Probabilistic stability analysis of rock slopes with coupled determining and random discontinuities
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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。
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.
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表 1 结构面分级
Table 1. Classification of discontinuities
结构面
级别特性 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 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 产状 空间位置 尺寸 高斯分布 √ √ √ 均匀分布 √ √ √ bootstrapped √ √ √ fish自定义 √ √ √ power-law / / √ fisher √ / / 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 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 表 4 简化岩质岩体力学参数取值
Table 4. Values of rock mass mechanics parameters of 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 表 5 简化岩质结构面力学参数取值
Table 5. Values of the discontinuity mechanics parameters of simplified rock slope
法向刚度
Kn/(GPa·m−1)切向刚度
Ks/(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 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 of 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 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 of left bank shoulder slope of Jinping Ⅰ Hydropower Station
结构面 法向刚度
Kn/(GPa·m−1)切向刚度
Ks/(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f42-9 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 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 迹长/m 26.21 3.32 负指数 2 倾角/(°) 61.26 8.11 对数正态 迹长/m 2.50 0.33 正态 3 倾角/(°) 59.05 5.99 正态 迹长/m 2.49 0.37 正态 4 倾角/(°) 70.01 11.30 均匀 迹长/m 3.07 1.62 正态 -
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