Intelligent Interpretation of Rock Mass Discontinuity Based on Three-Dimensional Laser Point Cloud
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摘要: 准确、高效、全面获取岩体结构面信息，对岩体的稳定性分析有着重要的意义.采用三维激光扫描设备进行岩体数据采集，基于岩体点云模型提出了结构面自动识别方法.通过对Ransac算法进行改进，引入了新的采样方法和评分准则，大大提升了Ransac算法的计算效率和提取精度，使之更好地适应粗糙不平的岩体点云数据；基于改进的Graham Scan算法可以精准描绘出结构面的凸凹边界，进而精细化计算出结构面尺寸.基于以上算法研发了结构面识别程序RDD（ransac discontinuity dtection），并且采用了两组标准几何体数据和一组岩体数据对程序进行测试.结果表明，标准几何体产状误差在1°以内，实际岩体最大误差在6°以内，结构面尺寸最大误差率为0.278%，满足工程限定的误差要求.
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关键词:
- 三维激光点云 /
- 结构面 /
- Ransac算法 /
- Graham Scan算法 /
- 工程地质
Abstract: The stability of rock mass is mainly controlled by a large number of internal discontinuities. Therefore, the accurate and efficient extraction of discontinuity information is a significant process to analyze the stability of rock mass. In the paper, the raw point cloud data is collected by three-dimensional laser scanner, a new approach about automatic extraction of discontinuity is proposed based on point cloud model of rock mass, which can automatically decipher the parameters of rock mass discontinuities. The new sampling method and evaluation method are successfully introduced based on the modified Ransac algorithm, the efficiency and accuracy of Ransac algorithm are rapidly improved to adapt rough point cloud data of rock mass. The modified Graham Scan algorithm is proposed to delineate the convex-concave boundary and to calculate the size for discontinuity. Based on the above algorithms, this paper developed a discontinuity extraction program named RDD (ransac discontinuity dtection). RDD is tested by two sets of standard geometry data and one set of rock mass data. The results indicate that the orientation error of standard geometry is less than 1ånd the maximum error of rock is less than 6°, which satisfy the prescriptive error requirements of engineering. -
图 1 [Qi]是Pi的近邻点集，n是Pi的法向量
Fig. 1. Qi is the subset of Pi, n is the normal vector of Pi
图 3 (a) Graham Scan边界检测效果；(b)改进后的Graham Scan边界检测效果
Fig. 3. (a) Boundary detection using Graham Scan, and (b) Boundary detection using modified Graham Scan
图 4 (a) 拟合平面的结果；(b)拟合平面的边界描绘
Fig. 4. (a) Result of the fitting plane, (b) Boundary delineation of the fitting plane
图 6 (a) 立方体模型；(b)立方体点云模型；(c)立方体平面识别
Fig. 6. (a)Cube Model; (b) cube point cloud Model; (c) identification of cube plane
图 7 (a) 二十面体模型；(b)二十面体点云模型；(c)二十面体平面识别
Fig. 7. (a)Icosahedron Model; (b) Icosahedron point cloud Model; (c) identification of Icosahedron plane
图 8 (a) 边坡照片；(b)边坡点云模型
Fig. 8. (a)Picture of the slope, (b) Point cloud data of the slope
图 11 结构面分组效果
a. Riquelme论文分组效果；b. 所提方法分组效果
Fig. 11. Picture showing the discontinuity sets
Algorithm 1 基于改进的Ransac算法提取平面
Algorithm 1. Extract plane based on modified Ransac algorithm
Input: P is a matrix which stores the point cloud. Output #1：Ψ is a matrix which stores the parameters of the extracted discontinuities.
Output #2：Pψ is a matrix which stores the points belonging to the corresponding discontinuities.
1：Ψ←Φ{extracted discontinuities}
2：C ←Φ{discontinuities candidates}
3: repeat
4: C ← C ∪ new candidates ()
5: m←best candidate(C)
6: if P(|m|, |c|)＞pt then
7: P ← P\Pm {remove points}
8: Ψ←Ψ ∪ m
9: C←C\Cm {remove invalid candidates}
10: end if
11: until P(τ, |c|)＞pt
12: return Ψ
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表 1 立方体平面几何信息提取
Table 1. Extraction of geometric properties of cube plane
平面 点云数量 倾角(°) 倾向(°) 面积(m2) 等效圆半径(m) 等效半径识别误差率(%) 平面1 8 162 90 180 0.983 0.559 0.179 平面2 8 134 90 90 0.984 0.56 0 平面3 8 109 0 180 0.979 0.558 0.357 平面4 8 120 0 0 0.981 0.559 0.179 平面5 8 101 90 90 0.986 0.56 0 平面6 8 121 90 0 0.982 0.559 0.179
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表 2 二十面体平面几何信息提取
Table 2. Identification of icosahedron plane
平面 点云数量 倾角(°) 倾向(°) 产状差值(°) 面积(m2) 等效圆半径(m) 等效半径识别误差率(%) 平面1 3 595 90 339.1 0.9 1.747 0.746 0.539 平面2 3 498 54.74 315 0.26 1.71 0.738 0.539 平面3 3 626 20.9 360 0.9 1.748 0.746 0.539 平面4 3 463 69.09 90 0.91 1.694 0.734 1.078 平面5 3 538 69.1 270 0.9 1.711 0.738 0.539 平面6 3 599 54.74 225 0.26 1.753 0.747 0.674
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表 3 Riquelme和RDD的产状计算结果对比
Table 3. Comparison of discontinuity orientation data between Riquelme and RDD
结构面组 Riquelme产状计算结果(°) RDD产状计算结果(°) 差值(°) J1 246.24/39.02(平面11) 244.54/38.60(平面11) 0.42 J1 256.86/52.30(平面12) 77.52/52.94(平面12) 0.64 J1 70.26/35.80(平面13) 250.37/35.83(平面13) 0.03 J1 252.68/35.48(平面14) 251.60/34.00(平面14) 1.48 J1 249.74/35.91(平面15) 250.24/36.12(平面15) 0.11 J1 70.47/35.92(平面16) 70.23/35.72(平面16) 0.24 J1 255.12/32.72(平面17) 251.61/36.00(平面17) 3.51 J2 339.47/83.25(平面21) 334.90/81.72(平面21) 4.57 J2 166.33/76.58(平面22) 346.15/72.81(平面22) 3.77 J2 160.20/89.86(平面23) 338.01/89.08(平面23) 1.22 J2 173.55/76.85(平面24) 353.81/76.58(平面24) 0.27 J3 136.59/82.58(平面31) 135.12/78.43(平面31) 4.15 J3 131.25/82.67(平面32) 317.69/87.73(平面32) 5.06 J3 143.91/89.70(平面33) 327.33/89.84(平面33) 0.14 J4 97.55/63.22(平面41) 99.30/68.12(平面41) 4.90 J4 91.07/50.19(平面42) 92.60/48.67(平面42) 1.53 J4 96.64/47.97(平面43) 96.59/48.04(平面43) 0.07 J5 123.42/76.15(平面51) 125.63/81.94(平面51) 5.79 J5 105.75/69.94(平面52) 106.90/70.43(平面52) 1.15
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表 4 CAD和RDD的结构面尺寸计算结果对比
Table 4. Comparison of discontinuity dimension data between Polyworks and RDD
结构面组 CAD计算面积(m2) RDD计算面积(m2) CAD计算尺寸(m) RDD计算尺寸(m) 尺寸误差率(%) J1 15.300 0(平面11) 15.321 7(平面11) 2.206 8 2.208 4 0.073 J1 0.435 2(平面12) 0.434 1(平面12) 0.372 2 0.371 7 0.134 J1 2.864 1(平面13) 2.863 6(平面13) 0.954 8 0.954 7 0.010 J1 23.321 2(平面14) 23.339 8(平面14) 2.724 6 2.725 7 0.040 J1 1.176 8(平面15) 1.174 9(平面15) 0.612 0 0.611 5 0.082 J1 5.935 9(平面16) 5.938 9(平面16) 1.374 6 1.374 9 0.022 J1 18.430 0(平面17) 18.429 2(平面17) 2.422 1 2.422 0 0.004 J2 1.355 2(平面21) 1.351 3(平面21) 0.656 8 0.655 8 0.152 J2 0.913 8(平面22) 0.918 9(平面22) 0.539 3 0.540 8 0.278 J2 2.102 0(平面23) 2.107 0(平面23) 0.818 0 0.819 0 0.122 J2 4.199 6(平面24) 4.194 6(平面24) 1.156 2 1.155 5 0.061 J3 15.380 0(平面31) 15.376 0(平面31) 2.212 6 2.212 3 0.014 J3 1.005 9(平面32) 1.002 8(平面32) 0.565 9 0.565 0 0.159 J3 2.134 8(平面33) 2.130 8(平面33) 0.824 3 0.823 6 0.085 J4 1.170 0(平面41) 1.170 0(平面41) 0.610 3 0.610 3 0 J4 6.971 6(平面42) 6.976 5(平面42) 1.489 7 1.490 2 0.034 J4 2.933 3(平面43) 2.930 3(平面43) 0.966 3 0.965 8 0.052 J5 2.955 4(平面51) 2.951 3(平面51) 0.969 9 0.969 2 0.072 J5 8.485 6(平面52) 8.491 1(平面52) 1.643 5 1.644 0 0.030
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