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


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.


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



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).


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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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