边坡滚石是国内山区地带常见自然灾害之一。在国内山区工程建设增加，山区旅游业大力发展的背景下，滚石伤人毁物情况屡有发生，故对滚石灾害的系统研究有着重要的理论意义和工程运用价值。在滚石灾害研究中，滚石运动特征研究是滚石防护结构设计的关键，与滚石能耗机制密切相关。同时在进行滚石运动分析时，涉及对滚石运动特征参数的确定，其中碰撞后的法向恢复系数是关键参数，其量值直接影响滚石运动轨迹和滚石滚落过程中的能量损耗。研究滚石滚落工程中的运动特征、边坡滚石碰撞恢复系数对滚石灾害的防控具有重要意义。

本文主要围绕着滚石灾害防护这一中心问题，通过自行设计搭建的模型试验台架，使用高速摄影仪拍摄滚石运动情况，并进行滚石运动学参数的解析，研究了垫层材料、边坡角度两边坡因素影响下滚石运动特征及碰撞恢复系数的变化规律，建立了边坡因素影响下交互回归模型，最后以渭南市临渭区危岩体为研究对象，计算了危岩体的坡脚动能和回弹高度，提出针对性的防控措施，本文主要工作包括以下几个方面：

利用滚石室内模型试验得到滚石滚落全过程运动轨迹图结合拍摄视频分析边坡因素影响下滚石的运动模式及特点；利用拍摄的滚石运动全过程视频解析滚石运动参数，研究边坡因素影响下滚石坡底动能的情况，反映坡面运动对滚石能量的损耗情况；关注模型试验中滚石最终坡底的首次碰撞行为，研究边坡因素影响下滚石坡底回弹高度的规律，回弹高度可以综合反映坡面能耗加上坡底材料性质对滚石运动的综合影响。

分别研究了两边坡因素对滚石碰撞恢复系数的作用；验证了两因素之间的交互作用，并探讨了交互作用的规律，发现当角度越大，垫层硬度越低时，交互作用越明显；最终生成了边坡因素影响下无交互作用、有交互作用2个回归模型，用F检验检测发现交互回归模型进行了显著改进，在数据上有更高的拟合度，这说明滚石的交互回归模型可靠度进一步提高，说明坡角和垫层之间确实存在交互作用，交互视角对于多因素分析至关重要，能给防护设计提供更准确的参考。 

以渭南市临渭区危岩体为例，运用本文提出的回归模型指导工程防护。对危岩失稳后的坡脚能量和回弹高度进行了模拟分析：模型1#，坡底能量小，回弹高度较高；模型2#，坡底能量较大，回弹高度较低。针对两模型不同的计算结果提供了相应防护措施形式建议。

Slope rolling is one of the common natural disasters in mountainous areas.Under the background of the increase of engineering construction and the vigorous development of tourism in mountainous areas, the occurrence of rolling stones injuring people and destroying things frequently occurs, so the systematic research on rolling rock disasters has vital theoretical worth and engineering application value. In the research of rolling rock disaster, the research on the characteristics of rolling rock movement is the key to the design of rolling rock protective structure, which is closely related to the mechanism of rolling rock energy consumption.When analyzing the motion of rolling stones,it involves the determination of the characteristic parameters of rolling stones. Among them, the normal coefficient of restitution after collision is a key parameter, and it directly affects the movement trajectory of the rolling stone and the energy loss in the rolling of the rolling stone. It is of great significance for the prevention and control of rolling rock disasters to study the motion characteristics of rolling rock collision and the coefficient of restitution of rolling rock collision on slopes.

Focusing on the central issue of rockfall disaster prevention, this paper uses a self-built model test bench, uses a high-speed camera to photograph the rockfall movement, analyzes the kinematic parameters of the rockfall, and analyzes the movement characteristics of the rockfall and the change of the collision coefficient of restitution under the influence of the slope factor. An interactive regression model under the influence of slope factors is established. Finally, taking the dangerous rock mass in Linwei District of Weinan City as the research object, the kinetic energy and rebound height of the perilous rock mass are calculated, and targeted protective measures are put forward. The main work of this paper includes the following aspects:

(1) Use the indoor model test of rolling stones to obtain the motion trajectory diagram of the whole process of rolling stones combined with the shooting video to analyze the movement mode and characteristics of the rolling stones under the influence of slope factors; use the video of the whole process of rolling stones to analyze the parameters of the rolling stones, and study the kinetic energy of the rolling stones at the bottom of the slope under the influence of slope factors, which can reflect the loss of rolling rock energy due to slope movement; pay attention to the first collision behavior of the final bottom of the rolling rock in the model test, and studies the law of of the slope factors affecting the rebound height of the bottom of the rolling rock, the rebound height can comprehensively reflect the comprehensive influence of the energy consumption of the slope and the material properties of the bottom of the slope on the movement of the rolling stones.

(2) The effect of the two slope factors on the collision coefficient of restitution was studied separately; the interaction between the two factors of the slope was verified, and the law of the interaction was discussed. It was found that when the angle was larger and the hardness of the cushion layer was lower, the interaction was more obvious. Finally, two regression models with no interaction and interaction under the influence of slope factors were generated, and the F test was used to detect the interaction. The regression model has been significantly improved, and the data has a higher degree of fit, which indicates that the reliability of rolling stone's interactive regression model has been further improved, indicating that there is indeed an interaction between the slope angle and the cushion. The interactive perspective is crucial for multi-factor analysis and can provide a more accurate reference for protection design.  

(3) Taking the dangerous rock mass in Linwei District of Weinan City as an example, the regression model proposed in this paper is used to guide engineering protection. The energy and rebound height of the slope toe after the instability of the dangerous rock are simulated and analyzed: Model 1#, the energy at the bottom of the slope is small, and the rebound height is higher; Model 2#, the energy at the bottom of the slope is larger, and the rebound height is lower. According to the different calculation results of the two models, suggestions on the form of corresponding protective measures are provided.

[1]胡厚田. 崩塌滚石研究[J]. 铁道工程学报. 2005, 增; 387-391.

[2]尚彦军, 杨志法, 袁广祥,等. 雅鲁藏布江大拐弯北部川藏公路地质灾害发育与分布研究[M]. 北京: 中国铁道出版社, 2010.

[3]张路青, 许兵, 尚彦军,等. 川藏公路南线八宿——林芝段滚石灾害的工程地质调查与评价[J]. 岩石力学与工程学报, 2004(09): 1551-1557.

[4]张路青, 杨志法, 张英俊. 公路沿线遭遇滚石的风险分析——方法研究[J]. 岩石力学与工程学报, 2005(S2): 5543-5548.

[5]Chau K T, Wong R H C, Wu J J. Coefficient of restitution and rotational motions of rockfall impacts[J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39(1): 69-77.

[6]Ritchie A M. Evaluation of rockfall and its control[J]. Highway research record, 1963 (17).

[7]Glover J, Bartelt P, Christen M, et al. Rockfall-simulation with irregular rock blocks[M]//Engineering Geology for Society and Territory-Volume 2. Springer, Cham, 2015: 1729-1733.

[8]Asteriou P, Tsiambaos G. Empirical model for predicting rockfall trajectory direction[J]. Rock Mechanics and Rock Engineering, 2016, 49(3): 927-941.

[9]Stevens W D. RocFall, a tool for probabilistic analysis, design of remedial measures and prediction of rockfalls[D]. , 1998.

[10]叶四桥, 陈洪凯, 许江. 落石运动模式与运动特征现场试验研究[J]. 土木建筑与环境工程, 2011, 33(02): 18-23+44.

[11]黄雨, 孙启登, 许强. 滚石运动特性研究新进展[J]. 振动与冲击, 2010, 29(10): 31-35+248-249.

[12]Paronuzzi P. Field evidence and kinematical back-analysis of block rebounds: the lavone rockfall, Northern Italy[J]. Rock mechanics and rock engineering, 2009, 42(5): 783-813.

[13]程强, 苏生瑞. 汶川地震崩塌滚石坡面运动特征[J]. 岩土力学, 2014, 35(03): 772-776.

[14]吕庆, 孙红月, 翟三扣,等. 边坡滚石运动的计算模型[J]. 自然灾害学报, 2003(02): 79-84.

[15]韩俊艳, 陈红旗, 杜修力. 典型斜坡滚石运动的理论计算研究[J]. 水文地质工程地质, 2010, 37(04): 92-96.

[16]俸锦福, 张俊红, 朱彬,等. 边坡滚石运动轨迹分段循环算法[J]. 中国地质灾害与防治学报, 2011, 22(04): 96-101.

[17]唐红梅, 易朋莹. 危岩落石运动路径研究[J]. 重庆建筑大学学报, 2003(01): 17-23.

[18]黄润秋, 刘卫华, 周江平,等. 滚石运动特征试验研究[J]. 岩土工程学报, 2007(09): 1296-1302.

[19]崔圣华, 裴向军, 黄润秋. 直线型斜坡滚石运动速度特征研究[J]. 工程地质学报, 2013, 21(06): 912-919.

[20]赵旭, 刘汉东, 姚爱军. 高边坡滚石计算方法比较研究[J]. 工程地质学报, 2010, 18(S1): 315-321.

[21]赵丽娜, 周科平, 高峰,等. 露天矿边坡滚石运动特征及控制[J]. 灾害学, 2008(03): 76-79.

[22]熊剑, 邓辉. 滚石运动模拟分析与危险性评价[J]. 路基工程, 2015(03): 51-54.

[23]黄俊光, 张帅. 基于动力有限元法的落石运动轨迹研究[J]. 长江科学院院报, 2021, 38(11): 73-79+93.

[24]何思明, 吴永, 杨雪莲. 滚石坡面冲击回弹规律研究[J]. 岩石力学与工程学报, 2008(S1): 2793-2798.

[25]于怀昌, 余宏明, 刘汉东. 边坡滚石运动学参数敏感性[J]. 山地学报, 2010, 28(02): 154-160.

[26]傅少君, 陈乾锐, 祝桥桥,等. 边坡滚石运动影响因素浅析[J]. 武汉大学学报(工学版), 2009, 42(06): 795-798.

[27]Heidenreich B. Small-and half-scale experimental studies of rockfall impacts on sandy slopes[R]. EPFL, 2004.

[28]Johnson K L, Johnson K L. Contact mechanics[M]. Cambridge university press, 1987.

[29]Thornton C. Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres[J]. 1997.

[30]Asteriou P, Saroglou H, Tsiambaos G. Rockfall: scaling factors for the coefficient of restitution[C]//ISRM International Symposium-EUROCK 2013. OnePetro, 2013.

[31]Labous L, Rosato A D, Dave R N. Measurements of collisional properties of spheres using high-speed video analysis[J]. Physical review E, 1997, 56(5): 5717.

[32]Kuwabara G, Kono K. Restitution coefficient in a collision between two spheres[J]. Japanese journal of applied physics, 1987, 26(8R): 1230.

[33]Alizadeh E, Bertrand F, Chaouki J. Development of a granular normal contact force model based on a non-Newtonian liquid filled dashpot[J]. Powder technology, 2013, 237: 202-212.

[34]Ye Y, Zeng Y. A size-dependent viscoelastic normal contact model for particle collision[J]. International Journal of Impact Engineering, 2017, 106: 120-132.

[35]梅雪峰, 胡卸文, 罗刚,等. 基于弹塑性理论的落石碰撞恢复系数和峰值冲击力研究[J]. 振动与冲击, 2019, 38(08): 14-20.

[36]杨海清, 周小平. 边坡落石运动轨迹计算新方法[J]. 岩土力学, 2009.30(11): 3411-3416.

[37]何思明, 吴永, 李新坡. 滚石冲击碰撞恢复系数研究[J]. 岩土力学, 2009,30(03): 623-627.

[38]章广成, 向欣, 唐辉明. 落石碰撞恢复系数的现场试验与数值计算[J]. 岩石力学与工程学报, 2011, 30(06): 1266-1273.

[39]Giani G P, Giacomini A, Migliazza M, et al. Experimental and theoretical studies to improve rock fall analysis and protection work design[J]. Rock Mechanics and Rock Engineering, 2004, 37(5): 369-389.

[40]Guzzetti F, Crosta G, Detti R, et al. STONE: a computer program for the three-dimensional simulation of rock-falls[J]. Computers & Geosciences, 2002, 28(9): 1079-1093.

[41]Chau K T, Wu J J, Wong R H C, et al. The coefficient of restitution for boulders falling onto soil slopes with various values of dry density and water content[M]//Slope Stability Engineering. Routledge, 2021: 1355-1360.

[42]Labiouse V, Heidenreich B. Half-scale experimental study of rockfall impacts on sandy slopes[J]. Natural Hazards and Earth System Sciences, 2009, 9(6): 1981-1993.

[43]黄润秋, 刘卫华. 滚石在平台上的运动特征分析[J]. 地球科学进展, 2008(05)： 517-523.

[44]黄润秋, 刘卫华. 基于正交设计的滚石运动特征现场试验研究[J]. 岩石力学与工程学报, 2009, 28(05): 882-891.

[45]Chau K T, Wong R H C, Liu J, et al. Shape effects on the coefficient of restitution during rockfall impacts[C]//9th ISRM Congress. OnePetro, 1999.

[46]叶四桥, 巩尚卿. 落石碰撞法向恢复系数的模型试验研究[J]. 中国铁道科学, 2015, 36(04): 13-19.

[47]胡杰, 李术才, 石少帅,等.隧道仰坡落石冲击模型试验研究与机制探讨[J].岩土力学, 2018, 39(07): 2527-2536.

[48]Asteriou P, Saroglou H, Tsiambaos G. Geotechnical and kinematic parameters affecting the coefficients of restitution for rock fall analysis[J]. International Journal of Rock Mechanics and Mining Sciences, 2012, 54: 103-113.

[49]章广成, 向欣, 唐辉明. 滚石碰撞恢复系数的现场试验与数值计算[J]. 岩石力学与工程学报, 2011, 30(06): 1266-1273.

[50]陆明. 危岩崩塌运动数值模拟及治理措施研究[D]. 广西: 广西大学, 2017.

[51]焦为. 典型危岩崩塌停积范围及影响因素分析[D]. 贵州: 贵州大学, 2015.

[52]胡聪. 高陡边坡危岩体失稳机理及崩塌滚石运动规律[D]. 山东: 山东大学, 2014.

[53]PFEIFFER T J, BOWEN T D. Computer simulation of rockfalls[J]. Bulletin of the association of Engineering Geologists, 1989, 26(1): 135-146.

[54]Agliardi F, Crosta G B. High resolution three-dimensional numerical modelling of rockfalls[J]. International Journal of Rock Mechanics and Mining Sciences, 2003, 40(4): 455-471.

[55]Peila D, Oggeri C, Castiglia C. Ground reinforced embankments for rockfall protection: design and evaluation of full scale tests[J]. Landslides, 2007, 4(3): 255-265.

[56]Ronco C, Oggeri C, Peila D. Design of reinforced ground embankments used for rockfall protection[J]. Natural Hazards and Earth System Sciences, 2009, 9(4): 1189-1199.

[57]王爽, 周晓军, 罗福君,等. 拱形棚洞受落石冲击的模型试验研究[J]. 振动与冲击, 2017, 36(12): 215-222.

[58]张中俭, 张路青. 滚石灾害防治方法浅析[J]. 工程地质学报，2007(05): 712-717.

[59]唐红梅. 危岩拦石墙计算方法研究[J] 中国地质灾害与防治学报, 2005(03): 12-15+30.

[60]赵旭, 刘汉东. 水电站高边坡滚石防护计算研究[J]. 岩石力学与工程学报, 2005(20): 144-150.

[61]叶四桥, 陈洪凯, 唐红梅. 基于落石计算的半刚性拦石墙设计[J]. 中国铁道科学, 2008(02): 17-22.

[62]刘天翔, 何思明, 王东坡,等. S210线轻钢结构滚石防护棚洞动力响应与优化研究[J]. 灾害学, 2015, 30(01): 69-74.

[63]黄润秋, 刘卫华. 平台对滚石停积作用试验研究[J]. 岩石力学与工程学报, 2009, 28(03): 516-524.

[64]赵红, 折学森, 卢和全,等. 边坡滚石破坏及防护技术研究[J]. 中国公路学报, 2013,26(03): 65-69.

[65]梁安宁. 隧道进口危岩体滚落特征分析及防护措施[J]. 路基工程, 2019(04): 228-232.

[66]林镇, 王浩, 龚匡周,等. 球状风化花岗岩边坡滚石灾害防护设计研究[J]. 福州大学学报(自然科学版), 2016, 44(05): 760-766.

[67]GB50021-2001岩土工程勘察规范[S]. 北京：中国建筑工业出版社, 2001.

[68]丁冰冰. 岩质边坡危岩落石室内模型试验研究[D]. 西南交通大学, 2015.

[69]Bozzolo D, Pamini R. Simulation of rock falls down a valley side[J]. Acta Mechanica, 1986, 63(1): 113-130.

[70]Azzoni A, La Barbera G, Zaninetti A. Analysis and prediction of rockfalls using a mathematical model[C]//International journal of rock mechanics and mining sciences & geomechanics abstracts. Pergamon, 1995, 32(7): 709-724.