地震作为诱发岩质边坡块体崩塌的重要因素，是研究岩质边坡块体稳定性不可或缺的内容。地震诱发边坡上大量块体失稳滑落进而导致滑坡灾害，严重威胁着国家基础工程建设以及人民生命、财产的安全性，国家相关领导高度关注因地震所诱发的次生地质灾害的基础防范工作。

地震既可看作一种动荷载也可看作一种循环荷载。而块体一般是由临空面或结构面共同组合切割形成的。在动荷载作用下，块体会受到地震惯性力的作用；在循环荷载作用下，块体结构面表面形态会出现退化现象，其抗剪强度会逐步降低，进而导致块体动力稳定性逐渐下降，所以结构面的强度特性对块体动力稳定性起着关键决定性作用，是分析岩质边坡块体动力稳定性的首要前提。但目前在考虑结构面震动劣化基础上进行边坡块体动力稳定性的相关研究相对匮乏，所以研究地震作用下岩质边坡块体动力稳定性具有重要的理论意义及工程研究价值。

因此本文以鲁甸王家坡岩质边坡块体为研究背景，采用现场勘探、理论分析和数值分析等方法，在考虑结构面震动劣化效应基础上，系统性研究地震作用下岩质边坡块体的动力稳定性。主要研究内容与研究成果如下：

（1）通过现场调查和文献查阅，阐述分析地震波传播特征及结构面在静力和地震等不同条件下的受力情况，进而分析地震作用下块体动力稳定性的影响因素，并着重研究结构面力学特性及地震对块体动力稳定性的影响。

（2）采用离散元法开展结构面循环剪切数值试验，研究结构面抗剪强度震动劣化效应，分析循环剪切次数、剪切幅值和起伏角度对剪应力的演化特征；基于回归分析法研究结构面的相对磨损效应以及相对速度影响效应，由此建立结构面震动劣化数学模型。

（3）基于坐标投影法原理，结合所构建的结构面震动劣化数学模型，提出一种考虑结构面震动劣化效应的边坡块体动力稳定性系数计算方法。进而对常见的两种失稳块体类型在地震作用下的动力稳定性进行分析，并推导出其动力稳定性系数数学公式。

（4）基于有限差分法，给出块体动力稳定性系数时程曲线和位移变化曲线，分析地震波波动特性对块体动力稳定性系数及位移的影响规律；基于突变理论提出块体位移动力响应放大系数突变判据，最终提出地震作用下岩质边坡块体动力稳定性评价方法，为边坡的灾害防治工作提供理论依据，具有重要的理论意义和工程参考价值。

As an important factor to induce the collapse of rock slope block, earthquake is an indispensable content to study the stability of rock slope block. Earthquake-induced instability and sliding of a large number of blocks on the slope leads to landslide disasters, which seriously threatens the safety of national infrastructure construction and people’s lives and property. The relevant national leaders pay highly attention to the basic prevention of secondary geological disasters caused by earthquakes.

Earthquake can be regarded as both a dynamic load and a cyclic load. And the block is generally formed by the combination of the free surface or the structural plane. Under dynamic loading, the block is affected by seismic inertia force; under cyclic loading, the surface morphology of block structural plane will degenerate, and its shear strength will gradually decrease, leading to the gradual decline of block stability. Therefore, the deformation and strength characteristics of structural plane play a decisive role in block stability, which is the primary prerequisite for analyzing the stability of the slope block. However, there is a lack of research on the dynamic stability of slope blocks based on the consideration of vibrational deterioration of the structural plane. Therefore, it has important theoretical significance and engineering research value to study the stability of rock slope blocks under earthquake.

Therefore, this paper takes the rocky slope of Wangjiapo in Ludian as the research background, and systematically studies the dynamic stability of rock slope block under earthquake based on the seismic deterioration of structural plane by using the methods of field exploration, theoretical analysis and numerical analysis. The main research contents and results are as follows:

(1) Through field investigation and literature review, the propagation characteristics of seismic waves and the stress conditions of structural planes under different conditions such as static force and earthquake are expounded and analyzed, and then the influencing factors of block dynamic stability under earthquake are analyzed, and the mechanical properties of structural planes and the influence of earthquake on block dynamic stability are emphatically studied.

(2) The discrete element method is used to carry out the numerical simulation of the cyclic shear of the structural plane, and to study the seismic degradation effect of the shear strength of the structural plane. The evolution characteristics of the cyclic shear number, shear amplitude and fluctuation angle on the shear stress are analyzed. Based on the regression analysis method, the relative wear effect and relative velocity effect of structural plane are studied, and the mathematical model of structural surface vibration degradation is established.

(3) Based on the principle of coordinate projection method and combined with the mathematical model of structural plane vibration degradation, a calculation method of dynamic stability coefficient of slope block considering the effect of structural plane vibration degradation is proposed. Then the dynamic stability of two common types of unstable blocks under earthquake is analyzed and the mathematical formula of dynamic stability coefficient is derived.

(4) Based on the finite difference method, the time history curve and displacement curve of block dynamic stability coefficient are given, and the influence of seismic wave characteristics on block dynamic stability coefficient and displacement is analyzed. Based on catastrophe theory, the catastrophe criterion of dynamic response amplification coefficient of block displacement is proposed. Finally, the evaluation method of block dynamic stability of rock slope under earthquake is proposed, which provides a theoretical basis for slope disaster prevention and control, and has important theoretical significance and engineering reference value.

[1] 夏宇. 塘垭矿山边坡块体稳定性研究[D]. 宜昌:三峡大学, 2020.

[2] 岳彩亚, 党亚民, 杨强, 等. 汶川8级大地震对川滇菱形区域内次级块体的运动影响分析[J]. 测绘通报, 2017(01): 30-34+57.

[3] 程丰, 李德威, Bartholomew J, 等. 玉树地震地表破裂特征及其破裂方式[J]. 大地构造与成矿学, 2012, 36(01): 69-75.

[4] 王阳, 李君, 刘雷, 等. 2013年芦山7.0级地震构造活动特征分析[J]. 高原地震, 2019, 31(02): 20-25.

[5] 胡志奇, 郑文衡, 陆明勇. 岩体动态应力在地震机理中的作用研究[J]. 大地测量与地球动力学, 2005(01): 108-112.

[6] Grasselli G. Shear strength of rock joints based on quantified surface description[D]. Lausanne: EPFL, 2001.

[7] Homand F, Belem T, Souley M. Friction and degradation of rock joint surfaces under shear loads[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2001, 25(10): 973-999.

[8] Jafari M K, Amini Hosseini K, Pellet F, et al. Evaluation of shear strength of rock joints subjected to cyclic loading[J]. Soil Dynamics and Earthquake Engineering, 2003, 23(7): 619-630.

[9] Fathi A, Moradian Z, Rivard P, et al. Shear mechanism of rock joints under pre-peak cyclic loading condition[J]. International Journal of Rock Mechanics and Mining Sciences, 2016, 83: 197-210.

[10] 刘博, 李海波, 刘亚群, 等. 循环荷载作用下节理凸起体概化破坏模型及剪切强度计算分析[J]. 岩石力学与工程学报, 2013, 32(S2): 3000-3008.

[11] 刘博, 李海波, 刘亚群. 循环剪切荷载作用下岩石节理变形特性试验研究[J]. 岩土力学, 2013, 34(09): 2475-2481+2488.

[12] 刘博, 李海波, 朱小明. 循环剪切荷载作用下岩石节理强度劣化规律试验模拟研究[J]. 岩石力学与工程学报, 2011, 30(10): 2033-2039.

[13] 陈占锋, 向娟, 范文臣. 循环剪切对岩石节理形貌与力学行为影响实验研究[J]. 中国科技论文, 2019, 14(02): 221-225+238.

[14] 倪卫达, 唐辉明, 刘晓, 等. 考虑结构面震动劣化的岩质边坡动力稳定分析[J]. 岩石力学与工程学报, 2013, 32(03): 492-500.

[15] Yang Z, Di C, Yen K. The effect of asperity order on the roughness of rock joints[J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38: 745-752.

[16] 张向阳, 曹平, 陈锐, 等. 循环剪切对节理面形貌及强度劣化规律的微观力学研究[J]. 有色金属(矿山部分), 2019, 71(04): 81-87.

[17] Belem T, Homand-Etienne F, Souley M. Fractal analysis of shear joint roughness[J]. International Journal of Rock Mechanics and Mining Sciences, 1997, 34(3): 130.e1-130.e16.

[18] Jiang Y, Li B, Tanabashi Y. Estimating the relation between surface roughness and mechanical properties of rock joints[J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(6): 837-846.

[19] Qiu X, Plesha M E, Huang X, et al. An investigation of the mechanics of rock joints—Part II. Analytical investigation[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1993, 30(3): 271-287.

[20] Huang X, Haimson B C, Plesha M E, et al. An investigation of the mechanics of rock joints—Part I. Laboratory investigation[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1993, 30(3): 257-269.

[21] 朱小明, 李海波, 刘博, 等. 含二阶起伏体的模拟岩体节理试样剪切特性试验研究[J]. 岩土力学, 2012, 33(02): 354-360.

[22] 朱小明, 李海波, 刘博, 等. 含一阶和二阶起伏体节理剪切强度的试验研究[J]. 岩石力学与工程学报, 2011, 30(09): 1810-1818.

[23] 朱小明, 李海波, 刘博. 循环剪切荷载作用下含二阶起伏体模拟岩石节理力学特性研究[J]. 岩土力学, 2014, 35(02): 371-379.

[24] 刘新荣, 邓志云, 刘永权, 等. 岩石节理峰前循环直剪试验颗粒流宏细观分析[J]. 煤炭学报, 2019, 44(07): 2103-2115.

[25] 郑博文, 祁生文. 岩体结构面动态剪切试验研究现状评述[J]. 地球物理学进展, 2015, 30(04): 1971-1980.

[26] 刘新荣, 许彬, 周小涵, 等. 软弱层峰前循环剪切宏细观累积损伤机制研究[J]. 岩土力学, 2021, 42(05): 1291-1303.

[27] Liu X, Liu Y, Lu Y, et al. Experimental and numerical study on pre-peak cyclic shear mechanism of artificial rock joints[J]. Structural Engineering and Mechanics, 2020, 74(3): 407-423.

[28] 董杉. 地震荷载作用下顺层岩质斜坡结构面剪切特性及形变位移计算方法研究[D]. 成都:成都理工大学, 2020.

[29] Patton F D. Multiple Modes of Shear Failure In Rock[C]//1st ISRM Congress. OnePetro, 1966.

[30] Barton N, Choubey V. The shear strength of rock joints in theory and practice[J]. Rock Mechanics, 1977, 10(1): 1-54.

[31] 赵坚. 岩石节理剪切强度的JRC-JMC新模型[J]. 岩石力学与工程学报, 1998(04): 1-9.

[32] Kulatilake P H, Shou G, Huang T H, et al. New peak shear strength criteria for anisotropic rock joints[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1995, 32(7): 673-697.

[33] Xia C C, Tang Z C, Xiao W M, et al. New Peak Shear Strength Criterion of Rock Joints Based on Quantified Surface Description[J]. Rock Mechanics and Rock Engineering, 2014, 47(2): 387-400.

[34] Lee H S, Park Y J, Cho T F, et al. Influence of asperity degradation on the mechanical behavior of rough rock joints under cyclic shear loading[J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(7): 967-980.

[35] Mroz Z, Giambanco G. A Interface Model for Analysis of Deformation Behaviour of Discontinuities[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1996, 20: 1-33.

[36] 李海波, 冯海鹏, 刘博. 不同剪切速率下岩石节理的强度特性研究[J]. 岩石力学与工程学报, 2006(12): 2435-2440.

[37] 尹显俊, 王光纶, 张楚汉. 岩体结构面切向循环加载本构关系研究[J]. 工程力学, 2005(06): 97-103+57.

[38] 王光纶, 尹显俊. 岩体结构面三维循环加载本构关系[J]. 清华大学学报(自然科学版), 2005(09): 1193-1197.

[39] 尹显俊, 王光纶. 岩体结构面法向循环加载本构关系研究[J]. 岩石力学与工程学报, 2005(07): 1158-1163.

[40] 肖卫国. 节理岩体本构模型和其细观力学方法理论研究[D]. 北京:北京交通大学, 2011.

[41] Ferrero A M, Migliazza M, Tebaldi G. Development of a New Experimental Apparatus for the Study of the Mechanical Behaviour of a Rock Discontinuity Under Monotonic and Cyclic Loads[J]. Rock Mechanics and Rock Engineering, 2010, 43(6): 685-695.

[42] Tsubota Y, Kunishi T, Iwakoke Y, et al. Fundamental studies on dynamic properties of rock joint under cyclic loading using mortar and Ryoke gneiss[J]. Dynamic Web Programming and HTML5, 2012: 225.

[43] 刘新荣, 邓志云, 刘永权, 等. 峰前循环剪切作用下岩石节理损伤特征与剪切特性试验研究[J]. 岩石力学与工程学报, 2018, 37(12): 2664-2675.

[44] 黄倩文. 砂岩结构面直剪破坏声发射特性识别试验研究[D]. 重庆:重庆交通大学, 2019.

[45] 祁生文, 伍法权, 孙进忠. 边坡动力响应规律研究[J]. 中国科学E辑:技术科学, 2003(S1): 28-40.

[46] 杨国香, 伍法权, 董金玉, 等. 地震作用下岩质边坡动力响应特性及变形破坏机制研究[J]. 岩石力学与工程学报, 2012, 31(04): 696-702.

[47] 周剑, 张路青, 王学良. 水平层状岩体边坡动力响应中的结构面效应研究[J]. 工程地质学报, 2011, 19(03): 352-358.

[48] Clough R W, Seed H B. Earthquake Resistance of Sloping Core Dams[J]. Journal of the Soil Mechanics and Foundations Division, 1963, 89(1): 209-242.

[49] Arango I, Seed H B. Seismic Stability and Deformation of Clay Slopes[J]. Journal of the Geotechnical Engineering Division, 1974, 100(2): 139-156.

[50] Anonymous. Initiation and displacement of landslide induced by earthquake — a study of shaking table model slope test[J]. Engineering Geology, 2011, 122(1-2): 106-114.

[51] Lin M L, Wang K L. Seismic slope behavior in a large-scale shaking table model test[J]. Engineering Geology, 2006, 86(2): 118-133.

[52] 王思敬, 薛守义. 岩体边坡楔形体动力学分析[J]. 地质科学, 1992(02): 177-182.

[53] 王建, 姚令侃, 蒋良潍. 边坡岩石块体动力响应及锚固抗震效应研究[J]. 公路交通科技, 2010, 27(03): 6-11.

[54] 王思敬, 张菊明. 边坡岩体滑动稳定的动力学分析[J]. 地质科学, 1982(02): 162-170.

[55] 薛守义, 王思敬, 刘建中. 块状岩体边坡地震滑动位移分析[J]. 工程地质学报, 1997(02): 36-41.

[56] 王勇智, 戚炜, 门玉明, 等. 强震区岩体动力破坏机制研究[J]. 岩土力学, 2005(11): 150-153.

[57] 周飞, 许强, 刘汉香, 等. 地震作用下含水平软弱夹层斜坡动力响应特性研究[J]. 岩土力学, 2016, 37(01): 133-139.

[58] 侯红娟, 许强, 吴金辉. 岩质斜坡动力响应特性的结构面效应研究[J]. 世界地震工程, 2015, 31(01): 224-231.

[59] 杨国香, 伍法权, 董金玉, 等. 地震作用下岩质边坡动力响应特性及变形破坏机制研究[J]. 岩石力学与工程学报, 2012, 31(04): 696-702.

[60] 董金玉, 杨国香, 伍法权, 等. 地震作用下顺层岩质边坡动力响应和破坏模式大型振动台试验研究[J]. 岩土力学, 2011, 32(10): 2977-2982+2988.

[61] 唐世雄, 么玉鹏, 刘鑫. 地震滑坡的形成机制及中美欧地震拟静力计算方法比较[J]. 西南公路, 2020(1): 5.

[62] 刘爱娟, 崔玉龙, 刘铁新. 考虑动态临界加速度的地震边坡永久位移预测模型研究[J]. 地震工程学报, 2021, 43(2): 8.

[63] 李亚鹏, 言志信. 地震作用下软弱夹层参数对岩质边坡锚固界面剪切作用影响[J]. 振动与冲击, 2019, 38(08): 48-53+79.

[64] 刘永权. 频发微震下库区顺层岩质边坡累积损伤演化机理及稳定性研究[D]. 重庆:重庆大学, 2017.

[65] 张昆祥. 地震诱发层状岩质斜坡动力响应数值模拟研究[D]. 北京:中国地质大学, 2020.

[66] Goodman R E. Methods of Geological Engineering in Discontinuous Rocks[M]. St. Paul: West Group, 1975.

[67] 侴万禧. 离散单元法的基本原理及其在岩体工程中的应用[J]. 岩石力学与工程学报, 1986(02): 165-172.

[68] 任青文. 块体单元法及其在岩体稳定分析中的应用[J]. 河海大学学报, 1995(01): 1-7.

[69] Shi G H, Goodman R E. Two dimensional discontinuous deformation analysis[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1985, 9(6): 541-556.

[70] 张彦君. 顺层岩质边坡地震稳定性及滑坡运移过程DDA模拟方法[D]. 大连:大连理工大学, 2019.

[71] Shahami M H, Bafghi A Y, Marji M F. Investigating the effect of external forces on the displacement accuracy of discontinuous deformation analysis (DDA) method[J]. Computers and Geotechnics, 2019, 111: 313-323.

[72] 冯登. 基于赤平极射投影和可靠度的岩质边坡稳定性分析方法[D]. 重庆:重庆交通大学, 2018.

[73] 石根华. 岩体稳定分析的赤平投影方法[J]. 中国科学, 1977(03): 260-271.

[74] 王思敬, 杨志法, 刘竹华, 等. 地下工程岩体稳定分析[M]. 北京:科学出版社, 1984.

[75] 杨志法, 王思敬, 高丙丽. 坐标投影图解法及其在岩石块体稳定分析中的应用[M]. 北京:科学出版社, 2008.

[76] Gao B, Li L, Chen L, et al. Visual research and determination of structural plane and free face of rock slopes[J]. Environmental Earth Sciences, 2021, 80(2): 48.

[77] 高丙丽, 陈立成, 张海祥, 等. CPG岩质边坡工程块体稳定性评价及可视化软件[P]. 中国专利: 2019SR0988878, 2019-09-24.

[78] 张菊明, 王思敬. 层状边坡岩体滑动稳定的三维动力学分析[J]. 工程地质学报, 1994(03): 1-12.

[79] 刘汉东. 考虑地震历时影响的岩质边坡楔体稳定性分析与计算[J]. 华北水利水电学院学报, 1991(4): 6.

[80] Fu X, Sheng Q, Tang H, et al. Seismic stability analysis of a rock block using the block theory and Newmark method[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2019, 43(7): 1392-1409.

[81] 徐栋栋. 基于块体理论的块体动力稳定性分析方法及应用[D]. 武汉:长江科学院, 2011.

[82] 祁生林, 祁生文, 伍法权, 等. 基于剩余推力法的地震滑坡永久位移研究[J]. 工程地质学报, 2004(01): 63-68.

[83] 杨昕光, 李永录. 中美边坡拟静力稳定分析方法的对比研究[J]. 工业建筑, 2019, 49(02): 98-102.

[84] Wang S, Wang F, Xiu Z. Dynamic shear strength of rock joints and its influence on key blocks[J]. Geofluids, 2019, 2019.

[85] Zhao T, Crosta G B, Dattola G, et al. Dynamic Fragmentation of Jointed Rock Blocks During Rockslide-Avalanches: Insights From Discrete Element Analyses[J]. Journal of Geophysical Research: Solid Earth, 2018, 123(4): 3250-3269.

[86] Tian Y, Wu Y, Li H, et al. Earthquake dynamic failure mechanism of dangerous rock based on dynamics and PFC3D[J]. Frontiers in Earth Science, 2021, 9: 644.

[87] Tian Y, Wang L, Jin H, et al. Dynamic response of seismic dangerous rock based on PFC and dynamics[J]. Advances in Civil Engineering, 2020, 2020.

[88] Yang Z, Di C, Yen K. The effect of asperity order on the roughness of rock joints[J]. International Journal of Rock Mechanics and Mining Sciences, 2001, 38(5): 745-752.

[89] Fox D J, KaÑa D D, Hsiung S M. Influence of interface roughness on dynamic shear behavior in jointed rock[J]. International Journal of Rock Mechanics and Mining Sciences, 1998, 35(7): 923-940.

[90] Hutson R W, Dowding C H. Joint asperity degradation during cyclic shear[J]. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1990, 27(2): 109-119.

[91] 倪卫达. 基于岩土体动态劣化的边坡时变稳定性研究[D]. 武汉:中国地质大学, 2014.

[92] 朱焕春. PFC及其在矿山崩落开采研究中的应用[J]. 岩石力学与工程学报, 2006(09): 1927-1931.

[93] Cundall P A, Strack O D. A discrete numerical model for granular assemblies[J]. Géotechnique, 1979, 29(1): 47-65.

[94] 杨志法, 高丙丽, 张路青, 等. 基于坐标投影图解的结构面和块体的计算机描述及其应用[J]. 岩石力学与工程学报, 2006(12): 2392-2398.

[95] 高丙丽. 坐标投影作图法的计算机化及其在结构面和块体稳定分析中应用[D]. 西安：西安科技大学, 2005.

[96] 孙玉科，牟会宠，姚宝魁. 边坡岩体稳定性分析[M]. 北京:科学出版社, 1988.

[97] Kuhlemeyer R L, Lysmer J. Finite Element Method Accuracy for Wave Propagation Problems[J]. Journal of the Soil Mechanics and Foundations Division, 1973, 99(5): 421-427.