Rock Joint Roughness Measurement and Quantification—A Review of the Current Status
Abstract
:1. Introduction
2. Rock Joint Roughness Measurement Techniques
2.1. Contact Methods
2.2. Non Contact Methods
3. Rock Joint Roughness Quantification Methods
3.1. Empirical Methods
3.2. Statistical Methods
3.2.1. Amplitude-Based Roughness Parameters
3.2.2. Slope-Based Roughness Parameters
3.2.3. Amplitude and Slope-Based Roughness Parameters
3.2.4. Relations between JRC and Statistical Parameters
3.3. Fractals-Based Methods
4. Effect of Non-Stationarity on Computed Roughness Parameters
5. Effect of Heterogeneity on Computed Roughness Parameters
6. Effect of Joint Size on Computed Roughness Parameters
7. Roughness Anisotropy
8. Effect of Sampling Interval and Resolution on Computed Roughness Parameters
9. Comparison between the Values Obtained for some of the Roughness Parameters
10. Discussion and Conclusions
11. Recommendations for Future Research
Funding
Conflicts of Interest
References
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Roughness Metric Number | Roughness Metric | Abbreviation | Reference(s) |
---|---|---|---|
1 | Centerline average value of the profile | CLA | Tse and Cruden [33] |
2 | The mean square value of the profile | MSV | Tse and Cruden [33] |
3 | Root mean square value of the profile, | RMS | Myers [29]; Tse and Cruden [33] |
4 | The mean inclination angle of the profile | θP | Yu and Vayssade [34]; Belem et al. [20] |
5 | The mean positive inclination angle of the profile | θP+ | Belem et al. [20] |
6 | The mean negative inclination angle of the profile | θP− | Belem et al. [20] |
7 | The standard deviation of the inclination angle of the profile | SD θP | Yu and Vayssade [34] |
8 | Root mean square of the slope of the profile | Z2 | Myers [29]; Tse and Cruden [33]; Yu and Vayssade [34] |
9 | Root mean square of the first derivative of the slope of the profile | Z3 | Myers [29]; Tse and Cruden [33] |
10 | Percentage excess distance measured along the profile where the slope is positive over the distance where the slope is negative | Z4 | Myers [29]; Tse and Cruden [33] |
11 | Autocorrelation function | ACF | Myers [29]; Wu and Ali [32] |
12 | Structure-function | SF | Myers [29]; Sayles and Thomas [31]; Yu and Vayssade [34] |
13 | Spectral density function | SDF | Wu and Ali [32] |
14 | Mean inclination angle for the surface | θS | Belem et al. [20] |
15 | Root mean square of the slope of the surface | Z2S | Belem et al. [20] |
16 | Maximum apparent dip angle in the shear direction/an empirical roughness parameter +1 | θMax/C + 1 | Grasselli et al. [21]; Tatone and Grasselli [36] |
17 | Roughness profile index | RP | Mandelbrot [30], Maerz et al. [8]; Yu and Vayssade [34] |
18 | Surface roughness coefficient | RS | El-Soudani [62];Belem et al. [20] |
19 | Surface Tortuosity coefficient | TS | Belem et al. [20] |
No. | Parameter | Formula | Equation No. | Reference(s) |
---|---|---|---|---|
1 | (1) | Tse and Cruden [33] | ||
2 | (2) | Myers [29]; Tse and Cruden [33]; | ||
3 | (3) | Tse and Cruden [33] | ||
4 | (4) | Belem et al. [20] | ||
5 | (5) | Belem et al. [20] | ||
6 | (6) | Belem et al. [20] | ||
7 | (7) | Belem et al. [20] | ||
8 | (8) | Myers [29]; Tse and Cruden [33]; Yu and Vayssade [34] | ||
9 | (9) | Myers [29]; Sayles and Thomas [31]; Yu and Vayssade [34] | ||
10 | (10) | Myers [29]; Tse and Cruden [33] | ||
11 | (11) | Myers [29]; Tse and Cruden [33] | ||
12 | (12) | Yu and Vayssade [34] | ||
13 | (13) | Mandelbrot [30] | ||
14 | (14) | Belem et al. [20] | ||
15 | (15a) | Belem et al. [20] | ||
(15b) | ||||
16 | (16) | Tatone and Grasselli [26] |
No. | Equation | R | Reference |
---|---|---|---|
1 | 0.993 | Yang et al. [71] | |
2 | 0.973 | Yu and Vayssade [34] | |
3 | 0.975 | Yu and Vayssade [34] | |
4 | 0.934 | Yu and Vayssade [34] | |
5 | 0.973 | Yu and Vayssade [34] | |
6 | 0.954 | Yu and Vayssade [34] | |
7 | ---- | Tatone and Grasselli [35] | |
8 | 0.884 | Li and Zhang [70] | |
9 | 0.876 | Li and Zhang [70] | |
10 | 0.993 | Yu and Vayssade [34] | |
11 | 0.972 | Yu and Vayssade [34] | |
12 | 0.954 | Yu and Vayssade [34] | |
13 | ------ | Tatone and Grasselli [35] | |
14 | 0.945 | Yu and Vayssade [34] | |
15 | 0.974 | Yu and Vayssade [34] | |
16 | 0.975 | Yu and Vayssade [34] | |
17 | 0.970 | Yu and Vayssade [34] | |
18 | 0.971 | Tatone and Grasselli [35] | |
19 | 0.900 | Gravanis and Pantelidis [72] |
Case | No. of Data | Rp | θP | θP− | |||
---|---|---|---|---|---|---|---|
Mean | CV * | Mean | CV * | Mean | CV * | ||
125 mm Z-Y profiles (0–125 mm) | 101 | 1.0166 | 0.0046 | 7.8842 | 0.1240 | −8.7253 | 0.1466 |
125 mm Z-Y profiles (125–250 mm) | 101 | 1.0186 | 0.0058 | 8.2994 | 0.1238 | −8.9835 | 0.1511 |
125 mm Z-Y profiles (250–375 mm) | 101 | 1.0195 | 0.0067 | 8.6479 | 0.1630 | −9.3509 | 0.1576 |
125 mm Z-Y profiles (375–500 mm) | 101 | 1.0177 | 0.0059 | 8.2288 | 0.1528 | −8.7103 | 0.1902 |
125 mm Z-Y profiles (500–625 mm) | 101 | 1.0191 | 0.0049 | 8.4616 | 0.1039 | −7.2657 | 0.1783 |
125 mm Z-Y profiles (625–750 mm) | 101 | 1.0179 | 0.0049 | 8.4051 | 0.1401 | −8.5723 | 0.1574 |
125 mm Z-Y profiles (750–875 mm) | 101 | 1.0529 | 0.0260 | 10.7150 | 0.1734 | −10.4767 | 0.1933 |
125 mm Z-Y profiles (875–1000 mm) | 101 | 1.0416 | 0.0157 | 10.6827 | 0.1431 | −10.8429 | 0.1764 |
Case | No. of Data | Rp | θp | θP− | |||
---|---|---|---|---|---|---|---|
Mean | CV * | Mean | CV * | Mean | CV * | ||
125 mm Z-X profiles (0–125 mm) | 51 | 1.0056 | 0.0041 | 4.0701 | 0.2572 | −4.1471 | 0.3755 |
125 mm Z-X profiles (125–250 mm) | 51 | 1.0059 | 0.0029 | 4.3144 | 0.2328 | −4.5201 | 0.2972 |
125 mm Z-X profiles (250–375 mm) | 51 | 1.0044 | 0.0021 | 3.8270 | 0.2222 | −3.9846 | 0.2871 |
125 mm Z-X profiles (375–500 mm) | 51 | 1.0060 | 0.0081 | 3.8499 | 0.3014 | −3.3280 | 0.3162 |
125 mm Z-X profiles (500–625 mm) | 51 | 1.0046 | 0.0025 | 3.9029 | 0.2484 | −3.6263 | 0.2583 |
125 mm Z-X profiles (625–750 mm) | 51 | 1.0045 | 0.0029 | 3.7001 | 0.2966 | −3.2946 | 0.3377 |
125 mm Z-X profiles (750–875 mm) | 51 | 1.0042 | 0.0025 | 3.6848 | 0.2718 | −3.3629 | 0.3017 |
125 mm Z-X profiles (875–1000 mm) | 51 | 1.0036 | 0.0022 | 3.3642 | 0.2694 | −3.0815 | 0.3524 |
Case | No. of Data | Dv | Kv | Dv × Kv | |
---|---|---|---|---|---|
Mean | Mean | Mean | |||
250 mm Z-X profiles | 0–250 mm | 51 | 1.1220 | 0.0108 | 0.0121 |
250–500 mm | 51 | 1.1598 | 0.0092 | 0.0107 | |
500–750 mm | 51 | 1.1249 | 0.0085 | 0.0096 | |
750–1000 mm | 51 | 1.1515 | 0.0071 | 0.0082 | |
250 mm Z-Y profiles | 0–250 mm | 101 | 1.1287 | 0.0352 | 0.0397 |
250–500 mm | 101 | 1.1183 | 0.0368 | 0.0412 | |
500–750 mm | 101 | 1.1284 | 0.0370 | 0.0418 | |
750–1000 mm | 78 | 1.3780 | 0.0812 | 0.1119 |
Case | No. of Data | DRL | A | DRL × A | |
---|---|---|---|---|---|
Mean | Mean | Mean | |||
250 mm Z-X profiles | 0–250 mm | 101 | 1.0720 | 0.0088 | 0.0094 |
250–500 mm | 101 | 1.1213 | 0.0089 | 0.0100 | |
500–750 mm | 101 | 1.0807 | 0.0081 | 0.0088 | |
750–1000 mm | 101 | 1.1299 | 0.0082 | 0.0093 | |
250 mm Z-Y profiles | 0–250 mm | 101 | 1.0881 | 0.0188 | 0.0205 |
250–500 mm | 101 | 1.0746 | 0.0189 | 0.0203 | |
500–750 mm | 101 | 1.1234 | 0.0215 | 0.0242 | |
750–1000 mm | 101 | 1.1851 | 0.0318 | 0.0377 |
Case | No. of Data | Rp | θP | θP− | |||
---|---|---|---|---|---|---|---|
Mean | CV * | Mean | CV * | Mean | CV * | ||
500 mm Z-Y profiles (0–500 mm) | 101 | 1.0181 | 0.0032 | 8.2674 | 0.0919 | −8.9498 | 0.0921 |
250 mm Z-Y profiles (0–500 mm) lumped | 202 | 1.0181 | 0.0045 | 8.2666 | 0.1145 | −8.9367 | 0.1267 |
125 mm Z-Y profiles (0–500 mm) lumped | 404 | 1.0181 | 0.0059 | 8.2650 | 0.1466 | −8.9425 | 0.1646 |
Case | No. of Data | Rp | θP | θP− | |||
---|---|---|---|---|---|---|---|
Mean | CV * | Mean | CV * | Mean | CV * | ||
1000 mm Z-X profiles | 101 | 1.0049 | 0.0016 | 3.8429 | 0.1061 | −3.8056 | 0.1164 |
1000 mm Z-Y profiles | 101 | 1.0255 | 0.0043 | 8.9285 | 0.0652 | −9.1881 | 0.0604 |
500 mm Z-X profiles | 402 | 1.0048 | 0.0022 | 3.8386 | 0.1582 | −3.7534 | 0.1968 |
500 mm Z-Y profiles | 202 | 1.0255 | 0.0092 | 8.9211 | 0.1105 | −9.2025 | 0.0920 |
250 mm Z-X profiles | 804 | 1.0048 | 0.0029 | 3.8393 | 0.2117 | −3.7265 | 0.2632 |
250 mm Z-Y profiles | 404 | 1.0255 | 0.0144 | 8.9181 | 0.1570 | −9.1591 | 0.1596 |
125 mm Z-X profiles | 408 | 1.0048 | 0.0040 | 3.8392 | 0.2716 | −3.6682 | 0.3438 |
125 mm Z-Y profiles | 808 | 1.0255 | 0.0174 | 8.9156 | 0.1874 | −9.1160 | 0.2074 |
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Kulatilake, P.H.S.W.; Ankah, M.L.Y. Rock Joint Roughness Measurement and Quantification—A Review of the Current Status. Geotechnics 2023, 3, 116-141. https://doi.org/10.3390/geotechnics3020008
Kulatilake PHSW, Ankah MLY. Rock Joint Roughness Measurement and Quantification—A Review of the Current Status. Geotechnics. 2023; 3(2):116-141. https://doi.org/10.3390/geotechnics3020008
Chicago/Turabian StyleKulatilake, Pinnaduwa H. S. W., and Mawuko Luke Yaw Ankah. 2023. "Rock Joint Roughness Measurement and Quantification—A Review of the Current Status" Geotechnics 3, no. 2: 116-141. https://doi.org/10.3390/geotechnics3020008
APA StyleKulatilake, P. H. S. W., & Ankah, M. L. Y. (2023). Rock Joint Roughness Measurement and Quantification—A Review of the Current Status. Geotechnics, 3(2), 116-141. https://doi.org/10.3390/geotechnics3020008