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An empirical method for design of grouted bolts in rock tunnels based on the Geological Strength Index (GSI)

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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.
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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
, Erdal Ünal
GEODATA SpA., Corso Duca degli Abruzzi, 48/E, 10129, Turin, Italy
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
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 eld 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 Modied-GSI is,
instead, recommended. The supporting action is assumed to be provided by rock bolts carrying a total load
dened 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 modied in
order to provide an optimized bolt pattern for any shape of tunnel. The modied 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 sufcient 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 difcult 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 benets of grouted
bolts in comparison to their alternative counterparts.
Broadly speaking, the empirical design methods based on rock
mass classication 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 eld 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-connement 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 eld tests, on the
Engineering Geology 107 (2009) 154166
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E-mail address: (R.R. Osgoui).
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other hand, are adopted to verify the performance of the bolting
Empirical methods, based on rock mass classications, 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 exible in terms of change in rock mass properties and
eld 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 sufciently 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 signicant
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 classication 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
modication 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 Modied-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 eld 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. Denition 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:
PfGSI;D;σcr ;De;γ;Cs;Sq
 ð1Þ
where GSI is the Geological Strength Index that denes the quality of
the rock mass; Dthe disturbance factor indicating the method of
excavation; σ
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 eld stress ratio (k), and S
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 Modied-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 dene 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 dened in such a way that
it does not contradict Ünal's equation (1983, 1992), whose
applicability has been widely accepted in the eld 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 modied version which previously proposed by
Seram and Pereira (1983) for σ
<100 MPa:
r10GSI 10
40 ð3Þ
The above equation can be re-written as:
ror EmHoek:ðÞ
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 signicant role in support pressure function as
a sensible way in considering the effect of the rock mass
disturbance and intact rock strength.
IV. The denitions 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 eld stress was taken into
account similar to the denition given by Ünal (1992).
VI. Since the effect of the horizontal to the vertical eld 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) 154166
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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
>100 MPa.
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 1D
100 CsSqγDeð5Þ
where σ
<1, S
=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
is the
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 specied in the following expressions:
 ð7Þ
where h
is the rock-load height. It is dened 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 1D
100 CsSqDeð8Þ
The most common form of the support pressure expression can be
written as below when S
P=100 1D
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 reects 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 dened 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 deciency of GSI in characterizing poor and very
poor rock mass where RMR falls below 30 (Hoek, 1994), the Modied-
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 Modied-GSI chart is considered as a supplementary
means for its counterparts (Fig. 1). The modied-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 Modied-GSI chart (left side of Fig. 1), two indicators
of poor rock mass; namely, Broken Structure Domain (BSTR) and Joint
Condition Index (I
) are dened. The latter is adopted and modied
from the Modied-RMR (Özkan, 1995; Ulusay et al.,1995; Ünal, 1996)
in order to use in Modied-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 dened 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 Modied-GSI to dene
the blockiness of rock mass. The original intervals of SR were adjusted
to be compatible with BSTR types in Modied-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 lling and weathering
conditions should be known as given in right hand of Fig. 1. ICR is
dened 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 Modied-GSI requirements. For joint condition
rating, the upper part of modied-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
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 Modied-GSI
2.1.2. The effect of excavation method
The tunnelling method has a signicant inuence 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) 154166
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Fig. 1. Modied-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) 154166
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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 inuential
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
refers to the strength loss parameter that quanties the jump
in strength from the intact state to the residual condition. The
parameter S
characterizes the brittleness of the rock material: ductile,
softening, or brittle. By denition, 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 (elasticbrittle plastic) with the minimum possible
value for the residual strength as highlighted in Fig. 2.Asarst 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 stressstrain 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 modied 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 eld 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, rstly dened by
Indraratna and Kaiser (1990), can be written as follows to adopt any
tunnel shape:
where dis the bolt diameter; λthe friction factor for boltgrout
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
tunnel axis.
Table 1
Modied 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 conned 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 signicant
oor 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
signicant 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) 154166
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The bolt density parameter reects 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 coefcient 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
approaches tanϕ
, depending on the degree of adhesion (bond
strength) at the boltgrout interface.
The bolt density parameter has been used to introduce the
equivalent strength parameters in terms of either MohrCoulomb
(c,ϕ) or HoekBrown (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
density parameter.
The supporting action is assumed to be provided by rock bolts
carrying a total support load dened by the rock- load height (Eq. (8)).
Hence, if the effective area of each bolt is dened 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:
Dening a factor of safety (FOS), which is dened 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 rst 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 HoekBrown 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
) used in empirical approach (adopted and modied from Hoek and Marinos, 2000; Singh et al., 1997).
Strains %(tunnel closure or
diameter) 100
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
12.5% Minor squeezing 0.30.5 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.
2.55% Severe squeezing 0.20.3 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.
510% Very severe squeezing 0.150.2 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
sheared zones.
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For MohrCoulomb material (Indraratna and Kaiser, 1990):
=kp1+βðÞ ð16bÞ
=C01+βðÞ ð16cÞ
kp= tan245 + ϕ
=1 + sinϕ
C0=2ctan 45 + ϕ
For HoekBrown material (Osgoui, 2007; Osgoui and Oreste, 2007):
s=1+βðÞ·s ð17cÞ
=1+βðÞ·σci ð17dÞ
where σ
and σ
are the maximum and the minimum principal
stresses; C
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 rst approximate of βcan easily be obtained through
a real characterization of rock mass because two signicant indicators
of rock mass characterization have been incorporated, i.e. the support
load and GSI or Modied-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 inuence 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 boltground
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:ctitious 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 Modied-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
plastic zone.
Based on results of numerous elasto-plastic analyses carried out by
Oreste (2003) and Osgoui (2007), a simple criterion that denes the
grouted bolt length (L
) has been recommended as:
ðÞ;where a=0:50:75 ð19Þ
where r
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 dened 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 owchart of Fig. 9.An
example of such informative tables that recommends the bolt
congurations 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 sufciently
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 sufciently 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 (eld 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 Denition L
(m) S
and S
(m) squared
pattern assumed
β/λβat λ=0.6 Possible yielding
around the tunnel
81100 Very good No support required 0.0 No yielding
6180 Good 2 to 3 2.02.5 0.060.04 0.0380.024 Minimal
4160 Fair 3 to 5 1.52.0 0.110.06 0.0670.038 Minimalmajor
3140 Relatively poor 5 to 6 1.01.25 0.250.11 0.1510.067 Major
2130 Poor 6 1.0 0.25 0.151 Majorexcessive
<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
Table 4
Parameters used in calculating Modied-GSI and support pressure.
Calculation of Modied-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 lling
Correction factor for squeezing ground
condition (S
1.8 ( Table 2), extreme degree of squeezing, considering
Modied-GSI=1315 Very poor rock mass Correction factor for stress eld (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 Modied-GSI of rock mass was approximately
calculated 1315 as, in detail, outlined in Table 4.
Having determined the Modied-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 nal 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 nal 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 sufcient 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
=0.9 m,
=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 dened 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 convergenceconne-
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 convergenceconnement analysis for Malatya tunnel.
164 R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154166
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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 signicant indicator of
tunnel stability. The GSI or Modied-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 sufciently 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.
Atlas Copco, 2004. MAI, International GmbH, Werkstraße 17, A-9710 Feistritz/ Drau.
Aydan, Ö. 1989. The Stabilisation of Rock Engineering Structures by Rockbolts. Ph.D
thesis, Nagoya University, Japan.
Aydan, Ö., Akagi, T., Kawamoto, T.,1996. The squeezing potential of rock around tunnels:
theory and prediction with examples taken from Japan. Rock Mech. Rock Eng.29 (3),
Barton, N., 2002. Some new Q value correlations to assist in site characterization and
tunnel design. Int. J. Rock Mech. Min. Sci. 39, 185216.
Barton, N., Lien, R., Lunde, J., 1974. Engineering classication of rock masses for the
design of tunnel support. Rock Mech. Rock Eng. 6 (4), 189239.
Bawden, W.F., Hyett, A.J., Lausch, P., 1992. An experimental procedure for the in situ
testing of cable bolts. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 29 (5), 525533.
Bhasin, R., Grimstad, E., 1996. The use of stressstrength relationship in the assessment
of tunnel stability. Proc. Recent Advances in Tunnelling Technology, New Delhi,
Bieniawski, Z.T., 1973. Engineering classication of jointed rock masses. Trans. S. Afr.
Inst. Civ. Eng. 15, 335344.
Bieniawski, Z.T., 1984. Rock Mechanics Design in Mining and Tunneling. A.A. Balkema.
272 pp.
Bieniawski, Z.T., 1989. Engineering Rock Mass Classication. John Wiley & Sons, New
York. 251 pp.
Brady, B.H.G., Loring, L., 1988. Analysis of rock reinforcement using nite difference
method. Comput. Geotech. 5, 123149.
Brown, E.T., Bray, J.W., Landanyi, B., Hoek, E., 1983. Ground response curves for rock
tunnels. J. Geotech. Eng. 109, 1539.
Cai, Y., Esaki, T., Jiang, Y., 2004a. A rock bolt and rock mass interaction model. Int. J. Rock
Mech. Min. Sci. 41, 10551067.
Cai, Y., Esaki, T.,Jiang, Y., 2004b. An analytical model to predict axial load in grouted rock
bolt for soft rock tunnelling. Tunnel. Underground Space Technol. 18, 347363.
Cai, M., Kaiser, P.K., Uno, H., Tasaka, Y., Minami, M., 2004c. Estimation of rock mass
deformation modulus and strength of jointed hard rock masses using the GSI
System. Int. J. Rock Mech. Min. Sci. 41 (1), 319.
Carranza-Torres, C., 2004. Elasto-plastic solution of tunnel problems using the
generalized form of the HoekBrown failure criterion. Int. J. Rock Mech. Min. Sci.
4 (supplement 1), 629639.
Carranza-Torres, C., Fairhurst, C., 2000. Application of convergenceconnement
method of tunnel design to rock masses that satisfy the HoekBrown failure
criterion. Tunnel. Underground Space Technol. 15, 187213.
Chen, S., Qiang, S., Chen, S., Egger, P., 2004. Composite element model of the fully-
grouted rock bolt. Rock Mech. Rock Eng. 37 (3), 193212.
Cundall, P., Carranza-Torres, C., Hart, R., 2003. A new constitutive model based on the
HoekBrown failure criterion. Proc. 3rd Int. FLAC Symposium. FLAC and numerical
modelling in geomechanics, Sudbury, Canada.
Duan, F. 1991. Numerical modelling of cable bolt support systems. Ph. D thesis. The
University of Utah. Utah.
Ducan Fama, M.E., 1993. Numerical modelling of yield zones in weak rocks. In: Hudson,
J.A. (Ed.), Comprehensive rock engineering, vol. 2. Pergamon, Oxford, pp. 4975.
Freeman, T.J., 1978. The behaviour of fully-bonded rock bolts in the Kielder
experimental tunnel. Tunn. Tunn. 10, 3740.
Grasso, P., Mahtab, A., Pelizza, S.,1989. Reinforcing a rock zone for stabilizing a tunnel in
complex formations. Proc. Int. Cong. Progress and Innovation in Tunnelling, vol. 2,
pp. 671678. Toronto.
Grimstad, E., Barton, N., 1993. Updating the Q-system for NMT. Int. Symp. Sprayed
Concrete, Fagernes, Norway, pp. 4666.
Guan, Z., Jiang, Y., Tanabasi, Y., Huang, H., 2007. Reinforcement mechanics of passive
bolts in conventional tunnelling. Int. J. Rock Mech. Min. Sci. 44, 625636.
Hoek, E., 1994. Strength of rock and rock masses. ISRM News J. 2 (2), 416.
Hoek, E., 1999. Putting numbers to geology an engineer's viewpoint. Q. J. Eng. Geol.
32 (1), 119 .
Hoek, E., Brown, E.T.,1980. Underground Excavations in Rock. Institution of Mining and
Metallurgy, London. 527 pp.
Hoek, E., Brown, E.T., 1997. Practical estimates of rock mass strength. Int. J. Rock Mech.
Min. Sci. 34 (8), 11651186.
Hoek, E., Marinos, P., 2000. Predicting Tunnel Squeezing. Tunnels and Tunnelling
International. Part 1 November Issue. 4551, Part 2 December, pp. 3436.
Hoek, E., Carranza-Torres, C.T., Corkum, B., 2002. HoekBrown failure criterion2002
edition. Proc. 5th North American Rock Mechanics Symposium, Toronto, Canada,
vol. 1, pp. 267273.
Hyett, A.J., Moosavi, M., Bawden, W.F., 1996. Load distribution along fully grouted bolts,
with emphasis on cable bolt reinforcement. Int. J. Numer. Anal. Methods Geomech.
20, 517544.
Indraratna, B., Kaiser, P.K., 1990. Design for grouted rock bolts based on the convergence
control method. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 27, 269281.
Kaiser, P.K., Diederichs, M., Yazici, S., 1992. Cable bolt performance during mining
induced stress changea case study. In: Kaiser, P.K., McCreath, D.R. (Eds.), Proc. Int.
Symposium on Rock Support, pp. 367376. Sudbury, Canada.
Karanam, U.M.R., Pasyapu, S.K., 2005. Experimental and numerical investigations of
stresses in a fully grouted rock bolts. Geotech. Geolog. Eng. 23, 297308.
Kilic, A., Ysar, E., Atis, C., 2003. Effect of bar shape on the pullout capability of fully-
grouted rockbolts. Tunnel. Underground Space Technol. 18, 16.
Labiouse, V., 1996. Ground response curves for rock excavations supported by
ungrouted tensioned rockbolts. Rock Mech. Rock Eng. 29 (2),1938.
Laubscher, D.H., 1977. Geomechanics classication of jointed rock massesmining
applications. Trans. Inst. Min. Metall. 86, A1A-7.
Li, C., Stillborg, B., 1999. Analytical models for rock bolts. Int. J. Rock Mech. Min. Sci. 36,
Lunardi, P., 2000. The design and construction of tunnels using the approach based on
the analysis of controlled deformation in rocks and soils. TT Int. (special
Marinos, V., Marinos, P., Hoek, E., 2005. The geological strength index: applications and
limitations. Bull. Eng. Geol. Environ. 64 (1), 5565.
Mark, C., 2000. Design of roof bolt system. Proc. National Institute for Occupational
Safety and Health (NIOSH).
Mark, C., Dolinar, D., Mucho, T.P., 2000. Summary of eld measurements of roof bolt
performance. Proc. National Institute for Occupational Safety and Health (NIOSH).
Oreste, P.P., 2003. Analysis of structural interaction in tunnels using the covergence
connement approach. Tunnel. Underground Space Technol. 18, 347363.
Oreste, P.P., Peila, D., 1996. Radial passive rockbolting in tunnelling design with a new
convergenceconnement model. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33,
Osgoui, R. 2007. Development of an elasto-plastic analytical model for design of grouted
rock bolts in tunnels with particular reference to poor rock masses. Ph. D thesis.
Middle East Technical University. Ankara. Turkey. 250 pp.
Osgoui, R., 2006. On the Assessment of the effect of the anisotropy in in-situ stress on
support pressure in tunnels. Proc. Int. Symp. In-Situ Rock Stress, Trondheim,
Norway, pp. 307317.
Osgoui, R., Ünal, E., 2005. Characterization of weak rock masses using GSI and the
estimation of support pressure. 40th U.S. Rock Mechanics Symposium, Anchorage,
Osgoui,R., Oreste, P.P., 2007. Convergencecontrol approach for rock tunnels reinforcedby
grouted bolts, using the homogenization concept. Geotech. Geolog. Eng. 25, 431440.
Özkan, İ. 1995. Modied rock mass rating (M-RMR) system and roof behavior model.
Ph. D thesis. Middle East Technical University. Ankara. Turkey. 370 pp.
Palmström, A., 1996. Characterizing rock masses by the RMi for use in practical rock
engineering, Part 1: the development of the rock mass index (RMi). Tunnel.
Underground Space Technol.11, 175188.
Palmström, A., 2000. Recent developments in rock support estimates by the RMi. J. Rock
Mech. Tunn. Technol. 6 (1), 119.
Palmström, A., Broch, E., 2006. Use and misuse of rock mass classication systems with
particular reference to the Q-system. Tunnel. Underground Space Technol. 21,
Panet, M., 1993. Understanding deformations in tunnels. In: Hudson, J.A. (Ed.), In
comprehensive rock engineering, vol. 1. Pergamon, Oxford, pp. 663690.
Pells, P.J., Bertuzzi, R., 2008. Discussion on article titled Use and misuse of rock mass
classication systems with particular reference to the Q-systemby Palmström and
Broch (Tunnel. Underground Space Technol; 21: 575593) Tunnel. Underground
Space Technol. 23, 340350.
Seram, J.L., Pereira, J.P., 1983. Considerations of the geomechanics classication of
Bieniawski. Proc. Int. on Engng Geol. And Underground Constr. LNEC. Lisbon.
Signer, S.D., 2000. Load behaviour of grouted bolts in sedimentary rock. Proc. National
Institute for Occupational Safety and Health (NIOSH).
Singh, B., Jethwa, J.L., Dube, A.K., Singh, B., 1992. Correlation between observed support
pressure and rock mass quality. Tunnel. Underground Space Technol. 7, 5974 .
Singh, B., Goel, R.K., Jethwa, J.L., Dube, A.K., 1997. Support pressureassessment in arched
underground openings through poor rock masses. Eng. Geol. 48, 5981.
Sönmez, H., Ulusay, R., 1999. Modications to the geological strength index (GSI) and
their applicability to stability of slopes. Int. J. Rock Mech. Min. Sci. 36, 743760.
Sönmez, H., Ulusay, R., 2002. A discussion on the HoekBrown failure criterion and
suggested modication to the criterion veried by slope stability case studies.
Yerbilimleri (Earth Sciences) 26, 7799.
Stille, H., Holmberg, M., Nord, G., 1989. Support of weak rock with grouted bolts and
shotcrete. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 26 (1), 99113.
Swoboda, G., Marence, M., 1991. FEM modelling of rockbolts. Proc., Comp. Meth. and Geomech., Cairns, Australia, pp. 15151520.
Ulusay, R., Özkan, İ., Ünal, E.,1995. Characterization of weak, stratied and clay bearing
rock masses for engineering applications. In: Mayer, L.R., Cook, N.W., Goodman, R.E.,
Tsang, C.F. (Eds.), Fractured and Jointed Rock Masses Conference. A.A. Balkema,
Lake Tahoe, California, pp. 233240.
165R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154166
Author's personal copy
Ünal, E. 1983. Development of design guidelines and roof control standards for coal
mine roofs, Ph.D. Thesis. The Pennsylvania State University. Department of Mineral
Engineering. State College. 355 pp.
Ünal, E., 1992. Rock reinforcement design and its application in mining. In: Kaiser, P.K.,
McCreath, D.R. (Eds.), Proc. Int. Symposium on Rock Support, pp. 541546. Sudbury,
Ünal, E., 1996. Modied rock mass classication: M-RMR system. In: Bieniawski, Z.T.
(Ed.), Milestone in Rock Engineering: A Jubilee Collection. InBalkema, pp. 203223.
Ward, W.H., Tedd, P., Berry, N.S.M., 1983. The Kielder experimental tunnel: nal results.
Géotechnique 33, 275291.
Wong, H., Subrin, D., Dias, D., 2006. Convergenceconnement analysis of a bolt-
supported tunnel using the homogenization method. Can. Geotech. J. 43, 462483.
166 R.R. Osgoui, E. Ünal / Engineering Geology 107 (2009) 154166
... The results show that the stress is in the decreasing zone when the coal pillar is less than 8 m, which is consistent with the distribution of the stress field in the EWC zone during the final mining [11,12]. The research on the influence of rock bolts on roof stability under the action of abutment pressure makes it more clear that bolt support is important for roadway support [13][14][15]. The surrounding rock is affected by the mining and will inevitably undergo deformation and failure, and the related tests also proved the failure rules of rock by abutment pressure [16,17]. ...
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The use of pre-excavation equipment withdrawal channels (EWCs) at the stop-production line is important for the rapid withdrawal of coal mining equipment. However, during the final mining period, the dynamic pressure of a pre-excavated double EWC is severe, which leads to instability of the surrounding rock around the EWCs. Therefore, in this paper, the methods of field monitoring, theoretical analysis, and numerical simulation were used to systematically study the stress and plastic zone evolution of a double EWC during the final mining period. Firstly, the distribution characteristics of mining abutment pressure and roadway failure modes under the action of mining abutment pressure were analyzed theoretically. Afterward, a FLAC3D mining numerical model was established according to the distribution of rock strata obtained from roof detection. Finally, the evolution laws of the stress fields and plastic zones of the EWCs during final mining were obtained by numerical simulation. The present study suggests that asymmetric stress distribution dominates asymmetric failure of the surrounding rock around the EWCs during the final mining period, and deformation failure within 10 m from the working face to the main EWC (MEWC) accounted for most of the roadway deformation. Based on the research results combined with actual production experience, the stability control technique of the surrounding rock with reinforcement of anchor cables and double-row buttress hydraulic support for the MEWC was put forward. After the field application, the ideal result was obtained.
... rough theoretical analysis, similar material simulation experiments, and numerical simulations, Yang et al. proposed a stress distribution law, determined the plastic failure range and reasonable coal pillar size near the working face, and achieved a good application effect [16,17]. Li et al. established a calculation model to examine the influence of three factors, i.e., the thickness and position of the interbedded coal seam and the width of the bifurcation roadway rock pillar, on the displacement, plastic zone, and asymmetric deformation of the critical points of the roadway. ...
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In this study, the 31113 fully mechanised working face in the Lijiahao Coal Mine was selected as the project background. The failure characteristics and optimum spacing of a double-withdrawal-channel surrounding rock were extensively investigated through field measurements, theoretical analysis, and numerical simulations. The following results were obtained. The loading influence range of the working face was fixed. Under the influence of mining, the stress distribution variation in the double-withdrawal channels with spacing and the influence of stress distribution on the surrounding rock stability of the withdrawal channels were determined. The optimum distance between the double-withdrawal channels to achieve the stability of the surrounding rock was at least 25 m, and engineering measures are required to limit the mining height in the final mining stage. The rationality of the main and auxiliary withdrawal channel spacing of 25 m and measures to limit the mining height in the final stage were demonstrated. The findings of this study provide a valuable reference for constructing the layout of withdrawal channels in the adjacent working faces of the same mining area.
Medium- to long-term weathering phenomena is one of the major causes of rock instability. Although many geo-protection technologies have been developed to mitigate the hazards such as slope failures of natural rock weathering, these techniques provide no self-healing function of the rock around the facilities. The status quo in rock instability problems is to provide rock maintenance and to constantly monitor the situation depending on the particular conditions. Improper rock maintenance comes with the risk of critical accidents which may result in human casualties as well as significant environmental destruction. It is therefore necessary to develop novel techniques to realise the continuous healing of weathered rock in the medium- and long-term. In this study, the electrodeposition method was applied for the first time to heal weathered rock mass in a series of fundamental experiments, using volcanic tuff sampled in Japan as the weathered rock model. It was noted that a reduction reaction occurs around the cathode side, and the electrodeposits fill the pores and cracks in the rocks selectively, thereby improving the surface hardness in a small specimen scale. Moreover, the application of a weak current over a lengthy period was shown to facilitate the deposition of stable crystals, such as calcite and magnesian calcite. The results of this study on electrodeposition on unstable rock formations show the potential of crack-healing and pore-filling in a self-organised manner.
The Hoek-Brown (H-B) criterion is one of the most commonly used rock failure criteria in recent years. This criterion includes a constant parameter called mi which is a fundamental parameter for estimating rock strength. Due to the importance of the mi parameter in the H-B criterion, it is necessary to conduct comprehensive studies on various aspects of the effect of this parameter on the behavior of rocks. Therefore, in this study, using numerical simulation of the Triaxial Compressive Strength (TCS) tests in PFC-2D code, the effects of microscopic properties of different rocks on the H-B parameter mi have been studied. Based on the results of this study, it was found that the effects of micro-parameters on the H-B parameter mi can be different depending on the type of rock, however this parameter has an inverse relationship to the micro-parameters of bond tensile strength and bond fraction of the rocks. Also, the mi parameter increases with an increase in the micro-parameters of the friction coefficient, the friction angle, the particle contact modulus, and the contact stiffness ratio of rocks.
This study investigates the interaction process between grouted bolts and tunnel surrounding rock, and establishes an analytical model for deep tunnels reinforced with active grouted rockbolts of the convergence-confinement type. The rock mass is assumed to be elastic-perfectly plastic, obeying the Hoek–Brown criterion. The longitudinal displacement profile is introduced to represent the space effect of the tunnel face, based on which the fictitious pressure along the tunnel axis is determined. Because of delayed installation and limited length of the rockbolts, a rock mass may behave elastically or plastically at bolt installation with the rockbolts anchored in different zones. Six different evolution paths possibly encountered on the basis of the relative magnitude between the anchorage and plastic zones are proposed. The tunnel displacement, plastic radii, and stresses are determined. The analytical results are validated by comparing with those obtained from numerical simulations and an existing model. A parametric analysis shows that doubling bolt length from 2 to 4 m in a 14-m-diameter tunnel reduces the tunnel wall displacement up to 20%. Installing rockbolts close to the tunnel face (less than 1 m) can reduce tunnel wall displacement up to 51%. Doubling the pretension load can reduce tunnel wall displacement up to about 20%. Increasing the support density can reduce the tunnel wall displacement by up to about 50%. The analysis shows that the proposed model outperforms Fahimifar’s model, which deals with infinite rockbolts, in solving tunnel responses under grouted rockbolts, particularly in the case of large cross-sectional tunnels excavated in poor geological conditions.
This paper presents the development and field-scale demonstration of a cementitious grout that enables detection in the subsurface via the addition of magnetite. Through the strategic use of a grout injection borehole and an array of monitoring boreholes for conducting pre- and post-injection magnetic surveys, combined with a geologically-based model for simulating the magnetic field anomaly, this technology can locate the post-injection magnetic grout volume within the subsurface. A series of laboratory tests were conducted to show that the addition of Bayferrox 318 M magnetite to a microfine cementitious grout does not detrimentally affect grout fluidity, penetrability, gelling, bleed and compressive strength. A magnetic grout with fluid to solid ratio = 0.7 and 15% magnetite content was then injected into a borehole interval at 40–50 m depth, and changes to the magnetic field were measured within six surrounding monitoring boreholes. Field trial results show that the measured magnetic anomalies (due to magnetic grout injection) correspond well to geological features identified in a nearby site investigation borehole and that these anomalies can be detected in monitoring boreholes at a distance of 3 m. By optimising the fit between model simulations of the magnetic anomaly and the field trial observations, the final geometry of the grouted rock features could be determined. Results show that grout preferentially penetrated into two coal beds and along two bedding planes that cross-cut the injection hole.
de Für Gebirge als Befestigungsuntergrund ist es aufgrund einer Vielzahl an möglichen Einbausituationen schwer, vorab auf das Tragverhalten und die Tragfähigkeit von Befestigungselementen schließen zu können. In diesem Fachbeitrag wird daher untersucht, wie sich ein Befestigungsmittel in anstehendem Fels bei geringen Einbindetiefen verhält und welche Untergrundparameter einen wesentlichen Einfluss auf das Tragverhalten und die Tragfähigkeit haben. Dazu werden Versuche an nachträglich installierten Befestigungen unterschiedlichen Wirkprinzips (Verbundanker, Spreizanker) in unterschiedlichen Lithologien Ostösterreichs vorgestellt. Es konnte gezeigt werden, dass mittels Gebirgsklassifikation auf die Eignung des Gebirges als Befestigungsuntergrund rückgeschlossen werden kann. Für eine Abschätzung der Tragfähigkeit ist eine kleinräumige Untersuchung jedoch unbedingt notwendig. Nicht nur das Vorhandensein von Trennflächen hat einen Einfluss auf die Tragfähigkeit, sondern auch deren Beschaffenheit. Analogien zu Beton als Untergrund konnten festgestellt werden. Abstract en Assessment of rock as a fastening foundation for post-installed fastenings with shallow embedment depths For rock as a base material for post installed anchors, it is difficult to draw conclusions about the load-bearing behavior and capacity in advance due to the large number of possible installation parameter. This technical article therefore examines how post-installed anchors with low embedment depths behave in rock and which rock parameters have a significant influence on the load-bearing behavior and capacity. For this purpose, tests on anchors with different operating principles (injectable adhesive anchor, mechanical bolt anchor) in different geologies in Eastern Austria were performed. It could be shown that rock classification can be used to infer the suitability of a rock as a base material, but a small-scale investigation also is necessary to estimate the load-bearing capacity. Not only the presence of joints has an influence on the load-bearing capacity, but also the joint condition. Analogies to cracked concrete could be shown.
Rock failure mechanism is one of the most important issues in rock mechanics engineering which plays a key role in the stability analysis of various structures. Therefore, different failure criteria have been proposed to understand the failure mechanism of rocks. One of the most commonly used rock failure criteria is the Hoek-Brown criterion, in which there is a parameter called mi, which is very important to the response provided by this criterion. Due to the importance of conducting extensive studies on this parameter, in this current research, by performing a series of experimental triaxial compressive strength test and numerical simulating in PFC-2D code, the effect of the Hoek-Brown constant mi on the failure mechanism and crack growth of different rocks has been studied. Based on the results of this study, it was found that the effect of parameter mi on the failure mechanism of different rocks varied according to the type of rocks, and the greatest effect of this parameter was on the peak strength of rocks. In addition, it was found that under higher lateral pressures, there are less destructive cracks in rocks, and as a result, they show more ductile behaviour.
Estimation of support pressure is extremely important to the support system design and the construction safety of tunnels. At present, there are many methods for the estimation of support pressure based on different rock mass classification systems, such as Q system, GSI system and RMR system. However, various rock mass classification systems are based on different tunnel geologic conditions in various regions. Therefore, each rock mass classification system has a certain regionality. In China, the BQ-Inex (BQ system) has been widely used in the field of rock engineering ever since its development. Unfortunately, there is still no estimation method of support pressure with BQ-index as parameters. Based on the field test data from 54 tunnels in China, a new empirical method considering BQ-Inex, tunnel span and rock weight is proposed to estimate the support pressure using multiple nonlinear regression analysis methods. And then the significance and necessity of support pressure estimation method for the safety of tunnel construction in China is explained through the comparison and analysis with the existing internationally widely used support pressure estimation methods of RMR system, Q system and GSI system. Finally, the empirical method of estimating the support pressure based on BQ-index was applied to designing the support system in the China’s high-speed railway tunnel—Zhengwan high-speed railway and the rationality of this method has been verified through the data of field test.
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The geological strength index (GSI) is one of the most exceptional rock mass classification system which is used to evaluate very weak and highly jointed rock mass by different approaches and related to rock mass geomechanical properties including generalized Hoek & Brown constants, deformation modulus, strength properties, and Poisson’s ratio for an appropriate design of tunnels, caverns, and other engineering structures. The distinctiveness of this system over the rock mass rating (RMR), Q-system, and other empirical methods is as follows: it utilized field observations, blockiness of rock mass, and surface joint characteristics during the evaluation process of rock mass and efficiently espoused as an empirical tool for estimation of geomechanical properties of rock mass required for pre-post stability of engineering structures using numerical modeling. This study presents the review of the 19 years of research studies conducted by different researchers about the GSI in a systematic way, i.e., origination, modifications, applications, and limitations. Furthermore, this study will provide a better understanding to field professionals (geologists, mining and civil engineers) about the qualitative and quantitative estimation of the GSI and its application as an empirical estimating tool for an appropriate design of engineering structures in rock mass environments.
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Rockbolts are still the best known method to increase the strenght of jointed rock arround a tunnel, especially in combination with a shotcrete lining. The effect of rock bolts was simulated up to now mainly with simple bar elements, which means that only the tension effect of the bolt is considered. Based on the rock bolt element of Aydan a new model was developed, which considers the special problem of the rock bolt effect at the crossing with joints in rock. From experiments it is wel known, that the large displacements at joint in combination with "dowel effect" of the bolt is an important of the loading capacity of the bolt. With a large displacements of the bolt at the intersection with a joint additional forces will act and increase the friction in the fault system. At the same timne the bolt will show a typical slip effect between bolt and grout. For steel elastic-idealplastic material is considered. The application of the model is shown on a normal shear test and on the calculation of an excavation of a road tunnel. The support system for this tunnel is shotcrete and untensioned rockbolts.
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SOME NEW Q–VALUE CORRELATIONS TO ASSIST IN SITE CHARACTERIZATION AND TUNNEL DESIGN N. Barton Nick Barton & Associates, Fjordveien 65c, 1363 Høvik, Norway Abstract The rock mass quality Q-value was originally developed to assist in the empirical design of tunnel and cavern reinforcement and support, but it has been used for several other tasks in rock engineering in recent years. This paper explores the application of Q and its six component parameters, for prediction, correlation and extrapolation of site investigation data, and for obtaining first estimates of some input data for both jointed distinct element and continuum-approximation modelling. Parameters explored here include P-wave velocity, static modulus of deformation, support pressure, tunnel deformation, Lugeon-value, and the possible cohesive and frictional strength of rock masses, undisturbed, or as affected by underground excavation. The effect of depth or stress level, and anisotropic strength, structure and stress are each addressed, and practical solutions suggested. The paper concludes with an evaluation of the potential improvements in rock mass properties and reduced support needs that can be expected from state-of-the-art pre-injection with fine, cementicious multi-grouts, based on measurements of permeability tensor principle value rotations and reductions, caused by grout penetration of the least favourable joint sets. Several slightly improved Q-parameter ratings form the basis of the predicted improvements in general rock mass properties that can be achieved by pre-grouting.
The work described here aims to model yield zones in weak rock in a relatively simple manner, and with a view to computational simulation. The widespread practice of modelling yield zones by a homogenous material of lower stiffness than the intact material is shown to be, potentially, an excellent approximation to the deformation theory of plasticity. An important point is emphasised - the in situ stress unloading from these regions of low stiffness must also be reduced. -from Author
This chapter discusses numerical modeling of yield zones in weak rock. Weakened or partly fractured materials can be modeled by a linear elastic material with a low modulus of elasticity. The major difficulty in the numerical modeling of geological materials is in the determination of the input parameters. Results of laboratory tests for such parameters as the modulus of elasticity and Mohr–Coulomb or Hoek–Brown failure properties are not always relevant to the rock in situ. Equivalent elastic properties of a weakened or yielded rock can be related, via the deformation theory of plasticity, to failure and postfailure properties such as pre-and postfailure cohesion and angle of friction of the rock. A major advantage of the deformation theory is ease of computation. The formulation is done in such a way that an iterative procedure can be set up with a linear elastic finite element program. In the incremental theories, the boundary tractions are reduced in increments until the material adjacent to the opening yields.
Modern tunnelling techniques monitor displacements during and following tunnel construction. The measurement of wall displacement - convergence - and models used in rock tunnel engineering are discussed. The deformations caused by tunnels driven into elastic, and yielding rock masses are analysed, and the chapter is concluded by an examination of time dependant deformations. -R.Gower