Simulation of Collapse of Granular Columns Using the Discrete Element Method
Publication: International Journal of Geomechanics
Volume 15, Issue 6
Abstract
In this study, a three-dimensional (3D) numerical investigation of axisymmetric collapse of granular columns has been conducted using the discrete element method (DEM). The simulated granular columns have a constant initial radius of 5.68 mm and three aspect ratios: 0.55, 1.0, and 2.0. The columns consist of uniform spherical quartz particles with a diameter of 0.32 mm. In the DEM model, rotational velocities of particles are reduced by a factor at every time step to partially account for the additional rolling resistance due to the effect of particle shape and hysteretic contact behavior. The simple linear contact model is used; however, its performance is improved by using different stiffness values calculated by nonlinear Hertz–Mindlin contact model for each aspect ratio. The simulated final deposit heights, runout distances, and energy dissipation values are in good agreement with experimental observations reported in the literature. The effects of initial porosity and rotational resistance on the final deposit profile and energy dissipation at different aspect ratios are investigated through a parametric study. For different aspect ratios, a higher rotational resistance leads to higher final deposit height, shorter runout distance, and less energy dissipation. A lower value of initial porosity leads to higher final deposit height; however, the runout distance and evolution of normalized potential, kinetic, and dissipated energies versus time are insensitive to the initial porosity for the granular columns investigated.
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Acknowledgments
Support of this study is provided by the U.S. National Science Foundation under Grant No. CMMI-1131383, the Open Fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology) under Grant No. SKLGP2012K001, and the Mid-Atlantic Universities Transportation Center (MAUTC). These supports are gratefully acknowledged. The authors are also very appreciative of Dr. Matthew Evans at Oregon State University for his help in speeding up the DEM simulations.
References
Ai, J., Chen, J. F., Rotter, J. M., and Ooi, J. Y. (2011). “Assessment of rolling resistance models in discrete element simulations.” Powder Technol., 206(3), 269–282.
Balmforth, N. J., and Kerswell, R. R. (2005). “Granular collapse in two dimensions.” J. Fluid Mech., 538, 399–428.
Brewster, R., Grest, G. S., Landry, J. W., and Levine, A. J. (2005). “Plug flow and the breakdown of bagnold scaling in cohesive granular flows.” Phys. Rev. E, 72(6), 061301.
Bui, H. H., Fukagawa, R., Sako, K., and Ohno, S. (2008). “Lagrangian mesh-free particle method (SPH) for large deformation and post-failure flows of geomaterial using elastic-plastic soil constitutive model.” Int. J. Numer. Anal. Meth. Geomech., 32(12), 1537–1570.
Casagrande, A. (1936). “Characteristics of cohesionless soils affecting the stability of slopes and earth fills.” J. Boston Soc. Civil Engrs., 23(1), 13–32.
Chaudhuri, B., Muzzio, F. J., and Tomassone, M. S. (2006). “Modeling of heat transfer in granular flow in rotating vessels.” Chem. Eng. Sci., 61(9), 6348–6360.
Chen, W., and Qiu, T. (2012). “Numerical simulations of granular materials using smoothed particle hydrodynamics method.” Int. J. Geomech., 127–135.
Cleary, P. W., and Frank, M. (2006). “Three-dimensional discrete element simulation of axisymmetric collapses of granular columns.” http://www.researchgate.net/publication/228530783_Three-Dimensional_Discrete_Element_Simulation_of_Axisymmetric_Collapses_of_Granular_Columns.
Cruden, D. M., and Varnes, D. J. (1996). “Landslide types and processes.” Landslides-investigation and mitigation: Transportation Research Board, Special Rep. No. 247, A. K. Turner and R. L. Schuster, eds., National Research Council, National Academy Press, Washington, DC, 36–75.
Cui, L., and O’Sullivan, C. (2006). “Exploring the macro- and micro-scale response of an idealised granular material in the direct shear apparatus.” Geotechnique, 56(7), 455–468.
Cui, L., O’Sullivan, C., and O’Neill, S. (2007). “An analysis of the triaxial apparatus using a mixed boundary three-dimensional discrete element model.” Geotechnique, 57(10), 831–844.
Cundall, P. A., and Strack, O. D. L. (1979). “A discrete numerical model for granular assemblies.” Geotechnique, 29(1), 47–65.
Datta, A., Mishra, B. K., Das, S. P., and Sahu, A. (2008). “A DEM analysis of flow characteristics of noncohesive particles in hopper.” Mater. Manuf. Processes, 23(2), 196–203.
Denlinger, R. P., and Iverson, R. M. (2004). “Granular avalanches across irregular three-dimensional terrain: 1. Theory and computation.” J. Geophys. Res.: Earth Surf., 109(F1), F01014.
Dobry, R., Ladd, R. S., Yokel, F. Y., Chung, R. M., and Powell, D. (1982). Prediction of pore water pressure buildup and liquefaction of sands during earthquakes by the cyclic strain method, NBS Building Science Series 138, National Bureau of Standards, Gaithersburg, MD.
Drake, T. G. (1991). “Granular flow: Physical experiments and their implications for microstructural theories.” J. Fluid Mech., 225(1), 121–152.
Dvorkin, J., and Nur, A. (1996). “Elasticity of high-porosity sandstones: Theory for two north sea data sets.” Geophysics, 61(5), 1363–1370.
Fraige, F. Y., and Langston, P. A. (2004). “Integration schemes and damping algorithms in distinct element models.” Adv. Powder Technol., 15(2), 227–245.
Frost, J., and Evans, T. (2009). “Membrane effects in biaxial compression tests.” J. Geotech. Geoenviron. Eng., 986–991.
Gingold, R. A., and Monaghan, J. J. (1977). “Smoothed particle hydrodynamics: Theory and application to non-spherical stars.” Monthly Notices Royal Astron. Soc., 181(3), 375–389.
Girolami, L., Hergault, V., Vinay, G., and Wachs, A. (2012). “A three-dimensional discrete-grain model for the simulation of dam-break rectangular collapses: Comparison between numerical results and experiments.” Granul. Matter, 14(3), 381–392.
Huang, H. and Tutumluer, E. (2014). “Image-aided element shape generation method in discrete-element modeling for railroad ballast.” J. Mater. Civ. Eng., 527–535.
Huang, J., da Silva, M. V., and Krabbenhoft, K. (2013). “Three-dimensional granular contact dynamics with rolling resistance.” Comput. Geotech., 49, 289–298.
Hungr O. (2008). “Simplified models of spreading flow of dry granular material.” Can. Geotech. J., 45(8), 1156–1168.
Hungr., O., and Evans, S. G. (2004). “Entrainment of debris in rock avalanches: An analysis of a long run-out mechanism.” Bull. Geol. Soc. Am., 116(9–10), 1240–1252.
Itasca. (2008). Particle flow code, PFC3D 4.0, Itasca Consulting Group, Inc., Minneapolis.
Iwashita, K., and Oda, M. (1998). “Rolling resistance at contacts in simulation of shear band development by DEM.” J. Eng. Mech., 285–292.
Iwashita, K., and Oda, M. (2000). “Micro-deformation mechanism of shear banding process based on modified distinct element method.” Powder Technol., 109(1–3), 192–205.
Jiang, M. J., Yu, H. S., and Harris, D. (2005). “A novel discrete model for granular material incorporating rolling resistance.” Comput. Geotech., 32(5), 340–357.
Kermani, E., Li, T., and Qiu, T. (2014). “Discrete element method simulation of granular column collapse.” GeoHubei Int. Conf.: Advances in Transportation Geotechnics and Materials for Sustainable Infrastructure, ASCE Geotechnical Special Publication (GSP 250), Yichang, Hubei, 1–8.
Ketterhagen, W. R., Curtis, J. S., Wassgren, C. R., and Hancock, B. C. (2008). “Modeling granular segregation in flow from quasi-three-dimensional, wedge-shaped hoppers.” Powder Technol., 179(3), 126–143.
Lacaze, L., and Kerswell, R. R. (2009). “Axisymmetric granular collapse: A transient 3D flow test of visco-plasticity.” Phys. Rev. Lett., 102(10), 108305.
Lagree, P. Y., Staron, L., and Popinet, S. (2011). “The granular column collapse as a continuum: Validity of a two-dimensional navier–stokes model with a .” J. Fluid Mech., 686(1), 378–408.
Lajeunesse, E., Mangeney-Castelnau, A., and Vilotte, J. P. (2004). “Spreading of a granular mass on a horizontal plane.” Phys. Fluids, 16(7), 2371–2381.
Lajeunesse, E., Quantin, C., Allemand, P., and Delacourt, C. (2006). “New insights on the runout of large landslides in the valles-marineris canyons, Mars.” Geophys. Res. Lett., 33(L04403), 1–4.
Lambe, T. W., and Whitman, R. V. (1969). Soil mechanics, John Wiley & Sons, New York.
Lemieux, A., et al. (2008). “Large-scale numerical investigation of solids mixing in a v-blender using the discrete element method.” Powder Technol., 181(2), 205–216.
Li, X. K., Chu, X. H., and Feng, Y. T. (2005a). “A discrete particle model and numerical modeling of the failure modes of granular materials.” Eng. Comput., 22(8), 894–920.
Li, Y., Xu, Y., and Thornton, C. (2005b). “A comparison of discrete element simulations and experiments for ‘sandpiles’ composed of spherical particles.” Powder Technol., 160(3), 219–228.
Liu, J., Yun, B., and Zhao, C. (2012). “Identification and validation of rolling friction models by dynamic simulation of sandpile formation.” Int. J. Geomech., 484–493.
Lo, C. Y., Bolton, M., and Cheng, Y. P. (2009). “Discrete element simulation of granular column collapse.” AIP Conf. Proc., 1145(1), 627–630.
Lube, G., Huppert, H. E., Sparks, R. S. J., and Freundt, A. (2005). “Collapses of two-dimensional granular columns.” Phys. Rev. E, 72(4), 041301.
Lube, G., Huppert, H. E., Stephan, R., Sparks, J., and Freundt, A. (2011). “Granular column collapses down rough, inclined channels.” J. Fluid Mech., 675, 347–368.
Lube, G., Huppert, H. E., Sparks, R. S. J., and Hallworth, M. A. (2004). “Axisymmetric collapses of granular columns.” J. Fluid Mech., 508(1), 175–199.
Lucy, L. B. (1977). “A numerical approach to the testing of the fission hypothesis.” Astron. J., 82(12), 1013–1024.
Mast, C. M., Arduino, P., Mackenzie-Helnwein, P., and Miller, G. R. (2014). “Simulating granular column collapse using the material point method.” Acta Geotech., in print
Mindlin, R. D., and Deresiewicz, H. (1953). “Elastic spheres in contact under varying oblique forces.” J. Appl. Mech., 20(3), 327–344.
Morrison, R. D., Shi, F., and Whyte, R. (2007). “Modelling of incremental rock breakage by impact-for use in DEM models.” Miner. Eng., 20(3), 303–309.
O’Sullivan, C. (2011). Particulate discrete element modelling: A geomechanics perspective, Taylor & Francis, New York.
O’Sullivan, C., Bray, J. D., and Riemer, M. (2004). “Examination of the response of regularly packed specimens of spherical particles using physical tests and discrete element simulations.” J. Eng. Mech., 1140–1150.
Parisi, D. R., Masson, S., and Martinez, J. (2004). “Partitioned distinct element method simulation of granular flow within industrial silos.” J. Eng. Mech., 771–779.
Poisel, R., and Preh, A. (2008). “3D landslide run out modelling using the particle flow code PFC3D.” Proc., 10th Int. Symp. Landslides and Engineered Slopes, CISMGE-CCES, CNCEG, CSRME and the Geotechnical Division of the Hong Kong Institution of Engineers, Xi’an, China, 873–879.
Portillo, P. M., Muzzio, F. J., and Ierapetritou, M. G. (2007). “Hybrid DEM-compartment modeling approach for granular mixing.” AIChE. J., 53(1), 119–128.
Rock, M., Morgeneyer, M., Schwedes, J., Brendel, L., Wolf, D. E., and Kadau, D. (2008). “Visualization of shear motions of cohesive powders in the true biaxial shear tester.” Particul. Sci. Technol., 26(1), 43–54.
Sjoblom, K. (2014). “Modeling soil crust formation by discrete element method.” Geo-Congress 2014 Technical Papers, Reston, VA,.
Staron, L., and Hinch, E. J. (2005). “Study of the collapse of granular columns using two-dimensional discrete-grain simulation.” J. Fluid Mech., 545(1), 1–27.
Staron, L., and Hinch, E. J. (2007). “The spreading of a granular mass: Role of grain properties and initial conditions.” Granul. Matter, 9(3–4), 205–217.
Suiker, A. S., and Fleck, N. A. (2004). “Frictional collapse of granular assemblies.” J. Appl. Mech., 71(3), 350–358.
Tapia-McClung, H., and Zenit, R. (2012). “Computer simulations of the collapse of columns formed by elongated grains.” Phys. Rev. E, 85(6), 061304.
Teufelsbauer, H., Wang, Y., Chiou, M. C., and Wu, W. (2009). “Flow–obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment.” Granul. Matter, 11(4), 209–220.
Urabe, C. (2005). “Dynamics of fluctuation of the top location of a sandpile.” J. Phys. Soc. Jpn., 74(9), 2475–2479.
Wensrich, C. M., and Katterfeld, A. (2012). “Rolling friction as a technique for modeling particle shape in DEM.” Powder Technol., 217, 409–417.
Zenit, R. (2005). “Computer simulations of the collapse of a granular column.” Phys. Fluids, 17(3), 031703.
Zhang, L., and Thornton, C. (2007). “A numerical examination of the direct shear test.” Geotechnique, 57(4), 343–354.
Zhang, W., Wang, J., and Jiang, M. (2013). “DEM-aided discovery of the relationship between energy dissipation and shear band formation considering the effects of particle rolling resistance.” J. Geotech. Geoenviron. Eng., 1512–1527.
Zhang, X., Krabbenhoft, K., and Sheng, D. (2014). “Particle finite element analysis of the granular column collapse problem.” Granul. Matter, 16(4), 609–619.
Zhao, T., Houlsby, G. T., and Utili, S. (2012). “Numerical simulation of the collapse of granular columns using DEM.” Discrete element modelling of particulate media, C. Wu, ed., The Royal Society of Chemistry, U.K., 133–140.
Zhou, Y. C., Wright, B. D., Yang, R. Y., Xu, B. H., and Yu, A. B. (1999). “Rolling friction in the dynamic simulation of sandpile formation.” Physica A, 269(2–4), 536–553.
Zhou, Y. C., Xu, B. H., Yu, A. B., and Zulli, P. (2002). “An experiment and numerical study of the angle of repose of coarse spheres.” Powder Technol., 125(1), 45–54.
Zhu, H. P., Zhou, Z. Y., Yang, R. Y., and Yu, A. B. (2007). “Discrete particle simulation of particulate systems: Theoretical developments.” Chem. Eng. Sci., 62(13), 3378–3392.
Zhu, H. P., Zhou, Z. Y., Yang, R. Y., and Yu, A. B. (2008). “Discrete particle simulation of particulate systems: A review of major applications and findings.” Chem. Eng. Sci., 63(23), 5728–5770.
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Published In
International Journal of Geomechanics
Volume 15 • Issue 6 • December 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Mar 8, 2014
Accepted: Nov 10, 2014
Published online: Apr 10, 2015
Discussion open until: Sep 10, 2015
Published in print: Dec 1, 2015
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