A theoretical model for the movement trajectory of the rockfall considering collision restitution coefficient

Accurate prediction of rockfall trajectory is foundation for the prevention and control of rock avalanche geological disasters in mountainous areas. A key factor influencing trajectory accuracy is the appropriate selection of the collision restitution coefficient between rockfalls and slope surfaces. However, current approaches often overlook the effects of incident velocity and the yield strength of the slope rock mass when determining this coefficient. To address this gap, this study focuses on the normal collision restitution coefficient. First, the commonly theoretical models for the normal collision restitution coefficient was analyzed and Thornton model was considered to be the most representative calculation model for the normal collision restitution coefficient at present. It can well reflect the impact of rockfall velocity and rockmass yield strength on the normal collision restitution coefficient. The proposed model was introduced into the current common rockfall trajectory calculation model, and the theoretical model for the rockfall trajectory considering the collision restitution coefficient was obtained. Then the corresponding calculation flow was given. The proposed model was applied to the movement prediction of a perilous rockmass in Jiuzhaigou Valley after its instability, and its movement trajectory was calculated. Validation using the Rocfall software yields consistent results, thereby supporting the reliability and applicability of the proposed theoretical model.