The pivotal aim of this study is to evaluate the rock mass characterization and deformation modulus. It is vital for rock mass classification to investigate important parameters of discontinuities. Therefore, Rock Mass Rating (RMR) and Tunneling quality index (Q) classification systems are applied to analyze 22 segments along proposed tunnel routes for hydropower in Kandiah valley, Khyber Pakhtunkhwa, Pakistan. RMR revealed the range of fair to good quality rocks, whereas Q yielded poor to fair quality rocks for investigated segments of the rock mass. Besides, E m values were acquired by empirical equations and computer-aided program RocLab, and both methods presented almost similar variation trend of their results. Hence, the correlations of E m with Q and RMR were carried out with higher values of the regression coefficient. This study has scientific significance to initially understand the rock mass conditions of Kandiah valley.
Geomechanical investigation of the rock mass is an essential part of the feasibility phase of hydropower projects when very little information is available, to ascertain the response of rock behavior under disturbance or excavation. Rock mass characteristics are determined by empirical classification systems to classify the rock mass [
Pakistan is facing a serious shortage of electricity, and Government is trying to develop hydropower, especially in Northern Pakistan to overcome the electricity disorder. In this regard, small hydropower is proposed along Kandiah River in Kandiah valley, KPK, Pakistan. Hence, the present study focuses on preliminary rock mass characterization with an assessment of required support and estimation of deformation modulus along proposed tunnel routes. Therefore, to achieve this goal, field observations including geological mapping, discontinuity surveys and sampling were conducted.
The study area is near about 30 Km long V-shaped valley with steep slopes on either side of Kandiah River. Tectonically it is situated in Kohistan Island Arc (KIA) and surrounded by two sutures formed by the collision of Indian plate with Eurasian plate, whereas the first suture is known as northern suture from Eurasian plate and the second suture is between Main Mantel Thrust (MMT) and Indian plate, respectively (
Tunnel routes were divided into segments and various traverses were made to mark geological contacts (
RMR and Q are universal classification systems, and these systems have been applied by many researchers in tunneling and underground excavation. Bieniawski [
had made over the many years e.g. [
R M R = R 1 + R 2 + R 3 + R 4 + R 5 + R 6 (1)
where, R 1 − R 6 are the above mentioned parameters of discontinuities.
Barton et al. [
Q = ( RQD / Jn ) × ( Jr / Ja ) × ( Jw / SRF ) (2)
RQD is rock quality designation, Jn is the joint set number, Jr and Ja are the ratings of roughness and alteration number, Jw is for water inflow and pressure effects, and SRF is the stress reduction factor. Moreover, terms Jr / Ja represents peak strength, RQD / Jn indicates the relative block size and Jw / SRF related to the effective strength of the rock mass. It is noticed by the Equation (1) and Equation (2) that RMR values are calculated by summation of all assigned ratings, whereas Q values are calculated by divisions and products of assigned ratings to parameters.
There are several equations proposed by different researchers to estimate deformation modulus (Em) based on Geomechanical classification systems e.g. [
In order to calculate the deformation modulus of rock mass, at least rating value of one rock mass classification system is required because joint’s properties (e.g. roughness, weathering, infilling material, aperture, persistence, etc.) have significant effect on rock mass deformation [
This paper highlights the characterization of rock mass by RMR and Q schemes. Furthermore, discontinuity surveys were conducted at various locations to collect the required parameters for the estimation of RMR and Q values. The orientation data of discontinuities were analysed by computer program DIPS (version 5.1) that show mostly 2 to 3 joints sets were prevailing in the study area. The field surveys revealed that discontinuity’s trend was mostly dipping towards the tunnel axis but at some points, the trend was away from tunnel axis, as well as at few locations strike was parallel to the tunnel axis.
The RMR values vary from 53 (fair) to 65 (good) with a mean of 57 (
The comparisons of RMR and Q values were analyzed by using the results of input parameters to calculate the empirical ratings for tunnel alignments. Along left tunnel route, RMR designated ten segments as a fair rock and only one segment (20+000 - 22+000) show good rock but according to Q system, same segments were designated as a poor rock except for three segments (3+000 - 5+000, 17+000 - 19+000, 20+000 - 22+000) that revealed a fair quality rock. Similarly, values of RMR along different segments of right tunnel route gave fair rock quality except for one segment (12+000 - 15+000) that designated as good quality of rock and Q system designated various segments as poor quality except for one segment (15+000 - 20+000) that presented fair quality of rock mass. The calculated ratings suggest that Q system provided a more conservative approach as compare to RMR system for rock mass classification. The variation in values of RMR and Q plotted in
Plots and curved | Equations | Equation No. | Researcher (s) |
---|---|---|---|
○ | Field Data | [ | |
◇ | Field Data | [ | |
□ | Field Data | [ | |
1 | E m = 2 R M R − 100 for R M R > 50 | 3 | [ |
2 | E m = 10 ( R M R − 10 ) / 40 | 4 | [ |
3 | E m = E i / 100 ( 0.0028 R M R 2 + 0.9 exp ( R M R / 22.82 ) ) , E i = 50 Gpa | 5 | [ |
4 | E m = E i ( 0.5 ( 1 − cos ( π R M R / 100 ) ) ) , E i = 50 Gpa | 6 | [ |
5 | E m = 0.1 ( R M R / 10 ) 3 | 7 | [ |
6 | E m = 10 Q c 1 / 3 where Q c = Q σ c i / 100 | 8 | [ |
7 | E m = ( 1 − d 2 ) σ c i 100 × 10 ( R M R − 10 ) / 40 | 9 | [ |
8 | E m = E i ( S a ) 0.4 E i = 50 GPa , s = exp ( ( G S I − 100 ) / 9 ) | 10 | [ |
9 | E m = E i S 1 / 4 E i = 50 GPa , s = exp ( ( G S I − 100 ) / 9 ) | 11 | [ |
10 | E m = 7 ( ± 3 ) Q ′ Q ′ = 10 ( ( R M R − 44 ) / 21 ) | 12 | [ |
Empirical Equation | Equation No. | Required Parameter | Reference |
---|---|---|---|
E m ( G P a ) = 40 log Q ( A v g . ) | 13 | Q | [ |
E m ( G P a ) = 8 Q 0.4 | 14 | Q | [ |
E m ( G P a ) = 2 R M R − 100 for R M R > 50 | 3 | RMR | [ |
E m ( G P a ) = 0.1 ( R M R / 10 ) 3 | 7 | RMR | [ |
E m ( G P a ) = 5.6 ( R M R ) 0.375 | 15 | RMR | [ |
E m ( G P a ) = 0.0736 e 0.0755 R M R | 16 | RMR | [ |
Chainage | Uniaxial compressive strength (Avg.) | Rock Quality Designation (Avg.) | Spacing (Avg.) | Discontinuity Condition | Water Condition | RMR Value | Description | Rock Class | GSI (RMR-5) | |
---|---|---|---|---|---|---|---|---|---|---|
From | To | |||||||||
0+00 | 1+000 | 7 | 8 | 10 | Persistence > 10 - 15 m, aperture > 1 - 5 mm, slightly rough to rough, slightly to moderately weathered | Approx. Damp to completely dry | 57 | Fair | III | 52 |
1+000 | 3+000 | 12 | 8 | 8 | 56 | Fair | III | 51 | ||
3+000 | 5+000 | 12 | 13 | 10 | 59 | Fair | III | 54 | ||
5+000 | 7+000 | 7 | 13 | 10 | 55 | Fair | III | 50 | ||
7+000 | 10+000 | 7 | 17 | 10 | 58 | Fair | III | 53 | ||
10+000 | 14+000 | 7 | 13 | 10 | 57 | Fair | III | 52 | ||
14+000 | 17+000 | 7 | 13 | 5 | 53 | Fair | III | 48 | ||
17+000 | 19+000 | 12 | 8 | 15 | 59 | Fair | III | 54 | ||
19+000 | 20+000 | 7 | 8 | 15 | 57 | Fair | III | 52 | ||
20+000 | 22+000 | 7 | 13 | 15 | 65 | Good | II | 60 | ||
22+000 | 24+000 | 7 | 13 | 15 | 57 | Fair | III | 52 |
Chainage | Uniaxial compressive strength (Avg.) | Rock Quality Designation (Avg.) | Spacing (Avg.) | Discontinuity Condition | Water Condition | RMR Value | Description | Rock Class | GSI (RMR-5) | |
---|---|---|---|---|---|---|---|---|---|---|
From | To | |||||||||
0+00 | 2+000 | 7 | 13 | 10 | Persistence > 10 - 15 m, aperture > 15 mm, slightly rough to rough, slightly to moderately weathered | Approx. damp to completely dry | 59 | Fair | III | 54 |
2+000 | 3+000 | 7 | 13 | 10 | 58 | Fair | III | 53 | ||
3+000 | 5+000 | 7 | 8 | 10 | 51 | Fair | III | 46 | ||
5+000 | 6+000 | 7 | 13 | 10 | 58 | Fair | III | 53 | ||
6+000 | 8+000 | 7 | 8 | 10 | 55 | Fair | III | 50 | ||
8+000 | 9+000 | 7 | 17 | 10 | 53 | Fair | III | 48 | ||
9+000 | 10+000 | 12 | 13 | 10 | 53 | Fair | III | 48 | ||
10+000 | 12+000 | 7 | 13 | 10 | 57 | Fair | III | 52 | ||
12+000 | 15+000 | 12 | 13 | 10 | 62 | Good | II | 57 | ||
15+000 | 20+000 | 7 | 13 | 8 | 57 | Fair | III | 52 | ||
20+000 | 22+000 | 4 | 13 | 15 | 51 | Fair | III | 46 |
Chainage | RQD (Avg.) | JN | JR (Avg.) | JA (Avg.) | JW (Avg.) | SRF (Avg.) | Q-Value | Description | |
---|---|---|---|---|---|---|---|---|---|
From | To | ||||||||
0+00 | 1+000 | 48 | 9 | 1.5 | 2 | 1 | 2.5 | 1.60 | Poor |
1+000 | 3+000 | 50 | 9 | 3 | 2 | 1 | 2.5 | 3.33 | Poor |
3+000 | 5+000 | 64 | 9 | 1.5 | 1 | 1 | 2.5 | 4.27 | Fair |
5+000 | 7+000 | 64 | 9 | 1.5 | 2 | 1 | 2.5 | 2.13 | Poor |
7+000 | 10+000 | 76 | 9 | 1.5 | 2 | 1 | 2.5 | 2.53 | Poor |
10+000 | 14+000 | 60 | 9 | 1.5 | 2 | 1 | 2.5 | 2.00 | Poor |
14+000 | 17+000 | 59 | 9 | 1.5 | 1 | 1 | 2.5 | 3.93 | Poor |
17+000 | 19+000 | 46 | 9 | 3 | 1 | 1 | 2.5 | 6.13 | Fair |
---|---|---|---|---|---|---|---|---|---|
19+000 | 20+000 | 48 | 9 | 3 | 2 | 1 | 2.5 | 3.20 | Poor |
20+000 | 22+000 | 62 | 9 | 3 | 2 | 1 | 2.5 | 4.13 | Fair |
22+000 | 24+000 | 64 | 9 | 1.5 | 2 | 1 | 2.5 | 2.13 | Poor |
Chainage | RQD (Avg.) | JN | JR (Avg.) | JA (Avg.) | JW (Avg.) | SRF (Avg.) | Q-Value | Description | |
---|---|---|---|---|---|---|---|---|---|
From | To | ||||||||
0+00 | 2+000 | 56 | 9 | 3 | 2 | 1 | 2.5 | 3.73 | Poor |
2+000 | 3+000 | 58 | 9 | 1.5 | 2 | 1 | 2.5 | 1.93 | Poor |
3+000 | 5+000 | 48 | 9 | 1.5 | 2 | 1 | 2.5 | 1.60 | Poor |
5+000 | 6+000 | 54 | 9 | 1.5 | 2 | 1 | 2.5 | 1.80 | Poor |
6+000 | 8+000 | 48 | 9 | 1.5 | 1 | 1 | 2.5 | 3.20 | Poor |
8+000 | 9+000 | 76 | 9 | 1.5 | 2 | 1 | 2.5 | 2.53 | Poor |
9+000 | 10+000 | 56 | 9 | 3 | 2 | 1 | 2.5 | 3.73 | Poor |
10+000 | 12+000 | 60 | 9 | 1.5 | 2 | 1 | 2.5 | 2.00 | Poor |
12+000 | 15+000 | 68 | 9 | 1.5 | 2 | 1 | 2.5 | 2.27 | Poor |
15+000 | 20+000 | 64 | 9 | 1.5 | 1 | 1 | 2.5 | 4.27 | Fair |
20+000 | 22+000 | 58 | 9 | 3 | 2 | 1 | 2.5 | 3.87 | Poor |
Sr. No. | RMR values | Q values | Estimated support by RMR | Estimated support by Q |
---|---|---|---|---|
1 | 41 - 60 | 1 - 4 | Systematic bolts 4.0 m long, 1.5 - 2.0 m spaced in crown and walls with wire mesh in the crown. 50 - 100 mm shotcrete in crown and 30 mm. | Systematic bolting with 40 - 100 mm unreinforced shotcrete. |
2 | 61 - 80 | 4 - 10 | Locally, bolts in crown 3 m long, spaced 2.5 m with occasional wire mesh. Shotcrete 50 mm in crown where required. | Systematic bolting |
In this study, Em values were calculated for total 22 segments along tunnel alignments by widely accepted empirical equations and presented in
The calculated values of Em from empirical equations were compared with rock mass quality (
The relationships of Em with Q and RMR were derived and presented in
The Em values were also determined by the computer-aided program RocLab by using various required parameters of rock mass like Geological strength index (GSI), UCS, etc. and listed in
Chainage | Em by using Q values | Em by using RMR values | Em by Using RocLab GPa | |||||
---|---|---|---|---|---|---|---|---|
Grimstad and Barton [ | Palmstrom and Singh [ | Bieniawski [ | Read et al. [ | Palmstrom [ | Gokceoglu et al. [ | |||
(Equation (13)) | (Equation (14)) | (Equation (3)) | (Equation (7)) | (Equation (15)) | (Equation (16)) | |||
0+00 | 1+000 | 8.16 | 9.65 | 14.00 | 18.52 | 25.51 | 5.44 | 10.68 |
1+000 | 3+000 | 20.92 | 12.95 | 12.00 | 17.56 | 25.34 | 5.05 | 11.66 |
3+000 | 5+000 | 25.20 | 14.29 | 18.00 | 20.54 | 25.84 | 6.33 | 13.20 |
5+000 | 7+000 | 13.16 | 10.83 | 10.00 | 16.64 | 25.17 | 4.68 | 9.18 |
7+000 | 10+000 | 16.15 | 11.60 | 16.00 | 19.51 | 25.67 | 5.87 | 13.84 |
10+000 | 14+000 | 12.04 | 10.56 | 14.00 | 18.52 | 25.51 | 5.44 | 12.14 |
14+000 | 17+000 | 23.79 | 13.84 | 6.00 | 14.89 | 24.82 | 4.02 | 7.76 |
17+000 | 19+000 | 31.51 | 16.53 | 18.00 | 20.54 | 25.84 | 6.33 | 14.08 |
19+000 | 20+000 | 20.21 | 12.74 | 14.00 | 18.52 | 25.51 | 5.44 | 10.34 |
20+000 | 22+000 | 24.65 | 14.11 | 30.00 | 27.46 | 26.79 | 9.96 | 16.22 |
22+000 | 24+000 | 13.16 | 10.83 | 14.00 | 18.52 | 25.51 | 5.44 | 10.11 |
Chainage | Em by using Q values | Em by using RMR values | Em by Using RocLab GPa | |||||
---|---|---|---|---|---|---|---|---|
Grimstad and Barton [ | Palmstrom and Singh [ | Bieniawski [ | Read et al. [ | Palmstrom [ | Gokceoglu et al. [ | |||
(Equation (13)) | (Equation (14)) | (Equation (3)) | (Equation (7)) | (Equation (15)) | (Equation (16)) | |||
0+00 | 2+000 | 22.88 | 13.55 | 18.00 | 20.54 | 25.84 | 6.33 | 11.32 |
2+000 | 3+000 | 11.45 | 10.41 | 16.00 | 19.51 | 25.67 | 5.87 | 11.42 |
3+000 | 5+000 | 8.16 | 9.65 | 2.00 | 13.27 | 24.46 | 3.46 | 7.14 |
5+000 | 6+000 | 10.21 | 10.12 | 16.00 | 19.51 | 25.67 | 5.87 | 13.34 |
6+000 | 8+000 | 20.21 | 12.74 | 10.00 | 16.64 | 25.17 | 4.68 | 10.78 |
8+000 | 9+000 | 16.15 | 11.60 | 6.00 | 14.89 | 24.82 | 4.02 | 10.26 |
9+000 | 10+000 | 22.88 | 13.55 | 6.00 | 14.89 | 24.82 | 4.02 | 10.63 |
10+000 | 12+000 | 12.04 | 10.56 | 14.00 | 18.52 | 25.51 | 5.44 | 12.14 |
12+000 | 15+000 | 14.22 | 11.10 | 24.00 | 23.83 | 26.32 | 7.94 | 14.99 |
15+000 | 20+000 | 25.20 | 14.29 | 14.00 | 18.52 | 25.51 | 5.44 | 9.89 |
20+000 | 22+000 | 23.49 | 13.74 | 2.00 | 13.27 | 24.46 | 3.46 | 7.30 |
Parameters | Relation | R2 | Equation No. |
---|---|---|---|
Q | Em = 6.3036Q − 0.7354 | 0.98 | 16 |
Em = 1.7308Q + 7.071 | 0.99 | 17 | |
Em = 5.1659Q + 2.371 | 0.96 | 18 | |
Em = 1.5264Q + 7.6272 | 0.98 | 19 | |
RMR | Em = 2RMR − 100 | 1.00 | 20 |
Em = 1.0556RMR − 41.541 | 0.99 | 21 | |
Em = 0.5008xRMR − 22.998 | 0.97 | 22 | |
Em = 0.1641RMR + 16.148 | 0.99 | 23 | |
Em = 0.9402RMR − 34.899 | 0.99 | 24 | |
Em = 0.387RMR − 16.461 | 0.98 | 25 | |
Em = 0.17RMR + 15.804 | 0.99 | 26 |
*y is for Em and x for RMR & Q.
Rock mass classification and deformation modulus were studied by RMR and Q schemes on the basis of field studies, laboratory studies, computation work, and graphical representation. RMR yielded fair to good quality rocks with values from 53 to 65 along left tunnel alignment and 51 to 62 along right tunnel alignment. While Q values vary between 1.60 to 6.13 for left tunnel alignment and 1.60 to 4.27 for right tunnel alignment with covering a range of poor to fair quality rocks. This study has predicted that segments of left tunnel alignment have fair rocks except for one segment (20+000 - 22+000) of good quality rocks, but Q values for the same segments presented poor rock quality except for three segments (3+000 - 5+000, 17+000 - 19+000, 20+000 - 22+000) that designated fair rock quality. Similarly, for right tunnel alignment, RMR values revealed fair rocks except for one segment (12+000 - 15+000) of good quality rocks, but Q yielded poor rock quality except for one segment (15+000 - 20+000) of fair rock quality. The estimated values of Em by various equations have the more or less similar trend of variation with respect to rock quality of study area, respectively. The plots of Em with RMR and Q indicated significant correlations (R2 = 0.96 - 1). Furthermore, this study revealed that Em values obtained by RocLab are on the lower side as compare to Em (Avg.) values obtained by empirical equations and both methods have witnessed their results with the almost similar trend of variation. Moreover, it is recommended that detail investigation of joints, weak zones and laboratory analyses for assessment of appropriate support along tunnel alignments would be necessary.
The authors declare no conflicts of interest regarding the publication of this paper.
Akram, M.S., Mirza, K., Zeeshan, M. and Jabbar, M.A. (2018) Assessment of Rock Mass Quality and Deformation Modulus by Empirical Methods along Kandiah River, KPK, Pakistan. Open Journal of Geology, 8, 947-964. https://doi.org/10.4236/ojg.2018.810057