Skip to main content
SpringerLink
Log in

The relation between dilatancy, effective stress and dispersive pressure in granular avalanches

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

Here we investigate three long-standing principles of granular mechanics and avalanche science: dilatancy, effective stress and dispersive pressure. We first show how the three principles are mechanically interrelated: Shearing of a particle ensemble creates a mechanical energy flux associated with random particle movements (scattering). Because the particle scattering is inhibited at the basal boundary, there is a spontaneous rise in the center of mass of the particle ensemble (dilatancy). This rise is connected to a change in potential energy. When the center of mass rises, there is a corresponding reaction at the base of the flow that is coupled to the vertical acceleration of the ensemble. This inertial stress is the dispersive pressure. Dilatancy is therefore not well connected to effective-stress-type relations, rather the energy fluxes describing the configurational changes of the particle ensemble. The strict application of energy principles has far-reaching implications for the modeling of avalanches and debris flows and other dangerous geophysical hazards.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Bagnold RA (1954) Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc R Soc Lond A 225(1160):49–63

    Article  Google Scholar 

  2. Bartelt P, Buser O, Platzer K (2006) Fluctuation-dissipation relations for granular snow avalanches. J Glaciol 52(179):631–643

    Article  Google Scholar 

  3. Bartelt P, Bühler O, Buser O, Christen M, Meier L (2012) Modeling mass-dependent flow regime transitions to predict the stopping and depositional behaviour of snow avalanches. J Geophys Res 117:F01015. doi:10.1029/2010JF001957

    Google Scholar 

  4. Bartelt P, Vera CV, Feistl T, Christen M, Bühler Y, Buser O (2015) Modelling cohesion in snow avalanche flow. J Glaciol 61(229):837–850. doi:10.3189/2015JoG14J126

    Article  Google Scholar 

  5. Bartelt P, Buser O, Vera VC, Bühler Y (2016) Configurational energy and the formation of mixed flowing/powder snow and ice avalanches. Ann Glaciol. doi:10.3189/2016AoG71A464

    Google Scholar 

  6. Bouchut F, Fernandez-Nieto DE, Mangeney A, Narbona-Reina G (2015) A two-phase two-layer model for fluidized granular flows with dilatancy effects. https://hal-upec-upem.archives-ouvertes.fr/hal-01161930

  7. Buser O, Bartelt P (2011) Dispersive pressure and density variations in snow avalanches. J Glaciol 57(205)

  8. Buser O, Bartelt P (2015) An energy-based method to calculate streamwise density variations in snow avalanches. J Glaciol. doi:10.3189/2015JoG14J054

    Google Scholar 

  9. George D, Iverson RM (2014) A depth-averaged debris-flow model that includes the effects of evolving dilatancy II. Numerical predictions and experimental tests. Proc R Soc A 470:20130820. doi:10.1098/rspa.2013.0820

    Article  MathSciNet  Google Scholar 

  10. Goodman RE (1999) Karl Terzaaghi. ASCE press, Reston

    Book  Google Scholar 

  11. Hunt ML, Zenit R, Campell CS, Brennen CE (2002) Revisiting the 1954 suspension experiments of RA Bagnold. J Fluid Mech 452:1–24

    Article  MATH  Google Scholar 

  12. Issler D, Gauer P (2008) Exploring the significance of the fluidized flow regime for avalanche hazard mapping. Ann Glaciol 49:193–198

    Article  Google Scholar 

  13. Iverson RM, Logan M, LaHusen RG, Berti M (2010) The perfect debris flow? Aggregated results from 28 large-scale experiments. J Geophys Res Earth Surf 115:F03005. doi:10.1029/2009JF001514

    Article  Google Scholar 

  14. Iverson R, George D (2014) A depth-averaged debris-flow model that includes the effects of evolving dilatancy I. Physical basis. Proc R Soc A 470:20130819. doi:10.1098/rspa.2013.0819

    Article  MathSciNet  Google Scholar 

  15. Kaitna R, Dietrich WE, Hsu L (2014) Surface slopes, velocity profiles and fluid pressure in coarse-grained debris flows saturated with water and mud. J Fluid Mech 741:277–403. doi:10.1017/jfm.2013.675

    Article  Google Scholar 

  16. Kaitna R, Palucis M, Yohannes B, Hill K, Dietrich WE (2015) Effects of coarse grain size distribution and fine particle content on pore fluid pressure and shear behavior in experimental debris flows. J Geophys Res Earth Surf. doi:10.1002/2015JF003725

    Google Scholar 

  17. Kowalski J, McElwaine JN (2013) Shallow two-component gravity-driven flows with vertical variation. J Fluid Mech 714:434–462

    Article  MathSciNet  MATH  Google Scholar 

  18. Le Roux J (2003) Can dispersive pressure cause inverse grading in grain flows? Discussion. J Sediment Res 73:333–334

    Article  Google Scholar 

  19. Legros F (2002) Can dispersive pressure cause inverse grading in grain flows? J Sediment Res 72:166–170

    Article  Google Scholar 

  20. Legros F (2003) Can dispersive pressure cause inverse grading in grain flows? Reply. J Sediment Res 73:335–335

    Article  Google Scholar 

  21. Leine R, Schweizer A, Christen M, Glover J, Bartelt P, Gerber W (2014) Simulation of rockfall trajectories with consideration of rock shape. Multibody Syst Dyn 32(2):241–271. doi:10.1007/s11044-013-9393-4

    Article  MathSciNet  MATH  Google Scholar 

  22. McArdell BW, Bartelt P, Kowalski J (2007) Field observations of basal forces and fluid pressure in a debris flow. Geophys Res Lett 34:L07406. doi:10.1029/2006GL029183

    Article  Google Scholar 

  23. Norem H, Irgens F, Schieldrop B (1987) A continuum model for calculating snow avalanche velocities. In: Salm B, Gubler H (eds) Avalanche formation, movements and effects. Proceedings of the Davos symposium, September 1986. IAHS Publication no. 162. IAHS Press, Inst. of Hydrology, Wallingford, pp 363–380

  24. Platzer K, Bartelt P, Kern M (2007) Measurements of dense snow avalanche basal shear to normal stress ratios (S/N). Geophys Res Lett 34(7):L07501

    Article  Google Scholar 

  25. Reynolds O (1886) Experiments showing dilatancy, a property of granular material, possibly connected with gravitation. In: Proceedings at the Royal Institution of Great Britain, Read February 12

  26. Reynolds O (1885) On the dilatancy of media composed of rigid particles in contact, with experimental illustrations. Philos Mag Ser 5(20):469–481

    Article  Google Scholar 

  27. Rowlinson J (2002) Cohesion. Cambridge University Press, Cambridge

    Book  Google Scholar 

  28. Savage S, Hutter K (1989) The motion of a finite mass of granular material down a rough incline. J Fluid Mech 199:177–215

    Article  MathSciNet  MATH  Google Scholar 

  29. Terzaghi C (1925) Principles of soil mechanics. Eng News Rec 95(19–23):25–27

    Google Scholar 

  30. Vera VC, Wikstroem JK, Bühler Y, Bartelt P (2015) Release temperature, snow-cover entrainment and the thermal flow regime of snow avalanches. J Glaciol. doi:10.3189/2015JoG14J117

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. WSL Institute for Snow and Avalanche Research SLF, Davos Dorf, Switzerland

    Perry Bartelt & Othmar Buser

Authors
  1. Perry Bartelt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Othmar Buser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Perry Bartelt.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bartelt, P., Buser, O. The relation between dilatancy, effective stress and dispersive pressure in granular avalanches. Acta Geotech. 11, 549–557 (2016). https://doi.org/10.1007/s11440-016-0463-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-016-0463-7

Keywords

Search

Navigation