The development of a country is directly related to the energy production. Unfortunately, Pakistan is facing worst energy crisis at present time. The basic and cheapest source of power production is hydropower in Pakistan due to the presence of natural topography which creates natural hydraulic heads along streams especially in hilly areas. Rock bursting is a common and serious form of disasters that can happen in deep underground excavations. The underground excavation passes through variable rock cover, this variation can induce instabilities like spalling, raveling, squeezing and rock bursting. In weak strata squeezing of rocks can take place and rock bursting can occur in un-jointed massive strata where rock mass strength is less than induced stresses [1] . The estimation of rock squeezing, bursting and deformation modulus of rock mass before excavation is one of the most important parameters of the rock mass to mitigate the chances of rock bursting in the excavation i.e. tunnel by applying safest and economical support with both empirical and numerical approaches. In China, during the construction phase of Jinping-II Hydropower project, hundreds of rock bursts occurred which caused damage to the structure, causalities and serious economic loss [2] . In the Sunjiawan Coal mine in 2005, a rock burst caused 215 dead and 30 people injured. Many deep tunnels in China, Canada, Switzerland, and Peru have experienced rock bursting of various degrees. Therefore, the assessment of rock bursting at pre-feasibility and feasibility stage is highly necessary to minimize the casualties. Zhang et al. [3] described the intense rockbursts in tunnels of Jingping II hydropower station by surveying the geological conditions and failure of the affected sections. Gong et al. [4] discussed the problems encountered due to in situ stresses etc. during TBM tunneling and suggested measures to overcome the problems. Kaya et al. [5] investigated the main cause of the failure occurrence mechanism at tunnel portal to determine the remedial measures. Several researchers [6] [7] [8] studied the geological conditions of rock mass to determine the estimated required support alignment by using Rock mass rating (RMR) and Tunneling quality index (Q-system) during excavation along tunnel. Panthee et al. [9] stated that the information of deformation modulus is also required in numerical modeling for underground excavations. The field tests i.e. Dilatometry, plate load tests, flat jack etc. to determine the deformation modulus are time-consuming, expansive and have more chances of error in readings during measurement [10] [11] [12] [13] [14] . Therefore, several researchers suggested empirical equations to determine the rock mass deformation modulus indirectly from correlations with empirical classification systems [15] - [21] . Many researchers [9] [10] [13] [14] [15] [19] [20] [22] - [27] have been studied deformation modulus with empirical equations on the basis of empirical classification systems as a input parameters such as Rock Quality Designation (RQD), Rock Mass Rating (RMR), Q-system (Q), Rock Mass Index (RMi) and Geological Strength Index (GSI).

The study area is located on Ushuriver, Swat valley, Khyber Pakhtunkhwa (KP), Pakistan (Figure 1). Ushuriver is a tributary of Swat River in the north of Kalam which is major tourist center in the Swat valley. The geological mapping, discontinuity surveys, and laboratory testing were conducted to classify rock mass by empirical classification systems i.e. RMR, Q, and RMi. Whereas, rock bursting, squeezing and deformation modulus of rock mass along tunnel route were assessed by empirical equations proposed by various researchers. In addition to that numerical analysis along proposed tunnel route was carried out using RS³ [28] in which displacement of rocks in all zones was calculated and advised support categories were assessed by implementing in the model to stable the rock mass during excavation. The detailed methodology of research work is given in Figure 2.

Total three rock units ranging in age from Mesozoic to Cenozoic Era are exposed along tunnel alignment (Figure 3(a)). The northern portion of study area consists of granodiorite while the southern part consists of meta-sediments mainly phyllites, schists, and slates. The meta-sediments have a uniform strike NE-SW and NW dip direction which is fairly steep and less steep towards the north. Granodiorite is grey, greenish grey, medium to coarse grained mainly composed of plagioclase, hornblende, and biotite. Where asschists/phyllites are grey, green in color, thin-bedded, occasionally silty with light grey thin-bedded limestone and quartzite is light to dark grey on the fresh surface and brownish grey on the weathered surface, thin to thick bedded and cherty at places. The soil units are divided as glacio-fluvial deposits, scree, slope wash that is thick at weir site as well as near powerhouse area. The terraces in study area comprised of Glacio-fluvial deposits, which consists of sub-angular to rounded gravels embedded in silt and clay. Scree and slope wash comprised of weathered, disintegrated material due to gravity lying on the toe of the slope. The geological cross section along tunnel presents the rock units intersecting along tunnel alignment shown in Figure 3(b).

In the empirical analysis, three methods i.e. rock mass rating (RMR), tunneling quality index (Q) and rock mass index (RMi) were used to classify rock mass. The total area of the tunnel was divided into eight segments and all required parameters (orientation, spacing, opening, roughness, the degree of weathering, filling, and groundwater conditions) were collected from each segment to quantify the rock mass by using empirical classification systems. The discontinuity data was plotted on DIPS [29] to assess the pattern of discontinuities and joint sets. In Figure 4, three plots are showing joints distribution in lithological units of granodiorite, quartzite, and phyllite.

Rock quality designation (RQD) was calculated with the help of joint volumetric count (J_v) by a relationship given by Palmstrom [30] (Equation (1)). J_v

represents the total number of joints per cubic meters which are calculated with the help of spacing of joints by following relationship given by Palmstorm [31] [32] [33] [34] .

R Q D = 110 − 2.5 J v (1)

J v = ∑ i = 1 J ( 1 S i ) (2)

where S_i is the average joint spacing in meters for the i^th joint and J is the total number of joint sets.

Bieniawski [35] [36] proposed Rock mass rating (RMR) to classify the rock mass. The RMR was calculated by summing all the ratings of six factors: the uniaxial compressive strength of the intact rock, RQD, joints spacing, joints condition, joints orientation. Whereas, tunneling quality index (Q) proposed by Barton et al. [37] that include six parameters as mentioned in Equation (3): RQD, the function of joint sets (Jn), discontinuity roughness (Jr), joint alteration (Ja), water pressure (Jw) and stress reduction factor (SRF). Rock mass index (RMi) is avolumetric parameter and expresses the relative strength of rock mass [38] . In Equation (4) q_c represents the uniaxial compressive strength of intact rock and joint parameter (J_P) presents the block volume (Vb) plus the joint condition (jC). The jC was measured by joint size (jL), joint alteration (jA) and joint roughness jR. The detailed ratings for each parameter of RMR, Q and RMi are summarized in Tables 1-3.

Q = [ R Q D / J n ] [ J r / J a ] [ J w / S R F ] (3)

R M i = q c ⋅ J P (4)

The calculated RMR ratings along chainage 0+876 - 7+000 presented fair rock quality and along 7+000 - 7+506 shows poor rock quality. The Q values gave fair quality rock at tunnel inlet (0+876 - 1+000), poor rock along chainage 1+000 - 7+000 and very poor quality rock along the chainage 7+000 - 7+506 of tunnel alignment. While rock class in RMi is slightly differed from rock class by RMR and Q. RMi shows the strong quality of rock along chainage 0+876 - 7+000 and medium quality rock for chainage 7+000 to 7+506 of tunnel alignment. By comparing calculated rock mass quality by all three systems it is concluded that rock mass from 0+876 to 7+000 lies in the fair quality of rock and along chainage 7+000 to 7+506 poor or very poor rock quality depicted. Along chainage 7+000 to 7+200, systems presented poor rock quality due to wide jointed and transition zone. Similarly, phyllite intersects the tunnel at chainage 7+200 to 7+506 that gave poor rock quality.

The ground conditions were also assessed by using tunneling quality index values. Singh et al. [39] suggested an empirical approach based on case histories and collected data based on rock mass quality (Q), overburden (H) and developed relations to determine the squeezing (Equation (5)) and non-squeezing (Equation (6)) of the ground. Similarly, Goel et al. [40] proposed an empirical relation based on rock mass number (N) that defined as stress free tunneling quality index (Q), which is used to avoid the problems and uncertainties in obtaining the correct values. The parameters to calculate the N (Equation (7)) are a tunnel tunneling quality index (Q) and tunnel span or diameter (B) to determine the squeezing (Equation (8)) and non-squeezing (Equation (9)) conditions of the ground.

H ≫ 350 Q 1/3 meters (5)

H ≪ 350Q 1/3 meters (6)

N = ( Q ) S R F =1 (7)

H ≫ 275 N 0.33 ⋅ B − 1 ( m ) (8)

H ≪ 275 N 0.33 ⋅ B − 1 ( m ) (9)

The values calculated with relation proposed by Singh et al. [39] in which SRF value of 2.5 were used that is presented in Table 4 and plotted in Figure 5(a) that shows whole tunnel lies in non-squeezing zone. Similarly, according to the approach of Goel et al. [40] the calculated values are listed in Table 4 that lies on the line AB (Figure 5(b)). So, the rock units were predicted in minor to non-squeezing conditions.

Sengupta [41] proposed relations of Equations (10) and (11) to calculate the field stresses for overburden less than 400 m and Stephansson [42] suggested the relation (Equations (12) and (13)) for overburden less than 1000 m. In anisotropic stress conditions, the tangential stresses vary around the periphery of the opening. According to Kirsch’s solution (Equations (15) and (16)), tangential stress will reach its maximum value where maximum principal stress (σ₁) is tangent to the excavation contour and minimum tangential stress value where its minimum principal stress is tangent to excavation contour. Hoek and Brown [42] proposed a method to estimate the tangential stresses for roof ( σ θ r ) and walls ( σ θ w in massive rocks according to excavation shapes (Equations (17) and (18)). The calculated values of field stresses are given in Table 5.

σ 1 = σ H = 1.5 + 1.2 σ v ( MPa ) (10)

σ 3 = σ h = 1.0 + 0.5 σ v ( MPa ) (11)

σ 1 = σ H = 2.8 + 1.48 σ v ( MPa ) (12)

σ 3 = σ h = 2.2 + 0.89 σ v ( MPa ) (13)

σ v = γ Z (14)

σ θ max = 3 σ 1 − σ 3 (15)

σ θ min = 3 σ 3 − σ 1 (16)

σ θ r = ( A × k − 1 ) σ z (17)

σ θ w = ( B − k ) σ z (18)

where σ θ is for tangential stress ( σ θ r   forroofand   σ θ w   forwall ), k is the horizontal/vertical stress ratio, σ_z is the vertical stress and A, B are the excavation geometry factors.

Moreover, several other approaches developed by researchers i.e. [42] [43] [44] [45] were used to assess rock bursting potential (Table 6) by using field stresses (Major, minor, intermediate, tangential stress). Hoek and brown [42] have made detail studies for the stability analysis in different tunnels in South Africa. The ratio of uniaxial compressive strength (σ_c) and tangential stress (σ_Θ) was compared in this study to assess the rock bursting condition. Grimstad and Barton [44] made a relation by using stress measurements, the strength of the rocks and arrived at relationships which also support the findings of Hoek and Brown [42] . They also described the bursting potential by using the ratio of compressive strength and tangential stress (σ_c/σ_Θ) as mentioned in Table 6. The detail results of rock bursting assessment by both researchers are given in Table 7. Palmstorm [45] used the rock mass index (RMi) that expresses the relative compressive strength of rock mass and tangential stress (σ_Θ) to assess the competency factor (Cg) as mentioned in Equation (19).

Cg = R M i / σ θ (19)

Russenes (1974) devised a relationship of point load strength (I_s(50)) of rocks and tangential stresses to assess the rock bursting during excavation. Point load strength was calculated according to the instructions of ASTM D 5731 - 95 [46] standard method. The tangential stress was calculated from the maximum and minimum principal stress. The acquired values were plotted in the graph produced by Russenes (Figure 6) and it was noted from Table 8 that chainage 1+000 - 3+600, 5+200 - 5+600 lies in moderate rock burst and 0+876 - 1+000, 3+600 - 5+200, 5+600 - 7+506 depicts no rock burst activity. The equations proposed by Palmstrom and Singh [10] (Equation (20)) and Read et al. [47] (Equation (21)) were used to estimate deformation modulus (E_m) in which RMR and Q values considered as input parameters. The calculated values of E_m along tunnel route are presented in Table 9.

E m ( GPa ) = 8 Q 0.4 (20)

E m ( GPa ) = 0.1 ( R M R / 10 ) 3 (21)

The rock quality was classified by the empirical methods RMR, Q, and RMi. Application of these empirical methods includes rock support estimation based on rock quality. In this study, RMR gave fair rock quality along chainage 0+876 to 7+000 and poor rock quality for chainage 7+000 - 7+506 and estimated support for these zones of the tunnel is suggested in Table 10. Barton et al. [37] established a chart to estimate support category in which Q-value and equivalent dimension (De) is used. De is calculated by dividing the span of the tunnel with equivalent support ratio (ESR). Support category proposed by Barton’s Q-system and recommended support is given in Table 10. The calculated support by empirical methods was installed in the RS³ model to control displacement along proposed tunnel alignment.

Panthee et al. [9] stated that use of numerical analyses has become avital partin the planning of engineering projects. Similarly many researchers [9] [48] - [56] have successfully utilized the numerical techniques to sort out the rock engineering problems. This study includes the numerical analyses using computer-aided program RS³ (v. 1.0) to excavate the headrace tunnel in horseshoe-shape with a 5 m diameter. In 3D model, Hoek and Brown failure criteria was used for isotropic material with aslice thickness of 15 m. There were two types of in-situ stresses used in the model; constant and gravitational stresses. In analyses, constant field stresses were used as deep excavations, where gravitational field stress is negligible across the height of model. The rock mass was allowed to deform both elastically and plastically for analyses. The in-situ vertical and horizontal stresses were assumed by the depth of tunnel. Whereas, the maximum number of iterations 500 for elastic and 1500 for plastic analysis to determine the displacement and rock mass failures. The external boundary was used as abox with anexpansion factor of 3 and a graded mesh with 4 nodded triangles were used for analyses. While a gradation factor of 0.1 and number of excavation nodes 110 were used and discretization of the excavation boundary was determined by the number of excavation nodes. Several models were prepared for every 400 m Section in different lithology along tunnel alignment. Firstly, support estimated by empirical methods was installed then support was optimized by RS³ model to control the displacement along the tunnel. Optimized support in each section shown in Table 11.

Numerical models are totally dependent on the quality of input parameters. Hence, if there is uncertainty in input parameters then it leads to uncertainty in the analysis. Models are prepared for elastic and plastic ground conditions as shown in Figures 7(a)-(d). Plastic ground condition is a worst scenario where yielding is maximum. Support is installed in both conditions to assess the variation in total displacement. The maximum total displacement along tunnel alignment is at section 2+400 - 2+800 having tunnel depth 600 m. Without support, in elastic conditions, total displacement is 14.5 mm which is reduced to 13.5 mm after installation of support. In plastic condition, total displacement without support in that zone is 19.2 mm which is reduced to 16.0 mm after installation of support. The section of inlet portal of the tunnel (chainage 0+876 to 1+000) with the depth of 165m comprised of massive and jointed granodiorite. In elastic conditions, this section has a total displacement of 1.4 mm that is reduced to 1.3 mm after installation of support. Similarly, the section of the tunnel (chainage 1+000 to 1+600) comprised of quartzite having 400 m overburden. In elastic conditions, the displacement of 10.4 mm was noted without the support and after installation of support, the displacement was reduced to 9.7 mm. Whereas, the displacement was slightly increased to 12.2 mm in plastic conditions and reduced to 10.7 mm after applied support. The tunnel section of chainage 2+400 - 2+800 has the maximum depth that results in maximum stresses. In elastic conditions, total displacement without support was 14.5 mm, which is reduced to 13.5 mm after installation of support and in plastic conditions displacement was reduced from 19.2 mm to 16.0 mm after installation of support. The section of the tunnel (chainage 7+000 - 7+200) intersects the jointed zone. In elastic conditions, total displacement was decreased from 10.5 mm to 8.3 mm after application of support and the length of the bolts in this zone was increased to 3 m due to widely spaced joints. In plastic conditions, the total displacement of 10.9 mm was encountered that was reduced to 8.4 mm after installation of support. The zone of chainage 7+200 - 7+506 near tunnel outlet intersects the phyllitethat gave displacement is 11.7 mm that is reduced to 7.8 mm after support installation in elastic conditions. While in plastic conditions, total displacement was 17.9 mm that is reduced to 9.6 mm after installation of support.

In this study classification of the rock mass, prediction of rock burst, squeezing and deformation modulus of rock mass were assessed along headrace tunnel of hydropower which is 7.506 km long and 5 m in diameter. Initially, rock mass was classified by using three empirical methods i.e. RMR, Q, RMi and it is concluded by comparing the results of these methods that rock mass from chainage 0+876 to 7+000 lies in fair rock and from 7+000 to 7+506 lies in poor rock class. Empirical relations proposed by several researchers were used to determine the rock burst and squeezing potential of the rock mass and comparison of results depicts that medium stress conditions exist at 1+000 to 4+000 which can induce rock spalling and rock burst. The chainage 2+400 - 2+800 has maximum tunnel depth (640 m) which can cause brittle failures in rock mass and medium rock burst can also be observed. The remaining sections may face minor spalling and light bursting. Initially, rock bolts of avg. 2 m long with shotcrete of 30 - 100 mm in thickness were estimated by RMR and Q to use in numerical analyses. In section 7+000 to 7+200 length of the bolts are increased to 3 m due to widely spaced joints with a high aperture. The total displacement of both elastic and plastic condition was measured by analyzing the numerical models in both supported and unsupported conditions for every section along tunnel alignment. In future, the detail study will be required with the help of subsurface drilling data.

The authors declare no conflicts of interest regarding the publication of this paper.

Akram, M.S., Mirza, K., Zeeshan, M., Ali, M. and Ahmed, L. (2018) Geotechnical Investigation and Prediction of Rock Burst, Squeezing with Remediation Design by Numerical Analyses along Headrace Tunnel in Swat Valley, Khyber Pakhtunkhwa, Pakistan. Open Journal of Geology, 8, 965-986. https://doi.org/10.4236/ojg.2018.810058