耦合确定性与随机结构面的岩质边坡概率稳定性分析

常志璐; 余琦; 钟敏; 蒋水华; 向晖; 关宏涛; 孟京京; 黄发明

doi:10.19509/j.cnki.dzkq.tb20240388

耦合确定性与随机结构面的岩质边坡概率稳定性分析

doi: 10.19509/j.cnki.dzkq.tb20240388

常志璐^{1a, 1b,},
余琦^1a,
钟敏^1a,
蒋水华^1a, ,,
向晖²,
关宏涛²,
孟京京^1a,
黄发明^1a

1a.
南昌大学工程建设学院
1b.
南昌大学资源与环境学院，南昌 330031
2.
中建铁路投资建设集团有限公司，北京 102600

基金项目: 国家自然科学基金项目（52222905, 42407241）；江西省自然科学基金资助项目（20242ACB221001, 20232ACB204031, 20224ACB204019, 20242BAB20241）；江西省水利科技计划资助项目（202325ZDKT07, 202426ZDKT12）

详细信息

作者简介:
常志璐：E-mail：zhiluchang@ncu.edu.cn

通讯作者:
E-mail：sjiangaa@ncu.edu.cn

计量
- 文章访问数: 144
- PDF下载量: 9
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-11
- 录用日期: 2024-10-22
- 修回日期: 2024-09-11
- 网络出版日期: 2024-10-22

Probabilistic stability analysis of rock slopes with coupled determining and random discontinuities

CHANG Zhilu^{1a, 1b
,},
YU Qi^1a,
ZHONG Min^1a,
JIANG ShuiHua^{1a
, ,},
XIANG Hui²,
GUAN Hongtao²,
MENG Jingjing^1a,
HUANG Faming^1a

1a.
Nanchang University School of Infrastructure Engineering
1b.
Nanchang University School of Resources & Environment, Nanchang University, Nanchang 330031, China
2.
China State Construction Railway Investment & Engineering Group Co., Ltd., Beijing 102600, China

More Information

Author Bio:
E-mail：zhiluchang@ncu.edu.cn

Corresponding author: E-mail：sjiangaa@ncu.edu.cn

摘要

摘要:
岩质边坡广泛发育确定性结构面和随机结构面，使得岩体具有不连续性和非均质性特征，直接影响边坡的稳定性、变形特征和破坏模式。然而，目前研究较少同时考虑确定性结构面和随机结构面网络对岩质边坡概率稳定性分析和破坏机制的影响。采用离散元方法和结构面网络模拟技术，构建了边坡确定性结构面和随机结构面耦合分析模型，并基于此提出了边坡概率稳定性分析方法，最后以简化岩质边坡模型和锦屏一级水电站左岸坝肩边坡（天然和开挖工况）为例，验证了该方法的有效性。结果表明：（1）提出的方法不仅可以准确模拟确定性结构面与随机结构面网络，而且实现了结构面网络与边坡模型耦合建模；（2）同时考虑确定性结构面和随机结构面边坡概率稳定性分析方法可以获得边坡稳定系数概率分布图，计算结果更全面并符合工程实际；（3）随机结构面网络在开挖边坡工况下对边坡稳定性影响更显著，并且控制边坡的失稳路径和和破坏机制。研究成果可为制定岩质边坡开挖和支护方案提供参考，同时为地质灾害防治提供理论依据。
- 岩质边坡 /
- 随机结构面网络模拟 /
- 确定性结构面 /
- 概率稳定性分析
Abstract: Objective
Stability analysis of rock slopes is crucial for ensuring the normal construction and safe operation of engineering facilities. Instability of slopes can cause severe casualties and economic losses. The widespread presence of determining and random discontinuities within rock slopes leads to rock mass discontinuity and heterogeneity, significantly affecting slope stability, deformation characteristics, and failure modes. Therefore, studying the development characteristics of discontinuities and their influence on slope stability is vital for slope protection and disaster prevention. However, existing studies rarely consider both determining discontinuities and random discontinuity networks when constructing rock slope models for probabilistic stability analysis and failure mechanisms.
Methods
In this study, a three-dimensional numerical slope model was constructed using Rhino software. The discrete fracture network (DFN) model was applied to generate both determining and random discontinuity networks based on field discontinuity data. A coupling analysis model for random discontinuities was then developed by integrating the slope model and discontinuity networks via 3DEC software. A probabilistic stability analysis method was proposed to analyze the effects of random discontinuities on slope stability. Finally, the proposed method was demonstrated using a simplified rock slope model to assess the impact of random discontinuity networks on slope stability, along with a probabilistic stability analysis of the left bank shoulder slope of the Jinping I Hydropower Station under natural and excavated slope conditions.
Results
The results indicate that (1) The proposed method effectively and accurately simulates both the deterministic and random discontinuity networks, as well as coupling the discontinuity network with the rock slope model. (2) The probabilistic distribution of the slope stability coefficient can be obtained, and the results are more comprehensive and aligned with engineering practice. (3) The random discontinuity network has a greater impact on slope stability under excavated slope conditions and alters the failure path and instability mechanism of the rock slope.
Conclusion
The research results provide references for excavation and support schemes for rock slopes in engineering practice and offer a theoretical basis for geological disaster prevention and control.
- rock slope /
- random discontinuity network simulation /
- determining discontinuity /
- probabilistic stability analysis

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图 1 确定性与随机结构面网络耦合建模框架

Figure 1. Coupling modelling framework for determining random discontinuity networks

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图 2 裂隙边坡生成示意图

Figure 2. Diagram of fracture slope formation

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图 3 块体单元间相互作用力示意图

F_n. 不同块体间相互作用力的法向分力；U_n. 块体间法向位移；F_s. 不同块体间相互作用力的切向分力；∆F_s. F_s的增量，表示剪力；∆U_s. U_s的增量，表示两离散单元间的相对位移

Figure 3. Diagram of the interaction forces between block elements

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图 4 岩质边坡简化模型

Figure 4. Simplified model of a rock slope

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图 5 3DEC生成的2种边坡模型图

Figure 5. Slope model diagrams generated via 3DEC

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图 6 考虑DFN的100组边坡稳定系数概率分布图

Figure 6. Probability distributions of 100 groups of slope stability coefficients considering the DFN

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图 7 Ⅱ₁-Ⅱ₁工程地质剖面图及开挖前实物图

Figure 7. Engineering geological profile of section Ⅱ₁-Ⅱ₁ and a photograph of the physical slope

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图 8 天然边坡（a）和开挖后边坡（b）计算模型

Figure 8. Calculation model diagram of the natural slope (a) and excavation slope (b)

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图 9 考虑确定性结构面天然（a）和开挖（b）边坡位移云图

Figure 9. Displacement cloud maps of natural and excavation slope considering determining discontinuities

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图 10 考虑DFN100组天然（a）和开挖（b）边坡稳定系数分布图

Figure 10. Probability distributions of 100 groups of natural (a) and excavation (b) slope stability coefficients considering the DFN

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图 11 考虑DFN模型的天然（a）和开挖（b）边坡位移云图

Figure 11. Displacement cloud maps of natural (a) and excavated (b) slopes considering the DFN model

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表 1 结构面分级

Table 1. Classification of discontinuities

结构面级别	特性
结构面级别	代表性结构面	发育情况	影响作用
Ⅰ级	深大断裂带	延伸数十公里、至少切穿一个构造层、宽度在数米以上	控制区域岩体稳定性
Ⅱ级	不整合面、原生软弱夹层、断层等	延伸数百米以上、宽度不超过3～5 m	组合控制岩体稳定性
Ⅲ级	断层、风化夹层、破碎带、层间错动等	延伸数百米范围、宽度约1 m	控制块体滑移机理
Ⅳ级	节理、层面、片理面等	延伸数米范围，不超过20～30 m、无明显宽度	影响岩体破坏方式、力学性质和应力分布情况
Ⅴ级	微小节理等	延展性极差、无厚度差别	影响岩块的强度和破坏方式

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表 2 DFN template参数及分布设置

Table 2. Parameters and distribution of the DFN template

分布特征	结构面参数
分布特征	产状	空间位置	尺寸
高斯分布	√	√	√
均匀分布	√	√	√
bootstrapped	√	√	√
fish自定义	√	√	√
power-law	/	/	√
fisher	√	/	/

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表 3 随机结构面参数及分布特征

Table 3. Parameters and distribution characteristics of random discontinuities

组别	倾角/(°)			迹长/m			空间位置
组别	分布特征	均值 μ	标准差 σ	分布特征	均值 μ	标准差 σ	分布特征	面密度
J₁	对数正态	80.5	6.32	对数正态	1.72	1.35	均匀	0.25
J₂	正态	39.1	8.47	负指数	2.48	1.70	均匀	0.25

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表 4 简化岩质岩体力学参数取值

Table 4. Values of rock mass mechanics parameters simplified rock slope

重度γ/ (kN·m⁻³)	体积模量 B/GPa	剪切模量 G/GPa	黏聚力 c/kPa	内摩擦角 $\varphi $/(°)
20.0	1.0	0.3	200.0	50.0

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表 5 简化岩质结构面力学参数取值

Table 5. Values of the discontinuity mechanics parameters simplified rock slope

	法向刚度 K_n/(GPa·m⁻¹)	切向刚度 K_s/(GPa·m⁻¹)	黏聚力 c/kPa	内摩擦角$\varphi $/(°)
DFN	20.0	2.0	15.0	29.4
确定性结构面	10.0	1.0	5.0	35.0

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表 6 锦屏一级水电站左岸边坡岩体参数取值

Table 6. Values of the rock mass mechanics parameters left bank shoulder slope of Jinping Ⅰ Hydropower Station

岩体类别	弹性模量 E/GPa	泊松比	重度γ/ (kN·m⁻³)	黏聚力 c/kPa	内摩擦角 $\varphi $/(°)
Ⅳ₂岩体	1.90	0.300	27	400	30.96
Ⅳ₁岩体	2.50	0.300	27	600	34.99
Ⅲ₂岩体	5.50	0.275	27	900	45.57
Ⅲ₁岩体	10.50	0.250	27	1500	46.94
Ⅱ岩体	23.50	0.225	27	2000	53.47

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表 7 锦屏一级水电站左岸边坡结构面参数取值

Table 7. Values of the discontinuity mechanics parameters left bank shoulder slope of Jinping Ⅰ Hydropower Station

结构面	法向刚度 K_n/(GPa·m⁻¹)	切向刚度 K_s/(GPa·m⁻¹)	黏聚力 c/kPa	内摩擦角 $\varphi $/(°)
煌斑岩脉X	6.0	6.0	20.0	16.7
断层f_42-9	4.0	4.0	20.0	16.7
断层f₅	5.0	5.0	20.0	16.7
断层f₈	5.0	5.0	20.0	16.7
断层f₂	5.0	5.0	20.0	16.7

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表 8 节理裂隙几何参数统计特征

Table 8. Statistical characteristics of the geometry

组号	统计特征	均值μ	标准差σ	分布类型
1	倾角/(°)	48.17	11.27	正态
1	迹长/m	26.21	3.32	负指数
2	倾角/(°)	61.26	8.11	对数正态
2	迹长/m	2.50	0.33	正态
3	倾角/(°)	59.05	5.99	正态
3	迹长/m	2.49	0.37	正态
4	倾角/(°)	70.01	11.30	均匀
4	迹长/m	3.07	1.62	正态

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