崩塌滚石是国内山区常见的自然灾害。随着我国山区现代化建设稳步推进，由于地震、强风以及强降雨等诱发滚石灾害，导致滚石伤人毁物情况屡有发生，为切实保障人民群众生命财产和基础设施的安全，对滚石灾害的防灾减灾研究是极为重要且意义重大。在滚石灾害研究中，滚石碰撞恢复系数(COR)是滚石防控设计的重要依据，对于滚石理论研究、数值仿真和工程实践评估至关重要。然而，目前滚石碰撞恢复系数的研究较少考虑多因素交互效应。因此，开展多因素交互作用下滚石碰撞恢复系数的响应研究对滚石灾害的防控设计具有重要意义。

本文主要围绕多因素交互作用对滚石碰撞恢复系数的响应这一中心问题。为实现滚石的初始条件差异性、释放条件一致性和可靠性的需求，自主研发了滚石释放装置，依托需求设计并搭建了室内模型试验系统，开展了边坡滚石试验研究，探讨了滚石碰撞恢复系数的影响因素并确定主控因素，研究了主控因素影响下滚石碰撞恢复系数的变化规律，建立了相关主控因素及其交互项的多因素交互模型，以重庆南岸区危岩边坡工程为依托，验证了边坡滚石的数值方法，对主控因素回归交互模型的可靠性和合理性进行评价和应用推广，本文主要工作包括以下三方面：

（1）通过室内试验系统，结合自主研发的滚石释放装置，利用高速摄影机录摄滚石运动全过程，采用分析软件解析滚石运动参量，开展滚石与边坡运动全过程动态响应研究；选取对滚石碰撞恢复系数影响作用较大的主控因素，分析主控因素滚石运动过程中对碰撞恢复系数的作用机理；通过垫层材料和边坡角度共同作用，探究碰撞恢复系数的交互作用，明确因素之间存在交互效应。

（2）结合统计回归的数学手段预测主控因素交互项的显著度，在此基础上，建立了主控因素作用的多元回归交互模型，考虑主控因素交互作用对滚石碰撞恢复系数的影响。研究结果表明：滚石形状对碰撞恢复系数的作用最显著，次之为垫层材料，再者为初始速度，边坡角度最弱；垫层材料和边坡角度交互作用对碰撞恢复系数的影响最显著，次之为滚石形状和垫层材料，再者滚石形状和初始速度，初始速度和垫层材料最弱。

（3）采用动力有限元数值模拟的手段，开展工程尺度的滚石运动研究和校核研究，建立危岩边坡仿真模型，对多因素交互回归模型进行评价，进一步校核多因素交互模型的合理性和可靠性；针对危岩工程决定性因素，比对数值解和半解析解，实现多因素交互模型的工程应用，为后续危岩工程防治设计提供理论依据。

Rolling rock collapse is the common natural disasters in mountainous areas in China. With the steady progress of the modernization in China's mountainous areas, the rolling rock disasters are induced by earthquakes, strong winds and heavy rainfall. The rolling rock disasters lead to the occurrence of injuries and destruction. In order to effectively protect the safety of people's lives, property and the safety of infrastructure, the research on the prevention and mitigation of rolling rock disasters is extremely significant. In the research of rolling rock disasters, the coefficient of restitution (COR) is an important basis for the design of rolling rock prevention and control. The COR is crucial for the theoretical research, numerical simulation, and engineering practice evaluation of rolling rock. However, the multi-factor interaction effects are rarely considered in the current research on the COR . So it is important to carry out the research of the multi-factor interaction effects on COR for the design of rolling rock collapse disasters prevention and control.

This paper focuses on the central issue of the response of multi-factor interaction effects on the COR. Rolling rock release device is developed independently to realize the requirement for variability of initial conditions and release conditions of consistency and reliability. The physical modeling system is designed and found, and the rolling rock test research is carried out. The influencing factors on the COR are explored, and the main control factors are determined. The effects of the main control factors on the COR are studied. The main control factors and its interaction term are modeled as a multi-factor interaction. Based on the Chongqing Nanan district dangerous rock-slope project, the numerical method of rock-slope is verified. The reliability and rationality of the multi-factor interaction model is evaluated and applied. The main works of this paper include the following three aspects:

Through the physical modeling system test system, the dynamic response research of the whole movement process of rock-slope is carried out, combining with the self-developed

rolling rock release device, recording the whole process of rolling rock movement by high-speed camera, and analyzing rolling rock movement parameters by analysis software. The main control factors of the significant effect on the COR is selected, which analyzes the mechanism of action to the main control factors on the COR during the movement. The interaction on the COR is explored through the common action of surface material and slope angle, which clarifies that there are interactive effects among factors.

On this basis, mathematical means are used to predict the significance of the interaction terms of the main control factors. Multi-factor regression interaction model of the main control factors is developed. The effect of the interaction of the main factors on the COR is considered. The results of the research show that: the effect of rock shape on the COR is the most significant, then the effects on the COR are in the rank of surface material, initial velocity, slope angle. The interaction of surface material and slope angle has the most significant effect on the COR, then the effects on the COR are in the rank of rock shape and surface material, rock shape and initial velocity, initial velocity and surface material.

Engineering-scale analytical studies and calibration studies are carried out in the process of rolling rock movement by dynamic finite element numerical simulation. The simulation model of dangerous rock-slope is established to evaluate the multi-factor regression interaction model, calibrating the rationality and reliability of multi-factor regression interaction model. Numerical and semi-analytical solutions are compared and combined with the influencing factors of dangerous rock engineering to realize the application of multi-factor regression interaction model. It is provided the theoretical basis for the design of subsequent dangerous rock engineering prevention and control.