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<p>Rockfall disasters are one of the major geologic disasters worldwide. The coefficient of restitution (COR) is a key parameter used to describe the path of rockfall in motion trajectory simulations. However, the effects of rockfall with different shapes on the COR are poorly understood. Six representative (spherical, ellipsoidal, cylindrical, discal, cuboid block, and cuboid schistose) rockfalls were selected, and 48 groups (960 times) of impact tests were conducted. The effects of mass, fall height, and impact angle on the COR of differently shaped rockfalls were investigated. In the experiments, the average normal coefficient of restitution and tangential coefficient of restitution values of spherical rockfall are the highest, with those of cuboid rockfall being approximately 30–73% and 52–93%, respectively, of those of spherical rockfall. The analysis revealed that shape affects the collision attitude between rockfall and the slope, subsequently influencing the COR. For spherical (spherical and ellipsoidal) rockfall, the COR was inversely proportional to the contact time between rockfall and the slope. For non-spherical (cylindrical, discal, cuboid block, and cuboid schistose) rockfall, the COR increased as the distance between the rockfall centroid projection and slope contact point decreased. Moreover, sphericity and the fullness index were proposed to quantitatively represent the rockfall shape. The relationship models between various rockfall shapes (ellipsoidal cylindrical, discal, cuboid block, and cuboid schistose) and their CORs were established to precisely quantify the effect of shape on rockfall CORs. Shape reduction coefficient was proposed to reasonably quantify the influence of rockfall shape on the COR. Through simulation, the motion trajectories of rockfalls with different shapes were compared. Finally, on-site rockfall impact tests verified the prediction accuracy of these calculation models. This research can be used to predict the COR values of various rockfall shapes, which is helpful to improve the prediction accuracy of rockfall trajectory and enhance the accuracy and cost-effectiveness of rockfall disaster prevention measures.</p>

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Effect of Rockfall Shape on the Coefficient of Restitution: Insights from Laboratory Rockfall Multi-Parameter Experiments

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Sheng-Wu Qin,
  • Xiao-Wei Liu,
  • Shuai-Ying Peng,
  • Chao-Biao Zhang,
  • Jing-Yu Yao,
  • Jiang-Feng Lv,
  • Feng Wan

摘要

Rockfall disasters are one of the major geologic disasters worldwide. The coefficient of restitution (COR) is a key parameter used to describe the path of rockfall in motion trajectory simulations. However, the effects of rockfall with different shapes on the COR are poorly understood. Six representative (spherical, ellipsoidal, cylindrical, discal, cuboid block, and cuboid schistose) rockfalls were selected, and 48 groups (960 times) of impact tests were conducted. The effects of mass, fall height, and impact angle on the COR of differently shaped rockfalls were investigated. In the experiments, the average normal coefficient of restitution and tangential coefficient of restitution values of spherical rockfall are the highest, with those of cuboid rockfall being approximately 30–73% and 52–93%, respectively, of those of spherical rockfall. The analysis revealed that shape affects the collision attitude between rockfall and the slope, subsequently influencing the COR. For spherical (spherical and ellipsoidal) rockfall, the COR was inversely proportional to the contact time between rockfall and the slope. For non-spherical (cylindrical, discal, cuboid block, and cuboid schistose) rockfall, the COR increased as the distance between the rockfall centroid projection and slope contact point decreased. Moreover, sphericity and the fullness index were proposed to quantitatively represent the rockfall shape. The relationship models between various rockfall shapes (ellipsoidal cylindrical, discal, cuboid block, and cuboid schistose) and their CORs were established to precisely quantify the effect of shape on rockfall CORs. Shape reduction coefficient was proposed to reasonably quantify the influence of rockfall shape on the COR. Through simulation, the motion trajectories of rockfalls with different shapes were compared. Finally, on-site rockfall impact tests verified the prediction accuracy of these calculation models. This research can be used to predict the COR values of various rockfall shapes, which is helpful to improve the prediction accuracy of rockfall trajectory and enhance the accuracy and cost-effectiveness of rockfall disaster prevention measures.