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Numerical Modeling for Engineering Analysis and Designing of Optimum Support Systems for Headrace Tunnel.

1. Introduction

Modeling of rock mass is a very difficult job due to the presence of discontinuities, anisotropic, heterogeneous, and nonelastic nature of rock mass, using empirical and numerical methods [1, 2]. The complex nature and different formation make the rock masses a difficult material for empirical and numerical modeling.

During initial stages of excavation projects, the detailed data are not available about strength properties, deformation modulus, in situ stresses, and hydrological of rock masses [3]. To handle the nonavailability of the detailed project data, the empirical methods like rock mass classification systems are considered to be used for solving engineering problems [4]. The empirical methods used defined input parameters in designing of any underground structures, recommendation of support systems, and determination of input parameters for numerical modeling [5]. The empirical methods classified the rock mass quantitatively into different classes having similar characteristics for easy understanding and construction of underground engineering structures [3]. Despite its wide applications, the empirical methods do not evaluate the performance of support systems, stress redistribution, and deformation around the tunnel [6]. Therefore, it is very important to consider these parameters in designing of optimum underground structure and support systems. This deficiency of empirical method is solved by numerical methods.

Numerical modeling is gaining more attention in the field of civil and rock engineering for prediction of rock mass response to various excavation activities [7]. The numerical methods are convenient, less costly, and less time-consuming for the analysis of redistribution stresses and their effects on the behavior of rock mass and designing of structures within the rock mass environment. Numerical methods give the exact mathematical solution for the problem based on the engineering judgment and input parameters like physical and strength parameters of rock masses [8-12].

In this study, the rock mass along the tunnel axis was assessed using rock mass rating (RMR) and tunneling quality index (Q-system). The support system was recommended by these two classification systems. The rock mass behavior with the interaction of two different support systems was analyzed based on stresses, total deformation, and plastic yield thickness around the tunnel using finite-element method- (FEM-) based [Phase.sup.2 software for selection of an appropriate support system for tunnel, which is of great importance for the practicing engineers in the field.

2. Geology of Project

Golen Gol hydropower project is 106 MW. The project is to be developed on the river Golen Gol, Chitral District, Khyber Pakhtunkhwa, Pakistan. The tunnel of diameter 3.7 m of horseshoe shape is to be constructed for diversion of water from intake to power house. The surface and subsurface geology through sample collection from surface and subsurface was studied. After investigations of the tunnel geology, it is concluded that the surface and subsurface geology of the project is same, and the headrace tunnel is to be passed through granite, quartz mica schist, marble, and calcareous quartzite. The granite rock is separated from metamorphosed rocks by the unconformity/Ayun Fault, which is also very distinctly recorded. The geology and cross-sectional view of tunnel alignment is shown in Figure 1.

3. Rock Mass Classification

Various rock mass classification system has been developed based on civil and mining engineering case studies by different researchers, like rock mass rating (RMR), tunneling quality index (Q-system), geological strength index (GSI), new Austrian tunneling method (NATM), rock structure rating (RSR), rock quality designation (RQD), and so on for assessment and classification of rock mass. In this research, RMR and Q systems were used due to its flexibility in terms of input parameters and widespread range for selection of support systems.

The latest version of RMR1989 developed by Biniawski was used in this research [5]. This system has widespread applications in the field of mining and civil engineering. This system used uniaxial compressive strength (UCS), rock quality designation (RQD), discontinuities spacing, discontinuities condition, ground water condition, and discontinuities orientation as input parameters for characterization and classification of rock mass. The RMR is calculated by adding the rating of these six parameters.

The Q-system is developed by Bortan in 1974 at Norwegian Geotechnical Institute (NGI). The Q-system has wide applications in underground excavations and field mapping, and it depends on the underground opening and its geometry. The value of this system may be different for undisturbed and disturbed rock [14]. This system classifies the rock mass environment into different classes on the basis of the rock quality designation (RQD), joint number (Jn), joint roughness number (Jr), joint alteration (Ja), joint water reduction factor (Jw), and stress reduction factor (SRF). The values of this system indicate the quality of rock mass and give description about the stability of an excavation within the rock mass environment. The maximum value of Q-system indicates good quality of rock meaning good stability and the minimum value indicates poor quality of rock meaning poor stability. The value of Q-system is calculated by using the following formula:

Q = RQD/Jn x Jr/Ja x Jw/SRF. (1)

The RMR and Q classification systems were applied on bore hole data and physical and strength properties determined in laboratory of the collected rock samples along tunnel alignment. Based on the results obtained from RMR and Q system, the rock mass along the tunnel axis was divided into three geotechnical units. The results of RMR and Q classification system are presented in Table 1.

4. In Situ Stresses

The in situ stresses are determined by direct and indirect methods. In direct methods, in situ stress determination methods like flat jack, overcoring and undercoring, and hydraulic fracturing are used. These methods are costly and time-consuming, the procedures used in determination of these stresses are difficult, and the results maybe questionable [9,15,16]. In direct methods, the developed empirical models were used for determination of vertical and horizontal stresses. In this study, the vertical stress was determined by

[[sigma].sub.v] = [gamma]H, (2)

where [gamma] is the unit weight of rock mass and H is the height of overburden.

The ratio between horizontal and vertical stress is K. However, it is convenient to use theoretical approach to determine horizontal stress from vertical stress. For horizontal stress determination, the following useful equation presented by [17] is used.

[[sigma].sub.h] = ([upsilon]/1 - [upsilon]) [[sigma].sub.b] + [beta]ErmG/1 - v (H + 100), (3)

where [upsilon] is Poisson's ratio, [beta] is the coefficient of thermal expansion and its value for rocks is 8 x [10.sup.-6]/[degrees]C (Singh, Rao, and Ramamurthy, 2002), Erm is Young's modulus of intact rock in MPa, G is the thermal gradient of rock ([degrees]C/m).

However, the following simple relationship is adopted in this study for determination of horizontal stress:

[[sigma].sub.h] = ([upsilon]/1 - [upsilon]) [[sigma].sub.v]. (4)

The vertical and horizontal stresses were determined using (2) and (4) for each geotechnical unit. The results are presented in Table 2.

5. Numerical Methods

Numerical modeling in rock and civil engineering is used as a tool that facilitates the site engineers to evaluate the rock mass behavior and its effects on engineering structures and support systems. Numerical modeling gives a sound understanding for solving complex engineering problems related to the tunnel shape, size, mine layout, and design of roof support system to consent consistent and technoeconomic feasible performance of mining structures throughout their planned life of operations [18]. The numerical modeling in rock engineering is the interesting field for research and innovations. Due to advancing of technology in the field of rock mechanics, different numerical methods like finite-difference method (FDM), finite-element method (FEM), and boundary element method (BEM) were developed by different researchers for solving engineering-related problems like design of underground openings or structures within the rock mass environment, support systems and evaluation of its performance, and analysis of stresses. Among these continuum numerical methods, the FEM is used mostly to solve rock engineering problems [19].

In FEM, the rock mass is modeled as a continuum and the discontinuities modeled discretely in the continuum model. The domain of representative model is discretized into defined elements that connect at certain points called nodes. By changing the surface/boundary conditions, the stress-strain and deformation can be analyzed. An appropriate constitutive model for material is used to define stress-strain relationship. In FEM, the models in multistage can easily be produced and analyzed quickly. It can handle material complexity and model a wide variety of support types. In finite-element analysis, liner elements are usually modeled as beam element and applied to model rock support, that is, steel sets, shotcrete, and concrete [19-21].

The numerical modeling in rock engineering is hot field for quality and innovative research [22,23]. The FEM is used in solving the rock engineering problems such as characterization [21], design support assessment [9, 24-26], and back analysis of tunnels [27]. This method resolved complex engineering problem utilizing plane strain two-dimensional (2D) analysis, axisymmetric 2D analysis, and three-dimensional (3D) analysis.

6. Results and Discussions

6.1. Input Parameters for Numerical Modeling. FEM-based software [Phase.sup.2] was used for the analysis of the design support system for the tunnel. The input parameters like physical and mechanical properties of rock mass, stresses (vertical and horizontal), deformation modulus of rock mass, and support systems recommended by RMR and Q-system as given in Table 2 were used in [Phase.sup.2] software. The [Phase.sup.2] software developed the simulated models for each defined geotechnical unit (GU). These simulated models were developed based on the following assumptions:

(a) Supports were installed instantly after excavation.

(b) Elastoplastic behavioral model using generalized Hoek-Brown criterion is used to simulate the models.

(c) Tunnel model is 2D considering plane strain problem.

For numerical analysis, three-stage models were adopted to confirm the in situ ground stresses. In first stage of simulated model, ground stress distributions were examined. In the next stage, induced stress distributions, yield points, and the induced displacement were analyzed. In the final stage, behavior of the recommended support systems was investigated.

6.2. Numerical Analysis for GU-1. For this section, the simulated model of tunnel was developed using input parameters as given in Table 2 in [Phase.sup.2] software. The horizontal and vertical stresses are validated using gravity loading through simulating model before excavation. The virgin stress sigma 1 before excavation was 19.36 MPa, and sigma 1 at crown and sidewalls of tunnel is 0MPa and 26 MPa, respectively, after excavation. The maximum virgin stress sigma 3 before was 5.35 MPa, and sigma 3 at crown and sidewalls of tunnel was 0.70 MPa and 0.70 MPa, respectively, after excavation.

For this section, the maximum stress concentration develops at sidewalls of the tunnel. The maximum deformation of 1.84 mm after excavation and before support was seen both at crown and base of the tunnel as shown in Figure 2(a). The thickness of plastic zone (yield zone of 50%) at crown and sidewalls is negligibly small; however, at the base, it is approximately 1112 mm as shown in Figure 2(b).

The recommended support systems by RMR and Q-system as discussed in Table 2 were installed in simulated models. The rock mass and support components both for RMR and Q support systems were in compression. For RMR support, the maximum axial stress in rock bolt and maximum axial force in shotcrete elements are 92.05 MPa and 0.972 MN, respectively. For Q support, the maximum axial stress in rock bolt and maximum axial force in shotcrete elements are 102.05 MPa and 4.35 MN, respectively. The total displacement in the tunnel after installation of RMR and Q recommended supports in simulated models was noted as before support, that is, 2.30 mm in case of RMR support and from 2.30 mm to 2.10 mm in case of Q support as shown in Figure 3.

After comparison and analysis of simulated models for RMR and Q supports, the maximum axial stress in rock bolts and maximum force in shotcrete for Q are greater than those for RMR support, the confining stress for Q support is greater than that for RMR support, the total displacement for Q support was found to be decreased as compared to RMR support from 1.84 mm to 1.68 mm, and the yield zone thickness decreased slightly greater in Q support than RMR support at the base of the tunnel as shown in Figure 3. Therefore, Q support seems to be more effective than RMR support for GU-1 section.

6.3. Numerical Analysis for GU-2. The input parameters used for simulation of models in [Phase.sup.2] software for this section are presented in Table 2. The horizontal and vertical stresses are validated using gravity loading through simulating one model before excavation. The virgin stress sigma 1 before excavation is 11.84 MPa, and sigma 1 at crown and sidewalls of tunnel is 0.85 MPa and 4.25 MPa, respectively, after excavation. The virgin stress sigma 3 before excavation is 2.10 MPa, and sigma 3 at crown and sidewalls of tunnel is 0 MPa and 0 MPa, respectively, after excavation. The maximum stress concentration develops at sidewalls of the tunnel. The maximum deformation of 3.15 mm after excavation and before support is seen both at the crown and base of the tunnel as shown in Figure 4(a). The thickness of plastic zone (50%) at crown, sidewalls, and base is approximately 4638 mm, 1117 mm, and 5468 mm, respectively. The yield elements and plastic zone (50%) before supports are shown in Figure 4(b).

The recommended support systems by RMR and Q-system as discussed in Table 2 were installed in simulated models. The rock mass and support components both for RMR and Q support systems are in compression. The sigma 1, sigma 3, yield elements, and plastic zone around the tunnel was found to be improved after installation of Q supports in simulated models as compared to RMR supports as shown in Figures 5(a) and 5(b). For RMR support, the maximum axial stress in rock bolt and maximum axial force in shotcrete elements are 193.24 MPa and 5.35 MN, respectively. For Q support, the maximum axial stress in rock bolt and maximum axial force in shotcrete elements are 119.82 MPa and 3.06 MN, respectively. The total displacement in tunnel after installation of RMR and Q recommended supports in simulated models decreased from 3.15 mm to 2.40 mm in the case of RMR support and from 3.15 mm to 2.55 mm in the case of Q support as shown in Figure 5.

After comparison and analysis of simulated models for Q supports, the axial stress in rock bolts is less than RMR supports, the confining stress for Q support is greater than RMR support, the plastic zone for Q support is more improved than RMR support, and the total displacement decreases approximately same for RMR and Q supports. Therefore, the Q support seems to be more effective than RMR support for GU-2 section.

6.4. Numerical Analysis for GU-3. The input parameters used for simulation of models in [Phase.sup.2] software for this section are presented in Table 2. The horizontal and vertical stresses are validated using gravity loading through simulating one model before excavation. The virgin stress sigma 1 before excavation is 11.52 MPa, and sigma 1 at crown and sidewalls of tunnel is 0 MPa and 21 MPa, respectively, after excavation. The virgin stress sigma 3 before and sigma 3 at crown and sidewalls of tunnel are 0.20 MPa and 0.20 MPa, respectively, after excavation. For this section, the maximum stress concentration develops at sidewalls of the tunnel as shown in above figures. The maximum deformation of 0.990 mm after excavation and before support is seen both at crown and base of the tunnel as shown in Figure 6(a). The thickness of plastic zone (50%) at crown is approximately 333 mm, and sidewall is negligibly small; however, at the base is approximately 1001 mm. The yield zone and yield elements before supports are shown in Figure 6(b).

The recommended support systems by RMR and Q-system as discussed in Table 2 were installed in simulated models. The rock mass and support components both for RMR and Q support systems are in compression. For RMR support, the maximum axial stress in rock bolt and maximum axial force in shotcrete elements are 34.50 MPa and 8.52 MN, respectively. For Q support, the maximum axial stresses in rock bolt and maximum axial force are 46.70 MPa and 1.13 MN, respectively. The thickness of plastic deformation was decreased after installation of RMR supports as compared to Q supports as shown in Figures 7(a) and 7(b), respectively. The total displacement in tunnel after installation of RMR and Q recommended supports in simulated models was found to be decreased from 0.990 mm to 0.810 mm in the case of RMR support and not decreased in the case of Q support as shown in Figure 7.

7. Conclusions

In this research, the empirical and numerical methods were used to evaluate rock mass quality and estimate the support element required for headrace tunnel and stability analysis of tunnel before and after support system installation for selection of optimum support systems. The stability analysis of models developed for each geotechnical unit in [Phase.sup.2], was carried out after installment of Q and RMR support systems. For Q support, the total displacement reduced from 1.84 mm to 1.68 mm and from 3.15 mm to 2.55 mm and did not reduce in GU-3, respectively; the maximum axial stresses in rock bolt and maximum axial force were observed as 102.05 MPa and 4.35 MN for GU-1, 119.82 MPa and 3.06 MN for GU-2, and 46.70 MPa and 1.13 MN, respectively, for GU-3; and 50% plastic zone thickness maximum reduced for GU-1 at base from 1112 mm to 1095 mm, for GU-2 at crown from 4638 mm to 3716 mm, and for GU-3 at base from 1001 mm to 894 mm. For RMR support systems, the total displacement reduced from 1.84 mm to 1.76 mm, from 3.15 mm to 2.40 mm, and from 0.990 mm to 0.810, respectively; the maximum axial stresses in rock bolt and maximum axial force were observed as 92.05 MPa and 0.972 MN for GU-1, 193.24 MPa and 5.35 MN for GU-2, and 34.50 MPa and 8.52 MN, respectively, for GU-3; and 50% plastic zone thickness maximum reduced for GU-1 at base from 1112 mm to 1100 mm, and for GU-2 and GU-3, it did not reduce. Based on analysis and comparison of results, it is concluded that Q support system seem to be good for GU-1 and GU-2 and RMR support system for GU-3.

https://doi.org/10.1155/2018/7159873

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Sajjad Hussain [ID], (1) Zahid Ur Rehman [ID], (1) Noor Mohammad, (1) Muhammad Tahir, (1) Khan Shahzada, (2) Sajjad Wali Khan, (2) Muhammad Salman, (2) Mujahid Khan, (2) and Akhtar Gul (2)

(1) Department of Mining Engineering, University of Engineering and Technology, Peshawar, Pakistan

(2) Department of Civil Engineering, University of Engineering and Technology, Peshawar, Pakistan

Correspondence should be addressed to Zahid Ur Rehman; engr.zahid@uetpeshawar.edu.pk

Received 23 August 2017; Accepted 18 February 2018; Published 21 March 2018

Academic Editor: Giuseppe Carlo Marano

Caption: Figure 1: Geology and cross-sectional view of tunnel alignment [13].

Caption: Figure 2: Maximum displacement and thickness of plastic zone before supports.

Caption: Figure 3: Yield elements and yield zone (50%) after RMR (a) and Q (b) supports. Deformation after RMR (c) and Q (d) supports.

Caption: Figure 4: Total displacement (a) and yield elements (b) with plastic zone (50%) before supports.

Caption: Figure 5: Yield elements and yield zone (50%) after RMR (a) and Q (b) supports. Total deformation after RMR (c) and Q (d) supports.

Caption: Figure 6: Total displacement (a) and yield elements (b) with plastic zone (50%) before supports.

Caption: Figure 7: Yield elements and yield zone (50%) after RMR (a) and Q (b) supports. Total deformation after RMR (a) and Q (d) supports.
Table 1: Results of rock mass classification.

1. Rock mass rating (RMR)

Average values of input          Uniaxial           Rock quality
parameters of RMR               compressive         designation
                                 strength              (RQD)
                                   (UCS)

Bore hole       Rock type

BH-1 at          Granite           125.4                87%
chainage
0 + 000 to
2 + 750

Rating                              12                   17

BH-2           Quartz mica         54.18                50%
                  schist

Rating                               7                   13

BH-3            Calcareous         106.7                80%
                quartzite

Rating                              12                   18

Average values of input       Discontinuities     Discontinuities
parameters of RMR                 spacing            condition

Bore hole       Rock type

BH-1 at          Granite       200 to 600 mm        Rough, hard
chainage                                          filling < 5 mm,
0 + 000 to                                      slightly weathered,
2 + 750                                              persistent
                                                    < 1 mm, and
                                                 aperture < 0.1 mm

Rating                              10                   25

BH-2           Quartz mica        <60 mm         Rough to slightly
                  schist                            rough, hard
                                                  filling < 5 mm,
                                                    unweathered,
                                                persistent 1-3 m to
                                                    3-10 m, and
                                                  aperture 0.1 to
                                                        1 mm

Rating                               5                   21

BH-3            Calcareous     60 to 200 mm      Rough to slightly
                quartzite                           rough, hard
                                                 filling < 5 mm to
                                                hard, filling > 5 mm,
                                                slightly weathered,
                                                 persistent < 1 mm,
                                                    and aperture
                                                       0.1 mm

Rating                               8                   23

Average values of input           Ground          Discontinuities
parameters of RMR                  water            orientation
                                 condition

Bore hole       Rock type

BH-1 at          Granite            Dry            Very favorable
chainage                                              to fair
0 + 000 to
2 + 750

Rating                              15                 -3.33

BH-2           Quartz mica          Dry            Very favorable
                  schist                            to favorable

Rating                              15                   -2

BH-3            Calcareous      Damp to dry        Very favorable
                quartzite                           to favorable

Rating                             12.5                  -2

2. Tunneling quality index (Q-system)

Average values of input        Rock quality            Joints
parameters of RMR               designation         number (Jn)
                                   (RQD)

Bore hole       Rock type

BH-1 at          Granite            88              Three joint
chainage                                             sets plus
0 + 000 to                                             random
2 + 750

Rating                              88                   12

BH-2              Quartz            50               Two joint
                  schist                                sets

Rating                              50                   4

BH-3            Calcareous          80               One joint
                quartzite                             set plus
                                                       random

Rating                              80                   3

Average values of input       Joint roughness     Joint alteration
parameters of RMR               number (Jr)             (Ja)

Bore hole       Rock type

BH-1 at          Granite         Rough and          Only surface
chainage                       irregular and       staining with
0 + 000 to                      undulating        unaffected joint
2 + 750                                                walls

Rating                               3                   1

BH-2              Quartz         Rough to         Unaltered joint
                  schist       slickensided      walls and surface
                                undulating         staining only

Rating                             2.11                  1

BH-3            Calcareous       Rough and        Unaltered joint
                quartzite      irregular and     walls to slightly
                                undulating      altered joint walls
                                                       having
                                                  nonsoftening to
                                                silty- or sandy-clay
                                                      coatings

Rating                               3                   2

Average values of input         Joint water       Stress reduction
parameters of RMR                reduction          factor (SRF)
                                factor (Jw)

Bore hole       Rock type

BH-1 at          Granite            Dry            Low stress to
chainage                        excavation         medium stress
0 + 000 to
2 + 750

Rating                               1                  1.75

BH-2              Quartz            Dry            Low stress to
                  schist        excavation         medium stress

Rating                               1                  1.23

BH-3            Calcareous      Damp to dry        Low stress to
                quartzite                          medium stress

Rating                             0.83                 1.62

Average values of input              Q
parameters of RMR                  value

Bore hole       Rock type

BH-1 at          Granite           12.57
chainage
0 + 000 to
2 + 750

Rating

BH-2              Quartz           21.95
                  schist

Rating

BH-3            Calcareous         20.49
                quartzite

Rating

Table 2: Parameters for numerical modeling.

Geotechnical         Unit          Modulus of    Poisson's
unit                weight         elasticity    ratio (u)
                (g/[cm.sup.3])       (MPa)

GU-1                 2.71            3.41e4        0.188

GU-2                 2.76           3.42 e4        0.051

GU-3                 2.69             5e4          0.277

Geotechnical           Hoek and Brown         Vertical     Horizontal
unit                     constants             stress        stress
                                               (MPa)         (MPa)
                  mb        s         a

GU-1            7.669    0.0117     0.503      19.00          5.23

GU-2            1.934    0.0060     0.504      11.70          2.06

GU-3            6.154    0.0256     0.502      11.60          3.02

Geotechnical        RMR support          Q-system support
unit

GU-1              Locally, 3m long           2m long
                 bolts in crown of      systematic bolting
                   20mm diameter       (fully grouted with
                 and fully grouted,       20mm diameter)
                  spacing between       with a spacing of
                 bolts of 2.5m with       2.32m between
                 occasionally wire         bolts; ?ber-
                  mesh, shotcrete       reinforced sprayed
                with a thickness of        concrete of
                     50mm where              50-60mm
                 necessary, and no      thickness at crown
                 steel set required

GU-2                  4m long                2m long
                systematic bolts of     systematic bolting
                   20mm diameter       (fully grouted with
                 and fully grouted,       20mm diameter)
                   spacing range        with a spacing of
                  between bolts of         2.5m between
                  1.5-2m in crown          bolts; ?ber-
                and walls with wire     reinforced sprayed
                   mesh in crown,          concrete of
                   shotcrete with            50-60mm
                 a thickness range      thickness at crown
                  of between 50mm
                    and 100m in
                   crown and 30mm
                  in the sides of
                   tunnel, and no
                 steel set required

GU-3              Locally, 3m long           2m long
                 bolts in crown of      systematic bolting
                   20mm diameter       (fully grouted with
                 and fully grouted,       20mm diameter)
                  spacing between       with a spacing of
                 bolts of 2.5m with       2.48m between
                 occasionally wire         bolts; ?ber-
                  mesh, shotcrete       reinforced sprayed
                with a thickness of        concrete of
                     50mm where              50-60mm
                 necessary, and no      thickness at crown
                 steel set required
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Title Annotation:Research Article
Author:Hussain, Sajjad; Rehman, Zahid Ur; Mohammad, Noor; Tahir, Muhammad; Shahzada, Khan; Khan, Sajjad Wal
Publication:Advances in Civil Engineering
Date:Jan 1, 2018
Words:4978
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