583_24650 Emperical Method

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Empirical and numerical analyses of support requirements for a

diversion tunnel at the Boztepe dam site, eastern Turkey

Zulfu Gurocaka ,, Pranshoo Solanki b , Musharraf M. Zaman c

aDepartment of Geology, Firat University, Elazig 23119, Turkey

b School of Civil Engineering and Environmental Science, University of Oklahoma, Norman, OK 73019-1024, USAc 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 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 convergenceconfinement 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 twomethods 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: Convergenceconfinement method; Finite element method; Geological strength index; HoekBrown failure criterion; Rock mass

quality; 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 engineers

and engineering geologists due to practicality. In

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 Dieder-

ichs, 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

Engineering Geology 91 (2007) 194 208

www.elsevier.com/locate/enggeo

Corresponding author. School of Civil Engineering and Environ-

mental 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:[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
mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.enggeo.2007.01.010http://dx.doi.org/10.1016/j.enggeo.2007.01.010mailto:[email protected]:[email protected]


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observations. Likewise, analytical and numerical

approaches are dependent upon the strength parameters

of associated rock masses that are used as input

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 maximumoverburden of about 38 m for basalts and about 27 m for

Fig. 1. The location map of study area.

Fig. 2. Geological map and cross-section of Boztepe dam site.

195Z. Gurocak et al. / Engineering Geology 91 (2007) 194208


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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 labo-

ratory testing on intact rock samples. These tests include

an evaluation of uniaxial compressive strength (c),

Young's modulus (E), Poisson's ratio (), unit weight

(), internal friction angle (), and cohesion (c). The

rock mass properties of the dam site were determined by

using different rock mass classification systems.

2. Geology, field and laboratory studies

The Boztepe dam site consists of various age units

ranging from the Upper Miocene to the Quaternary.

MiddleUpper 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 mem-

bers. As seen in Fig. 2, atthe dam site, the main valley isin

tuffite with basalt forming the plateau to the east. The

tuffites are dirty white or light grey colored and well-

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 lavaswhile 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 sectionalong 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). Table 1

Engineering properties of joints and bedding surfaces and their

percentage distribution

Properties Spacing Description Percentage

Basalt Tuffite

Spacing (mm) a b20 Extremely close

spacing

5 2

2060 Very close spacing 33 16

60200 Close spacing 42 69

200600 Moderate spacing 20 10

6002000 Wide spacing 3

Persistence (m)a b1 Very low persistence 33 8

13 Low persistence 56 9

310 Medium persistence 11 34

1020 High persistence 31

N20 Very high persistence 14

Aperture (mm)a b0.1 Very tight 8 12

0.10.25 Tight 14

0.250.50 Partly open 10 2

0.502.50 Open 16 202.510 Moderately wide 48 51

N10 Wide 4 15

Roughnessa IV Rough undulating 11 5

V Smooth undulating 3 7

VI Slickensided

undulating

10

VII Rough planar 61 88

VIII Smooth planar 6

IX Slickensided planar 9

Weathering (Wc)b

1.2 Fresh/Unweathered 22

1.22 Moderately weathered 67 2

N2.0 Weathered 11 98

a

According toISRM (1981).b According toSingh and Gahrooee (1989).

196 Z. Gurocak et al. / Engineering Geology 91 (2007) 194208


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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 bySingh and Gahrooee (1989):

Wc rcJCS

; 1

where

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

JCS Strength of discontinuity surface (MPa).

JCS was calculated from the following equation:

LogJCS0:00088gR1:01; 2

where

Bulk volume weight (kN/m3), and

R Hardness value from rebounding of Schmidt

hammer.

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



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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: 14/100

Joint set 1: 80/220

Joint set 2: 87/259

Joint set 3: 77/305

The major orientations of the joint sets for basalts are

listed below:

Joint set 1: 78/192

Joint set 2: 71/3

Joint set 3: 67/287Joint set 4: 72/99

According to ISRM (1981), the joint sets in the

basalts have close to very close spacing, low persis-

tence, 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 summa-

rized 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 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 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 ofthe 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 2

Laboratory tests results of basalts and tuffites

Properties Min Max Mean Std. err.

Basalt

Uniaxial compressive strength (c, MPa) 8.72 76.46 40.64 19.67

Young's modulus (E, GPa) 1.6 96.7 30.91 47.17Poisson's ratio () 0.241 0.286 0.27 0.02316

Unit weight (, kN/m3) 23.10 28.10 25.55 1.48

Cohesion (c, MPa) 12 a

Internal friction angle (, deg) 42a

Tuffite

Uniaxial compressive strength (c, MPa) 1.97 21.20 8.21 5.72

Young's modulus (E, GPa) 0.6 10.5 2.23 2.615

Poisson's ratio () 0.17 0.22 0.20 0.02517

Unit weight (, kN/m3) 12.00 22.10 16.50 0.04

Cohesion (c, MPa) 1.80a

Internal friction angle (, deg) 33a

Std. err.: standard error.a Values obtained by using triaxial test.

Table 3

RMR89 rating for basalts and tuffites

Classification

parameters

Basalt Tuffite

Value of

parameters

Rating Value of

parameters

Rating

Uniaxial

compressive

strength (MPa)

40.64 5 8.21 2

RQD (%) 62 12 25 6

Discontinuity

spacing (cm)

160 7.3 90 6

Discontinuitycondition

Persistence (m) 13 4 310 2

Aperture (mm) 2.503.00 1 2.510 0

Roughness Rough-planar 5 Rough-planar 5

Filling Calciteb5 mm 4 calciteN5 mm 2

Weathering Moderately 3 Highly 1

Groundwater

condition

Dry 15 Dry 15

Basic RMR value 56.3 39

Rating adjustment

for joint

orientation

Very

favorable/Fair

0/5 Fair 5

RMR 56.3/51.3 34

Rock mass quality Fair rock Poor rock



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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 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 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.

QRQDJn

Jr

Ja

Jw

SRF: 3

Recently,Barton (2002)defined a new parameter, Qc,

to improve correlation among the engineering parameters:

QcQ rc100

; 4

wherec 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

and very poor rock mass, respectively (Table 4). The Qcvaluesfor basalt and tuffite are 0.42 and 0.013, respectively.

4. Estimation of rock mass properties

The rock mass properties such as HoekBrown

constants, deformation modulus (Emass) and uniaxial

compressive strength of rock mass (cmass) were

calculated by means of empirical equations in accor-

dance with the RMR89,Q,Qcand GSI.

4.1. Geological strength index (GSI) and HoekBrown

parameters

The geological strength index (GSI) was developed by

Hoek 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 HoekBrown

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 byMarinos and Hoek (2000).

TheHoek 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 equa-

tions for calculating rock mass constants (i.e., mb,sand a):

mbmi exp GSI1002814D

; 5

sexp GSI10093D

; 6

a121

6 eGSI=15e20=3

; 7

where D is a factor that depends upon the degree of

disturbance to which the rock mass is subjected to by blast

Table 4

Q rating for basalts and tuffites

Classification parameters Basalt Tuffite

Value of parameters Rating Value of parameters Rating

RQD (%) 62% 62 25% 25

Joint 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 1.5

Joint alteration number (ja) Moderately altered 6 Highly altered 8

Joint water reduction factor (jw) Dry excavation or minor inflow 1 Dry excavation or minor inflow 1

Stress reduction factor (SRF) Medium stress 1 Low stress, near surface 2.5

Q 1.03 0.156

Rock mass quality Poor rock Very poor rock

Table 5

GSI and calculated HoekBrown parameters values

Unit GSI mi constant mb constant s constant a constant

Basalt 48 25 3.903 0.0031 0.507

Tuffite 32 13 1.146 0.0005 0.520



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damage and stress relaxation tests. In this study, the value of

Dis considered zero. The calculated GSI is and the Hoek

Brown constants are listed inTable 5.

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):

rcmassrci mb4samb8smb=4sa1

21a2a ; 8

where ci is uniaxial compressive strength of the intactrock,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 6were used for determining deformation modulus

of rock masses. The calculated values of rock mass

deformation modulus are summarized in Table 7.

5. Tunnel stability and support analysis

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 deter-

mine 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

gH;

20

where is unit weight of the intact rock in MN/m3, and

H is the depth of overburden in m.

The horizontal stress was determined from the

following equation suggested bySheorey et al. (2001):

rh m1m

rvbEmassG1m

H100; 21

where =8 1 06/C (coefficient of linear thermal

expansion), G=0.024 C/m (geothermal gradient), is

the Poisson's ratio, Emass

is deformation modulus of

rock mass, MPa.

The far-field stress 0 was calculated using the

following equation:

r0rvrh1rh23

; 22

where hland h2 are horizontal stresses.

Table 6

Selected equations for estimating deformation modulus of rock mass

Emass

Author Equations Equation

number

Bieniawski(1978)

For RMRN

50,

Emass2RMR100(9)

Serafim and

Pereira

(1983)

For RMRb50,

Emass10RMR1040

(10)

Hoek and

Brown

(1997)

Emassffiffiffiffiffiffiffiffirci

100

r 10

GSI1040

(11)

Read et al.

(1999) Emass0:1 RMR

10 3 (12)

Ramamurthy

(2001)EmassEiexpRMR100=17:4 (13)

Ramamurthy

(2001)EmassEiexp0:8625 logQ2:875 (14)

Barton (2002) Emass10Q1=3c (15)

Hoek et al.

(2002) Emass

1

D

2 ffiffiffiffiffiffiffiffi

rci

100r 10

GSI1040

(16)

Ramamurthy

(2004)EmassEiexp0:00355100RMR (17)

Ramamurthy

(2004)EmassEiexp0:003525010:3logQ (18)

Hoek and

Diederichs

(2006)

EmassEi 0:02 11e6015DGSI=11

(19)

RMR=rock mass rating.

Q = rock mass quality.

Qc=rock mass quality rating or normalized Q.GSI= geological strength index.

ci= uniaxial comprehensive strength of intact rock.

Ei=Young's modulus.

D = disturbance factor.



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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.

5.1. Empirical approach

Bieniawski (1974) used RMR, width of opening W

(m), and unit weight of overburden (kN/m3) to

determine the support pressure. From the formula

below, the support pressure Proof, is found in kN/m2:

Proof 100RMR100

Wg: 23

Another approach was proposed by Barton et al.

(1974) that depends on rock mass quality, Q, and

discontinuity roughness,Jr. The roof support pressure,

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

equation:

Proof 200Jr

Q1=3: 24

The support pressure was calculated as 0.135 MPa

according to the Barton et al. (1974) approach and0.059 MPa according to theBieniawski (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 Qcriterion 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 RMR89system on the one hand, basaltsand 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 RMR89andQsystems are presented inTable 8.

5.2. Theoretical approach

In this study, a theoretical approach, called the

convergenceconfinement technique, was used for

stability analysis. This methodology has been describedbyCarranza-Torres and Fairhurst (1999)for rock masses

that satisfy the HoekBrown criterion. A cylindrical

tunnel of radiusR, subjected to a uniform far-field stress

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.

Basalt 7.6 5.68 15.57 2.16 1.77 7.49 5.68 13.77 12.92 6.91 7.96 4.72

Tuffite 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.

Table 8

Estimated support categories of basalts and tuffites

Unit Basalt Tuffite

RMR

classification

system

RMR 56.3/51.3 34

Fair rock Poor rock

Support Systematic bolts

4 m long, spaced

1.52 m in crown

and walls with

wire mesh in crown.

50100 mm in crown

and 30 mm in sides.

Systematic bolts

45 m long,

spaced 11.5 m

in crown and walls

with wire mesh.

100150 mm in

crown and 100 mm

in sides.

Qclassification

system

Q 1.03 0.156

Poor rock Very poor rock

ESR 1.6 1.6

De 3.125 3.125

Support Systematic bolting,

4 m long, spaced

1.7 m with 4050 mm

unreinforced shotcrete

4 m long bolting,

spaced 1.31.5 m

and 90120 mm

fibre reinforced

shotcrete

De Excavation span; diameter or height

m

Excavation support ratioESR

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 convergenceconfinement method

Unit 0(MPa)

Gmass(GPa)

Pi(MPa)

Picr

(MPa)

Rpl(m)

urel

(mm)

urpl

(mm)

Strain

(%)

Basalt 0.53 3.13 0.000049 0.000 0.00 0.211 0.000 0.0084

Tuffite 0.22 0.58 0.00191 0.0143 3.47 0.000 0.441 0.0176



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0, and internal pressure Pi was considered. The rock

mass, in which the tunnel is excavated, is assumed tosatisfy the HoekBrown failure criterion.

The actual critical internal pressure Picr is defined as

(Carranza-Torres and Fairhurst, 2000):

Pcri P

i s

m2b

mbrci; 25

where

s and mb HoekBrown constants,

ci uniaxial compressive strength, and

Pi scaled critical internal pressure.

The scaled critical internal pressure is evaluated from

the following equation:

P

i 1

16 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi116S0

p 2; 26

in which S0is the scaled far-field stress given by:

S0 r0mbrci

sm2b

; 27

where 0is far-field stress, and Piis the scaled internal

pressure defined by:

Pi pimbrci

sm2b

; 28

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

the inward elastic displacementurel of the tunnel wall is

given by:

uelrr0Pi

2GmassR; 29

where0is far-field stress,Piis scaled internal pressure,

Ris the tunnel radius and Gmassis 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

Table 10

Material properties of basalts and tuffites for numerical model

Property Basalt Tuffite

Value

Material type Isotropic Isotropic

Young's modulus (GPa) 7.96 1.40Poisson's ratio 0.27 0.20

Compressive strength (MPa) 10.61 1.08

mparameter 3.903 1.146

sparameter 0.0031 0.0005

Material type Plastic Plastic

Dilation parameter 0 0

mresidual 1.9515 0.573

sresidual 0.00155 0.00025

Table 11

Stresses and displacements before and after support for basalts and tuffites

Location Parameter Basalt Tuffite

Before support After support Before support After support

Right wall 1(MPa) 0.964 0.920 0.072 0.315

3(MPa) 0.052 0.136 9.80e003 0.129

x-displacement (m) 0.205 1.79e004 1.20e003 2.22e004

y-displacement (m) 1.32e003 2.37e007 1.76e005 1.09e006

Total displacement (m) 0.205e004 1.79e004 1.20e003 2.22e004

Roof 1(MPa) 0.953 0.939 0.080 0.3133(MPa) 0.057 0.128 0.011 0.131

x-displacement (m) 1.60e006 1.84e007 1.07e005 2.20e004



Left Wall 1(MPa) 0.960 0.938 0.068 0.310

3(MPa) 0.054 0.127 8.74e003 0.131




Floor 1(MPa) 0.964 0.943 0.083 0.313

3(MPa) 0.082 0.130 0.011 0.130






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expected to occur. Then the radius of the broken zone

Rplis defined by:

RplR exp2ffiffiffiffiffiffiPcri

p

ffiffiffiffiffiPi

p : 30

Hoek and Brown (1997) suggested the following

equation to evaluate the total plastic deformation urpl

for rock masses:

uplrR

2Gmass

r0Pcri

12m2

ffiffiffiffiffiffiP

i

q

S0P

i

124

35 Rpl

R

2 12m

4 S0P

i

ln RplR

2

12m

2

ffiffiffiffiffiffiP

i

q

S0P

i

2 ln Rpl

R

1

31whereRis the tunnel radius,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 Emass21 m; 32

where Emass is the deformation modulus of the rockmass.

Internal pressure Pi was assumed to be zero in this

study for unsupported tunnel cases in basalt and tuffite.

The calculated parameters of0,Gmass,Pi,Picr,Rpl,ur

el,

urpl 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

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



11/15

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 werecalculated 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 anal-

ysis were obtained from the estimated values presented

in Section 4. The HoekBrown failure criterion wasused 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

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



12/15

times the tunnel radius. A total of 3048 three-nodded-

triangular 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 inFigs. 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

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



13/15

unsupported tunnel in basalts and tuffites are 2.05e004

and 1.20e003 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 inFig. 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 100-

mm-thick shotcrete are proposed. For tuffites, 5-m-long

rock bolts with 1-m spacing and 150-mm-thick shotcrete

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



14/15

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 inFigs. 7 and 8.

The maximum total displacement values for basalt and

tuffites decreased to 1.79e004 and 2.20e004 mm,

respectively, as shown in Table 11. For basalts and

tuffites, the radius of plastic zone and the maximum total

displacements obtained from Phase

2

FEM analysis forunsupported and supported cases are presented in

Table 12.

6. Conclusions

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 toestimate the support requirements for the diversion

tunnel. The HoekBrown 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 usedto 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 consider-

ing the support elements, the numerical analysis showed

that there was a considerable decrease in both the

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.

References

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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 2.68 2.50 2.05e004 1.79e004

Tuffite 4.21 2.50 1.20e003 2.20e004



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