A New 3D Visualization Method for Rock Mass Fractures and Its Application
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摘要: 快速准确地识别岩体裂隙的三维分布特征是西南山区铁路防灾减灾的关键.本研究提出了一套岩体裂隙可视化新方法，基于测窗调查的裂隙数据，依托球坐标及极射赤平投影进行数字化处理及降维，利用K-Means++聚类算法、Fisher分布模型和蒙特卡洛模拟，完成裂隙产状数据的自动分组和模拟，最后运用Python及圆盘模型实现岩体裂隙三维可视化.本研究采用坐标变换和三角网格曲面的方式，更有利于与其他三维建模软件嵌套分析.水电站工程的先行应用研究表明产状数据服从Fisher分布，本文的模型相对于传统玫瑰花图和施密特图有着一定的优势.因此，本文建立的岩体裂隙模型具有直观快速反映区域裂隙网络三维分布特征的优点，研究成果可以直接服务于西南山区铁路施工阶段隧道掌子面及洞壁的节理裂隙三维识别以及防灾减灾研究.Abstract: Identifying the three-dimensional distribution characteristics of rock mass fractures quickly and accurately is the key to the prevention and reduction of disasters on the railway in the mountainous area of southwest China. In this study, a new method for rock mass fracture visualization is proposed. The digital processing and dimension reduction of data are completed by the spherical coordinates and polar stereographic projection. K-Means++ clustering algorithm, Fisher distribution model and Monte Carlo simulation are used for automatic fracture occurrence data classification and simulation. Finally, the 3D visualization of fracture data is realized by Python and disc model. This research adopts coordinate transformation and triangular mesh surface, which is more conducive to nested analysis with other 3D modeling software. The advance application research of Hydropower Station project shows that the occurrence data correspond to Fisher distribution, and the model in this paper has certain advantages over the traditional rose chart and Schmidt chart. Therefore, the rock mass fracture model established in this paper describes the 3D distribution characteristics of regional fracture network intuitively and quickly. The research results can be directly applied to the fracture 3D visualization of tunnel face image and future disaster prevention and reduction of the railway in the mountain area of southwest China.
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图 3 分组及模拟
a. 极点图；b. 肘部法则；c. 极点分组（蓝色第一组，绿色第二组，红十字为中心，下同）；d. 极点模拟（模拟数据量和原始数据量一致，由于原始数据有重叠，所以图中看起来模拟的数据大于原始数据量）
Fig. 3. Grouping and simulation
图 4 裂隙网络三维建模流程
a. 水平圆盘；b. 倾角为φ的圆盘；c. 产状为θ∠φ的圆盘；d. 裂隙网络模型
Fig. 4. 3D modeling process of fracture network
图 6 PD04可视化结果
a. PD04产状玫瑰花图；b. PD04施密特图；c. PD04极点图；d. 肘部法则；e. 极点分组（蓝色为第1组，绿色为第2组，紫色为第3组）；f. 极点模拟（实际测窗大小为5 m，模拟时方盒长为10 m，所以此处模拟数据量按线密度扩大两倍）
Fig. 6. The visualization results of PD04
表 1 平硐数据
Table 1. Adit data
平硐编号 方位角（°） 高程（m） 深度（m） PD1 8 968.385 79.0 PD2 122 975.735 167.8 PD03 112；158；176 972.504 542.8 PD04 10 1 080.377 69.5 PD6 115 1 300.986 94.4 PD8 112 1 200.033 94.4 PD11 146；179 972.290 41.0 PD16 116 973.941 108.5 PD24 8 967.382 152.0 PD201 112 971.405 102.0 PD202 112 971.870 101.0 PD203 112 1 083.563 145.3 PD203-204 202 1 082.493 100.8 PD204 37；112 1 079.504 125.5 
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表 2 平硐PD04数据
Table 2. Adit data of PD04
编号 产状 起点坐标（m） 终点坐标（m） 迹长（m） 同组间距（m） 1 305°∠22° (15.00, 1.65) (16.45, 1.85) 1.65 0 2 305°∠27° (16.50, 1.68) (15.80, 1.68) 0.70 0 3 245°∠24° (16.40, 1.57) (15.85, 1.50) 0.55 0 4 275°∠65° (16.62, 1.38) (15.00, 1.34) 2.10 0 5 100°∠25° (17.66, 1.20) (15.00, 1.40) 2.90 0 6 0°∠35° (16.75, 0.70) (16.15, 0.90) 0.60 0 7 90°∠23° (15.00, 1.10) (16.00, 0.90) 1.00 0 8 90°∠31° (16.40, 0.75) (15.90, 0.65) 0.50 0 9 90°∠32° (16.00, 0.70) (16.20, 0.45) 1.34 0 10 0°∠55° (16.45, 1.80) (17.20, 0.00) 1.90 0 … … … … … …
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表 3 模型验证
Table 3. Model validation
分组 RMSE MAE MAPE R2 第一组 0.276 0.288 0.097 0.714 第二组 0.014 0.096 0.060 0.867 第三组 0.211 0.333 0.042 0.950
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