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: fshalabi@hu.edu.jo

123

Geotech Geol Eng (2009) 27:237–248

DOI 10.1007/s10706-008-9225-0

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)

238 Geotech Geol Eng (2009) 27:237–248

123

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

Geotech Geol Eng (2009) 27:237–248 239

123

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

240 Geotech Geol Eng (2009) 27:237–248

123

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

123

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

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

123

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

123

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

123

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

123

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

Geotech Geol Eng (2009) 27:237–248 247

123

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