System Reliability Analysis of Multi-Slip Surface Slopes Based on Geological Structure Detection
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摘要:
地质结构识别与强度参数不确定性量化是岩质边坡稳定性评估的核心问题.为此，提出了一种基于地质结构探测的多滑面边坡系统可靠度分析方法.该方法首先结合多道勒夫波分析（multichannel analysis of Love waves，MALW）与初至旅行时层析成像（first-arrival travel time tomography，FATT），实现软弱层与断层探测效果的互补.随后，通过弹性波速折减软弱层强度参数，统计获取其概率分布.最后，考虑参数不确定性，计算边坡地表位移及单一滑面与系统失效概率.该方法在两个边坡案例的测试中表明：多阶频散曲线对边坡深部及浅部软弱层的反演精度均优于基阶频散曲线，且勒夫波较瑞雷波受岩层界面起伏的影响更小.边坡断层在初至旅行时记录中表现为特定范围内的波动特征，基于该特征的反演可定位局部断层.对于多滑面边坡案例，结合地表位移，地质结构与各滑面单一失效概率，确定边坡主要受深层滑面控制.且该边坡系统失效概率受内摩擦角变异系数的影响远大于黏聚力.此方法能够有效探测边坡地质结构，定位软弱层与断层.可考虑软弱层内部裂隙结构和风化程度的影响，折减强度参数并量化其不确定性.能够准确识别关键控制滑动面，定量评估各潜在滑动面及系统失效概率，为边坡防治提供了科学依据和参考.
Abstract:The identification of geological structures and the quantification of uncertainties in strength parameters are crucial for assessing the stability of rock slopes. This study proposes a system reliability analysis method for multi-slip surface slopes based on geological structure detection. The method integrates multichannel analysis of Love waves (MALW) and first-arrival travel time tomography (FATT) to achieve complementary detection of weak layers and faults. Elastic wave velocities are used to reduce the strength parameters of weak layers, and their probabilistic distributions are statistically derived. By incorporating parameter uncertainties, the surface displacement of slopes and the failure probabilities of individual slip surfaces and the entire system are calculated. Case studies indicate that multi-mode dispersion curves achieve higher inversion accuracy for both deep and shallow weak layers compared to fundamental-mode dispersion curves, and Love waves are less affected by undulations at rock layer interfaces than Rayleigh waves. Slope faults exhibit characteristic wave fluctuations within specific ranges in first-arrival travel time records. Inversion based on these features enables the localization of local faults.In the case of multi-slip surface slopes, deep slip surfaces are identified as the primary controlling factor, and the system failure probability is more significantly affected by the coefficient of variation of the internal friction angle than by cohesion. This method effectively detects geological structures, locates weak layers and faults, and quantifies uncertainties in strength parameters, providing a scientific basis for slope stability analysis and mitigation measures.
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图 1 基于地质结构探测的多滑面边坡系统可靠度计算流程
Fig. 1. Workflow for system reliability analysis of multi-slip surface slopes based on geological structure detection
图 2 算例边坡横波速度剖面及MALW、FATT布设
a.模型Ⅰ及MALW测点；b.模型Ⅱ及FATT炮点和接收器；c.MALW线性阵列
Fig. 2. Shear wave velocity profiles of the example slope and layout for MALW and FATT
图 3 边坡倾斜面二维交错有限差分网格
Fig. 3. 2D staggered finite difference grid of the inclined slope surface
图 4 模型Ⅰ测点P1多道勒夫波信号及其频散能量分布
a.多道勒夫波记录；b.频散能量图
Fig. 4. Multichannel Love wave signals and dispersion energy distribution at observation point P1 of Model I
图 5 边坡反演层状结构
a.模型Ⅰ测点P1一维反演结果；b.模型Ⅰ二维速度剖面
Fig. 5. Inverted layered structure of the slope
图 7 速度模型与初至旅行时
a.初始速度模型；b.反演速度剖面；c.观测与初始初至旅行时对比；d.反演与初始初至旅行时对比
Fig. 7. Velocity model and first-arrival travel times
图 10 响应面预测与数值模拟对比
a. X方向地表位移对比；b. 安全系数对比
Fig. 10. Comparison between response surface predictions and numerical simulations
图 11 X方向地表位移概率分布
a.测点D8；b.测点D9；c.测点D10
Fig. 11. Probability distribution of surface displacement in the X-direction
图 12 边坡X方向位移云图及潜在滑动面
a.滑动面S1；b.滑动面S2
Fig. 12. Contour map of slope displacement in the X-direction and potential sliding surfaces
图 13 边坡安全系数收敛图及概率分布
a~b. 滑动面S1；c~d. 滑动面S2
Fig. 13. Convergence and probability distribution of slope safety factors
图 14 不同波动范围模型及对应频散能量图
a~c. 横波速度模型；d~f. 瑞雷波频散能量图；g~i. 勒夫波频散能量图
Fig. 14. Models with different fluctuation ranges and corresponding dispersion energy diagrams
图 16 不同变异系数下系统失效概率
Fig. 16. System failure probability under different coefficients of variation
表 1 各层参数设置
Table 1. Parameters of each layer
层号 Vs
(m/s)Kv ρ
(g/cm3)υ c (kPa) φ (°) E (GPa) 1 1 180 / 2.13 0.25 300 31 2.00 2 906 0.6 2.0 0.30 20 20 0.68 3 1 790 / 2.36 0.25 800 40 6.00 4 1 078 0.7 2.0 0.30 20 20 0.68 5 2 200 / 2.46 0.25 1 300 47 9.00 断层 232 / 1.75 0.30 30 25 0.50 注：Vs为横波波速；Kv为岩石完整性系数；ρ为密度，υ为泊松比；c为黏聚力；φ为内摩擦角. 
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表 2 勒夫波模拟的边界条件设置
Table 2. Boundary condition settings for Love wave simulation
网格类型 $ {\rho }_{y} $ $ \mu $ $ {\tau }_{xy} $ $ {\tau }_{zy} $ H 0.5$ {\rho }_{1} $ $ {\mu }_{1} $ 0 / VR 0.5$ {\rho }_{1} $ $ {\mu }_{1} $ / 0 IR 0.5$ {\rho }_{1} $ $ {\mu }_{1} $ 0 / OR 0.5$ {\rho }_{1} $ $ {\mu }_{1} $ / 0 注：$ {\rho }_{y} $及$ \mu $为自由界面网格的密度和拉梅系数；$ {\rho }_{1} $及$ {\mu }_{1} $为相邻固体网格的密度和拉梅系数；$ {\tau }_{xy} $及$ {\tau }_{zy} $为xy方向和zy方向应力分量.
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表 3 边坡强度参数
Table 3. Strength parameters of the slope
层号 ρ (g/cm3) c (kPa) φ (°) 1 2.13 300 31 2 2.00 logN (17.90, 2.14) logN (17.82, 2.29) 3 2.36 800 40 4 2.00 logN (18.60, 2.74) logN (18.53, 2.85) 5 2.46 1 300 47 断层 1.75 logN (30, 6) logN (25, 4) 注：ρ为密度；c及φ为黏聚力和内摩擦角；logN (μ, σ) 表示参数服从均值和标准差分别为μ和σ的对数正态分布.
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表 4 地表位移及安全系数响应面系数
Table 4. Response surface coefficients for surface displacement and safety factor
系数 D8 D9 D10 系数 FS1 FS2 a 94.239 4 97.855 0 0.177 8 a 2.413 6 0.803 1 b1 0.077 3 0.167 8 -0.000 2 b1 -0.052 0 0.014 3 b2 -1.636 6 -0.055 3 0.000 1 b2 0.025 6 0.005 8 b3 -0.351 4 -0.511 9 0.010 3 b3 -0.038 7 -0.037 8 b4 -5.560 9 -7.465 9 0.036 1 b4 -0.043 4 0.016 9 b5 -0.050 4 -0.037 3 -0.000 3 c1 0.001 7 -0.000 1 b6 -0.233 3 -0.272 3 -0.001 3 c2 0.000 8 0.001 6 c1 -0.004 1 -0.004 8 0 c3 0.000 7 0.000 6 c2 0.035 0 -0.000 7 0 c4 0.000 9 -0.000 3 c3 0.007 1 0.010 3 -0.000 2 ε 0.023 0 0.026 0 c4 0.130 4 0.173 4 -0.000 8 R2 0.971 5 0.954 6 c5 0.000 1 -0.000 2 0 c6 0.002 4 0.002 5 0 ε 0.211 0 0.250 9 0.002 0 R2 0.965 0 0.977 9 0.955 6 注：D8，D9及D10分别为对应测点的X方向位移；FS1为沿潜在滑动面S1破坏的安全系数；FS2为沿潜在滑动面S2破坏的安全系数.
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表 5 边坡模型参数
Table 5. Parameters of the slope model
层号 Vs (m/s) Vp (m/s) ρ (g/cm3) h 1 400 980 1.7 5 2 200 490 1.7 5 3 600 1470 1.7 半无限空间 注：Vs及Vp分别为横波速度及纵波速度；ρ为密度；h为层厚.
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