Exploration of Probability Distribution of Velocities and Trajectory of Rolling Stone Based on Stochastic Rolling Stone Collision

Rockfall is one of the common geological disasters in China, which causes huge losses to the country and the people. Based on the impulse and impulse moment theorems, and considering the stochastic factors in the process of rolling stone collision, a stochastic collision model of the rockfall-wall is established, and the analytical solution for the velocity of the rolling stone after collision is obtained. When considering the initial rotation of the rolling stone, the predicted result from the model agrees with the experimental result, and when the initial rotation is ignored, the result obtained from the model will underestimate/overestimate the rebound velocity, and the maximum reaches 20%. Furthermore, the probability distribution and the fit curve for the velocity and trajectory of the rolling stone depends on the project. The result shows that the rebound velocity and angle of the rolling stone follow a typical Gaussian distribution, and the horizontal distance and bounce height follow the Gaussian and exponential distribution, respectively. The prediction of the velocity and trajectory of the rolling stone provides a theoretical basis for the optimal design of engineering structures.