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.
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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.
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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−100Þ=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−RMRÞ
(17)
Ramamurthy
(2004)
Emass ¼ Ei exp−0:0035½250ð1−0:3logQÞ
(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.
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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
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(1), 185–216.
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rock masses for the design of tunnel support. Rock Mech. 4,
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Bieniawski, Z.T., 1974. Geomechanics classification of rock masses
and its application in tunneling. Proceedings of the Third
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Bieniawski, Z.T., 1978. Determining rock mass deformability:
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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
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Gurocak, Z., 1999. The investigation of the geomechanical properties
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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
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