Complex Structural Plane Distribution of High-Steep Rock Slope and Division of Statistical Homogeneous Zones
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摘要: 为根据结构面的空间分布特征合理划分岩体结构均质区，以西藏昌都市洛隆县察达村冻措曲左岸高陡岩质斜坡为研究对象，采用无人机多角度贴近摄影技术获取研究区高精度影像数据，并于室内完成斜坡高清三维实景模型重建与结构面信息解译；在大量结构面调查的基础上，分析研究了斜坡结构面的发育规律与成因机制.基于结构面空间分布特征，引入组内相关系数法，考虑结构面产状与密度，联合38等分施密特投影网进行岩体统计均质区划分，并与Pearson相关系数法进行对比.结果表明斜坡结构受构造应力场、断层以及风化作用控制，表现为结构面产状与密度在空间内差异性分布，斜坡最终被划分为14个不同的均质区.针对结构面产状与密度存在空间分异性的特点，Pearson相关系数法对样本间的一致性判别力较弱，而组内相关系数法评价效果较好，更适用于复杂岩体结构的统计均质区划分，具有一定的应用价值.Abstract: In order to reasonably demarcate the structural homogeneity according to the spatial distribution characteristics of the structural plane, this paper takes the high-steep rock slope of the left bank of Dongcuoqu, Chada Village, Luolong County, Changdu City, Xizang as the research object, adopts the multi-angle nap-of-the-object photography technology to obtain the high-precision image data of the study area and realize the reconstruction of slope 3D real scene model and the interpretation of structural plane information. Based on plenty of structural plane investigations, the development and genetic mechanism of structural plane are analyzed. On the basis of the spatial distribution characteristics of discontinuities with considering the orientation and density, the intraclass correlation coefficient method was introduced, combined with Schmidt plot divided into 38 equal areas, to divide structural homogeneity of rock mass and compared with Pearson's correlation coefficient method. The results show that the slope structure is controlled by tectonic stress field, fault and weathering, with the orientation and density of structural plane distributed differently in space. In addition, the slope is finally divided into 14 different homogeneous zones. In view of the characteristics of spatial differentiation of the orientation and density of structural plane, Pearson's correlation coefficient method has a weak ability to discriminate the homogeneity between samples, while the intraclass correlation coefficient method has a better evaluation effect, which is more suitable for the division of statistical homogeneity of complex rock structure with certain application value.
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图 1 研究区地质图及斜坡现场照片：研究区地质图（a），野外照片（b）
Fig. 1. Regional geological map and site photos of the slope: regional geological map (a), site photos of the slope (b)
图 2 多角度无人机贴近摄影测量示意：地形单元多角度贴近摄影（a），结构面多角度贴近摄影（b）
Fig. 2. Schematic views of UAV multi-angle nap-of -the-object photogrammetry: multi-angle close to terrain units for photogrammetry (a), multi-angle close to the structural planes for photogrammetry (b)
图 3 下半球等面积38网格划分
Fig. 3. Lower hemispherical surface divided into 38 equal area windows
图 4 斜坡多角度贴近模型（a）与结构面分组情况（b）
Fig. 4. Multi-angle nap-of -the-object model of the slope (a) and groups of dominant structure plane (b)
图 5 断裂影响带内结构面发育情况
a.低角度断层伴生结构面；b.高角度断层伴生结构面；c.断裂带结构（高角度断层上盘）
Fig. 5. The development of structural planes in the structure of the fault zone
图 7 随机结构面迹长分布直方图
Fig. 7. Histogram of trace length distribution of random discontinuities
图 8 随机结构面极点玫瑰花图
a.随机结构面优势组Ⅰ；b.随机结构面优势组Ⅱ；c.随机结构面优势组Ⅲ
Fig. 8. Pole rose diagrams of random discontinuities
图 9 斜坡风化层与致密层
a.风化层（高程：4 055 m）；b.致密层（高程：3 834 m）
Fig. 9. Weathered and compacted layer of slope
图 10 结构面密度随与坡顶距离的变化
Fig. 10. Variation of random discontinuities density with distance from slope top
图 11 斜坡统计均质区划分结果
a.坡面圆形窗口布设图；b.斜坡分区图
Fig. 11. Structural domain boundaries of the slope
表 1 ICC数据结构
Table 1. Data structure of ICC
受试者 测量者 1 2 … j … k 1 $ {x}_{11} $ $ {x}_{12} $ … $ {x}_{1j} $ … $ {x}_{1k} $ 2 $ {x}_{21} $ $ {x}_{22} $ … $ {x}_{2j} $ … $ {x}_{2k} $ … … … … … … … i $ {x}_{i1} $ $ {x}_{i2} $ … $ {x}_{ij} $ … $ {x}_{ik} $ … … … … … … … 
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表 2 不同类型ICC计算公式
Table 2. ICC calculation formulas of different types
McGraw and Wong（1996） Shrout and Fleiss（1979） 计算表达式 模型 类型 定义 单因素随机效应模型 单个测量者 绝对一致性 ICC（1, 1） $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{W}}}{M{S}_{\mathrm{R}}+(k+1)M{S}_{\mathrm{W}}} $ 单因素随机效应模型 多个测量者 绝对一致性 ICC（1, k） $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{W}}}{M{S}_{\mathrm{R}}} $ 双因素随机效应模型 单个测量者 一致性 - $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{E}}}{M{S}_{\mathrm{R}}+(k+1)M{S}_{\mathrm{E}}} $ 双因素随机效应模型 多个测量者 一致性 - $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{E}}}{M{S}_{\mathrm{R}}} $ 双因素随机效应模型 单个测量者 绝对一致性 ICC（2, 1） $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{E}}}{M{S}_{\mathrm{R}}+\left(k-1\right)M{S}_{\mathrm{E}}+\frac{k}{n}(M{S}_{\mathrm{C}}-M{S}_{\mathrm{E}})} $ 双因素随机效应模型 多个测量者 绝对一致性 ICC（2, k） $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{E}}}{M{S}_{\mathrm{R}}+\frac{M{S}_{\mathrm{C}}-M{S}_{\mathrm{E}}}{n}} $ 双因素混合效应模型 单个测量者 一致性 ICC（3, 1） $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{E}}}{M{S}_{\mathrm{R}}+(k-1)M{S}_{\mathrm{E}}} $ 双因素混合效应模型 多个测量者 一致性 ICC（3, k） $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{E}}}{M{S}_{\mathrm{R}}} $ 双因素混合效应模型 单个测量者 绝对一致性 - $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{E}}}{M{S}_{\mathrm{R}}+\left(k-1\right)M{S}_{\mathrm{E}}+\frac{k}{n}(M{S}_{\mathrm{C}}-M{S}_{\mathrm{E}})} $ 双因素混合效应模型 多个测量者 绝对一致性 - $ \frac{M{S}_{\mathrm{R}}-M{S}_{\mathrm{E}}}{M{S}_{\mathrm{R}}+\frac{M{S}_{\mathrm{C}}-M{S}_{\mathrm{E}}}{n}} $ 注：MSR. 行均方；MSW. 剩余均方；MSE. 误差均方；MSC. 列均方；n. 受试者数目；k. 测量值数目.
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表 3 4个采集窗口内随机结构面优势分组结果
Table 3. Clustering results of random discontinuities in four acquisition windows
窗口信息 结构面信息 序号 面积(m2) 产状 位置 总条数 优势组序 产状 倾向(°) 倾角(°) X(m) Y(m) Z(m) 倾向(°) 倾角(°) 1 3 547.5 106 59 3 359 902 17 229 759 3 814.5 342 1 159 77 2 236 63 3 133 35 2 662.3 135 61 3 359 805 17 229 802 3 716.3 94 1 170 65 2 203 70 3 97 55 3 857.9 128 62 3 360 257 17 229 963 3 749.4 47 1 149 72 2 245 80 3 66 36 4 2 347.5 179 75 3 360 403 17 229 727 3 987.3 140 1 158 77 2 224 76 3 118 39
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表 4 38等面积施密特网格内结构面
Table 4. Random discontinuities based on 38 equal area Schmidt grids
施密特网格编号 窗口编号 1 2 … 36 1 $ {n}_{\mathrm{1,1}} $ $ {n}_{\mathrm{1,2}} $ $ {n}_{\mathrm{1,36}} $ 2 $ {n}_{\mathrm{2,1}} $ $ {n}_{\mathrm{2,2}} $ $ {n}_{\mathrm{2,36}} $ … 38 $ {n}_{\mathrm{38,1}} $ $ {n}_{\mathrm{38,2}} $ $ {n}_{\mathrm{38,36}} $
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表 5 相邻窗口统计均质区划分结果
Table 5. Structural domain boundaries between adjacent windows
ICC系数法均质区窗口编号 窗口内结构面个数标准差 Pearson相关系数法均质区窗口编号 窗口内结构面个数标准差 1、2 7 1、2 7 3、4、7 20.2 3、4、7、8、14 63.1 8、14 42.5 5、6 11 5、6 11 9、10、11 8.5 9、10、11 8.5 12、13 53.5 12、13 53.5 15、16 21 15、16 21 17 - 17 - 18~20 35.9 18~23、25~29 75.3 21~23、27~29 35.5 25、26 1.5 24、30 24.5 24、30 24.5 31、32 4.5 31、32 4.5 33~36 47.4 33~36 47.4
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