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Technical Note

An empirical method for design of grouted bolts in rock tunnels based on the

Geological Strength Index (GSI)

Reza R. Osgoui

a,

⁎, Erdal Ünal

b

a

GEODATA SpA., Corso Duca degli Abruzzi, 48/E, 10129, Turin, Italy

b

Mining Engineering Department, Middle East Technical University, 06531/Ankara, Turkey

abstractarticle info

Article history:

Received 14 April 2008

Received in revised form 4 May 2009

Accepted 16 May 2009

Available online 27 May 2009

Keywords:

Empirical design method

Grouted bolt

Bolt density

Geological Strength Index (GSI)

Malatya railroad tunnel

The procedure presented in this paper has been developed for the design of grouted rock bolts in rock

tunnels during preliminary design stage. The proposed approach provides a step-by-step procedure to set up

a series of practical guidelines for optimum pattern of rock bolting in a variety of rock mass qualities. For this

purpose, a new formula for the estimation of the rock load (support pressure) is recommended. Due to its

wide-spread acceptance in the ﬁeld of rock engineering, the Geological Strength Index (GSI) is adopted in

support pressure equation. For poor and very poor rock mass where the GSI< 27, the use of Modiﬁed-GSI is,

instead, recommended. The supporting action is assumed to be provided by rock bolts carrying a total load

deﬁned by the rock load height. The mechanism of bolting is assumed to rely on roof arch forming and

suspension principle. Integrated with support pressure function, the bolt density parameter is modiﬁed in

order to provide an optimized bolt pattern for any shape of tunnel. The modiﬁed bolt density can also be used

in analysis of a reinforced tunnel in terms of Ground Reaction Curve (GRC) in such a way as to evaluate the

reinforced rock mass and the tunnel convergence. By doing so, the effectiveness of the bolting pattern is well

evaluated. The proposed approach based on GSI is believed to overcome constrains and limitations of existing

empirical bolt design methods based on RMR or Q-system, which are doubtful in poor rock mass usage. The

applicability of the proposed method is illustrated by the stability analysis and bolt design of a rail-road

tunnel in Turkey.

© 2009 Elsevier B.V. All rights reserved.

1. Introduction

Currently, rock reinforcement technique (rock-bolting) is used in

almost all types of underground structures due to its performance,

cost-effectiveness, and safety. The structures reinforced by bolts are, in

general, very reliable and long lasting. The main objective of rock bolts

should be to assist the rock mass in supporting itself by building a

ground arch and by increasing the inherent strength of the rock mass.

One of such type of bolts is the grouted bolts that develop load as the

rock mass deforms. Small displacements are normally sufﬁcient to

mobilize axial bolt tension by shear stress transmission from the rock

mass to the bolt surface. Grouted bolts have been successfully applied

in a wide range of rock mass qualities especially in poor rock mass and

foundtobeoftenmoreeconomicalandmoreeffectivethan

mechanical rock bolts. Owing to their grouting effect on improvement

of rock mass, grouted rock-bolts have been widely used in tunnelling

under difﬁcult ground condition. They are also widely used in mining

for the stabilization of roadways, intersections, and permanent

tunnels in preliminary design stage. Simplicity of installation,

versatility and lower cost of rebars are the further beneﬁts of grouted

bolts in comparison to their alternative counterparts.

Broadly speaking, the empirical design methods based on rock

mass classiﬁcation systems (Bieniawski,1973; Barton et al.,1974; Ünal,

1983; Bieniawski, 1989; Ünal, 1992; Grimstad and Barton, 1993;

Palmström, 1996, 2000; Mark, 2000), the methods dependent on

laboratory and ﬁeld tests (Bawden et al., 1992; Hyett et al.,1996; Kilic

et al., 2003; Karanam and Pasyapu, 2005), the performance assess-

ment methods (Freeman, 1978; Ward et al., 1983; Kaiser et al., 1992;

Signer, 2000; Mark et al., 2000), the analytical methods based on rock-

support interaction theory and convergence-conﬁnement approach

(Hoek and Brown, 1980; Aydan, 1989; Stille et al., 1989; Oreste and

Peila, 1996; Labiouse,1996;Li and Stillborg,1999; Carranza-Torres and

Fairhurst, 2000; Oreste, 2003; Cai et al., 2004a,b; Wong et al., 2006;

Guan et al., 2007) or based on equivalent material concept (Grasso

et al., 1989; Indraratna and Kaiser, 1990; Osgoui, 2007; Osgoui and

Oreste, 2007), and the numerical techniques (Brady and Loring, 1988;

Duan, 1991; Swoboda and Marence, 1991; Chen et al., 2004)are the

methods utilized in designing an effective rock-bolt system.

Generally, analytical and numerical methods are not directly used

for dimensioning bolts in preliminary stage of design. However, they

are used to evaluate the effectiveness of bolt system in order to modify

the bolt pattern if necessary. The laboratory and ﬁeld tests, on the

Engineering Geology 107 (2009) 154–166

⁎Corresponding author. Tel.: +39 011581 0628.

E-mail address: ros@geodata.it (R.R. Osgoui).

0013-7952/$ –see front matter © 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.enggeo.2009.05.003

Contents lists available at ScienceDirect

Engineering Geology

journal homepage: www.elsevier.com/locate/enggeo

Author's personal copy

other hand, are adopted to verify the performance of the bolting

system.

Empirical methods, based on rock mass classiﬁcations, such as

those mentioned earlier are the only ways to dimension the bolt

system. Although a great number of such methods have been

developed so far, they suffer from many limitations. For instance,

their bolting patterns are qualitative, rather than quantitative and

they are independent of calculations. They cannot correlate the

necessary bolt length and thickness of failure zone around the tunnel.

They are less ﬂexible in terms of change in rock mass properties and

ﬁeld stress. Not all empirical methods focus on the grouted bolts in

wide range of rock mass qualities. Furthermore, in weak rock mass, the

available empirical methods do not provide a sufﬁciently sensitive

guide for bolt design (Indraratna and Kaiser,1990). It is not only due to

the uncertainties in frictional behaviour of such bolts but also their

effect on rock mass improvement has not intuitively understood.

As the bolting pattern suggested by RMR (Rock Mass Rating) and

Q-system depends only on the rock mass quality, some signiﬁcant

critics have recently arisen. Palmström and Broch (2006) and Pells

and Bertuzzi (2008) have agreed that the “well-known Q-support

chart gives only indication of the support to be applied, and it should

be tempered by sound and practical engineering judgement”.

Furthermore, the results of many experiences by Pells and Bertuzzi

(2008) put forward this statement: “the classiﬁcation systems should

not solely be used as the primary tool for the design of primary

support”.

The proposed approach is intended to alleviate such limitations

and constrains. Integrated with existing elasto-plastic solutions, the

proposed approach makes it possible to set up several applicable

bolting patterns for any rock mass condition and tunnel size. With

modiﬁcation of the bolt density parameter that exhibits the frictional

behaviour of bolt and its link with the proposed support pressure

function, a new approach in depicting the bolting pattern for any

shape of tunnel is achieved. The key base of the proposed approach

falls in the estimation of the support pressure by using the Geological

Strength Index (GSI) or the Modiﬁed-GSI (Osgoui, 2007) because of its

successful acceptance in characterization of a broad range of rock

mass qualities. In addition, the proposed support pressure function is

applicable in squeezing ground condition and anisotropic ﬁeld stress.

Consequently, the rockload which bolts should carry is more realistic.

The bolt density parameter obtained through the support pressure

function can also be used in evaluating the reinforcement degree of

the rock mass around the tunnel by means of GRC (Indraratna and

Kaiser, 1990; Osgoui, 2007; Osgoui and Oreste, 2007). This reinforce-

ment effect of the grouted bolts helps in reducing ultimate support

pressure.

2. Deﬁnition of support pressure (rock load) based on the

Geological Strength Index (GSI)

One of the most important steps in dimensioning the bolt system

of a tunnel is that of determining the support pressure that bolts

should carry since miscalculations of support pressure may lead to a

failure in bolt system.

In general, the load that acts on a support system is referred to as the

support pressure. It denotes the rock pressure that results from the rock-

load heightabove the tunnel excavation. In this case, boltsare expected

to provide the support pressure as a resistance force required to carry

the weight of the failed rock above the tunnel. The support pressure

function implicitly depends on the parameters indicated below:

P≈fGSI;D;σcr ;De;γ;Cs;Sq

ð1Þ

where GSI is the Geological Strength Index that deﬁnes the quality of

the rock mass; Dthe disturbance factor indicating the method of

excavation; σ

cr

the residual compressive strength of the rock in the

broken zone around the tunnel; D

e

the equivalent diameter of the

excavation; γthe unit weight of rock mass; C

s

the correction factor for

the horizontal to vertical ﬁeld stress ratio (k), and S

q

the correction

factor for the squeezing ground condition.

Similar to its previous counterpart, developed by Ünal (1983, 1992,

1996), the main advantage of the newly proposed approach is that the

quality of the rock mass is considered as the GSI. Due to its accepted

applicability in a broad range of rock mass qualities, the GSI was

chosen to signify the rock mass quality in the proposed support

pressure formula. This makes it possible to estimate the support

pressure (support load) for tunnels in various rock mass qualities

provided that the GSI has initially been determined. The Modiﬁed-GSI

has to be used for very poor or poor rock masses where the GSI< 27,

instead of the GSI, for support pressure estimation (Osgoui and Ünal,

2005). It is, therefore, suggested that the new approach be applied toa

wide spectrum of rock masses, with qualities ranging from very good

to very poor. The steps that were followed to deﬁne the support load

function were:

I. The original support load function previously developed by

Ünal (1983,1992) is considered to be the main basis for the new

equation because it uses Bieniawski's RMR system (1973),

which quantitatively evaluates the quality of the rock mass. The

original Ünal load equation is (Ünal 1983, 1992):

P=100 −RMR

100 γBð2Þ

where Bis the longest span of the opening.

II. The new support pressure function is deﬁned in such a way that

it does not contradict Ünal's equation (1983, 1992), whose

applicability has been widely accepted in the ﬁeld of mining

and tunnelling.

III. The importance of the two parameters (i.e. method of

excavation and residual strength of the rock), which are

directly related to the damage extension in the rock mass

around the tunnel, was inspired by the rock mass deformation

equation introduced by Hoek et al. (2002). This deformation

modulus is a modiﬁed version which previously proposed by

Seraﬁm and Pereira (1983) for σ

ci

<100 MPa:

Em=1−D

2

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

σci

100

r10GSI −10

40 ð3Þ

The above equation can be re-written as:

Em

10GSI−10

40

=1−D

2

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

σci

100

ror EmHoek:ðÞ

EmSerafim & Pereira

ðÞ

=1−D

2

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

σci

100

r

ð4Þ

Looking at Eqs. (3) and (4), it can be found that the right hand

of the equality is a reduction factor for the estimation of the

deformation modulus in weak rock masses. This reduction

factor can play a signiﬁcant role in support pressure function as

a sensible way in considering the effect of the rock mass

disturbance and intact rock strength.

IV. The deﬁnitions of squeezing ground conditions and their

correction factors were adopted through descriptions originally

introduced by Singh et al. (1992, 1997) and Hoek and Marinos

(2000).

V. The effect of the anisotropy in ﬁeld stress was taken into

account similar to the deﬁnition given by Ünal (1992).

VI. Since the effect of the horizontal to the vertical ﬁeld stress (k)

was studied through a 2-D numerical plane strain analysis

(Osgoui, 2006), so the proposed support function is valid only

155R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166

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for cases where the horizontal stresses are equal in each

direction.

VII. The proposed support pressure function applies for σ

ci

<

100 MPa. The maximum value of σ

ci

that should be used in

the proposed equation must be 100 MPa even if σ

ci

>100 MPa.

σ

ci

is the uniaxial compressive strength of the intact rock.

Considering the original Ünal load Eq. (2), substituting the GSI for

RMR, and taking into consideration the reduction factor for rock mass

quality through disturbance and strength factors (Eq. (4)), the new

equation to estimate the support pressure was proposed in such a way

as to keep its original perception:

P=100 −1−D

2

ﬃﬃﬃﬃﬃﬃ

σcr

100

qGSI

hi

100 CsSqγDeð5Þ

where σ

cr

=S

r

·σ

ci

,0<S

r

<1, S

r

=post-peak strength reduction factor,

characterizing the brittleness of the rock material as explained later

on.

It should be noted that in the aforementioned equations, D

e

is the

equivalent diameter of the excavation and it is used for any tunnel

shape. It can easily be obtained from:

De=ﬃﬃﬃﬃﬃﬃ

4A

π

rð6Þ

where Ais the cross-section area of the excavation.

Taking into account Ünal's rock-load height concept (Ünal, 1983,

1992), the support pressure function can be dependent on the

parameters speciﬁed in the following expressions:

P≈fh

t;γ;Cs;Sq

ð7Þ

where h

t

is the rock-load height. It is deﬁned as the height of the

potential instability zone, above the tunnel crown, which will

eventually fall if not supported properly.

Considering support pressure functions (1) and (7) and Eq. (5), the

rock-load height, instead, can be expressed as:

ht=100 −1−D

2

ﬃﬃﬃﬃﬃﬃ

σcr

100

qGSI

hi

100 CsSqDeð8Þ

The most common form of the support pressure expression can be

written as below when S

r

=1:

P=100 −1−D

2

ﬃﬃﬃﬃﬃﬃ

σcr

100

qGSI

hi

100 CsSqγDe=γhtð9Þ

2.1. Parameters used in support pressure

2.1.1. Geological Strength Index (GSI) estimation

In view of the fact that the Geological Strength Index (GSI) plays

the most dominant role in determining the support pressure, it is of

paramount importance that the GSI of a rock mass be estimated

accurately. GSI accounts for a large percentage of the support pressure

value since it directly reﬂects the quality of the rock mass around the

tunnel. Hence, a distinction to estimate GSI for either fair to good

quality rock mass or poor to very poor rockmass must be applied. The

boundary that initiates the threshold of poor rock mass is deﬁned as

RMR=30. For fair to good quality rock mass if RMR> 30 then

GSI=RMR.Consequently, either qualitative GSI charts (Hoek and

Brown, 1997; Hoek, 1999; Hoek and Marinos, 2000; Marinos et al.,

2005) or quantitative GSI charts (Sönmez and Ulusay, 1999, 2002; Cai

et al., 2004c) can readily be used.

Due to obvious deﬁciency of GSI in characterizing poor and very

poor rock mass where RMR falls below 30 (Hoek, 1994), the Modiﬁed-

GSI should, instead, be directly or indirectly determined (Osgoui,

2007). The original and the existing GSI charts found in literature are

not capable of characterizing poor and very poor rock mass as denoted

by N/A in the relevant parts. By adding measurable quantitative input

in N/A parts of existing GSI charts, they will be enhanced in

characterizing poor rock mass while maintaining its overall simplicity.

Further, the new Modiﬁed-GSI chart is considered as a supplementary

means for its counterparts (Fig. 1). The modiﬁed-GSI chart is valid for

poor and very poor rock mass with GSI ranging between 6 and 27. In

the case of GSI greater than 27, the existing GSI charts mentioned

earlier should be used.

To set up the Modiﬁed-GSI chart (left side of Fig. 1), two indicators

of poor rock mass; namely, Broken Structure Domain (BSTR) and Joint

Condition Index (I

JC

) are deﬁned. The latter is adopted and modiﬁed

from the Modiﬁed-RMR (Özkan, 1995; Ulusay et al.,1995; Ünal, 1996)

in order to use in Modiﬁed-GSI. For this purpose, a block in the matrix

of 2×2 of GSI chart is selected in terms of two axes signifying the rock

mass blockiness (interlocking) and joint surface conditions.

As shown in the left side of Fig. 1, the vertical axis of the matrix

presents quantitatively the degree of jointing in terms of BSTR.

Generally speaking, broken drill-core zones recovered from a very

weak rock mass having a length greater than 25 cm are deﬁned as

BSTR. Various types of BSTR domains can be categorized into 5 groups

based on their size and composition (Osgoui and Ünal, 2005; Osgoui,

2007). Furthermore, the Structure Rating (SR) suggested by Sönmez

and Ulusay (1999, 2002) was integrated with Modiﬁed-GSI to deﬁne

the blockiness of rock mass. The original intervals of SR were adjusted

to be compatible with BSTR types in Modiﬁed-GSI.

The horizontal axis, on the other hand, is assigned for the joint

condition rating. In order to determine the Joint Condition Index (I

JC

),

BSTR type, Intact Core Recovery (ICR), and ﬁlling and weathering

conditions should be known as given in right hand of Fig. 1. ICR is

deﬁned as the total length of the cylindrical core pieces greater than

2 cm divided by the total length of the structural region or drill-run.

The ICR for poor and very poor rock masses is considered to be less

than 25 to satisfy the Modiﬁed-GSI requirements. For joint condition

rating, the upper part of modiﬁed-GSI chart is divided into 2

categories; namely, poor and very poor. For ICR< 25%, the total rating

of joint condition index varies between 0 and 16. A simple way for

determining joint condition index “I

JC

”is presented in the right side of

Fig. 1.

In the absence of the necessary parameters for GSI determination,

the following exponential equation provides a correlation between

the Rock Mass Rating (RMR) and the Geological Strength Index (GSI)

for a poor rock mass (Osgoui and Ünal, 2005):

GSI = 6e0:05RMR if RMR <30 ð10Þ

This correlation has proved to be compatible with those ascer-

tained from many case studies and calibrated with the Modiﬁed-GSI

chart.

2.1.2. The effect of excavation method

The tunnelling method has a signiﬁcant inﬂuence on the support

pressure. Conventional excavation methods (Drill & Blast) cause

damage to the rock mass whereas controlled blasting and mechanized

tunnelling with Tunnel Boring Machine, TBM, leave the rock mass

undisturbed. Singh et al. (1992, 1997) declared that the support

pressure could be decreased to 20% for such cases. Moreover, the

effects of rock interlocking and stress change (relaxation) as a result of

the ground unloading cause a disturbance in the rock mass.

The value of RMR used in the original support pressure equation

(Ünal 1983, 1992) included the adjustment for the effects of the

blasting damage, change in in-situ stress, and major faults and

156 R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166

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Fig. 1. Modiﬁed-GSI chart suggested to be used in proposed approach (GSI< 27: poor to very poor rock mass).

157R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166

Author's personal copy

fractures (Bieniawski 1984, 1989). Since GSI is substituted for RMR in

proposed approach, those factors should, similarly, be incorporated

with the proposed equation. The disturbance factor (D) originally

recommended by Hoek et al. (2002) is taken into account to adjust the

value of GSI. This factor ranges from D=0 for undisturbed rock

masses, such as those excavated by a tunnel boring machine, to D=1

for extremely disturbed rock masses. This factor also allows the

disruption of the interlocking of the individual rock pieces within rock

masses as a result of the discontinuity pattern (Marinos et al., 2005).

For the same properties of rock mass and tunnel, the support pressure

increases as the disturbance factor increases from 0 to 1. Indications

for choosing the disturbance factor are given in Table 1.

2.1.3. The effect of residual strength of intact rock

Since the broken zone extension around an underground opening

depends on the strength parameters of the rock, it is suggested that

the compressive strength of the rock material as an inﬂuential

parameter in estimating the thickness of the broken zone (rock-load

height) and support pressure be taken into account. In the majority of

sophisticated closed-form solutions for tunnels, the residual strength

parameters are allowed for in calculations in accordance with the post

failure behaviour of the rock. It is also substantiated thatthe extension

of the broken zone relies on the residual value of the intact rock

strength (Hoek and Brown, 1980; Brown et al., 1983; Indraratna and

Kaiser, 1990; Carranza-Torres, 2004).

Hence, the effect of the compressive strength of a rock material

must be included in the form of the residual value because it loses its

initial value due to stress relief or an increase in the strain. A stress

reduction scale should, therefore, be considered as:

σcr =Sr·σci ð11Þ

where S

r

refers to the strength loss parameter that quantiﬁes the jump

in strength from the intact state to the residual condition. The

parameter S

r

characterizes the brittleness of the rock material: ductile,

softening, or brittle. By deﬁnition, S

r

will fall within the range

0<S

r

<1, where S

r

=1 implies no loss of strength and the rock

material is ductile, or perfectly plastic. In contrast, if S

r

tends to 0, the

rock is brittle (elastic–brittle plastic) with the minimum possible

value for the residual strength as highlighted in Fig. 2.Asaﬁrst guess

in proposed support pressure equation (Eq. (5)), S

r

=1 is taken into

account for the poor and very poor rock masses with GSI< 27 because

their post-failure behaviour is perfectly-plastic (Hoek and Brown,

1997 ). For average and good quality rock masses, on the other hand,

the exact value of the residual strength for the intact rock can be

determined from stress–strain response of rock in laboratory tests, so

the value of S

r

can readily be obtained (Aydan et al., 1996; Cundall

et al., 2003).

2.1.4. The effect of squeezing ground condition

In view of the fact that almost all deep tunnelling works in poor

rock masses undergo squeezing ground, it is of paramount importance

to take this effect into consideration in precisely estimating the

support pressure. The squeezing degree is expressed in terms of

tunnel convergence or closure (Indraratna and Kaiser, 1990; Singh

et al., 1992, 1997), strength factor (Bhasin and Grimstad, 1996; Hoek

and Marinos, 2000), or critical strain concept (Hoek and Marinos,

2000; Lunardi, 2000). Since tunnel convergence (closure) is an

important indicator of tunnel stability, the squeezing behaviour has

been evaluated in terms of tunnel convergence in the current study.

The squeezing correction factor used in the proposed approach were

adopted and modiﬁed from the results of Singh et al. (1992,1997) and

Hoek and Marinos (2000), as outlined in Table 2.

2.1.5. The effect of anisotropy in ﬁeld stress

Numerical analysis of the broken zone around the tunnel implied

that the extension of failure heights above tunnels and consequently

the support pressure depend upon the magnitude of the stress ratio

(k) For arch-shaped and rectangular tunnels, the extent of the failure

zone decreases as the value of kchanges from 0.3 to 0.5; conversely,

the height of the failure zone starts to increase again as the value of k

approaches 2.5 (Osgoui, 2006).

The failure height (obtained from numerical methods) and rock-

load height (determined by the proposed formula) ratio yields a value

called the stress correction factor (C

s

). This correction value should be

applied when using Eqs. (5), (8), and (9). Therefore, a multiplier (C

s

)

is required to correct the stress ratio. For the reason of reliability, the

minimum value of C

s

is suggested as 1.0 for k=0.5. Fig. 3 aims at

choosing the stress correction factor for proposed approach.

3. Bolt density parameter

The dimensionless bolt density parameter, ﬁrstly deﬁned by

Indraratna and Kaiser (1990), can be written as follows to adopt any

tunnel shape:

β=πdλ

SLθ=πdλre

SLST

ð12Þ

where dis the bolt diameter; λthe friction factor for bolt–grout

interface that relates the mobilized shear stress acting on the grouted

bolt to the stress acting normal to the bolt; r

e

the equivalent radius of

the tunnel opening; S

T

the transversal bolt spacing around the tunnel;

S

L

the longitudinal bolt spacing along the tunnel axis; θthe angle

between tow adjacent bolts (i.e. S

T

=r

e

×θ) in an axi-symmetrical

problem and considering identical bolt with equal spacing along the

tunnel axis.

Table 1

Modiﬁed guideline for estimating disturbance factor (D), which initially suggested by

Hoek et al. (2002).

Description of rock mass Suggested

value for D

Excellent quality controlled blasting or excavation by Tunnel Boring

Machine results in minimal disturbance to the conﬁned rock mass

surrounding a tunnel.

D=0

Mechanical or hand excavation in poor quality rock masses (no blasting)

results in minimal disturbance to the surrounding rock mass.

D=0

Usual blasting that causes local damages. D=0.5

In mechanical excavation where squeezing problems result in signiﬁcant

ﬂoor heave unless a proper invert is placed.

D=0.5

Very poor quality blasting in tunnel results in severe damages, extending 2

or 3 m, in the surrounding rock mass.

D=0.8

Very poor quality blasting along with a intensive squeezing ground

condition in tunnel —unexpectedly heavy blasting in caverns leading to

signiﬁcant cracks propagation on roof and walls.

D=1

Fig. 2. Different post-peak strength models of rocks.

158 R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166

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The bolt density parameter reﬂects the relative density of bolts

with respect to the tunnel perimeter and takes into consideration the

shear stresses on the bolt surface, which oppose the rock mass

displacements near the tunnel wall.

The value of βvaries between 0.05 and 0.20 for most cases. For

tunnels excavated in very poor rock mass analyzed by Indraratna and

Kaiser (1990) very high values for β(in excess of 0.4) were reached by

very intensive bolting patterns. The friction factor λ, being analogous

to the coefﬁcient of friction, relates the mean mobilized shear stress to

the stress applied normal to the bolt surface. Indraratna and Kaiser

(1990) suggested that the magnitude of λfor smooth rebars falls in

the range tan (φ

g

/2) < λ<tan (2φ

g

/3) and for shaped-rebars

approaches tanϕ

g

, depending on the degree of adhesion (bond

strength) at the bolt–grout interface.

The bolt density parameter has been used to introduce the

equivalent strength parameters in terms of either Mohr–Coulomb

(c⁎,ϕ⁎) or Hoek–Brown (s⁎,m⁎,σ

ci

⁎) failure criteria (Grasso et al.,

1989; Indraratna and Kaiser, 1990; Osgoui, 2007; Osgoui and Oreste,

2007). The equivalent strength parameters, marked with ⁎, belong to

the reinforced plastic zone around the tunnel. Consequently, the

concept of equivalent plastic zone has been introduced to describe the

extent of yielding reinforced with grouted bolts.

As grouted bolts effectively improve the apparent strength of the

rock mass, the behaviour of the improved ground around a reinforced

tunnel can ideally be represented by Ground Reaction Curve (GRC),

using elasto-plastic solutions found in the literature, for example:

Brown et al. (1983),Panet (1993),Ducan Fama (1993),Labiouse

(1996),Carranza-Torres and Fairhurst (2000),Carranza-Torres

(2004),Osgoui (2007), and Osgoui and Oreste (2007).

4. Bolt design

Since during initial stage of the bolt design, the pattern (bolt

spacing) is not known, it is not advisable to determine the bolt density

parameter through guessed pattern. Instead, the combination of the

bolt density parameter and support load function is supposed to

provide a practical way to obtain more realistic value for the bolt

density parameter.

The supporting action is assumed to be provided by rock bolts

carrying a total support load deﬁned by the rock- load height (Eq. (8)).

Hence, if the effective area of each bolt is deﬁned as the area of

longitudinal and transversal spacing (see Fig. 4), the following

equation relates the acting support load (Eq. (5)) to the bolt capacity

(C

b

) in a condition of equilibrium:

Cb=P·S

T·S

Lð13Þ

Deﬁning a factor of safety (FOS), which is deﬁned as the resistant

force to the imposing force, Eq. (13) can be re-written as:

FOS = Cb

P·S

T·S

L

ð14Þ

A value for FOS is suggested only for mining applications as

suggested by Bieniawski (1984). By substituting Eq. (14) into Eq. (12)

and equating FOS=1(limiting equilibrium state), the correlation

between the rock bolt density (β) and the support load (P) will be:

β=Pπdλre

Cb

ð15Þ

The main application of the Eq. (15) is that of determining the bolt

density parameter that considers the support pressure. Simulta-

neously, the already determined bolt density parameter can then be

used as the ﬁrst estimate of βin analysis of the reinforced tunnel in

terms of the Ground Reaction Curve (GRC) so as to evaluate the

reinforced rock mass and the tunnel convergence. By doing so, the

effectiveness of the bolting pattern is consequently evaluated. For this

purpose, the equivalent strength parameters of the reinforced rock

mass around the tunnel can be determined in terms of either Mohr–

Coulomb or Hoek–Brown failure criteria.

Fig. 3. Suggested values for stress correction factor (Cs) used in proposed formula

(hf: failure height by numerical method, ht; rock-load height by empirical approach).

Table 2

Suggested values for squeezing ground condition correction factors (S

q

) used in empirical approach (adopted and modiﬁed from Hoek and Marinos, 2000; Singh et al., 1997).

Strains %(tunnel closure or

convergence/tunnel

diameter) ⁎100

Rock mass strength/

in-situ stress (σ

cm

/P

o

)

Comments Suggested correction factor

(S

q

)for squeezing ground

condition

<1% No squeezing >0.5 Mostly (>1.0) The strength of the rock mass exceeds the stress level at the face and mostly around the cavity.

The ground behaviour is elastic. Instabilities are associated with rock block and rock wedge

failures.

1.0

1–2.5% Minor squeezing 0.3–0.5 The magnitude of stress at the face approaches the strength of the rock mass. The behaviour is

elastic-plastic. The deformability gradient at the face is low. On the periphery of the cavity the

stresses exceed the strength of the rock mass, SR< 1, resulting in the formation of a plastic zone

around the excavation.

1.5

2.5–5% Severe squeezing 0.2–0.3 The magnitude of stress at the face exceeds the strength of the rock mass. Although face is in

plastic zone, the deformation gradient is low for typical advance rate; therefore, immediate

collapse of the face is prevented. The plastic state at the face in conjunction with the

development of the plastic zone around the tunnel results in severe overall stability.

0.8

5–10% Very severe squeezing 0.15–0.2 At tunnel face and periphery, the stress-to-strength state results in high deformation gradient

and critical conditions for stability.

1.6

>10% Extreme squeezing <0.15 Immediate collapse (very short stand-up-time) of the face during excavation. This behaviour is

associated with non-cohesive soils and very poor rock mass rock masses such as these found in

sheared zones.

1.8

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For Mohr–Coulomb material (Indraratna and Kaiser, 1990):

σ1=C0

⁎+kp

⁎σ3ð16aÞ

kp

⁎=kp1+βðÞ ð16bÞ

C0

⁎=C01+βðÞ ð16cÞ

kp= tan245 + ϕ

2

=1 + sinϕ

1−sinϕð16dÞ

C0=2ctan 45 + ϕ

2

=2ccosϕ

1−sinϕð16eÞ

For Hoek–Brown material (Osgoui, 2007; Osgoui and Oreste, 2007):

σ1=σ3+σci

⁎mb

⁎σ3

σci

⁎+s⁎

!

a

ð17aÞ

mb

⁎=1+βðÞ·m

bð17bÞ

s⁎=1+βðÞ·s ð17cÞ

σci

⁎=1+βðÞ·σci ð17dÞ

where σ

1

and σ

3

are the maximum and the minimum principal

stresses; C

0

the uniaxial compressive strength of rock mass; ϕthe

friction angle of rock mass, cthe cohesion of rock mass, m

b

,s,athe

strength constants of rock mass, and σ

ci

the uniaxial compressive

strength of the intact rock. The superscript ⁎stands for the material

with properties equivalent to those of a reinforced rock mass.

Substituting the equivalent strength parameters (Eqs. (16) and

(17)) for the strength parameters of the original rock mass in elasto-

plastic solution makes it possible to produce the GRC of a reinforced

rock mass as illustrated in Fig. 5.

Furthermore, the advantage of using the Eq. (15) is attributed to

the fact that the ﬁrst approximate of βcan easily be obtained through

a real characterization of rock mass because two signiﬁcant indicators

of rock mass characterization have been incorporated, i.e. the support

load and GSI or Modiﬁed-GSI.

For an equal-spaced bolting pattern, the bolts spacing is calculated

by Eq. (18) which is derived from Eqs. (13) and (15):

Ss=ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

πdλre

β

sð18Þ

It is interesting, at this point, to note that the inﬂuence of bolt–

ground interaction, a very important design parameter, was included

in the proposed method. The friction factor, λ, integrated in bolt

density parameter is a characteristic parameter for the bolt–ground

interaction. Based on the results of the experimental tests (Indraratna

and Kaiser, 1990) and of the numerical analyses (Osgoui, 2007), the

value of λ=0.6 provides more realistic result for shaped-rebars.

The variation of the bolt density parameter with the support

pressure for a tunnel with the span of 5 m reinforced with the

Fig. 4. Bolting pattern (transversal and longitudinal) for a circular tunnel.

Fig. 5. Typical Ground Reaction Curve (GRC) in presence of rock reinforcement. Key:

P:ﬁctitious support pressure; u

r

: radial displacement of the tunnel wall.

160 R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166

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different types of grouted rock-bolts (MAI-bolts, Atlas Copco, 2004)is

represented in Fig. 6, indicating that with increasing support load;

more severe bolt density is required to satisfy the minimum stability

condition of the tunnel.

Fig. 7 illustrates the correlation of the bolt density parameter βand

support load for a tunnel of 2.5 m diameter which is excavated in

relatively poor to very poor rock mass (GSI< 40). For the different

range of support loads provided at GSI< 40, the variations of bolt

density βchange between 0.10 and 0.25 depending on the types of

applied grouted bolts.

With reference to Fig. 7, it can be inferred that the appropriate

choice of bolt density parameter in design, regardless of grouted bolt

types, can lead to the same results for different support pressure

magnitudes. To illustrate, for a support pressure of 0.296 MPa

associated with Modiﬁed-GSI=23, the primary stability of the tunnel

can be achieved by installation of arbitrary pattern of grouted bolts of

25 mm, 32 mm, and 51 mm in diameters corresponding to bolt

densities of 0.23, 0.16, and 0.11, respectively. It should be noted that

the usage of the thicker and longer grouted bolts having higher yield

capacity is preferably suggested in poor rock masses.

Since tunnel convergence is the main indicator of tunnelstability,the

bolting performance is best evaluated in terms of its effect of the tunnel

convergence. This technique has plentifully addressed in literature

(Indraratna and Kaiser,1990; Oreste, 2003; Osgoui and Oreste, 2007).

4.1. Bolt length

Although many empirical approaches have been suggested, the

only appropriate criterion for bolt length is to know the thickness of

the plastic zone around the tunnel using existing elasto-plastic

solutions. To have a successful bolting pattern, the anchor length of

the grouted bolt should exceed the thickness of the plastic

zone, taking into account the radius of reinforced plastic zone in

presence of bolts (r

pe

⁎) and the radius of the tunnel (r

e

) as shown in

Fig. 8. In this way, the systematic bolts around the tunnel perform

properly, particularly in reducing the convergence of the tunnel.

Substituting the equivalent strength parameters (Eqs. (16) and

(17)) for the strength parameters of the original rock mass in elasto-

plastic solution makes it possible to determine the radius of reinforced

plastic zone.

Based on results of numerous elasto-plastic analyses carried out by

Oreste (2003) and Osgoui (2007), a simple criterion that deﬁnes the

grouted bolt length (L

b

) has been recommended as:

rpe

⁎<re+a·L

b

ðÞ;where a=0:50:75 ð19Þ

where r

pe

⁎is the reinforced plastic zone radius. In fact, this criterion

provides the prevention of the plastic zone radius further than the

anchor length of the bolt.

5. Comparison with alternative empirical design methods

The RMR system of Bieniawski (1973, 1989) has been acknowl-

edged to be applicable to fully grouted rock bolts in all type of rock

Fig. 6. Variation of the bolt density parameter with support pressure (rock load) for

different types of grouted bolts in terms of their yield capacity and diameter.

Fig. 7. Correlation between the bolt density parameterand support pressure for a tunnel

of 2.5 m radius excavated in relatively poor to very poor rock mass (GSI< 40) and

undergoing a very high squeezing, σh

σv=1:5.

Fig. 8. The extension of reinforced plastic zone with respect to bolt length in a

systematic bolt pattern around a circular tunnel.

161R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166

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masses. The design tables and recommendations proposed by

Bieniawski are intended for tunnels in the order of 10 m width,

excavated by the drill and blast method at depths of less than 1000 m

and reinforced by 20 mm diameter grouted bolts. Supplemental

support by shotcrete, wire mesh and steel sets are also suggested for

poorer ground. Conversely, in not all types of rock mass qualities, the

use of the grouted bolts has been recommended in Q-system (Barton

et al., 1974; Grimstad and Barton, 1993; Barton, 2002). Most recently,

Palmström and Broch (2006) have also pointed out that “the

suggested support systems by Q-systemwork best in a limited domain

between 0.1 and 40 and outside this range, supplementary methods

and calculations should be applied”.

With the help of the proposed method, it is possible to set up

several informative tables, like that of Bieniawski (1973, 1989) and

Barton et al. (1974), for any rock mass condition and tunnel size

provided that the rock mass quality is accurately deﬁned and the bolt

density parameter and the strength parameters of reinforced rock

mass are estimated accurately. For this purpose, the proposed

methodology can be applied as shown in the ﬂowchart of Fig. 9.An

example of such informative tables that recommends the bolt

conﬁgurations is represented in Table 3.

It should be noted that only a change in bolt length for

displacement control in the poor rock mass is not enough. For

instance, a bolt density parameter (β) more than doubles is needed as

the spacing is decreased from 1.5 m to 1.0 m when the quality of rock

mass diminishes from fair to poor. Hence, a further reduction of the

bolt spacing for the poorest rock class would provide a sufﬁciently

high magnitude for βto curtail displacements more effectively than

by increasing the bolt length. This is supported by Laubscher (1977)

who proposed a bolt spacing less than 0.75 m for poor ground at

RMR<30.

Since RMR or Q-system may not provide a sufﬁciently sensitive

guide to properly design the grouted bolts in relatively poor to very

poor rock mass (for rock classes RMR< 40) as also reported by

Indraratna and Kaiser (1990), the proposed alternative design method

provides a sound basis for effective bolt design in such rock masses as

indicated in Table 3.

6. Application of the proposed empirical approach: a case study

from Turkey

The 537 m long Malatya railroad tunnel being 5 m wide, situated in

the South-Eastern part of Turkey, was excavated in 1930 through a toe

of a paleo-landslide material. This sheared zone of rock-mass around

the tunnel consists of metavolcanics, schist, fractured limestone

blocks, antigorite and radiolarite in patches. The matrix material

consists of clay and schist with low swelling potential. Limestone

blocks are heavily jointed and highly fractured and weathered. There

are also voids within the rock mass (Osgoui and Ünal, 2005). Ever

since 1930, this horseshoe shape tunnel has struggled with severe

Fig. 9. Computational steps of the proposed methodology for design of grouted bolt.

Table 3

Recommended grouted bolt densities for a reinforced tunnel of 2.5 m radius for different rock classes (ﬁeld stress= 15 MPa, grouted bolt diameter=32 mm), key: the use of bolt

couplings for installation of long bolts in small diameter tunnel must be applied.

GSI Deﬁnition L

b

(m) S

T

and S

L

(m) squared

pattern assumed

β/λβat λ=0.6 Possible yielding

around the tunnel

81–100 Very good No support required 0.0 No yielding

61–80 Good 2 to 3 2.0–2.5 0.06–0.04 0.038–0.024 Minimal

41–60 Fair 3 to 5 1.5–2.0 0.11–0.06 0.067–0.038 Minimal–major

31–40 Relatively poor 5 to 6 1.0–1.25 0.25–0.11 0.151–0.067 Major

21–30 Poor ≥6 1.0 0.25 0.151 Major–excessive

<20 Very poor ≥6 0.8 0.39 0.236 Excessive

Fig. 10. Huge collapse as e result of remarkable amount of convergence in squeezing

ground condition in Malatya Railroad Tunnel.

162 R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166

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stability problems. These problems are associated with the existence

of a very poor rock mass around the tunnel, underground water or

seepage pressure, and considerable amount of convergence (squeez-

ing phenomenon). A large amount of deformation developing through

many years and leading to misalignment of the tunnel was observed.

This excessive deformation is mainly attributed to the squeezing

Table 4

Parameters used in calculating Modiﬁed-GSI and support pressure.

Calculation of Modiﬁed-GSI (Fig. 1) Estimation of the support pressure

Prevailing BSTR type= 2 Completely loss of blockiness Rock mass unit weight (γ) 0.025 MN/m

3

Intact core recovery (ICR) < 25% Disturbance factor (d) 0.5 (Table 1), usual blasting with local damage

Joint condition index (I

JC

)=7 ICR <25%, bs =2, completely

weathered W=2, without ﬁlling

Correction factor for squeezing ground

condition (S

q

)

1.8 ( Table 2), extreme degree of squeezing, considering

σcm

Po=0:101

Modiﬁed-GSI=13–15 Very poor rock mass Correction factor for stress ﬁeld (C

s

) 1.4 (Fig. 3), best assumption for relatively shallow tunnel

in very poor rock mass is k=σh

σv=1:0

σ

cr

=5 MPa σ

ci

=5 MPa, S

r

=1(Eq. (11)), for perfectly plastic material

that should be used for very poor rock mass.

Fig. 11. Systematic bolt pattern around Malatya Railroad Tunnel.

163R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166

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ground condition in which the rock stress exceeds its strength in the

passage of time.

As for squeezing ground condition, the in-situ stress was assumed

to equal to product of the depth below surface and the unit weight of

the rock mass. Considering that the vertical in-situ stress and the rock

mass strength were 1.54 MPa and 0.156 MPa, the rock mass strength to

in-situ stress ratio is 0.101. Hence, even from this criterion, a huge

amount of convergence would have been anticipated. In 2002, a

collapse occurred inside the tunnel followed by a failure in support

system. This phenomenon was ascribed, to a great extent, to the

severe squeezing ground condition along with remarkable amount of

uncontrolled convergence as shown in Fig. 10.

Following a comprehensive geological and geomechanical inves-

tigation, the overall Modiﬁed-GSI of rock mass was approximately

calculated 13–15 as, in detail, outlined in Table 4.

Having determined the Modiﬁed-GSI, the expected support load

was estimated 0.31 MPa using Eq. (5). The value of parameters used in

estimating the support pressure is given in Table 4.

The primary support system prior to rehabilitation of the Malatya

Tunnel was comprised of steel-sets, concrete lining, and ﬁnal bricking.

In some parts of tunnel withstood a severe squeezing condition, the

support system failed. In order to re-design the support system, the

use of grouted bolts was recommended as an active primary support

element to control the convergence, followed by a convergence

measurement program. The ﬁnal lining was comprised of the

combination of the steel-sets and concrete lining to guarantee the

long term stability of the tunnel.

In order to understand the short term behaviour of the tunnel and

to evaluate its stability before rock bolts applications, a series of

convergence measurements were carried out. Atotal of 15 monitoring

stations were set up inside the tunnel, 11 of which were installed in

the deformed section and 4 of which were set up in the non-deformed

part. The period of convergence monitoring of the tunnel was around

100 days. A maximum horizontal displacement of 8.78 mm was

recorded in 3 stations inside the deformed part of the tunnel,

indicating that there were still horizontal movements.

For poor rock mass surrounding the Malatya tunnel, MAI-bolts

(Atlas Copco, 2004), which are self-driving full column cement-

grouted bolts, were preferred to be the most suitable because drill

holes usually close before the bolt has been installed, and the injection

operation associated with rock-bolting make the ground improved in

terms of engineering parameters. Therefore,it was expected that with

the use of systematically grouted bolts the extent of the yielding and

convergence decreased. The MAI-bolts, like ordinary grouted bolts,

develop load as the rock mass deforms. Relatively small displacements

are normally sufﬁcient to mobilize axial bolt tension by shear stress

transmission from the rock to the bolt surface (Indraratna and Kaiser,

1990).

For rock reinforcement design, the squeezed-section of the tunnel

that should be supported was divided into three groups namely; A1,

A2, and B. Using MAI-bolts with diameter of 32 mm and yield capacity

of 280 kN, the bolt density (Eq. (15)) was obtained β=0.17. Then, the

bolt spacing was calculated 0.94 m, using Eq. (18), to create a

systematic bolting pattern of 1.0 m ×0.9 m (i.e. S

T

=1.0m×S

L

=0.9 m,

S

T

,S

L

=transversal and longitudinal spacing, respectively).

Depending on group types of the tunnel section, the bolt length

(L

b

) of 6 m and 9 m were preferred to satisfy the criterion considered

in Section 4.1. These deﬁned lengths prevented the plastic zone

thickness from exceeding the anchor length of the bolts. A total of 15

rock bolts were installed around the tunnel except for invert. Floor

was supported by installing 5 grouted bolts with the length of 5 m. The

bolt pattern applied for Malatya tunnel is illustrated in Fig. 11.

It is interesting to note that based on the convergence–conﬁne-

ment analysis, the equilibrium support load (pressure) of 0.31 MPa for

1.12% strain (ur

ri%= 0:028

2:5× 100) is achieved through a combination of

two support elements as illustrated in Fig.12. This value of the support

pressure is equal to thatwhich estimated from the empirical equation.

TH type of steel-sets, spaced at 1 m, embedded in a 20 cm thick

concrete will produce maximum and equilibrium support pressures of

2.6 MPa and 2.3 MPa, respectively. Alternatively, a 1.0 m× 1.0 m

pattern of 34 mm diameter mechanical rock bolts together with a

20 cm concrete lining will provide the required support pressure.

However, in view of the uncertainty associated with the reliability of

the anchorage in this poor rock mass, the use of mechanical rock bolts

should be avoided.

7. Conclusions

An empirical-based method for design of grouted bolts in tunnels

has been developed. The proposed approach provides a step-by-step

procedure to design the grouted bolt and to set up the practical

guidelines for optimum pattern of rock bolting. Incorporating the bolt

density parameter and support pressure function, a practical means to

depict the optimized bolting pattern for any shape of tunnel has been

Fig. 12. Required support pressure obtained by convergence–conﬁnement analysis for Malatya tunnel.

164 R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166

Author's personal copy

introduced. The obtained bolt density parameter can also be used in

analysis of the reinforced tunnel in terms of GRC, whereby the

reduction in tunnel convergence can be more comprehensible.

Therefore, the effectiveness of a bolting pattern can be best evaluated

in terms of tunnel convergence which is the signiﬁcant indicator of

tunnel stability. The GSI or Modiﬁed-GSI included in the support

pressure function makes it possible to effectively design the grouted

bolts for a wide range of rock mass qualities. Since RMR or Q-system

may not provide a sufﬁciently sensitive guide to properly design the

grouted bolts in relatively poor to very poor rock mass, the proposed

alternative design method based on GSI provides a sound basis for

effective bolt design in such rock masses as in turn applied in Malatya

railroad tunnel in Turkey.

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