Predicting the velocity and trajectory of a rockfall after collision considering the effects of slope properties

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.

Automated summary

The study aims to establish a statistical model of random rockfall-slope collision considering the movement of the impacted stones using the impulse moment theorem. The means and standard deviations of rebound velocity are calculated based on probability theory. The probability distribution functions of the horizontal and vertical distances are analyzed.