Abstract
Rockfall events are a common geological hazard in the mountain areas of western China and frequently occur on unstable slopes. The purpose of this study was to establish a statistical model of random rockfall–slope collision using the impulse moment theorem considering that the impacted stones are moving. The rebound velocity of rockfall is random because the microstructure of the ground and slope can be described with statistical properties. The analytical solutions of the rebound particles are obtained as formulas for the incident velocity, incident angle, impacted rock movement, slope angle, and ground surface microstructure. The means and standard deviations of rebound velocity are fitted with slope angle to calculate formulas based on probability theory, which agrees with the previous results. The probability distribution functions of the horizontal distance and vertical distance follow a Gaussian distribution and a negative exponential distribution under the given slope angle, respectively. A formula of trajectory is also given.
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Acknowledgements
This study was supported by the National Natural Science Foundation of China (Grant no. 12262021). The authors would like to express their sincere appreciation for this support.
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This study was supported by the National Natural Science Foundation of China (Grant no. 12262021).
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S-ZD contributed to conceptualization, methodology, funding acquisition, and writing—original draft. G-LL provided software and was involved in data curation, validation, formal analysis, and writing—review and editing. XY contributed to investigation, data curation, project administration, and visualization. X-RW provided software was involved in data curation and project administration.
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Duan, SZ., Li, GL., Yang, X. et al. Predicting the velocity and trajectory of a rockfall after collision considering the effects of slope properties. Nat Hazards 120, 2057–2072 (2024). https://doi.org/10.1007/s11069-023-06278-2
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DOI: https://doi.org/10.1007/s11069-023-06278-2