Granular Matter

, 20:13 | Cite as

Numerical simulation of 2D granular flow entrainment using DEM

Original Paper


To understand the entrainment process in granular flow, numerical experiments have been conducted using a Discrete Element Method model. A flow channel of 8 m long with \(15^\circ \) slope is setup with monitoring points located in an erodible bed. Particles, ranging from 3 to 4 mm in diameters, are used in the simulations. In the simulations, translational, rotational and average velocities, total volume, shear stresses are calculated in the measurement circles. The sizes of the measurement circles have been varied to see their effects on the results. It is found the minimum size of the measurement circles should include 20–30 particles. An new analytical model has been developed to calculate entrainment in granular flow. Results of the numerical experiment are compared with analytical model. Shear stresses at the interface between flowing particles in motion and the immobile particles in the channel bed, change of depth of erosion and entrainment rate are used to verify the analytical model. It is found that the calculated shear stresses in the PFC model agree well with the shear stresses calculated using Mohr–Coulomb frictional relationship in the analytical model. The calculated depth of erosion using the new analytical model is also compared with that from dynamic and static entrainment model. The results indicates that the analytical model is able to capture the mechanism of erosion and it can be used in granular flow analysis.


Granular flow Entrainment Numerical experiment Debris flow Discrete element method 



This study is sponsored by the Natural Science and Engineering of Canada Discovery Grant.

Compliance with ethical standards

Conflict of interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.


  1. 1.
    Albaba, A., Lambert, S., Nicot, F., Chareyre, B.: Relation between microstructure and loading applied by a granular flow to a rigid wall using DEM modeling. Granul. Matter 17(5), 603–616 (2015)CrossRefGoogle Scholar
  2. 2.
    Banton, J., Villard, P., Jongmans, D., Scavia, C.: Two-dimensional discrete element models of debris avalanches: parameterization and the reproducibility of experimental results. J. Geophys. Res. 114, F04013 (2009). ADSCrossRefGoogle Scholar
  3. 3.
    Berger, C., McArdell, B.W., Schlunegger, F.: Direct measurement of channel erosion by debris flows, Illgraben, Switzerland. J. Geophys. Res. Earth Surf. 116(F01002) (2011).
  4. 4.
    Bishop, A.W.: Correspondence. Géotechnique 4(1), 43–45 (1954)CrossRefGoogle Scholar
  5. 5.
    Bouchut, F., Ionescu, I.R., Mangeney, A.: An analytic approach for the evolution of the static/flowing interface in viscoplastic granular flows. Commun. Math. Sci. 14(8), 2101–2126 (2016)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Caquot, A.: Equilibre des Massifs a’ Frottement Interne. Stabilite des Terres Pulv6rents et Coherentes. Gauthier Villars, Paris (1934)Google Scholar
  7. 7.
    Cheng, N.S., Law, A.W.K., Lim, S.Y.: Probability distribution of bed particle instability. Adv. Water Resour. 26(4), 427–433 (2003)ADSCrossRefGoogle Scholar
  8. 8.
    Chigira, M.: Dry debris flow of pyroclastic fall deposits triggered by the 1978 Izu-Oshima-Kinkai earthquake: the “collapsing” landslide at Nanamawari, Mitaka-Iriya, southern Izu Peninsula. Nat. Disaster Sci. 4(2), 1–32 (1982)Google Scholar
  9. 9.
    Chou, S.H., Lu, L.S., Hsiau, S.S.: DEM simulation of oblique shocks in gravity-driven granular flows with wedge obstacles. Granul. Matter 14(6), 719–732 (2012)CrossRefGoogle Scholar
  10. 10.
    Crosta, G.B., Imposimato, S., Roddeman, D.: Granular flows on erodible and non erodible inclines. Granul. Matter 17(5), 667–685 (2015)CrossRefGoogle Scholar
  11. 11.
    Cundall, P.A.: A computer model for simulating progressive, large scale movements in blocky rock systems. In: Proceedings of the International Symposium on Rock Mechanics, Editors: Anonymous, Nancy, France, October 4–6, 1971, vol. 2, pp. 129–136. Rubrecht, Germany (1971)Google Scholar
  12. 12.
    Cundall, P.A., Strack, O.D.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  13. 13.
    Egashira, S., Honda, N., Itoh, T.: Experimental study on the entrainment of bed material into debris flow. Phys. Chem. Earth Part C Sol. Terr. Planet. Sci. 26(9), 645–650 (2001)ADSGoogle Scholar
  14. 14.
    Fenton, J.D., Abbott, J.E.: Initial movement of grains on a stream bed: the effect of relative protrusion. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 352(1671), 523–537 (1977)ADSCrossRefGoogle Scholar
  15. 15.
    He, J.M., Li, X., Li, S.D., Yin, Y.P., Qian, H.T.: Study of seismic response of colluvium accumulation slope by particle flow code. Granul. Matter 12(5), 483–490 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    Higashitani, K., Iimura, K., Harota, M., Suzuki, M., Watanabe, S.: Simulation of entrainment of agglomerates from plate surfaces by shear flows. Chem. Eng.Sci. 64(7), 1455–1461 (2009)CrossRefGoogle Scholar
  17. 17.
    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
  18. 18.
    Hungr, O., Leroueil, S., Picarelli, L.: The Varnes classification of landslide types, an update. Landslides 11(2), 167–194 (2014)CrossRefGoogle Scholar
  19. 19.
    Hutter, K., Koch, T., Plüss, C., Savage, S.B.: The dynamics of avalanches of granular-materials from initiation to runout. 2. Experiments. Acta Mech. 109(1–4), 127–165 (1995)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Itasca, Consulting Group Inc., PFC2D Particle Flow Code in 2 Dimensions. User’s Guide (2002)Google Scholar
  21. 21.
    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. 115(F03005), (2010).
  22. 22.
    Iverson, R.M., Reid, M.E., Logan, M., LaHusen, R.G., Godt, J.W., Griswold, J.P.: Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment. Nat. Geosci. 4(2), 116–121 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    Iverson, R.M.: Elementary theory of bed-sediment entrainment by debris flows and avalanches. J. Geophys. Res. 117(F03006) (2012).
  24. 24.
    Iverson, R.M., Ouyang, C.: Entrainment of bed material by Earth-surface mass flows: review and reformulation of depth-integrated theory. Rev. Geophys. 53(1), 27–58 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    Kang, C., Chan, D., Su, F., Cui, P.: Runout and entrainment analysis of an extremely large rock avalanche—a case study of Yigong, Tibet, China. Landslides 14(1), 123–139 (2017)CrossRefGoogle Scholar
  26. 26.
    Kang, C., Chan, D.: Modelling of entrainment in debris flow analysis for dry granular material. Int. J. Geomech. (ASCE) 17, 04017087 (2017)CrossRefGoogle Scholar
  27. 27.
    Li, W.C., Li, H.J., Dai, F.C., Lee, L.M.: Discrete element modeling of a rainfall-induced flowslide. Eng. Geol. Eng. Geol. 149, 22–34 (2012)ADSCrossRefGoogle Scholar
  28. 28.
    Li, X.P., He, S.M., Luo, Y., Wu, Y.: Discrete element modeling of debris avalanche impact on retaining walls. J. Mt. Sci. 7(3), 276–281 (2010)CrossRefGoogle Scholar
  29. 29.
    Lin, J., Wu, W.: A general rotation averaging method for granular materials. Granul. Matter 19(3), 44 (2017)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Luna, B.Q., Remaitre, A., van Asch, T.W.J., Malet, J.P., van Westen, C.J.: Analysis of debris flow behavior with a one dimensional run-out model incorporating entrainment. Eng. Geol. 128, 63–75 (2012)CrossRefGoogle Scholar
  31. 31.
    Mangeney, A., Roche, O., Hungr, O., Mangold, N., Faccanoni, G., Lucas, A.: Erosion and mobility in granular collapse over sloping beds. J. Geophys. Res. 115(F03040) (2010).
  32. 32.
    McCoy, S.W., Kean, J.W., Coe, J.A., Staley, D.M., Wasklewicz, T.A., Tucker, G.E.: Evolution of a natural debris flow: in situ measurements of flow dynamics, video imagery, and terrestrial laser scanning. Geology 38(8), 735–738 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    McCoy, S.W., Kean, J.W., Coe, J.A., Tucker, G.E., Staley, D.M., Wasklewicz, T.A.: Sediment entrainment by debris flows: in situ measurements from the headwaters of a steep catchment. J. Geophys. Res. Earth Surf. 117(F03016) (2012).
  34. 34.
    McCoy, S.W., Tucker, G.E., Kean, J.W., Coe, J.A.: Field measurement of basal forces generated by erosive debris flows. J. Geophys. Res. Earth Surf. 118(2), 589–602 (2013). ADSCrossRefGoogle Scholar
  35. 35.
    McDougall, S., Hungr, O.: A model for the analysis of rapid landslide motion across three-dimensional terrain. Can. Geotech. J. 41(6), 1084–1097 (2004)CrossRefGoogle Scholar
  36. 36.
    Medina, V.H., Bateman, A., Hurlimann, M.: A 2D finite volume model for bebris flow and its application to events occurred in the Eastern Pyrenees. Int. J. Sediment Res. 23(4), 348–360 (2008)CrossRefGoogle Scholar
  37. 37.
    Melosh, H.J.: Acoustic fluidization: can sound waves explain why dry rock debris appears to flow like a fluid in some energetic geologic events? Am. Sci. 71(2), 158–165 (1983)Google Scholar
  38. 38.
    Montserrat, S., Tamburrino, A., Roche, O., Niño, Y., Ihle, C.F.: Enhanced run-out of dam-break granular flows caused by initial fluidization and initial material expansion. Granul. Matter 18(1), 1–9 (2016)CrossRefGoogle Scholar
  39. 39.
    Okada, Y., Ochiai, H.: Coupling pore-water pressure with distinct element method and steady state strengths in numerical triaxial compression tests under undrained conditions. Landslides 4(4), 357–369 (2007)CrossRefGoogle Scholar
  40. 40.
    Potyondy, D.O., Cundall, P.A.: A bonded-particle model for rock. Int. J. Rock Mech. Min. Sci. 41(8), 1329–1364 (2004)CrossRefGoogle Scholar
  41. 41.
    Reid, M.E., Iverson, R.M., Logan, M.A.T.T.H.E.W., LaHusen, R.G., Godt, J.W., Griswold, J.P.: Entrainment of bed sediment by debris flows:results from large-scale experiments. In: Genevois R., Hamilton, D.L., Prestininzi, A. (eds.) Proceedings of Fifth International Conference on Debris-flow Hazards Mitigation, Mechanics, Prediction and Assessment, Casa Editrice Universita La Sapienza, Rome, June 14–17, 2011, pp. 367–374 (2011)Google Scholar
  42. 42.
    Remaître, A., van Asch, ThWJ, Malet, J.P., Maquaire, O.: Influence of check dams on debris-flow run-out intensity. Nat. Hazards Earth Syst. Sci. 8(6), 1403–1416 (2008)ADSCrossRefGoogle Scholar
  43. 43.
    Remaître, A., Malet, J.P, Maquaire, O.: Sediment budget and morphology of the 2003 Faucon debris flow (South French Alps): scouring and channel-shaping processes. In: Malet J.P., Remaitre A., and Bogaard T. (eds.) Proceedings of the International Conference on Landslide Processes: From géomorphologie Mapping to Dynamic Modelling, Strasbourg, France, February 6–7, 2009, pp. 75–80. CERG, Strasbourg (2009)Google Scholar
  44. 44.
    Salciarini, D., Tamagnini, C., Conversini, P.: Discrete element modeling of debris-avalanche impact on earthfill barriers. Phys. Chem. Earth 35(3), 172–181 (2010)CrossRefGoogle Scholar
  45. 45.
    Savage, S.B., Hutter, K.: The dynamics of avalanches of antigranulocytes materials from initiation to runout analysis. Acta Mech. 86, 201–223 (1991)MathSciNetCrossRefMATHGoogle Scholar
  46. 46.
    Shodja, H.M., Nezami, E.G.: A micromechanical study of rolling and sliding contacts in assemblies of oval granules. Int. J. Numer. Anal. Methods Geomech. 27(5), 403–424 (2003)CrossRefMATHGoogle Scholar
  47. 47.
    Skempton, A.W.: The pore-pressure coefficients A and B. Geotechnique 4(4), 143–147 (1954)CrossRefGoogle Scholar
  48. 48.
    Wu, F.C., Chou, Y.J.: Rolling and lifting probabilities for sediment entrainment. J. Hydraul. Eng. 129(2), 110–119 (2003)CrossRefGoogle Scholar
  49. 49.
    Xu, Q., Shang, Y.J., van Asch, ThWJ, Wang, S.T., Zhang, Z.Y., Dong, X.J.: Observations from the large, rapid Yigong rock slide-debris avalanche, southeast Tibet. Can. Geotech. J. 49(5), 589–606 (2012)CrossRefGoogle Scholar
  50. 50.
    Zhou, G.G., Ng, C.W.: Numerical investigation of reverse segregation in debris flows by DEM. Granul. Matter 12(5), 507–516 (2010)CrossRefMATHGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of AlbertaEdmontonCanada
  2. 2.College of Civil Engineering and ArchitectureThree Gorges UniversityYichangChina

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