Abstract
One of the two independent key parameters of the Hoek–Brown failure criterion, mi, is calculated using 3-axial test data consisting of at least five major and minor principal stresses and the regression method. In the absence of 3-axial test data, the guideline chart, which provides mi values, is commonly used in practice. However, mi values calculated from regression analyses have a much greater spread than that proposed in the Guideline. Therefore, simplified models, based on some strength properties, have been proposed to calculate mi values. But some of these prediction models were based on a few types of rock and limited data. In this study, an alternative method for predicting mi using internal friction angle (ϕ), which is determined from classical 3-axial test, is proposed. First a brief description of the proposed method was given and a summary on the existing methods for predicting mi was discussed with their limitations, and the data selection criteria used by the authors were also described. In order to assess the prediction performance of the proposed method, a database, consisting of 125 data sets and representing a total of 26 different rock types, was compiled from a well-known dataset and published sources. Results of the comparisons between the proposed method and some of the current prediction methods mainly suggested that the proposed method yields the best mi predictions. It is also noted that for sedimentary rocks, the ranges of mi estimated from this method were closer to those proposed in the Guideline chart.
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The authors gratefully thank the two anonymous reviewers for their valuable and constructive comments.
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Appendix: Published geomechanical values of the rock types which were compiled from the literature and used in this study and mi values predicted from some methods
Appendix: Published geomechanical values of the rock types which were compiled from the literature and used in this study and mi values predicted from some methods
Rock data no. Rock type (Reference no. ) | UCS (σc) (MPa) | TS (σt) (MPa) | mi (Calculated) (From data- base) | ϕexperimental (°) | Range of mi in the guideline | mi predicted from ϕexp. (This study) | R-index (mi ≅ σc/σt) | mi from UCS-TS based method (Arshadnejad and Nick 2016) (rock type) | mi from special form of R-index (ϕ) (Mehrishal et al. 2015) | mi from TS-based method (Wang and Shen 2017) | mi from UCS-based method (Shen and Karakus 2014) | Absolute prediction errors calculated for the models used | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
This study | R-index | UCS-TS method | Special form of R | TS-based model | UCS-based model | ||||||||||||
1. Siltstone (1) | 46.00 | 6.42** | 2.6 | 40.0 | 5–9 | 8.97 | 7.17 | 6.96 (S) | 9.19 | 6.37 | 4.57 | 4.36 | 6.59 | ||||
2. Mudstone (1) | 41.40 | 4.10** | 11.2 | 42.5 | 2–9 | 10.29 | 10.10 | 9.05 (S) | 10.32 | 0.91 | 1.1 | 2.15 | 0.88 | ||||
3. Mudstone (1) | 44.56 | 4.18** | 11.2 | 45.0 | 2–9 | 11.84 | 10.66 | 9.43 (S) | 11.64 | 0.64 | 0.54 | 1.77 | 0.44 | ||||
4. Siltstone (1) | 61.09 | 10.78** | 7.0 | 37.5 | 5–9 | 7.84 | 5.67 | 5.78 (S) | 8.22 | 0.84 | 1.33 | 1.22 | 1.22 | ||||
5. Siltstone (1) | 89.49 | 11.34** | 3.7 | 31.0 | 5–9 | 5.48 | 7.89 | 7.50 (S) | 6.24 | 1.78 | 4.19 | 3.8 | 2.54 | ||||
6. Mudstone (1) | 119.77 | 10.00** | 15.2 | 49.5 | 2–9 | 15.49 | 11.98 | 10.31 (S) | 14.68 | 0.29 | 3.22 | 4.89 | 0.52 | ||||
7. Marl (1) | 84.42 | 7.19** | 5.5 | 33.0 | 5–9 | 6.13 | 11.74 | 10.15 (S) | 6.78 | 0.63 | 6.24 | 4.65 | 1.28 | ||||
8. Ignimbrite (1) | 6.58 | 0.60** | 7.7 | 38.5 | 8–18 | 8.28 | 10.97 | 10.15 (I) | 8.59 | 0.58 | 3.27 | 2.45 | 0.89 | ||||
9. Siltstone (1) | 15.56 | 2.23** | 9.8 | 44.0 | 5–9 | 11.19 | 6.98 | 6.82 (S) | 11.09 | 1.39 | 2.82 | 2.98 | 1.29 | ||||
10. Marl (1) | 82.76 | 7.24** | 7.4 | 43.0 | 5–9 | 10.58 | 11.43 | 9.95 (S) | 10.57 | 3.18 | 4.03 | 2.55 | 3.17 | ||||
11. Mudstone (1) | 15.10 | 2.92** | 5.9 | 33.0 | 2–9 | 6.13 | 5.17 | 5.36 (S) | 6.78 | 0.23 | 0.73 | 0.54 | 0.88 | ||||
12. Marl ((1) | 11.99 | 1.68** | 4.5 | 36.5 | 5–9 | 7.43 | 7.14 | 6.94 (S) | 7.87 | 2.93 | 2.64 | 2.44 | 3.37 | ||||
13. Ignimbrite (1) | 12.88 | 1.78** | 8.3 | 43.5 | 8–18 | 10.88 | 7.24 | 7.18 (I) | 10.82 | 2.58 | 1.06 | 1.12 | 2.52 | ||||
14. Ignimbrite (1) | 9.65 | 1.22** | 14.8 | 47.0 | 8–18 | 13.30 | 7.91 | 7.73 (I) | 12.87 | 1.5 | 6.89 | 7.07 | 1.93 | ||||
15. Marl (1) | 23.76 | 1.44** | 11.2 | 41.0 | 5–9 | 9.47 | 16.5 | 13.22 (S) | 9.62 | 1.73 | 5.3 | 2.02 | 1.58 | ||||
16. Mudstone (1) | 10.35 | 1.25** | 4.5 | 31.0 | 2–9 | 5.48 | 8.28 | 7.78 (S) | 6.24 | 0.98 | 3.78 | 3.28 | 1.74 | ||||
17. Sandstone (2) | 53.92 | - | 14.80 | 40.24 | 13–21 | 9.09 | 9.29 | 17.73 | 5.71 | 5.51 | 2.93 | ||||||
18. Marble (3) | 94.30 | - | 5.50 | 33.20 | 6–12 | 6.20 | 6.84 | 8.20 | 0.7 | 1.34 | 2.70 | ||||||
19. Limestone (3) | 62.60 | - | 7.10 | 35.80 | 9–15 | 7.15 | 7.63 | 11.83 | 0.05 | 0.53 | 4.73 | ||||||
20. Limestone (3) | 116.80 | - | 21.80 | 53.20 | 9–15 | 19.79 | 18.05 | 10.77 | 2.01 | 3.75 | 11.03 | ||||||
21. Marble (4) | 89.00 | - | 6.80 | 35.69 | 6–12 | 7.11 | 7.60 | 8.47 | 0.31 | 0.80 | 1.67 | ||||||
22 . Gneiss (4) | 160.00 | - | 24.30 | 51.28 | 23–33 | 17.37 | 16.18 | 6.93 | 8.12 | ||||||||
23 . Schist (4) | 60.00 | - | 5.40 | 31.75 | 9–15 | 5.72 | 6.44 | 0.32 | 1.04 | ||||||||
24. Granite (5) | 126.68 | - | 41.61 | 60.37 | 29–35 | 35.30 | 28.53 | 37.97 | 6.31 | 13.08 | 3.64 | ||||||
25. Marble (6) | 69.83 | - | 4.93 | 28.00 | 6–12 | 4.58 | 5.54 | 9.68 | 0.35 | 0.61 | 4.75 | ||||||
26. Marble (6) | 119.30 | - | 7.16 | 34.40 | 6–12 | 6.63 | 7.19 | 7.21 | 0.534 | 0.03 | 0.04 | ||||||
27. Sandstone (7) | 70.00 | - | 11.76 | 35.40 | 13–21 | 7.00 | 7.50 | 16.57 | 4.76 | 4.26 | 4.81 | ||||||
28. Quartzite (8) | 310.00 | - | 68.00 | 65.00 | 17–23 | 58.78 | 40.58 | 9.22 | 27.42 | ||||||||
29. Coal (8) | 53.00 | - | 6.30 | 30.00 | 5–9 | 5.17 | 6.00 | 7.45 | 1.13 | 0.30 | 1.15 | ||||||
30. Sandstone (8) | 122.00 | - | 22.70 | 52.00 | 13–21 | 18.22 | 16.84 | 4.48 | 5.86 | ||||||||
31. Norite (8) | 270.00 | - | 22.50 | 55.00 | 15–25 | 22.53 | 20.08 | 0.03 | 2.42 | ||||||||
32. Limestone (9) | 52.00 | 4.00** | 8.60 | - | 9–15 | - | 13.00 | 10.98 (S) | 15.60 | 12.16 | 4.40 | 2.38 | 7.00 | 3.56 | |||
33. Granite (9) | 226.00 | 13.00** | 29.00 | - | 29–35 | - | 17.38 | 15.25 (I) | 23.05 | 33.82 | 11.62 | 13.75 | 5.95 | 4.82 | |||
34. Dolomite (10) | 95.26 | - | 6.99 | 31.12 | 6–12 | 5.52 | 6.27 | 1.47 | 0.72 | ||||||||
35. Granodiorite (10) | 270.00 | - | 17.38 | 48.18 | 26–32 | 14.28 | 13.68 | 3.10 | 3.70 | ||||||||
36. Mudstone (11) | 173.20 | - | 22.40 | 53.10 | 2–9 | 19.65 | 17.94 | 2.75 | 4.46 | ||||||||
37. Pyroclastic rock (11) | 165.00 | - | 45.44 | 61.10 | 8–24 | 37.88 | 30.05 | 7.56 | 15.39 | ||||||||
38. Granitic rock (12) | 63.08 | - | 29.5 | 56.20 | 26–35 | 24.69 | 21.63 | 43.55 | 4.81 | 7.87 | 14.05 | ||||||
39. Granitic rock (12) | 110.40 | - | 34.20 | 58.20 | 26–35 | 29.05 | 24.60 | 39.03 | 5.15 | 9.60 | 4.83 | ||||||
40. Granitic rock (12) | 119.00 | - | 23.70 | 53.90 | 26–35 | 20.79 | 18.80 | 38.45 | 2.91 | 4.90 | 14.75 | ||||||
41. Granitic rock (12) | 81.10 | - | 9.40 | 40.80 | 26–35 | 9.37 | 9.53 | 41.51 | 0.03 | 0.13 | 32.11 | ||||||
42. Granitic rock (12) | 139.90 | - | 15.10 | 47.70 | 26–35 | 13.87 | 13.35 | 37.23 | 1.23 | 1.75 | 22.13 | ||||||
43. Granitic rock (12) | 101.50 | - | 24.90 | 51.80 | 26–35 | 17.98 | 16.65 | 39.69 | 6.92 | 8.25 | 14.79 | ||||||
44. Granitic rock (12) | 129.20 | - | 41.60 | 59.00 | 26–35 | 31.14 | 25.95 | 10.46 | 15.65 | ||||||||
45. Andesite (13) | 68.30 | 6.48** | 10.16 | - | 20–30 | - | 10.54 | 9.81 (I) | 0.38 | 0.35 | |||||||
46. Tuff (14) | 74.66 | 8.18** | 6.39 | 40.96 | 8–18 | 9.45 | 9.13 | 8.70 (I) | 9.60 | 3.06 | 2.74 | 2.31 | 3.21 | ||||
47. Tuff (14) | 74.13 | 7.29** | 6.75 | 41.45 | 8–18 | 9.71 | 10.17 | 9.52 (I) | 9.82 | 2.96 | 3.42 | 2.77 | 3.07 | ||||
48 . Sandstone (15) | 136.60 | 14.90** | 15.70 | - | 13–21 | 9.17 | 8.41 (S) | 12.06 | 6.53 | 7.29 | 3.64 | ||||||
49. Schist (16)* | 92.90 | 8.44 | 20.25 | 46.96 | 9–15 | 13.27 | 11.01 | 11.50 (M) | 12.85 | 6.98 | 9.24 | 8.75 | 7.40 | ||||
50. Quartz diorite (17)* | 155.10 | 12.30 | 18.27 | 49.63 | 20–30 | 15.62 | 12.61 | 11.44 (I) | 14.78 | 2.65 | 5.66 | 6.83 | 3.50 | ||||
51. Granite (17)* | 223.90 | 12.94 | 21.23 | 55.44 | 29–35 | 23.29 | 17.30 | 15.18 (I) | 20.63 | 23.10 | 33.88 | 2.06 | 3.93 | 6.05 | 0.60 | 1.87 | 12.66 |
52. Sandstone (17)* | 145.80 | 6.80 | 23.00 | 53.50 | 13–21 | 20.21 | 21.44 | 16.33 (S) | 18.36 | 14.90 | 13.69 | 2.79 | 1.56 | 6.67 | 4.63 | 8.10 | 9.31 |
53. Limestone (17)* | 56.40 | 5.40 | 14.66 | 45.73 | 9–15 | 12.35 | 10.44 | 9.28 (S) | 12.07 | 14.34 | 3.16 | 2.31 | 4.22 | 5.38 | 2.59 | 0.32 | 11.50 |
54. Gneiss (17)* | 326.80 | 15.90 | 17.87 | 54.59 | 23–33 | 21.86 | 20.55 | 19.44 (M) | 19.59 | 3.99 | 2.69 | 1.58 | 1.73 | ||||
55. Granodiorite (17)* | 83.30 | 12.10 | 11.04 | 48.39 | 26–32 | 14.46 | 6.88 | 6.90 (I) | 13.84 | 3.42 | 4.163 | 4.14 | 2.79 | ||||
56 . Limestone (17)* | 128.10 | 9.40 | 13.00 | 42.79 | 9–15 | 10.45 | 13.63 | 11.38 (S) | 10.46 | 12.28 | 10.62 | 2.54 | 0.64 | 1.61 | 2.53 | 0.71 | 2.37 |
57. Quartz diorite (17)* | 184.50 | 14.90 | 11.90 | 46.69 | 20–30 | 13.06 | 12.38 | 11.26(I) | 12.67 | 1.16 | 0.48 | 0.64 | 0.77 | ||||
58. Granite breccia (17)* | 363.00 | 17.80 | 15.84 | 49.26 | 29–35 | 15.26 | 20.39 | 17.72 (I) | 14.49 | 0.58 | 4.55 | 1.88 | 1.35 | ||||
59. Gneiss (17)* | 44.70 | 16.60 | 5.34 | 45.59 | 23–33 | 12.25 | 2.69 | 3.92 (M) | 11.99 | 6.91 | 2.65 | 1.42 | 6.65 | ||||
60. Diorite (17)* | 58.80 | 12.80 | 6.10 | 39.37 | 20–30 | 8.67 | 4.59 | 4.94 (I) | 8.93 | 2.57 | 1.51 | 1.16 | 2.83 | ||||
61. Lamprophyre (17)* | 140.40 | 12.50 | 8.17 | 40.22 | No range | 9.08 | 11.23 | 10.36 (I) | 9.28 | 0.91 | 3.06 | 2.19 | 1.11 | ||||
62. Quartz diorite (17)* | 76.00 | 9.90 | 13.34 | 49.26 | 20–30 | 15.26 | 7.68 | 7.54 (I) | 14.49 | 1.92 | 5.66 | 5.80 | 1.14 | ||||
63. Agglomerate tuff (17)* | 100.10 | 9.30 | 7.93 | 43.55 | 8–18 | 10.91 | 10.76 | 9.99 (I) | 10.85 | 2.98 | 2.83 | 2.06 | 2.92 | ||||
64. Quartzite (17)* | 168.10 | 13.70 | 7.36 | 35.58 | 17–23 | 7.07 | 12.27 | 12.54 (M) | 7.56 | 0.29 | 4.91 | 5.18 | 0.20 | ||||
65. Andesite (17)* | 225.20 | 9.70 | 6.23 | 33.04 | 20–30 | 6.15 | 23.22 | 20.09 (I) | 6.79 | 0.08 | 16.99 | 13.87 | 0.57 | ||||
66. Diorite (17)* | 144.60 | 12.70 | 6.55 | 35.77 | 20–30 | 7.14 | 11.39 | 10.48 (I) | 7.62 | 0.59 | 4.84 | 3.93 | 1.07 | ||||
67. Basalt (17)* | 99.00 | 10.80 | 4.31 | 35.58 | 20–30 | 7.07 | 9.17 | 8.73 (I) | 7.56 | 2.76 | 4.86 | 4.42 | 3.25 | ||||
68. Rhyolite (17)* | 112.00 | 12.50 | 5.43 | 30.13 | 20–30 | 5.21 | 8.96 | 8.56 (I) | 6.03 | 0.22 | 3.53 | 3.13 | 0.60 | ||||
69. Sandston e (18)* | 125.40 | 10.90 | 7.02 | 37.07 | 13–21 | 7.66 | 11.50 | 9.99 (S) | 8.06 | 13.12 | 14.24 | 0.64 | 4.48 | 2.97 | 1.05 | 6.10 | 7.22 |
70. Sandstone (18)* | 115.40 | 11.66 | 7.56 | 36.52 | 13–21 | 7.44 | 9.90 | 8.91 (S) | 7.87 | 12.88 | 14.55 | 0.12 | 2.34 | 1.35 | 0.31 | 5.32 | 6.99 |
71. Quartzite (19)* | 224.10 | 15.70 | 15.72 | 50.80 | 17–23 | 16.83 | 14.27 | 14.19 (M) | 15.75 | 1.12 | 1.45 | 1.53 | 0.04 | ||||
72. Granodiorite (20)* | 230.00 | 17.00 | 18.15 | 51.59 | 26–32 | 17.73 | 13.53 | 12.17 (I) | 16.46 | 0.42 | 4.62 | 5.98 | 1.69 | ||||
73. Sandstone (21)* | 104.00 | 6.01 | 13.36 | 40.55 | 13–21 | 9.25 | 17.30 | 13.73 (S) | 9.42 | 15.40 | 14.95 | 4.12 | 3.93 | 0.36 | 3.94 | 2.04 | 1.58 |
74. Sandstone (22)* | 127.50 | 8.04 | 9.11 | 41.04 | 13–21 | 9.50 | 15.86 | 12.81 (S) | 9.64 | 14.24 | 14.18 | 0.39 | 6.75 | 3.70 | 0.53 | 5.13 | 5.07 |
75. Sandstone (23)* | 42.00 | 3.00 | 14.12 | 43.25 | 13–21 | 10.72 | 14.00 | 11.62 (S) | 10.69 | 18.58 | 18.92 | 3.40 | 0.12 | 2.50 | 3.43 | 4.46 | 4.80 |
76. Limestone (24)* | 186.20 | 8.14 | 5.32 | 40.39 | 9 –15 | 9.17 | 22.87 | 17.23 (S) | 9.35 | 12.79 | 10.04 | 3.85 | 17.55 | 11.91 | 4.04 | 7.47 | 4.73 |
77. Marble (24)* | 102.80 | 7.45 | 8.53 | 30.56 | 6 –12 | 5.34 | 13.80 | 13.80 (M) | 6.13 | 10.63 | 7.82 | 3.19 | 5.28 | 5.28 | 2.39 | 2.10 | 0.70 |
78. Coal (25)* | 6.90 | 0.83 | 15.13 | 30.98 | 5–9 | 5.47 | 8.31 | 7.80 (S) | 6.24 | 24.06 | 31.04 | 9.66 | 6.82 | 7.33 | 8.89 | 8.93 | 15.91 |
79. Coal (25)* | 13.20 | 0.76 | 10.33 | 31.5 | 5–9 | 5.64 | 17.37 | 13.77 (S) | 6.37 | 25.10 | 19.71 | 4.69 | 7.04 | 3.44 | 3.96 | 14.76 | 9.38 |
80. Coal (25)* | 51.40 | 3.41 | 4.21 | 31.29 | 5–9 | 5.57 | 15.07 | 12.31 (S) | 6.32 | 12.21 | 7.61 | 1.36 | 10.86 | 8.10 | 2.11 | 8.00 | 3.40 |
81. Coal (25)* | 23.90 | 2.07 | 8.73 | 31.29 | 5–9 | 5.57 | 11.55 | 10.02 (S) | 6.32 | 15.52 | 13.01 | 3.16 | 2.82 | 1.29 | 2.41 | 6.79 | 4.28 |
82. Coal (25)* | 21.80 | 1.79 | 8.67 | 31.08 | 5–9 | 5.50 | 12.18 | 10.44 (S) | 6.26 | 16.64 | 13.88 | 3.17 | 3.51 | 1.77 | 2.41 | 7.96 | 5.20 |
83. Coal (25)* | 21.70 | 2.45 | 10.03 | 35.58 | 5–9 | 7.07 | 8.86 | 8.19 (S) | 7.56 | 14.31 | 13.92 | 2.96 | 1.17 | 1.84 | 2.47 | 4.28 | 3.89 |
84. Coal (25)* | 15.70 | 2.69 | 12.40 | 33.79 | 5–9 | 6.41 | 5.84 | 5.92 (S) | 7.01 | 13.68 | 17.46 | 5.99 | 6.56 | 6.481 | 5.39 | 1.28 | 5.06 |
85. Coal (25)* | 23.60 | 0.76 | 10.10 | 34.67 | 5–9 | 6.73 | 31.05 | 22.37 (S) | 7.27 | 25.10 | 13.13 | 3.37 | 20.95 | 12.27 | 2.83 | 15.00 | 3.03 |
86. Coal (25)* | 15.90 | 0.62 | 8.92 | 33.84 | 5–9 | 6.43 | 25.65 | 18.96 (S) | 7.02 | 27.67 | 17.31 | 2.49 | 16.74 | 10.05 | 1.89 | 18.76 | 8.39 |
87. Coal (25)* | 10.40 | 0.89 | 12.76 | 32.38 | 5–9 | 5.93 | 11.69 | 10.11 (S) | 6.61 | 23.27 | 23.29 | 6.83 | 1.07 | 2.65 | 6.16 | 10.50 | 10.53 |
88. Coal (25)* | 30.30 | 1.10 | 8.87 | 33.64 | 5–9 | 6.36 | 27.55 | 20.15 (S) | 6.96 | 21.02 | 11.02 | 2.51 | 18.68 | 11.28 | 1.91 | 12.15 | 2.15 |
89. Coal (25)* | 13.50 | 1.10 | 10.42 | 33.94 | 5–9 | 6.46 | 12.27 | 10.50 (S) | 7.05 | 21.02 | 19.41 | 3.96 | 1.85 | 0.08 | 3.37 | 10.60 | 8.99 |
90. Coal (25)* | 25.40 | 1.10 | 9.09 | 35.01 | 5–9 | 6.85 | 23.09 | 17.36 (S) | 7.38 | 21.02 | 12.47 | 2.24 | 14.00 | 8.27 | 1.71 | 11.93 | 3.38 |
91. Coal (25)* | 13.70 | 0.69 | 12.94 | 32.22 | 5–9 | 5.87 | 19.86 | 15.34 (S) | 6.56 | 26.29 | 19.21 | 7.07 | 6.92 | 2.40 | 6.38 | 13.35 | 6.27 |
92.. Coal (25)* | 13.10 | 0.55 | 14.48 | 34.33 | 5–9 | 6.60 | 23.82 | 17.82 (S) | 7.17 | 29.31 | 19.82 | 7.88 | 9.34 | 3.34 | 7.31 | 14.83 | 5.34 |
93. Coal (25)* | 21.50 | 0.76 | 9.78 | 35.05 | 5–9 | 6.87 | 28.29 | 20.62 (S) | 7.39 | 25.10 | 14.01 | 2.91 | 18.51 | 10.85 | 2.39 | 15.31 | 4.23 |
94. Coal (25)* | 25.00 | 1.10 | 11.79 | 35.39 | 5–9 | 7.00 | 22.73 | 17.13 (S) | 7.50 | 21.02 | 12.61 | 4.79 | 10.94 | 5.34 | 4.29 | 9.22 | 0.82 |
95. Coal (25)* | 19.70 | 0.89 | 15.38 | 36.57 | 5–9 | 7.46 | 22.13 | 16.76 (S) | 7.89 | 23.27 | 14.90 | 7.92 | 6.75 | 1.38 | 7.49 | 7.88 | 0.49 |
96. Sandstone (26)* | 48.00 | 3.85 | 11.57 | 34.82 | 13–21 | 6.78 | 12.47 | 10.63 (S) | 7.32 | 17.37 | 18.27 | 4.79 | 0.90 | 0.94 | 4.25 | 3.64 | 6.70 |
97. Sandstone (27)* | 140.20 | 14.02 | 3.98 | 45.59 | 13–21 | 12.25 | 10.00 | 8.98 (S) | 11.99 | 12.26 | 13.83 | 8.28 | 6.03 | 5.00 | 8.01 | 8.10 | 9.85 |
98. Sandstone (28)* | 115.20 | 9.52 | 15.17 | 39.02 | 13–21 | 8.51 | 12.10 | 10.39 (S) | 8.79 | 13.61 | 14.55 | 6.66 | 3.07 | 4.78 | 6.38 | 6.10 | 0.62 |
99. Sandstone (29)* | 80.80 | 7.00 | 12.13 | 40.05 | 13–21 | 9.00 | 11.54 | 10.02 (S) | 9.21 | 14.78 | 15.96 | 3.13 | 0.59 | 2.11 | 2.91 | 5.32 | 3.84 |
100. Sandstone (29)* | 83.90 | 7.60 | 9.64 | 41.04 | 13–21 | 9.50 | 11.04 | 9.68 (S) | 9.64 | 14.46 | 15.80 | 0.14 | 1.40 | 0.04 | 0.00 | 2.04 | 6.16 |
101. Sandstone (29)* | 91.80 | 10.50 | 7.65 | 37.97 | 13–21 | 8.04 | 8.74 | 8.11 (S) | 8.39 | 13.25 | 15.44 | 0.39 | 1.09 | 0.46 | 0.74 | 5.13 | 7.79 |
102. Sandstone (30)* | 41.40 | 2.64 | 12.97 | 39.70 | 13–21 | 8.83 | 15.68 | 12.70 (S) | 9.06 | 19.24 | 18.99 | 4.14 | 2.71 | 0.27 | 3.91 | 4.46 | 6.02 |
103 . Sandstone (30)* | 57.20 | 2.67 | 10.51 | 37.07 | 13–21 | 7.66 | 21.42 | 16.32 (S) | 8.06 | 19.18 | 17.46 | 2.85 | 10.91 | 5.81 | 2.45 | 5.80 | 6.95 |
104. Sandstone (30)* | 44.30 | 2.86 | 16.76 | 42.94 | 13–21 | 10.54 | 15.49 | 12.58 (S) | 10.54 | 18.82 | 18.66 | 6.22 | 1.27 | 4.18 | 6.22 | 8.28 | 1.90 |
105. Sandstone (30)* | 95.50 | 6.31 | 13.38 | 43.85 | 13–21 | 11.09 | 15.13 | 12.35 (S) | 11.01 | 15.20 | 15.28 | 2.29 | 1.75 | 1.03 | 2.37 | 1.57 | 1.90 |
106. Sandstone (30)* | 179.10 | 11.06 | 9.74 | 39.03 | 13–21 | 8.52 | 16.19 | 13.03 (S) | 8.80 | 13.07 | 12.98 | 1.22 | 6.45 | 3.29 | 0.95 | 2.66 | 3.24 |
107 . Sandstone (30)* | 97.00 | 5.39 | 17.80 | 45.87 | 13–21 | 12.45 | 18.00 | 14.17 (S) | 12.16 | 15.86 | 15.22 | 5.35 | 0.20 | 3.63 | 5.64 | 4.82 | 2.58 |
108. Sandstone (30)* | 92.00 | 6.67 | 17.38 | 45.00 | 13–21 | 11.84 | 13.79 | 11.49 (S) | 11.64 | 14.98 | 15.43 | 5.54 | 3.59 | 5.89 | 5.74 | 5.60 | 1.95 |
109. Sandston e (31)* | 79.30 | 3.10 | 19.07 | 40.05 | 13–21 | 9.00 | 25.58 | 18.92 (S) | 9.21 | 18.42 | 16.04 | 10.07 | 6.52 | 0.15 | 9.85 | 6.26 | 3.03 |
110. Sandston e (32)* | 24.30 | 3.29 | 7.22 | 39.03 | 13–21 | 8.52 | 7.39 | 7.13 (S) | 8.80 | 18.13 | 21.81 | 1.30 | 0.17 | 0.09 | 1.58 | 8.67 | 14.60 |
111. Sandstone (33)* | 81.30 | 8.72 | 19.81 | 50.91 | 13–21 | 16.95 | 9.32 | 8.51 (S) | 15.85 | 13.93 | 15.93 | 2.86 | 10.49 | 11.30 | 3.97 | 2.07 | 3.88 |
112. Sandstone (33)* | 62.80 | 8.82 | 17.79 | 51.81 | 13–21 | 17.99 | 7.12 | 6.93 (S) | 16.66 | 13.89 | 17.04 | 0.20 | 10.67 | 10.86 | 1.13 | 1.82 | 0.75 |
113. Sandstone (33)* | 69.30 | 9.59 | 16.55 | 52.67 | 13–21 | 19.07 | 7.23 | 7.01 (S) | 17.50 | 13.58 | 16.61 | 2.52 | 9.32 | 9.54 | 0.95 | 3.32 | 0.06 |
114. Marble (34)* | 28.90 | 4.48 | 7.09 | 33.04 | 6–12 | 6.15 | 6.45 | 7.65 (M) | 6.79 | 14.87 | 15.72 | 0.94 | 0.64 | 0.56 | 0.30 | 7.78 | 8.63 |
115. Granite (34)* | 81.60 | 6.94 | 34.03 | 53.90 | 29–35 | 20.79 | 11.76 | 10.77 (I) | 18.80 | 30.76 | 41.46 | 13.24 | 22.27 | 23.26 | 15.23 | 3.27 | 7.43 |
116. Sandstone (35)* | 67.70 | 4.79 | 12.82 | 42.64 | 13–21 | 10.37 | 14.13 | 11.71 (S) | 10.39 | 16.38 | 16.71 | 2.45 | 1.31 | 1.11 | 2.44 | 3.55 | 3.89 |
117 . Quartzite (35)* | 103.40 | 9.97 | 12.93 | 50.22 | 17–23 | 16.21 | 10.37 | 10.97 (M) | 15.26 | 3.29 | 2.56 | 1.96 | 2.33 | ||||
118. Limestone (36)* | 68.00 | 8.50 | 10.52 | 44.30 | 9–15 | 11.38 | 8.00 | 7.58 (S) | 11.25 | 12.63 | 11.68 | 0.86 | 2.52 | 2.94 | 0.73 | 2.12 | 1.17 |
119. Carbonatite (37) | 113.06 | 9.05** | 12.45 | 47.32 | No range | 13.56 | 12.49 | 11.35 (I) | 13.09 | 1.11 | 0.04 | 1.10 | 0.64 | ||||
120. Syenite (37) | 90.74 | 7.53** | 16.60 | 49.41 | No range | 15.40 | 12.05 | 11.00 (I) | 14.60 | 1.20 | 4.55 | 5.60 | 2.00 | ||||
121. Carbonatite and Syenite (37) | 110.36 | 8.75** | 13.01 | 47.65 | No range | 13.83 | 12.61 | 11.44 (I) | 13.31 | 0.82 | 0.40 | 1.57 | 0.30 | ||||
122.. Amarelo Pais Granite (38) | 85.45 | 6.65** | 40.96 | 57.59 | 29–35 | 27.60 | 12.85 | 11.63 (I) | 23.63 | 31.37 | 41.08 | 13.36 | 28.11 | 29.33 | 17.33 | 9.59 | 0.12 |
123. Blanco Mera Granite (38) | 137.96 | 6.12** | 37.82 | 59.52 | 29–35 | 32.62 | 22.54 | 19.52 (I) | 26.89 | 32.60 | 37.33 | 5.20 | 15.28 | 18.30 | 10.93 | 5.22 | 0.49 |
124. Vilachan Granite (38) | 122.65 | 6.93** | 28.23 | 54.91 | 29–35 | 22.38 | 17.70 | 15.51 (I) | 19.97 | 30.78 | 38.22 | 5.85 | 10.53 | 12.72 | 8.26 | 2.55 | 9.99 |
125. Dolerite (39) | 141.10 | 9.60 | 18.30 | 55.50 | No range | 23.39 | 14.70 | 13.09 (I) | 20.71 | 5.09 | 3.60 | 5.21 | 2.41 | ||||
Average absolute prediction error | 3.23 | 5.54 | 4.74 | 3.75 | 6.41 | 5.97 | |||||||||||
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Karakul, H., Ulusay, R. A new internal friction angle–based approach for estimating Hoek–Brown constant mi and its comparison with those estimated from some current methods. Bull Eng Geol Environ 81, 316 (2022). https://doi.org/10.1007/s10064-022-02820-x
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DOI: https://doi.org/10.1007/s10064-022-02820-x