Seepage and Instability Characteristics of Slope Based on Spatial Variation Structure of Saturated Hydraulic Conductivity
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摘要: 以往研究一般采用单随机变量方法（SRV）或基于水平或垂直方向波动范围生成的空间变异随机场来模拟岩土参数的空间变异性，对具有倾斜定向特征的空间变异随机场未有涉及.基于条件模拟相关理论和非侵入式随机有限元的理论框架，提出了利用序贯高斯模拟方法进行斜坡参数条件随机场模拟并运用有限元方法进行斜坡渗流和稳定性分析的方法.针对理想边坡，对各向同性和几何各向异性的共7种空间变异结构的饱和渗透系数（Ks）各进行了200次条件随机场模拟，基于条件随机场模拟结果进行了有限元渗流和稳定性计算，对每种空间变异结构多次计算结果进行了统计分析.结果表明：本文所提出的方法不仅再现了研究区域参数的空间二阶统计特性，通过设定变异函数参数进行不同空间变异类型、变异程度、变异定向性的随机场模拟，同时利用现场观测数据对随机场模拟结果进行条件限制，从而提高了随机场的赋值精度；Ks的空间变异结构对孔隙水压力的分布规律、地下水位线变化范围、稳定性系数和最危险滑动面分布特征均有一定程度的影响.本研究为库岸斜坡稳定性评价提供方法支撑.Abstract: In the previous studies, the spatial variability of geotechnical parameters was simulated based on singe random variable approach (SRV) or random field approach (RF) according to the horizontal or vertical fluctuation range. The spatial variable conditional random field with slant directional characteristics was not involved. Based on the conditional modelling theory and the framework of non-intrusive stochastic finite element method, an original method has been proposed to study the slope seepage and instability characteristics considering spatial variation structure of Ks. This method firstly simulates the conditional random fields of slope parameters taking advantage of sequential Gaussian simulation method (SGS). The Ks random field realizations of a hypothetic slope has been generated in terms of seven different spatial variation structures repeatedly for 200 times. The considered scenarios involved isotropic structure with various ranges (a) and geometric anisotropic structure with various maximum correlation orientations. Seepage and stability analysis was then performed repeatedly according to the assignment random field using finite element method (FEM). According to the FEM analysis results, statistical analysis was then carried out to find the seepage and instability characteristic of the considering seven spatial variation scenarios. The results, on the one hand, show that the proposed method has the priority of reproducing the second-order spatial statistical characteristic of parameters within the study area by the means of changing the variogram parameters to simulate random fields with different spatial variation types, degrees and orientations. The uncertainty of the random field value assignment adjacent to the measurement locations is also much reduced due to the constraints of field measurements. On the other hand, the results show that the spatial variation structure of Ks has a certain impact on pore-water pressure distribution, phreatic line variation bound, factor of safety and most critical slip surface distribution. This research provides methodology support for reservoir slope stability evaluation.
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图 3 斜坡随机场模拟示意图
图中数字编号为SGeMS系统给每个单元分配的序号
Fig. 3. Simulated random field diagram of slope
图 4 序贯高斯模拟条件随机场流程
Fig. 4. Flow chart of sequential Gaussian conditional random field simulation
图 5 不同空间变异结构的土性参数随机场模型
a.各向同性；b.各向同性；c.各向同性；d.几何异性，δ=90°；e.几何异性，δ=β；f.几何异性，δ=180°-β；g.几何异性，δ=0°
Fig. 5. Random field of parameters with different spatial variation structure
图 6 基于条件随机场的非侵入式随机有限元分析方法流程
Fig. 6. Flow chart of non-intrusive finite element analysis method based on conditional random field simulation
图 8 Ks空间变异结构b的渗流模拟结果
图中数字表示孔隙水压力(kPa)
Fig. 8. Seepage simulation result of a representative realization (spatial variation structure b)
图 9 XX孔隙水压力中位数剖面
a.各向同性情况与确定性分析；b.几何异性情况与确定性分析
Fig. 9. Median value of pore water pressure along section XX
图 10 YY孔隙水压力中位数剖面
a.各向同性情况与确定性分析；b.几何异性情况与确定性分析
Fig. 10. Median value of pore water pressure profiles along section YY
图 11 负孔隙水压力界限与归一化变程相关关系
Fig. 11. Correlation between bound of negative pore water pressure and normalized range
图 13 地下水位变化范围与归一化变程相关关系
Fig. 13. Correlation between bound of groundwater table and normalized range
图 14 不同渗透系数空间变异结构的稳定性系数平均值
Fig. 14. Mean value of stability coefficient under various spatial variation cases of Ks
表 1 理想斜坡计算模型参数
Table 1. Parameters for the hypothetic slope study cases
参数(单位) 值 坡高H(m) 50 坡角β(°) 27 垂直降雨量q(m/s) 5×10-7 饱和渗透系数Ks均值(m/s) 5×10-5 有效粘聚力c′均值(kPa) 12 有效内摩擦角ϕ′均值(°) 26 KsA(m/s) 8×10-5 KsF(m/s) 5×10-5 KsE(m/s) 3×10-5 KsD(m/s) 4×10-5 注：KsA、KsF、KsE和KsD分别代表A、F、E和D处的Ks. 
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表 2 负孔隙水压力界限值
Table 2. Inter quartile range values of negative pore water pressure
IQR(kPa) 各向同性类型 几何异性类型 a b c d e f g XX 15.29 20.77 37.58 31.00 29.09 22.62 86.21 YY 17.30 20.38 44.25 31.30 84.10 53.40 55.58
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表 3 地下水位变化范围D
Table 3. Bounds of groundwater table D
参数 各向同性 各向异性 a b c d e f g D(m) 12.61 14.73 18.75 19.15 17.60 15.07 14.93
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