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Fully implicit discrete element method for granular column collapse

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Abstract

This paper discusses the development of a fully implicit discrete element method and its application to granular column collapse simulations. In the developed model, both the translational and angular velocities are solved implicitly and simultaneously. The model is verified by simulating a single particle bouncing on a flat surface and rolling on a slope; it is then validated through a granular column collapse simulation using many particles. The verification indicates that the restitution coefficient between the particle and the bottom surface estimated from the calculated results generally agrees with that of an input parameter, and the time-series variations of the translational and angular velocities of the particle on a slope are also in perfect agreement with the theoretical values. In the granular column collapse simulation, the performance of the proposed model with respect to the runout distance and deposition shape of the collapsed granular column is investigated in comparison to a previous experiment. The simulations are conducted for a total of ten cases by varying the initial aspect ratios of the granular column, and the calculated results are found to agree well with the experimental results.

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References

  1. Cundall PA, Strack ODL (1979) A distinct numerical model for granular assemblies. Geotechnique 29:47–65. https://doi.org/10.1680/geot.1979.29.1.47

    Article  Google Scholar 

  2. Lisjak A, Grasselli G (2014) A review of discrete modeling techniques for fracturing processes in discontinuous rock masses. J Rock Mech Geotech Eng 6:301–314. https://doi.org/10.1016/j.jrmge.2013.12.007

    Article  Google Scholar 

  3. Fathipour-Azar H, Wang J, Jalali SME, Torabi SR (2020) Numerical modeling of geomaterial fracture using a cohesive crack model in grain-based DEM. Comput Part Mech 7:645–654. https://doi.org/10.1007/s40571-019-00295-4

    Article  Google Scholar 

  4. González JM, Zárate F, Oñate E (2018) Pulse fracture simulation in shale rock reservoirs: DEM and FEM-DEM approaches. Comp Part Mech 5:355–373. https://doi.org/10.1007/s40571-017-0174-3

    Article  Google Scholar 

  5. Ramírez-Gómez Á (2020) The discrete element method in silo/bin research. recent advances and future trends. Part Sci Tech 38:210–227. https://doi.org/10.1080/02726351.2018.1536093

    Article  Google Scholar 

  6. Coetzee CJ, Els DNJ (2009) Calibration of discrete element parameters and the modelling of silo discharge and bucket filling. Comput Electron Agr 65:198–212. https://doi.org/10.1016/j.compag.2008.10.002

    Article  Google Scholar 

  7. Gonzárez-montellano C, Ayuga F, Ooi JY (2011) Discrete element modelling of grain flow in a planar silo: influence of simulation parameters. Granul Matter 13:149–158. https://doi.org/10.1007/s10035-010-0204-9

    Article  Google Scholar 

  8. Feng Y, Yuan Z (2021) Discrete element method modeling of granular flow characteristics transition in mixed flow. Comp Part Mech 8:21–34. https://doi.org/10.1007/s40571-019-00309-1

    Article  Google Scholar 

  9. Mori Y, Sakai M (2021) Visualization study on the coarse graining DEM for large-scale gas-solid flow systems. Particuology 59:24–33. https://doi.org/10.1016/j.partic.2020.07.001

    Article  Google Scholar 

  10. Mori Y, Sakai M (2021) Development of a robust Eulerian-Lagrangian model for the simulation of an industrial solid-fluid system. Chem Eng J 406:126841. https://doi.org/10.1016/j.cej.2020.126841

    Article  Google Scholar 

  11. Tsuji Y, Kawaguchi T, Tanaka T (1993) Discrete particle simulation of two-dimensional fluidized bed. Powder Technol 77:79–87. https://doi.org/10.1016/0032-5910(93)85010-7

    Article  Google Scholar 

  12. Golshan S, Sotudeh-Gharebagh R, Zarghami R, Mosotoufi N, Blais B, Kuipers JAM (2020) Review and implementation of CFD-DEM applied to chemical process systems. Chem Eng Sci. https://doi.org/10.1016/j.ces.2020.115646

    Article  Google Scholar 

  13. Hobbs A (2009) Simulation of an aggregate dryer using coupled CFD and DEM methods. Int J Comput Fluid Dynam 23:199–207. https://doi.org/10.1080/10618560802680971

    Article  MATH  Google Scholar 

  14. Azmir J, Hou Q, Yu A (2018) Discrete particle simulation of food grain drying in a fluidized bed. Powder Technol 323:238–249. https://doi.org/10.1016/j.powtec.2017.10.019

    Article  Google Scholar 

  15. Hilton J, Ying D, Cleary P (2013) Modelling spray coating using a combined CFD-DEM and spherical harmonic formulation. Chem Eng Sci 99:141–160. https://doi.org/10.1016/j.ces.2013.05.051

    Article  Google Scholar 

  16. Singh RI, Brink A, Hupa M (2013) CFD modeling to study fluidized bed combustion and gasification. Appl Therm Eng 52:585–614. https://doi.org/10.1016/j.applthermaleng.2012.12.017

    Article  Google Scholar 

  17. Balaam NP, Poulos HG, Brown PT (1978) Settlement analysis of soft clays reinforced with granular piles. Proc. 5th Asian Conf Soil Eng 81–92

  18. Bui HH, Fukagawa R, Sako K, Ohno S (2008) Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using an elastic-plastic soil constitutive soil. Int J Numer Anal Methods Geomech 32:1537–1570. https://doi.org/10.1002/nag.688

    Article  MATH  Google Scholar 

  19. Ikari H, Gotoh H (2016) SPH-based simulation of granular collapse on an inclined bed. Mech Res Commun 73:12–18. https://doi.org/10.1016/j.mechrescom.2016.01.014

    Article  Google Scholar 

  20. Aranson IS, Tsimring LS (2001) Continuum description of avalanches in granular media. Phys Rev E. https://doi.org/10.1103/PhysRevE.64.020301

    Article  Google Scholar 

  21. Lagrée PY, Staron L, Popinet S (2011) The granular column collapse as a continuum: validity of a two-dimensional Navier-Stokes model with a μ(I)-rheology. J Fluid Mech 686:378–408. https://doi.org/10.1017/jfm.2011.335

    Article  MathSciNet  MATH  Google Scholar 

  22. Bui HH, Nguyen GD, (2017) A coupled fluid-solid SPH approach to modelling flow through deformable porous media. Int J Solids Struct 125:244–264. https://doi.org/10.1016/j.ijsolstr.2017.06.022

    Article  Google Scholar 

  23. Gotoh H, Khayyer A (2018) On the state-of-the-art of particle methods for coastal and ocean engineering. Coast Eng J 60:79–103. https://doi.org/10.1080/21664250.2018.1436243

    Article  Google Scholar 

  24. Tsuruta N, Gotoh H, Suzuki K, Ikari H, Shimosako K (2019) Development of PARISPHERE as the particle-based numerical wave flume for coastal engineering problems. Coast Eng J 61:41–62. https://doi.org/10.1080/21664250.2018.1560683

    Article  Google Scholar 

  25. Ikari H, Yamano T, Gotoh H (2020) Multiphase particle method using an elastoplastic solid phase model for the diffusion of dumped sand from a split hopper. Comput Fluids 208:104639. https://doi.org/10.1016/j.compfluid.2020.104639

    Article  MathSciNet  MATH  Google Scholar 

  26. Razavitoosi SL, Ayyoubzadeh SA, Valizadeh A (2014) Two-phase SPH modelling of waves caused by dam break over a movable bed. Int J Sediment Res 29:344–356. https://doi.org/10.1016/S1001-6279(14)60049-4

    Article  Google Scholar 

  27. Naito N, Meada K, Kohno H, Ushiwatari Y, Suzuki K, Kawase R (2020) Rockfall impacts on sand cushions with different soil mechanical characteristics using discrete element method. Soil Found 60:384–397. https://doi.org/10.1016/j.sandf.2020.02.008

    Article  Google Scholar 

  28. Schmeeckle MW (2014) Numerical simulation of turbulence and sediment transport of medium sand. J Geophys Res-Earth 119:1240–1262. https://doi.org/10.1002/2013JF002911

    Article  Google Scholar 

  29. Seli P, Pirker S, Lichtenegger T (2018) Onset of sediment transport in mono- and bidisperse beds under turbulent shear flow. Comp Part Mech 5:203–212. https://doi.org/10.1007/s40571-017-0163-6

    Article  Google Scholar 

  30. Zhang B, Xu D, Zhang B, Ji C, Munjiza A, Williams J (2020) Numerical investigation on the incipient motion of non-spherical sediment particles in bedload regime of open channel flows. Comp Part Mech 7:987–1003. https://doi.org/10.1007/s40571-020-00323-8

    Article  Google Scholar 

  31. Harada E, Tazaki T, Gotoh H (2020) Numerical investigation of ripple in oscillating water tank by DEM-MPS coupled solid-liquid two-phase flow model. J Hydro-Environ Res 32:26–47. https://doi.org/10.1016/j.jher.2020.07.001

    Article  Google Scholar 

  32. Tazaki T, Harada E, Gotoh H (2021) Vertical sorting process in oscillating water tank using DEM-MPS coupling model. Coast Eng 165:103765. https://doi.org/10.1016/j.coastaleng.2020.103765

    Article  Google Scholar 

  33. Harada E, Ikari H, Tazaki T, Gotoh H (2021) Numerical simulation for coastal morphodynamics using DEM-MPS method. Appl Ocean Res 117:102905. https://doi.org/10.1016/j.apor.2021.102905

    Article  Google Scholar 

  34. Harada E, Gotoh H, Ikari H, Khayyer A (2018) Numerical simulation for sediment transport using MPS-DEM coupling model. Adv Water Res 129:354–364. https://doi.org/10.1016/j.advwatres.2017.08.007

    Article  Google Scholar 

  35. Harada E, Ikari H, Khayyer A, Gotoh H (2019) Numerical simulation for swash morphodynamics by DEM-MPS coupling model. Coast Eng J 61:2–14. https://doi.org/10.1080/21664250.2018.1554203

    Article  Google Scholar 

  36. Helbing D, Farkas I, Vicsek T (2000) Simulating dynamical features of escape panic. Nature 407:487–490. https://doi.org/10.1038/35035023

    Article  Google Scholar 

  37. Gotoh H, Harada E, Andoh E (2012) Simulation of pedestrian contra-flow by multi-agent DEM model with self-evasive action model. Safety Sci 50:326–332. https://doi.org/10.1016/j.ssci.2011.09.009

    Article  Google Scholar 

  38. Harada E, Gotoh H, Rahman NBA (2015) A switching action model for DEM-based multi-agent crowded behavior simulator. Safety Sci 79:105–115. https://doi.org/10.1016/j.ssci.2015.06.001

    Article  Google Scholar 

  39. Samiei K (2014) Implicit and explicit algorithms in Discrete Element Method. LAP LAMBERT Academic Publishing

  40. Tuley R, Danby M, Shrimpton J, Palmer M (2010) On the optimal numerical time integration for Lagrangian DEM within implicit flow solvers. Comput Chem Eng 58:211–222. https://doi.org/10.1016/j.compchemeng.2013.06.018

    Article  Google Scholar 

  41. Jasion G, Shrimpton J, Danby M, Takeda K (2011) Performance of numerical integrators on tangential motion of DEM within implicit flow solvers. Comput Chem Eng 35:2218–2226. https://doi.org/10.1016/j.compchemeng.2011.02.017

    Article  Google Scholar 

  42. Shi G (1992) Discontinuous deformation analysis: a new numerical model for the statics and dynamics of deformable block structures. Eng Comput 9:157–168. https://doi.org/10.1108/eb023855

    Article  Google Scholar 

  43. Koyama T, Nishiyama S, Yang M, Ohnishi Y (2011) Modeling the interaction between fluid flow and particle movement with discontinuous deformation analysis (DDA) method. Int J Numer Anal Meth Geomech 35:1–20. https://doi.org/10.1002/nag.890

    Article  MATH  Google Scholar 

  44. Gotoh H, Sumi T, Sakai T (2006) Numerical movable bed based on implicit distinct element method. Doboku Gakkai Ronbunshuu B 62(2):201–209. https://doi.org/10.2208/jscejb.62.201 (in Japanese)

    Article  Google Scholar 

  45. Yoshida H, Masuya H, Imai K (1988) Impulsive properties of falling rocks on sand-layers by means of Cundall’s discrete block method. Doboku Gakkai Ronbunshu 392:297–306 (in Japanese)

    Article  Google Scholar 

  46. Kawaguchi T, Tanaka T, Tsuji Y (1992) Numerical simulation of fluidized bed using the Discrete Element Method : the case of spouting bed. Transactions of the Japan Society of Mechanical Engineers Series B 58:2119–2125 (in Japanese)

    Article  Google Scholar 

  47. Harada E, Gotoh H (2008) Computational mechanics of vertical sorting of sediment in sheetflow regime by 3D granular material model. Coast Eng J 50:19–45. https://doi.org/10.1142/S0578563408001715

    Article  Google Scholar 

  48. Lajeunesse E, Monnier JB, Homsy GM (2005) Granular slumping on a horizontal surface. Phys Fluids 17:103302. https://doi.org/10.1063/1.2087687

    Article  MATH  Google Scholar 

  49. Girolami L, Hergault V, Vinay G, 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 14:381–392. https://doi.org/10.1007/s10035-012-0342-3

    Article  Google Scholar 

  50. Shimosaka A, Shirakawa Y, Hidaka J (2012) Effects of particle shape and size distribution on size segregation of particles. J Chem Eng Jpn. https://doi.org/10.1252/jcej.12we179

    Article  Google Scholar 

  51. Gingold RA, Monghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181:375–389. https://doi.org/10.1093/mnras/181.3.375

    Article  MATH  Google Scholar 

  52. Shao SD, Lo EYM (2003) Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv Water Res 26(7):787–800. https://doi.org/10.1016/S0309-1708(03)00030-7

    Article  Google Scholar 

  53. Koshizuka S, Oka Y (1996) Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nuclear Sci Eng 123:421–434. https://doi.org/10.13182/NSE96-A24205

    Article  Google Scholar 

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Acknowledgements

This work was supported by JSPS KAKENHI Grant No. JP21H01433 and JP21K04271. We would like to thank Editage (www.editage.com) for English language editing.

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  1. Department of Civil and Earth Resources Engineering, Kyoto University, Katsura campus, Nishikyo-ku, Kyoto, Japan

    Hiroyuki Ikari & Hitoshi Gotoh

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  1. Hiroyuki Ikari
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  2. Hitoshi Gotoh
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All authors contributed to the conception and design of the study. Material preparation and data collection and analysis were performed by HI. The first draft of the manuscript was written by HI. HG supervised the conduct of the study. All authors read and approved the final manuscript.

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Correspondence to Hiroyuki Ikari.

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Ikari, H., Gotoh, H. Fully implicit discrete element method for granular column collapse. Comp. Part. Mech. 10, 261–271 (2023). https://doi.org/10.1007/s40571-022-00485-7

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