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A two-fluid model for immersed granular avalanches with dilatancy effects

Published online by Cambridge University Press:  23 August 2021

E.P. Montellà Open the ORCID record for E.P. Montellà [Opens in a new window] ,
J. Chauchat Open the ORCID record for J. Chauchat [Opens in a new window] ,
B. Chareyre Open the ORCID record for B. Chareyre [Opens in a new window] ,
C. Bonamy Open the ORCID record for C. Bonamy [Opens in a new window]  and
T.J. Hsu Open the ORCID record for T.J. Hsu [Opens in a new window]
E.P. Montellà*
Affiliation:
University of Grenoble Alpes, LEGI, G-INP, CNRS, 38000 Grenoble, France
J. Chauchat
Affiliation:
University of Grenoble Alpes, LEGI, G-INP, CNRS, 38000 Grenoble, France
B. Chareyre
Affiliation:
University of Grenoble Alpes, 3SR, G-INP, CNRS, 38000 Grenoble, France
C. Bonamy
Affiliation:
University of Grenoble Alpes, LEGI, G-INP, CNRS, 38000 Grenoble, France
T.J. Hsu
Affiliation:
Civil and Environmental Engineering, Center for Applied Coastal Research, University of Delaware, Newark, DE 19711, USA
*
†Email address for correspondence: [email protected]
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Abstract

When a deposited layer of granular material fully immersed in a liquid is suddenly inclined above a certain critical angle, it starts to flow down the slope. The initial dynamics of these underwater avalanches strongly depends on the initial volume fraction. If the granular bed is initially loose, i.e. looser than the critical state, the avalanche is triggered almost instantaneously and exhibits a strong acceleration, whereas for an initially dense granular bed, i.e. denser than the critical state, the avalanche's mobility remains low for some time before it starts flowing normally. This behaviour can be explained by a combination of geometrical granular dilatancy and pore pressure feedback on the granular media. In this contribution, a continuum formulation is presented and implemented in a three-dimensional continuum numerical model. The originality of the present model is to incorporate dilatancy as an elasto-plastic normal stress or pressure and not as a modification of the friction coefficient. This allows an explanation of the two different behaviours of initially loose and dense underwater avalanches. It also highlights the contribution from each depth-resolved variable in the strongly coupled transition to a flowing avalanche. The model compares favourably with existing experiments for the initiation of underwater granular avalanches. Results reveal the interplay between shear-induced changes of the granular stress and fluid pressure in the dynamics of avalanches. The characteristic time of the triggering phase is nearly independent of the local rheological parameters, whereas the initial drop in pore pressure and the surface velocity at steady state still strongly depend on them. Finally, the multidimensional capabilities of the model are illustrated for the two-dimensional Hele-Shaw configuration and some of the observed differences between one-dimensional simulations and experiments are clarified.

JFM classification

Geophysical and Geological Flows: Sediment transport Granular media: Wet granular material Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 925 , 25 October 2021 , A13
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alshibli, K.A. & Cil, M.B. 2018 Influence of particle morphology on the friction and dilatancy of sand. J. Geotech. Geoenviron. 144 (3), 04017118.CrossRefGoogle Scholar
Amarsid, L., Delenne, J.-Y., Mutabaruka, P., Monerie, Y., Perales, F. & Radjai, F. 2017 Viscoinertial regime of immersed granular flows. Phys. Rev. E 96 (1), 012901.CrossRefGoogle ScholarPubMed
Baumgarten, A.S. & Kamrin, K. 2019 A general fluid–sediment mixture model and constitutive theory validated in many flow regimes. J. Fluid Mech. 861, 721–764.CrossRefGoogle Scholar
Bonamy, C., Chauchat, J., Montellà, E.P., Chassagne, R., Mathieu, A. & Higuera, P. 2021 SedFoam/Sedfoam: release 3.2. Available at: doi:10.5281/zenodo.5095239.CrossRefGoogle Scholar
Bouchut, F., Fernández-Nieto, E.D., Mangeney, A. & Narbona-Reina, G. 2016 A two-phase two-layer model for fluidized granular flows with dilatancy effects. J. Fluid Mech. 801, 166–221.CrossRefGoogle Scholar
Boyer, F., Guazzelli, É. & Pouliquen, O. 2011 Unifying suspension and granular rheology. Phys. Rev. Lett. 107 (18), 188301.CrossRefGoogle ScholarPubMed
Chauchat, J., Cheng, Z., Nagel, T., Bonamy, C. & Hsu, T.-J. 2017 SedFoam-2.0: a 3-d two-phase flow numerical model for sediment transport. Geosci. Model Develop. 10 (12), 4367–4392.CrossRefGoogle Scholar
Chauchat, J. & Médale, M. 2014 A three-dimensional numerical model for dense granular flows based on the $\mu(I)$ rheology. J. Comput. Phys. 256, 696–712.CrossRefGoogle Scholar
Cheal, O. & Ness, C. 2018 Rheology of dense granular suspensions under extensional flow. J. Rheol. 62 (2), 501–512.CrossRefGoogle Scholar
Cheng, Z., Hsu, T.-J. & Calantoni, J. 2017 Sedfoam: a multi-dimensional Eulerian two-phase model for sediment transport and its application to momentary bed failure. Coast. Engng 119, 32–50.CrossRefGoogle Scholar
Chèvremont, W., Chareyre, B. & Bodiguel, H. 2019 Quantitative study of the rheology of frictional suspensions: influence of friction coefficient in a large range of viscous numbers. Phys. Rev. Fluids 4 (6), 064302.CrossRefGoogle Scholar
David, L.G. & Richard, M. 2011 A two-phase debris-flow model that includes coupled evolution of volume fractions, granular dilatancy, and pore-fluid pressure. Ital. J. Engng Geol. Environ. 43, 415–424.Google Scholar
Divoux, T. & Géminard, J.-C. 2007 Friction and dilatancy in immersed granular matter. Phys. Rev. Lett. 99 (25), 258301.CrossRefGoogle ScholarPubMed
Dsouza, P.V. & Nott, P.R. 2020 A non-local constitutive model for slow granular flow that incorporates dilatancy. J. Fluid Mech. 888.CrossRefGoogle Scholar
Ergun, S. 1952 Fluid flow through packed columns. Chem. Engng Prog. 48, 89–94.Google Scholar
Gallier, S., Lemaire, E., Peters, F. & Lobry, L. 2014 Rheology of sheared suspensions of rough frictional particles. J. Fluid Mech. 757, 514–549.CrossRefGoogle Scholar
George, D.L. & Iverson, R.M. 2014 A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests. Proc. R. Soc. Lond. A 470 (2170), 20130820.Google Scholar
Iverson, R.M. 1997 The physics of debris flows. Rev. Geophys. 35 (3), 245–296.CrossRefGoogle Scholar
Iverson, R.M. 2005 Regulation of landslide motion by dilatancy and pore pressure feedback. J. Geophys. Res. 110, F02015.CrossRefGoogle Scholar
Iverson, R.M. & George, D.L. 2014 A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis. Proc. R. Soc. Lond. A 470 (2170), 20130819.Google Scholar
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 soil porosity. Science 290 (5491), 513–516.CrossRefGoogle ScholarPubMed
Jasak, H. & Uroić, T. 2020 Practical computational fluid dynamics with the finite volume method. In Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids, pp. 103–161. Springer.Google Scholar
Johnson, P.C. & Jackson, R. 1987 Frictional–collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176, 67–93.CrossRefGoogle Scholar
Lecampion, B. & Garagash, D.I. 2014 Confined flow of suspensions modeled by a frictional rheology. J. Fluid Mech. 759, 197–235.CrossRefGoogle Scholar
Lee, C.-H. 2021 Two-phase modelling of submarine granular flows with shear-induced volume change and pore-pressure feedback. J. Fluid Mech. 907.CrossRefGoogle Scholar
Lee, C.-H. & Huang, Z. 2018 A two-phase flow model for submarine granular flows: with an application to collapse of deeply-submerged granular columns. Adv. Water Resour. 115, 286–300.CrossRefGoogle Scholar
Mari, R., Seto, R., Morris, J.F. & Denn, M.M. 2014 Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions. J. Rheol. 58 (6), 1693–1724.CrossRefGoogle Scholar
Mathieu, A., Chauchat, J., Bonamy, C. & Nagel, T. 2019 Two-phase flow simulation of tunnel and lee-wake erosion of scour below a submarine pipeline. Water 11 (8), 1727.CrossRefGoogle Scholar
Mitchell, J.K. & Soga, K. 2005 Fundamentals of Soil Behavior, vol. 3. John Wiley & Sons.Google Scholar
Mutabaruka, P., Delenne, J.-Y., Soga, K. & Radjai, F. 2014 Initiation of immersed granular avalanches. Phys. Rev. E 89 (5), 052203.CrossRefGoogle ScholarPubMed
Nova, R. & Wood, D.M. 1982 A constitutive model for soil under monotonic and cyclic loading. In Soil Mechanics–Transient and Cyclic Loading (ed. G.N. Pande & O.C. Zienkiewicz), pp. 343–373. Wiley.Google Scholar
Pailha, M. 2009 Dynamique des avalanches granulaires immergées: rôle de la fraction volumique initiale. PhD thesis, Université de Provence-Aix-Marseille I.Google Scholar
Pailha, M., Nicolas, M. & Pouliquen, O. 2008 Initiation of underwater granular avalanches: influence of the initial volume fraction. Phys. Fluids 20 (11), 111701.CrossRefGoogle Scholar
Pailha, M. & Pouliquen, O. 2009 A two-phase flow description of the initiation of underwater granular avalanches. J. Fluid Mech. 633, 115–135.CrossRefGoogle Scholar
Pitman, E.B. & Le, L. 2005 A two-fluid model for avalanche and debris flows. Phil. Trans. R. Soc. Lond. A 363 (1832), 1573–1601.Google ScholarPubMed
Pouliquen, O. & Renaut, N. 1996 Onset of granular flows on an inclined rough surface: dilatancy effects. J. Phys. II 6 (6), 923–935.Google Scholar
Pudasaini, S.P., Wang, Y. & Hutter, K. 2005 Modelling debris flows down general channels. Nat. Hazards Earth Syst. Sci. 5 (6), 799–819.CrossRefGoogle Scholar
Revil-Baudard, T. & Chauchat, J. 2013 A two-phase model for sheet flow regime based on dense granular flow rheology. J. Geophys. Res.: Oceans 118 (2), 619–634.CrossRefGoogle Scholar
Reynolds, O. 1885 LVII. On the dilatancy of media composed of rigid particles in contact. With experimental illustrations. Lond. Edin. Dublin Phil. Mag. J. Sci. 20 (127), 469–481.CrossRefGoogle Scholar
Roscoe, K.H., Schofield, A.N. & Wroth, C.P. 1958 On the yielding of soils. Geotechnique 8 (1), 22–53.CrossRefGoogle Scholar
Rowe, P.W. 1962 The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proc. R. Soc. Lond. A 269 (1339), 500–527.Google Scholar
Schofield, A. & Wroth, P. 1968 Critical State Soil Mechanics. McGraw-Hill.Google Scholar
Si, P., Shi, H. & Yu, X. 2018 Development of a mathematical model for submarine granular flows. Phys. Fluids 30 (8), 083302.CrossRefGoogle Scholar
Sun, J. & Sundaresan, S. 2011 A constitutive model with microstructure evolution for flow of rate-independent granular materials. J. Fluid Mech. 682, 590–616.CrossRefGoogle Scholar
Trulsson, M., Andreotti, B. & Claudin, P. 2012 Transition from the viscous to inertial regime in dense suspensions. Phys. Rev. Lett. 109 (11), 118305.Google ScholarPubMed
Utter, B. & Behringer, R.P. 2004 Transients in sheared granular matter. Eur. Phys. J. E 14 (4), 373–380.CrossRefGoogle ScholarPubMed
Vo, T.T., Nezamabadi, S., Mutabaruka, P., Delenne, J.-Y. & Radjai, F. 2020 Additive rheology of complex granular flows. Nat. Commun. 11 (1), 1–8.CrossRefGoogle ScholarPubMed
Wang, C., Wang, Y., Peng, C. & Meng, X. 2017 Dilatancy and compaction effects on the submerged granular column collapse. Phys. Fluids 29 (10), 103307.CrossRefGoogle Scholar
Yin, Z.-Y., Jin, Z., Kotronis, P. & Wu, Z.-X. 2018 Novel SPH SIMSAND–based approach for modeling of granular collapse. Intl J. Geomech. 18 (11), 04018156.CrossRefGoogle Scholar
Yu, M.-L. & Lee, C.-H. 2019 Multi-phase-flow modeling of underwater landslides on an inclined plane and consequently generated waves. Adv. Water Resour. 133, 103421.CrossRefGoogle Scholar