基于DDA水–力耦合的三峡库区消落带岸坡破坏特征研究

doi:10.3724/1000-6915.jrme.2025.0277

摘要
图/表
参考文献
相关文章 (0)

全文: PDF (4766 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要降雨和库水位变化是造成消落带劣化的两大关键驱动因素，揭示三峡库区消落带岸坡在降雨与库水位变化等典型工况下的破坏演化机制与主控模式，提升对库区岸坡稳定性进行精准分析与数值模拟的能力，对库区岸坡稳定性分析具有重要的指导意义。基于非连续变形分析（DDA）方程推导水压力荷载子矩阵，并基于离散裂隙网络（DFN）提出了DFN-Voronoi块体离散的新方法。以青石6号坡为例，利用DDA水–力耦合方法，分别开展短期强降雨（45 mm/h）和库水位下降时的消落带岸坡破坏特征模拟分析。基于DFN-Voronoi块体离散的DDA水–力耦合计算方法，通过非连续介质变形模拟、渗流–应力动态耦合以及多阶段破坏模式可视化，系统揭示了不同工况下消落带岸坡破坏的演化机制与模式特征。结果表明：在2种裂隙类型的单轴压缩模拟中，所提出的DFN-Voronoi模型比传统Voronoi模型模拟结果的最大位移量误差分别降低了17%和13%，有效避免了随机离散导致的不合理破坏面生成。在案例模拟分析中，45 mm/h降雨工况下，随着水–力耦合作用的持续累积，消落带劣化呈现渐进式发展，具体表现为前缘弯曲溃屈剪出破坏，后缘推挤拉裂破坏。在库水位逐渐下降过程中，坡表离散块体失稳滚落，后缘张拉滑移破坏加剧，后者成为库水下降过程中消落带岸坡的主要破坏形式。基于DDA水–力耦合分析，揭示了经典工况下三峡库区消落带岸坡破坏模式，可为消落带岸坡稳定性评估、分阶段加固治理提供数值工具与理论参考。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	王林峰1
	2
	蔡波1
	谢明君1
	唐宁1
	杨智中1

关键词 ：边坡工程；三峡库区消落带；非连续变形分析（DDA）；水&ndash, 力耦合；DFN-Voronoi块体离散法；破坏特征

Abstract：Rainfall and changes in reservoir water levels are two key drivers of degradation in the hydro-fluctuation belt. This study aims to elucidate the damage evolution mechanism and the primary control modes of bank slopes within the hydro-fluctuation belt of the Three Gorges Reservoir area under typical conditions of rainfall and reservoir level fluctuations. By enhancing the accuracy of analysis and numerical simulation of bank slope stability in the reservoir area, this research holds significant value for guiding stability assessments of bank slopes in the region.
Initially, the water pressure loading sub-matrix is derived from the equations of discontinuous deformation analysis (DDA), and a novel method of DFN-Voronoi block discretization is proposed based on the discrete fracture network (DFN). Subsequently, a simulation analysis of the damage characteristics of the hydro-fluctuation belt—considering conditions of short-term heavy rainfall (45 mm/h) and reservoir water level decline—is conducted using the DDA hydro-mechanical coupling method, exemplified by the No. 6 slope of Qingshi. Through the DFN-Voronoi block discrete DDA coupled hydro-mechanical calculation method, the evolution mechanism and characteristic patterns of bank slope damage in hydro-fluctuation belts under varying conditions are systematically revealed. This is achieved by simulating the deformation of discontinuous media, the dynamic coupling of seepage and stress, and the visualization of multi-stage damage patterns. The results indicate that during uniaxial compression simulations across different fracture types, the proposed DFN-Voronoi model achieves a reduction in maximum displacement errors of 17% and 13%, respectively, compared to the traditional Voronoi model, effectively preventing unreasonable damage surfaces resulting from stochastic discretization. In case simulation analyses, under a working condition of 45 mm/h rainfall, the continuous accumulation of hydro-mechanical coupling leads to gradual degradation of the hydro-fluctuation belt. This iWANG Linfeng1, 2, CAI Bo1, XIE Mingjun1, TANG Ning1, YANG Zhizhong1
s specifically manifested as bending and collapse of the leading edge due to flexural shear damage, alongside pushing and pulling crack damage at the trailing edge. As the reservoir water level gradually declines, discrete blocks on the slope surface become destabilized and roll down, exacerbating tension-slip damage at the trailing edge. This latter form of damage emerges as the predominant type affecting bank slopes in the hydro-fluctuation belt during periods of reservoir water decline. Based on the DDA hydro-mechanical coupling analysis, this study reveals the damage patterns of bank slopes in the hydro-fluctuation belt of the Three Gorges Reservoir area under classical working conditions. The findings can provide numerical tools and reference values for evaluating the stability of bank slopes in the hydro-fluctuation belt and for managing reinforcement efforts in phases.

Key words： slope engineering')" href="#">

slope engineering hydro-fluctuation belt of the Three Gorges Reservoir Area discontinuous deformation analysis (DDA) hydro-mechanical coupling DFN-Voronoi block discretization method

')" href="#">failure characteristics

引用本文:

王林峰1，2，蔡波1，谢明君1，唐宁1，杨智中1. 基于DDA水–力耦合的三峡库区消落带岸坡破坏特征研究[J]. 岩石力学与工程学报, 2025, 44(9): 2262-2276.
WANG Linfeng1, 2, CAI Bo1, XIE Mingjun1, TANG Ning1, YANG Zhizhong1.

Failure characteristics of bank slopes in hydro-fluctuation belt of the Three Gorges Reservoir Area based on DDA hydro-mechanical coupling

. , 2025, 44(9): 2262-2276.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2025.0277 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I9/2262

[25]	KIM Y I，AMADEI B，PAN E. Modeling the effect of water，excavation sequence and rock reinforcement with discontinuous deformation analysis[J]. International Journal of Rock Mechanics and Mining Sciences，1999，36(7)：949-970.
[14]	刘国阳，李俊杰，康飞. 基于3D DDA方法滚石平台防护作用研究[J]. 防灾减灾工程学报，2020，40(5)：679-689.(LIU Guoyang，LI Junfei，KANG Fei，et al. Study on the protective effect of rockfall platform based on 3D DDA method[J]. Journal of Disaster Prevention and Mitigation Engineering，2020，40(5)：679-689.(in Chinese))
[1]	白林丰，黄波林，秦臻，等. 基于裂隙网络渗流差异的消落带岩体劣化空间预测方法[J]. 工程地质学报，2023，31(2)：449-459.(BAI Linfeng，HUANG Bolin，QIN Zhen，et al. Spatial prediction method of rock mass deterioration in drawdown zone based on seepage difference of fracture network[J]. Journal of Engineering Geology，2023，31(2)：449-459.(in Chinese))
[26]	胡训健，卞康，刘建，等. 离散裂隙网络对岩石力学性质和声发射特性影响的颗粒流分析[J]. 岩土力学，2022，43(增1)：542-552.(HU Xunjian，BIAN Kang，LIU Jian，et al. Particle flow code analysis of the effect of discrete fracture network on rock mechanical properties and acoustic emission characteristics[J]. Rock and Soil Mechanics，2022，43(Supp.1)：542-552.(in Chinese))
[15]	KAIDI S，ROUAINIA M，OUAHSINE A. Stability of breakwaters under hydrodynamic loading using a coupled DDA/FEM approach[J]. Ocean Engineering，2012，55：62-70.
[2]	闫国强，黄波林，殷跃平，等. 三峡库区岸坡消落带岩体劣化分形特征与演化预测研究[J]. 地质学报，2023，97(7)：2 399-2 407.(YAN Guoqiang，HUANG Bolin，YIN Yueping，et al. Research on fractal characteristics and evolution prediction of rock mass deteriorating in bank slope drawdown zone of the Three Gorges Reservoir area[J]. Acta Geologica Sinica，2023，97(7)：2 399-2 407.(in Chinese))
[27]	吴小刚，倪智伟，朱君星，等. 冻融循环作用下裂隙灰岩的力学特性及裂纹扩展特征研究[J]. 重庆大学学报，2025，48(8)：1-13.(WU Xiaogang，NI Zhiwei，ZHU Junxing，et al. Study on the mechanical properties and crack propagation characteristics of fractured limestone under freeze-thaw cycles[J]. Journal of Chongqing University，2025，48(8)：1-13.(in Chinese))
[16]	CHOO L Q，ZHAO Z，CHEN H，et al. Hydraulic fracturing modeling using the discontinuous deformation analysis(DDA) method[J]. Computers and Geotechnics，2016，76：12-22.
[3]	殷跃平，黄波林，李滨，等. 三峡库区消落带溶蚀岩体劣化指标研究[J]. 地质学报，2021，95(8)：2 590-2 600.(YIN Yueping，HUANG Bolin，LI Bin，et al. Research on the deterioration index of karst rock mass in the fluctuating water level zone of Three Gorges Reservoir area[J]. Acta Geologica Sinica，2021，95(8)：2 590-2 600.(in Chinese))
[28]	李宏强，姚忠劭，曾志杭，等. 冻融循环单轴压缩下不等长交叉裂隙砂岩变形破坏特征研究[J]. 三峡大学学报：自然科学版，2024，46(6)：65-72.(LI Hongqiang，YAO Zhongshao，ZENG Zhihang，et al. Study on deformation and failure characteristics of sandstone with unequal length cross cracks under uniaxial compression of freeze-thaw cycle[J]. Journal of China Three Gorges University：Natural Sciences，2024，46(6)：65-72.(in Chinese))
[4]	刘新荣，郭雪岩，许彬，等. 含消落带劣化岩体的危岩边坡动力累积损伤机制研究[J]. 岩土力学，2023，44(3)：637-648.(LIU Xinrong，GUO Xueyan，XU Bin，et al. Investigation on dynamic cumulative damage mechanism of the dangerous rock slope including deteriorated rock mass in hydro-fluctuation belt[J]. Rock and Soil Mechanics，2023，44(3)：637-648.(in Chinese))
[17]	李利平，范宏运，刘洪亮，等. 三维DDA方法的验证及其在隧道围岩垮塌控制中的应用[J]. 东南大学学报：自然科学版，2024，54(3)：531-538.(LI Liping，FAN Hongyun，LIU Hongliang，et al. Validation of 3D DDA method and its application to the control of rock collapse in tunnels[J]. Journal of Southeast University：Natural Science，2024，54(3)：531-538.(in Chinese))
[29]	WANG S，WANG L Q，ZHANG W G，et al . Fracture mode of water-immersed sandstone based on micro CT and statistical damage model under triaxial compression[J]. Engineering Fracture Mechanics，2025，35：110781.
[5]	刘新荣，王 ?，许彬，等. 消落带劣化下含锯齿状结构面岩质边坡动力响应机制研究[J]. 岩石力学与工程学报，2022，41(12)：2 377-2 388.(LIU Xinrong，WANG Yan，XU Bin，et al. Investigation on dynamic response mechanism of slopes with serrated structural planes under degradation of rock mass in hydro-fluctuation belt[J]. Chinese Journal of Rock Mechanics and Engineering，2022，41(12)：2 377-2 388.(in Chinese))
[18]	巩师林，凌道盛，胡成宝，等. 非连续变形分析中块体大转动问题研究[J]. 岩土力学，2020，41(11)：3 810-3 822.(GONG Shilin，LING Daosheng，HU Chengbao，et al. Study on large rotation problem of a block in discontinuous deformation analysis[J]. Rock and Soil Mechanics，2020，41(11)：3 810-3 822.
[6]	黄波林，王健，殷跃平，等. 基于裂隙网络的消落带岩体劣化区域分布研究[J]. 地下空间与工程学报，2020，16(6)：1 901-1 908. (HUANG Bolin，WANG Jian，YIN Yueping，et al. Spatial distribution analysis of degraded karst rock mass in fluctuation zone based on fracture network[J]. Chinese Journal of Underground Space and Engineering，2020，16(6)：1 901-1 908.(in Chinese))
[19]	PENG S，LI X，GAO J，et al. Representation of brittle rock plasto-elastic behaviour based on tangible cracks in discontinuous deformation analysis[J]. Engineering Fracture Mechanics，2023，283：109214.
[30]	殷跃平，黄波林，张枝华，等. 三峡工程库区地质灾害防治[M]. 北京：科学出版社，2022：384-389.(YIN Yueping，HUANG Bolin，ZHANG Zhihua，et al. Prevention and control of geological disasters in the Three Gorges Project Reservoir area[M]. Beijing：Science Press，2022：384-389.(in Chinese))
[31]	闫国强. 三峡库区典型灰岩顺层岸坡劣化演变与失稳机制研究[博士学位论文][D]. 武汉：中国地质大学，2022.(YAN Guoqiang. Study on the deterioration evolution and destabilization mechanism of typical tuff bedded bank slopes in Three Gorges Reservoir area[Ph. D. Thesis][D]. Wuhan：China University of Geosciences，2022.(in Chinese))
[7]	刘新荣，景瑞，缪露莉，等. 巫山段消落带岸坡库岸再造模式及典型案例分析[J]. 岩石力学与工程学报，2020，39(7)：1 321-1 332. (LIU Xinrong，JING Rui，MIU Luli，et al. Reconstruction models and typical case analysis of the fluctuation belt of reservoir bank slopes in Wushan[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(7)：1 321-1 332.(in Chinese))
[20]	CHEN K T，WU J H. Simulating the failure process of the Xinmo landslide using discontinuous deformation analysis[J]. Engineering Geology，2018，239：269-281.
[32]	王力，南芳芸，王世梅，等. 三峡库区降雨型滑坡入渗特征及变形机制-基于一维和二维模型试验研究[J]. 岩土力学，2023，44(5)：1 363-1 374.(WANG Li，NAN Fangyun，WANG Shimei，et al. Infiltration characteristics and deformation mechanism of rainfall-induced landslides in Three Gorges Reservoir Area based on 1D and 2D model tests[J]. Rock and Soil Mechanics，2023，44(5)：1 363-1 374.(in Chinese))
[8]	CHENG L，LIU Y R，YANG Q，et al. Mechanism and numerical simulation of reservoir slope deformation during impounding of high arch dams based on nonlinear FEM[J]. Computers and Geotechnics，2017，81：143-154.
[21]	GAO J，MITANI Y，CHEN G，et al. Extension of discontinuous deformation analysis method for coupled reactive transport problems[J]. Computers and Geotechnics，2024，165：105839.
[33]	黄波林，殷跃平，张枝华，等. 三峡工程库区岩溶岸坡消落带岩体劣化特征研究[J]. 岩石力学与工程学报，2019，38(9)：1 786-1 796. (HUANG Bolin，YIN Yueping，ZHANG Zhihua，et al . Study on deterioration characteristics of shallow rock mass in water the level fluctuation zone of karst bank slopes in Three Gorges Reservoir area[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(9)：1 786-1 796.(in Chinese))
[22]	GAO J，PENG S，CHEN G，et al. Coupled hydro-mechanical analysis for water inrush of fractured rock masses using the discontinuous deformation analysis[J]. Computers and Geotechnics，2023，56：105247.
[9]	XU W J，WANG S，BILAL M. LEM-DEM coupling for slope stability analysis[J]. Science China Technological Sciences，2020，63(2)：329-340.
[10]	SHI G H. Discontinuous deformation analysis-A new numerical model for the statics and dynamics of block systems[Ph. D. Thesis][D]. Berkeley：University of California，1988.
[34]	闫国强，黄波林，代贞伟，等. 三峡库区巫峡段典型岩体劣化特征研究[J]. 水文地质工程地质，2020，47(4)：62-72.(YAN Guoqiang，HUANG Bolin，DAI Zhenwei，et al. A study of the deterioration effect of limestone bank slope rock mass at the Wuxia section of the Three Gorges Reservoir area[J]. Hydrogeology and Engineering Geology，2020，47(4)：62-72.(in Chinese))
[23]	何传永，孙平. 非连续变形分析方法程序与工程应用[M]. 北京：中国水利水电出版社，2009：26-31.(HE Chuanyong，SUN Ping. Procedures and engineering applications of discontinuous deformation analysis methods[M]. Beijing：China Water Conservancy and Hydropower Press，2009：26-31.(in Chinese))
[35]	余姝，张枝华，黄波林，等. 三峡库区青石—抱龙段顺层灰岩库岸坡变形破坏机制[J]. 中国地质灾害与防治学报，2019，30(3)：18-23.(YU Shu，ZHANG Zhihua，HUANG Bolin，et al. Deformation mechanism of bedding limestone bank slope from Qingshi to Baolong，the Three Gorges Area[J]. The Chinese Journal of Geological Hazard and Control，2019，30(3)：18-23.(in Chinese))
[11]	SHI G H，GOODMAN R E. Generalization of two dimensional discontinuous deformation analysis for forward modeling[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1989，13(4)：359-380.
[24]	HUITT J L. Fluid flow in simulated fractures[J]. AICHE Journal，1956，2(2)：259-264.
[36]	黄波林，殷跃平，李滨，等. 三峡工程库区岩溶岸坡岩体劣化及其灾变效应[J]. 水文地质工程地质，2020，47(4)：51-61.(HUANG Bolin，YIN Yueping，LI Bin，et al. Rock mass deterioration and its catastrophic effect of karst bank slope in the Three Gorges Project Reservoir area[J]. Hydrogeology and Engineering Geology，2020，47(4)：51-61.(in Chinese))
[25]	KIM Y I，AMADEI B，PAN E. Modeling the effect of water，excavation sequence and rock reinforcement with discontinuous deformation analysis[J]. International Journal of Rock Mechanics and Mining Sciences，1999，36(7)：949-970.
[12]	刘国阳，孟海怡，宁宝宽，等. 基于三维非连续变形分析的巨石崩塌运动研究[J]. 岩土力学，2022，43(1)：246-256.(LIU Guoyang，MENG Haiyi，NING Baokuan，et al. Study on collapse and movement of a boulder based on 3D discontinuous deformation analysis[J]. Rock and Soil Mechanics，2022，43(1)：246-256.(in Chinese))
[13]	刘国阳，赵晟泽，钟智瑞，等. 柱状危岩体失稳运动三维DDA方法数值模拟分析[J]. 防灾减灾工程学报，2025，45(1)：179-187. (LIU Guoyang，ZHAO Shengze，ZHONG Zhirui，et al. Numerical simulation analysis of instability movement of columnar dangerous rock mass using 3D DDA[J]. Journal of Disaster Prevention and Mitigation Engineering，2025，45(1)：179-187.(in Chinese))
[26]	胡训健，卞康，刘建，等. 离散裂隙网络对岩石力学性质和声发射特性影响的颗粒流分析[J]. 岩土力学，2022，43(增1)：542-552.(HU Xunjian，BIAN Kang，LIU Jian，et al. Particle flow code analysis of the effect of discrete fracture network on rock mechanical properties and acoustic emission characteristics[J]. Rock and Soil Mechanics，2022，43(Supp.1)：542-552.(in Chinese))
[14]	刘国阳，李俊杰，康飞. 基于3D DDA方法滚石平台防护作用研究[J]. 防灾减灾工程学报，2020，40(5)：679-689.(LIU Guoyang，LI Junfei，KANG Fei，et al. Study on the protective effect of rockfall platform based on 3D DDA method[J]. Journal of Disaster Prevention and Mitigation Engineering，2020，40(5)：679-689.(in Chinese))
[27]	吴小刚，倪智伟，朱君星，等. 冻融循环作用下裂隙灰岩的力学特性及裂纹扩展特征研究[J]. 重庆大学学报，2025，48(8)：1-13.(WU Xiaogang，NI Zhiwei，ZHU Junxing，et al. Study on the mechanical properties and crack propagation characteristics of fractured limestone under freeze-thaw cycles[J]. Journal of Chongqing University，2025，48(8)：1-13.(in Chinese))
[15]	KAIDI S，ROUAINIA M，OUAHSINE A. Stability of breakwaters under hydrodynamic loading using a coupled DDA/FEM approach[J]. Ocean Engineering，2012，55：62-70.
[28]	李宏强，姚忠劭，曾志杭，等. 冻融循环单轴压缩下不等长交叉裂隙砂岩变形破坏特征研究[J]. 三峡大学学报：自然科学版，2024，46(6)：65-72.(LI Hongqiang，YAO Zhongshao，ZENG Zhihang，et al. Study on deformation and failure characteristics of sandstone with unequal length cross cracks under uniaxial compression of freeze-thaw cycle[J]. Journal of China Three Gorges University：Natural Sciences，2024，46(6)：65-72.(in Chinese))
[16]	CHOO L Q，ZHAO Z，CHEN H，et al. Hydraulic fracturing modeling using the discontinuous deformation analysis(DDA) method[J]. Computers and Geotechnics，2016，76：12-22.
[29]	WANG S，WANG L Q，ZHANG W G，et al . Fracture mode of water-immersed sandstone based on micro CT and statistical damage model under triaxial compression[J]. Engineering Fracture Mechanics，2025，35：110781.
[17]	李利平，范宏运，刘洪亮，等. 三维DDA方法的验证及其在隧道围岩垮塌控制中的应用[J]. 东南大学学报：自然科学版，2024，54(3)：531-538.(LI Liping，FAN Hongyun，LIU Hongliang，et al. Validation of 3D DDA method and its application to the control of rock collapse in tunnels[J]. Journal of Southeast University：Natural Science，2024，54(3)：531-538.(in Chinese))
[30]	殷跃平，黄波林，张枝华，等. 三峡工程库区地质灾害防治[M]. 北京：科学出版社，2022：384-389.(YIN Yueping，HUANG Bolin，ZHANG Zhihua，et al. Prevention and control of geological disasters in the Three Gorges Project Reservoir area[M]. Beijing：Science Press，2022：384-389.(in Chinese))
[18]	巩师林，凌道盛，胡成宝，等. 非连续变形分析中块体大转动问题研究[J]. 岩土力学，2020，41(11)：3 810-3 822.(GONG Shilin，LING Daosheng，HU Chengbao，et al. Study on large rotation problem of a block in discontinuous deformation analysis[J]. Rock and Soil Mechanics，2020，41(11)：3 810-3 822.
[31]	闫国强. 三峡库区典型灰岩顺层岸坡劣化演变与失稳机制研究[博士学位论文][D]. 武汉：中国地质大学，2022.(YAN Guoqiang. Study on the deterioration evolution and destabilization mechanism of typical tuff bedded bank slopes in Three Gorges Reservoir area[Ph. D. Thesis][D]. Wuhan：China University of Geosciences，2022.(in Chinese))
[32]	王力，南芳芸，王世梅，等. 三峡库区降雨型滑坡入渗特征及变形机制-基于一维和二维模型试验研究[J]. 岩土力学，2023，44(5)：1 363-1 374.(WANG Li，NAN Fangyun，WANG Shimei，et al. Infiltration characteristics and deformation mechanism of rainfall-induced landslides in Three Gorges Reservoir Area based on 1D and 2D model tests[J]. Rock and Soil Mechanics，2023，44(5)：1 363-1 374.(in Chinese))
[19]	PENG S，LI X，GAO J，et al. Representation of brittle rock plasto-elastic behaviour based on tangible cracks in discontinuous deformation analysis[J]. Engineering Fracture Mechanics，2023，283：109214.
[33]	黄波林，殷跃平，张枝华，等. 三峡工程库区岩溶岸坡消落带岩体劣化特征研究[J]. 岩石力学与工程学报，2019，38(9)：1 786-1 796. (HUANG Bolin，YIN Yueping，ZHANG Zhihua，et al . Study on deterioration characteristics of shallow rock mass in water the level fluctuation zone of karst bank slopes in Three Gorges Reservoir area[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(9)：1 786-1 796.(in Chinese))
[20]	CHEN K T，WU J H. Simulating the failure process of the Xinmo landslide using discontinuous deformation analysis[J]. Engineering Geology，2018，239：269-281.
[21]	GAO J，MITANI Y，CHEN G，et al. Extension of discontinuous deformation analysis method for coupled reactive transport problems[J]. Computers and Geotechnics，2024，165：105839.
[34]	闫国强，黄波林，代贞伟，等. 三峡库区巫峡段典型岩体劣化特征研究[J]. 水文地质工程地质，2020，47(4)：62-72.(YAN Guoqiang，HUANG Bolin，DAI Zhenwei，et al. A study of the deterioration effect of limestone bank slope rock mass at the Wuxia section of the Three Gorges Reservoir area[J]. Hydrogeology and Engineering Geology，2020，47(4)：62-72.(in Chinese))
[22]	GAO J，PENG S，CHEN G，et al. Coupled hydro-mechanical analysis for water inrush of fractured rock masses using the discontinuous deformation analysis[J]. Computers and Geotechnics，2023，56：105247.
[35]	余姝，张枝华，黄波林，等. 三峡库区青石—抱龙段顺层灰岩库岸坡变形破坏机制[J]. 中国地质灾害与防治学报，2019，30(3)：18-23.(YU Shu，ZHANG Zhihua，HUANG Bolin，et al. Deformation mechanism of bedding limestone bank slope from Qingshi to Baolong，the Three Gorges Area[J]. The Chinese Journal of Geological Hazard and Control，2019，30(3)：18-23.(in Chinese))
[23]	何传永，孙平. 非连续变形分析方法程序与工程应用[M]. 北京：中国水利水电出版社，2009：26-31.(HE Chuanyong，SUN Ping. Procedures and engineering applications of discontinuous deformation analysis methods[M]. Beijing：China Water Conservancy and Hydropower Press，2009：26-31.(in Chinese))
[36]	黄波林，殷跃平，李滨，等. 三峡工程库区岩溶岸坡岩体劣化及其灾变效应[J]. 水文地质工程地质，2020，47(4)：51-61.(HUANG Bolin，YIN Yueping，LI Bin，et al. Rock mass deterioration and its catastrophic effect of karst bank slope in the Three Gorges Project Reservoir area[J]. Hydrogeology and Engineering Geology，2020，47(4)：51-61.(in Chinese))