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Flow models of fluidized granular masses with different basal resistance terms

  • Wu, Hengbin (College of Civil Engineering, Chongqing Three Gorges University) ;
  • Jiang, Yuanjun (Key Laboratory of Mountain Hazards and Earth Surface Processes, Institute of Mountain Hazards & Environment, Chinese Academy of Sciences) ;
  • Zhang, Xuefu (State Key Laboratory Breeding Base of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University)
  • Received : 2014.09.01
  • Accepted : 2015.02.14
  • Published : 2015.06.25

Abstract

Proper modelling of the basal resistance terms is key in simulating the motion of fluidized granular flow. In this paper, standard depth-averaged governing equations of granular flow are used together with the classical Coulomb, Voellmy, and velocity dependent friction models (VDFM). A high-resolution modified TVDLF method is implemented to solve the partial differential equations without numerical oscillations. The effects of basal resistance terms on the motion of granular flows such as geometric shape evolution, travel times and final deposits are analyzed. Based on the numerical results, the predictions of the front and rear end positions and developing length of granular flow with Coulomb friction model show excellent agreements with experiment results reported by Hutter et al. (1995), and illustrate the validity of the numerical approach. For the Voellmy model, the higher value of turbulent coefficient than reality may obtain more reasonable predicted runout for the small-scale avalanche or granular flow. The energy exchange laws indicate that VDFM is different from the Coulomb and Voellmy models, although the flow characteristics of both three models fit the measurements and observations very well.

Keywords

References

  1. Bagnold, R.A. (1954), "Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear", Proc. R. Soc. London, Ser. A., 225(1160), 49-63. https://doi.org/10.1098/rspa.1954.0186
  2. Camassa, R. and Holm, D.D. (1993), "An integrable shallow water equation with peaked solitons", Phys. Rev. Lett., 71(11), 1661. https://doi.org/10.1103/PhysRevLett.71.1661
  3. Chen, H. and Lee, C.F. (2003), "A dynamic model for rainfall-induced landslides on natural slopes", Geomorphology, 51(4), 269-288. https://doi.org/10.1016/S0169-555X(02)00224-6
  4. Chen, G.Q., Li, T.B. and He, Y.H. (2012), "Formation mechanism of groundwater for the land subsidence", Res. J. Chem. Environ., 16(s2), 56-62.
  5. Chen, G.Q., Huang, R.Q., Xu, Q., Li, T.B. and Zhu, M.L. (2013a), "Progressive modelling of the gravity-induced landslide using the local dynamic strength reduction method", J. Mt. Sci-Engl., 10(4), 532-540. https://doi.org/10.1007/s11629-013-2367-4
  6. Chen, G.Q., Li, T.B., Gao, M.B., Chen, Z.Q. and Xiang, T.B. (2013b), "Deformation warning and dynamic control of dangerous disaster for large underground caverns", Disaster Adv., 6(s1), 422-430.
  7. Delinger, R.P. and Iverson, R.M. (2001), "Flow of variably fluidized granular masses across threedimensional terrain: 2. Numerical predictions and experimental tests", J. Geophys. Res., 106(B1), 553-566. https://doi.org/10.1029/2000JB900330
  8. Domnik, B. and Pudasaini, S.P. (2012), "Full two-dimensional rapid chute flows of simple viscoplastic granular materials with a pressure-dependent dynamic slip-velocity and their numerical simulations", J. Non-Newtonian Fluid Mech., 173-174, 72-86. https://doi.org/10.1016/j.jnnfm.2012.03.001
  9. Domnik, B., Pudasaini, S.P., Katzenbach, R. and Miller, S.A. (2013), "Coupling of full two-dimensional and depth-averaged models for granular flows", J. Non-Newtonian Fluid Mech., 201, 56-68. https://doi.org/10.1016/j.jnnfm.2013.07.005
  10. Fei, M., Sun, Q., Zhong, D. and Zhou, G.G. (2012), "Simulations of granular flow along an inclined plane using the Savage-Hutter model", Particuology, 10(2), 236-241. https://doi.org/10.1016/j.partic.2011.11.007
  11. Fernandez-Nieto, E.D., Bouchut, F., Bresch, D., Castro Diaz, M.J. and Mangeney, A. (2008), "A new Savage-Hutter type model for submarine avalanches and generated tsunami", J. Comput. Phys., 227(16), 7720-7754. https://doi.org/10.1016/j.jcp.2008.04.039
  12. Fischer, J.T., Kowalski, J. and Pudasaini, S.P. (2012), "Topographic curvature effects in applied avalanche modeling", Cold Reg. Sci. Technol., 74, 21-30.
  13. Gray, J.M.N.T., Wieland, M. and Hutter, K. (1999), "Gravity-driven free surface flow of granular avalanches over complex basal topography", Proc. R. Soc. London, Ser. A., 455(1985), 1841-1874. https://doi.org/10.1098/rspa.1999.0383
  14. Hungr, O. (2008), "Simplified models of spreading flow of dry granular material", Can. Geotech. J., 45(8), 1156-1168. https://doi.org/10.1139/T08-059
  15. Hungr, O. and Evans, S.G. (1996), "Rock avalanche runout prediction using a dynamic model", Proceedings of the 7th International Symposium on Landslides, Trondheim, Norway, June.
  16. Hungr, O. and McDougall, S. (2009), "Two numerical models for landslide dynamic analysis", Comput. Geosci., 35(5), 978-992. https://doi.org/10.1016/j.cageo.2007.12.003
  17. Hutter, K. and Schneider, L. (2010), "Important aspects in the formulation of solid-fluid debris-flow models. Part II. Constitutive modelling", Continuum Mech. Thermodyn., 22(5), 391-411. https://doi.org/10.1007/s00161-010-0154-9
  18. Hutter, K., Savage, S.B. and Nohguchi, Y. (1989), "Numerical, analytical, and laboratory experimental studies of granular avalanche flows", Ann. Glaciol., 13, 109-116. https://doi.org/10.1017/S0260305500007722
  19. Hutter, K., Koch, T., Pluuss, C. and Savage, S.B. (1995), "The dynamics of avalanches of granular materials from initiation to runout. Part II. Experiments", Acta Mech., 109(1-4), 127-165. https://doi.org/10.1007/BF01176820
  20. Iverson, R.M. (1997), "The physics of debris flows", Rev. Geophys., 35(3), 245-296. https://doi.org/10.1029/97RG00426
  21. Iverson, R.M. and Denlinger, R.P. (2001), "Flow of variably fluidized granular masses across threedimensional terrain: 1. Coulomb mixture theory", J. Geophys. Res., 106(B1), 537-552. DOI: 10.1029/2000JB900329
  22. Johnson, C.G. and Gray, J.M.N.T. (2011), "Granular jets and hydraulic jumps on an inclined plane", J. Fluid Mech., 675, 87-116. https://doi.org/10.1017/jfm.2011.2
  23. Li, X., He, S., Luo, Y. and Wu, Y. (2012), "Simulation of the sliding process of Donghekou landslide triggered by the Wenchuan earthquake using a distinct element method", Environ. Earth Sci., 65(4), 1049-1054. https://doi.org/10.1007/s12665-011-0953-8
  24. McClung, D.M. and Mears, A.I. (1995), "Dry-flowing avalanche run-up and run-out", J. Glaciol., 41(138), 359-372. https://doi.org/10.1017/S0022143000016233
  25. Ouyang, C., He, S., Xu, Q., Luo, Y. and Zhang, W. (2013), "A MacCormack-TVD finite difference method to simulate the mass flow in mountainous terrain with variable computational domain", Comput. Geosci., 52, 1-10. https://doi.org/10.1016/j.cageo.2012.08.024
  26. Pirulli, M., Bristeau, M.O., Mangeney, A. and Scavia, C. (2007), "The effect of the earth pressure coefficients on the runout of granular material", Environ. Modell. Softw., 22(10), 1437-1454. https://doi.org/10.1016/j.envsoft.2006.06.006
  27. Pitman, E.B. and Le, L. (2005), "A two-fluid model for avalanche and debris flows", Phil. Trans. R. Soc. A, 363(1832), 1573-1601. https://doi.org/10.1098/rsta.2005.1596
  28. Pitman, E.B., Nichita, C.C., Patra, A., Bauer, A., Sheridan, M. and Bursik, M. (2003), "Computing granular avalanches and landslides", Phys. Fluids, 15(12), 3638-3646. https://doi.org/10.1063/1.1614253
  29. Pouliquen, O. (1999a), "On the shape of granular fronts down rough inclined planes", Phys. Fluids, 11(7), 1956-1958. https://doi.org/10.1063/1.870057
  30. Pouliquen, O. (1999b), "Scaling laws in granular flows down rough inclined planes", Phys. Fluids, 11(3), 542-548. https://doi.org/10.1063/1.869928
  31. Pouliquen, O. and Forterre, Y. (2002), "Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane", J. Fluid Mech., 453, 133-151.
  32. Pudasaini, S.P. (2012), "A general two-phase debris flow model", J. Geophys. Res., 117(F3). DOI: 10.1029/2011JF002186
  33. Pudasaini, S.P. (2014), "Dynamics of submarine debris flow and tsunami", Acta Mech., 225(8), 2423-2434. https://doi.org/10.1007/s00707-014-1126-0
  34. Pudasaini, S.P. and Domnik, B. (2009), "Energy considerations in accelerating rapid shear granular flows", Nonlinear Proc. Geoph., 16(3), 399-407. https://doi.org/10.5194/npg-16-399-2009
  35. Pudasaini, S.P. and Hutter, K. (2007), Avalanche Dynamics: Dynamics of Rapid Flows of Dense Granular Avalanches, Springer, New York, NY, USA.
  36. Pudasaini, S.P. and Krautblatter, M. (2014), "A two-phase mechanical model for rock-ice avalanches", J. Geophys. Res. Earth Surf., 119(10), 2272-2290. https://doi.org/10.1002/2014JF003183
  37. Pudasaini, S.P. and Kroner, C. (2008), "Shock waves in rapid flows of dense granular materials: Theoretical predictions and experimental results", Phys. Rev. E, 78(4), 041308. https://doi.org/10.1103/PhysRevE.78.041308
  38. Pudasaini, S.P., Wang, Y. and Hutter, K. (2005a), "Modelling debris flows down general channels", Nat. Hazard. Earth. Sys., 5(6), 799-819. https://doi.org/10.5194/nhess-5-799-2005
  39. Pudasaini, S.P., Hsiau, S.S., Wang, Y. and Hutter, K. (2005b), "Velocity measurements in dry granular avalanches using particle image velocimetry technique and comparison with theoretical predictions", Phys. Fluids, 17(9), 093301. https://doi.org/10.1063/1.2007487
  40. Salm, B. (1993), "Flow transition and runout distances of flowing avalanches", Ann. Glaciol., 18, 221-226. https://doi.org/10.1017/S0260305500011551
  41. Savage, S.B. and Hutter, K. (1989), "The motion of a finite mass of granular material down a rough incline", J. Fluid Mech., 199, 177-215. https://doi.org/10.1017/S0022112089000340
  42. Savage, S.B. and Hutter, K. (1991), "The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis", Acta Mech., 86(1-4), 201-223. https://doi.org/10.1007/BF01175958
  43. Tai, Y.C., and Kuo, C.Y. (2008), "A new model of granular flows over general topography with erosion and deposition", Acta Mech., 199(1-4), 71-96. https://doi.org/10.1007/s00707-007-0560-7
  44. Tai, Y.C., Noelle, S., Gray, J.M.N.T. and Hutter, K. (2002), "Shock-capturing and front-tracking methods for granular avalanches", J. Comput. Phys., 175(1), 269-301. https://doi.org/10.1006/jcph.2001.6946
  45. Teufelsbauer, H., Wang, Y., Pudasaini, S.P., Borja, R.I. and Wu, W. (2011), "DEM simulation of impact force exerted by granular flow on rigid structures", Acta Geotech., 6(3), 119-133. https://doi.org/10.1007/s11440-011-0140-9
  46. Thornton, A.R. (2005), "A study of segregation in granular gravity driven free surface flows", Ph.D. Dissertation; The University of Manchester, Manchester, England.
  47. Toro, E.F. (2001), Shock-capturing Methods for Free-surface Shallow Flows, John Wiley and Sons, NJ, USA.
  48. Toth, G. and Odstrcil, D. (1996), "Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magneto hydrodynamic problems", J. Comput. Phys., 128(1), 82-100. https://doi.org/10.1006/jcph.1996.0197
  49. Wang, X., Morgenstern, N.R. and Chan, D.H. (2010), "A model for geotechnical analysis of flow slides and debris flows", Can. Geotech. J., 47(12), 1401-1414. https://doi.org/10.1139/T10-039
  50. Yee, H. (1989), "A class of high resolution explicit and implicit shock capturing methods", NASA TM-101088.

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