Trajectory Analysis of the Rockfall Based on the Effect of Rotating Angular Velocity

The trajectory of a rolling stone begins and is characteristically accompanied by a certain initial rotation. Considering the influence of the initial rotation, the four basic motion forms of a rolling rock movement are analyzed, based on contact mechanics and kinematics principles. The speed calculationF formulas for a rolling rock mass were obtained. Besides, taking the dangerous rock slope of Changheba Hydropower Station in Sichuan Province as an example, the entire moving process of a rolling stone was simulated using “Rocfall software”, and the influence of an initial rotation on total kinetic energy, bounce height, and trajectory of the rolling stone during the movement was analyzed. According to the results, the determination of the most dangerous position during the movement of the rolling stone is not be affected by the initial rotation angular velocity. However, the maximum bounce height of the rolling stone at the most dangerous position increases with the increase of the initial rotation; the initial rotation of a rolling stone affects the longest distance and total horizontal distance. The probability density distribution of total kinetic energy and horizontal distance followed the Gaussian distribution; the influence of initial rotation on the central value can not be ignored. In this case, if the rotation was ignored, the rockfall disaster range would be underestimated, the rate can reach up to 94% when ω=200rad/s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega =200\hbox {rad/s}$$\end{document}. The initial rotation of a rolling stone has a different sensitivity to the slope characteristics. The smooth and hard surface was the most sensitive. The larger the angular velocity, the more sensitive the slope. Therefore, the influence of a rocking stone rotating velocity and slope surface material must be considered in investigating the trajectory of the rockfalls and the provision of protective measures.