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An empirical method for design of grouted bolts in rock tunnels based on the
Geological Strength Index (GSI)
Reza R. Osgoui
⁎, Erdal Ünal
GEODATA SpA., Corso Duca degli Abruzzi, 48/E, 10129, Turin, Italy
Mining Engineering Department, Middle East Technical University, 06531/Ankara, Turkey
Received 14 April 2008
Received in revised form 4 May 2009
Accepted 16 May 2009
Available online 27 May 2009
Empirical design method
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.
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
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: email@example.com (R.R. Osgoui).
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other hand, are adopted to verify the performance of the bolting
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
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
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:
where GSI is the Geological Strength Index that deﬁnes the quality of
the rock mass; Dthe disturbance factor indicating the method of
the residual compressive strength of the rock in the
broken zone around the tunnel; D
the equivalent diameter of the
excavation; γthe unit weight of rock mass; C
the correction factor for
the horizontal to vertical ﬁeld stress ratio (k), and S
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
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):
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
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
The above equation can be re-written as:
EmSerafim & Pereira
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
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
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for cases where the horizontal stresses are equal in each
VII. The proposed support pressure function applies for σ
100 MPa. The maximum value of σ
that should be used in
the proposed equation must be 100 MPa even if σ
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:
=post-peak strength reduction factor,
characterizing the brittleness of the rock material as explained later
It should be noted that in the aforementioned equations, D
equivalent diameter of the excavation and it is used for any tunnel
shape. It can easily be obtained from:
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:
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:
The most common form of the support pressure expression can be
written as below when S
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
) 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
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
”is presented in the right side of
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
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
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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
refers to the strength loss parameter that quantiﬁes the jump
in strength from the intact state to the residual condition. The
characterizes the brittleness of the rock material: ductile,
softening, or brittle. By deﬁnition, S
will fall within the range
<1, where S
=1 implies no loss of strength and the rock
material is ductile, or perfectly plastic. In contrast, if S
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
=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
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
). This correction value should be
applied when using Eqs. (5), (8), and (9). Therefore, a multiplier (C
is required to correct the stress ratio. For the reason of reliability, the
minimum value of C
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
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
the equivalent radius of
the tunnel opening; S
the transversal bolt spacing around the tunnel;
the longitudinal bolt spacing along the tunnel axis; θthe angle
between tow adjacent bolts (i.e. S
×θ) in an axi-symmetrical
problem and considering identical bolt with equal spacing along the
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.
Mechanical or hand excavation in poor quality rock masses (no blasting)
results in minimal disturbance to the surrounding rock mass.
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.
Very poor quality blasting in tunnel results in severe damages, extending 2
or 3 m, in the surrounding rock mass.
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.
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
/2) < λ<tan (2φ
/3) and for shaped-rebars
, 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
⁎) 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
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
) in a condition of equilibrium:
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
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:
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).
Suggested values for squeezing ground condition correction factors (S
) used in empirical approach (adopted and modiﬁed from Hoek and Marinos, 2000; Singh et al., 1997).
Strains %(tunnel closure or
Rock mass strength/
in-situ stress (σ
Comments Suggested correction factor
)for squeezing ground
<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
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.
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.
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.
>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
159R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154–166
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For Mohr–Coulomb material (Indraratna and Kaiser, 1990):
kp= tan245 + ϕ
=1 + sinϕ
C0=2ctan 45 + ϕ
For Hoek–Brown material (Osgoui, 2007; Osgoui and Oreste, 2007):
are the maximum and the minimum principal
the uniaxial compressive strength of rock mass; ϕthe
friction angle of rock mass, cthe cohesion of rock mass, m
strength constants of rock mass, and σ
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):
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
: radial displacement of the tunnel wall.
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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
⁎) and the radius of the tunnel (r
) 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
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
) has been recommended as:
ðÞ;where a=0:50:75 ð19Þ
⁎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
Fig. 8. The extension of reinforced plastic zone with respect to bolt length in a
systematic bolt pattern around a circular tunnel.
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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
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
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.
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
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.
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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
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
Intact core recovery (ICR) < 25% Disturbance factor (d) 0.5 (Table 1), usual blasting with local damage
Joint condition index (I
)=7 ICR <25%, bs =2, completely
weathered W=2, without ﬁlling
Correction factor for squeezing ground
1.8 ( Table 2), extreme degree of squeezing, considering
Modiﬁed-GSI=13–15 Very poor rock mass Correction factor for stress ﬁeld (C
) 1.4 (Fig. 3), best assumption for relatively shallow tunnel
in very poor rock mass is k=σh
=5 MPa σ
=5 MPa, S
=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.
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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,
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
=transversal and longitudinal spacing, respectively).
Depending on group types of the tunnel section, the bolt length
) 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
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.
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
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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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