| Rockfall hazards have clear regional characteristics,mainly concentrated in mountainous areas in provinces such as Sichuan,Yunnan,Guizhou,Gansu,and Tibet in China.When the randomness and uncertainty of rockfall trajectories,as well as the huge kinetic energy generated during the falling process,pose a serious threat to residential areas and transportation routes near the mountains,it constitutes the second largest geological hazard-rockfall hazard.The random collision process between rockfall and slope cushion layer is a key part of the rockfall movement process.In this paper,considering the random factors such as slope angle,cushion layer micro-topography,incoming rockfall particle velocity,and angle,etc.,a theoretical model of rockfall-slope cushion layer random collision was established to analyze the mechanical characteristics of rockfall particles in this process,mainly including the following contents:(1)The random collision process of rockfall-slope cushion layer is simplified into a three-particle(incoming rockfall particle,impacted particle,and supported particle on the cushion layer)collision model.The random factors such as slope angle,cushion layer micro-topography,cushion particle size,incoming rockfall particle velocity,and angle are considered.Based on the principle of impulse and angular impulse,a random collision mechanics equation is established to obtain the analytical solution of rockfall velocity after collision.(2)Based on the above random collision model of rockfall-slope cushion layer and utilizing probability and statistics theory,the probability density function of rockfall velocity after collision and trajectory is derived.By comparing the experimental results,the reliability of the research method is confirmed.The probability distribution of rebound velocity,rebound angle,and rebound angular velocity follows the Gaussian distribution based on the probability theory.When the radius ratio of rockfall to cushion particles is greater than the critical radius ratio Rcr,the radius ratio no longer affects the collision process.The average values and standard deviations of rockfall velocity after collision,rebound angle,and rebound angular velocity are proposed as functions of the radius ratio and slope angle of rockfall and cushion particles.(3)Based on the discrete element method,numerical simulation of the random collision process between rockfall and slope cushion layer is conducted to reproduce the dynamic evolution process.The impact force,impact depth,post-collision velocity,and post-collision rockfall energy change on the slope cushion layer are analyzed with respect to cushion layer thickness,slope height,and slope properties.The results show that the impact depth of rockfall increases with the increase of cushion particle size and incoming velocity,and the impact force and rockfall energy consumption are highest when the cushion layer thickness is 0.5m.The post-collision angular velocity of rockfall decreases faster with the increase of cushion layer thickness. |
