds.) Flysch Sedimentology in North America (Lajoie, J. ed.). Business and Economics Science Ltd., pp. 253–272 (1970)Google Scholar
  26. 26.
    Ottino, J.M., Khakhar, D.V.: Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32(1), 55–91 (2000)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Savage, S.B., Lun, C.K.K.: Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid Mech. 189, 311–335 (1988)ADSCrossRefGoogle Scholar
  28. 28.
    Rognon, P.G., Roux, J.-N., Naaim, M., Chevoir, F.: Dense flows of bidisperse assemblies of disks down an inclined plane. Phys. Fluids 19(5), 058101 (2007)ADSCrossRefzbMATHGoogle Scholar
  29. 29.
    May, L.B.H., Golick, L.A., Phillips, K.C., Shearer, M., Daniels, K.E.: Shear-driven size segregation of granular materials: modeling and experiment. Phys. Rev. E 81, 051301 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    Wiederseiner, S., Andreini, N., Epely-Chauvin, G., Moser, G., Monnereau, M., Gray, J.M.N.T., Ancey, C.: Experimental investigation into segregating granular flows down chutes. Phys. Fluids A 23(1), 013301 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    Marks, B., Rognon, P., Einav, I.: Grainsize dynamics of polydisperse granular segregation down inclined planes. J. Fluid Mech. 690, 499–511 (2012)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Fan, Y., Boukerkour, Y., Blanc, T., Umbanhowar, P.B., Ottino, J.M., Lueptow, R.M.: Stratification, segregation, and mixing of granular materials in quasi-two-dimensional bounded heaps. Phys. Rev. E 86(5), 051305 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    Staron, L., Phillips, J.C.: Segregation time-scale in bi-disperse granular flows. Phys. Fluids 26(3), 033302 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    Gray, J.M.N.T., Gajjar, P., Kokelaar, P.: Particle-size segregation in dense granular avalanches. C. R. Phys. 16(1), 73–85 (2015)ADSCrossRefGoogle Scholar
  35. 35.
    Tunuguntla, D.R., Weinhart, T., Thornton, A.R.: Comparing and contrasting size-based particle segregation models. Comput. Part. Mech. 4(4), 387–405 (2017)CrossRefGoogle Scholar
  36. 36.
    Edwards, A.N., Vriend, N.M.: Size segregation in a granular bore. Phys. Rev. Fluids 1(6), 064201 (2016)ADSCrossRefGoogle Scholar
  37. 37.
    Thornton, A.R., Gray, J.M.N.T.: Breaking size segregation waves and particle recirculation in granular avalanches. J. Fluid Mech. 596, 261–284 (2008)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Gray, J.M.N.T., Ancey, C.: Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts. J. Fluid Mech. 629, 387–423 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Gray, J.M.N.T., Kokelaar, B.P.: Large particle segregation, transport and accumulation in granular free-surface flows. J. Fluid Mech. 652, 105–137 (2010)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Gray, J.M.N.T., Kokelaar, B.P.: Erratum large particle segregation, transport and accumulation in granular free-surface flows—erratum. J. Fluid Mech. 657, 539 (2010)ADSCrossRefzbMATHGoogle Scholar
  41. 41.
    Phillips, J.C., Hogg, A.J., Kerswell, R.R., Thomas, N.H.: Enhanced mobility of granular mixtures of fine and coarse particles. Earth Planet. Sci. Lett. 246(34), 466–480 (2006)ADSCrossRefGoogle Scholar
  42. 42.
    Gray, J.M.N.T., Ancey, C.: Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts. J. Fluid Mech. 629, 387–423 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Kokelaar, B.P., Graham, R.L., Gray, J.M.N.T., Vallance, J.W.: Fine-grained linings of leveed channels facilitate runout of granular flows. Earth Planet. Sci. Lett. 385, 172–180 (2014)ADSCrossRefGoogle Scholar
  44. 44.
    Gray, J.M.N.T., Thornton, A.R.: A theory for particle size segregation in shallow granular free-surface flows. Proc. R. Soc. A Math. Phys. Eng. Sci. 461, 1447–1473 (2005)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Marks, B., Eriksen, J.A., Dumazer, G., Sandnes, B., Måløy, K.J.: Size segregation of intruders in perpetual granular avalanches. J. Fluid Mech. 825, 502–514 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Gajjar, P., van der Vaart, K., Thornton, A.R., Johnson, C.G., Ancey, C., Gray, J.M.N.T.: Asymmetric breaking size-segregation waves in dense granular free-surface flows. J. Fluid Mech. 794, 460–505 (2016)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Gajjar, P., Gray, J.M.N.T.: Asymmetric flux models for particle-size segregation in granular avalanches. J. Fluid Mech. 757, 297–329 (2014)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    van der Vaart, K., Gajjar, P., Epely-Chauvin, G., Andreini, N., Gray, J.M.N.T., Ancey, C.: Underlying asymmetry within particle size segregation. Phys. Rev. Lett. 114(23), 238001 (2015)ADSCrossRefGoogle Scholar
  49. 49.
    Golick, L.A., Daniels, K.E.: Mixing and segregation rates in sheared granular materials. Phys. Rev. E 80, 042301 (2009)ADSCrossRefGoogle Scholar
  50. 50.
    Davies, T.R.H.: Debris-flow surges—experimental simulation. J. Hydrol. 29(1), 18–46 (1990)Google Scholar
  51. 51.
    Armanini, A., Capart, H., Fraccarollo, L., Larcher, M.: Rheological stratification in experimental free-surface flows of granular–liquid mixtures. J. Fluid Mech. 532, 269–319 (2005)ADSCrossRefzbMATHGoogle Scholar
  52. 52.
    Leonardi, A., Cabrera, M., Wittel, F.K., Kaitna, R., Mendoza, M., Wu, W., Herrmann, H.J.: Granular-front formation in free-surface flow of concentrated suspensions. Phys. Rev. E 92(5), 052204 (2015)ADSCrossRefGoogle Scholar
  53. 53.
    Mahapatra, P.S., Mathew, S., Panchagnula, M.V., Vedantam, S.: Effect of size distribution on mixing of a polydisperse wet granular material in a belt-driven enclosure. Granul. Matter 18(2), 1–12 (2016)CrossRefGoogle Scholar
  54. 54.
    Chambon, G., Ghemmour, A., Laigle, D.: Gravity-driven surges of a viscoplastic fluid: an experimental study. J. Non Newton. Fluid Mech. 158(1), 54–62 (2009)CrossRefGoogle Scholar
  55. 55.
    Chambon, G., Ghemmour, A., Naaim, M.: Experimental investigation of viscoplastic free-surface flows in a steady uniform regime. J. Fluid Mech. 754, 332–364 (2014)ADSCrossRefGoogle Scholar
  56. 56.
    Wiederseiner, S., Andreini, N., Epely-Chauvin, G., Ancey, C.: Refractive-index and density matching in concentrated particle suspensions: a review. Exp. Fluids 50, 1183–1206 (2011)CrossRefGoogle Scholar
  57. 57.
    Dijksman, J.A., Rietz, F., Lőrincz, K.A., van Hecke, M., Losert, W.: Invited article: refractive index matched scanning of dense granular materials. Rev. Sci. Instrum. 83(1), 011301 (2012)ADSCrossRefGoogle Scholar
  58. 58.
    Hübl, J., Steinwendtner, H.: Estimation of rheological properties of viscous debris flow using a belt conveyor. Phys. Chem. Earth Part B Hydrol. Oceans Atmos. 25(9), 751–755 (2000)ADSCrossRefGoogle Scholar
  59. 59.
    Weinhart, T., Hartkamp, R., Thornton, A.R., Luding, S.: Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface. Phys. Fluids 25(7), 070605 (2013)ADSCrossRefGoogle Scholar
  60. 60.
    Tunuguntla, D.R., Thornton, A.R., Weinhart, T.: From discrete elements to continuum fields: extension to bidisperse systems. Comput. Part. Mech. 3(3), 349–365 (2016)CrossRefGoogle Scholar
  61. 61.
    Goldhirsch, I.: Stress, stress asymmetry and couple stress: from discrete particles to continuous fields. Granul. Matter 12(3), 239–252 (2010)CrossRefzbMATHGoogle Scholar
  62. 62.
    Weinhart, T., Thornton, A.R., Luding, S., Bokhove, O.: Closure relations for shallow granular flows from particle simulations. Granul. Matter 14(4), 531–552 (2012)CrossRefGoogle Scholar
  63. 63.
    Batchelor, G.K.: A brief guide to two-phase flow. Theor. Appl. Mech. 1, 27–40 (1989)ADSCrossRefGoogle Scholar
  64. 64.
    du Pont, S.C., Gondret, P., Perrin, B., Rabaud, M.: Granular avalanches in fluids. Phys. Rev. Lett. 90(4), 044301 (2003)ADSCrossRefGoogle Scholar
  65. 65.
    Shattuck, M.D., Ingale, R.A., Reis, P.M.: Granular thermodynamics. AIP Conf. Proc. 1145(1), 43–50 (2009)ADSCrossRefGoogle Scholar
  66. 66.
    Capart, H., Young, D.L., Zech, Y.: Voronoï imaging methods for the measurement of granular flows. Exp. Fluids 32(1), 121–135 (2002)CrossRefGoogle Scholar
  67. 67.
    Thornton, A.R., Weinhart, T., Ogarko, V., Luding, S.: Multi-scale methods for multi-component granular materials. Comput. Methods Mater. Sci 13(2), 197–212 (2013)Google Scholar
  68. 68.
    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.: Mercurydpm: a fast and flexible particle solver part a: technical advances. In: Proceedings of 7th International Conference on DEM, Springer, pp. 1353–1360 (2017)Google Scholar
  69. 69.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  70. 70.
    Silbert, L.E., Ertaş, D., Grest, G.S., Halsey, T.C., Levine, D., Plimpton, S.J.: Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64(5), 051302 (2001)ADSCrossRefGoogle Scholar
  71. 71.
    Beare, W.G., Bowden, F.P.: Physical properties of surfaces. I. Kinetic friction. Philos. Trans. R. Soc. A 234(741), 329–354 (1935)ADSCrossRefGoogle Scholar
  72. 72.
    Weinhart, T., Thornton, A.R., Luding, S., Bokhove, O.: From discrete particles to continuum fields near a boundary. Granul. Matter 14(2), 289–294 (2012)CrossRefGoogle Scholar
  73. 73.
    Thornton, A.R., Weinhart, T., Luding, S., Bokhove, O.: Frictional dependence of shallow-granular flows from discrete particle simulations. Eur. Phys. J. E 35(12), 127 (2012)CrossRefGoogle Scholar
  74. 74.
    Jing, L., Kwok, C.Y., Leung, Y.F.: Micromechanical origin of particle size segregation. Phys. Rev. Lett. 118(11), 118001 (2017)ADSCrossRefGoogle Scholar
  75. 75.
    Gray, J.M.N.T., Ancey, C.: Multi-component particle-size segregation in shallow granular avalanches. J. Fluid Mech. 678, 535–588 (2011)ADSCrossRefzbMATHGoogle Scholar
  76. 76.
    Silbert, L.E., Landry, J.W., Grest, G.S.: Granular flow down a rough inclined plane: transition between thin and thick piles. Phys. Fluids 15(1), 1–10 (2003)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  77. 77.
    Rajchenbach, J.: Dense, rapid flows of inelastic grains under gravity. Phys. Rev. Let. 90(14), 144302 (2003)ADSCrossRefGoogle Scholar
  78. 78.
    Bagnold, R.A.: Experiments on a gravity-free dispersion of large solid spheres in a newtonian fluid under shear. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 225(1160), 49–63 (1954)ADSCrossRefGoogle Scholar
  79. 79.
    Hungr, O., Evans, S.G.: Entrainment of debris in rock avalanches: an analysis of a long run-out mechanism. Geol. Soc. Am. Bull. 116(9–10), 1240–1252 (2004)ADSCrossRefGoogle Scholar
  80. 80.
    Kokelaar, B.P., Graham, R.L., Gray, J.M.N.T., Vallance, J.W.: Fine-grained linings of leveed channels facilitate runout of granular flows. Earth Planet. Sci. Lett. 385, 172–180 (2014)ADSCrossRefGoogle Scholar
  81. 81.
    Pouliquen, O.: Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11(3), 542–548 (1999)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  82. 82.
    Saingier, G., Deboeuf, S., Lagrée, P.-Y.: On the front shape of an inertial granular flow down a rough incline. Phys. Fluids 28(5), 053302 (2016)ADSCrossRefGoogle Scholar
  83. 83.
    Jing, L., Kwok, C.Y., Leung, Y.F., Sobral, Y.D.: Effect of geometric base roughness on size segregation. EPJ Web Conf. 140, 03056 (2017)CrossRefGoogle Scholar
  84. 84.
    Staron, L., Phillips, J.C.: How large grains increase bulk friction in bi-disperse granular chute flows. Comput. Part. Mech. 3(3), 367–372 (2016)CrossRefGoogle Scholar
  85. 85.
    Goujon, C., Thomas, N., Dalloz-Dubrujeaud, B.: Monodisperse dry granular flows on inclined planes: role of roughness. Eur. Phys. J. E 11(2), 147–157 (2003)CrossRefGoogle Scholar
  86. 86.
    Jing, L., Kwok, C.Y., Leung, Y.F., Sobral, Y.D.: Characterization of base roughness for granular chute flows. Phys. Rev. E 94(5), 052901 (2016)ADSCrossRefGoogle Scholar
  87. 87.
    Takahashi, T.: Debris flow. Annu. Rev. Fluid Mech. 13(1), 57–77 (1981)ADSCrossRefGoogle Scholar
  88. 88.
    Jessop, D.E., Kelfoun, K., Labazuy, P., Mangeney, A., Roche, O., Tillier, J.-L., Trouillet, M., Thibault, G.: Lascar pyroclastic flow deposits, and implication for flow dynamics and rheology. J. Volcanol. Geotherm. Res. 245(81–97), 2012 (1993)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Civil and Environmental EngineeringStanford UniversityStanfordUSA
  2. 2.Multiscale Mechanics, ET/MESA+University of TwenteEnschedeThe Netherlands
  3. 3.Department of Civil EngineeringThe University of Hong KongHong KongChina
  4. 4.Henry Moseley X-Ray Imaging Facility, School of MaterialsUniversity of ManchesterManchesterUK
  5. 5.School of Mathematics and Manchester centre for Nonlinear DynamicsUniversity of ManchesterManchesterUK
  6. 6.Environmental Hydraulics LaboratoryÉcole Polytechnique Fédérale de LausanneÉcublens, LausanneSwitzerland

Personalised recommendations