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http://dx.doi.org/10.12989/gae.2015.8.6.811

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)
Publication Information
Geomechanics and Engineering / v.8, no.6, 2015 , pp. 811-828 More about this Journal
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
granular flow; avalanche dynamics; basal resistance terms; deposition process;
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1 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.   DOI
2 Iverson, R.M. (1997), "The physics of debris flows", Rev. Geophys., 35(3), 245-296.   DOI
3 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   DOI
4 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.   DOI
5 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.   DOI
6 McClung, D.M. and Mears, A.I. (1995), "Dry-flowing avalanche run-up and run-out", J. Glaciol., 41(138), 359-372.   DOI
7 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.   DOI
8 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.   DOI
9 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.   DOI
10 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.   DOI   ScienceOn
11 Pouliquen, O. (1999a), "On the shape of granular fronts down rough inclined planes", Phys. Fluids, 11(7), 1956-1958.   DOI
12 Pouliquen, O. (1999b), "Scaling laws in granular flows down rough inclined planes", Phys. Fluids, 11(3), 542-548.   DOI
13 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.
14 Pudasaini, S.P. (2012), "A general two-phase debris flow model", J. Geophys. Res., 117(F3). DOI: 10.1029/2011JF002186   DOI
15 Pudasaini, S.P. (2014), "Dynamics of submarine debris flow and tsunami", Acta Mech., 225(8), 2423-2434.   DOI
16 Pudasaini, S.P. and Domnik, B. (2009), "Energy considerations in accelerating rapid shear granular flows", Nonlinear Proc. Geoph., 16(3), 399-407.   DOI
17 Pudasaini, S.P. and Hutter, K. (2007), Avalanche Dynamics: Dynamics of Rapid Flows of Dense Granular Avalanches, Springer, New York, NY, USA.
18 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.   DOI
19 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.   DOI
20 Pudasaini, S.P., Wang, Y. and Hutter, K. (2005a), "Modelling debris flows down general channels", Nat. Hazard. Earth. Sys., 5(6), 799-819.   DOI
21 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.   DOI
22 Salm, B. (1993), "Flow transition and runout distances of flowing avalanches", Ann. Glaciol., 18, 221-226.   DOI
23 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.   DOI   ScienceOn
24 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.   DOI
25 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.   DOI
26 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.   DOI
27 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.   DOI
28 Thornton, A.R. (2005), "A study of segregation in granular gravity driven free surface flows", Ph.D. Dissertation; The University of Manchester, Manchester, England.
29 Toro, E.F. (2001), Shock-capturing Methods for Free-surface Shallow Flows, John Wiley and Sons, NJ, USA.
30 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.   DOI
31 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.   DOI
32 Yee, H. (1989), "A class of high resolution explicit and implicit shock capturing methods", NASA TM-101088.
33 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.   DOI
34 Camassa, R. and Holm, D.D. (1993), "An integrable shallow water equation with peaked solitons", Phys. Rev. Lett., 71(11), 1661.   DOI
35 Chen, H. and Lee, C.F. (2003), "A dynamic model for rainfall-induced landslides on natural slopes", Geomorphology, 51(4), 269-288.   DOI
36 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.
37 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.   DOI
38 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.
39 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.   DOI
40 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.   DOI
41 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.   DOI
42 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.   DOI
43 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.   DOI
44 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.   DOI
45 Fischer, J.T., Kowalski, J. and Pudasaini, S.P. (2012), "Topographic curvature effects in applied avalanche modeling", Cold Reg. Sci. Technol., 74, 21-30.
46 Hungr, O. (2008), "Simplified models of spreading flow of dry granular material", Can. Geotech. J., 45(8), 1156-1168.   DOI
47 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.
48 Hungr, O. and McDougall, S. (2009), "Two numerical models for landslide dynamic analysis", Comput. Geosci., 35(5), 978-992.   DOI
49 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.   DOI
50 Hutter, K., Savage, S.B. and Nohguchi, Y. (1989), "Numerical, analytical, and laboratory experimental studies of granular avalanche flows", Ann. Glaciol., 13, 109-116.   DOI