Probabilistic Analysis of Large Slope Deformation Considering Soil Spatial Variability with Rotated Anisotropy
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摘要: 为揭示土体参数旋转各向异性空间变异性对边坡大变形特征的影响规律，将土体不排水抗剪强度参数模拟为旋转各向异性随机场，提出采用多重响应面法对随机场样本进行边坡稳定性安全系数高效求解和升序排列，进而使用随机物质点法按序模拟随机场样本的边坡大变形过程.以一饱和不排水粘土边坡为例，研究了旋转各向异性随机场的旋转角度β和弱主方向自相关长度θ2对边坡大变形特征和破坏模式的影响.结果表明：提出的基于多重响应面的随机物质点方法可以高效开展边坡大变形概率分析；β和θ2对边坡大变形特征和破坏模式均有显著影响；边坡大变形破坏的影响距离、滑动距离和滑动体积的平均值与标准差均随θ2的增加而增加；边坡大变形过程中可能产生4种破坏模式，其中深层滑动和渐进式滑动为该边坡模型的主要概率失稳模式.因此，提出的方法为边坡大变形概率分析提供了一条有效途径，考虑参数旋转各向异性空间变异性的边坡大变形概率分析对准确评估边坡失稳风险具有一定的理论参考意义.Abstract: To explore the influence of spatial variability of soil parameters with rotated anisotropy on probabilistic large slope deformation characteristics, a multiple response surface-based random material point method is proposed in this study. First, random field theory is employed to simulate the spatial variability of soil parameters with rotated anisotropy. Then, the multiple response surface method is used to evaluate the factor of safety (FS) of each random field sample, based on which the FSs for all random field samples are sorted efficiently in an ascending order. Finally, the random material point method is used to sequentially simulate the large deformation features of a slope for the failed samples with the FS at less than 1. An undrained clay slope is taken as the illustrative example, where the undrained shear strength of the soil is simulated as a rotated anisotropic random field. The effect of the rotational angle β and the autocorrelation length θ2 in the minor principal direction of the rotated anisotropic random field on the large deformation features and failure modes of the slope are systematically studied. The results show that the proposed method can be efficiently conducted for probabilistic analysis of large slope deformation. Both β and θ2 have significant effects on large slope deformation features and failure modes. In terms of large deformation features, the mean and standard deviation of the influence distance, sliding distance, and sliding volume increase with the increase of θ2. There might be four failure modes when considering the rotated anisotropic spatial variability of the undrained strength of the slope, among which the deep sliding mechanism and progressive failure are the two main probabilistic failure modes. Therefore, the proposed method provides an effective way for the probabilistic large slope deformation analysis as well as a good theoretical reference for an accurate risk assessment of slope stability.
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图 1 不同土体参数空间变异性现象
a.各向同性；b.横观各向异性；c.旋转各向异性；d.一般各向异性
Fig. 1. Practical phenomenon of soil spatial variability
图 2 不同空间变异性形式下随机场自相关系数三维曲面
a.各向同性随机场（θ1=1 m、θ2=1 m、β=0°）；b.横观各向异性随机场（θ1=5 m、θ2=1 m、β=0°）；c.旋转各向异性随机场（θ1=5 m、θ2=1 m、β=45°）
Fig. 2. Autocorrelation coefficient 3-D surfaces of random field under different forms of spatial variability
图 3 MPM计算流程示意
a.映射阶段；b.拉格朗日阶段；c.对流阶段
Fig. 3. Schematic diagram of material point method calculation flow
图 4 土体强度参数随机场属性值与物质点之间的映射方式
Fig. 4. The mapping mode between the random field properties and material points
图 5 随机多重响应面‒物质点法计算流程
Fig. 5. Flow chart of proposed random multiple response surface-material point method
图 8 物质点强度折减法确定性计算结果
a.折减系数为1.383；b.折减系数为1.384
Fig. 8. Deterministic slope stability analysis results by material point method with shear strength reduction method
图 10 MRSM和随机极限平衡法结果对比(R2=1)
Fig. 10. Comparison of multiple response surface method and random limit equilibrium method (R2=1)
图 12 滑动距离的均值和标准差收敛曲线
Fig. 12. Convergence curves of the mean and standard deviation of sliding distance
图 13 不同工况下的边坡破坏概率
Fig. 13. Probability of slope failure under different working conditions
图 14 边坡大变形特征统计值随旋转角度的变化曲线
a.影响距离；b.滑动距离；c.滑动体积
Fig. 14. Variations of statistics of slope large deformation features with rotational angle
图 15 不同旋转角度下滑动距离超越概率曲线
Fig. 15. Exceedance probability curves of sliding distance under different rotational angles
图 16 不同旋转角度下边坡大变形特征随弱主方向自相关长度的变化关系
a.影响距离；b.滑动距离；c.滑动体积
Fig. 16. Variations of statistics of large slope deformation features with the autocorrelation length in the minor principal direction under different rotational angles
图 17 不同弱主方向自相关长度下滑动距离超越概率曲线
a. β=0°; b. β=45°; c. β=135°
Fig. 17. Exceedance probability curves of sliding distance under different autocorrelation lengths in the minor principal direction
图 18 边坡破坏模式占比随旋转角度变化曲线
Fig. 18. Variations of proportion of slope failure modes with rotational angle
图 19 不同旋转角度下边坡破坏模式占比随弱主方向自相关长度的变化
a. β=0°; b. β=45°; c.β=135°
Fig. 19. Variations of proportion of slope failure modes with autocorrelation length in the minor principal direction under different rotational angles
图 20 不同破坏模式下边坡大变形特征分布直方图
a.影响距离；b.滑动距离；c.滑动体积
Fig. 20. Histograms of large slope deformation features under different failure modes
表 1 边坡土体参数
Table 1. Slope soil parameters
土体重度γ(kN·m-3) 弹性模量E(MPa) 泊松比$ \upsilon $ 不排水抗剪强度Su(kPa) 残余强度Su, res(kPa) 软化模量H(kPa) 19 100 0.3 100 0.5Su -50 
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表 2 概率分析工况参数
Table 2. Parameters used for various probabilistic analysis cases
土体参数 均值(kPa) 变异系数 概率分布 随机场样本数 强主方向自相关长度θ1(m) 弱主方向自相关长度θ2(m) 旋转角度
β(°)不排水抗剪强度Su 100 0.3 对数正态随机场 40 000 24 3 0、45、135 6 0、30、45、60、90、120、135、180 9 0、45、135 12 0、45、135
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表 3 不同破坏模式下边坡大变形特征统计值
Table 3. Statistics of large slope deformation features under different failure modes
序号 破坏模式 均值 标准差 影响距离（m） 滑动距离（m） 滑动体积（m2） 影响距离（m） 滑动距离（m） 滑动体积（m2） 1 浅层滑动 ‒ ‒ ‒ ‒ ‒ ‒ 2 中层滑动 16.84 20.37 583.49 4.50 3.95 99.66 3 深层滑动 23.47 16.77 899.14 6.89 4.50 186.87 4 渐进式滑动 27.05 25.09 963.65 9.36 6.93 309.77
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