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Axisymmetric column collapses of bi-frictional granular mixtures

Published online by Cambridge University Press:  12 May 2023

Teng Man Open the ORCID record for Teng Man [Opens in a new window] ,
Zaohui Zhang ,
Herbert E. Huppert  and
Sergio A. Galindo-Torres Open the ORCID record for Sergio A. Galindo-Torres [Opens in a new window]
Teng Man
Affiliation:
Key Laboratory of Coastal Environment and Resources of Zhejiang Province (KLaCER), School of Engineering, Westlake University, 600 Dunyu Road, Hangzhou, Zhejiang 310030, PR China
Zaohui Zhang
Affiliation:
Key Laboratory of Coastal Environment and Resources of Zhejiang Province (KLaCER), School of Engineering, Westlake University, 600 Dunyu Road, Hangzhou, Zhejiang 310030, PR China College of Environmental and Resource Sciences, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, PR China
Herbert E. Huppert
Affiliation:
Institute of Theoretical Geophysics, King's College, University of Cambridge, King's Parade, Cambridge CB2 1ST, UK
Sergio A. Galindo-Torres*
Affiliation:
Key Laboratory of Coastal Environment and Resources of Zhejiang Province (KLaCER), School of Engineering, Westlake University, 600 Dunyu Road, Hangzhou, Zhejiang 310030, PR China
*
†Email address for correspondence: s.torres@westlake.edu.cn
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Abstract

The behaviour of granular column collapses is associated with the dynamics of geohazards, such as debris flows, landslides and pyroclastic flows, yet their underlying physics is still not well understood. In this paper, we explore granular column collapses using the sphero-polyhedral discrete element method, where the system contains two types of particles with different frictional properties. We impose three different mixing ratios and multiple different particle frictional coefficients, which lead to different run-out distances and deposition heights. Based on our previous work and a simple mixture theory, we propose a new effective initial aspect ratio for the bi-frictional granular mixture, which helps unify the description of the relative run-out distances. We analyse the kinematics of bi-frictional granular column collapses and find that deviations from classical power-law scaling in both the dimensionless terminal time and the dimensionless time when the system reaches the maximum kinetic energy may result from differences in the initial solid fraction and initial structures. To clarify the influence of initial states, we further decrease the initial solid fraction of granular column collapses, and propose a trial function to quantitatively describe its influence. Due to the utilization of a simple mixture theory of contact occurrence probability, this study can be associated with the friction-dependent rheology of granular systems and friction-induced granular segregations, and further generalized to applications with multiple species of particles in various natural and engineering mixtures.

JFM classification

Granular media: Granular media Mixing: Granular mixing Nonlinear Dynamical Systems: Pattern formation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , A4
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

Alonso-Marroquín, F., Ramírez-Gómez, Á., González-Montellano, C., Balaam, N., Hanaor, D.A.H., Flores-Johnson, E.A., Gan, Y., Chen, S. & Shen, L. 2013 Experimental and numerical determination of mechanical properties of polygonal wood particles and their flow analysis in silos. Granul. Matt. 15 (6), 811–826.CrossRefGoogle Scholar
Bagnold, R.A. 1954 Experiments on a gravity-free dispersion of large solid spheres in a newtonian fluid under shear. Proc. R. Soc. Lond. A 225 (1160), 49–63.Google Scholar
Belheine, N., Plassiard, J.-P., Donzé, F.-V., Darve, F. & Seridi, A. 2009 Numerical simulation of drained triaxial test using 3d discrete element modeling. Comput. Geotech. 36 (1–2), 320–331.CrossRefGoogle Scholar
Bougouin, A., Lacaze, L. & Bonometti, T. 2019 Collapse of a liquid-saturated granular column on a horizontal plane. Phys. Rev. Fluids 4, 124306.CrossRefGoogle Scholar
Cabrejos-Hurtado, J., Galindo Torres, S.A. & Pedroso, D.M. 2016 Assessment of the mechanical behaviour of granular media by dem-based true triaxial tests. In Advances of Computational Mechanics in Australia, Applied Mechanics and Materials (ed. Y. Gu, H. Guan, E. Sauret, S. Saha, H. Zhan & R. Persky), vol. 846, pp. 428–433. Trans Tech Publications.CrossRefGoogle Scholar
Cabrera, M. & Estrada, N. 2019 Granular column collapse: analysis of grain-size effects. Phys. Rev. E 99, 012905.CrossRefGoogle ScholarPubMed
Fern, E.J. & Soga, K. 2017 Granular column collapse of wet sand. In 1st International Conference on Material Point Method (MPM 2017), vol. 175, pp. 14–20. Procedia Engineering.Google Scholar
Foerster, S.F., Louge, M.Y., Chang, H. & Allia, K. 1994 Measurements of the collision properties of small spheres. Phys. Fluids 6 (3), 1108–1115.CrossRefGoogle Scholar
Galindo-Torres, S.A. 2013 A coupled discrete element lattice Boltzmann method for the simulation of fluid–solid interaction with particles of general shapes. Comput. Meth. Appl. Mech. Engng 265, 107–119.CrossRefGoogle Scholar
Galindo-Torres, S.A. & Pedroso, D.M. 2010 Molecular dynamics simulations of complex-shaped particles using voronoi-based spheropolyhedra. Phys. Rev. E 81 (6), 061303.CrossRefGoogle ScholarPubMed
Galindo-Torres, S.A., Zhang, X. & Krabbenhoft, K. 2018 Micromechanics of liquefaction in granular materials. Phys. Rev. Appl. 10 (6), 064017.CrossRefGoogle Scholar
Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441 (7094), 727.CrossRefGoogle ScholarPubMed
Lacaze, L. & Kerswell, R.R. 2009 Axisymmetric granular collapse: a transient 3d flow test of viscoplasticity. Phys. Rev. Lett. 102 (10), 108305.CrossRefGoogle ScholarPubMed
Lajeunesse, E., Monnier, J.B. & Homsy, G.M. 2005 Granular slumping on a horizontal surface. Phys. Fluids 17 (10), 103302.CrossRefGoogle Scholar
Li, X., Dong, M., Jiang, D., Li, S. & Shang, Y. 2020 The effect of surface roughness on normal restitution coefficient, adhesion force and friction coefficient of the particle-wall collision. Powder Technol. 362, 17–25.CrossRefGoogle Scholar
Lorenz, A., Tuozzolo, C. & Louge, M.Y. 1997 Measurements of impact properties of small, nearly spherical particles. Expl Mech. 37, 292–298.CrossRefGoogle Scholar
Lube, G., Huppert, H.E., Sparks, R.S.J. & Freundt, A. 2005 Collapses of two-dimensional granular columns. Phys. Rev. E 72 (4), 041301.CrossRefGoogle ScholarPubMed
Lube, G., Huppert, H.E, Sparks, R.S.J. & Hallworth, M.A. 2004 Axisymmetric collapses of granular columns. J. Fluid Mech. 508, 175–199.CrossRefGoogle Scholar
Man, T., Huppert, H.E., Li, L. & Galindo-Torres, S.A. 2021 a Deposition morphology of granular column collapses. Granul. Matt. 23 (3), 1–12.CrossRefGoogle Scholar
Man, T., Huppert, H.E., Li, L. & Galindo-Torres, S.A. 2021 b Finite-size analysis of the collapse of dry granular columns. Geophys. Res. Lett. 48 (24), e2021GL096054.CrossRefGoogle Scholar
Man, T., Huppert, H.E., Zhang, Z. & Galindo-Torres, S.A. 2022 Influence of cross-section shape on granular column collapses. Powder Technol. 407, 117591.CrossRefGoogle Scholar
Man, T., Zhang, P., Ge, Z., Galindo-Torres, S.A. & Hill, K.M. 2023 Friction-dependent rheology of dry granular systems. Acta Mech. Sin. 39 (1), 1–12.CrossRefGoogle Scholar
Martinez, F., Tamburrino, A., Casis, V. & Ferrer, P 2022 Segregation effects on flow's mobility and final morphology of axisymmetric granular collapses. Granul. Matt. 24, 101.CrossRefGoogle Scholar
MiDi, G.D.R. 2004 On dense granular flows. Eur. Phys. J. E 14 (4), 341–365.CrossRefGoogle Scholar
Pouliquen, O., Cassar, C., Jop, P., Forterre, Y. & Nicolas, M. 2006 Flow of dense granular material: towards simple constitutive laws. J. Stat. Mech. 2006 (07), P07020.CrossRefGoogle Scholar
Pournin, L. & Liebling, T.M. 2005 A generalization of distinct element method to tridimensional particles with complex shapes. In Powders and Grains 2005 (ed. R. Garcia-Rojo, H.J. Herrmann & S. McNamara), vol. II, pp. 1375–1378. A.A. Balkema.Google Scholar
Roche, O., Gilbertson, M., Phillips, J.C. & Sparks, R.S.J. 2002 Experiments on deaerating granular flows and implications for pyroclastic flow mobility. Geophys. Res. Lett. 29, 40-1–40-4.CrossRefGoogle Scholar
Rondon, L., Pouliquen, O. & Aussillous, P. 2011 Granular collapse in a fluid: role of the initial volume fraction. Phys. Fluids 23 (7), 073301.CrossRefGoogle Scholar
Scherer, P.O.J. 2017 Equations of Motion, pp. 289–321. Springer.Google Scholar
Staron, L. & Hinch, E.J. 2005 Study of the collapse of granular columns using two-dimensional discrete-grain simulation. J. Fluid Mech. 545, 1–27.CrossRefGoogle Scholar
Staron, L. & Hinch, E.J. 2007 The spreading of a granular mass: role of grain properties and initial conditions. Granul. Matt. 9 (3–4), 205.CrossRefGoogle Scholar
Thompson, E.L. & Huppert, H.E. 2007 Granular column collapses: further experimental results. J. Fluid Mech. 575, 177–186.CrossRefGoogle Scholar
Warnett, J.M., Denissenko, P., Thomas, P.J., Kiraci, E. & Williams, M.A. 2014 Scalings of axisymmetric granular column collapse. Granul. Matt. 16 (1), 115–124.CrossRefGoogle Scholar
Wu, Y., Wang, D. & Li, P. 2021 The collapse of a granular column onto an erodible bed: dynamics and morphology scaling. Granul. Matt. 23, 31.CrossRefGoogle Scholar
Zenit, R. 2005 Computer simulations of the collapse of a granular column. Phys. Fluids 17 (3), 031703.CrossRefGoogle Scholar
Zhang, C.-G., Yin, Z.-Y., Wu, Z.-X. & Jin, Y.-F. 2018 Influence of particle shape on granular column collapse by three-dimensional DEM. In Proceedings of GeoShanghai 2018 International Conference: Fundamentals of Soil Behaviours (ed. A. Zhou, J. Tao, X. Gu & L. Hu), pp. 840–848. Springer.CrossRefGoogle Scholar

Man et al. Supplementary Movie 1

Collapse of granular columns with a mixing ratio of Grain#1 : Grain#2 = 9 : 1.

Download Man et al. Supplementary Movie 1(Video)
Video 5.6 MB

Man et al. Supplementary Movie 2

Collapse of granular columns with a mixing ratio of Grain#1 : Grain#2 = 7 : 3.

Download Man et al. Supplementary Movie 2(Video)
Video 12.3 MB

Man et al. Supplementary Movie 3

Collapse of granular columns with a mixing ratio of Grain#1 : Grain#2 = 5 : 5.

Download Man et al. Supplementary Movie 3(Video)
Video 6.1 MB