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Geological characteristics, disaster mechanisms and stability analysis methods of rock slope toppling |
| LIU Caihua1, 2*, FAN Kai1, 2, SUN Chaoyi1, 2, ZHANG Wei1, 2, YUAN Jiahao1, 2 |
(1. State Key Laboratory of Geomechanics and Geotechnical Engineering Safety, Institute of Rock and Soil Mechanics, Chinese
Academy of Sciences, Wuhan, Hubei 430071, China; 2. University of Chinese Academy of Sciences, Beijing 100049, China) |
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Abstract Toppling failure is a typical type of disaster associated with rock slopes. The deformation behaviors and mechanisms underlying the evolution of rock slope toppling are complex, influenced by adverse geological conditions and external loads. Investigating the deformation characteristics, failure modes, and disaster mechanisms of rock slope toppling, as well as proposing methods for stability evolution, are urgent issues in slope engineering. Approximately 220 cases of toppling slopes in China have been collected, and the regional distribution of these cases is presented. The relationships between toppling failure and several key factors, such as slope height, slope angle, terrain obliquity, and lithology, are thoroughly analyzed. Building on existing classification methods for rock slope toppling, a four-level classification method is proposed based on the tendency relationship between the dominant discontinuity and the slope, the dominant or subordinate status of toppling deformation, the deformation characteristics of the toppling body, and the combination of toppling strata. The deformation behaviors and failure mechanisms of typical toppling types, including block toppling, flexural toppling, and composite toppling, are revealed through a combination of physical model tests and numerical simulations. Systematic presentations of stability analysis approaches, including the G&B method, equivalent continuum method, Liu method, cantilever beam method, and composite analysis method, are provided, along with discussions on their limitations and evolving trends. This research is expected to serve as an important reference for theoretical studies and engineering practices related to rock slope toppling.
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[1] 何满潮. 滑坡地质灾害远程监测预报系统及其工程应用[J]. 岩石力学与工程学报，2009，28(6)：1 081–1 090.(HE Manchao. Real-time remote monitoring and forecasting system for geological disasters of landslides and its engineering application[J]. Chinese Journal of Rock Mechanics and Engineering，2009，28(6)：1 081–1 090. (in Chinese))
[2] 《中国减灾》编辑部. 全国灾害实录(2004年8，9月)[J]. 中国减灾，2004，(10)：61–64.(Editorial Office of Disaster Reduction in China. Record of national disasters(August and September 2004)[J]. Disaster Reduction in China，2004，(10)：61–64.(in Chinese))
[3] 黄润秋. 20世纪以来中国的大型滑坡及其发生机制[J]. 岩石力学与工程学报，2007，26(3)：433–454.(HUANG Runqiu. Large-scale landslides and their sliding mechanisms in China since the 20th century[J]. Chinese Journal of Rock Mechanics and Engineering，2007，26(3)：433–454.(in Chinese))
[4] 王佳佳，殷坤龙，肖莉丽. 基于GIS和信息量的滑坡灾害易发性评价——以三峡库区万州区为例[J]. 岩石力学与工程学报，2014，33(4)：797–808.(WANG Jiajia，YIN Kunlong，XIAO Lili. Landslide susceptibility assessment based on GIS and weighted information value：A case study of Wanzhou District，Three Gorges Reservoir[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(4)：797–808.(in Chinese))
[5] 国家统计局. 中国统计年鉴[M]. 北京：中国统计出版社，2024：248.(National Bureau of Statistics of China. China statistical yearbook[M]. Beijing：China Statistics Press，2024：248.(in Chinese))
[6] HUANG R Q，LI W L. Formation，distribution and risk control of landslides in China[J]. Journal of Rock Mechanics and Geotechnical Engineering，2011，3(2)：97–116.
[7] 黄润秋，李渝生，严 明. 斜坡倾倒变形的工程地质分析[J]. 工程地质学报，2017，25(5)：1 165–1 181.(HUANG Runqiu，LI Yusheng，YAN Ming. The implication and evaluation of toppling failure in engineering geology practice[J]. Journal of Engineering Geology，2017，25(5)：1 165–1 181.(in Chinese))
[8] 刘才华，陈从新. 层状岩质边坡稳定性[M]. 北京：科学出版社，2012：126.(LIU Caihua，CHEN Congxin. Layered rock slope stability[M]. Beijing：Science Press，2012：126.(in Chinese))
[9] 邱 俊，任光明，王云南. 层状反倾–顺倾边坡倾倒变形形成条件及发育规模特征[J]. 岩土力学，2016，37(增2)：513–524.(QIU Jun，REN Guangming，WANG Yunnan. Characteristics of forming conditions and development scale of toppling in anti-dip and dip stratified slopes[J]. Rock and Soil Mechanics，2016，37(Supp.2)：513–524.(in Chinese))
[10] 任光明，夏 敏，李 果，等. 陡倾顺层岩质斜坡倾倒变形破坏特征研究[J]. 岩石力学与工程学报，2009，28(增1)：3 193–3 200. (REN Guangming，XIA Min，LI Guo，et al. Study on toppling deformation and failure characteristics of steep bedding rock slope[J]. Chinese Journal of Rock Mechanics and Engineering，2009，28(Supp.1)：3 193–3 200.(in Chinese))
[11] 王思敬. 金川露天矿边坡变形机制及过程[J]. 岩土工程学报，1982，4(1)：76–83.(WANG Sijing. On the mechanism and process of slope deformation in an open pit mine[J]. Chinese Journal of Geotechnical Engineering，1982，4(1)：76–83.(in Chinese))
[12] 安晓凡，李 宁，孙闻博. 岩质边坡倾倒变形机制及稳定性研究综述[J]. 中国地质灾害与防治学报，2018，29(3)：1–11.(AN Xiaofan，LI Ning，SUN Wenbo. Review on the mechanism and stability of toppling deformation of rock slopes[J]. The Chinese Journal of Geological Hazard and Control，2018，29(3)：1–11.(in Chinese))
[13] 丁小军，刘卫明，王 佐，等. 软质岩边坡倾倒变形机制及处治工程实例[M]. 北京：人民交通出版社，2011：4.(DING Xiaojun，LIU Weiming，WANG Zuo，et al. Mechanism for toppling deformation and treatment engineering examples of soft rock slope[M]. Beijing：People?s Communications Press，2011：4.(in Chinese))
[14] 宁奕冰，唐辉明，张勃成，等. 澜沧江深层倾倒体演化过程及失稳机制研究[J]. 岩石力学与工程学报，2021，40(11)：2 199–2 213. (NING Yibing，TANG Huiming，ZHANG Bocheng，et al. Evolution process and failure mechanism of a deep-seated toppling slope in the Lancang River Basin[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(11)：2 199–2 213.(in Chinese))
[15] NING Y B，TANG H M，ZHANG G C，et al. A complex rockslide developed from a deep-seated toppling failure in the upper Lancang River，Southwest China[J]. Engineering Geology，2021，293：1–15.
[16] 王士天，黄润秋，李渝生. 雅砻江锦屏水电站重大工程地质问题研究[M]. 成都：成都科技大学出版社，1998：130–140.(WANG Shitian，HUANG Runqiu，LI Yusheng. Key engineering geology problems and research on Jinping Hydropower Station in Yalongjiang River[M]. Chengdu：Chengdu University of Science and Technology Press，1998：130–140.(in Chinese))
[17] 任光明，夏 敏，曾 强，等. 白龙江干流典型滑移–倾倒型滑坡的特征及形成机制[J]. 成都理工大学学报：自然科学版，2015，42(1)：18–25.(REN Guangming，XIA Min，ZENG Qiang，et al. Characteristics and formation mechanism of typical sliding-toppling landslides in Bailong River trunk streams of Gansu，China[J]. Journal of Chengdu University of Technology：Science and Technology，2015，42(1)：18–25.(in Chinese))
[18] 常 昊，常祖峰，刘昌伟. 金沙江断裂带活动与大型滑坡群的关系研究：以金沙江拿荣—绒学段为例[J]. 地震地质，2021，43(6)：1 435–1 458.(CHANG Hao，CHANG Zufeng，LIU Changwei. The relationship between activity of Jinsha River Fault Zone and large-scale landslides：A case study of the section between Narong and Rongxue along the Jinsha River[J]. Seismology and Geology，2021，43(6)：1 435–1 458.(in Chinese))
[19] 陈 宇. 金沙江旭龙水电站近坝区滑坡分形特征及危险性评价[硕士学位论文][D]. 长春：吉林大学，2016.(CHEN Yu. Fractal characteristics of landslide and risk assessment in the near dam region of Xulong Hydropower Station in Jinsha River[M. S. Thesis][D]. Changchun：Jilin University，2016.(in Chinese))
[20] GOODMAN R E，BRAY J W. Toppling of rock slopes[C]// Proceedings of ASCE Specialty Conference on Rock Engineering for Foundations and Slopes. Colorado，USA：[s. n.]，1976：201–234.
[21] CRUDEN D M，HU X Q. Topples on underdip slopes in the High-wood Pass，Alberta，Canada[J]. Quarterly Journal of Engineering Geology and Hydrogeology，1994，27(1)：57–68.
[22] ADHIKARY D P，DYSKIN A V，Jewell R J，et al. A study of the mechanism of flexural toppling failure of rock slopes[J]. Rock Mechanics and Rock Engineering，1997，30(2)：75–93.
[23] 龚逸非，姚爱军，李彦霖，等. 反倾层状岩质边坡块状–弯曲倾倒变形演化过程试验研究[J]. 岩石力学与工程学报，2024，43(10)：2 497–2 510.(GONG Yifei，YAO Aijun，LI Yanlin，et al. Experimental study on block-flexure toppling deformation evolution process of anti-dip layered rock slopes[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(10)：2 497–2 510.(in Chinese))
[24] 郭明珠，谷坤生，王天成. 反倾岩质斜坡振动台试验研究综述[J]. 工程抗震与加固改造，2021，43(6)：157–167.(GUO Mingzhu，GU Kunsheng，WANG Tiancheng. Summary of shaking table test research on anti-dip rock slope[J]. Earthquake Resistant Engineering and Retrofitting，2021，43(6)：157–167.(in Chinese))
[25] 汪小刚，张建红，赵毓芝，等. 用离心模型研究岩石边坡的倾倒破坏[J]. 岩土工程学报，1996，18(5)：18–25.(WANG Xiaogang，ZHANG Jianhong，ZHAO Yuzhi，et al. Study on the toppling failure of rock slope using centrifugal model[J]. Chinese Journal of Geotechnical Engineering，1996，18(5)：18–25.(in Chinese))
[26] 陈孝兵，李渝生，赵小平. 底摩擦重力试验在倾倒变形岩体稳定性研究中的应用[J]. 地学前缘，2008，(2)：300–304.(CHEN Xiaobing，LI Yusheng，ZHAO Xiaoping. The application of bottom-friction gravity test to the study of the stability of the toppling rock mass[J]. Earth Science Frontiers，2008，(2)：300–304.(in Chinese))
[27] ADHIKARY D P，DYSKIN A V，JEWELL R J. Numerical modelling of the flexural deformation of foliated rock slopes[J]. International Journal of Rock Mechanics and Mining Science and Geomechanics Abstracts，1996，33(6)：595–606.
[28] 黄 达，马 昊，孟秋杰，等. 软硬互层岩质反倾边坡弯曲倾倒离心模型试验与数值模拟研究[J]. 岩土工程学报，2020，42(7)：1 286–1 295.(HUANG Da，MA Hao，MENG Qiujie，et al. Centrifugal model test and numerical simulation for anaclinal rock slopes with soft-hard interbedded structures[J]. Chinese Journal of Geotechnical Engineering，2020，42(7)：1 286–1 295.(in Chinese))
[29] AMINI M，ARDESTANI A. Stability analysis of the North-eastern slope of Daralou copper open pit mine against a secondary toppling failure[J]. Engineering Geology，2019，249：89–101.
[30] CUNDALL P A. A computer model for simulating progressive，large-scale movements in blocky rock systems[C]// Proceedings of Symposium of International Society of Rock Mechanics. Nancy，France：[s.n.]，1971：2–8.
[31] ADHIKARY D P，DYSKIN A V. Modelling of progressive and instantaneous failures of foliated rock slopes[J]. Rock Mechanics and Rock Engineering，2007，40(4)：349–362.
[32] ZHENG Y，CHEN C，LIU T，et al. Study on the mechanisms of flexural toppling failure in anti-inclined rock slopes using numerical and limit equilibrium models[J]. Engineering Geology，2018，237：116–128.
[33] SCHOLTES L，DONZE F V. Modelling progressive failure in fractured rock masses using a 3D discrete element method[J]. International Journal of Rock Mechanics and Mining Sciences，2012，52(6)：18–30.
[34] 陈祖煜，张建红，汪小刚. 岩石边坡倾倒稳定分析的简化方法[J]. 岩土工程学报，1996，18(6)：96–99.(CHEN Zuyu，ZHANG Jianhong，WANG Xiaogang. Simplified method for stability analysis of rock slope toppling[J]. Chinese Journal of Geotechnical Engineering，1996，18(6)：96–99.(in Chinese))
[35] 汪小刚，贾志欣，陈祖煜，等. 岩质边坡倾倒破坏的稳定分析方法[J]. 水利学报，1996，(3)：7–12.(WANG Xiaogang，JIA Zhixin，CHEN Zuyu，et al. The research of stability analysis of toppling failure of jointed rock slope[J]. Journal of Hydraulic Engineering，1996，(3)：7–12.(in Chinese))
[36] 陈祖煜，蔡云鹏，王玉杰，等. 边坡倾倒稳定分析Goodman-Bray法：改进、测试与应用[J]. 中国公路学报，2018，31(2)：30–38.(CHEN Zuyu，CAI Yunpeng，WANG Yujie，et al. Goodman-Bray method for slope toppling stability analysis：improvement，testing and application[J]. China Journal of Highway and Transport，2018，31(2)：30–38.(in Chinese))
[37] LIU C H，JAKSA M B，MEYERS A G. Improved analytical solution for toppling stability analysis of rock slopes[J]. International Journal of Rock Mechanics and Mining Sciences，2008，45(8)：1361–1 372.
[38] LIU C H，JAKSA M B，MEYERS A G. A transfer coefficient method for rock slope toppling[J]. Canadian Geotechnical Journal，2009，46(1)：1–9.
[39] 刘才华，陈从新. 地震作用下岩质边坡块体倾倒破坏分析[J]. 岩石力学与工程学报，2010，29(增1)：3 193–3 198.(LIU Caihua，CHEN Congxin. Analysis of toppling failure of rock slopes due to earthquakes[J]. Chinese Journal of Rock Mechanics and Engineering，2010，29(Supp.1)：3 193–3 198.(in Chinese))
[40] AYDAN Ö，KAWAMOTO T. Toppling failure of discontinuous rock slopes and their stabilization[J]. Journal of the Mining and Metallurgical Institute of Japan，1987，103(7)：763–770.
[41] AYDAN Ö，KAWAMOTO T. The stability of slopes and underground openings against flexural toppling and their stabilisation[J]. Rock Mechanics and Rock Engineering，1992，25(3)：143–165.
[42] 卢海峰，刘泉声，陈从新. 反倾岩质边坡悬臂梁极限平衡模型的改进[J]. 岩土力学，2012，33(2)：577–584.(LU Haifeng，LIU Quansheng，CHEN Congxin. Improvement of cantilever beam limit equilibrium model of counter-tilt rock slopes[J]. Rock and Soil Mechanics，2012，33(2)：577–584.(in Chinese))
[43] 蔡静森，晏鄂川，王章琼，等. 反倾层状岩质边坡悬臂梁极限平衡模型研究[J]. 岩土力学，2014，35(增1)：15–28.(CAI Jingsen，YAN Echuan，WANG Zhangqiong，et al. Study of cantilever beam limit equilibrium model of anti-dip layered rock slopes[J]. Rock and Soil Mechanics，2014，35(Supp.1)：15–28.(in Chinese))
[44] 郑 允，陈从新，刘秀敏，等. 层状反倾边坡弯曲倾倒破坏计算方法探讨[J]. 岩石力学与工程学报，2015，34(增2)：4 252–4 261. (ZHENG Yun，CHEN Congxin，LIU Xiumin，et al. Investigation on calculation method of layered counter-tilt slope for flexural toppling failure[J]. Chinese Journal of Rock Mechanics and Engineering，2015，34(Supp.2)：4 252–4 261.(in Chinese))
[45] 陈从新，郑 允，孙朝燚. 岩质反倾边坡弯曲倾倒破坏分析方法研究[J]. 岩石力学与工程学报，2016，35(11)：2 174–2 187.(CHEN Congxin，ZHENG Yun，SUN Chaoyi. An analytical approach on flexural toppling failure of counter-tilt slopes of layered rock[J]. Chinese Journal of Rock Mechanics and Engineering，2016，35(11)：2 174–2 187.(in Chinese))
[46] 孙朝燚，陈从新，郑 允，等. 岩质反倾边坡复合倾倒破坏分析[J]. 湖南大学学报：自然科学版，2020，47(1)：130–138.(SUN Chaoyi，CHEN Congxin，ZHENG Yun，et al. Analysis of composite toppling failure of anti-dip rock slopes[J]. Journal of Hunan University：Natural Sciences，2020，47(1)：130–138.(in Chinese))
[47] AMINI M，MAJDI A，VESHADI M A. Stability analysis of rock slopes against block-flexure toppling failure[J]. Rock Mechanics and Rock Engineering，2012，45(4)：519–532.
[48] 张海娜，胡瑞奇，常 锦，等. 反倾岩质边坡块状–弯曲复合倾倒破坏分析方法研究[J]. 岩石力学与工程学报，2023，42(6)：1 482–1 496.(ZHANG Haina，HU Ruiqi，CHANG Jin，et al. Analytical analysis of block-flexure toppling failure of anti-dip bedding rock slopes[J]. Chinese Journal of Rock Mechanics and Engineering，2023，42(6)：1 482–1 496.(in Chinese))
[49] 王俊杰，郭建军. 反倾岩质边坡次生倾倒机制及稳定性分析[J]. 岩土工程学报，2019，41(9)：1 619–1 627.(WANG Junjie，GUO Jianjun. Mechanism and stability of secondary toppling of counter-tilt rock slopes[J]. Chinese Journal of Geotechnical Engineering，2019，41(9)：1 619–1 627.(in Chinese))
[50] 徐建城. 坡脚劣化条件下三峡库区反倾岩质边坡的破坏模式及稳定性分析[硕士学位论文][D]. 宜昌：三峡大学，2023.(XU Jiancheng. Failure mode and stability analysis of anti-dip rock slope in the Three Gorges Reservoir Area under slope foot degradation[M. S. Thesis][D]. Yichang：China Three Gorges University，2023.(in Chinese))
[51] 郭建军. 节理化岩质边坡次生倾倒破坏机制及稳定性分析方法[博士学位论文][D]. 重庆：重庆交通大学，2018.(GUO Jianjun. Analysis method of failure mechanism and stability for the secondary toppling of jointed rock slope[Ph. D. Thesis][D]. Chongqing：Chongqing Jiaotong University，2018.(in Chinese))
[52] 陈祖煜，汪小刚，杨 健，等. 岩质边坡稳定分析：原理•方法•程序[M]. 北京：中国水利水电出版社，2005：64–73.(CHEN Zuyu，WANG Xiaogang，YANG Jian，et al. Rock slope stability analysis—Theory，method and programs[M]. Beijing：China Water and Power Press，2005：64–73.(in Chinese))
[53] 郭明珠，刘 晃，王欢欢，等. 金沙江上游贡扎村岩质滑坡发育特征及演化成因分析[J]. 地震研究，2021，44(2)：242–250.(GUO Mingzhu，LIU Huang，WANG Huanhuan，et al. Analysis of causes and the development characteristics of the rock landslide in Gonza Village，the Upper Jinsha River[J]. Journal of Seismological Research，2021，44(2)：242–250.(in Chinese))
[54] 宁奕冰. 澜沧江中上游深层倾倒体变形失稳过程及稳定性评价研究[博士学位论文][D]. 武汉：中国地质大学，2022.(NING Yibing. Study on the deformation and instability process and stability evaluation of deep-seated toppling in the upper-middle Lancang River[Ph. D. Thesis][D]. Wuhan：China University of Geosciences，2022.(in Chinese))
[55] 王 飞. 雅砻江上游互层斜坡深层倾倒变形破坏机制及稳定性评价[博士学位论文][D]. 武汉：中国地质大学，2019.(WANG Fei. Failure mechanism and stability assessment of deep-seated toppling in interlayered rock slopes at upstream of Yalong River[Ph. D. Thesis][D]. Wuhan：China University of Geosciences，2019.(in Chinese))
[56] 母剑桥. 反倾边坡倾倒破裂面优势形态及变形稳定性分析方法研究[博士学位论文][D]. 成都：成都理工大学，2017.(MU Jianqiao. Research on the optimized shape of toppling fracture plane in obsequent slope and the deformation stability analysis method[Ph. D. Thesis][D]. Chengdu：Chengdu University of Technology，2017.(in Chinese))
[57] 邢一飞，张 诚，王建辉. 西南地区典型弯曲倾倒式滑坡变形演化机制及防治研究[J]. 科学技术与工程，2016，16(22)：156–161.(XING Yifei，ZHANG Cheng，WANG Jianhui. Evolution mechanism and prevention of typical bending deformation dump landslide in Southwest China[J]. Science Technology and Engineering，2016，16(22)：156–161.(in Chinese))
[58] 陆文博，晏鄂川，邹 浩，等. 我国倾倒变形体发育规律研究[J]. 长江科学院院报，2017，34(8)：111–119.(LU Wenbo，YAN Echuan，ZOU Hao，et al. Development rules of toppling deformation slopes in China[J]. Journal of Yangtze River Scientific Research Institute，2017，34(8)：111–119.(in Chinese))
[59] 张成强. 倾倒变形边坡库水作用机制及稳定性分析[硕士学位论文][D]. 成都：成都理工大学，2018.(ZHANG Chengqiang. Reservoir water mechanism and stability analysis of toppling slope[M. S. Thesis][D]. Chengdu：Chengdu University of Technology，2018.(in Chinese))
[60] 张御阳. 陡缓结构面反倾层状岩质斜坡变形破坏演化机制研究[博士学位论文][D]. 成都：成都理工大学，2019.(ZHANG Yuyang. Evolution mechanism of deformation and failure of anti-dip stratified rocky slope with steep and gentle structural planes[Ph. D. Thesis][D]. Chengdu：Chengdu University of Technology，2019.(in Chinese))
[61] 张泽林. 茨哈峡水电站近坝库岸稳定性研究[硕士学位论文][D]. 兰州：兰州大学，2010.(ZHANG Zelin. Investigation on stability of the bank slope of the dam near Cihaxia Hydropower Station[M. S. Thesis][D]. Lanzhou：Lanzhou University，2010.(in Chinese))
[62] 邹 浩. 西部水电工程倾倒变形体岩体质量评价体系与应用研究[博士学位论文][D]. 武汉：中国地质大学，2016.(ZOU Hao. Study on rock quality classification system and its application of toppling deformation rock in Western Hydropower Projects[Ph. D. Thesis][D]. Wuhan：China University of Geosciences，2016.(in Chinese))
[63] 王林康，郑子涵，章广成，等. 顺层陡倾岩质边坡倾倒模式试验[J]. 地质科技通报，2025，44(2)：340–354.(WANG Linkang，ZHENG Zihan，ZHANG Guangcheng，et al. Test study on the toppling mode of steep bedding rock slope[J]. Geological Science and Technology Information，2025，44(2)：340–354.(in Chinese))
[64] 魏恺泓. 大型顺层倾倒边坡变形破坏演化机制与稳定性评价研究[博士学位论文][D]. 成都：成都理工大学，2022.(WEI Kaihong. Study on deformation and fracture evolution mechanism and stability evaluation of large bedding toppling slope[Ph. D. Thesis][D]. Chengdu：Chengdu University of Technology，2022.(in Chinese))
[65] 汪鸣飞，章广成，包刘磊，等. 顺层陡倾岩质边坡变形机制探究[J]. 安全与环境工程，2021，28(5)：107–120.(WANG Mingfei，ZHANG Guangcheng，BAO Liulei，et al. Research on deformation mechanism of steep bedding rock slope[J]. Safety and Environmental Engineering，2021，28(5)：107–120.(in Chinese))
[66] 薛永强. 陡倾顺层岩质边坡倾倒变形机制研究[硕士学位论文][D]. 青岛：山东科技大学，2017.(XUE Yongqiang. The mechanism of toppling deformation on steep bedding rock slope[M. S. Thesis][D]. Qingdao：Shandong University of Science and Technology，2017.(in Chinese))
[67] 王 楷. 那曲河某水电站库岸大型中陡倾顺层岩质滑坡发育特征及形成机制研究[硕士学位论文][D]. 成都：成都理工大学，2021.(WANG Kai. Study on the development characteristics and formation mechanism of large intermediate-steep dip bedding rock landslide on the bank of a hydropower station on the Naqu River[M. S. Thesis][D]. Chengdu：Chengdu University of Technology，2021.(in Chinese))
[68] 安晓凡，巨广宏，李 宁. 岩质边坡倾倒破坏模式与机制分析[J]. 西北水电，2022，(1)：10–21.(AN Xiaofan，JU Guanghong，LI Ning. Analysis on mode and mechanism of toppling failure for rock slopes[J]. Northwest Hydropower，2022，(1)：10–21.(in Chinese))
[69] 陆兆臻. 工程地质原理[M]．北京：中国水利水电出版社，2001.(LU Zhaozhen. Principles of engineering geology[M]. Beijing：China Water and Power Press，2001.(in Chinese))
[70] 肖 远. 边坡层状岩体弯曲蠕变机制及分析方法[博士学位论文][D]. 北京：中国科学院地质研究所，1989.(XIAO Yuan. Bending creep mechanism and analysis method of slope stratified rock mass [Ph. D. Thesis][D]. Beijing：Institute of Geology，Chinese Academy of Sciences，1989.(in Chinese))
[71] 冉从彦，张世殊，林 红. 水电工程倾倒变形体分类及其判识初探[C]// 第十一届全国工程地质大会论文集. 成都：中国电建集团成都勘测设计研究院有限公司，2020：130–137.(RAN Congyan，ZHANG Shishu，LIN Hong. Preliminary study on classification and identification of toppling deformation bodies in hydropower projects[C]// Proceedings of the 11th National Engineering Geology Conference. Chengdu：ChinaPower Chengdu Engineering Corporation Limited，2020：130–137.(in Chinese))
[72] ALEJANO L R，MARQUEZ I G，ALEGRIA R M. Analysis of a complex toppling circular slope failure[J]. Engineering Geology，2010，114：93–104.
[73] MOHTARAMI E，JAFARI A，AMINI M. Stability analysis of slopes against combined circular toppling failure[J]. International Journal of Rock Mechanics and Mining Sciences，2014，67：43–56.
[74] AMINI M，AKBAR A，MOHAMMAD H K. Stability analysis of slide-toe-toppling failure[J]. Engineering Geology，2017，228：82–96.
[75] AMINI M，HASSAN S，KAMRAN E. Stability analysis of slopes with a potential of slide-head toppling failure[J]. International Journal of Rock Mechanics and Mining Sciences，2018，112：108–121.
[76] 杨保军，何 杰，吉 刚，等. 岩质边坡滑动–倾倒组合破坏模式稳定性分析[J]. 岩土力学，2014，35(8)：2 335–2 341.(YANG Baojun，HE Jie，JI Gang，et al. Stability analysis of sliding-toppling composite failure of rock slope[J]. Rock and Soil Mechanics，2014，35(8)：2 335–2 341.(in Chinese))
[77] HOEK E，BRAY J. Rock slope engineering[M]. London：The Institute of Mining and Metallurgy，1977：257–270.
[78] WYLLIE D C，MAH C. Rock slope engineering[M]. London：CRC Press，2004：200–217.
[79] NICHOL S L，HUNGR O，EVANS S G. Large-scale brittle and ductile toppling of rock slopes[J]. Canadian Geotechnical Journal，2002，39(4)：773–788.
[80] 黄润秋，林 锋，向喜琼. 贵州省崩滑地质灾害形成机制研究[M]. 成都：成都科技大学出版社，2013：742–743.(HUANG Runqiu，LIN Feng，XIANG Xiqiong. Research on formation mechanism of rockfall and landslide geological disasters in Guizhou Province[M]. Chengdu：Chengdu University of Science and Technology Press，2013：742–743.(in Chinese))
[81] CRUDEN D M，VARNES D J. Landslide types and processes[C]// TURNER A K，SCHUSTER R L，ed. Landslides：Investigation and Mitigation. Washington，DC：Transportation Research Board，US National Research Council，1996：36–75.
[82] HUANG R Q. Understanding the mechanism of large-scale landslides[C]// Engineering Geology for Society and Territory. Swizerland：Springer，2015：13–32.
[83] VARNES D J. Slope movement types and processes[J]. Special Report，1978，176：11–33.
[84] 刘海军，赵建军，巨能攀. 岩质边坡倾倒破坏的力学分析[J]. 岩土力学，2016，37(增1)：289–294.(LIU Haijun，ZHAO Jianjun，JU Nengpan. Mechanical analysis of toppling failure of rock slopes[J]. Rock and Soil Mechanics，2016，37(Supp.1)：289–294.(in Chinese))
[85] 霍逸康，石振明，郑鸿超，等. 软硬互层反倾岩质边坡稳定性影响因素分析及破坏模式研究[J]. 工程地质学报，2023，31(5)：1 680–1 688. (HUO Yikang，SHI Zhenming，ZHENG Hongchao，et al. Study on influence factors of stability and failure modes of anti-dip rock slope with soft and hard interbeds[J]. Journal of Engineering Geology，2023，31(5)：1 680–1 688.(in Chinese))
[86] 史文兵，续建科，唐晓玲. 反倾向层状岩质边坡失稳模式及支护对策[J]. 水利与建筑工程学报，2011，9(1)：95–97.(SHI Wenbing，XU Jianke，TANG Xiaoling. Failure models and supporting measures of antidip sandwich rock slope[J]. Journal of Water Resources and Architectural Engineering，2011，9(1)：95–97.(in Chinese))
[87] FREDLUND D G，KRAHN J. Comparison of slope stability methods of analysis[J]. Canadian Geotechnical Journal，1977，14(3)：429–439.
[88] 鲍 杰，李渝生，曹广鹏，等. 澜沧江某水电站近坝库岸岩体倾倒变形的成因机制[J]. 地质灾害与环境保护，2011，22(3)：47–51. (BAO Jie，LI Yusheng，CAO Guangpeng，et al. Genetic mechanism of the toppling deformation near the dam of a hydropower station on the Lancang River[J]. Journal of Geological Hazards and Environment Preservation，2011，22(3)：47–51.(in Chinese))
[89] 张丙先. 西藏玉曲河下游岸坡倾倒变形机制及稳定性分析[J]. 吉林大学学报：地球科学版，2018，48(5)：1 539–1 545.(ZHANG Bingxian. Analysis of toppling deformation mechanism and stability of bank slope in the downstream of Yuqu River，Xizang[J]. Journal of Jilin University：Earth Science，2018，48(5)：1 539–1 545.(in Chinese))
[90] 卢增木，陈从新，左保成，等. 对影响逆倾层状边坡稳定性因素的模型试验研究[J]. 岩土力学，2006，27(4)：629–632.(LU Zengmu，CHEN Congxin，ZUO Baocheng，et al. Experimentation research on factors influencing stability of anti-dip layered slope[J]. Rock and Soil Mechanics，2006，27(4)：629–632.(in Chinese))
[91] ZHAO Q，YANG Z P，ZHANG S B，et al. Exploring the toppling deformation mechanisms and failure modes of anti-dip layered rocky slopes：insights from physical model experiments[J]. Landslides，2025，22(6)：895–923.
[92] 孙书伟，李 圆，杨晓锐，等. 不同岩层倾角顺倾层状岩质边坡破坏机制研究[J]. 岩石力学与工程学报，2024，43(7)：1 607–1 620. (SUN Shuwei，LI Yuan，YANG Xiaorui，et al. Study on the failure mechanism of rock slopes with dipped layered structures under various rock dip conditions[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(7)：1 607–1 620.(in Chinese))
[93] ZHANG B C，TANG H M，SUMI S，et al. Exploring the deformation and failure characteristics of interbedded anti-inclined rock slopes：Insights from physical modelling tests[J]. Rock Mechanics and Rock Engineering，2024，57(5)：1 603–1 628.
[94] 郑 达，张 硕，郑 光. 基于坡角变化的反倾层状岩质斜坡倾倒变形离心模型试验研究[J]. 岩土工程学报，2021，43(3)：439–447.(ZHENG Da，ZHANG Shuo，ZHENG Guang. Centrifugal model tests on toppling deformation of counter-tilt layered rock slopes based on change of slope angle[J]. Chinese Journal of Geotechnical Engineering，2021，43(3)：439–447.(in Chinese))
[95] 杨 豪，魏玉峰，裴向军，等. 含陡缓倾结构面反倾岩坡折断面演化特征的离心试验研究[J]. 岩土力学，2022，43(5)：1 215–1 225. (YANG Hao，WEI Yufeng，PEI Xiangjun，et al. Centrifugal test study of fracture evolution characteristics of anti-dip rock slope with steep and gently dipping structural planes[J]. Rock and Soil Mechanics，2022，43(5)：1 215–1 225.(in Chinese))
[96] 巨能攀，邓天鑫，李龙起，等. 强震作用下陡倾顺层斜坡倾倒变形机制离心振动台试验[J]. 岩土力学，2019，40(1)：99–108.(JU Nengpan，DENG Tianxin，LI Longqi，et al. Centrifugal shaking table test on toppling deformation mechanism of steep bedding slope under strong earthquake[J]. Rock and Soil Mechanics，2019，40(1)：99–108.(in Chinese))
[97] 黄 鹏，张 咪，乔 鹏. 高原寒区碎裂松动岩体成因机制研究[J]. 人民珠江，2018，39(12)：44–53.(HUANG Peng，ZHANG Mi，QIAO Peng. Study on the genetic mechanism of cataclastic loose rock mass on the Lanchang River Basin of the Qinghai—Xizang Plateau[J]. Pearl River，2018，39(12)：44–53.(in Chinese))
[98] ZHANG J H，CHEN Z Y，WANG X G. Centrifuge modeling of rock slopes susceptible to block toppling[J]. Rock Mechanics and Rock Engineering，2006，40(4)，363–382.
[99] 张国新，赵 妍，石根华，等. 模拟岩石边坡倾倒破坏的数值流形法[J]. 岩土工程学报，2007，29(6)：800–805.(ZHANG Guoxin，ZHAO Yan，SHI Genhua，et al. Toppling failure simulation of rock slopes by numerical manifold method[J]. Chinese Journal of Geotechnical Engineering，2007，29(6)：800–805.(in Chinese))
[100] CHEN C，LI H，CHIU Y，et al. Dynamic response of a physical anti-dip rock slope model revealed by shaking table tests[J]. Engineering Geology，2020，277：105772.
[101] 龚逸非，姚爱军，谷坤生，等. 强震作用下反倾薄层岩质斜坡倾倒破坏机制及动力响应研究[J]. 振动与冲击，2023，42(20)：263–274.(GONG Yifei，YAO Aijun，GU Kunsheng，et al. Dynamic response and toppling failure mechanism of anti-dip thin-layered rock slope under strong earthquake[J]. Journal of Vibration and Shock，2023，42(20)：263–274.(in Chinese))
[102] NING Y B，ZHANG G C，TANG H M，et al. Process analysis of toppling failure on anti-dip rock slopes under seismic load in Southwest China[J]. Rock Mechanics and Rock Engineering，2019，52(11)：4 439–4 455.
[103] 王润清. 弯曲倾倒型岩质边坡稳定性分析及离心试验研究[硕士学位论文][D]. 大连：大连理工大学，2020.(WANG Runqing. Stability analysis and centrifugal modeling tests of rock slopes against flexural toppling failure[M. S. Thesis][D]. Dalian：Dalian University of Technology，2020.(in Chinese))
[104] 张雨林，涂国祥，张 银，等. 河流下切对陡倾层状岩体深层倾倒变形的影响[J]. 中国科技论文，2022，17(8)：915–922.(ZHANG Yulin，TU Guoxiang，ZHANG Yin，et al. Influence of river down-cutting on deep toppling deformation of steep dipping layered rock mass[J]. Science Paper Online，2022，17(8)：915–922.(in Chinese))
[105] 郑 达，王沁沅，毛 峰，等. 反倾层状岩质边坡深层倾倒变形关键致灾因子及成灾模式的离心试验研究[J]. 岩石力学与工程学报，2019，38(10)：1 954–1 963.(ZHENG Da，WANG Qinyuan，MAO Feng，et al. Centrifuge model test study on key hazard-inducing factors of deep toppling deformation and disaster patterns of counter- tilt layered rock slopes[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(10)：1 954–1 963.(in Chinese))
[106] 王沁沅. 反倾层状岩质边坡深层倾倒变形关键致灾因子及成灾模式研究[硕士学位论文][D]. 成都：成都理工大学，2020.(WANG Qinyuan. Research on key hazard factors of deep toppling deformation and disaster pattern of anti-dip layered-rock slope[M. S. Thesis][D]. Chengdu：Chengdu University of Technology，2020.(in Chinese))
[107] 赵 华，李文龙，卫俊杰，等. 反倾边坡倾倒变形演化过程的模型试验研究[J]. 工程地质学报，2018，26(3)：749–757.(ZHAO Hua，LI Wenlong，WEI Junjie，et al. Model test study on toppling deformation evolution process of counter-tilt slope[J]. Journal of Engineering Geology，2018，26(3)：749–757.(in Chinese))
[108] 左保成. 反倾岩质边坡破坏机制研究[硕士学位论文][D]. 武汉：中国科学院武汉岩土力学研究所，2004.(ZUO Baocheng. Study on losing stability mechanism of counter-tilt rock slopes[M. S. Thesis][D]. Wuhan：Institute of Rock and Soil Mechanics，Chinese Academy of Sciences，2004.(in Chinese))
[109] 左保成，陈从新，刘小巍，等. 反倾岩质边坡破坏机制模型试验研究[J]. 岩石力学与工程学报，2005，24(19)：107–113.(ZUO Baocheng，CHEN Congxin，LIU Xiaowei，et al. Modeling experiment study on failure mechanism of counter-tilt rock slope[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(19)：107–113.(in Chinese))
[110] ZHENG Y，WU R F，YAN C Z，et al. Numerical study on flexural toppling failure of rock slopes using the finite discrete element method[J]. Bulletin of Engineering Geology and the Environment，2024，83(4)：111.
[111] 苗 朝，沈军辉，杨佳丽，等. 雅砻江甲西滑坡倾倒弯曲–拉裂形成机制研究[J]. 防灾减灾工程学报，2015，35(3)：411–417.(MIAO Zhao，SHEN Junhui，YANG Jiali，et al. Study on the formation mechanism of toppling flexure and tensile cracking of the Jiaxi landslide on the Yalong River[J]. Journal of Disaster Prevention and Mitigation Engineering，2015，35(3)：411–417.(in Chinese))
[112] GUI J Y，DING B D，PÉREZ-REY I，et al. Stability against toppling of a single rock block resting on an irregular rough base[J]. Environmental Earth Sciences，2024，83(12)：660.
[113] 王 飞，唐辉明，宁奕冰，等. 基于演化过程的互层斜坡深层倾倒稳定性评价[J]. 地质科技情报，2019，38(5)：186–194.(WANG Fei，TANG Huiming，NING Yibing，et al. Stability analysis of deep-seated toppling in interlayered rock slopes based on evolution process[J]. Geological Science and Technology Information，2019，38(5)：186–194.(in Chinese))
[114] 龚柏城，苑久超，王 磊，等. 软硬岩互层反倾高边坡变形破坏过程物理模型试验研究[J]. 地质灾害与环境保护，2024，35(1)：87–95.(GONG Bocheng，YUAN Jiuchao，WANG Lei，et al. experimental study on physical model of deformation evolution mode of high slope with anti-dip of soft and hard rock[J]. Journal of Geological Hazards and Environment Preservation，2024，35(1)：87–95.(in Chinese))
[115] 李彦奇，黄 达，孟秋杰. 基于离心机和数值模拟的软硬互层反倾层状岩质边坡变形特征分析[J]. 水文地质工程地质，2021，48(4)：141–150.(LI Yanqi，HUANG Da，MENG Qiujie. An analysis of the deformation characteristics of soft-hard interbedded anti-tilting layered rock slope based on centrifuge and numerical simulation[J]. Hydrogeology and Engineering Geology，2021，48(4)：141–150.(in Chinese))
[116] ZHANG B C，FANG K，TANG H M，et al. Block-flexure toppling in an anaclinal rock slope based on multi-field monitoring[J]. Engineering Geology，2023，327：107340.
[117] WYLLIE D C．Toppling rock slopes failures：Examples of analysis and stabilization[J]. Journal of Geotechnical Engineering，1983，109(8)：1 039–1 062.
[118] 李天扶. 论层状岩石边坡的倾倒破坏[J]. 西北水电，2006，(3)：4–6.(LI Tianfu. On toppling failure of bedded rock slope[J]. Northwest Hydropower，2006，(3)：4–6.(in Chinese))
[119] 胡惠华，张奇华，张 鹏. 基于板梁状陡坡地基倾倒稳定性分析的G-B改进模型研究[J]. 中南大学学报：自然科学版，2022，53(10)：4 123–4 131.(HU Huihua，ZHANG Qihua，ZHANG Peng. Research of improved G-B model for toppling stability analysis of plate-shaped steep slope foundation[J]. Journal of Central South University：Science and Technology，2022，53(10)：4 123–4 131.(in Chinese))
[120] 高连通，晏鄂川，谢良甫. 考虑地下水作用的Goodman–Bray方法改进及应用[J]. 长江科学院院报，2015，32(2)：78–83.(GAO Liantong，YAN Echuan，XIE Liangfu. Improved Goodman-Bray method in consideration of groundwater effect[J]. Journal of Yangtze River Scientific Research Institute，2015，32(2)：78–83.(in Chinese))
[121] BOBET A. Analytical solutions for toppling failure[J]. International Journal of Rock Mechanics and Mining Sciences，1999，36：971–980.
[122] SAGASETA C，SANCHEZ J M，CANIZAL J. A general analytical solution for the required anchor force in rock slopes with toppling failure[J]. International Journal of Rock Mechanics and Mining Sciences，2001，38(4)：421–435.
[123] 郑 允，陈从新，刘婷婷，等. 坡顶荷载作用下岩质边坡倾倒破坏分析[J]. 岩土力学，2015，36(9)：2 639–2 647.(ZHENG Yun，CHEN Congxin，LIU Tingting，et al. Analysis of toppling failure of rock slopes under the loads applied on the top[J]. Rock and Soil Mechanics，2015，36(9)：2 639–2 647.(in Chinese))
[124] 李 泽，胡 政，刘文连，等. 考虑平动–转动力学效应的露天矿山节理岩质边坡塑性极限分析[J]. 岩石力学与工程学报，2018，37(增2)：4 056–4 068.(LI Ze，HU Zheng，LIU Wenlian，et al. Plastic limit analysis of open-pit mine jointed rock slope considering translation-rotation mechanisms[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(Supp.2)：4 056–4 068.(in Chinese))
[125] 王家臣，杨胜利，李良晖. 急倾斜煤层水平分段综放顶板“倾倒-滑塌”破坏模式[J]. 中国矿业大学学报，2018，47(6)：1 175–1 184. (WANG Jiachen，YANG Shengli，LI Lianghui. Toppling-slumping failure mode in horizontal sublevel top-coal caving face in steeply-inclined seam[J]. Journal of China University of Mining and Technology，2018，47(6)：1 175–1 184.(in Chinese))
[126] 王 伟. 黄山石灰石矿露采高边坡结构面特性及破坏机制研究[硕士学位论文][D]. 武汉：中国地质大学，2015.(WANG Wei. Study on characteristics of structural plane and failure mechanism of open pit mining high-steep slopes in Huangshan Limestone Mine[M. S. Thesis][D]. Wuhan：China University of Geosciences，2015.(in Chinese))
[127] 屈 新，苏立君，徐兴倩，等. 地震作用下反倾向层状岩质边坡弯曲倾倒稳定性分析[J]. 长江科学院院报，2022，39(8)：105–112. (QU Xin，SU Lijun，XU Xingqian，et al. Analysis of flexural toppling stability of anti-dip layered rock slopes under seismic action[J]. Journal of Yangtze River Scientific Research Institute，2022，39(8)：105–112.(in Chinese))
[128] 陈红旗，黄润秋. 反倾层状边坡弯曲折断的应力及挠度判据[J]. 工程地质学报，2004，(3)：243–246.(CHEN Hongqi，HUANG Rongqiu. Stress and flexibility criteria of bending and breaking in a counter-tendency layered slope[J]. Journal of Engineering Geology，2004，(3)：243–246.(in Chinese))
[129] 贺琮栖，魏玉峰，王 洋，等. 层状边坡倾倒变形多级折断面分布深度计算模型[J]. 岩土力学，2022，43(10)：2 809–2 818.(HE Congqi，WEI Yufeng，WANG Yang，et al. Calculation model of multistage fracture surface distribution depth of layered slope toppling deformation[J]. Rock and Soil Mechanics，2022，43(10)：2 809– 2 818.(in Chinese))
[130] 田钱钱. 弯曲倾倒型岩质边坡稳定性分析方法研究[硕士学位论文][D]. 绍兴：绍兴文理学院，2023.(TIAN Qianqian. Study on stability analysis method of flexural toppling rock slope[M. S. Thesis][D]. Shaoxing：Shaoxing University，2023.(in Chinese))
[131] 赵 维，王润清，年廷凯. 基于弯曲倾倒破坏模式的反倾岩质边坡稳定性解析方法[J]. 岩石力学与工程学报，2019，38(增2)：3 287–3 295.(ZHAO Wei，WANG Runqing，NIAN Tingkai. Analytical method for stability of anti-dip rock slope based on flexural toppling failure mode[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(Supp.2)：3 287–3 295.(in Chinese))
[132] ZHENG Y，CHEN C X，LIU T T，et al. Theoretical and numerical study on the block-flexure toppling failure of rock slopes[J]. Engineering Geology，2019，263：105309.
[133] MAJDI A，AMINI M. A new analytical method for analysis of flexural toppling failure in rock slopes[C]// Proceedings of the 42nd U. S. Rock Mechanics Symposium. San Francisco，California，USA：[s. n.]，2008：10–15.
[134] AMINI M，MAJDI A，AYDAN Ö. Stability analysis and the stabilization of flexural toppling failure[J]. Rock Mechanics and Rock Engineering，2009，42(6)：751–782.
[135] MAJDI A，AMINI M. Analysis of geo-structural defects in flexural toppling failure[J]. International Journal of Rock Mechanics and Mining Sciences，2011，48(2)：175–186.
[136] 王润清，陈从新，郑 允，等. 考虑变形协调的地震作用下反倾岩质边坡弯曲倾倒稳定性分析方法[J]. 岩石力学与工程学报，2024，43(1)：146–156.(WANG Runqing，CHEN Congxin，ZHENG Yun，et al. Analytical method for flexural toppling failure of anti-dip rock slopes under seismic loads considering deformation coordination[J]. Chinese Journal of Rock Mechanics and Engineering，2024，43(1)：146–156.(in Chinese))
[137] JIN L L，FU W X，WANG Y，et al. A novel method for evaluating stability and mechanism of flexural toppling based on energy conservation principle and numerical simulation[J]. International Journal of Rock Mechanics and Mining Sciences，2024，183：105896.
[138] 李爱民. 突变理论在反倾岩质边坡稳定性评价中的应用研究[博士学位论文][D]. 长沙：中南大学，2004.(LI Aimin. Application of catastrophe theory to stability evaluation of anti-dip rock slope[Ph. D. Thesis][D]. Changsha：Central South University，2004.(in Chinese))
[139] LEUNG C F，KHEOK S C. Computer aided analysis of rock slope stability[J]. Rock Mechanics and Rock Engineering，1987，20(2)：111–122.
[140] AKSOY H，ERCANOGLU M. Fuzzified kinematic analysis of discontinuity-controlled rock slope instabilities[J]. Engineering Geology，2007，89(3/4)：206–219.
[141] SMITH J V. A new approach to kinematic analysis of stress-induced structural slope instability[J]. Engineering Geology，2015，187：56–59. |
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2026, Vol. 45 
