A Novel Discontinuity Roughness Parameter and Its Correlation with Joint Roughness Coefficients
Abstract
:1. Introduction
- (1)
- The roughness evaluation index changes from two-dimensional to three-dimensional;
- (2)
- A single index turns to a combination of multiple indicators;
- (3)
- Simply considering the geometric characteristics of roughness to develops into considering the size effect, anisotropy, and point spacing effect of roughness in an all-round development.
2. Digital Representation of the Barton Ten Standard Profiles
2.1. Interpolation Processing of the Barton Ten Standard Profiles after Image Processing
2.2. Roughness Feature Extraction and Interpolation Effect Verification
3. A New Joint Roughness Parameter
3.1. Average Undulation Amplitude of the Discontinuity Profile
3.2. Anisotropy Parameter of Discontinuity Roughness
3.3. New Joint Roughness Parameter and Its Correlation with Joint Roughness Coefficients
4. Discussion
5. Conclusions
- 1.
- The comparative analysis of the JRC value calculated by the different interpolation conditions of the Barton standard profile and the JRC theoretical value shows that the interpolation effect of the nearest neighbor interpolation method is the best for , , and . The nearest neighbor interpolation method is used to digitally characterize the Barton standard profiles and lays a reliable data foundation for the establishment of new discontinuity roughness parameters.
- 2.
- The discontinuity roughness parameter also considers the size effect, anisotropy characteristics, and point spacing effects of the rock discontinuity roughness. The ratio of the average undulation amplitude to the horizontal projection length is used to reflect the size effect characteristics. The average ratio of the vertical to the horizontal projection length of the potential contact parts of the discontinuity profile in the shear direction is used to reflect the anisotropic characteristics.
- 3.
- The average undulation amplitude of the discontinuity profile reflects the characteristics of the overall undulation amplitude, and its value changes with the position of the reference line. The minimum average undulation amplitude is used to indicate the overall undulation amplitude, which is taken as the minimum value as the relationship is satisfied. The average undulation amplitude decreases with the increase in the point spacing.
- 4.
- The anisotropy parameter depends on the total number of discrete segments of the potential contact part. The key is to determine the potential contact part. In this work, the potential contact part is defined as the discrete segments of the discontinuity profile with a slope in the range [−30°, 0]. The relationship between JRC and shows that the selection of potential contact parts is reasonable.
- 5.
- Using , the JRC evaluation equation for discontinuity surface roughness with different point spacing is established. The correlation between and JRC can be expressed as:
- 6.
- The roughness index reflects the gentle slope characteristics of the rock discontinuity profiles in the shear direction and ignores the segments with steep slopes greater than 30° on the discontinuity profiles. During shearing, the steep segments are the first to come into contact. Only when the steep segments are broken, can the gentle segments prevent the shear slip of rock discontinuities. In addition, the slope interval of [−30°, 0] may not be the advantageous slope interval for all natural rock discontinuities. Therefore, the influence of for steep slope segments greater than 30° should be considered for the roughness anisotropy parameter in the future.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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JRC Range | Nearest Neighbor Interpolation Method | Linear Interpolation Method | Cubic Spline Interpolation Method | Piecewise Cubic Hermitian Polynomial Interpolation Method | Cubic Polynomial Interpolation Method | |||||||||||||||
Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | ||||||||||||||||
0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | |
0–2 | 0.087 | 0.074 | 0.052 | 0.027 | 0.085 | 0.073 | 0.052 | 0.027 | 0.086 | 0.073 | 0.053 | 0.033 | 0.086 | 0.073 | 0.053 | 0.033 | 0.086 | 0.073 | 0.053 | 0.033 |
2–4 | 0.114 | 0.101 | 0.092 | 0.072 | 0.113 | 0.101 | 0.092 | 0.072 | 0.114 | 0.101 | 0.092 | 0.073 | 0.113 | 0.101 | 0.091 | 0.073 | 0.113 | 0.101 | 0.091 | 0.073 |
4–6 | 0.154 | 0.134 | 0.117 | 0.096 | 0.151 | 0.132 | 0.117 | 0.096 | 0.154 | 0.133 | 0.116 | 0.095 | 0.152 | 0.133 | 0.116 | 0.095 | 0.152 | 0.133 | 0.116 | 0.095 |
6–8 | 0.174 | 0.161 | 0.146 | 0.124 | 0.172 | 0.161 | 0.146 | 0.124 | 0.172 | 0.161 | 0.145 | 0.123 | 0.172 | 0.16 | 0.145 | 0.123 | 0.172 | 0.16 | 0.145 | 0.123 |
8–10 | 0.203 | 0.192 | 0.177 | 0.153 | 0.201 | 0.191 | 0.177 | 0.153 | 0.201 | 0.191 | 0.176 | 0.152 | 0.201 | 0.191 | 0.176 | 0.152 | 0.201 | 0.191 | 0.176 | 0.152 |
10–12 | 0.191 | 0.175 | 0.152 | 0.14 | 0.189 | 0.175 | 0.153 | 0.14 | 0.19 | 0.175 | 0.152 | 0.14 | 0.19 | 0.175 | 0.152 | 0.139 | 0.19 | 0.175 | 0.152 | 0.139 |
12–14 | 0.275 | 0.253 | 0.225 | 0.177 | 0.273 | 0.253 | 0.225 | 0.177 | 0.277 | 0.26 | 0.229 | 0.179 | 0.277 | 0.26 | 0.229 | 0.179 | 0.277 | 0.26 | 0.229 | 0.179 |
14–16 | 0.344 | 0.308 | 0.252 | 0.205 | 0.343 | 0.307 | 0.252 | 0.205 | 0.343 | 0.307 | 0.253 | 0.203 | 0.343 | 0.307 | 0.252 | 0.203 | 0.343 | 0.307 | 0.252 | 0.203 |
16–18 | 0.373 | 0.343 | 0.287 | 0.242 | 0.37 | 0.343 | 0.287 | 0.242 | 0.372 | 0.344 | 0.289 | 0.244 | 0.371 | 0.344 | 0.29 | 0.244 | 0.371 | 0.344 | 0.29 | 0.244 |
18–20 | 0.411 | 0.375 | 0.334 | 0.276 | 0.402 | 0.37 | 0.331 | 0.274 | 0.401 | 0.37 | 0.33 | 0.27 | 0.401 | 0.37 | 0.33 | 0.27 | 0.401 | 0.37 | 0.33 | 0.27 |
JRC Range | Nearest Neighbor Interpolation Method | Linear Interpolation Method | Cubic Spline Interpolation Method | Piecewise Cubic Hermitian Polynomial Interpolation Method | Cubic Polynomial Interpolation Method | |||||||||||||||
Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | ||||||||||||||||
0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | |
0–2 | 0.001 | 0.001 | 0.003 | 0.003 | 0.001 | 0.001 | 0.003 | 0.003 | 0.001 | 0.001 | 0.003 | 0.004 | 0.001 | 0.001 | 0.003 | 0.004 | 0.001 | 0.001 | 0.003 | 0.004 |
2–4 | 0.001 | 0.003 | 0.008 | 0.021 | 0.001 | 0.003 | 0.008 | 0.021 | 0.001 | 0.003 | 0.008 | 0.021 | 0.001 | 0.003 | 0.008 | 0.021 | 0.001 | 0.003 | 0.008 | 0.021 |
4–6 | 0.002 | 0.005 | 0.014 | 0.037 | 0.001 | 0.004 | 0.014 | 0.037 | 0.002 | 0.004 | 0.014 | 0.036 | 0.001 | 0.004 | 0.014 | 0.036 | 0.001 | 0.004 | 0.014 | 0.036 |
6–8 | 0.002 | 0.007 | 0.021 | 0.062 | 0.002 | 0.006 | 0.021 | 0.061 | 0.002 | 0.006 | 0.021 | 0.06 | 0.002 | 0.006 | 0.021 | 0.06 | 0.002 | 0.006 | 0.021 | 0.06 |
8–10 | 0.003 | 0.009 | 0.031 | 0.093 | 0.003 | 0.009 | 0.031 | 0.093 | 0.003 | 0.009 | 0.031 | 0.092 | 0.003 | 0.009 | 0.031 | 0.092 | 0.003 | 0.009 | 0.031 | 0.092 |
10–12 | 0.002 | 0.008 | 0.023 | 0.078 | 0.002 | 0.008 | 0.023 | 0.079 | 0.002 | 0.008 | 0.023 | 0.079 | 0.002 | 0.008 | 0.023 | 0.078 | 0.002 | 0.008 | 0.023 | 0.078 |
12–14 | 0.005 | 0.016 | 0.051 | 0.126 | 0.005 | 0.016 | 0.051 | 0.125 | 0.005 | 0.017 | 0.053 | 0.128 | 0.005 | 0.017 | 0.053 | 0.128 | 0.005 | 0.017 | 0.053 | 0.128 |
14–16 | 0.007 | 0.024 | 0.063 | 0.168 | 0.007 | 0.024 | 0.063 | 0.167 | 0.007 | 0.024 | 0.064 | 0.165 | 0.007 | 0.024 | 0.063 | 0.165 | 0.007 | 0.024 | 0.063 | 0.165 |
16–18 | 0.009 | 0.029 | 0.082 | 0.233 | 0.009 | 0.029 | 0.082 | 0.234 | 0.009 | 0.03 | 0.084 | 0.238 | 0.009 | 0.03 | 0.084 | 0.239 | 0.009 | 0.03 | 0.084 | 0.239 |
18–20 | 0.011 | 0.035 | 0.111 | 0.303 | 0.01 | 0.034 | 0.11 | 0.299 | 0.01 | 0.034 | 0.109 | 0.291 | 0.01 | 0.034 | 0.109 | 0.292 | 0.01 | 0.034 | 0.109 | 0.292 |
JRC Range | Nearest Neighbor Interpolation Method | Linear Interpolation Method | Cubic Spline Interpolation Method | Piecewise Cubic Hermitian Polynomial Interpolation Method | Cubic Polynomial Interpolation Method | |||||||||||||||
Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | ||||||||||||||||
0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | |
0–2 | 1.004 | 1.003 | 1.001 | 1.0 | 1.004 | 1.003 | 1.001 | 1.0 | 1.004 | 1.003 | 1.001 | 1.001 | 1.004 | 1.003 | 1.001 | 1.001 | 1.004 | 1.003 | 1.001 | 1.001 |
2–4 | 1.006 | 1.005 | 1.004 | 1.003 | 1.006 | 1.005 | 1.004 | 1.003 | 1.006 | 1.005 | 1.004 | 1.003 | 1.004 | 1.005 | 1.004 | 1.003 | 1.004 | 1.005 | 1.004 | 1.003 |
4–6 | 1.012 | 1.009 | 1.007 | 1.005 | 1.011 | 1.009 | 1.007 | 1.005 | 1.011 | 1.009 | 1.007 | 1.005 | 1.011 | 1.009 | 1.007 | 1.004 | 1.011 | 1.009 | 1.007 | 1.004 |
6–8 | 1.015 | 1.013 | 1.01 | 1.008 | 1.014 | 1.013 | 1.01 | 1.008 | 1.014 | 1.013 | 1.01 | 1.007 | 1.014 | 1.012 | 1.01 | 1.007 | 1.014 | 1.012 | 1.01 | 1.007 |
8–10 | 1.02 | 1.018 | 1.015 | 1.011 | 1.019 | 1.018 | 1.015 | 1.011 | 1.019 | 1.018 | 1.015 | 1.011 | 1.019 | 1.018 | 1.015 | 1.011 | 1.019 | 1.018 | 1.015 | 1.011 |
10–12 | 1.018 | 1.015 | 1.011 | 1.01 | 1.017 | 1.015 | 1.011 | 1.01 | 1.017 | 1.015 | 1.011 | 1.01 | 1.017 | 1.015 | 1.011 | 1.01 | 1.017 | 1.015 | 1.011 | 1.01 |
12–14 | 1.035 | 1.03 | 1.024 | 1.015 | 1.035 | 1.03 | 1.025 | 1.015 | 1.036 | 1.032 | 1.025 | 1.016 | 1.036 | 1.032 | 1.025 | 1.016 | 1.036 | 1.032 | 1.025 | 1.016 |
14–16 | 1.054 | 1.045 | 1.031 | 1.021 | 1.054 | 1.044 | 1.031 | 1.021 | 1.054 | 1.044 | 1.031 | 1.02 | 1.054 | 1.044 | 1.031 | 1.02 | 1.054 | 1.044 | 1.031 | 1.02 |
16–18 | 1.062 | 1.054 | 1.039 | 1.028 | 1.062 | 1.054 | 1.039 | 1.028 | 1.062 | 1.054 | 1.039 | 1.029 | 1.062 | 1.054 | 1.04 | 1.029 | 1.062 | 1.054 | 1.04 | 1.029 |
18–20 | 1.07 | 1.062 | 1.051 | 1.036 | 1.068 | 1.061 | 1.051 | 1.036 | 1.069 | 1.062 | 1.051 | 1.035 | 1.069 | 1.061 | 1.05 | 1.035 | 1.069 | 1.061 | 1.050 | 1.035 |
JRC Range | Nearest Neighbor Interpolation Method | Linear Interpolation Method | Cubic Spline Interpolation Method | Cubic Polynomial Interpolation Method | Theoretical Value of JRC | ||||||||||||
Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | ||||||||||||||
0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | ||
0–2 | −1.34 | −0.93 | −0.79 | −1.21 | −1.71 | −1.07 | −0.88 | −1.21 | −1.47 | −0.99 | −0.65 | −0.49 | −1.58 | −1.04 | −0.68 | −0.54 | 0.4 |
2–4 | 1.96 | 2.62 | 4.46 | 3.37 | 1.81 | 2.6 | 4.45 | 3.4 | 1.91 | 2.58 | 4.4 | 3.44 | 1.81 | 2.56 | 4.39 | 3.43 | 2.8 |
4–6 | 5.62 | 5.72 | 6.68 | 5.36 | 5.38 | 5.6 | 6.67 | 5.37 | 5.59 | 5.65 | 6.65 | 5.3 | 5.46 | 5.61 | 6.63 | 5.29 | 5.8 |
6–8 | 7.07 | 7.79 | 8.74 | 7.54 | 6.91 | 7.74 | 8.72 | 7.53 | 6.98 | 7.75 | 8.67 | 7.45 | 6.93 | 7.74 | 8.66 | 7.44 | 6.7 |
8–10 | 8.99 | 9.75 | 10.53 | 9.55 | 8.82 | 9.68 | 10.53 | 9.55 | 8.86 | 9.67 | 10.49 | 9.5 | 8.85 | 9.68 | 10.49 | 9.51 | 9.5 |
10–12 | 8.23 | 8.72 | 9.11 | 8.68 | 8.12 | 8.72 | 9.15 | 8.7 | 8.15 | 8.7 | 9.13 | 8.65 | 8.14 | 8.7 | 9.13 | 8.63 | 10.8 |
12–14 | 12.67 | 12.81 | 12.77 | 11.18 | 12.58 | 12.81 | 12.77 | 11.16 | 12.76 | 13.11 | 12.94 | 11.28 | 12.75 | 13.1 | 12.93 | 11.27 | 12.8 |
14–16 | 15.4 | 14.98 | 13.8 | 12.9 | 15.36 | 14.94 | 13.79 | 12.9 | 15.36 | 14.94 | 13.83 | 12.8 | 15.37 | 14.94 | 13.8 | 12.81 | 14.5 |
16–18 | 16.4 | 16.18 | 15.01 | 15.1 | 16.31 | 16.16 | 15.01 | 15.1 | 16.36 | 16.19 | 15.08 | 15.24 | 16.34 | 16.21 | 15.1 | 15.25 | 16.7 |
18–20 | 17.59 | 17.16 | 16.4 | 17.02 | 17.3 | 17.02 | 16.34 | 16.92 | 17.28 | 17.0 | 16.31 | 16.71 | 17.29 | 17.0 | 16.31 | 16.73 | 18.7 |
Average relative error (%) | −6.58 | −1.8 | 8.06 | −4.02 | −8.54 | −2.39 | 7.96 | −3.94 | −7.41 | −2.12 | 7.78 | −4.15 | −8.17 | −2.28 | 7.68% | −4.20 |
JRC Range | Nearest Neighbor Interpolation Method | Linear Interpolation Method | Cubic Spline Interpolation Method | Cubic Polynomial Interpolation Method | Theoretical Value of JRC | ||||||||||||
Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | ||||||||||||||
0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | ||
0–2 | −1.44 | −0.65 | −0.89 | −1.24 | −1.81 | −1.06 | −0.89 | −1.24 | −1.56 | −1.06 | −0.72 | −0.49 | −1.68 | −1.06 | −0.72 | −0.53 | 0.4 |
2–4 | 1.86 | 2.75 | 4.36 | 3.37 | 1.71 | 2.75 | 4.36 | 3.4 | 1.81 | 2.53 | 4.31 | 3.44 | 1.72 | 2.53 | 4.31 | 3.43 | 2.8 |
4–6 | 5.57 | 5.76 | 6.59 | 5.36 | 5.15 | 5.63 | 6.59 | 5.36 | 5.57 | 5.63 | 6.56 | 5.3 | 5.15 | 5.63 | 6.56 | 5.28 | 5.8 |
6–8 | 7.02 | 7.78 | 8.67 | 7.53 | 6.69 | 7.69 | 8.63 | 7.53 | 7.02 | 7.69 | 8.58 | 7.45 | 6.69 | 7.69 | 8.58 | 7.45 | 6.7 |
8–10 | 8.93 | 9.68 | 10.45 | 9.54 | 8.69 | 9.62 | 10.45 | 9.54 | 8.691 | 9.62 | 10.41 | 9.5 | 8.69 | 9.62 | 10.41 | 9.51 | 9.5 |
10–12 | 8.18 | 8.71 | 9.03 | 8.68 | 7.91 | 8.71 | 9.07 | 8.69 | 8.18 | 8.71 | 9.07 | 8.7 | 7.91 | 8.71 | 9.05 | 8.63 | 10.8 |
12–14 | 12.54 | 12.72 | 12.69 | 11.17 | 12.54 | 12.72 | 12.69 | 11.15 | 12.67 | 13.02 | 12.86 | 11.27 | 12.67 | 13.02 | 12.86 | 11.26 | 12.8 |
14–16 | 15.31 | 14.88 | 13.72 | 12.9 | 15.23 | 14.83 | 13.71 | 12.89 | 15.23 | 14.83 | 13.75 | 12.8 | 15.31 | 14.83 | 13.71 | 12.81 | 14.5 |
16–18 | 16.3 | 16.06 | 14.93 | 15.09 | 16.23 | 16.04 | 14.93 | 15.1 | 16.23 | 16.08 | 15.0 | 15.23 | 16.23 | 16.1 | 15.02 | 15.25 | 16.7 |
18–20 | 17.51 | 17.03 | 16.32 | 17.01 | 17.21 | 16.89 | 16.26 | 16.91 | 17.15 | 16.87 | 16.23 | 16.7 | 17.21 | 16.87 | 16.23 | 16.72 | 18.7 |
Average relative error (%) | −7.58 | −1.66 | 6.99 | −4.06 | −10.35 | −2.24 | 6.92 | −4.02 | −8.25 | −2.82 | 6.71 | −4.14 | −10.16 | −2.80 | 6.67 | −4.26 |
JRC Range | Nearest Neighbor Interpolation Method | Linear Interpolation Method | Cubic Spline Interpolation Method | Cubic Polynomial Interpolation Method | Theoretical Value of JRC | ||||||||||||
Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | Point Spacing (mm) | ||||||||||||||
0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | 0.25 | 0.5 | 1 | 2 | ||
0–2 | 0.38 | 1.41 | 0.81 | −0.98 | 0.22 | 1.41 | 0.81 | −0.98 | 0.3 | 1.41 | 0.94 | −0.6 | 0.3 | 1.41 | 0.94 | −0.6 | 0.4 |
2–4 | 2.16 | 3.3 | 3.55 | 3.38 | 2.1 | 3.23 | 3.55 | 3.38 | 2.16 | 3.23 | 3.48 | 3.38 | 0.3 | 3.23 | 3.48 | 3.38 | 2.8 |
4–6 | 4.69 | 5.31 | 5.17 | 5.3 | 4.52 | 5.26 | 5.17 | 5.3 | 4.65 | 5.26 | 5.17 | 5.3 | 4.56 | 5.26 | 5.12 | 5.22 | 5.8 |
6–8 | 5.92 | 7.05 | 7.09 | 7.51 | 5.76 | 7.01 | 7.04 | 7.51 | 5.84 | 7.01 | 7.0 | 7.39 | 5.76 | 6.97 | 7.0 | 7.39 | 6.7 |
8–10 | 7.8 | 9.0 | 9.12 | 9.53 | 7.64 | 8.93 | 9.12 | 9.53 | 7.67 | 8.93 | 9.08 | 9.48 | 7.64 | 8.93 | 9.08 | 9.48 | 9.5 |
10–12 | 7.05 | 8.0 | 7.55 | 8.69 | 6.95 | 8.0 | 7.55 | 8.69 | 6.98 | 7.96 | 7.55 | 8.64 | 6.98 | 7.96 | 7.55 | 8.64 | 10.8 |
12–14 | 12.11 | 12.75 | 12.26 | 11.18 | 12.01 | 12.75 | 12.29 | 11.14 | 12.24 | 13.14 | 12.56 | 11.29 | 12.24 | 13.14 | 12.53 | 11.26 | 12.8 |
14–16 | 16.34 | 16.19 | 14.07 | 13.0 | 16.3 | 16.12 | 14.04 | 13.0 | 16.28 | 16.12 | 14.12 | 12.9 | 16.3 | 16.12 | 14.07 | 12.9 | 14.5 |
16–18 | 17.94 | 18.13 | 16.11 | 15.23 | 17.78 | 18.1 | 16.11 | 15.23 | 17.85 | 18.15 | 16.28 | 15.38 | 17.83 | 18.19 | 16.31 | 15.41 | 16.7 |
18–20 | 19.35 | 19.68 | 18.91 | 17.11 | 19.02 | 19.5 | 18.82 | 17.0 | 19.12 | 19.55 | 18.78 | 16.78 | 19.09 | 19.52 | 18.76 | 16.8 | 18.7 |
Average relative error (%) | −9.79 | 0.93 | −2.43 | −3.92 | −11.34 | 0.24 | −2.55 | −4.02 | −10.36 | 0.62 | −2.58 | −4.30 | −18.09 | 0.55 | −2.76 | −4.47 |
JRC Range | 0–2 | 2–4 | 4–6 | 6–8 | 8–10 | 10–12 | 12–14 | 14–16 | 16–18 | 18–20 | |
---|---|---|---|---|---|---|---|---|---|---|---|
Point spacing | 0.25 | 0.1013 | 0.3631 | 0.3519 | 0.4685 | 1.0219 | 1.2732 | 1.2356 | 1.0752 | 1.4151 | 0.8137 |
0.50 | 0.1008 | 0.3591 | 0.3520 | 0.4673 | 1.0170 | 1.2725 | 1.2367 | 1.0736 | 1.4158 | 0.8131 | |
1.00 | 0.1000 | 0.3532 | 0.3483 | 0.4647 | 1.0052 | 1.2685 | 1.2425 | 1.0691 | 1.4109 | 0.8078 | |
2.00 | 0.0937 | 0.3383 | 0.3420 | 0.4562 | 0.9733 | 1.2621 | 1.2335 | 1.0619 | 1.4052 | 0.8008 |
Point Spacing | 0–2 | 2–4 | 4–6 | 6–8 | 8–10 | 10–12 | 12–14 | 14–16 | 16–18 | 18–20 | |
---|---|---|---|---|---|---|---|---|---|---|---|
0.25 mm | −10°–0° | 0.1505 | 0.0956 | 0.1139 | 0.1022 | 0.1022 | 0.0876 | 0.1028 | 0.0830 | 0.1145 | 0.1439 |
−20°–0° | 0.1651 | 0.1282 | 0.1780 | 0.1647 | 0.1624 | 0.1521 | 0.1354 | 0.1522 | 0.1807 | 0.1969 | |
−30°–0° | 0.1740 | 0.1309 | 0.2184 | 0.2171 | 0.2094 | 0.1753 | 0.1903 | 0.2124 | 0.2271 | 0.3019 | |
−40°–0° | 0.1740 | 0.1309 | 0.2184 | 0.2281 | 0.2261 | 0.1753 | 0.2089 | 0.2464 | 0.2751 | 0.3312 | |
−50°–0° | 0.1740 | 0.1309 | 0.2184 | 0.2281 | 0.2261 | 0.1796 | 0.2218 | 0.2624 | 0.3052 | 0.3526 | |
−60°–0° | 0.1740 | 0.1309 | 0.2184 | 0.2281 | 0.2261 | 0.1796 | 0.2286 | 0.2624 | 0.3133 | 0.3526 | |
−70°–0° | 0.1740 | 0.1309 | 0.2184 | 0.2281 | 0.2261 | 0.1796 | 0.2286 | 0.2624 | 0.3133 | 0.3526 | |
−80°–0° | 0.1740 | 0.1309 | 0.2184 | 0.2281 | 0.2261 | 0.1796 | 0.2286 | 0.2624 | 0.3133 | 0.3730 | |
−90°–0° | 0.1740 | 0.1309 | 0.2184 | 0.2281 | 0.2261 | 0.1796 | 0.2286 | 0.2624 | 0.3133 | 0.3730 | |
0.50 mm | −10°–0° | 0.0785 | 0.0758 | 0.0765 | 0.0724 | 0.0852 | 0.0882 | 0.0778 | 0.0798 | 0.0820 | 0.1000 |
−20°–0° | 0.1013 | 0.0932 | 0.1293 | 0.1422 | 0.1406 | 0.1475 | 0.1402 | 0.1542 | 0.1658 | 0.1671 | |
−30°–0° | 0.1013 | 0.0932 | 0.1474 | 0.1704 | 0.1830 | 0.1588 | 0.1838 | 0.2287 | 0.2240 | 0.2496 | |
−40°–0° | 0.1013 | 0.0932 | 0.1474 | 0.1704 | 0.1830 | 0.1588 | 0.1978 | 0.2422 | 0.2486 | 0.2828 | |
−50°–0° | 0.1013 | 0.0932 | 0.1474 | 0.1704 | 0.1830 | 0.1588 | 0.2061 | 0.2422 | 0.2773 | 0.2896 | |
−60°–0° | 0.1013 | 0.0932 | 0.1474 | 0.1704 | 0.1830 | 0.1588 | 0.2061 | 0.2422 | 0.2773 | 0.2896 | |
−70°–0° | 0.1013 | 0.0932 | 0.1474 | 0.1704 | 0.1830 | 0.1588 | 0.2061 | 0.2422 | 0.2773 | 0.3075 | |
−80°–0° | 0.1013 | 0.0932 | 0.1474 | 0.1704 | 0.1830 | 0.1588 | 0.2061 | 0.2422 | 0.2773 | 0.3075 | |
−90°–0° | 0.1013 | 0.0932 | 0.1474 | 0.1704 | 0.1830 | 0.1588 | 0.2061 | 0.2422 | 0.2773 | 0.3075 | |
1.00 mm | −10°–0° | 0.0585 | 0.0710 | 0.0705 | 0.0544 | 0.0495 | 0.0834 | 0.0761 | 0.0582 | 0.0726 | 0.0960 |
−20°–0° | 0.0585 | 0.0710 | 0.1118 | 0.1110 | 0.1076 | 0.1267 | 0.1302 | 0.1649 | 0.1970 | 0.1769 | |
−30°–0° | 0.0585 | 0.0710 | 0.1210 | 0.1395 | 0.1524 | 0.1317 | 0.1692 | 0.2077 | 0.2140 | 0.2285 | |
−40°–0° | 0.0585 | 0.0710 | 0.1210 | 0.1395 | 0.1524 | 0.1317 | 0.1692 | 0.2077 | 0.2230 | 0.2527 | |
−50°–0° | 0.0585 | 0.0710 | 0.1210 | 0.1395 | 0.1524 | 0.1317 | 0.1692 | 0.2077 | 0.2429 | 0.2705 | |
−60°–0° | 0.0585 | 0.0710 | 0.1210 | 0.1395 | 0.1524 | 0.1317 | 0.1692 | 0.2077 | 0.2429 | 0.2705 | |
−70°–0° | 0.0585 | 0.0710 | 0.1210 | 0.1395 | 0.1524 | 0.1317 | 0.1692 | 0.2077 | 0.2429 | 0.2705 | |
−80°–0° | 0.0585 | 0.0710 | 0.1210 | 0.1395 | 0.1524 | 0.1317 | 0.1692 | 0.2077 | 0.2429 | 0.2705 | |
−90°–0° | 0.0585 | 0.0710 | 0.1210 | 0.1395 | 0.1524 | 0.1317 | 0.1692 | 0.2077 | 0.2429 | 0.2705 | |
2.00 mm | −10°–0° | 0.0238 | 0.0496 | 0.0949 | 0.0599 | 0.0534 | 0.0712 | 0.0644 | 0.0998 | 0.0659 | 0.0933 |
−20°–0° | 0.0238 | 0.0496 | 0.1119 | 0.0939 | 0.0855 | 0.1145 | 0.1217 | 0.1624 | 0.1708 | 0.1222 | |
−30°–0° | 0.0238 | 0.0496 | 0.1119 | 0.1083 | 0.1260 | 0.1145 | 0.1326 | 0.1972 | 0.2052 | 0.2074 | |
−40°–0° | 0.0238 | 0.0496 | 0.1119 | 0.1083 | 0.1260 | 0.1145 | 0.1326 | 0.1972 | 0.2052 | 0.2074 | |
−50°–0° | 0.0238 | 0.0496 | 0.1119 | 0.1083 | 0.1260 | 0.1145 | 0.1326 | 0.1972 | 0.2052 | 0.2074 | |
−60°–0° | 0.0238 | 0.0496 | 0.1119 | 0.1083 | 0.1260 | 0.1145 | 0.1326 | 0.1972 | 0.2052 | 0.2074 | |
−70°–0° | 0.0238 | 0.0496 | 0.1119 | 0.1083 | 0.1260 | 0.1145 | 0.1326 | 0.1972 | 0.2052 | 0.2074 | |
−80°–0° | 0.0238 | 0.0496 | 0.1119 | 0.1083 | 0.1260 | 0.1145 | 0.1326 | 0.1972 | 0.2052 | 0.2074 | |
−90°–0° | 0.0238 | 0.0496 | 0.1119 | 0.1083 | 0.1260 | 0.1145 | 0.1326 | 0.1972 | 0.2052 | 0.2074 |
JRC Profile | 0–2 | 2–4 | 4–6 | 6–8 | 8–10 | 10–12 | 12–14 | 14–16 | 16–18 | 18–20 | |
---|---|---|---|---|---|---|---|---|---|---|---|
Point spacing 0.25 mm | JRC | 0.4 | 2.8 | 5.8 | 6.7 | 9.5 | 10.8 | 12.8 | 14.5 | 16.7 | 18.7 |
(×10-2) | 0.1013 | 0.3631 | 0.3519 | 0.4685 | 1.0219 | 1.2732 | 1.2356 | 1.0752 | 1.4151 | 0.8137 | |
0.1740 | 0.1309 | 0.2184 | 0.2171 | 0.2094 | 0.1753 | 0.1903 | 0.2124 | 0.2271 | 0.3019 | ||
Point spacing 0.50 mm | JRC | 0.4 | 2.8 | 5.8 | 6.7 | 9.5 | 10.8 | 12.8 | 14.5 | 16.7 | 18.7 |
(×10-2) | 0.1008 | 0.3591 | 0.3520 | 0.4673 | 1.0170 | 1.2725 | 1.2367 | 1.0736 | 1.4158 | 0.8131 | |
0.1013 | 0.0932 | 0.1474 | 0.1704 | 0.1830 | 0.1588 | 0.1838 | 0.2287 | 0.2240 | 0.2496 | ||
Point spacing 1.00 mm | JRC | 0.4 | 2.8 | 5.8 | 6.7 | 9.5 | 10.8 | 12.8 | 14.5 | 16.7 | 18.7 |
(×10-2) | 0.1000 | 0.3532 | 0.3483 | 0.4647 | 1.0052 | 1.2685 | 1.2425 | 1.0691 | 1.4109 | 0.8078 | |
0.0585 | 0.0710 | 0.1210 | 0.1395 | 0.1524 | 0.1317 | 0.1692 | 0.2077 | 0.2140 | 0.2285 | ||
Point spacing 2.00 mm | JRC | 0.4 | 2.8 | 5.8 | 6.7 | 9.5 | 10.8 | 12.8 | 14.5 | 16.7 | 18.7 |
(×10-2) | 0.0937 | 0.3383 | 0.3420 | 0.4562 | 0.9733 | 1.2621 | 1.2335 | 1.0619 | 1.4052 | 0.8008 | |
0.0238 | 0.0496 | 0.1119 | 0.1083 | 0.1260 | 0.1145 | 0.1326 | 0.1972 | 0.2052 | 0.2074 |
Point Spacing (mm) | Fitting Results | Correlation Coefficient R2 | |
---|---|---|---|
0.25 | 0.9517 | ||
0.50 | 0.9615 | ||
1.00 | 0.9697 | ||
2.00 | 0.9512 |
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Zhang, H.; Zhang, C.; Yang, Z.; Li, Z.; Wang, C. A Novel Discontinuity Roughness Parameter and Its Correlation with Joint Roughness Coefficients. Energies 2021, 14, 7631. https://doi.org/10.3390/en14227631
Zhang H, Zhang C, Yang Z, Li Z, Wang C. A Novel Discontinuity Roughness Parameter and Its Correlation with Joint Roughness Coefficients. Energies. 2021; 14(22):7631. https://doi.org/10.3390/en14227631
Chicago/Turabian StyleZhang, Huizhen, Changsuo Zhang, Zejin Yang, Zhiqiang Li, and Chenlong Wang. 2021. "A Novel Discontinuity Roughness Parameter and Its Correlation with Joint Roughness Coefficients" Energies 14, no. 22: 7631. https://doi.org/10.3390/en14227631
APA StyleZhang, H., Zhang, C., Yang, Z., Li, Z., & Wang, C. (2021). A Novel Discontinuity Roughness Parameter and Its Correlation with Joint Roughness Coefficients. Energies, 14(22), 7631. https://doi.org/10.3390/en14227631