The Influence of Gravel Particle Diameter and Slope Angle on a Rockfall–Cushion Layer Collision

Rockfall is a significant geological hazard in the mountain areas of Western China, which causes damage to residential and infrastructures. Velocity analysis of rock impacts on the cushion layers is a powerful method to predict the effectiveness of a protective cushion. Thus, this study investigates the velocity, angle, and angular velocity of rockfall after collision, considering the cushion layer's statistical nature, different slope angles, and collision positions. A stochastic collision model of the rockfall–cushion layer is established in this study to understand the mechanism of the collision process. Impulse and impulse moment theorems form the basis for the analytical solution of the velocity after the collision. The results show that the radius ratio of rockfall and cushion particle and slope angle are essential for rockfall–cushion layer collision. The probability distributions of rebound velocity, rebound angle, and rebound angular velocity follow the Gaussian distribution based on probability theory. When the radius ratio of rockfall and cushion particle is larger than the critical radius ratio R_cr, the radius ratio of rockfall and cushion particle no longer affects the collision process. The mean and standard deviation of rebound velocity, rebound angle, and rebound angular velocity after collision are fitted as the radius ratio of rockfall and cushion particle and slope angle functions, respectively. Therefore, it cannot ignore the influence of the radius ratio of rockfall and cushion particle, slope angle, and microstructure of slope surfaces in designing protective cushions.