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A two-phase flow description of the initiation of underwater granular avalanches

Published online by Cambridge University Press:  25 August 2009

MICKAËL PAILHA  and
OLIVIER POULIQUEN
MICKAËL PAILHA*
Affiliation:
Laboratoire IUSTI, UMR 6595 CNRS, Aix Marseille Université (UI, UII), 5 rue Enrico Fermi, 13465 Marseille cedex 13, France
OLIVIER POULIQUEN
Affiliation:
Laboratoire IUSTI, UMR 6595 CNRS, Aix Marseille Université (UI, UII), 5 rue Enrico Fermi, 13465 Marseille cedex 13, France
*
†Email address for correspondence: mickael.pailha@etu.univ-provence.fr
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Abstract

A theoretical model based on a depth-averaged version of two-phase flow equations is developed to describe the initiation of underwater granular avalanches. The rheology of the granular phase is based on a shear-rate-dependent critical state theory, which combines a critical state theory proposed by Roux & Radjai (1998), and a rheological model recently proposed for immersed granular flows. Using those phenomenological constitutive equations, the model is able to describe both the dilatancy effects experienced by the granular skeleton during the initial deformations and the rheology of wet granular media when the flow is fully developed. Numerical solutions of the two-phase flow model are computed in the case of a uniform layer of granular material fully immersed in a liquid and suddenly inclined from horizontal. The predictions are quantitatively compared with experiments by Pailha, Nicolas & Pouliquen (2008), who have studied the role of the initial volume fraction on the dynamics of underwater granular avalanches. Once the rheology is calibrated using steady-state regimes, the model correctly predicts the complex transient dynamics observed in the experiments and the crucial role of the initial volume fraction. Quantitative predictions are obtained for the triggering time of the avalanche, for the acceleration of the layer and for the pore pressure.

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Type
Papers
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Journal of Fluid Mechanics , Volume 633 , 25 August 2009 , pp. 115 - 135
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Ancey, C., Coussot, P. & Evesque, P. 1999 A theoretical framework for granular suspensions in a steady simple shear flow. J. Rheol. 43, 1673–1699.CrossRefGoogle Scholar
Armanini, A., Capart, H., Fraccarollo, L. & Larcher, M. 2005 Rheological stratification in experimental free-surface flows of granular-liquid mixtures. J. Fluid Mech. 532, 269–319.CrossRefGoogle Scholar
Berzi, D. & Jenkins, J. T. 2008 a A theoretical analysis of free-surface flows of saturated granular liquid mixtures. J. Fluid Mech. 608, 393–410.CrossRefGoogle Scholar
Berzi, D. & Jenkins, J. T. 2008 b Approximate analytical solutions in a model for highly concentrated granular-fluid flows. Phys. Rev. E 78, 011304.CrossRefGoogle Scholar
Brady, J. F. & Bossis, G. 1988 Stokesian dynamics. Ann. Rev. Fluid Mech. 20, 111–157.CrossRefGoogle Scholar
Cassar, C., Nicolas, M. & Pouliquen, O. 2005 Submarine granular flows down inclined plane. Phys. Fuids 17, 103301.Google Scholar
Courrech du Pont, S., Gondret, P., Perrin, B. & Rabaud, M. 2003 Granular avalanches in fluids. Phys. Rev. Lett. 90, 044301.CrossRefGoogle ScholarPubMed
Da Cruz, F., Emam, S., Prochnow, M., Roux, J. N. & Chevoir, F. 2005. Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72, 021309.CrossRefGoogle ScholarPubMed
Doppler, D., Gondret, P., Loiseleux, T.Meyer, S. & Rabaud, M. 2007 Relaxation dynamics of water-immersed granular avalanches J. Fluid Mech. 577, 161–181.CrossRefGoogle Scholar
Forterre, Y. & Pouliquen, O. 2008 Flow of dense granular media. Ann. Rev. Fluid Mech. 40, 1–24.CrossRefGoogle Scholar
GDR MiDi 2004 On dense granular flows. Eur. Phys. J. E 14, 341–365.CrossRefGoogle Scholar
Géminard, J. C., Losert, W. & Gollub, J. P. 1999 Frictional mechanics of wet granular material. Phys. Rev. E 59, 5881–5890.CrossRefGoogle ScholarPubMed
Hampton, M. A., Lee, H. J. & Locat, J. 1996 Submarine landslides. Rev. Geophys. 34, 33–59.CrossRefGoogle Scholar
Huang, N., Ovarlez, G., Bertrand, F., Rodts, S., Coussot, P. & Bonn, D. 2005 Flow of wet granular materials. Phys. Rev. Lett. 94, 028301CrossRefGoogle ScholarPubMed
Iistad, T., Marr, J. G., Elverhoi, A. & Harbitz, C. B. 2004 Laboratory studies of subaqueous debris flows by measurements of pore fluid pressure and total stress. Marine Geol. 213, 403–414.CrossRefGoogle Scholar
Imran, J., Parker, G., Locat, J. & Lee, H. 2001 One-dimensional numerical model of muddy subaqueous and subaerial debris flows. J. Hydr. Engng 127, 959–968.CrossRefGoogle Scholar
Iverson, R. M. 1985 A constitutive equation for mass–movement behaviour. J. Geol. 93, 143–160.CrossRefGoogle Scholar
Iverson, R. M. 1997 The physics of debris flows. Rev. Geophys. 35, 245–296.CrossRefGoogle Scholar
Iverson, R. M. 2000 Landslide triggering by rain infiltration. Water Resour. Res. 36, 1897–1910.CrossRefGoogle Scholar
Iverson, R. M. 2005 Regulation of landslide motion by dilatancy and pore pressure feedback. J. Geophys. Res. 110, F02015.Google Scholar
Iverson, R. M. & Denlinger, R. P. 2001 a Flow of variably fluidized granular masses across three-dimensional terrain 1. Coulomb Mixture theory. J. Geophys. Res. 106, 537–552.CrossRefGoogle Scholar
Iverson, R. M. & Denlinger, R. P. 2001 b Flow of variably fluidized granular masses across three-dimensional terrain 2. Numerical predictions and experimental tests. J. Geophys. Res. 106, 553–566.Google Scholar
Iverson, R. M. & Lahusen, R. G. 1989 Dynamic pore pressure fluctuations in rapidly shearing granular materials. Science 246, 796–798.CrossRefGoogle ScholarPubMed
Iverson, R. M., Reid, M. E., Iverson, N. R., Lahusen, R. G., Logan, M., Mann, J. E., & Brien, D. L. 2000 Acute sensitivity of landslide rates to initial porosity. Science 290, 513–516.CrossRefGoogle Scholar
Jackson, R. 1997 Locally averaged equations of motion for a mixture of identical spherical particles and a Newtonian fluid. Ch. Engng Sci. 52, 2457–2469.CrossRefGoogle Scholar
Jackson, R. 2000 The Dynamics of Fluidized Particles. Cambridge University Press.Google Scholar
Jain, N., Ottino, J. M. & Lueptow, R. M. 2004 Effect of interstitial fluid on a granular flow layer. J. Fluid Mech. 508, 23–44.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441, 727–730.CrossRefGoogle ScholarPubMed
Legros, F. 2002. The mobility of long-runout landslides. Engng Geol. 63, 301–331.CrossRefGoogle Scholar
Major, J. J. & Iverson, R. M. 1999 Debris-flow deposition: effects of pore-fluid pressure ad friction concentrated at flow margins. Geol. Soc. Am. Bull. 111, 1424–1434.2.3.CO;2>CrossRefGoogle Scholar
Morris, J. F. & Boulay, F. 1999 Curvilinear flows of noncolloidal suspensions: the role of normal stresses. J. Rheol. 43, 1213–1237.CrossRefGoogle Scholar
Okura, Y., Kitahara, H., Ochiai, H.Sammori, T. & Kawanami, A. 2002 Landslide fluidization process by flume experiments. Engng Geol. 66, 65–78.CrossRefGoogle Scholar
Ouriemi, M., Aussillous, P. & Guazzelli, E. In press. Bed-load transport by shearing flows J. Fluid Mech.Google Scholar
Pailha, M., Nicolas, M. & Pouliquen, O. 2008 Initiation of underwater granular avalanches: influence of the initial volume fraction. Phys. Fluids 20, 111701.CrossRefGoogle Scholar
Pastor, M., Quecedo, M., González, E., Herreros, M. I., Fernández Merodo, J. A. & Mira, P. 2004 Simple approximation to bottom friction for bingham fluid depth integrated models. J. Hydr. Engrg 130, 149–155.CrossRefGoogle Scholar
Pitman, E. B. & Le, L. 2005 A two-fluid model for avalanches and debris flows. Phil. Trans. R. Soc. A 363, 1573–1601.CrossRefGoogle ScholarPubMed
Reynolds, O. 1886. Dilatancy. Nature 33, 429–430.Google Scholar
Rice, J. R. 1975 On the stability of dilatant hardening for saturated rock masses. J. Geophys. Res. 80, 1531–1536.CrossRefGoogle Scholar
Roux, S. & Radjai, F. 1998 Texture-dependent rigid plastic behaviour. In Proceedings: Physics of Dry Granular Media, September 1997, Cargèse, France, pp. 305–311 (eds. Herrmann, H. J. et al. ). Kluwer.Google Scholar
Roux, S. & Radjai, F. 2001 Statistical approach to the mechanical behaviour of granular media. In Mechanics for a New Millennium (eds. Aref, H. & Philips, J. W.), pp. 181–196. Kluwer.CrossRefGoogle Scholar
Rudnicki, J. W. 1984 Effects of dilatant hardening on the development of concentrated shear deformation in fissured rock masses. J. Geophys. Res. 89, 9259–9270.CrossRefGoogle Scholar
Schaeffer, D. G. & Iverson, R. 2008 Steady and intermittent slipping in a model of landslide motion regulated by pore-pressure feedback. SIAM Appl. Math. 69, 768–786.CrossRefGoogle Scholar
Schofield, A. & Wroth, P. 1968 Critical Soil Mechanics. McGraw-Hill.Google Scholar
Wood, D. M. 1990 Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press.Google Scholar