An empirical method for calculating the roughness coefficient of structural plane with line-plane combination
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摘要:
岩体结构面的剪切力学特性主要取决于其表面粗糙特征，结构面粗糙系数是表征该粗糙特征的主要方法。目前对结构面粗糙系数的研究局限于单一维度，多角度且定量化计算结构面粗糙系数能避免单一维度分析导致计算精度不准的局限性。采用立方体花岗岩，通过巴西劈裂的方式制备含结构面的试样；利用高精度三维扫描仪对试样结构面进行扫描，得到结构面的点云数据，同时借助逆向软件对点云数据进行三维重构。研究了点云数据Z方向上的分布频率，剖面线剖面比与节理粗糙系数（JRC）值的关系，结构面面积比与JRC均值的关系。研究表明：点云数据Z方向上的分布频率可以作为初步评估结构面粗糙度的手段；剖面线剖面比与JRC数值、结构面面积比与JRC均值有二次函数的关系。通过数值分析建立了结构面JRC均值与剖面比、面积比的二元函数关系，并得到结构面JRC均值的经验计算公式。本次研究为结构面粗糙度提供了一种“点-线-面”逐渐深入的多角度评估思路，得到的经验公式为计算结构面JRC均值提供了一种新的计算方法。
Abstract:The shear mechanical properties of structural plane are mainly determined by the surface roughness, and the roughness coefficient is the main method to characterize the roughness. At present, the research on the roughness coefficient is limited to a single dimension. Multi-angle and quantitative calculation of the roughness coefficient of structural plane can avoid the limitation of inaccurate calculation caused by single dimension analysis. Cubic granite blocks with structural plane are prepared by Brazilian splitting. High-precision 3D scanner is used to scan the prepared structural interview samples and obtain the point cloud data of the structural planes. At the same time, three-dimensional reconstruction of point cloud data is carried out by reverse software. The distribution frequency in the Z direction of the point cloud data, the relationship between the section ratio and joint roughness coefficient (JRC) values of the section line, and the relationship between the structural plane area ratio and the mean JRC values are studied. The results show that the distribution frequency in the Z direction of point cloud data can be used as a preliminary method to evaluate the roughness of structural surface. The relationships between section ratio and JRC value as well as area ratio of structural plane and mean JRC are both quadratic function. By numerical analysis, the binary function relation between the mean JRC of the structural planes and the section ratio and area ratio is established, and the empirical formula of the mean JRC of the structural plane is obtained. This study provides a "point-line-plane" idea to evaluate the roughness of discontinuities. The obtained empirical formula provides a new method for calculating the mean value of JRC of the structural plane.
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Key words:
- profile ratio /
- area ratio /
- structural plane /
- joint roughness coefficient /
- calculation method
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表 1 拟合公式表
Table 1. Table of fitting formulas
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表 2 点云数据统计表
Table 2. Statistical table of point cloud data
编号 点数 最大值/mm 最小值/mm 高差/mm 均值/mm S1 1218937 40.058 0.981 39.077 22.050 S2 1111054 30.640 12.765 17.875 22.820 S3 1088516 32.568 8.304 24.264 20.708 S4 1114106 53.192 31.284 21.908 42.682 S5 1066901 26.803 14.064 12.739 20.668 S6 1064899 30.471 12.020 18.451 20.787 S7 1112041 30.997 9.428 21.569 20.359 S8 1074548 35.688 5.524 30.164 23.831 S9 1034419 27.192 0.079 27.113 18.420 S10 1038317 18.051 1.212 16.839 11.554
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表 3 S4试样剖面比统计表
Table 3. Statistical table of profile ratio of sample S4
序号 基准长度/mm 实际长度/mm 剖面比 序号 基准长度/mm 实际长度/mm 剖面比 1 147.946 2 149.348 7 1.009 5 9 150.276 6 153.983 7 1.024 7 2 149.152 1 152.422 0 1.021 9 10 150.074 5 153.291 8 1.021 4 3 149.209 1 151.769 9 1.017 2 11 150.276 8 153.530 2 1.021 7 4 149.416 3 151.581 7 1.014 4 12 150.171 1 153.031 4 1.019 0 5 150.135 4 152.689 3 1.017 0 13 150.042 8 153.703 8 1.024 4 6 149.924 5 152.605 1 1.017 9 14 150.210 1 154.129 6 1.026 1 7 149.966 1 153.246 1 1.021 9 15 147.501 0 150.102 4 1.017 6 8 150.082 6 153.455 6 1.022 5
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表 4 试样面积比
Table 4. Area ratios of samples
编号 基准面积/mm2 真实面积/mm2 面积比 S1 22 350 24 116.034 1 1.079 0 S2 22 350 23 423.588 8 1.048 0 S3 22 350 23 201.424 4 1.038 1 S4 21 025 22 435.221 3 1.067 1 S5 22 200 22 641.000 0 1.019 9 S6 21 316 22 213.150 6 1.042 1 S7 21 609 22 986.338 9 1.063 7 S8 22 201 22 808.410 4 1.027 4 S9 21 756 22 973.348 3 1.056 0 S10 22 052 23 216.181 8 1.052 8
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表 5 试样数据统计
Table 5. Statistical data of the tested samples
序号 平均剖面比 面积比 JRC均值 S1 1.032 2 1.079 0 8.93 S2 1.029 8 1.048 0 8.62 S3 1.026 0 1.038 1 8.51 S4 1.029 5 1.067 1 8.78 S5 1.015 0 1.019 9 6.68 S6 1.016 0 1.042 1 7.86 S7 1.024 9 1.063 7 9.14 S8 1.018 0 1.027 4 7.18 S9 1.040 5 1.056 0 8.95 S10 1.026 3 1.052 8 8.90
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