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DEM verification of the damping effect in a freely falling particle motion for quasi- and non-quasi-static conditions

  • Zhihua ZhangEmail author
  • Yifeng Wang
  • Wensheng Xu
  • Shi Sun
Original Paper
  • 30 Downloads

Abstract

The discrete element method (DEM) has been widely used in numerical evaluations in geotechnical engineering; however, simple analysis and verification are still needed to obtain the interaction mechanism between a single particle and a wall under a damping effect. A single freely falling particle model is proposed, and the analytical solutions for the stages of particle freefall, fixed wall contact, and rebound are obtained for different damping types and values. Timestepping in quasi-static and non-quasi-static conditions is considered for better understanding of the DEM hypothesis. The numerical results are quite consistent with the analytical solution. The linear and exponential relationships between the restitution coefficient and the local and viscous damping, respectively, are obtained and formulized. Kinetic energy dissipation is larger with the viscous damping effect than for the local damping when comparing the particle rebound height. Verification of the analytical and numerical solutions has been conducted with the previous studies which shows good agreement. The timestep is no longer constant when the particle velocity exceeds approximately 1.55 m/s, which means the DEM system is no longer quasi-static.

Keywords

Discrete element method Analytical solution Damping coefficient Timestepping Quasi-static condition 

Notes

Acknowledgments

The project was financially supported by the sub-topic “Study on calculation method of design flood for disaster causing in mountain basin” of the National Key R&D Program of China (no. 2017YFC1502503), “the Fundamental Research Funds for the Central Universities” (2017-YB-014; 2017-ZY-013), and the National Natural Science Foundation of China (no. 51408450).

References

  1. Bai XM, Keer LM, Wang QJ, Snurr RQ (2009) Investigation of particle damping mechanism via particle dynamics simulations. Granul Matter 11:417–429CrossRefGoogle Scholar
  2. Caserta AJ, Navarro HA, Cabezas-Gómez L (2016) Damping coefficient and contact duration relations for continuous nonlinear spring-dashpot contact model in DEM. Powder Technol 302:462–479CrossRefGoogle Scholar
  3. Chen F, Drumm EC, Guiochon G (2007) Prediction/verification of particle motion in one dimension with the discrete element method. Int J Geomech 7(5):344–352CrossRefGoogle Scholar
  4. Chung YC, Ooi JY (2011) Benchmark tests for verifying discrete element modelling codes at particle impact level. Granul Matter 13:643–656CrossRefGoogle Scholar
  5. Chung YC, Ooi JY (2008) A study of influence of gravity on bulk behaviour of particulate solid. Particuology 6:467–474CrossRefGoogle Scholar
  6. Crowe C, Sommerfeld M, Tsuji Y (1997) Multiphase flows with droplets and particles. CRC Press, Boca RatonGoogle Scholar
  7. Cui Y, Nouri A, Chan D, Rahmati E (2016) A new approach to the DEM simulation of sand production. J Pet Sci Eng 147:56–67CrossRefGoogle Scholar
  8. Cui Y, Chan D, Nouri A (2017a) Discontinuum modeling of solid deformation pore-water diffusion coupling. Int J Geomech 17(8):04017033CrossRefGoogle Scholar
  9. Cui Y, Chan D, Nouri A (2017b) Coupling of solid deformation and pore pressure for undrained deformation – a discrete element method approach. Int J Numer Anal Met 41(18):1943–1961CrossRefGoogle Scholar
  10. Cui Y, Jiang Y, Guo C (2019a) Investigation of the initiation of shallow failure in widely graded loose soil slopes considering interstitial flow and surface runoff. Landslides. 16(4):815–828CrossRefGoogle Scholar
  11. Cui Y, Cheng D, Choi CE, Jin W, Lei Y, Kargel JS (2019b) The cost of rapid and haphazard urbanization: lessons learned from the Freetown landslide disaster. Landslides. 16(6):1167–1176CrossRefGoogle Scholar
  12. Cundall PA (1987) Distinct element models of rock and soil structure. Analytical and computational methods in engineering rock mechanics. E.T. Brown, ed., George Allen and Unwin, London, 129-163Google Scholar
  13. Cundall PA (1971) A computer model for simulating progressive large scale movements in blocky rock systems. in Proceedings of the Symposium of the International Society of Rock Mechanics (Nancy, France, 1971), Vol. 1, Paper No. II-8Google Scholar
  14. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65CrossRefGoogle Scholar
  15. Foerster SF, Louge MY, Chang AH, Allia K (1994) Measurements of the collision properties of small spheres. Phys Fluids 6:1108–1115CrossRefGoogle Scholar
  16. Flores P, Machado M, Silva MT, Martins JM (2011) On the continuous contact force models for soft materials in multibody dynamics. Multibody Syst Dyn 25:357–375CrossRefGoogle Scholar
  17. Garg R, Galvin J, Li T, Pannala S (2012) Open-source MFIX-DEM software for gas-solids flows: part I- verification studies. Powder Technol 220:122–137CrossRefGoogle Scholar
  18. Giacomini A, Buzzi O, Renard B, Giani GP (2009) Experimental studies on fragmentation of rock falls on impact with rock surfaces. Int J Rock Mech Min 46(4):708–715CrossRefGoogle Scholar
  19. Gu X, Yang J, Huang M (2013) DEM simulations of the small strain stiffness of granular soils: Effect of stress ratio. Granul Matter 15(3):287–298CrossRefGoogle Scholar
  20. Hentz S, Daudeville L, Donze FV (2004) Identification and validation of a discrete element model for concrete. J Eng Mech 130(6):709–719CrossRefGoogle Scholar
  21. Itasca Consulting Group: Inc. PFC3D, Version 4.0. Minneapolis: Itasca (2004)Google Scholar
  22. Jankowski R (2005) Non-linear viscoelastic modelling of earthquake-induced structural pounding. Earthq Eng Struct Dyn 34(6):595–611CrossRefGoogle Scholar
  23. Kharaz AH, Gorham DA, Salman AD (2001) An experimental study of the elastic rebound of spheres. Powder Technol 120:281–291CrossRefGoogle Scholar
  24. Navarro HA, Braun MPDS (2013) Linear and nonlinear hertzian contact models for materials in multibody dynamics. 22nd International Congress of Mechanical EngineeringGoogle Scholar
  25. Pöschel T, Schwager T (2005) Computational granular dynamics: models and algorithms. Springer-Verlag, BerlinGoogle Scholar
  26. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min 41:1329–1364CrossRefGoogle Scholar
  27. Shäfer J, Dippel S, Wolf DE (1996) Force schemes in simulations of granular materials. J Phys I Fr 6(1):5–20CrossRefGoogle Scholar
  28. Stevens AB, Hrenya CM (2005) Comparison of soft-sphere models to measurements of collision properties during normal impacts. Powder Technol 154(23):99–109CrossRefGoogle Scholar
  29. Thornton C, Ning Z, Wu CY, Nasrullah M, Li LY (2001) Contact mechanics and coefficients of restitution. In: Poschel T, Luding S (eds) Granular Gases. Springer, Berlin, pp 55–66Google Scholar
  30. Yang ZX, Yang J, Wang LZ (2012) On the influence of inter-particle friction and dilatancy in granular materials: a numerical analysis. Granul Matter 14:433–447CrossRefGoogle Scholar
  31. Yao M, Anandarajah A (2003) Three dimensional discrete element method of analysis of clays. J Eng Mech 129(6):585–596CrossRefGoogle Scholar
  32. Ye K, Li L, Zhu H (2009) A note on the Hertz contact model with nonlinear damping for pounding simulation. Earthq Eng Struct Dyn 38(9):1135–1142CrossRefGoogle Scholar
  33. Yu B, Yi W, Zhao H (2018) Experimental study on the maximum impact force by rock fall. Landslides. 15(2):233–242CrossRefGoogle Scholar
  34. Zhang Z, Zhang X, Qiu H, Daddow M (2016) Dynamic characteristics of track-ballast-silty clay with irregular vibration levels generated by high-speed train based on DEM. Constr Build Mater 125:564–573CrossRefGoogle Scholar
  35. Zhang Z, Zhang X, Tang Y, Cui Y (2018a) Discrete element analysis of a cross-river tunnel under random vibration levels induced by trains operating during the flood season. J Zhejiang Univ Sci A 19(5):246–366CrossRefGoogle Scholar
  36. Zhang Z, Cui Y, Chan D, Taslagyan K (2018b) DEM simulation of shear vibrational fluidization of granular material. Granul Matter 20(4):71CrossRefGoogle Scholar
  37. Zhang Z, Zhang X, Cui Y, Qiu H (2019) Discrete element modelling of a cross-river tunnel under subway trainoperation during peak and off-peak periods. Arab J Geosci 12(3):102.  https://doi.org/10.1007/s12517-019-4279-2 CrossRefGoogle Scholar
  38. Zhou W, Ma X, Ng TT, Ma G, Li SL (2016) Numerical and experimental verification of a damping model used in DEM. Granul Matter 18:1–12CrossRefGoogle Scholar
  39. Zhu HP, Zhou ZY, Yang RY, Yu AB (2007) Discrete particle simulation of particulate system: theoretical developments. Chem Eng Sci 62(13):3378–3396CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  1. 1.Changjiang River Scientific Research Institute of Changjiang Water Resources CommissionWuhanChina
  2. 2.Central and Southern China Municipal Engineering Design & Research Institute Co., Ltd.HangzhouChina

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