583 24650 emperical method

(2007) 194–208www.elsevier.com/locate/enggeo

Engineering Geology 91

Empirical and numerical analyses of support requirements for adiversion 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, Turkeyb School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019-1024, USA

c Research and Graduate Education, College of Engineering, University of Oklahoma, Norman, OK 73019-1024, USA

Received 29 September 2006; received in revised form 10 January 2007; accepted 25 January 2007Available online 3 February 2007

Abstract

This paper presents the engineering geological properties and support design of a planned diversion tunnel at the Boztepe damsite that contains units of basalt and tuffites. Empirical, theoretical and numerical approaches were used and compared in this studyfocusing on tunnel design safety. Rock masses at the site were characterized using three empirical methods, namely rock massrating (RMR), rock mass quality (Q) and geological strength index (GSI). The RMR, Q and GSI ratings were determined by usingfield data and the mechanical properties of intact rock samples were evaluated in the laboratory. Support requirements wereproposed accordingly in terms of different rock mass classification systems. The convergence–confinement method was used as thetheoretical 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 twomethods were compared with each other. This comparison suggests that a more reliable and safe design could be achieved by usinga 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 massquality; Rock mass rating

1. Introduction

The design of an underground structure involves theuse of both empirical and numerical approaches.Empirical methods are generally preferred by engineersand engineering geologists due to practicality. In

⁎ Corresponding author. School of Civil Engineering and Environ-mental Science, University of Oklahoma, 202West Boyd Street, Room334, Norman, OK 73019-1024, USA. Tel.: +1 405 301 4341; fax: +1405 325 4217.

E-mail addresses: [email protected], [email protected](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 massclassification systems have been employed by manyresearchers and have gained a universal acceptance(Barton, 2002; Ramamurthy, 2004; Hoek and Dieder-ichs, 2006). These rock mass classification systems wereoriginally obtained from many tunneling case studies.However, these empirical methods do not provide thestress distributions and deformations around the tunnel.Therefore, particular attention should be given to thesefactors when using empirical methods. Specifically,when conducting an analysis, the determination of thevalues of stress distributions and deformations for therock mass in question, is very sensitive to the field

Fig. 1. The location map of study area.

195Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

observations. Likewise, analytical and numericalapproaches are dependent upon the strength parametersof associated rock masses that are used as input

Fig. 2. Geological map and cross-

parameters when using an analytical and numericalapproach. Therefore, the stability analysis of a tunnel islikely to suggest a safer design if a combination ofempirical, theoretical, and numerical approaches is used.

The field site used in this study is located 10 kmnorthwest of Yazihan, in the north of the city of Malatya,in eastern Turkey (Fig. 1). The Boztepe dam which isunder construction on the Yagca stream is located at thissite. The dam project is designed to regulate waterdrainage and irrigate the agricultural areas of theYazihan plain. The design of the Boztepe dam projectis under the supervision of General Directorate of StateHydraulic Works (DSI, 1997), of Ministry of Energyand Natural Resources in Turkey. The diversion tunnelof the Boztepe dam has a length of 565 m, havingcircular geometry with 5 m in diameter. It cuts acrossbasalts and tuffites. The tunnel will have a maximumoverburden of about 38 m for basalts and about 27 m for

section of Boztepe dam site.

Fig. 3. The histograms for RQD of basalts (A) and tuffites (B). Table 1Engineering properties of joints and bedding surfaces and theirpercentage distribution

Properties Spacing Description Percentage

Basalt Tuffite

Spacing (mm) a b20 Extremely closespacing

5 2

20–60 Very close spacing 33 1660–200 Close spacing 42 69200–600 Moderate spacing 20 10600–2000 Wide spacing – 3

Persistence (m)a b1 Very low persistence 33 81–3 Low persistence 56 93–10 Medium persistence 11 3410–20 High persistence – 31N20 Very high persistence – 14

Aperture (mm)a b0.1 Very tight 8 120.1–0.25 Tight 14 –0.25–0.50 Partly open 10 20.50–2.50 Open 16 202.5–10 Moderately wide 48 51N10 Wide 4 15

Roughnessa IV Rough undulating 11 5V Smooth undulating 3 7VI Slickensided

undulating10 –

VII Rough planar 61 88VIII Smooth planar 6 –IX Slickensided planar 9 –

Weathering (Wc)b ≤1.2 Fresh/Unweathered 22 –

1.2–2 Moderately weathered 67 2N2.0 Weathered 11 98

a According to ISRM (1981).b According to Singh and Gahrooee (1989).

196 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

tuffites. The dam site is located within the YamadagVolcanics, which is composed of basalt, tuffite andagglomerate. Geological mapping and geotechnicaldescriptions were conducted in the field.

The physical, mechanical and elastic properties of therocks under consideration were determined from labo-ratory testing on intact rock samples. These tests includean evaluation of uniaxial compressive strength (σc),Young's modulus (E), Poisson's ratio (ν), unit weight(γ), internal friction angle (ϕ), and cohesion (c). Therock mass properties of the dam site were determined byusing different rock mass classification systems.

2. Geology, field and laboratory studies

The Boztepe dam site consists of various age unitsranging from the Upper Miocene to the Quaternary.Middle–Upper Miocene volcano-sedimentary rocks thatare known as Yamadag Volcanics, are exposed in theregion. These rocks are a part of the extensive Miocenevolcanism in the Eastern Anatolian Region. The Yamadagvolcanites are represented in the study area by fourdifferent rock units extending upwards from a sandstone–claystone through tuffite, basalt and agglomerate mem-bers. As seen in Fig. 2, at the dam site, themain valley is intuffite with basalt forming the plateau to the east. Thetuffites are dirty white or light grey colored and well-

bedded, with bed thicknesses ranging from300 to 600mmin the lower levels and 50 to 200 mm in the upper levels.Joints within the tuffite are commonly altered and filledwith clay or calcite having 20 to 30 mm thickness.

The basalts overlying the tuffites are dark grey incolor. In the lower levels, they are mainly pillar lavaswhile near the top they commonly occur as columnarstructures (Gurocak, 1999). Vesicles are rare and thebasalts are generally well-jointed. The agglomeratemember overlying the basalts is generally dark in colorand massive in structure. The individual boulders areweakly rounded, having a maximum size of 0.7 m. Thisunit also contains interlayer of tuff and basalt flows.Overlying the agglomerate are mainly Quaternarydeposits, namely talus and alluvial materials.

During the field surveys, engineering geological mapof the Boztepe dam site and the geological cross sectionalong the diversion tunnel was constructed. The fieldstudies also included the orientation, persistence,spacing, opening, roughness, the degree of weatheringand filling of discontinuities in the basalts and tuffites.

Fig. 4. Stereographic projection of bedding surface (A) and joint sets (B) in tuffites and joint sets (C) in basalts.

197Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

In addition, an examination was made of 1195m of thecore, from 20 boreholes drilled by the General Directorateof State Hydraulic Works (DSI, 1997). The RQD valuesof the basalts and tuffites were determined. Thehistograms shown in Fig. 3 were prepared using theRQD divisions proposed by Deere (1964). From thisfigure, the rock quantities of the basalts have the followingdistribution: 6% excellent, 14% good, 32% fair, 23%poor, and 25% very poor. Similarly, the tuffites have thefollowing 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 activeregion, the basalts exposed around the Boztepe dam sitecontain systematic joint sets. However, tuffites aresedimentary rocks and contain bedding surfaces. Table 1shows the main orientation, spacing, persistence, apertureand roughness of discontinuities. These were describedusing the scan-line survey method following the ISRM(1981) description criteria. The degree of weathering ofthe discontinuous surfaceswas assessed using the Schmidt

hammer and theweathering index was calculated from theequation proposed by Singh and Gahrooee (1989):

Wc ¼ rcJCS

; ð1Þ

where

σc Uniaxial compressive strength of fresh rock(MPa), and

JCS Strength of discontinuity surface (MPa).

JCS was calculated from the following equation:

LogJCS ¼ 0:00088gRþ 1:01; ð2Þ

where

γ Bulk volume weight (kN/m3), andR Hardness value from rebounding of Schmidt

hammer.

Table 2Laboratory tests results of basalts and tuffites

Properties Min Max Mean Std. err.

BasaltUniaxial compressive strength (σc,MPa) 8.72 76.46 40.64 19.67Young's modulus (E, GPa) 1.6 96.7 30.91 47.17Poisson's ratio (ν) 0.241 0.286 0.27 0.02316Unit weight (γ, kN/m3) 23.10 28.10 25.55 1.48Cohesion (c, MPa) 12 a

Internal friction angle (ϕ, deg) 42a

TuffiteUniaxial compressive strength (σc,MPa) 1.97 21.20 8.21 5.72Young's modulus (E, GPa) 0.6 10.5 2.23 2.615Poisson's ratio (ν) 0.17 0.22 0.20 0.02517Unit weight (γ, kN/m3) 12.00 22.10 16.50 0.04Cohesion (c, MPa) 1.80a

Internal friction angle (ϕ, deg) 33a

Std. err.: standard error.a

Table 3RMR89 rating for basalts and tuffites

Classificationparameters

Basalt Tuffite

Value ofparameters

Rating Value ofparameters

Rating

Uniaxialcompressivestrength (MPa)

40.64 5 8.21 2

RQD (%) 62 12 25 6Discontinuityspacing (cm)

160 7.3 90 6

DiscontinuityconditionPersistence (m) 1–3 4 3–10 2Aperture (mm) 2.50–3.00 1 2.5–10 0Roughness Rough-planar 5 Rough-planar 5Filling Calciteb5 mm 4 calciteN5 mm 2Weathering Moderately 3 Highly 1

Groundwatercondition

Dry 15 Dry 15

Basic RMR value 56.3 39Rating adjustmentfor jointorientation

Veryfavorable/Fair

0/−5 Fair −5

RMR 56.3/51.3 34Rock mass quality Fair rock Poor rock

198 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

In the study area, a total of 388 bedding surfaces and520 joint measurements were taken from tuffites andbasalts. Discontinuity orientations were processedutilizing a commercially available software DIPS 3.01(Diederichs and Hoek, 1989), based on equal-areastereographic projection, and major joint sets weredistinguished for basalts and tuffites (Fig. 4).

The following major orientations of the beddingsurface for tuffites were observed:

Bedding surface: 14/100Joint set 1: 80/220Joint set 2: 87/259Joint set 3: 77/305

The major orientations of the joint sets for basalts arelisted below:

Joint set 1: 78/192Joint set 2: 71/3Joint set 3: 67/287Joint set 4: 72/99

According to ISRM (1981), the joint sets in thebasalts have close to very close spacing, low persis-tence, moderate width, rough-planar and moderatelyweathered character. The discontinuities in tuffiteshave close spacing, medium to high persistence,moderate width, and rough-planar and weatheredcharacter.

Uniaxial compressive strength, deformability, unitweight and triaxial compressive strength tests wereconducted in accordance with the ISRM suggested

Values obtained by using triaxial test.

methods (ISRM, 1981). Pertinent results are summa-rized in Table 2. The average uniaxial compressivestrength of basalts is 40.64 MPa, Young's modulus is30.91 GPa, Poisson's ratio is 0.27, unit weight is25.55 kN/m3, cohesion is 12 MPa and friction angle is42°. The average uniaxial compressive strength oftuffites 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 forquantitative descriptions of the rock mass quality. Thisin turn led to the development of many empirical designsystems involving rock masses. Many researchersdeveloped rock mass classification systems. Some ofthe most widely used rock mass classification systemsinclude RMR and Q. These two classification systemsare utilized in this research.

3.1. RMR system

Bieniawski (1974) initially developed the rock massrating (RMR) system based on experience in tunnelprojects in South Africa. Since then, this classificationsystem has undergone significant changes. Thesechanges are mostly due to the ratings added for ground

Table 4Q rating for basalts and tuffites

Classification parameters Basalt Tuffite

Value of parameters Rating Value of parameters Rating

RQD (%) 62% 62 25% 25Joint set number (Jn) Four joint sets plus random joints 15 Three joint sets and a bedding surface plus random joints 12Joint alteration number (Jr) Rough planar 1.5 Rough-planar 1.5Joint alteration number ( ja) Moderately altered 6 Highly altered 8Joint water reduction factor ( jw) Dry excavation or minor inflow 1 Dry excavation or minor inflow 1Stress reduction factor (SRF) Medium stress 1 Low stress, near surface 2.5Q 1.03 0.156Rock mass quality Poor rock Very poor rock

199Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

water, joint condition and joint spacing. In order to usethis system, the uniaxial compressive strength of theintact rock, RQD, joint spacing, joint condition, jointorientation and ground water conditions have to beknown. In this study, the RMR classification system(Bieniawski, 1989) is used and the results are summa-rized in Table 3. This rating classifies basalt as a fairrock mass, while tuffite as a poor rock mass.z

3.2. Q system

Barton et al. (1974) developed the Q rock massclassification system. This system is also known as theNGI (Norwegian Geotechnical Institute) rock massclassification system. It is defined in terms of RQD, thefunction of joint sets (Jn), discontinuity roughness (Jr),joint alteration (Ja), water pressure (Jw) and stressreduction factor (SRF). Barton (2002) compiled thesystem again and made some changes on the supportrecommendations. He also included the strength factorof the rock material in the system.

Q ¼ RQDJn

JrJa

JwSRF

: ð3Þ

Recently, Barton (2002) defined a new parameter, Qc,to improve correlation among the engineering parameters:

Qc ¼ Qrc100

; ð4Þ

whereσc 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

Table 5GSI and calculated Hoek–Brown parameters values

Unit GSI mi constant mb constant s constant a constant

Basalt 48 25 3.903 0.0031 0.507Tuffite 32 13 1.146 0.0005 0.520

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–Brownconstants, deformation modulus (Emass) and uniaxialcompressive strength of rock mass (σcmass) werecalculated by means of empirical equations in accor-dance with the RMR89, Q, Qc and GSI.

4.1. Geological strength index (GSI) and Hoek–Brownparameters

The geological strength index (GSI) was developed byHoek et al. (1995). The GSI is based on the appearance ofa rock mass and its structure. Marinos and Hoek (2001)used additional geological properties in the Hoek–Brownfailure criterion and introduced a new GSI chart forheterogeneous weak rock masses. The value of GSI wasobtained 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 usedfor determining the rock mass properties of basalt at thedam site. Hoek et al. (2002) suggested the following equa-tions for calculating rock mass constants (i.e.,mb, s and a):

mb ¼ mi expGSI−10028−14D

� �; ð5Þ

s ¼ expGSI−1009−3D

� �; ð6Þ

a ¼ 12þ 16

e−GSI=15−e−20=3� �

; ð7Þ

where D is a factor that depends upon the degree ofdisturbance to which the rock mass is subjected to by blast

Table 6Selected equations for estimating deformation modulus of rock massEmass

Author Equations Equationnumber

Bieniawski(1978)

For RMRN50,

Emass ¼ 2RMR−100

(9)

Serafim andPereira(1983)

For RMRb50,

Emass ¼ 10RMR−10

40

(10)

Hoek andBrown(1997)

Emass ¼ffiffiffiffiffiffiffiffirci100

r10

GSI−1040

(11)

Read et al.(1999) Emass ¼ 0:1

RMR10

� �3 (12)

Ramamurthy(2001)

Emass ¼ Eiexp½ðRMR−100Þ�=17:4 (13)

Ramamurthy(2001)

Emass ¼ Eiexpð0:8625 logQ−2:875Þ (14)

Barton (2002) Emass ¼ 10Q1=3c

(15)

Hoek et al.(2002) Emass ¼ 1−

D

2

� � ffiffiffiffiffiffiffiffirci100

r10

GSI−1040

(16)

Ramamurthy(2004)

Emass ¼ Eiexp−0:0035½5ð100−RMRÞ� (17)

Ramamurthy(2004)

Emass ¼ Eiexp−0:0035½250ð1−0:3logQÞ� (18)

Hoek andDiederichs(2006)

Emass ¼ Ei 0:02þ 1

1þ eð60þ15D−GSIÞ=11

� � (19)

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.

200 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

damage and stress relaxation tests. In this study, the value ofD is considered zero. The calculated GSI is and the Hoek–Brown constants are listed in Table 5.

4.2. Strength and deformation modulus of rock masses

Several empirical equations have been suggested bydifferent researchers for estimating the strength andmodulus of rock masses based on the RMR, Q and GSIvalues. In this study, the strength of rock masses wascalculated from the following equation suggested byHoek et al. (2002):

rcmass ¼ rciðmb þ 4s−aðmb−8sÞÞðmb=4þ sÞa−1

2ð1þ aÞð2þ aÞ ; ð8Þ

where σci is uniaxial compressive strength of the intactrock, mb, s and a are rock mass constants. The strengthof rock masses for basalt and tuffite were determined as10.6 and 1.08 MPa, respectively.

The deformation modulus of rock masses wascalculated suggested by different researchers based onRMR, Q and GSI values. In this study, the equations inTable 6 were used for determining deformation modulusof rock masses. The calculated values of rock massdeformation modulus are summarized in Table 7.

5. Tunnel stability and support analysis

A reliable stability analysis and prediction of thesupport capacity are some of the most difficult tasks inrock engineering. Therefore, in the current study severalmethods are used to conduct stability analysis and deter-mine the support capacity. For the tunnel support designof the diversion tunnel at the Boztepe dam site, empirical,theoretical and numerical approaches were employed.

The vertical stress was assumed to increase linearlywith depth due to its overburden weight, as follows:

rv ¼ gH ; ð20Þwhere γ is unit weight of the intact rock in MN/m3, andH is the depth of overburden in m.

The horizontal stress was determined from thefollowing equation suggested by Sheorey et al. (2001):

rh ¼ m1−m

rv þ bEmassG1−m

ðH þ 100Þ; ð21Þ

where β=8×10−6/°C (coefficient of linear thermalexpansion), G=0.024 °C/m (geothermal gradient), ν isthe Poisson's ratio, Emass is deformation modulus ofrock mass, MPa.

The far-field stress σ0 was calculated using thefollowing equation:

r0 ¼ rv þ rh1 þ rh23

; ð22Þ

where σhl and σh2 are horizontal stresses.

Table 7Calculated 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.

Basalt 7.6 – 5.68 15.57 2.16 1.77 7.49 5.68 13.77 12.92 6.91 7.96 4.72Tuffite – 3.98 1.02 3.93 0.05 0.06 2.35 1.02 0.70 0.75 0.17 1.40 1.51

Avrg: average. St. dev.: standard deviation. Eq.: equation.

201Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

The 5-m-diameter tunnel was excavated at amaximum depth of 38 m in basalt and 27 m in tuffitebelow the ground surface. The far-field stresses forbasalt and tuffite were determined as 0.53 MPa and0.22 MPa, respectively.

5.1. Empirical approach

Bieniawski (1974) used RMR, width of opening W(m), and unit weight of overburden γ (kN/m3) todetermine the support pressure. From the formulabelow, the support pressure Proof, is found in kN/m2:

Proof ¼ 100−RMR100

� �Wg: ð23Þ

Another approach was proposed by Barton et al.(1974) that depends on rock mass quality, Q, anddiscontinuity roughness, Jr . The roof support pressure,

Table 8Estimated support categories of basalts and tuffites

Unit Basalt Tuffite

RMRclassificationsystem

RMR 56.3/51.3 34Fair rock Poor rock

Support Systematic bolts4 m long, spaced1.5–2 m in crownand walls withwire mesh in crown.50–100 mm in crownand 30 mm in sides.

Systematic bolts4–5 m long,spaced 1–1.5 min crown and wallswith wire mesh.100–150 mm incrown and 100 mmin sides.

Q classificationsystem

Q 1.03 0.156Poor rock Very poor rock

ESR 1.6 1.6De 3.125 3.125Support Systematic bolting,

4 m long, spaced1.7 m with 40–50 mmunreinforced shotcrete

4 m long bolting,spaced 1.3–1.5 mand 90–120 mmfibre reinforcedshotcrete

De ¼ Excavation span; diameter or height ðmÞExcavation support ratio ðESRÞ

Proof (kN/m2), was calculated by using the following

equation:

Proof ¼ 200Jr

Q1=3: ð24Þ

The support pressure was calculated as 0.135 MPaaccording to the Barton et al. (1974) approach and0.059 MPa according to the Bieniawski (1974) approachfor the basalts. However, for tuffite the correspondingvalues were found to be 0.072 MPa and 0.055 MPa,respectively. As one can see that from these results, thesupport pressure obtained from the Q criterion is greaterthan obtained by the RMR criterion and is consideredmore realistic.

The tunnel supports were defined in accordance withthe recommendations of the RMR and Q systems.Bieniawski (1989) suggested supports for different rockmass classes in the RMR89 system. As noted earlier,according to the RMR89 system on the one hand, basaltsand tuffites are fair and poor rock masses, respectively.Correspondingly according to the Q system on the otherhand, basalts and tuffites are poor and very poor rockmasses, respectively. A summary of the estimated supportsusing the RMR89 and Q systems are presented in Table 8.

5.2. Theoretical approach

In this study, a theoretical approach, called theconvergence–confinement technique, was used forstability analysis. This methodology has been describedby Carranza-Torres and Fairhurst (1999) for rock massesthat satisfy the Hoek–Brown criterion. A cylindricaltunnel of radius R, subjected to a uniform far-field stress

Table 9Far-field stress, shear modulus of rock mass, actual critical internalpressure, radius of plastic zone, maximum deformation and strainvalues obtained from the convergence–confinement method

Unit σ0

(MPa)Gmass

(GPa)Pi

(MPa)Pi

cr

(MPa)Rpl

(m)urel

(mm)urpl

(mm)Strain(%)

Basalt 0.53 3.13 0.000049 0.000 0.00 0.211 0.000 0.0084Tuffite 0.22 0.58 0.00191 0.0143 3.47 0.000 0.441 0.0176

Table 10Material properties of basalts and tuffites for numerical model

Property Basalt Tuffite

Value

Material type Isotropic IsotropicYoung's modulus (GPa) 7.96 1.40Poisson's ratio 0.27 0.20Compressive strength (MPa) 10.61 1.08m parameter 3.903 1.146s parameter 0.0031 0.0005Material type Plastic PlasticDilation parameter 0° 0°m residual 1.9515 0.573s residual 0.00155 0.00025

202 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

σ0, and internal pressure Pi was considered. The rockmass, in which the tunnel is excavated, is assumed tosatisfy the Hoek–Brown failure criterion.

The actual critical internal pressure Picr is defined as

(Carranza-Torres and Fairhurst, 2000):

Pcri ¼ P

⁎i −

s

m2b

� �mbrci; ð25Þ

where

s and mb Hoek–Brown constants,σci uniaxial compressive strength, andPi⁎ scaled critical internal pressure.

Table 11Stresses and displacements before and after support for basalts and tuffites

Location Parameter Basalt

Before support

Right wall σ1 (MPa) 0.964σ3 (MPa) 0.052x-displacement (m) 0.205y-displacement (m) 1.32e−003Total displacement (m) 0.205e−004

Roof σ1 (MPa) 0.953σ3 (MPa) 0.057x-displacement (m) 1.60e−006y-displacement (m) 0.204e−004Total displacement (m) 0.204e−004

Left Wall σ1 (MPa) 0.960σ3 (MPa) 0.054x-displacement (m) 0.204e−004y-displacement (m) 6.35e−007Total displacement (m) 0.204e−004

Floor σ1 (MPa) 0.964σ3 (MPa) 0.082x-displacement (m) 1.06e−006y-displacement (m) 0.204e−004Total displacement (m) 0.204e−004

The scaled critical internal pressure is evaluated fromthe following equation:

P⁎i ¼ 1

161−

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 16S0

p� �2; ð26Þ

in which S0 is the scaled far-field stress given by:

S0 ¼ r0mbrci

þ s

m2b

; ð27Þ

where σ0 is far-field stress, and Pi is the scaled internalpressure defined by:

Pi ¼ pimbrci

þ s

m2b

; 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, andthe inward elastic displacement ur

el of the tunnel wall isgiven by:

uelr ¼ r0−Pi

2GmassR; ð29Þ

where σ0 is far-field stress, Pi is scaled internal pressure,R is the tunnel radius and Gmass is the shear modulus ofthe rock mass.

If the internal pressure Pi, on the other hand, is lessthan the actual critical internal pressure Pi

cr, failure is

Tuffite

After support Before support After support

0.920 0.072 0.3150.136 9.80e−003 0.1291.79e−004 1.20e−003 2.22e−0042.37e−007 1.76e−005 1.09e−0061.79e−004 1.20e−003 2.22e−0040.939 0.080 0.3130.128 0.011 0.1311.84e−007 1.07e−005 2.20e−0041.80e−004 1.18e−003 1.03e−0061.80e−004 1.18e−003 4.37e−0040.938 0.068 0.3100.127 8.74e−003 0.1311.79e−004 1.20e−003 2.20e−0043.91e−007 4.64e−006 1.03e−0061.79e−004 1.20e−003 2.20e−0040.943 0.083 0.3130.130 0.011 0.1301.74e−007 8.03e−006 9.32e−0071.81e−004 1.19e−003 2.21e−0041.81e−004 1.19e−003 2.21e−004

Fig. 5. Stresses around tunnel before and after support for basalts.

203Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

expected to occur. Then the radius of the broken zoneRpl is defined by:

Rpl ¼ R exp2ffiffiffiffiffiffiPcri

p−

ffiffiffiffiffiPi

p� �: ð30Þ

Hoek and Brown (1997) suggested the followingequation to evaluate the total plastic deformation ur

pl

for rock masses:

uplrR

2Gmass

r0−Pcri

¼ 1−2m2

ffiffiffiffiffiffiP⁎i

q

S0−P⁎i

þ 1

24

35 Rpl

R

� �2

þ 1−2m

4 S0−P⁎i

� �

� lnRpl

R

� � 2−1−2m2

ffiffiffiffiffiffiP⁎i

q

S0−P⁎i

2 lnRpl

R

� �þ 1

ð31Þwhere R is the tunnel radius, ν is the Poisson's ratio, andGmass is the shear modulus of rock mass. Carranza-

Torres and Fairhurst (2000) suggested the followingequation for calculating rock mass shear modulus:

Gmass ¼ Emass

2ð1þ mÞ ; ð32Þ

where Emass is the deformation modulus of the rockmass.

Internal pressure Pi was assumed to be zero in thisstudy for unsupported tunnel cases in basalt and tuffite.The calculated parameters of σ0, Gmass, Pi, Pi

cr, Rpl, urel,

urpl and strain for basalt and tuffite are summarized in

Table 9.The actual critical internal pressure (Pi

cr =0.0 MPa) isless than the internal pressure (Pi =0.000049 MPa) forbasalt. In this case, basalts will behave elastically andfailure will not occur. The inward elastic displacementof tunnel walls and strain were calculated as 0.211 mmand 0.0084%, respectively. For tuffites, the actual

Fig. 6. Stresses around tunnel before and after support for tuffites.

204 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

internal pressure (Picr =0.0143 MPa) is higher than the

internal pressure (Pi =0.00191 MPa). Tuffites willbehave plastically and failure is expected to occur. Theradius of plastic zone and the strain for tuffite werecalculated as 3.47 m and 0.0176%, respectively.

Hoek and Marinos (2000) suggested that forformations with strain values less than one, fewstability problems are expected. Simple tunnel supportdesign methods are suggested to be used for suchcases.

5.3. Numerical approach

In order to verify the results of the empiricalanalyses, a two-dimensional hybrid element model,called Phase2 Finite Element Program (Rocscience,

1999), was used in the numerical analysis conductedhere in. The rock mass properties assumed in this anal-ysis were obtained from the estimated values presentedin Section 4. The Hoek–Brown failure criterion wasused to identify elements undergoing yielding and theplastic zones of rock masses in the vicinity of tunnelperimeter. Plastic post-failure strength parameters wereused in this analysis and residual parameters wereassumed as half of the peak strength parameters.

The far-field stresses for basalt and tuffite were usedas 0.53 MPa and 0.22 MPa, respectively, as determinedin Section 5.2. To simulate the excavation of thediversion tunnel in basalt and tuffite, two different finiteelement models were generated using the same meshand tunnel geometry, but different material properties.The outer model boundary was set at a distance of 6

Fig. 7. The displacement behavior and extent of plastic zone before and after support for basalts.

205Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

times the tunnel radius. A total of 3048 three-nodded-triangular elements were used in the finite elementmesh. The following sections were used:

Section I tunnel running through basaltSection II tunnel running through tuffite

The required parameters and their numerical valuesfor basalts and tuffites are given in Table 10. For

unsupported and supported cases, total displacementsand stresses at the walls, roof and floor of the tunnel forthe two different rock types are presented in Table 11 andFigs. 5 and 6. The total displacement behavior and extentof plastic zone before and after support for basalt andtuffite are given in Figs. 7 and 8, respectively.

It can be seen from Figs. 7 and 8 that the extent offailure zone for basalts is less than the corresponding zonefor tuffites. The maximum total displacement values for

Fig. 8. The displacement behavior and extent of plastic zone before and after support for tuffites.

206 Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

unsupported tunnel in basalts and tuffites are 2.05e−004and 1.20e−003 m, respectively. The displacement valuesfor basalt and tuffites are very small. However, the extentof plastic zone and elements undergoing yielding suggestthat there would be stability problems for the tunneldriven in basalts and tuffites. In basalts, only some yieldedelements were observed and the thickness of plastic zonewas limited, as shown in Fig. 7.

The support elements used consist of rock bolts andshotcrete, as proposed by the empirical methods. Theproperties of support elements, such as length, boltpatterns and thickness of shotcrete are similar to thoseproposed by the empirical methods. For tunnel inbasalts, 4-m-long rock bolts with 2-m spacing and 100-mm-thick shotcrete are proposed. For tuffites, 5-m-longrock bolts with 1-m spacing and 150-mm-thick shotcrete

Table 12Radius 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 2.68 2.50 2.05e−004 1.79e−004Tuffite 4.21 2.50 1.20e−003 2.20e−004

207Z. Gurocak et al. / Engineering Geology 91 (2007) 194–208

are proposed as support elements. After consideringsupport measures in the numerical model, not only thenumber of yielded elements but also the extent of plasticzone decreased substantially, as shown in Figs. 7 and 8.The maximum total displacement values for basalt andtuffites decreased to 1.79e−004 and 2.20e−004 mm,respectively, as shown in Table 11. For basalts andtuffites, the radius of plastic zone and the maximum totaldisplacements obtained from Phase2 FEM analysis forunsupported and supported cases are presented inTable 12.

6. Conclusions

In this study, empirical methods were used toestimate the rock mass quality and support elementsfor basalts and tuffites in the diversion tunnel at theBoztepe dam site. Based on the information collected inthe field and laboratory, the RMR and Q classificationsystems were used to characterize the rock masses.These classification systems were also employed toestimate the support requirements for the diversiontunnel. The Hoek–Brown parameters and supportmeasure recommendations from the empirical resultswere used as input in the numerical analyses.

According to the results obtained from the empirical,theoretical and numerical analysis, there were somestability problems for basalts. The empirical methodsrecommend the utilization of rock bolts and shotcrete assupport elements for basalts. The results of theoreticaland numerical method show that basalts are expected tohave some deformations. Numerical modeling was usedto evaluate the performance of the recommendedsupport system. However, the results from the finiteelement methods are similar to the results from theempirical methods. When the recommended supportsystems were considered, the displacements werereduced significantly in the numerical analysis.

The empirical approach indicated that substantialsupport was necessary for tuffites, and both theoreticaland numerical approaches agreed concerning theimportant stability problems. However, after consider-ing the support elements, the numerical analysis showedthat there was a considerable decrease in both the

number of yielded elements and the size of plastic zonearound the tunnel.

The results obtained from the empirical, theoreticaland numerical approaches were fairly comparable.However, the validity of the proposed support systemsshould be checked by comparing the results obtained bya combination of empirical, theoretical and numericalmethods with the measurements that will be carried outduring construction.

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