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ORIGINAL PAPER
Elasto-plastic Behavior of Raghadan Tunnel Based on RMRand Hoek–Brown Classifications
Faisal I. Shalabi Æ Husam A. Al-Qablan ÆOmar H. Al-Hattamleh
Received: 28 August 2007 / Accepted: 11 May 2008 / Published online: 31 May 2008
� Springer Science+Business Media B.V. 2008
Abstract Lining contact pressure and ground defor-
mation of Raghadan transportation tunnel (Amman,
Jordan) were investigated. The tunnel is 1.1 km in
length and 13.5 m in diameter. This study was
intended to integrate useful relations among the
widely used rock classification system (RMR: rock
mass rating), Hoek–Brown classification, and lining-
ground interaction. The materials encountered along
the tunnel alignment were limestone, dolomatic
limestone, marly limestone, dolomite, and sillicified
limestone. The ground conditions along the tunnel
alignment including bedding planes, joint sets and
joint conditions, rock quality, water flow, and rock
strength were evaluated based on the drilled bore-
holes and rock exposures. Elasto-plastic finite
element analyses were conducted to study the effect
of rock mass conditions and tunnel face advance on
the behavior of lining-ground interaction. The results
of the analyses showed that lining contact pressure
decreases linearly with the increase in RMR value.
Also the results showed that tunnel lining contact
pressure and crown inward displacement decreases
with the increase in the unsupported distance (dis-
tance between tunnel face and the end of the erected
lining). Ground displacement above the tunnel crown
was found to be increases in an increasing rate with
the decrease in the depth above the crown. This
displacement was also found to be affected by the
RMR value and the unsupported distance.
Keywords Tunnels � Contact pressure �Deformations � FE analyses � RMR �Elasto-plastic
1 Introduction
Ground deformation and lining-ground contact pres-
sure are very important issues that should be
considered in tunnel design. Many empirical
approaches were developed to evaluate qualitatively
or quantitatively the ground conditions and behavior
of tunneling. Empirical approaches are widely used
and considered the basis of most tunnels design.
These approaches include the prediction of rock loads
and span of final tunnel lining based on the observed
loads on initial timber lining (Bierbaumer 1913), the
prediction of rock loads on the roof of tunnel
(Terzaghi 1946), rock load recommendations (Stini
1950), Relation between rock quality designation
(RQD) and rock loads (Deere et al. 1969), rock loads
based on dropping rock wedges at the crown
(Cording and Deere 1972; Cording and Mahar
1974), rock structure rating (RSR) (Wickham et al.
1974), rock quality index for determination rock mass
characteristics and tunnel support, Q-index (Barton
F. I. Shalabi (&) � H. A. Al-Qablan � O. H. Al-Hattamleh
Department of Civil Engineering, Hashemite University,
13115 Zarqa, Jordan
e-mail: [email protected]
123
Geotech Geol Eng (2009) 27:237–248
DOI 10.1007/s10706-008-9225-0
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et al. 1974, 1980), and geomechanics classification of
jointed rock masses and RMR (Bieniawski 1976,
1989). Shalabi (2004) used most of the above
empirical approaches to analyze and predict the
primary support of Raghadan tunnel.
Besides the empirical approaches evaluation,
many researchers attempted to evaluate ground
deformation and stresses around the underground
opening using analytical solutions (Morgan 1961;
Hoeg 1968; Dar and Bates 1974; Kulhawy 1974;
Mohraz et al. 1975; Wood 1975; Einstein and
Schwartz 1979; Pan and Hudson 1988; Penzien
and Wu 1998; Carranza-Torres and Fairhurst 1999;
Augarde and Burd 2001; Shalabi and Cording
2005).
In this study, ground deformation and contact
pressure of Raghadan tunnel were also investigated
using an analytical approach. The tunnel is 1.1 km in
length and 13.5 m in diameter. In this work, the
geological and geotechnical information about the
ground around and along the tunnel alignment were
used to evaluate Hoek–Brown strength parameters.
These parameters were then used to predict the
Mohr–Coulomb plastic model parameters, which was
used in the analysis. Useful practical relations among
the widely used rock classification system (RMR
system) and lining ground interaction are intended to
be developed in this study. The analyses were
performed using ABAQUS (2005) finite element
software using axisymmetric finite element model
with simulation of ground excavation and lining
erection.
2 Geology Along the Tunnel Alignment
The geology of the area along the tunnel alignment
belongs to the cretaceous period. The upper creta-
ceous forms two major groups namely, Balqa group
(group B) and Ajlun group (group A). Balqa group is
mainly consists of sillicified limestone, chalk marl,
and phosphorite, while Ajlun group is mainly consists
of massive limestone, nodular limestone, and echin-
odal limestone. The investigations showed that the
proposed tunnel will pass through sillicified lime-
stone (B2 formation), massive limestone (A2
formation), and echinodal limestone (A5/6 forma-
tion). Here, B2, A7, and A5/6 are local names for the
rock formations.
3 Prediction of Rock Mass Engineering Properties
Based on RMR Classification and Hoek–Brown
Strength Model
Engineering investigation program was carried out in
order to evaluate the rock conditions along and
around the tunnel. The program included drilling
boreholes, laboratory testing, and field mapping of
rock discontinuities. Figure 1 shows the tunnel loca-
tion, rock formations, and the locations of the drilled
boreholes.
3.1 Laboratory Tests
Laboratory tests were performed on rock samples
extracted from the boreholes. The tests included the
unconfined compressive strength and rock density.
Figure 2 shows the results of the unconfined com-
pressive strength of the tested rock samples for the
three rock formations.
3.2 Rock Quality and Discontinuity Mapping
RQD was evaluated based on the extracted borehole
samples for the three rock formations. For A5/6
formation (marlstone and limestone rocks) the RQD
values were between 20 and 40, while A7 formation
(massive limestone rock) the RQD values were
between 20 and 50, and for B2 formation (sillicified
limestone rock), the RQD value was around 20.
Rock mass discontinuities were also mapped along
the tunnel alignment throughout many rock expo-
sures. Discontinuities mapping include: orientation,
spacing, material filling, roughness, continuity (per-
sistence), aperture (opening) were determined
according to ISRM (1981). Tables 1 and 2 provide
Fig. 1 Rock formations along the alignment of Raghadan
tunnel with boreholes location (Shalabi 2004)
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summaries for the encountered bedding planes, joint
sets, and the properties of these discontinuities.
3.3 RMR Classification and Hoek–Brown
Strength Parameters of Jointed Rock Masses
Based on the above information, the rock mass along
the tunnel alignment was classified according to
Bieniawski 1989. The values of RMR according to
this classification depend on rock intact strength,
RQD, discontinuities conditions, spacing, orientation,
and groundwater inflow. Table 3 shows the range of
the RMR values for the three rock formations.
The values of RMR were used to evaluate the
modulus of elasticity of rock mass, Er, (Serafim and
Pereira 1983) and the geological strength index (GSI)
(Hoek et al. 1995) according to the following rela-
tions, respectively:
Er ¼ 10RMR�10
40ð Þ ð1ÞGSI ¼ RMR89 � 5 ð2Þ
It should be mentioned here that in Eq. 2 the GSI
values for the three rock formations were evaluated
by setting a value of 15 for ground water rating and a
value of zero for the adjustment of joint orientation
for the RMR89 rating (Hoek et al. 1995).
Table 1 Bedding planes along the alignment of Raghadan
tunnel (Shalabi 2004)
Exposure location Rock formation Bedding planes
Dip
(slope angle)
Slope
direction
E1 B2 – –
E2 B2 10–15 N-S
E3 B2 20–30 N15E
E4 B2 20–30 N50W
E5 B2 35 N10E
E6 B2 70–80 N45W
E7 A7 40–45 N20E
E8 A7 20–25 N-S
E9 A7 20–30 N20E
E10 B2 20–25 N-S
E11 A7 30 N-S
E12 A7 – –
E13 A7 10–20 N70W
E14 A7 15 S60W
A5/6 formation
Samples2 3 4 5 6 7 8 9 10
Unc
onfin
ed c
ompr
essi
ve s
tren
tgh,
KP
a
0
10000
20000
30000
40000
50000
60000
70000
80000
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 320
10000
20000
30000
40000
50000
60000
70000
80000
A7 formation
Unc
onfin
ed c
ompr
essi
ve s
tren
tgh,
KP
a
Samples
0
10000
20000
30000
40000
50000
60000
70000
80000
Unc
onfin
ed c
ompr
essi
ve s
tren
tgh,
KP
a
Samples
B2 formation
2 3 4 5 6 7 8
(a)
(b)
(c)
Fig. 2 Unconfined compressive strength of the tested rock
samples for the three rock formations
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Table 4 shows the range Er, and GSI for the three
rock formations based on the range of RMR89 values.
GSI values were also evaluated based on rock
classification provided by Marinos and Hoek
(2000), as shown in Table 4. In this table it can be
seen that the range of GSI values obtained from using
Eq. 2 is close to the GSI range obtained from using
Marinos and Hoek (2000) classification.
Hoek–Brown modified strength criterion for
jointed rock masses was used in the analysis. The
formula is given by the following equation (Hoek
et al. 1995):
Table 2 Joint sets and their properties along the alignment of Raghadan tunnel (Shalabi 2004)
Exposure
location
Rock
formation
Sets of joints
Set #1 Set #2 Set #3
Dip
angle
Strike Spacing
(m)
Aperture
(mm)
Dip
angle
Strike Spacing
(m)
Aperture
(mm)
Dip
angle
Strike Spacing
(m)
Aperture
(mm)
E1 B2 90 S50E 1.5–2 1–3 90 S10W 0.2–0.5 1–3 – –
E2 B2 90 S40E 0.4–1 1–3 70–
90
S60W 0.2–1.5 1–3 – –
E3 B2 70 S40E 0.4–0.5 1–3 – – – – – –
E4 B2 70 S40E 0.4–0.5 1–3 – – – – – –
E5 B2 – – – – – – – – – –
E6 B2 – – – – – – – – – –
E7 A7 – – – – – – – – – –
E8 A7 50 S20E 1.5–2 1–3 90 N-S 0.3–0.5 2–5
(calcite)
90 S30E 0.1–0.3 1–3
E9 A7 – – – – – – – – – –
E10 B2 90 N80E 0.3–0.5 1–3 – – – – – –
E11 A7 – – – – – – – – – –
E12 A7 75 S50W 0.2–0.3 1–3 90 N20W 0.5–1 1–3 – –
E13 A7 – – – – – – – – – –
E14 A7 90 S50W 0.1–0.3 1–3 – – – – – –
Table 3 Range of RMR values of rock masses for Raghadan tunnel
Parameter A5/6 formation A7 formation B2 formation
Value Rating Value Rating Value Rating
Uniaxial compressive strength (MPa) 0.5–21 0–2 10–50 2–4 25–76 2–7
RQD 20–40 3–8 10–50 3–10 20 3
Discontinuity spacing 0.2 m–2 m 8–15 0.2 m–2 m 8–15 0.4 m–2 m 10–15
Discontinuity condition
Persistence 1–3 m 4 1–3 m 4 1–3 m 4
Aperture 1–3 mm 2 1–3 mm 2 1–3 mm 2
Roughness Slightly rough 3 Slightly rough 3 Slightly rough 3
Filling (gouge) 2 2 2
Weathering Mod. weathered 3 Mod. weathered 3 Mod. weathered 3
Groundwater Damp-wet 9 Damp-wet 9 Dry-damp 12
Discontinuity orientation Fair -5 Fair -5 Fair -5
Range of RMR 29–43 31–47 36–46
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r01 ¼ r03 þ rc mbr03rcþ s
� �a
ð3Þ
The parameter mb in Eq. 3 depends on the intact
rock parameter, mi and the GSI value, as shown in the
following equation:
mb
mi¼ exp
GSI� 100
28
� �ð4Þ
The parameters a and s depends on the GSI value
as follows:
s ¼ expGSI� 100
9
� �; a ¼ 0:5; GSI� 25 ð5Þ
s ¼ 0; a ¼ 0:65� GSI
200GSI\25 ð6Þ
where rc, unconfined compressive strength of the
intact rock; r03 and r01 are the minor and major
principal stresses, respectively.
To be used in the finite element analysis, Hoek–
Brown strength parameters were converted to Mohr–
Coulomb strength parameters (cohesion intercept, c, and
angle of internal friction, /) according to the solution
that was established by Balmer (1952) which converts
the principal stresses (r01 and r03) to normal (rn) and
shear (s) stresses according to the following equations:
rn ¼ r3 þr1 � r3
or1=or3 þ 1ð7Þ
s ¼ ðrn � r3Þffiffiffiffiffiffiffiffiffiffiffiffiffiffior1=r3
pð8Þ
According to Hoek et al. (1995), the ratio between
the change in the major principal stress and the
change in the minor principal stress depends on the
value of GSI. For GSI [ 25 this ratio is given by:
or1
or3
¼ 1þ mbrc
2ðr1 � r3Þð9Þ
and for GSI \ 25, the ratio will be:
or1
or3
¼ 1þ amab
r3
rc
� �a�1
ð10Þ
Mohr–Coulomb strength parameters were
obtained for the three rock formations (A5/6, A7,
and B2) for the ranges of GSI and RMR provided in
Table 4 using both Balmer (1952) solution and
Marinos and Hoek (2000) approach, as shown in
Table 5. As can be seen in this table, the two
approaches show slight difference in the evaluated
Table 4 Ranges of Er and GSI for the three rock formations
A5/6 formation A7 formation B2 formation
Range of RMR for GSI calculation by setting: 40–54 42–58 44–54
Ground water rating = 15
Discontinuity orientation rating = 0
Range of rock mass modulus of elasticity, Er (MPa) 2985–6683 3350–8414 4467–7943
Range of GSI (Eq. 2) 35–49 37–53 39–49
Range of GSI (Marinos and Hoek (2000)) 33–47 35–50 36–46
Bold values indicate calculated RMR and the Used RMR for GSI calculations
Table 5 Mohr–Coulomb strength parameters and plastic properties for the three rock formations
A5/6 formation A7 formation B2 formation
Mohr–Coulomb strength parameters
based on Balmer (1952). Inside
parenthesis, c and u are based
on Marinos and Hoek (2000)
c (MPa) 0.008–0.47 (0.015–0.78) 0.16–1.25 (0.3–2.0) 0.43–1.69 (0.78–2.8)
u (degree) 31–34.5 (27–31) 31.1–35 (28–32) 32–34.3 (30–32)
Plastic properties Yield stress, ry (kPa) Corresponding yield strain, ep
340 0.0040
1100 0.0050
13000 0.0065
50000 0.0075
Geotech Geol Eng (2009) 27:237–248 241
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A5/6 (case1)
σn (MPa)0.00 0.04 0.08 0.12 0.16 0.20
τ (M
Pa)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
A5/6 (case 2)
σn (MPa)
σn (MPa) σn (MPa)
σn (MPa) σn (MPa)
0 1 2 3 4 5 6 7 8 9 10
τ (M
Pa)
0
1
2
3
4
5
6
7
8
9
10
A 7 (case 3)
0 1 2 3 4 5
τ (M
Pa)
0
1
2
3
4
5
A 7 (case 4)
0 4 8 12 16 20
τ (M
Pa)
0
4
8
12
16
20
B2 (case 5)
0 1 2 3 4 5 6 7 8 9 10
τ (M
Pa)
0
1
2
3
4
5
6
7
8
9
10
B2 (case 6)
0 3 6 9 12 15 18 21 24 27 30
τ (M
Pa)
0
3
6
9
12
15
18
21
24
27
30
Fig. 3 Relationship between shear strength and normal stress for the three rock formations and for the range of the obtained GSI
value
242 Geotech Geol Eng (2009) 27:237–248
123
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values of shear strength parameters. Table 5 also
shows the plastic properties of the three rock
formations. The plastic properties (yield stress and
yield strain) were obtained from the results of the
stress–strain compression tests performed on differ-
ent rock samples. The relations between the shear
strength and normal stress for the three rock forma-
tions are shown in Fig. 3.
4 Loading Conditions and Excavation Sequences
of the Finite Element Analysis
The tunnel analyses including lining deformation,
contact pressure on the concrete lining, and defor-
mation at different locations above the crown were
performed using ABAQUS finite element software.
Figure 4 shows the finite element mesh with the
applied load and boundary conditions. Axisymmet-
ric condition was considered in the analysis. The
ground excavation was simulated step by step by
deactivation of the model elements within the
tunnel radius, R. The concrete lining was intro-
duced by activating the lining elements. For each
step of excavation and lining erection, elasto-plastic
deformation was considered for the material around
the tunnel opining. An excavation length of 52 m
(4.3 tunnel diameter) was considered in the analysis
in order to investigate the deformation and contact
pressure at a distance not affected by the tunnel
face disturbance. In this analysis, three cases were
considered. In case 1, lining erection was intro-
duced directly after excavation (unsupported
distance, d = 0), while in case 2, the lining was
introduced with unsupported distance equal to one
third tunnel radius (d = R/3), and finally, in case 3,
the lining was introduced with unsupported distance
equal to tunnel radius (d = R). Figure 5 shows
tunnel lining, unsupported distance, d, and points of
observation.
5 Results of the Finite Element Analysis
5.1 Lining-Ground Contact Pressure
Figures 6 and 7 show the contact pressure on the
liner along the tunnel axis at different tunnel faces
for RMR values equal to 31 and 47, respectively. In
these figures it can be seen that as the excavation
Fig. 4 Axisymmetric finite element mesh and boundary conditions of Raghadan tunnel
Geotech Geol Eng (2009) 27:237–248 243
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proceeds, the contact pressure on the lining
increases. These figures also show that the contact
pressure curves are steep near the tunnel face and
there is almost no change in the contact pressure at
a distance equal to two tunnel diameters (2D)
behind the tunnel face. These results are consistent
with the results obtained by Shalabi (2005) on the
time-dependent behavior of tunneling in squeezing
ground. The results of analysis also show that as the
RMR value increases, the lining contact pressure
decreases. For RMR value of 31 and tunnel face at a
distance of 8R (Fig. 6a), the contact pressure is
about 25% of the overburden pressure (Po), while
for RMR value of 47 (Fig. 7a) the contact pressure
is about 13% of the overburden pressure.
Considering the effect of unsupported distance, d
(d is the distance between the advanced tunnel face
and the end of the erected concrete lining, as shown
in Fig. 5). Figure 8 shows that as the unsupported
distance increases, the lining contact pressure
decreases. For RMR value of 47, Fig. 8b shows that
the contact pressure dropped from 13% of the
overburden pressure for unsupported distance equal
to zero (d = 0) to about 3% of the overburden
pressure for unsupported distance equal to tunnel
radius, while for RMR value of 31 (Fig. 8a), the
contact pressure dropped from 25% of the overburden
for d = 0–5% of the overburden for d = R (consid-
erable reduction in contact pressure as RMR
decreases). This behavior is attributed to the stress
relief as the tunnel face advances.
Figure 9 shows the relationship between lining
contact pressure and RMR value for different unsup-
ported distances and for the three rock formations. In
this figure it can be seen that as the unsupported
distance increases, the contact pressure decreases in a
decreasing rate with the RMR value. When extended,
the three curves are expected to have a contact
pressure of 1% of the overburden (very small percent)
at RMR value equal to about 61 (According to
Bieniawski (1989) a value of RMR of 61 indicates
good quality rock mass).
Fig. 5 Tunnel lining and the different points of measurements
at different sections
Normalized distance along tunnel axis, z/R0
Con
tact
pre
ssur
e on
the
liner
to th
e bu
rden
pres
sure
, P/P
o (%
) C
onta
ct p
ress
ure
on th
e lin
er to
the
burd
enpr
essu
re, P
/Po
(%)
0
10
20
30
40
50
Tunnel face at 8R6R4R2RR
z
R Tunnel face
Excavation
Unsupported distance, d = 0m1: Face at R2: Face at 2R3: Face at 4R4: Face at 6R5: Face at 8R
1 2
3 4 5
RMR = 31 A7 formation
0
10
20
30
40
50
Normalized distance along tunnel axis, z/R
1: Face at R2: Face at 2R3: Face at 4R4: Face at 6R5: Face at 8R
Unsupported distance, d = 6m
RMR = 31 A7 formation
54321
z
R Tunnel face
Excavation
(a)
(b)
1 2 3 4 5 6 7 8 9 10
0 2 4 6 8 10
Fig. 6 Lining contact pressure along tunnel axis at different
tunnel faces and unsupported distances. RMR = 31
244 Geotech Geol Eng (2009) 27:237–248
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Figure 10 shows the relationship between lining
contact pressure and compressibility ratio, c. Accord-
ing to Peck et al. (1972), the compressibility ratio is a
measure of the extensional relative stiffness between
the tunnel lining and the ground and it is given by the
equation:
C ¼ Emð1� v2l ÞR
Eltð1þ vmÞð1� 2vmÞð11Þ
where Em and vm are the ground elastic modulus and
Poisson’s ratio, respectively, and El, vl, t, and R are the
lining elastic modulus, Poison’s ratio, thickness, and
radius, respectively. Figure 10 shows the same trend as
of Fig. 9. As the compressibility ratio increases, lining
contact pressure decreases. The rate of contact pressure
decrease with the increase in c increases as the unsup-
ported distance d decreases. It should be mentioned here
that the unsupported distance d also depends on the local
ground conditions, method of excavation, and rate of
tunnel advance. This distance may vary from section to
section along the tunnel alignment.
5.2 Tunnel Crown Deformation
Crown deformation of the tunnel was also analyzed in
this work. Figure 11 shows the normalized crown inward
displacement with the normalized distance along the
Normalized distance along tunnel axis, z/R0 1 2 3 4 5 6 7 8 9 10
0
10
20
30
40
50
Tunnel face at 8R6R4R2RR
z
R Tunnel face
Excavation
Unsupported distance, d = 0 m
1: Face at R2: Face at 2R3: Face at 4R4: Face at 6R5: Face at 8R
1 2 3 4 5
RMR = 47 A7 formation
0 2 4 6 8 100
10
20
30
40
50
Unsupported distance, d =6m
RMR = 47 A7 formation
1: Face at R2: Face at 2R3: Face at 4R4: Face at 6R5: Face at 8R
z
R Tunnel face
Excavation
Normalized distance along tunnel axis, z/R
Con
tact
pre
ssur
e on
the
liner
to th
e bu
rden
pres
sure
, P/P
o (%
) C
onta
ct p
ress
ure
on th
e lin
er to
the
burd
enpr
essu
re, P
/Po
(%)
5432
(a)
(b)
Fig. 7 Lining contact pressure along tunnel axis at different
tunnel faces and unsupported distances. RMR = 47
Normalized distance along tunnel axis, z/R0 1 2 3 4 5 6 7 8 9 10
Con
tact
pre
ssur
e on
the
liner
to th
e bu
rden
pres
sure
, P/P
o (%
) C
onta
ct p
ress
ure
on th
e lin
er to
the
burd
enpr
essu
re, P
/Po
(%)
0
10
20
30
40
50
z
R Tunnel face
Excavation
1
2
3
RMR = 47Tunnel face at 8R
A7 formation
0 1 2 3 4 5 6 7 8 90
10
20
30
40
50
Normalized distance along tunnel axis, z/R
A7 formationRMR = 31Tunnel face at 8R
1: Unsupported dist. = 0
2: Unsupported dist. = R/3
3: Unsupported dist. = R
1: Unsupported dist. = 0
2: Unsupported dist. = R/3
3: Unsupported dist. = R
1
2
3
z
R Tunnel face
Excavation
(a)
(b)
Fig. 8 Lining contact pressure along tunnel axis at different
unsupported distances and RMR values. Tunnel face at
distance of 8R
Geotech Geol Eng (2009) 27:237–248 245
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tunnel axis for different unsupported distances. In this
figure, Ua is the crown displacement, R is the tunnel
radius, Po is the overburden pressure, and Er is the
modulus of elasticity of the rock mass. In this figure it can
be seen that the crown displacement started to level off at
a distance of about 1.5D (D: tunnel diameter) behind the
tunnel face. This result is consistent with the results
obtained by Ranken et al. (1987), Panet and Guenot
(1982) using the elastic analysis. Also this figure shows
that as the unsupported lining distance increases, the
crown displacement increases. This behavior is mainly
due to the delay in lining erection.
Figure 12 shows the normalized crown inward
displacement with the RMR value for different
unsupported distance. In this figure it can be seen
that for the same RMR value, the normalized crown
inward displacement increases as the unsupported
distance increases. Also, this figure shows that the
normalized inward displacement increases linearly
with the increases in RMR value. This result should
not make any confusion since the rock modulus, Er
on the Y-axis is also depends of the RMR value.
5.3 Radial Ground Movement Above the Crown
Ground deformation above the tunnel crown was also
investigated. Figure 13 shows the normalized inward
displacement at Z/R = 4.5 section (Sect. 2 on Fig. 5).
Here, the tunnel face was at a distance of 8R. In this
figure, Z is the horizontal distance from the tunnel inlet,
U1 is the radial ground movement, and X is the depth in
RMR
Con
tact
pre
ssur
e on
the
liner
to th
e bu
rden
pr
essu
re, P
/Po
(%)
020 25 30 35 40 45 50 55 60 65 70
5
10
15
20
25
30
35
40
45
50
Tunnel face at 8Rz
R Tunnel face
Excavation
Extended curves
Unsupported dist. = 0Unsupported dist. = R/3Unsupported dist. = R
Fig. 9 Lining contact pressure vs. RMR value for different
unsupported distances. Tunnel face at a distance of 8R
Compressibility ratio, C1.0
Con
tact
pre
ssur
e on
the
liner
to th
e bu
rden
pr
essu
re, P
/Po
(%)
0
5
10
15
20
25
30
35
40
45
50
Tunnel face at 8Rz
R Tunnel face
Excavation Unsupported dist. = 0Unsupported dist. = R/3
Unsupported dist. = R
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Fig. 10 Lining contact pressure vs. compressibility ratio for
different unsupported distances. Tunnel face at a distance of 8R
Normalized distance along tunnel axis, z/R0 1 2 3 4 5 6 7 8 9 10
Nor
mal
ized
cro
wn
inw
ard
disp
lace
men
t, (U
a/R
)/(P
o/E
r)
-5
-4
-3
-2
-1
0
Tunnel face at 8R
z
R Tunnel face
Excavation
1
2
3
1 Unsupported dist. = 0
3 Unsupported dist. = R
2 Unsupported dist. = R/3
RMR = 47
0 1 2 3 4 5 6 7 8 9 10-5
-4
-3
-2
-1
0
Tunnel face at 8R
RMR = 31 12
3
Normalized distance along tunnel axis, z/R
Nor
mal
ized
cro
wn
inw
ard
disp
lace
men
t, (U
a/R
)/(P
o/E
r)
z
R Tunnel face
Excavation
A7 formation
A7 formation(a)
(b)
Fig. 11 Normalized crown inward displacement along the
tunnel for different unsupported distances and RMR values.
Tunnel face at a distance of 8R
246 Geotech Geol Eng (2009) 27:237–248
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the ground measured from the tunnel crown. In this
figure it can be seen that the normalized inward
displacement increases in an increasing rate as the
normalized depth (X/R) decreases. Also, this figure
shows that as the unsupported distance increases, the
normalized inward displacement increases. In this figure
the RMR value has more effect on the radial displace-
ment as the unsupported distance deceases. It should also
be noticed in Fig. 13 that the modulus of elasticity or
rock mass, Er depends on the RMR value.
6 Conclusions
Lining deformation and contact pressure of Raghadan
Tunnel (Jordan) were analyzed analytically based on
RMR and Hoek–Brown classifications using Mohr–
Coulomb plastic model. The results of the analysis
led to the following conclusions:
1. Lining contact pressure increases with tunnel face
advance. The zone of influence extends about two
tunnel diameters (2D) behind the tunnel face.
2. Lining contact pressure decreases linearly with
the increase in RMR value. The contact pressure
is close to zero for RMR values greater than 61.
3. Lining contact pressure decreases linearly with
the increase in the compressibility ratio, C.
4. As the unsupported distance increases, lining
contact pressure significantly decreases, espe-
cially for low RMR values.
5. Effect of tunnel face advance on crown displace-
ment extends to about 1.5 tunnel diameters
(1.5D) behind the tunnel face.
6. Tunnel crown displacement increases with the
increase in unsupported distance. The results
were also found to be changed linearly with the
RMR value.
7. Ground displacement above the tunnel
crown increases in an increasing rate with
the decrease in the normalized depth (X/R).
The results were also found to be affected
by the RMR value and the unsupported
distance.
RMR20N
orm
aliz
ed c
row
n in
war
d di
spla
cem
ent,
(Ua/
R)/
(Po/
Er)
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
Tunnel face at 8Rz
R Tunnel face
Excavation
Unsupported dist. = 0Unsupported dist. = R/3Unsupported dist. = R
25 30 35 40 45 50 55 60 65 70
Fig. 12 Normalized crown inward displacement versus RMR
values for different unsupported distances. Tunnel face at a
distance of 8R
Normalized inward displacement, (U1/R)/(Po/Er)
-3.0-2.5-2.0-1.5-1.0-0.50.0
Nor
mal
ized
dis
tanc
e fr
om th
e cr
own,
X/R
0
1
2
3
4
5
Section-2 at Z/R =4.5
RMR = 47
Tunnel face at 8R
Unsupported dist. = R
Unsupported dist. = R/3
Unsupported dist. = 0
-3.0-2.5-2.0-1.5-1.0-0.50.00
1
2
3
4
5
Section-2 at Z/R =4.5
RMR = 31
Tunnel face at 8R
Unsupported dist. = R
Unsupported dist. = R/3
Unsupported dist. = 0
Nor
mal
ized
dis
tanc
e fr
om th
e cr
own,
X/R
Normalized inward displacement, (U1/R)/(Po/Er)
A7 formation
A7 formation(a)
(b)
Fig. 13 Ground inward displacement around the tunnel for
different unsupported distances and RMR values. Tunnel face
at a distance of 8R
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