Skip to main content
Log in

Flow resistance in the transition from dense to dilute granular-fluid flows

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

Substantial research work has been focusing on the flow resistance of dense granular-fluid geophysical flows, e.g., debris flows. However, the mechanism of flow resistance as the dense debris flows transition to the dilute debris flow range (volumetric solid concentration 60% to 40%) remains an unsolved problem. Based on the accurate measurements of normal/shear stresses and pore fluid pressure at the flume base, we analyze the flow resistance of a series of controlled debris flow model tests, covering the flow regime from friction dominated to viscous/collisional dominated. We find that the flow resistance, excluding the Coulomb frictional component, can be well described by a visco-collisional scaling relationship. The solid–fluid interaction in the dilute range would facilitate a quick rebalance against the gravity driven force in the transient flow condition. Finally, a heuristic model is proposed to unify the flow resistance for dense and dilute debris flows.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Availability of data and materials

The experimental data is available upon request to the first author (D. Song, drsong@imde.ac.cn).

References

  1. Hungr, O.: Simplified models of spreading flow of dry granular material. Can. Geotech. J. 45(8), 1156–1168 (2008). https://doi.org/10.1139/T08-059

    Article  Google Scholar 

  2. Kaitna, R., Palucis, M.C., Yohannes, B., Hill, K.M., Dietrich, W.E.: 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. 121(2), 415–441 (2016). https://doi.org/10.1002/2015JF003725

    Article  ADS  Google Scholar 

  3. Zhou, G.G.D., Song, D., Choi, C.E., Pasuto, A., Sun, Q.C., Dai, D.F.: Surge impact behavior of granular flows: effects of water content. Landslides 15(4), 695–709 (2018). https://doi.org/10.1007/s10346-017-0908-6

    Article  Google Scholar 

  4. Haas, T., Braat, L., Leuven, J.R., Lokhorst, I.R., Kleinhans, M.G.: Effects of debris flow composition on runout, depositional mechanisms, and deposit morphology in laboratory experiments. J. Geophys. Res. Earth Surf. 120(9), 1949–1972 (2015). https://doi.org/10.1002/2015JF003525

    Article  ADS  Google Scholar 

  5. Wang, Y.F., Dong, J.J., Cheng, Q.G.: Velocity-dependent frictional weakening of large rock avalanche basal facies: Implications for rock avalanche hypermobility? J. Geophys. Res. Solid Earth 122, 1648–1676 (2017). https://doi.org/10.1002/2016JB013624

    Article  ADS  Google Scholar 

  6. Hu, W., Huang, R., McSaveney, M., Yao, L., Xu, Q., Feng, M., Zhang, X.: Superheated steam, hot CO2 and dynamic recrystallization from frictional heat jointly lubricated a giant landslide: field and experimental evidence. Earth Planet. Sci. Lett. 510, 85–93 (2019). https://doi.org/10.1016/j.epsl.2019.01.005

    Article  ADS  Google Scholar 

  7. Lucas, A., Mangeney, A., Ampuero, J.P.: Frictional velocity-weakening in landslides on Earth and on other planetary bodies. Nat. Commun. 5, 3417 (2014). https://doi.org/10.1038/ncomms4417

    Article  ADS  Google Scholar 

  8. Scaringi, G., Hu, W., Xu, Q., Huang, R.: Shear-rate-dependent behavior of clayey bimaterial interfaces at landslide stress levels. Geophys. Res. Lett. 45(2), 766–777 (2018). https://doi.org/10.1002/2017GL076214

    Article  ADS  Google Scholar 

  9. Zhou, G.G.D., Li, S., Song, D., Choi, C.E., Chen, X.Q.: Depositional mechanisms and morphology of debris flow: physical modelling. Landslides 16(2), 315–332 (2019). https://doi.org/10.1007/s10346-018-1095-9

    Article  Google Scholar 

  10. Courrech Dupont, S., Gondret, P., Perrin, B., Rabaud, M.: Granular avalanches in fluids. Phys. Rev. Lett. 90(4), 044301 (2003). https://doi.org/10.1103/PhysRevLett.90.044301

    Article  ADS  Google Scholar 

  11. McArdell, B.W., Bartelt, P., Kowalski, J.: Field observations of basal forces and fluid pore pressure in a debris flow. Geophys. Res. Lett. (2007). https://doi.org/10.1029/2006GL029183

    Article  Google Scholar 

  12. Iverson, R.M., George, D.L.: A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis. Proc. R. Soc. Lond. Ser. A (2014). https://doi.org/10.1098/rspa.2013.0820

    Article  MATH  Google Scholar 

  13. Iverson, R.M.: Scaling and design of landslide and debris-flow experiments. Geomorphology 244, 9–20 (2015). https://doi.org/10.1016/j.geomorph.2015.02.033

    Article  ADS  Google Scholar 

  14. Nagl, G., Hübl, J., Kaitna, R.: Velocity profiles and basal stresses in natural debris flows. Earth Surf. Proc. Land. 45(8), 1764–1776 (2020). https://doi.org/10.1002/esp.4844

    Article  ADS  Google Scholar 

  15. GDR MiDi: On dense granular flows. Eur. Phys. J. E 14(4): 341–365. https://doi.org/10.1140/epje/i2003-10153-0 (2004).

  16. Boyer, F., Guazzelli, É., Pouliquen, O.: Unifying suspension and granular rheology. Phys. Rev. Lett. 107(18), 188301 (2011). https://doi.org/10.1103/PhysRevLett.107.188301

    Article  ADS  Google Scholar 

  17. Trulsson, M., Andreotti, B., Claudin, P.: Transition from the viscous to inertial regime in dense suspensions. Phys. Rev. Lett. 109(11), 118305 (2012). https://doi.org/10.1103/PhysRevLett.109.118305

    Article  ADS  Google Scholar 

  18. Ancey, C., Evesque, P.: Frictional-collisional regime for granular suspension flows down an inclined channel. Phys. Rev. E 62(6), 8349 (2000). https://doi.org/10.1103/PhysRevE.62.8349

    Article  ADS  Google Scholar 

  19. Rauter, M., Fischer, J.T., Fellin, W., Kofler, A.: Snow avalanche friction relation based on extended kinetic theory. Nat. Hazard. 16(11), 2325–2345 (2016). https://doi.org/10.5194/nhess-16-2325-2016

    Article  Google Scholar 

  20. Bartelt, P., Salm, B., Gruber, U.: Calculating dense-snow avalanche runout using a Voellmy-fluid model with active/passive longitudinal straining. J. Glaciol. 45(150), 242–254 (1999). https://doi.org/10.3189/S002214300000174X

    Article  ADS  Google Scholar 

  21. Acheson, D.J.: Instability. Elementary Fluid Mechanics (Oxford University Press, 1990).

  22. Bartelt, P., Bühler, Y., Buser, O., Christen, M., Meier, L.: Modeling mass-dependent flow regime transitions to predict the stopping and depositional behavior of snow avalanches. J. Geophys. Res. Earth Surf. (2012). https://doi.org/10.1029/2010JF001957

    Article  Google Scholar 

  23. Iverson, R.M., Logan, M., LaHusen, R.G., Berti, M.: The perfect debris flow? Aggregated results from 28 large-scale experiments. J. Geophys. Res. Earth Surf. (2010). https://doi.org/10.1029/2009JF001514

    Article  Google Scholar 

  24. Platzer, K., Bartelt, P., Kern, M.: Measurements of dense snow avalanche basal shear to normal stress ratios (S/N). Geophys. Res. Lett. (2007). https://doi.org/10.1029/2006GL028670

    Article  Google Scholar 

  25. Liu, Y., Wang, H., Chen, H.Y., Hu, K.H., Wang, X.K.: The properties of dilute debris flow and hyper-concentrated flow in different flow regimes in open channels. J. Mt. Sci. 14, 1728 (2017). https://doi.org/10.1007/s11629-016-4132-y

    Article  Google Scholar 

  26. Takahashi, T.: Mechanical characteristics of debris flow. J. Hydraul. Div. 104(8), 1153–1169 (1978)

    Article  Google Scholar 

  27. 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). https://doi.org/10.1017/S0022112005004283

    Article  ADS  MATH  Google Scholar 

  28. Cassar, C., Nicolas, M., Pouliquen, O.: Submarine granular flows down inclined planes. Phys. Fluids 17(10), 103301 (2005). https://doi.org/10.1063/1.2069864

    Article  ADS  MATH  Google Scholar 

  29. Kaitna, R., Dietrich, W.E., Hsu, L.: Surface slopes, velocity profiles and fluid pressure in coarse-grained debris flows saturated with water and mud. J. Fluid Mech. 741, 377 (2014). https://doi.org/10.1017/jfm.2013.675

    Article  ADS  Google Scholar 

  30. 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. Earth Surf. (2012). https://doi.org/10.1029/2011JF002185

    Article  Google Scholar 

  31. 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). https://doi.org/10.1016/j.epsl.2013.10.043

    Article  ADS  Google Scholar 

  32. Iverson, R.M.: The physics of debris flows. Rev. Geophys. 35(3), 245–296 (1997). https://doi.org/10.1029/97RG00426

    Article  ADS  Google Scholar 

  33. Berzi, D., Larcan, E.: Flow resistance of inertial debris flows. J. Hydraul. Eng. 139(2), 187–194 (2012). https://doi.org/10.1061/(ASCE)HY.1943-7900.0000664

    Article  Google Scholar 

  34. Iverson, R.M.: Mechanics of debris flows and rock avalanches. In: Fernando, H.J.S. (ed.) Handbook of Environmental Fluid Dynamics, vol. 1, pp. 573–587. CRC Press Taylor Francis (2013)

    Google Scholar 

  35. Rickenmann, D., Weber, D., Stepanov, B.: Erosion by debris flows in field and laboratory experiments. Debris-flow hazards mitigation: mechanics, prediction, and assessment, 883–894 (2003)

  36. Jenkins, J.T., Zhang, C.: Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14, 1228–1235 (2002). https://doi.org/10.1063/1.1449466

    Article  ADS  Google Scholar 

  37. Bartelt, P., Buser, O.: The relation between dilatancy, effective stress and dispersive pressure in granular avalanches. Acta Geotech. 11(3), 549–557 (2016). https://doi.org/10.1007/s11440-016-0463-7

    Article  Google Scholar 

  38. Bartelt, P., Buser, O.: Reply to “Discussion of “The relation between dilatancy, effective stress and dispersive pressure in granular avalanches” by P. Bartelt and O. Buser. Acta Geotech. 11(6), 1469–1473 (2016). https://doi.org/10.1007/s11440-016-0503-3

    Article  Google Scholar 

  39. Bagnold, R.A.: Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. A 225, 49–63 (1954). https://doi.org/10.1098/rspa.1954.0186

    Article  ADS  Google Scholar 

  40. Pitman, E.B., Le, L.: A two-fluid model for avalanche and debris flows. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 363(1832), 1573–1601 (2005). https://doi.org/10.1098/rsta.2005.1596

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Baumgarten, A.S., Kamrin, K.: A general fluid–sediment mixture model and constitutive theory validated in many flow regimes. J. Fluid Mech. 861, 721–764 (2019). https://doi.org/10.1017/jfm.2018.914

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial supports from the National Natural Science Foundation of China (Grant No. 41925030, 42077256, and 51809261), CAS “Light of West China” Program, and the Sichuan Science and Technology Program (Grant No. 2020YJ0002). Support from the DDFORS (Dongchuan Debris Flow Observation and Research Station) of Chinese Academy of Sciences is acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. G. D. Zhou.

Ethics declarations

Conflict of interest

The authors declare no conflicts of interest on the submitted work.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, D., Zhou, G.G.D. & Chen, Q. Flow resistance in the transition from dense to dilute granular-fluid flows. Granular Matter 23, 73 (2021). https://doi.org/10.1007/s10035-021-01134-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10035-021-01134-1

Keywords

Navigation