Introduction
Literature review
Term | Definition | Calculation | Original | Anisotropy | EJRC | References |
---|---|---|---|---|---|---|
θ
ci
| Slope index of element surfaces facing shearing direction | θc = θ*max/(1 + C) | θ*max/C; θ*max/(1 + C) | √ | √ | |
θ
s
| Surface angularity of the entire surface |
\( {\theta}_s=\frac{1}{n}\sum_{I=1}^n{\alpha}_{ij} \)
|
θ
s
| √ | ||
θ
si
| Surface angularity of element surfaces facing shearing direction |
\( {\theta}_{si}=\frac{1}{m_s}\sum_{I=1}^{m_s}{\alpha}_{ij,s} \)
|
θ
s
’
| √ | √ | Lee et al. (2011) |
θ
2
s
| Root mean square of the slopes of entire surface |
\( {\theta}_{2s}=\sqrt{\frac{\sum \sum {tan}^2{\alpha}_{ij}}{n}} \)
| Z2s; Sdq; Z2 | |||
θ
2
si
| Root mean square of the slopes facing shearing direction |
\( {\theta}_{2 si}=\sqrt{\frac{\sum \sum {tan}^2{\alpha}_{ij,s}}{m_s}} \)
|
Z
2,k
| √ | √ | Zhang et al. (2009) |
Term | Definition | Calculation | Original | Anisotropy | EJRC | References |
---|---|---|---|---|---|---|
S
s
| Ratio of actual and nominal areas |
\( {S}_s=\frac{A_t}{A_n} \)
| Rs; Rs–1; Sts; SRs; Sdr | |||
S
bap
| Brightened area percentage |
\( {S}_{bap}=\frac{A_b}{A_t}\times 100\% \)
|
BAP
| √ | √ | Ge et al. (2012) |
S
dr
| Degree of joint interface relative surface roughness | Sdr = 1–1/Ss |
DR
r
| Belem et al. (2000) | ||
S
ts
| Surface tortuosity coefficient |
\( {S}_{ts}=\frac{A_t}{A_n} cos\phi \)
|
T
s
| Belem et al. (2000) |
Term | Definition | Parameter | Original | References |
---|---|---|---|---|
Z
rms
| Root mean square height of z |
\( {Z}_{rms}={\left(\frac{1}{N}\iint {z_{ij}}^2 dxdy\right)}^{1/2} \)
| RMS; Sq | |
Z
Sz
| Ten-point height |
\( {Z}_{Sz}=\frac{\sum_1^5\left|{z}_{pi}\right|+\sum_1^5\left|{z}_{vi}\right|}{10} \)
|
S
z
| ISO 25178–2: 2012 |
Z
sa
| Mean of the absolute of z |
\( {Z}_{sa}=\frac{1}{m\times n}\sum_{j=1}^m\sum_{I=1}^n\left|{z}_{ij}\right| \)
|
S
a
| |
Z
ss
| Skewness of the surface |
\( {Z}_{ss}=\frac{\frac{1}{m\times n}\sum_{j=1}^m\sum_{I=1}^n{z_{ij}}^3}{{Z_{rms}}^3} \)
|
S
sk
| ISO 25178–2: 2012 |
Z
sk
| Kurtosis of the surface |
\( {Z}_{sk}=\frac{\frac{1}{m\times n}\sum_{j=1}^m\sum_{I=1}^n{z_{ij}}^4}{{Z_{rms}}^4} \)
|
S
kw
| ISO 25178–2: 2012 |
Z
range
| Range of z | Zrange = zmax– zmin | Range; Sp | |
V
svi
| Valley fluid retention index |
\( {V}_{svi}=\frac{V_v\left({h}_{0.8}\right)}{Z_{rms}\left(M-1\right)\left(N-1\right)\varDelta x\varDelta y} \)
|
S
vi
| ISO 25178–2: 2012 |
V
sci
| Core fluid retention index |
\( {V}_{sci}=\frac{V_v\left({h}_{0.05}\right)-{V}_v\left({h}_{0.8}\right)}{Z_{rms}\left(M-1\right)\left(N-1\right)\varDelta x\varDelta y} \)
|
S
ci
| ISO 25178–2: 2012 |
Experiments
Sample preparation
Mechanical properties
Sample no. | φb (°) | JCS (MPa) | σn/JCS | τ (kPa) | STD |
---|---|---|---|---|---|
1 | 28.0 | 33.62 | 0.01 | 585.38 | 60.1 |
2 | 30.6 | 25.93 | 0.02 | 672.42 | 35.2 |
3 | 28.0 | 15.02 | 0.03 | 710.05 | 135.0 |
4 | 28.0 | 28.69 | 0.02 | 670.76 | 83.5 |
5 | 28.0 | 26.41 | 0.02 | 458.71 | 48.3 |
6 | 28.0 | 31.94 | 0.02 | 629.93 | 160.2 |
7 | 28.0 | 21.95 | 0.02 | 617.60 | 91.1 |
8 | 28.0 | 20.13 | 0.02 | 619.29 | 143.8 |
9 | 28.0 | 18.30 | 0.03 | 356.84 | 93.3 |
10 | 28.0 | 28.95 | 0.02 | 607.11 | 47.0 |
11 | 29.7 | 36.06 | 0.01 | 352.57 | 16.7 |
12 | 28.0 | 23.08 | 0.02 | 703.71 | 66.0 |
13 | 24.1 | 71.19 | 0.01 | 223.50 | 8.9 |
14 | 27.9 | 39.29 | 0.01 | 530.50 | 128.5 |
15 | 27.9 | 42.99 | 0.01 | 697.75 | 50.0 |
16 | 27.9 | 41.50 | 0.01 | 659.50 | 97.7 |
17 | 27.9 | 37.49 | 0.01 | 627.00 | 66.5 |
18 | 27.9 | 36.27 | 0.01 | 717.75 | 125.5 |
19 | 27.9 | 40.94 | 0.01 | 641.50 | 93.0 |
20 | 27.9 | 33.71 | 0.01 | 820.75 | 61.2 |
21 | 27.9 | 40.71 | 0.01 | 668.50 | 73.8 |
22 | 27.8 | 53.76 | 0.01 | 852.79 | 65.8 |
23 | 27.9 | 27.37 | 0.02 | 248.50 | 61.2 |
24 | 27.9 | 25.47 | 0.02 | 453.25 | 91.4 |
25 | 27.9 | 71.01 | 0.01 | 264.75 | 4.8 |
26 | 27.8 | 47.47 | 0.01 | 491.19 | 80.7 |
27 | 27.9 | 31.85 | 0.02 | 695.75 | 73.4 |
28 | 27.8 | 42.75 | 0.01 | 460.87 | 47.8 |
29 | 27.8 | 51.81 | 0.01 | 537.75 | 58.2 |
30 | 27.8 | 35.76 | 0.01 | 706.17 | 72.8 |
31 | 27.8 | 47.09 | 0.01 | 518.86 | 47.4 |
32 | 27.8 | 67.60 | 0.01 | 406.13 | 73.3 |
33 | 27.8 | 67.60 | 0.01 | 409.09 | 26.3 |
34 | 27.8 | 51.81 | 0.01 | 480.37 | 97.9 |
35 | 27.8 | 63.20 | 0.01 | 473.90 | 66.5 |
36 | 27.8 | 56.50 | 0.01 | 417.60 | 77.3 |
37 | 27.8 | 55.62 | 0.01 | 448.68 | 39.6 |
38 | 27.9 | 44.76 | 0.01 | 645.50 | 98.8 |
Surface measurements
Sample no. | Variation of height parameters between upper and lower surface (%) | Difference of height parameters between pre- and post-shear surfaces (%) | ||||
---|---|---|---|---|---|---|
V
rms
|
V
sa
|
V
range
|
D
rms
|
D
sa
|
D
range
| |
1 | − 2.78 | − 3.18 | − 3.49 | 0.30 | 0.29 | 0.44 |
2 | 1.41 | 1.48 | 1.49 | 0.08 | 0.09 | 0.13 |
3 | − 2.43 | −2.61 | − 2.70 | 0.29 | 0.30 | 0.4 |
4 | 1.28 | 1.44 | 1.50 | 0.90 | 0.90 | 1.35 |
5 | 2.89 | 2.99 | 3.10 | 0.41 | 0.42 | 0.42 |
6
| − 0.91 | − 1.02 | − 1.08 | 1.14 | 1.17 | 1.18 |
7
| 2.73 | 3.15 | 3.20 | 0.04 | 0.05 | 0.05 |
8
| 2.84 | 3.20 | 3.51 | 0.24 | 0.25 | 0.25 |
9
| − 3.07 | − 3.52 | − 3.83 | 0.37 | 0.37 | 0.56 |
10
| − 3.19 | − 3.72 | − 3.76 | 1.24 | 1.27 | 1.28 |
11
| 1.63 | 1.76 | 1.76 | 1.10 | 1.12 | 1.13 |
12
| 2.50 | 2.75 | 2.90 | 0.19 | 0.19 | 0.28 |
13
| 2.47 | 2.76 | 2.78 | 0.71 | 0.72 | 1.08 |
14
| − 4.68 | − 4.68 | − 2.93 | 0.14 | 0.14 | 0.23 |
15
| 1.37 | 1.37 | 1.62 | 0.06 | 0.06 | 0.26 |
16
| − 3.02 | − 3.01 | 0.83 | 0.06 | 0.06 | 1.49 |
17
| − 2.25 | − 2.25 | − 0.49 | 0.10 | 0.11 | 1.43 |
18
| 0.56 | 0.59 | 0.30 | 0.32 | 0.32 | 1.52 |
19
| 2.54 | 2.60 | 2.62 | 0.60 | 0.60 | 0.10 |
20
| 1.19 | 1.32 | 1.45 | 0.76 | 0.76 | 1.44 |
21
| − 0.18 | − 0.20 | − 0.21 | 0.24 | 0.24 | 0.61 |
22
| 2.34 | 2.81 | 3.04 | 0.29 | 0.29 | 0.44 |
23
| 1.84 | 2.03 | 2.09 | 1.09 | 1.07 | 1.60 |
24
| 0.96 | 1.05 | 1.10 | 0.87 | 0.89 | 0.90 |
25
| 0.48 | 0.56 | 0.59 | 1.07 | 0.64 | 1.34 |
26
| 2.40 | 2.79 | 2.89 | 0.66 | 0.65 | 1.23 |
27
| − 2.12 | − 2.33 | − 2.33 | 0.47 | 0.48 | 2.16 |
28
| 2.99 | 3.38 | 3.65 | 1.04 | 1.06 | 2.02 |
29
| − 1.60 | − 1.78 | − 1.93 | 0.89 | 0.87 | 1.31 |
30
| − 2.51 | − 2.77 | − 2.87 | 1.15 | 1.17 | 1.18 |
31
| 1.65 | 1.87 | 2.03 | 0.09 | 0.09 | 0.09 |
32
| 2.34 | 2.51 | 2.73 | 1.14 | 1.17 | 1.18 |
33
| 2.77 | 3.02 | 3.05 | 0.66 | 0.66 | 0.67 |
34
| 0.77 | 0.86 | 0.93 | 0.52 | 0.53 | 0.54 |
35
| − 3.13 | − 3.39 | − 3.55 | 0.12 | 0.13 | 0.13 |
36
| 2.82 | 2.89 | 3.06 | 1.00 | 1.02 | 1.03 |
37
| 0.73 | 0.81 | 0.84 | 0.45 | 0.46 | 0.47 |
38
| − 1.57 | − 1.79 | − 1.81 | 0.28 | 0.27 | 0.36 |
Empirical equations for the entire surface
Slope parameters
Variable | Equation | R2 |
---|---|---|
θ
s
| JRC = 2.9θs0.7 + SI0.809–5.6 | 0.902 |
θ
g
| JRC = 3.9θg0.6 + SI0.815–7.7 | 0.900 |
θ
2s
| JRC = 36.5S2s0.5 + SI0.845–7.8 | 0.883 |
S
sT
| JRC = 47.7(SsT – 1)0.3 + SI0.836–6.7 | 0.889 |
S
sF
| JRC = 47.8(SsF – 1)0.3 + SI0.837–6.7 | 0.888 |
V
an
| JRC = 43.9Van0.1+ SI0.087–34.4 | 0.824 |
Z
sa
| JRC = 58.5Zsa0.1 – SI-0.071 – 48.9 | 0.804 |
Z
rms
| JRC = 63.2Zrms0.1+ SI-0.090 – 54.7 | 0.798 |
Z
range
| JRC = 15.5 Zrange0.2 + SI0.166–15.8 | 0.759 |