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Two- and three dimensional evolution of granular avalanche flow — theory and experiments revisited

  • K. Hutter
Part of the Acta Mechanica Supplementum book series (ACTA MECH.SUPP., volume 1)

Summary

Rockfalls, sturzstroms, landslides and snow and ice avalanches have been conjectured to be describable by a plastic continuum of the Mohr-Coulomb type with a constant internal angle of friction. Bed resistance is modeled through a sliding law by additively composing the basal traction of a Mohr-Coulomb stress with bed friction angle δ and a viscous drag that is proportional to the first or second power of the sliding velocity. The theoretical model takes advantage of depth averaging and presents field equations for the height and surface-parallel volume fluxes.

Results are reviewed that have been obtained with this theory in chute flows along straight and curved beds and unconfined motions of a finite mass of a cohesionsless granular material down plane and curved beds. The results are compared with experimental findings from extensive laboratory tests, and inferences are drawn that derive from such comparisons.

Keywords

Granular Material Similarity Solution Incline Plane Viscous Drag Snow Avalanche 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Voellmy, A.: Über die Zerstörungskraft von Lawinen. Schweizerische Bauzeitung 73, 159–162, 212–217, 246–249, 280–285 (1955).Google Scholar
  2. [2]
    Salm, B.,: On nonuniform steady flow of avalanching snow. IUGG/IAHS General Assembly, Bern, Switzerland, IAHS Publ. No. 79, 19–29 (1968).Google Scholar
  3. [3]
    Perla, I. P., Cheng, T. T., McClung, D. M.: A two parameter model of snow avalanche motion. J. Glaciol. 26(94), 197–207 (1980).Google Scholar
  4. [4]
    Savage, S. B., Hutter, K.: The dynamics of avalanches of granular materials from initiation to runout, Part I. Analysis. Acta Mech. 86, 201–223 (1990).MathSciNetCrossRefGoogle Scholar
  5. [5]
    Savage, S. B.: Flow of granular materials. In: Theoretical and applied mechanics (P. Germain, M. Piau, D. Caillerie, eds.), Elsevier Scientific Publ. V. V. North Holland, IUTAM 1989, 241–266Google Scholar
  6. [6]
    Hutter, K., Szidarovsky, F., Yakowitz, S.: Plane steady shear flow of a cohesionless granular material down an inclined plane: a model for flow avalanches, Part I. Theory. Acta Mech. 63, 87–112 (1986).MATHCrossRefGoogle Scholar
  7. [7]
    Hutter, K., Szidarovsky, F., Yakowitz, S.: Plane steady shear flow of a cohesionless granular material down an inclined plane: a model for flow avalanches, Part II. Numerical results. Acta Mech. 65, 239–261 (1986).CrossRefGoogle Scholar
  8. [8]
    Savage, S. B., Hutter, K.: The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177–215 (1989).MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Hutter, K., Koch, T.: Motion of a granular avalanche in an exponentially curved chute: experiments and theoretical predictions. Phil. Trans. Roy. Soc London A 334, 93–138 (1991).Google Scholar
  10. [10]
    Hutter, K., Nohguchi, Y.: Similarity solutions for a Voellmy model of snow avalanches with finite mass. Acta Mech. 82, 99–127 (1990).MATHCrossRefGoogle Scholar
  11. [11]
    Savage, S. B., Nohguchi, Y.: Similarity solutions for avalanches of granular materials down curved beds. Acta Mech. 75, 153–174 (1988).MATHCrossRefGoogle Scholar
  12. [12]
    Nohguchi, Y., Hutter, K., Savage, S. B.: Similarity solutions for a finite mass granular avalanche with variable friction. Continuum Mechanics and Thermodynamics 1, 239–265 (1989).MathSciNetCrossRefGoogle Scholar
  13. [13]
    Huber, A.: Schwallwellen in Seen als Folge von Felsstürzen. Mitteilung No. 47 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie an der ETH, 1–122 (1980).Google Scholar
  14. [14]
    Plüss, Ch.: Experiments on granular avalanches. Diplomarbeit, Abt. X, Eidg. Technische Hochschule, Zürich, pp. 1–113 (1987).Google Scholar
  15. [15]
    Koch, T.: Bewegung einer Granulatlawine entlang einer gekrümmten Bahn. Diplomarbeit, Technische Hochschule Darmstadt, 1–122 (1989).Google Scholar
  16. [16]
    Hutter, K., Plüss, Ch., Maeno, N.: Some implications deduced from laboratory experiments on granular avalanches. Mitteilung No. 94 der Versuchsanstalt fur Wasserbau, Hydrologie und Glaziologie an der ETH, 323–344 (1988).Google Scholar
  17. [17]
    Hutter, K., Plüss, Ch., Savage, S. B.: Dynamics of avalanches of granular materials from initiation to runout, Part II. Laboratory experiments (in preparation).Google Scholar
  18. [18]
    Alean, J.: Untersuchungen über Entstehungsbedingungen und Reichweiten von Eislawinen. Mitteilung Nr. 74 der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie an der ETH, 1–217 (1984).Google Scholar
  19. [19]
    Lang, R. M.: An experimental and analytical study on gravity driven free surface flows of cohesionless granular media. Dr. rer. nat. dissertation, Technische Hochschule Darmstadt (forth-coming).Google Scholar
  20. [20]
    Hutter, K., Siegel, M., Savage, S. B., Nohguchi, Y.: Twodimensional spreading of a granular avalanche down an inclined plane. Part I. Theory. Acta Mech. (submitted).Google Scholar
  21. [21]
    Hutter, K., Siegel, M.: Two-dimensional similarity solutions for finite mass granular avalanches with Coulomb and viscous-type frictional resistance. J. Glaciol. (submitted).Google Scholar
  22. [22]
    Lang, R. M., Leo, B. R., Hutter, K.: Flow characteristics of an unconfined, non-cohesive, granular medium down an inclined curved surface, preliminary experimental results. Ann. Glaciol. 13, 146–153 (1989).Google Scholar

Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • K. Hutter
    • 1
  1. 1.Institut fur MechanikTechnische HochschuleDarmstadtGermany

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