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  • 1. Engineering Geology 91 (2007) 194 – 208 Empirical and numerical analyses of support requirements for a diversion tunnel at the Boztepe dam site, eastern Turkey Zulfu Gurocak a,⁎, Pranshoo Solanki b , Musharraf M. Zaman c a Department of Geology, Firat University, Elazig 23119, Turkey School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019-1024, USA Research and Graduate Education, College of Engineering, University of Oklahoma, Norman, OK 73019-1024, USA b c Received 29 September 2006; received in revised form 10 January 2007; accepted 25 January 2007 Available online 3 February 2007 Abstract This paper presents the engineering geological properties and support design of a planned diversion tunnel at the Boztepe dam site that contains units of basalt and tuffites. Empirical, theoretical and numerical approaches were used and compared in this study focusing on tunnel design safety. Rock masses at the site were characterized using three empirical methods, namely rock mass rating (RMR), rock mass quality (Q) and geological strength index (GSI). The RMR, Q and GSI ratings were determined by using field data and the mechanical properties of intact rock samples were evaluated in the laboratory. Support requirements were proposed accordingly in terms of different rock mass classification systems. The convergence–confinement method was used as the theoretical approach. Support systems were also analyzed using a commercial software based on the finite element method (FEM). The parameters calculated by empirical methods were used as input parameters for the FEM analysis. The results from the two methods were compared with each other. This comparison suggests that a more reliable and safe design could be achieved by using a combination of empirical, analytical and numerical approaches. © 2007 Elsevier B.V. All rights reserved. Keywords: Convergence–confinement method; Finite element method; Geological strength index; Hoek–Brown failure criterion; Rock mass quality; Rock mass rating 1. Introduction The design of an underground structure involves the use of both empirical and numerical approaches. Empirical methods are generally preferred by engineers and engineering geologists due to practicality. In ⁎ Corresponding author. School of Civil Engineering and Environmental Science, University of Oklahoma, 202 West Boyd Street, Room 334, Norman, OK 73019-1024, USA. Tel.: +1 405 301 4341; fax: +1 405 325 4217. E-mail addresses:, (Z. Gurocak). 0013-7952/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.enggeo.2007.01.010 designing tunnel supports, the RMR and Q rock mass classification systems have been employed by many researchers and have gained a universal acceptance (Barton, 2002; Ramamurthy, 2004; Hoek and Diederichs, 2006). These rock mass classification systems were originally obtained from many tunneling case studies. However, these empirical methods do not provide the stress distributions and deformations around the tunnel. Therefore, particular attention should be given to these factors when using empirical methods. Specifically, when conducting an analysis, the determination of the values of stress distributions and deformations for the rock mass in question, is very sensitive to the field
  • 2. Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 Fig. 1. The location map of study area. observations. Likewise, analytical and numerical approaches are dependent upon the strength parameters of associated rock masses that are used as input 195 parameters when using an analytical and numerical approach. Therefore, the stability analysis of a tunnel is likely to suggest a safer design if a combination of empirical, theoretical, and numerical approaches is used. The field site used in this study is located 10 km northwest of Yazihan, in the north of the city of Malatya, in eastern Turkey (Fig. 1). The Boztepe dam which is under construction on the Yagca stream is located at this site. The dam project is designed to regulate water drainage and irrigate the agricultural areas of the Yazihan plain. The design of the Boztepe dam project is under the supervision of General Directorate of State Hydraulic Works (DSI, 1997), of Ministry of Energy and Natural Resources in Turkey. The diversion tunnel of the Boztepe dam has a length of 565 m, having circular geometry with 5 m in diameter. It cuts across basalts and tuffites. The tunnel will have a maximum overburden of about 38 m for basalts and about 27 m for Fig. 2. Geological map and cross-section of Boztepe dam site.
  • 3. 196 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 bedded, with bed thicknesses ranging from 300 to 600 mm in the lower levels and 50 to 200 mm in the upper levels. Joints within the tuffite are commonly altered and filled with clay or calcite having 20 to 30 mm thickness. The basalts overlying the tuffites are dark grey in color. In the lower levels, they are mainly pillar lavas while near the top they commonly occur as columnar structures (Gurocak, 1999). Vesicles are rare and the basalts are generally well-jointed. The agglomerate member overlying the basalts is generally dark in color and massive in structure. The individual boulders are weakly rounded, having a maximum size of 0.7 m. This unit also contains interlayer of tuff and basalt flows. Overlying the agglomerate are mainly Quaternary deposits, namely talus and alluvial materials. During the field surveys, engineering geological map of the Boztepe dam site and the geological cross section along the diversion tunnel was constructed. The field studies also included the orientation, persistence, spacing, opening, roughness, the degree of weathering and filling of discontinuities in the basalts and tuffites. Fig. 3. The histograms for RQD of basalts (A) and tuffites (B). tuffites. The dam site is located within the Yamadag Volcanics, which is composed of basalt, tuffite and agglomerate. Geological mapping and geotechnical descriptions were conducted in the field. The physical, mechanical and elastic properties of the rocks under consideration were determined from laboratory testing on intact rock samples. These tests include an evaluation of uniaxial compressive strength (σc), Young's modulus (E), Poisson's ratio (ν), unit weight (γ), internal friction angle (ϕ), and cohesion (c). The rock mass properties of the dam site were determined by using different rock mass classification systems. Table 1 Engineering properties of joints and bedding surfaces and their percentage distribution Properties Spacing Percentage Basalt Tuffite Spacing (mm) a Persistence (m)a Aperture (mm)a 2. Geology, field and laboratory studies The Boztepe dam site consists of various age units ranging from the Upper Miocene to the Quaternary. Middle–Upper Miocene volcano-sedimentary rocks that are known as Yamadag Volcanics, are exposed in the region. These rocks are a part of the extensive Miocene volcanism in the Eastern Anatolian Region. The Yamadag volcanites are represented in the study area by four different rock units extending upwards from a sandstone– claystone through tuffite, basalt and agglomerate members. As seen in Fig. 2, at the dam site, the main valley is in tuffite with basalt forming the plateau to the east. The tuffites are dirty white or light grey colored and well- Description Roughnessa Weathering (Wc) b a b b20 Extremely close spacing 20–60 Very close spacing 60–200 Close spacing 200–600 Moderate spacing 600–2000 Wide spacing b1 Very low persistence 1–3 Low persistence 3–10 Medium persistence 10–20 High persistence N20 Very high persistence b0.1 Very tight 0.1–0.25 Tight 0.25–0.50 Partly open 0.50–2.50 Open 2.5–10 Moderately wide N10 Wide IV Rough undulating V Smooth undulating VI Slickensided undulating VII Rough planar VIII Smooth planar IX Slickensided planar ≤1.2 Fresh/Unweathered 1.2–2 Moderately weathered N2.0 Weathered According to ISRM (1981). According to Singh and Gahrooee (1989). 5 2 33 42 20 – 33 56 11 – – 8 14 10 16 48 4 11 3 10 16 69 10 3 8 9 34 31 14 12 – 2 20 51 15 5 7 – 61 6 9 22 67 11 88 – – – 2 98
  • 4. Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 197 Fig. 4. Stereographic projection of bedding surface (A) and joint sets (B) in tuffites and joint sets (C) in basalts. In addition, an examination was made of 1195 m of the core, from 20 boreholes drilled by the General Directorate of State Hydraulic Works (DSI, 1997). The RQD values of the basalts and tuffites were determined. The histograms shown in Fig. 3 were prepared using the RQD divisions proposed by Deere (1964). From this figure, the rock quantities of the basalts have the following distribution: 6% excellent, 14% good, 32% fair, 23% poor, and 25% very poor. Similarly, the tuffites have the following distribution of rock quality: 4% excellent, 11% good, 28% fair, 21% poor, and 36% very poor. As the study area is located in a seismically active region, the basalts exposed around the Boztepe dam site contain systematic joint sets. However, tuffites are sedimentary rocks and contain bedding surfaces. Table 1 shows the main orientation, spacing, persistence, aperture and roughness of discontinuities. These were described using the scan-line survey method following the ISRM (1981) description criteria. The degree of weathering of the discontinuous surfaces was assessed using the Schmidt hammer and the weathering index was calculated from the equation proposed by Singh and Gahrooee (1989): Wc ¼ rc ; JCS ð1Þ where σc JCS Uniaxial compressive strength of fresh rock (MPa), and Strength of discontinuity surface (MPa). JCS was calculated from the following equation: LogJCS ¼ 0:00088gR þ 1:01; ð2Þ where γ R Bulk volume weight (kN/m3), and Hardness value from rebounding of Schmidt hammer.
  • 5. 198 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 Table 2 Laboratory tests results of basalts and tuffites Properties Min Max Mean Std. err. Basalt Uniaxial compressive strength (σc, MPa) Young's modulus (E, GPa) Poisson's ratio (ν) Unit weight (γ, kN/m3) Cohesion (c, MPa) Internal friction angle (ϕ, deg) 8.72 1.6 0.241 23.10 12 a 42a 76.46 96.7 0.286 28.10 40.64 30.91 0.27 25.55 19.67 47.17 0.02316 1.48 Tuffite Uniaxial compressive strength (σc, MPa) Young's modulus (E, GPa) Poisson's ratio (ν) Unit weight (γ, kN/m3) Cohesion (c, MPa) Internal friction angle (ϕ, deg) 1.97 0.6 0.17 12.00 1.80a 33a 21.20 10.5 0.22 22.10 8.21 2.23 0.20 16.50 5.72 2.615 0.02517 0.04 Std. err.: standard error. a Values obtained by using triaxial test. In the study area, a total of 388 bedding surfaces and 520 joint measurements were taken from tuffites and basalts. Discontinuity orientations were processed utilizing a commercially available software DIPS 3.01 (Diederichs and Hoek, 1989), based on equal-area stereographic projection, and major joint sets were distinguished for basalts and tuffites (Fig. 4). The following major orientations of the bedding surface for tuffites were observed: Bedding surface: Joint set 1: Joint set 2: Joint set 3: 14/100 80/220 87/259 77/305 The major orientations of the joint sets for basalts are listed below: Joint Joint Joint Joint set set set set 1: 2: 3: 4: 78/192 71/3 67/287 72/99 According to ISRM (1981), the joint sets in the basalts have close to very close spacing, low persistence, moderate width, rough-planar and moderately weathered character. The discontinuities in tuffites have close spacing, medium to high persistence, moderate width, and rough-planar and weathered character. Uniaxial compressive strength, deformability, unit weight and triaxial compressive strength tests were conducted in accordance with the ISRM suggested methods (ISRM, 1981). Pertinent results are summarized in Table 2. The average uniaxial compressive strength of basalts is 40.64 MPa, Young's modulus is 30.91 GPa, Poisson's ratio is 0.27, unit weight is 25.55 kN/m3, cohesion is 12 MPa and friction angle is 42°. The average uniaxial compressive strength of tuffites is 8.21 MPa, Young's modulus is 2.23 GPa, Poisson's ratio is 0.20, unit weight is 16.50 kN/m3, cohesion is 1.80 MPa and friction angle is 33°. 3. Rock mass classification systems Rock mass classification systems are important for quantitative descriptions of the rock mass quality. This in turn led to the development of many empirical design systems involving rock masses. Many researchers developed rock mass classification systems. Some of the most widely used rock mass classification systems include RMR and Q. These two classification systems are utilized in this research. 3.1. RMR system Bieniawski (1974) initially developed the rock mass rating (RMR) system based on experience in tunnel projects in South Africa. Since then, this classification system has undergone significant changes. These changes are mostly due to the ratings added for ground Table 3 RMR89 rating for basalts and tuffites Classification parameters Basalt Value of parameters Rating Value of parameters Rating Uniaxial compressive strength (MPa) RQD (%) Discontinuity spacing (cm) Discontinuity condition Persistence (m) Aperture (mm) Roughness Filling Weathering Groundwater condition Basic RMR value Rating adjustment for joint orientation RMR Rock mass quality 40.64 5 8.21 2 62 160 12 7.3 25 90 6 6 1–3 2.50–3.00 Rough-planar Calcite b 5 mm Moderately Dry 4 1 5 4 3 15 3–10 2.5–10 Rough-planar calcite N 5 mm Highly Dry 2 0 5 2 1 15 56.3 0/−5 Fair 39 −5 Very favorable/Fair 56.3/51.3 Fair rock Tuffite 34 Poor rock
  • 6. Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 199 Table 4 Q rating for basalts and tuffites Classification parameters Basalt Tuffite Value of parameters RQD (%) Joint set number (Jn) Joint alteration number (Jr) Joint alteration number ( ja) Joint water reduction factor ( jw) Stress reduction factor (SRF) Q Rock mass quality Rating Value of parameters 62% 62 Four joint sets plus random joints 15 Rough planar 1.5 Moderately altered 6 Dry excavation or minor inflow 1 Medium stress 1 1.03 Poor rock water, joint condition and joint spacing. In order to use this system, the uniaxial compressive strength of the intact rock, RQD, joint spacing, joint condition, joint orientation and ground water conditions have to be known. In this study, the RMR classification system (Bieniawski, 1989) is used and the results are summarized in Table 3. This rating classifies basalt as a fair rock mass, while tuffite as a poor rock mass.z 3.2. Q system Barton et al. (1974) developed the Q rock mass classification system. This system is also known as the NGI (Norwegian Geotechnical Institute) rock mass classification system. It is defined in terms of RQD, the function of joint sets (Jn), discontinuity roughness (Jr), joint alteration (Ja), water pressure (Jw) and stress reduction factor (SRF). Barton (2002) compiled the system again and made some changes on the support recommendations. He also included the strength factor of the rock material in the system. Q¼ RQD Jr Jw : Jn Ja SRF ð3Þ Recently, Barton (2002) defined a new parameter, Qc, to improve correlation among the engineering parameters: Qc ¼ Q rc ; 100 ð4Þ Rating 25% 25 Three joint sets and a bedding surface plus random joints 12 Rough-planar 1.5 Highly altered 8 Dry excavation or minor inflow 1 Low stress, near surface 2.5 0.156 Very poor rock and very poor rock mass, respectively (Table 4). The Qc values for basalt and tuffite are 0.42 and 0.013, respectively. 4. Estimation of rock mass properties The rock mass properties such as Hoek–Brown constants, deformation modulus (Emass) and uniaxial compressive strength of rock mass (σcmass) were calculated by means of empirical equations in accordance with the RMR89, Q, Qc and GSI. 4.1. Geological strength index (GSI) and Hoek–Brown parameters The geological strength index (GSI) was developed by Hoek et al. (1995). The GSI is based on the appearance of a rock mass and its structure. Marinos and Hoek (2001) used additional geological properties in the Hoek–Brown failure criterion and introduced a new GSI chart for heterogeneous weak rock masses. The value of GSI was obtained from the last form of the quantitative GSI chart, which was proposed by Marinos and Hoek (2000). The Hoek and Brown (1997) failure criterion was used for determining the rock mass properties of basalt at the dam site. Hoek et al. (2002) suggested the following equations for calculating rock mass constants (i.e., mb, s and a): GSI−100 mb ¼ mi exp ; ð5Þ 28−14D Table 5 GSI and calculated Hoek–Brown parameters values Unit GSI mi constant mb constant s constant 48 32 25 13 3.903 1.146 0.0031 0.0005 0.507 0.520 ð6Þ ð7Þ a constant Basalt Tuffite GSI−100 ; s ¼ exp 9−3D 1 1 a ¼ þ e−GSI=15 −e−20=3 ; 2 6 where σc is uniaxial comprehensive strength of intact rock. According to the Q classification system, basalt and tuffite at the dam site can be considered as poor rock mass where D is a factor that depends upon the degree of disturbance to which the rock mass is subjected to by blast
  • 7. 200 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 damage and stress relaxation tests. In this study, the value of D is considered zero. The calculated GSI is and the Hoek– Brown constants are listed in Table 5. Table 6 Selected equations for estimating deformation modulus of rock mass Emass Author Equations Equation number Bieniawski (1978) For RMR N 50, (9) Serafim and Pereira (1983) For RMR b 50, 4.2. Strength and deformation modulus of rock masses Several empirical equations have been suggested by different researchers for estimating the strength and modulus of rock masses based on the RMR, Q and GSI values. In this study, the strength of rock masses was calculated from the following equation suggested by Hoek et al. (2002): rcmass ðmb þ 4s−aðmb −8sÞÞðmb =4 þ sÞa−1 ; ¼ rci 2ð1 þ aÞð2 þ aÞ ð8Þ where σci is uniaxial compressive strength of the intact rock, mb, s and a are rock mass constants. The strength of rock masses for basalt and tuffite were determined as 10.6 and 1.08 MPa, respectively. The deformation modulus of rock masses was calculated suggested by different researchers based on RMR, Q and GSI values. In this study, the equations in Table 6 were used for determining deformation modulus of rock masses. The calculated values of rock mass deformation modulus are summarized in Table 7. A reliable stability analysis and prediction of the support capacity are some of the most difficult tasks in rock engineering. Therefore, in the current study several methods are used to conduct stability analysis and determine the support capacity. For the tunnel support design of the diversion tunnel at the Boztepe dam site, empirical, theoretical and numerical approaches were employed. The vertical stress was assumed to increase linearly with depth due to its overburden weight, as follows: rv ¼ gH; ð20Þ where γ is unit weight of the intact rock in MN/m , and H is the depth of overburden in m. The horizontal stress was determined from the following equation suggested by Sheorey et al. (2001): 3 m bEmass G rv þ ðH þ 100Þ; 1−m 1−m Emass ¼ 10 (10) RMR−10 40 rffiffiffiffiffiffiffiffi rci GSI−10 10 40 100 Hoek and Brown (1997) Emass ¼ Read et al. (1999) RMR 3 Emass ¼ 0:1 10 Ramamurthy (2001) Emass ¼ Ei exp½ðRMR−100ÞŠ=17:4 (13) Ramamurthy (2001) Emass ¼ Ei expð0:8625 logQ−2:875Þ (14) Barton (2002) 1=3 Emass ¼ 10Qc (15) (11) (12) rffiffiffiffiffiffiffiffi rci GSI−10 10 40 100 (16) Hoek et al. (2002) 5. Tunnel stability and support analysis rh ¼ Emass ¼ 2RMR−100 ð21Þ where β = 8 × 10− 6/°C (coefficient of linear thermal expansion), G = 0.024 °C/m (geothermal gradient), ν is the Poisson's ratio, Emass is deformation modulus of rock mass, MPa. Emass ¼ Ramamurthy (2004) Emass ¼ Ei exp−0:0035½5ð100−RMRÞŠ (17) Ramamurthy (2004) Emass ¼ Ei exp−0:0035½250ð1−0:3logQÞŠ (18) Emass ¼ Ei 0:02 þ (19) Hoek and Diederichs (2006) 1− D 2 1 1þ eð60þ15D−GSIÞ=11 RMR = rock mass rating. Q = rock mass quality. Qc = rock mass quality rating or normalized Q. GSI = geological strength index. σci = uniaxial comprehensive strength of intact rock. Ei = Young's modulus. D = disturbance factor. The far-field stress σ0 was calculated using the following equation: r0 ¼ rv þ rh1 þ rh2 ; 3 where σhl and σh2 are horizontal stresses. ð22Þ
  • 8. Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 201 Table 7 Calculated values of deformation modulus of rock masses Emass Modulus of rock mass (Emass, GPa) Eq. (9) Eq. (10) Eq. (11) Eq. (12) Eq. (13) Eq. (14) Eq. (15) Eq. (16) Eq. (17) Eq. (18) Eq. (19) Avrg St. dev. 7.6 – Basalt Tuffite – 3.98 5.68 1.02 15.57 3.93 2.16 0.05 1.77 0.06 7.49 2.35 5.68 1.02 13.77 0.70 12.92 0.75 6.91 0.17 7.96 1.40 4.72 1.51 Avrg: average. St. dev.: standard deviation. Eq.: equation. The 5-m-diameter tunnel was excavated at a maximum depth of 38 m in basalt and 27 m in tuffite below the ground surface. The far-field stresses for basalt and tuffite were determined as 0.53 MPa and 0.22 MPa, respectively. Proof (kN/m2), was calculated by using the following equation: 5.1. Empirical approach The support pressure was calculated as 0.135 MPa according to the Barton et al. (1974) approach and 0.059 MPa according to the Bieniawski (1974) approach for the basalts. However, for tuffite the corresponding values were found to be 0.072 MPa and 0.055 MPa, respectively. As one can see that from these results, the support pressure obtained from the Q criterion is greater than obtained by the RMR criterion and is considered more realistic. The tunnel supports were defined in accordance with the recommendations of the RMR and Q systems. Bieniawski (1989) suggested supports for different rock mass classes in the RMR89 system. As noted earlier, according to the RMR89 system on the one hand, basalts and tuffites are fair and poor rock masses, respectively. Correspondingly according to the Q system on the other hand, basalts and tuffites are poor and very poor rock masses, respectively. A summary of the estimated supports using the RMR89 and Q systems are presented in Table 8. Bieniawski (1974) used RMR, width of opening W (m), and unit weight of overburden γ (kN/m3) to determine the support pressure. From the formula below, the support pressure Proof, is found in kN/m2: Proof ¼ 100−RMR W g: 100 ð23Þ Another approach was proposed by Barton et al. (1974) that depends on rock mass quality, Q, and discontinuity roughness, Jr . The roof support pressure, Table 8 Estimated support categories of basalts and tuffites Unit Basalt RMR RMR 56.3/51.3 classification Fair rock system Support Systematic bolts 4 m long, spaced 1.5–2 m in crown and walls with wire mesh in crown. 50–100 mm in crown and 30 mm in sides. Tuffite 34 Poor rock Systematic bolts 4–5 m long, spaced 1–1.5 m in crown and walls with wire mesh. 100–150 mm in crown and 100 mm in sides. Q classification Q 1.03 0.156 system Poor rock Very poor rock ESR 1.6 1.6 De 3.125 3.125 Support Systematic bolting, 4 m long bolting, 4 m long, spaced spaced 1.3–1.5 m 1.7 m with 40–50 mm and 90–120 mm unreinforced shotcrete fibre reinforced shotcrete De ¼ Excavation span; diameter or height ðmÞ Excavation support ratio ðESRÞ Proof ¼ 200 1=3 Q : Jr ð24Þ 5.2. Theoretical approach In this study, a theoretical approach, called the convergence–confinement technique, was used for stability analysis. This methodology has been described by Carranza-Torres and Fairhurst (1999) for rock masses that satisfy the Hoek–Brown criterion. A cylindrical tunnel of radius R, subjected to a uniform far-field stress Table 9 Far-field stress, shear modulus of rock mass, actual critical internal pressure, radius of plastic zone, maximum deformation and strain values obtained from the convergence–confinement method Unit σ0 Gmass Pi (MPa) (GPa) (MPa) Basalt 0.53 Tuffite 0.22 3.13 0.58 Pi cr Rpl uel upl Strain r r (MPa) (m) (mm) (mm) (%) 0.000049 0.000 0.00 0.211 0.000 0.0084 0.00191 0.0143 3.47 0.000 0.441 0.0176
  • 9. 202 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 Table 10 Material properties of basalts and tuffites for numerical model Property Basalt Material type Young's modulus (GPa) Poisson's ratio Compressive strength (MPa) m parameter s parameter Material type Dilation parameter m residual s residual Isotropic 7.96 0.27 10.61 3.903 0.0031 Plastic 0° 1.9515 0.00155 Tuffite Value Isotropic 1.40 0.20 1.08 1.146 0.0005 Plastic 0° 0.573 0.00025 σ0, and internal pressure Pi was considered. The rock mass, in which the tunnel is excavated, is assumed to satisfy the Hoek–Brown failure criterion. The actual critical internal pressure Picr is defined as (Carranza-Torres and Fairhurst, 2000): Picr ¼ ⁎ s Pi − 2 mb rci ; mb ð25Þ The scaled critical internal pressure is evaluated from the following equation: 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 ⁎ 1− 1 þ 16S0 ; ð26Þ Pi ¼ 16 in which S0 is the scaled far-field stress given by: S0 ¼ r0 s þ ; mb rci m2 b ð27Þ where σ0 is far-field stress, and Pi is the scaled internal pressure defined by: Pi ¼ pi s þ ; mb rci m2 b ð28Þ where pi is uniform internal pressure. If the internal pressure Pi is greater than the actual critical internal pressure Picr, no failure will occur, and the behavior of the surrounding rock mass is elastic, and el the inward elastic displacement ur of the tunnel wall is given by: uel ¼ r r0 −Pi R; 2Gmass ð29Þ where σ0 is far-field stress, Pi is scaled internal pressure, R is the tunnel radius and Gmass is the shear modulus of the rock mass. If the internal pressure Pi, on the other hand, is less than the actual critical internal pressure Picr, failure is where s and mb Hoek–Brown constants, σci uniaxial compressive strength, and scaled critical internal pressure. Pi⁎ Table 11 Stresses and displacements before and after support for basalts and tuffites Location Parameter Basalt Before support After support Before support After support Right wall σ1 (MPa) σ3 (MPa) x-displacement (m) y-displacement (m) Total displacement (m) σ1 (MPa) σ3 (MPa) x-displacement (m) y-displacement (m) Total displacement (m) σ1 (MPa) σ3 (MPa) x-displacement (m) y-displacement (m) Total displacement (m) σ1 (MPa) σ3 (MPa) x-displacement (m) y-displacement (m) Total displacement (m) 0.964 0.052 0.205 1.32e − 003 0.205e − 004 0.953 0.057 1.60e − 006 0.204e − 004 0.204e − 004 0.960 0.054 0.204e − 004 6.35e − 007 0.204e − 004 0.964 0.082 1.06e − 006 0.204e − 004 0.204e − 004 0.920 0.136 1.79e − 004 2.37e − 007 1.79e − 004 0.939 0.128 1.84e − 007 1.80e − 004 1.80e − 004 0.938 0.127 1.79e − 004 3.91e − 007 1.79e − 004 0.943 0.130 1.74e − 007 1.81e − 004 1.81e − 004 0.072 9.80e − 003 1.20e − 003 1.76e − 005 1.20e − 003 0.080 0.011 1.07e − 005 1.18e − 003 1.18e − 003 0.068 8.74e − 003 1.20e − 003 4.64e − 006 1.20e − 003 0.083 0.011 8.03e − 006 1.19e − 003 1.19e − 003 0.315 0.129 2.22e − 004 1.09e − 006 2.22e − 004 0.313 0.131 2.20e − 004 1.03e − 006 4.37e − 004 0.310 0.131 2.20e − 004 1.03e − 006 2.20e − 004 0.313 0.130 9.32e − 007 2.21e − 004 2.21e − 004 Roof Left Wall Floor Tuffite
  • 10. Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 203 Fig. 5. Stresses around tunnel before and after support for basalts. expected to occur. Then the radius of the broken zone Rpl is defined by: Àpffiffiffiffiffiffi pffiffiffiffiffiÁ Rpl ¼ R exp2 Picr − Pi : ð30Þ Hoek and Brown (1997) suggested the following pl equation to evaluate the total plastic deformation ur for rock masses: qffiffiffiffiffiffi 2 3 ⁎ 2 Rpl upl 2Gmass 41−2m Pi 1−2m r ¼ þ 15 þ ⁎ R r0 −Picr R 2 S0 −P⁎ 4 S0 −Pi i qffiffiffiffiffiffi ⁎ !2 ! Rpl Rpl 1−2m Pi þ1 Â ln − 2 ln 2 S0 −P⁎ R R i ð31Þ where R is the tunnel radius, ν is the Poisson's ratio, and Gmass is the shear modulus of rock mass. Carranza- Torres and Fairhurst (2000) suggested the following equation for calculating rock mass shear modulus: Gmass ¼ Emass ; 2ð1 þ mÞ ð32Þ where Emass is the deformation modulus of the rock mass. Internal pressure Pi was assumed to be zero in this study for unsupported tunnel cases in basalt and tuffite. el The calculated parameters of σ0, Gmass, Pi, Picr, Rpl, ur , pl ur and strain for basalt and tuffite are summarized in Table 9. The actual critical internal pressure (Picr = 0.0 MPa) is less than the internal pressure (Pi = 0.000049 MPa) for basalt. In this case, basalts will behave elastically and failure will not occur. The inward elastic displacement of tunnel walls and strain were calculated as 0.211 mm and 0.0084%, respectively. For tuffites, the actual
  • 11. 204 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 Fig. 6. Stresses around tunnel before and after support for tuffites. internal pressure (Picr = 0.0143 MPa) is higher than the internal pressure (Pi = 0.00191 MPa). Tuffites will behave plastically and failure is expected to occur. The radius of plastic zone and the strain for tuffite were calculated as 3.47 m and 0.0176%, respectively. Hoek and Marinos (2000) suggested that for formations with strain values less than one, few stability problems are expected. Simple tunnel support design methods are suggested to be used for such cases. 5.3. Numerical approach In order to verify the results of the empirical analyses, a two-dimensional hybrid element model, called Phase2 Finite Element Program (Rocscience, 1999), was used in the numerical analysis conducted here in. The rock mass properties assumed in this analysis were obtained from the estimated values presented in Section 4. The Hoek–Brown failure criterion was used to identify elements undergoing yielding and the plastic zones of rock masses in the vicinity of tunnel perimeter. Plastic post-failure strength parameters were used in this analysis and residual parameters were assumed as half of the peak strength parameters. The far-field stresses for basalt and tuffite were used as 0.53 MPa and 0.22 MPa, respectively, as determined in Section 5.2. To simulate the excavation of the diversion tunnel in basalt and tuffite, two different finite element models were generated using the same mesh and tunnel geometry, but different material properties. The outer model boundary was set at a distance of 6
  • 12. Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 205 Fig. 7. The displacement behavior and extent of plastic zone before and after support for basalts. times the tunnel radius. A total of 3048 three-noddedtriangular elements were used in the finite element mesh. The following sections were used: Section I tunnel running through basalt Section II tunnel running through tuffite The required parameters and their numerical values for basalts and tuffites are given in Table 10. For unsupported and supported cases, total displacements and stresses at the walls, roof and floor of the tunnel for the two different rock types are presented in Table 11 and Figs. 5 and 6. The total displacement behavior and extent of plastic zone before and after support for basalt and tuffite are given in Figs. 7 and 8, respectively. It can be seen from Figs. 7 and 8 that the extent of failure zone for basalts is less than the corresponding zone for tuffites. The maximum total displacement values for
  • 13. 206 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 Fig. 8. The displacement behavior and extent of plastic zone before and after support for tuffites. unsupported tunnel in basalts and tuffites are 2.05e − 004 and 1.20e − 003 m, respectively. The displacement values for basalt and tuffites are very small. However, the extent of plastic zone and elements undergoing yielding suggest that there would be stability problems for the tunnel driven in basalts and tuffites. In basalts, only some yielded elements were observed and the thickness of plastic zone was limited, as shown in Fig. 7. The support elements used consist of rock bolts and shotcrete, as proposed by the empirical methods. The properties of support elements, such as length, bolt patterns and thickness of shotcrete are similar to those proposed by the empirical methods. For tunnel in basalts, 4-m-long rock bolts with 2-m spacing and 100mm-thick shotcrete are proposed. For tuffites, 5-m-long rock bolts with 1-m spacing and 150-mm-thick shotcrete
  • 14. Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 207 Table 12 Radius of plastic zone and maximum total displacements obtained from Phase2 Unit Radius of plastic zone, Rpl (m) Maximum total displacement (m) Unsupported Supported Unsupported Supported Basalt Tuffite 2.68 4.21 2.50 2.50 2.05e − 004 1.20e − 003 1.79e − 004 2.20e − 004 are proposed as support elements. After considering support measures in the numerical model, not only the number of yielded elements but also the extent of plastic zone decreased substantially, as shown in Figs. 7 and 8. The maximum total displacement values for basalt and tuffites decreased to 1.79e − 004 and 2.20e − 004 mm, respectively, as shown in Table 11. For basalts and tuffites, the radius of plastic zone and the maximum total displacements obtained from Phase2 FEM analysis for unsupported and supported cases are presented in Table 12. number of yielded elements and the size of plastic zone around the tunnel. The results obtained from the empirical, theoretical and numerical approaches were fairly comparable. However, the validity of the proposed support systems should be checked by comparing the results obtained by a combination of empirical, theoretical and numerical methods with the measurements that will be carried out during construction. 6. Conclusions Barton, N., 2002. Some new Q-value correlations to assist in site characterization and tunnel design. Int. J. Rock Mech. Min. Sci. 39 (1), 185–216. Barton, N.R., Lien, R., Lunde, J., 1974. Engineering classification of rock masses for the design of tunnel support. Rock Mech. 4, 189–239. Bieniawski, Z.T., 1974. Geomechanics classification of rock masses and its application in tunneling. Proceedings of the Third International Congress on Rock Mechanics, vol. 11A. International Society of Rock Mechanics, Denver, pp. 27–32. Bieniawski, Z.T., 1978. Determining rock mass deformability: experience from case histories. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 15, 237–247. Bieniawski, Z.T., 1989. Engineering Rock Mass Classifications. Wiley, New York. 251 pp. Carranza-Torres, C., Fairhurst, C., 1999. The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek– Brown failure criterion. Int. J. Rock Mech. Min. Sci. 36 (6), 777–809. Carranza-Torres, C., Fairhurst, C., 2000. Application of the convergence–confinement method of tunnel design to rock masses that satisfy the Hoek–Brown failure criterion. Tunn. Undergr. Space Technol. 15 (2), 187–213. Deere, D.U., 1964. Technical description of rock cores for engineering purposes. Rock Mech. Rock Eng. 1, 17–22. Diederichs, M.S., Hoek, E., 1989. DIPS 3.01, Advanced Version Computer Programme, Rock Engineering Group. Department of Civil Engineering, University of Toronto. General Directorate of State Hydraulic Works (DSI), 1997. Planning Report of the Boztepe Dam (Malatya), IX. Region Directorate of the State Hydraulic Works. Elazig, Turkey. Gurocak, Z., 1999. The investigation of the geomechanical properties and alteration degrees of the rock units at the Boztepe (Malatya/ Turkey) dam site. Ph.D. Thesis. Firat University. Faculty of Engineering, 106 p. (in Turkish). Hoek, E., Brown, E.T., 1997. Practical estimates of rock mass strength. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 27 (3), 227–229. Hoek, E., Diederichs, M.S., 2006. Empirical estimation of rock mass modulus. Int. J. Rock Mech. Min. Sci. 43, 203–215. In this study, empirical methods were used to estimate the rock mass quality and support elements for basalts and tuffites in the diversion tunnel at the Boztepe dam site. Based on the information collected in the field and laboratory, the RMR and Q classification systems were used to characterize the rock masses. These classification systems were also employed to estimate the support requirements for the diversion tunnel. The Hoek–Brown parameters and support measure recommendations from the empirical results were used as input in the numerical analyses. According to the results obtained from the empirical, theoretical and numerical analysis, there were some stability problems for basalts. The empirical methods recommend the utilization of rock bolts and shotcrete as support elements for basalts. The results of theoretical and numerical method show that basalts are expected to have some deformations. Numerical modeling was used to evaluate the performance of the recommended support system. However, the results from the finite element methods are similar to the results from the empirical methods. When the recommended support systems were considered, the displacements were reduced significantly in the numerical analysis. The empirical approach indicated that substantial support was necessary for tuffites, and both theoretical and numerical approaches agreed concerning the important stability problems. However, after considering the support elements, the numerical analysis showed that there was a considerable decrease in both the References
  • 15. 208 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208 Hoek, E., Marinos, P., 2000. Predicting Tunnel Squeezing. Tunnels and Tunneling International. Part 1 – November 2000, Part 2 – December 2000. Hoek, E., Carranza-Torres, C., Corkum, B., 2002. Hoek–Brown failure criterion – 2002 edition. In: Hammah, R., Bawden, W., Curran, J., Telesnicki, M. (Eds.), Proceedings of NARMSTAC 2002, Mining Innovation and Technology. Toronto – 10 July 2002. University of Toronto, pp. 267–273. Hoek, E., Kaiser, P.K., Bawden, W.F., 1995. Support of Underground Excavations in Hard Rock. Balkema, Rotterdam. 215 pp. International Soil and Rock Mechanics ISRM, 1981. In: Brown, E.T. (Ed.), Rock Characterization, Testing and Monitoring, ISRM Suggested Methods. Pergamon Press, Oxford, p. 211. Marinos, P., Hoek, E., 2000. GSI: a geologically friendly tool for rock mass strength estimation. Proceedings of the GeoEng2000 at the international conference on geotechnical and geological engineering, Melbourne. Technomic publishers, Lancaster, pp. 1422–1446. Marinos, P., Hoek, E., 2001. Estimating the geotechnical properties of heterogeneous rock masses such as flysch. Bull. Eng. Geol. Environ. 60, 85–92. Ramamurthy, T., 2001. Shear strength response of some geological materials in triaxial compression. Int. J Rock Mech. Min. Sci. 38, 683–697. Ramamurthy, T., 2004. A geo-engineering classification for rocks and rock masses. Int. J. Rock Mech. Min. Sci. 41, 89–101. Read, S.A.L., Richards, L.R., Perrin, N.D., 1999. Applicability of the Hoek–Brown failure criterion to New Zealand greywacke rocks. Proceedings 9th Int. Society for Rock Mechanics Congress, Paris, vol. 2, pp. 655–660. Rocscience, 1999. A 2D finite element program for calculating stresses and estimating support around the underground excavations. Geomechanics Software and Research. Rocscience Inc., Toronto, Ontario, Canada. Serafim, J.L., Pereira, J.P., 1983. Considerations of the geomechanics classification of Bieniawski. Proceedings International Symposium Engineering Geology and Underground Construction, vol. 1. Balkema, Rotterdam, pp. 1133–1142. Sheorey, P.R., Murali, M.G., Sinha, A., 2001. Influence of elastic constants on the horizontal in situ stress. Int. J. Rock Mech. Min. Sci. 38 (1), 1211–1216. Singh, B., Gahrooee, D.R., 1989. Application of rock mass weakening coefficient for stability assessment of slopes in heavily jointed rock masses. Int. J. Surf. Min. Reclam. Environ. 3, 217–219.