Assessment of Rock Mass Quality and Deformation Modulus by Empirical Methods along Kandiah River , KPK , Pakistan

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, Em 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 Em 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.


Introduction
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 [1].Hence, Rock Mass Rating (RMR) and Tunneling quality index (Q) classification systems are pivotal to classify the rock mass.Extensive studies

Geological Setting of Study Area
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 (Figure 1) [26].Chilas Complex (CC) and Gilgit Complex (GC) are two prevailing major geological units in the study area.The CC dominantly composed of intermediate to basic plutonic rocks such as diorite (Figure2(a)), gabbro, anorthosite, pyroxenite and GC comprising metasediments such as psammite (Figure2(b)) and protolith of metasediments.Moreover, Pleistocene unconsolidated deposits are also observed in the valley at different places, which are the result of river bed deposits, fan deposits, talus, fluvial deposits, scree and glacial deposits.

Data Geological Mapping and Discontinuity Survey
Tunnel routes were divided into segments and various traverses were made to mark geological contacts (Figure 3).According to International Society for Rock Mechanics [27], physical parameters (orientation, spacing, persistence, aperture, roughness, the number of joint sets, infilling material and hydraulic conditions)were frequently executed of all those discontinuities that were intersecting the reference line by measuring tape of approx.10 m during scanline surveys [28].

Rock Mass Rating (RMR) and Tunneling Quality Index (Q)
RMR and Q are universal classification systems, and these systems have been applied by many researchers in tunneling and underground excavation.Bieniawski [29] developed RMR system by providing quantitative data for reinforcement of tunnel techniqueslike rock bolts, shotcrete etc.The modifications Figure 1.Regional tectonic map of study area (Modified after Tahirkheli and Jan [26]).had made over the many years e.g.[29] [30] [31] [32] [33].In beginning, the system was established for only tunnels but with the passage of time, this system is also used for foundations, rock slopes, and mining problems.The following parameters were investigated during field work to calculate the RMR values: Uniaxial compressive strength (UCS), spacing, rock quality designation (RQD), ground water conditions, discontinuity conditions and orientation of discontinuities [3] [8] [10].The RMR values are estimated by following equation [29]: where, 1 6 R R − are the above mentioned parameters of discontinuities.
Barton et al. [34] proposed Q system that was used to determine rock mass quality and required support estimation for tunnels.The overall Q values ranged between 0.001 (exceptionally poor) to 1000 (exceptionally good) and can be estimated by using this expression: RQD is rock quality designation, J n is the joint set number, J r and J a are the ratings of roughness and alteration number, J w is for water inflow and pressure effects, and SRF is the stress reduction factor.Moreover, terms Jr Ja  4 by Hoek and Diederichs [7] and relevant equations are listed in Table 1.
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 [24] [40].Hence, equations proposed by different researchers (Table 2) in which RMR and Q values considered as input parameters to estimate E m .

Rock Mass Classification
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 (Table 3) on left route and values ranged between 51 (fair) to 62 (good) with average 56 (Table 4) for the right route of the tunnel.Moreover, Q values of rock mass ranged between 1.60 (poor) to 6.13 (fair) with an average of 3.22 along left tunnel route and 1.60 (poor) to 4.27 (fair) with an average of 2.81 along right tunnel alignment.The detail ratings of all required parameters with Q values are listed in Table 5 and Table 6.
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 quali-ty 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 Figure 5 and estimated support for specific rock class is summarized in Table 7.
Table 1.Empirical equations and field data of different researchers plotted in Figure 4 (after Hoek and Diederichs [7]).

Estimation of Rock Mass Deformation Modulus
In this study, E m values were calculated for total 22 segments along tunnel alignments by widely accepted empirical equations and presented in Table 8 and Table 9. E m values of left tunnel alignment obtained from Palmstrom and Singh [21] (9.65 -16.53 GPa, Avg.12.54 GPa) are on the lower side as compare to Grimstad and Barton [41] ranged between 8.16 -31.51 GPa with an average of 19 GPa by using Q values.However, the range of E m values calculated with RMR values by Bieniawski [15] is 6 -30 GPa with average 15.09GPa and by Read et al. [20] values range between 14.89 -27.46 GPa (average 19.20 GPa).Similarly, E m values vary between 4.02 -9.96 GPa with an average of 5.82 GPa by Gokceoglu et al. [22] and the equation of Palmstrom [42] provides the values range of 24.82 - 26.79 GPa with average 25.59 GPa.The E m values of right tunnel alignment calculated from Palmstrom and Singh [21] vary within the range of 9.65 -14.29 GPa with an average of 11.94 GPa and values by Grimstad and Barton [41] ranged between 8.16 -25.20 GPa with an average of 16.99 GPa by using Q values.Likewise, calculated values of E m using RMR values by Bieniawski [15] vary between 2 -24 GPa with average 11.64 GPa and by Read et al. [20] values range between 13.27 -23.83 GPa with average 17.58.Likewise, E m values vary between 3.46 -7.94 GPa with average 5.14 GPa by Gokceoglu et al. [22], and values cal-culated by Palmstrom [42] vary between 24.46 -26.32 GPa with average 25.30 GPa.
The calculated values of E m from empirical equations were compared with rock mass quality (Figure 6 and Figure 7) to understand the similarity or inconsistency emanating.However, the pattern of E m with rock mass quality was observed significantly for all equations.According to Kayabasi et al. [23] and Panthee et al. [43], significant results between E m calculated by using empirical equations and rock mass class were not observed but Hoek and Diederichs [7] revealed that E m values increases with an increase in rock mass class (Figure 4) by using exponentially or power function (Table 1).In this study, E m values were calculated by different equations where few equations gave high values, and several equations provided E m values of the lower range.
The relationships of E m with Q and RMR were derived and presented in Figure 8 and Figure 9.The E m values show significant positive correlation with Q and RMR.The E m values for left tunnel alignment calculated by Grimstad and Barton [41] & Palmstrom and Singh [21] show apositive correlation with Q values (R 2 = 0.96 and 0.98) as shown in Figure 8.Likewise, the calculated values of E m with equations suggested by Bieniawski [15], Read et al. [20], Gokceoglu et al. [22], Palmstrom [42] have been plotted against RMR values (Figure 9) that presented direct correlation (R 2 = 1, 0.99, 0.97 and 0.99).Similarly, E m values for right tunnel alignment calculated by Grimstad and Barton [41] & Palmstrom and Singh [21] provides positive correlation with Q values ( R 2 = 0.98 and 0.99) as shown in Figure 8 and likewise, E m values obtained from Bieniawski [15], Read et al. [20], Gokceoglu et al. [22], Palmstrom [42] were plotted against RMR values of right tunnel alignment and displays significant positive direct relationship (R 2 = 1, 0.99, 0.98 and 0.99) (Figure 9).In the light of above discussion, relations provided in Table 10 can be used to predict E m by Q and RMR values with an accuracy of R 2 = 0.96 -1.00 for similar properties of the rock mass and rock type of this study.
The E m 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 Table 8 and Table 9.Estimated E m values for left tunnel alignment vary between 7.76 -16.22 GPaby RocLab and E m values (Avg.) of each segment acquired by all stated empirical equations ranged between 13.40 -22.38 GPa.Similarly, for right tunnel alignment, RocLab provides the E m values range of 7.14 -14.99 GPa and E m values (Avg.) by all empirical equations along each segment ranged between 10. 23 -18.19 GPa.It can be observed in Figure 10 that fluctuation of obtained E m values by both ways has the more or less similar trend.On the other hand, it should be noted that provided values by RocLab are on the lower side as compare to average values obtained by empirical equations (Figure 10).However, the present research is based on the data of few locations devoid of detail observation of rock mass.Therefore, results can be improved by conducting more discontinuity data in detail by following the same approach.[20] GPa Palmstrom [42] GPa Gokceoglu et al.

Figure 2 .
Figure 2. Exposed Rocks Unit of (a) Diorite belonging to Chilas Complex; (b) Psammite belonging to Gilgit Complex in study area.

Figure 3 .
Figure 3. Geological map of study area.

Figure 4 .
Figure 4. Comparison of rock mass deformation modulus by using different empirical equations with data from in situ measurements (after Hoek and Diederichs [7]).

Figure 5 .
Figure 5.Comparison of RMR and Q values for (a) left tunnel alignment (b) right tunnel alignment.

Figure 6 .
Figure 6.Comparison of E m values with Q ratings for (a) left; (b) right tunnel alignment.

Figure 7 .
Figure 7.Comparison of E m values with Q ratings for (a) left; (b) right tunnel alignment.

Figure 8 .
Figure 8. Relationship between estimated E m values and Q values.

Figure 9 .
Figure 9. Relationship between estimated E m values and RMR values for (a) left; (b) right tunnel alignment.

Figure 10 .
Figure 10.Variation of E m values obtained by RocLab and empirical equations (avg.)along (a) left; (b) right proposed tunnel alignments.
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 E m by various equations have the more or less similar trend of variation with respect to rock quality of study area, respectively.

.2. Estimation of Deformation Modulus Based on RMR and Q
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

Table 2 .
Empirical equations for estimation of deformation modulus (E m ) by using RMR and Q values.

Table 7
. Estimated support categories of rock mass according to RMR and Q (after[29] [41]).

Table 8 .
Calculated values of deformation modulus along left tunnel alignment.

Table 9 .
Calculated values of deformation modulus along right tunnel alignment.

Table 10 .
Correlations of E m with RMR and Q values for present study area.
*y is for E m and x for RMR & Q.