Flow Resistance of Inertial Debris Flows
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 2
Abstract
This work deals with the evaluation of the most suitable expression for the motion resistance of a debris flow. In particular, it focuses on inertial debris flows, i.e., granular-fluid mixtures in which the particle inertia dominates both the fluid viscous force and turbulence; it provides, through an order-of-magnitude analysis, the criterion to be satisfied for a debris flow to be considered inertial and shows that most of real-scale debris flows match this description. The analytical relation between flow depth, depth-averaged velocity, and tangent of the angle of inclination of the free surface is then used in steady, uniform flow conditions to approximate the flow resistance in depth-averaged mathematical models of debris flows. That resistance formula is tested against experimental results on the longitudinal profile of steady, fully saturated waves of water and gravel over both rigid and erodible beds, and against field measurements of real events. The notable agreement, especially in comparison with the results obtained using other resistance formulas for debris flows proposed in the literature, assesses the validity of the theory.
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Acknowledgments
The authors are grateful to Prof. James Jenkins for his support and discussions related to this work.
References
Arattano, M., Mortara, G., Deganutti, A. M., and Marchi, L. (1996). “Esperienze di monitoraggio delle collate detritiche nel torrente Moscardo (Alpi Carniche).” [experience from debris flow monitoring in the Moscardo torrent], Geoingegneria Ambientale e Mineraria, 2–3, Supplemento: Quaderni di Studi no.20: Studi sui Debris Flow, 33–43 (in Italian).
Armanini, A., Capart, H., Fraccarollo, L., and Larcher, M. (2005). “Rheological stratification in experimental free-surface flows of granular-liquid mixtures.” J. Fluid Mech., 532, 269–319.
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.
Berzi, D. (2011). “Analytical solution of collisional sheet flows.” J. Hydraul. Eng., 137(10), 1200–1207.
Berzi, D., Di Prisco, C. G., and Vescovi, D. (2011). “Constitutive relations for steady, dense granular flows.” Phys. Rev. E, 84(3), 031301.
Berzi, D., and Jenkins, J. T. (2008a). “A theoretical analysis of free-surface flows of saturated granular-liquid mixtures.” J. Fluid Mech., 608, 393–410.
Berzi, D., and Jenkins, J. T. (2008b). “Approximate analytical solutions in a model for highly concentrated granular-fluid flows.” Phys. Rev. E, 78(1), 011304.
Berzi, D., and Jenkins, J. T. (2009). “Steady inclined flows of granular-fluid mixtures.” J. Fluid Mech., 641, 359–387.
Berzi, D., and Jenkins, J. T. (2011). “Surface flows of inelastic spheres.” Phys. Fluids, 23(1), 013303.
Berzi, D., Jenkins, J. T., and Larcher, M. (2010). “Debris flows: Recent advances in experiments and modeling.” Adv. Geophys., 52, 103–138.
Buser, O., and Frutiger, H. (1980). “Observed maximum run-out distance of snow avalanches and the determination of the friction coefficients and .” J. Glaciol., 26(94), 121–130.
Chow, V. T. (1959). Open-channel hydraulics, McGraw-Hill, New York.
Courrech du Pont, S.Gondret, P., Perrin, B., and Rabaud, M. (2003). “Granular avalanches in fluids.” Phys. Rev. Lett., 90(4), 044301.
da Cruz, F., Enman, S., Prochnow, M., Roux, J.-N., and Chevoir, F. (2005). “Rheophysics of dense granular materials: Discrete simulation of plane shear flows.” Phys. Rev. E, 72(2), 021309.
Derksen, J. J. (2008). “Scalar mixing by granular particles.” AIChE J., 54(7), 1741–1747.
Forterre, Y., and Pouliquen, O. (2003). “Long-surface-wave instability in dense granular flows.” J. Fluid Mech., 486, 21–50.
Garcia Aragon, J. A. (1996). “A hydraulic shear stress model for rapid, highly concentrated flow.” J. Hydraul. Res., 34(5), 589–596.
G.D.R. Midi. (2004). “On dense granular flows.” Eur. Phys. J. E: Soft Matter Biol. Phys., 14(4), 341–365.
Goldhirsch, I. (2003). “Rapid granular flows.” Annu. Rev. Fluid Mech., 35(1), 267–293.
Hotta, N., and Miyamoto, K. (2008). “Phase classification of laboratory debris flows over a rigid bed based on the relative flow depth and friction coefficients.” Int. J. Erosion Control Eng., 1(2), 54–61.
Hungr, O. (1995). “A model for the runout analysis of rapid flow slides, debris flows, and avalanches.” Can. Geotech. J., 32(4), 610–623.
Iverson, R. M. (1997). “The physics of debris flows.” Rev. Geophys., 35(3), 245–296.
Iverson, R. M., and LaHusen, R. G. (1993). “Friction in debris flows: Inferences from large-scale flume experiments.” Hydraulic engineering ’93, H. W. Shen, S. T. Su, and F. Wen, eds., ASCE, New York, 1604–1609.
Iverson, R. M., Logan, M., LaHusen, R. G., and Berti, M. (2010). “The perfect debris flow? Aggregated results from 28 large-scale experiments.” J. Geophys. Res., 115, F03005.
Jenkins, J. T. (2001). “Boundary conditions for collisional grain flows at bumpy, frictional walls.” Granular gases, T. Poschel and S. Luding, eds., Springer, Berlin, 125–139.
Jenkins, J. T. (2006). “Dense shearing flows of inelastic disks.” Phys. Fluids, 18(10), 103307.
Jenkins, J. T. (2007). “Dense inclined flows of inelastic spheres.” Granular Matter, 10(1), 47–52.
Jenkins, J. T., and Askari, E. (1991). “Boundary conditions for rapid granular flows: Phase interfaces.” J. Fluid Mech., 223, 497–508.
Jenkins, J. T., and Berzi, D. (2010). “Dense inclined flows of inelastic spheres: Tests of an extension of kinetic theory.” Granular Matter, 12(2), 151–158.
Jenkins, J. T., and Hanes, D. M. (1998). “Collisional sheet flows of sediment driven by a turbulent fluid.” J. Fluid Mech., 370, 29–52.
Jenkins, J. T., and Savage, S. B. (1983). “A theory for the rapid flow of identical, smooth, nearly elastic particles.” J. Fluid Mech., 130, 187–202.
Jop, P., Forterre, Y., and Pouliquen, O. (2005). “Crucial role of sidewalls in granular surface flows: Consequences for the rheology.” J. Fluid Mech., 541, 167–192.
Joseph, G. G., Zenit, R., Hunt, M. L., and Rosenwinkel, A. M. (2001). “Particle-wall collisions in a viscous fluid.” J. Fluid Mech., 433, 329–346.
Mitarai, N., and Nakanishi, H. (2005). “Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow.” Phys. Rev. Lett., 94(12), 128001.
Mitarai, N., and Nakanishi, H. (2007). “Velocity correlations in dense granular shear flows: Effects on energy dissipation and normal stress.” Phys. Rev. E, 75(3), 031305.
Naef, D., Rickenmann, D., Rutschmann, P., and Mcardell, B. W. (2006). “Comparison of flow resistance relations for debris flows using a one-dimensional finite element simulation model.” Nat. Hazard. Earth Sys., 6(1), 155–165.
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.
Pouliquen, O. (1999a). “Scaling laws in granular flows down rough inclined planes.” Phys. Fluids, 11(3), 542–548.
Pouliquen, O. (1999b). “On the shape of granular fronts down rough inclined planes.” Phys. Fluids, 11(7), 1956–1958.
Pugh, F. J., and Wilson, K. C. (1999). “Velocity and concentration distributions in sheet flow above plane beds.” J. Hydraul. Eng., 125(2), 117–125.
Richman, M. W. (1988). “Boundary conditions based upon a modified Maxwellian velocity distribution for flows of identical, smooth, nearly elastic spheres.” Acta Mech., 75(1), 227–240.
Rickenmann, D. (1999). “Empirical relationships for debris flows.” Nat. Hazards, 19(1), 47–77.
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.
Takahashi, T. (1991). Debris flow, Balkema, Rotterdam, Netherlands.
Torquato, S. (1995). “Nearest-neighbor statistics for packings of hard spheres and disks.” Phys. Rev. E, 51(4), 3170–3182.
Tubino, M. A., and Lanzoni, S. (1993). “Rheology of debris flows: Experimental observations and modeling problems.” Excerpta Ital. Contrib. Field Hydraul. Eng., 7, 201–236.
Wang, Z., and Zhang, X. (1990). “Initiation and laws of motion of debris flow.” Proc. Hydraulics/Hydrology of Arid Lands, ASCE, New York, 596–691.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 139 • Issue 2 • February 2013
Pages: 187 - 194
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Sep 23, 2011
Accepted: Jul 18, 2012
Published online: Jul 23, 2012
Published in print: Feb 1, 2013
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