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1. INTRODUCTION
To estimate the support pressure in extremely
weak rock mass accurately, it is essential that such
rock mass be quantitatively characterized. In the
characterization of poor and very poor rock
masses, the application of existing GSI indices is
hindered by the fact that the use of the index for
weak rock mass is to some extent subjective and
requires long-term experience [1, 2, 3, 4, 5, and 6].
The method presented in this paper deals with
overcoming such inconveniences and uncertainties
present in previous methods. In order to better
characterize a weak rock mass, two important
indicators, namely Broken Structural Domain
(BSTR) and Joint Condition Index (I
jc
) from
Ünal’s M-RMR classification system [7] have
been added to the procedure.
Reliable prediction of tunnel support pressure
(rock load) is a difficult task in the area of tunnel
engineering and has been highly subjective and
open to argument. Starting with Terzaghi’s rock
load concept [8], several empirical approaches
using rock mass classification systems have been
developed for the estimation of tunnel support
pressure [9,10,11,12,13,14,15,16]. Among them,
Barton’s Q-dependent and Ünal’s RMR-dependent
approaches have been widely used.
The proposed empirical approach briefly presented
in this paper is a sophisticated version of Ünal’s
RMR-dependent approach, taking into
consideration almost all important factors
affecting the amount of rock load. The main
advantage of this new approach lies in the fact that
it is applicable to overstressed and squeezing rock
mass.
The rock-load heights obtained from the proposed
approach were compared with plastic zone (failure
height) attained from the elasto-plastic closed-
form solutions for a circular tunnel. The
ARMA/USRMS 05-701
Characterization of Weak Rock Masses Using GSI-Index and the
Estimation of Support-Pressure
Osgoui, R.
Mining Engineering Department, Middle East Technical University, Ankara, Turkey
Ünal, E.
Mining Engineering Department, Middle East Technical University, Ankara, Turkey
Copyright 2005, ARMA, American Rock Mechanics Association
This paper was prepared for presentation at Alaska Rocks 2005, The 40th U.S. Symposium on Rock Mechanics (USRMS): Rock Mechanics for Energy, Mineral and Infrastructure
Development in the Northern Regions, held in Anchorage, Alaska, June 25-29, 2005.
This paper was selected for presentation by a USRMS Program Committee following review of information contained in an abstract submitted earlier by the author(s). Contents of the paper,
as presented, have not been reviewed by ARMA/USRMS and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of USRMS,
ARMA, their officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited.
Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where
and by whom the paper was presented.
ABSTRACT:
Ever since its development, the GSI-Index has attracted interest in the field of rock engineering. In spite of some
uncertainties and inadequacies, the GSI-Index has found acceptance for characterizing various types of rock masses. In this study,
firstly a quantitative approach was presented to determine the GSI-Index for weak rock masses. Secondly, empirical equations
were developed for the estimation of rock-load height and support pressure. Thirdly, the results obtained from the proposed
empirical approach were compared with those acquired from closed-form and numerical solutions and a reasonable agreement was
obtained. Finally, a new empirical approach that can be used in rock reinforcement design of tunnels excavated in poor and very
poor rock masses was briefly presented. The developed design method was applied to the Malatya No: 7 railroad tunnel excavated
in squeezing rock condition, miss-aligned due to stress and water effect, as well as having poor support conditions.
A paper published at the 40th U.S. Rock Mechanics Symposium - June 25-29, 2005 -
Anchorage, Alaska.
evaluation of the results indicated that the
empirical approach is remarkably compatible with
closed-form solutions.
For arch-shaped and rectangular tunnels, in order
to examine the influential factors (the shape of the
tunnel, GSI, span, and anisotropy in field stress)
on failure height, a total of 96 Finite Element
Analyses (FEA) were carried out. In addition, a
correction factor for considering the effect of the
anisotropy in field stress was obtained.
The new approaches presented in this paper
characterizing poor and very poor rock mass and
estimating support pressure can be regarded as an
integrated design approach to tunnel engineering.
Estimating the support pressure, we were able to
achieve a step-by-step procedure for designing a
systematic rock-bolting. This guided design
method was utilized as a case study for the No: 7
Malatya railroad-tunnel that has suffered from
squeezing ground condition over the years.
2. MODIFIED GSI-INDEX FOR POOR AND
VERY POOR ROCK MASS
Few attempts have been made to properly
characterize poor and very poor rock mass so far.
However, with the advent of the Geological
Strength Index “GSI-Index”, it has been a
universal rock-mass characterization approach
capable of characterizing a wide spectrum of rock
masses [17, 18, and 19].
The GSI-Index is estimated based on geological
descriptions of rock mass involving two factors;
rock structure or block size, and joint or block
surface conditions [17, 18, and 19].
The original method used to determine the GSI-
Index is mostly based on a descriptive approach,
rendering the system somewhat subjective and
difficult to use. The quantitative approaches, on
the other hand, have been presented by others to
overcome such perplexities [3,4,and 6].
Nevertheless, existing amendments are not
sufficient to characterize poor and very poor rock
mass accurately.
Although careful consideration has been given to
precise wording for each category and to the
relative weights assigned to each combination of
structural and surface conditions, the use of the
GSI-Index involves some subjectivity. The salient
deficiency in determining the GSI-Index is in
characterizing poor and very poor rock mass
where the RMR of a prescribed rock mass is
below approximately 30. Therefore, the estimation
of the GSI value for very poor rock masses
composed of frequently tectonically disturbed
alteration requires that some special challenges be
overcome [1]. In addition, long-term experience
and sound judgment are required for successfully
determining the GSI-Index for a large variety of
the rock masses ranging from very good to very
poor.
In order to overcome such uncertainties and
perplexities and to reduce the deficiency in
determining the GSI-Index in weak rock mass, a
quantitatively supplementary approach has been
recommended by incorporating both visual
impression and quantitative measures of rock mass
structure. The resulting approach adds quantitative
measures, apart from visual impression, to render
the system more objective.
To determine the GSI-Index for poor and very
poor rock mass, two indicators of weak rock mass,
namely the Broken Structural Domain (BSTR) and
the Joint Condition Index (I
jc
) of the Modified
RMR-System were adopted. In addition, eight
quantitative or visual parameters were embedded
into the system to assist the user. All information
required for using in Modified GSI-Index can
readily be obtained from overall field observation,
scan-line mapping, and/or core-box surveying.
The details associated with the Modified GSI-
Index will be explained in detail in subsequent
publication of the authors.
2.1. Broken Structural Domain (BSTR) Indicator
Generally speaking, broken drill-core zones
recovered from a very weak rock mass having a
length greater than 25 cm are defined as Broken
Structural Domain (BSTR) [7]. Various types of
BSTR domains can be categorized into 5 groups
based on their size and composition as shown in
Figures 1 and 2. BSTR types included in the
Modified GSI-Index to define the rock-mass
structure are demonstrated in Figure 3.
2.2. Joint Condition Index (I
jc
)Indicator
In order to determine the I
jc
-Index BSTR type,
Intact Core Recovery (ICR) vales, filling
condition, and weathering conditions should be
known as shown in Table 1 [7, 20].
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
(Disintegrated / Decomposed or BSTR 3/4/5, and
Foliated /Laminated / Sheared or BSTR 1/ 2) is
considered to be less than 25 to satisfy the
Modified GSI-Index requirements.
For joint condition rating, the upper part of
modified GSI chart (Figure 3) 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 of
determining joint condition index “I
JC
“is
presented in Table 1.
Figure 1. Various types of Broken Structural Domain
(BSTR)
Figure 2. Core-box surveying for No: 7 Malatya Railroad
tunnel project. Various types of BSTR are marked.
A poor and very poor rock mass having GSI
between 5 and 27 can, therefore, be easily
characterized. Moreover, this new Modified GSI
( Joint Condition Index) I
JC
BSTR 1 bs=0
BSTR 2 bs=2
Without Filling
BSTR 3 bs=4 I
JC
= (bs) +(W /2) +4
BSTR 4 bs=6
BSTR 5 bs=8
t
f
≥ 5 mm soft 0
t
f
: filling thickness hard 4
With Filling
1 mm ≤ t
f
≤ 5 mm soft I
JC
= (bs/2) +(W /2)
hard I
JC
= (bs/2) +(W /2) +4
t
f
≤ 1 mm I
JC
= (bs) +(W /2) +4
Intact Core
Recocery
ICR < 25
Rating
Unal 1996 ISRM 1981 Class Wc
Unweathered Fresh 1 <1,1 8
Slightly Weathered Slightly Weathered 2 1,1- 1,5 7
Moderately Weathered Moderately Weathere
d
3 1,5-2,0 6
Highly Weathere
d
Highly Weathered 4 >2,0 4
Very Highly Weathered Completely Weathere
d
52
Decomposed Residual Soil 6 0
W
c
= R
f
/ R
w
If Wc is known, Rating = 10,7-2,7 Wc
(Gokceoğlu & Aksoy 2000
)
Condition
where R
f
is the rebound number obtained from fresh rock
surface and Rw is the rebound number gained from the
weathered rock surface in Schmidt hammer test
We athe ring
"W"
chart considerably satisfies and supplements the
previous counterparts developed by others.
An indirect way of determining the GSI value for
weak rock mass from RMR was suggested by
Osgoui and Ünal [21] as shown in Equation (1).
RMR
eGSI
05.0
6= (1)
3. ROCK-LOAD HEIGHT AND SUPPORT
PRESSURE
3.1. The concept of rock-load height
This concept was primarily suggested during a
comprehensive study of roof strata in U.S. coal
mines by Ünal [10, 11]. The theory predicts the
load on the support system based upon the rock
quality and span. Ünal’s rock-load height concept
states that above any underground opening
excavated, a roof arch and a ground arch form.
The existence of these two arches can be identified
by examining the stress distribution in the roof
strata. The support must withstand the weight of
the roof arch and the portion of the ground arch
load actively transferred on the roof arch. The
major portion of the strata pressure (passive load),
on the other hand, is transferred to the sides of the
opening due to the existence of the roof arch
preserved by the support system. Hence, the total
Table 1. Joint Condition Index”I
jc
” determination
load that should be carried by support system is
limited by the rock-load height, which is defined
as the height of the potential instability zone,
above the roof line and crown for rectangular,
arch-roof, horse shoe openings, which will
eventually fall if not properly supported. The new
proposed empirical equation is dependent on the
parameters shown in Equation (2):
),,,( SChfP
t
γ
≈ (2)
The rock-load height, on the other hand, can be
expressed as shown in Equation (3):
CSB
GSI
D
h
cr
t
100
1002
1100
−−
=
σ
(3)
where
GSI : Geological Strength Index, which defines
the quality of the rock mass,
D: disturbance factor indicating the method of
excavation (drill and blast or TBM),
σ
cr
: uniaxial compressive strength of rock material
for the broken zone around the tunnel,
B: the span of the tunnel,
γ: the unit weight of overburden,
C: the correction factor for horizontal to vertical
field stress ratio (k), and
S: correction factor for squeeze and non-squeeze
ground condition.
3.2.
Support pressure
Few empirical approaches for estimating support
pressure have been found to contain more
dominant geotechnical parameters [1]. Most have
limitations in their usage .Having realized the
inadequacies of existing approaches, an attempt
has been made to develop a more comparative
approach to estimate the support pressure for
tunnels [1].
The proposed empirical function is purely defined
as:
6010
16
15
14
13
12
11
10
8
9
17
18
19
20
21
22
23
24
25
26
27
01234567891012 11131516 14
7
6
DISINTEGRATED / DECOMPOSED
*Poorly interlocked, heavily broken rock
mass with a mixture or angular and
rounded rock pieces.
*Weak rock mass as a result of intense
jointing or because of low strength of
rock material itself. *Very highly weathered.
CLASS 8
BSTR 3 / 4 / 5
RQD < 20
RQD=0
BSTR 1 / 2
CLASS 9
*Tectonically sheared extremely weak rock
indicating broken structure; prevails over
any other discontinuity set resulting in
complete lack of blockiness.
*Tectonically deformed, intensively folded/
Faulted, sheared with chaotic structure of
broken rock mass. *Presence of clay minerals.
*Advance degree of weathering.
*Tectonic fatigue and sheared discontinuities,
often resulting in a soil-like material.
FOLIATED / LAMINATED / SHEARED
Detemination of Modified GSI-Index
For Poor and Very Poor Rock Mass
POOR
VERY POOR
without filling
with filling
ICR<25
ICR<25
JOINT CONDITION INDEX
SR
Jv
λ
BlockVolume, Vb (cm )
3
100
1
0.1
0cm
1cm
3cm
56
Sj
29x10
3
35
100
20
0
SR: Structure Ratio
Jv: Volumetric Joint Count (#/m )
λ: Joint Frequency (#/m)
Sj: Joint Spacing (cm)
3
BSTR 1
BSTR 2 BSTR 3 BSTR 4 BSTR 5
Numbers shown on diagonal lines indicate the GSI values vary between 6 and 27.
Figure 3. Determination of Modified GSI-Index for poor and very poor rock mass
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20
Span B(m)
Rock Loads (Support pressure) per unit length of tunnel P (Mpa/m)
D=0
s
s
ci =100 Mpa
s=1
S=1
C=1
g =0.0251 MN/
m3
GSI=10
GSI=30
GSI=50
GSI=70
GSI=90
),,,,,,( SCBDGSIfP
cr
γ
σ
≈
(4)
As indicated by the foregoing support pressure
function, nearly all influentially geotechnical
parameters are taken into consideration. Similar to
its previous counterpart developed by Ünal [10],
this newly proposed approach has as it’s the main
advantage the fact that the quality of rock mass is
considered as the GSI-Index. Due to its accepted
applicability in poor rock mass, the GSI-Index was
chosen to show the rock mass quality as explained
previously.
It makes it possible to estimate the support
pressure for poor rock masses as long as the
Modified GSI-Index is used. It is, therefore,
preferred that the new empirical approach be
applied to a wide spectrum of rock mass, the
quality ranging from very good to very poor.
The new empirical equation, which was proposed
based upon geotechnical parameters, is shown in
Equation (5).
BCS
GSI
D
P
cr
γ
σ
100
100
)
2
1(100
−−
= (5)
where
cicr
s
σ
σ
.
=
0<s<1
s: post-peak strength reduction factor
characterizing the brittleness of the rock material.
The most common form of the expression can be
written when s=1 as shown in Equation (6):
t
ci
hBCS
GSI
D
P
γγ
σ
=
−−
=
100
100
)
2
1(100
(6)
The rock load per unit length of tunnel can also be
expressed as shown in Equation (7).
2
100
100
)
2
1(100
BCS
GSI
D
P
ci
γ
σ
−−
= (7)
Figure 4. The variation of support pressure as a function of roof span in different rock class
The variation of the support pressure per unit
length of tunnel with tunnel span for different
quality of rock mass is demonstrated in Figure 4.
3.3.
Parameters used in calculating support
pressure
i)
The effect of the disturbance factor “D”
The method of construction has a significant
influence on support pressure. Conventional
excavation methods (drill & blast) cause damage
to the rock mass whereas controlled blasting and
machine tunneling (TBM) keep the rock mass
undisturbed. Singh et al. [13, 16] declared that
support pressure could be decreased up to 20% for
cases such as these. In the newly proposed
empirical approach, this effect was adopted from
that pointed out by Hoek et al. [22].
In tunnels, the effects of heavy blast damage as
well as stress relief (relaxation) as a result of the
ground being unloaded cause a disturbance in the
rock mass. The disturbance factor “D” varies
between 0 and 1 for undisturbed and disturbed
rock mass, respectively. Results indicate that for
the same properties of rock mass and opening,
support pressure increases as the disturbance
factor decreases. For example, in a rock mass
having a GSI of 50, the support pressure being
imposed on the tunnel can be as much as 40 % if a
blasting operation is carried out very poorly (D
=1).
A guideline for choosing the disturbance factor is
given in Table 2. Note that these are guidelines
only and the reader would be well advised to apply
the given values with caution. However, they can
be used to provide a realistic starting point for any
Table 2. Suggested value for Disturbance factor “ D”
Description of rock mass Suggested value of D
Excellent quality controlled blasting or
excavation by Tunnel Boring Machine
results in minimal disturbance to the
confined rock mass surrounding a tunnel.
D=0
Mechanical or hand excavation in poor
quality rock masses (no blasting) results in
minimal disturbance to the surrounding rock
mass
D=0
Usual blasting that causes local damages D= 0.5
In mechanical excavation where squeezing
problems result in significant floor heave
unless a proper invert is placed
D=0.5
Very poor quality blasting in tunnel results in
severe damages, extending 2 or 3 m, in the
surrounding rock mass
D=0.8
Very poor quality blasting along with a
intensive squeezing ground condition in
tunnel - unexpectedly heavy blasting in
caverns leading to significant cracks
propagation on roof and walls
D=1
design and, if the observed or measured
performance of the excavation turns out to be
better than predicted, the disturbance factor can be
reduced.
ii)
The effect of intact rock strength
Seeing how the broken zone extension around an
underground opening is dependent on the strength
parameters of the rock, it is suggested that the
compressive strength of 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
behavior of the rock. It is also substantiated that
the extension of the broken zone relies on the
residual value of the intact rock mass strength [23,
24, 25, and 26]. Hence, the effect of the
compressive strength of 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
must, therefore, be considered as:
cicr
s
σ
σ
.
=
(8)
where s refers to the strength loss parameter
quantifying the jump in strength from the intact
condition to residual condition. The parameter s
characterizes the brittleness of the rock material:
ductile, softening, and brittle. By definition, s will
fall within the range 0<s<1. Where s= 1 implies no
loss of strength and the rock material is ductile, or
perfectly plastic. By contrast, if s=0, the rock is
brittle (elasto-brittle plastic) with the minimum
possible value for the residual strength (i.e.
σ
1
=σ
3
).
iii)
Correction factor for squeezing ground
condition “S”
There as been a recent interest in tunnels which
have undergone large deformation. The cause of
great deformation of tunnels is said to be due to
the yielding of intact rock under a redistribution
state of stress following excavation which exceeds
the rock’s strength. If this deformation takes place
gradually it is termed as squeezing [27].
Squeezing of rock is time dependent large
deformation which occurs around the tunnel and is
essentially associated with creep caused by
exceeding the shear stress limit. Deformation may
cease during construction or continue over a long
time period [28]. Squeezing can occur in both
rock and soil as long as the particular combination
of induced stress and material properties pushes
some zones around the tunnel beyond the shear
stress limit at which creep starts. The magnitude of
tunnel convergence associated with squeezing, the
rate of deformation, and the extent of the yielding
zone around the tunnel depend on the geological
conditions, the in-situ stresses relative to rock
mass strength, the ground water flow and pore
pressure and the rock mass properties [29].
Owing to the fact that almost all tunneling
operations in weak rock mass withstand squeezing
ground condition, it is of paramount importance to
take this effect into consideration in precisely
estimating the support pressure [1].
The squeezing degree has been expressed in terms
of normalized tunnel convergence (closure)
[13,16], normalized convergence ratio [25],
competency factor or strength factor [30,15], and
critical strain concept [30]. Since the tunnel
convergence is an important indicator of tunnel
stability, the squeezing behavior has been
evaluated in terms of tunnel convergence in the
current study.
The guideline for squeeze correction factor
presented herein was adopted from the results of
many case-histories throughout the whole world
[12, 13, 14, 15, 16, 27, 29, 30] as given in Table 3.
Table 3. Suggested values for squeezing ground condition
factor (S)
Strains %
(Tunnel closure or
convergence/
tunnel diameter
)*100
Rock mass
strength/In-situ
stress
(
σ
cm / Po)
Suggested correction
factor "S" for
squeezing ground
condition
Less than 1%
no squeezing
> 0.5 1
1- 2,5
minor squeezing
0.3-0.5 1.5
2,5 -5
severe squeezing
0.2-0.3 0.8
5- 10,0 very
severe squeezing
0.15-0.2 1.6
More than 10
extreme
squeezing
< 0.15 1.8
The design of the tunnel is dominated by face stability issues and ,
while two-dimensional finite analysis are generally carried out,
some estimates of the effects of forepolling and face reinforcement
are required.
Severe face instability as well as squeezing of the tunnel make this
an extremely difficult three-dimensional problem for which no
effective design methods are currently available. Most solutions are
based on experience.
Remarks
Few stability problems and very simple tunnel support design
methods can be used. Tunnel support recommendations based upon
rock mass classifications provide an adequate basis for design.
Convergence confinement methods are used to predict the
formation of a plastic zone in the rock mass surrounding a tunnel
and of the interaction between the progressive development of this
zone and different types of support.
Two- dimensional finite element analysis, incorporating support
elements and excavation sequence, is normally used for this type of
problem. Face stability is generally not a major problem.
iv)
Correction factor for horizontal to vertical
stress ratio “k”
Detailed information about this factor is given in
section 4.3.
4.
ANALYTICAL AND NUMERICAL
APPROACHES FOR ROCK-LOAD HEIGHT
ESTIMATION
When an opening is being excavated, the
excavation removes the boundary stress around
the circumference of the opening, and the process
may be simulated by gradually reducing the
internal support pressure. As support pressure is
reduced, a plastic zone forms when the material is
overstressed. This region of the rock mass in the
plastic state is called the plastic zone (broken zone
or yielding zone or overstressed zone), which may
propagate in the course of tunnel excavation. The
configuration of the plastic zone around a tunnel
may depend on a number of factors such as the
anisotropy in initial stress state, the tunnel’s shape,
and the rock mass properties and so on.
Note that from this point on, the failure zone
above the tunnel span will be called “rock-load
height” and “failure height” when estimated by the
proposed empirical method and analytical or
numerical methods, respectively.
The primary objectives of the analytical and
numerical analyses carried out in this study are as
follows:
To determine the extent of the failure zone
(failure height) around various tunnel
shapes
To investigate the effect of rock mass
quality “GSI”, roof span “B”, and
anisotropy in field stress on failure zone
To compare rock–load height (h
t
),
calculated by proposed empirical approach
with failure height (h
f
) determined by the
analytical and numerical studies.
To find the correction factor for horizontal
to vertical stress ratio “k”
4.1.
Comparison of the rock-load height
obtained from proposed empirical approach
with that determined by closed-form
solutions
For circular tunnels, in order to compare the
analytically calculated failure height and
empirically obtained rock-load height in an
analogous manner [i.e. the radius of the plastic
zone and rock load-height can be regarded as the
same], the radius of plastic zone is called
Equivalent Rock-load Height “ERH”. Note that
Equivalent Rock-load Height is only in the case of
the axi-symmetrical condition of a circular tunnel.
In this case, an axi-symmetrical plastic zone,
which looks like a circular ring, can exist only
when the stress ratio (k) is equal to 1. As the stress
ratio (k) departs from one, the plastic zone
becomes more and more like an elliptical ring and
the region of the plastic zone expands in the
direction of the small initial stress component.
These findings have been also reported by Pan &
Chen [31].
In this part, the rock-load height of the proposed
empirical approach is compared with equivalent
rock-load height gained from available elasto-
plastic methods [23, 25, 26, 31, 32, 33, 34, 35, and
36]. Figure 5 shows the results of the comparison
between the Equivalent Rock-load Height of
closed-form solutions and that of the proposed
empirical approach for various types of rock mass.
As can be inferred, rock-load height obtained from
the proposed empirical approach is quite
compatible with the analytically obtained
equivalent rock-load heights. It should at this point
be noted that some approaches (indicated by
indices R in Fig. 5), result in higher values of
equivalent rock-load height for the same quality of
rock mass. This is due to the effect of the residual
parameters included in their analyses. In such
analyses, the post-peak response of the rock mass
around the tunnel is taken into consideration, i.e.
in the broken zone the rock mass constants are
given residual (ultimate) values.
Figure 5. The relationship between Equivalent Rock-load Heights (ERH) or radius of plastic zone obtained from existing closed-
form solutions and GSI. The proposed empirical approach indicates a good agreement. Note that the Index R indicates that in some
solutions the residual strength parameters were taken into consideration.
0
2
4
6
8
10
12
14
0 102030405060708090100
Geological Strength Index (GSI)
Equivalent Rock-load Height (ERH) or radius of plastic zone (m
Duncan Fama 93
Detournay 1988-Senseny
1989
Pan & Chen 1990-
Florence & Schwer 1978
Indraratna & Kaiser 1990
Ogawa & Lo 1987
Hoek & Brown 1980-
Ladanyi 1974
Carranza- Torres 1999
Carranza-Torres 2004
Hoek & Brown 1980 R.
Indraratna & Kaiser 1990
R.
Ogawa & Lo R.
Proposed Empirical
Approach
Proposed Empirical Approach
Radius of the Tunnel = 2.5m
Far field stress=7.5 Mpa
Unit weight of rock mass=0.025MN/m3
D=0
C=1
S=1
mi=10
σci=50 Mpa
4.2. Comparison of the rock-load height obtained
from the proposed empirical approach with
that determined by numerical methods for
arch-shaped and rectangular tunnels
Numerical methods are capable of modeling and
analyzing non-circular tunnels in an anisotropic
field of stress. Provided that the input properties are
sufficiently realistic, an elasto-plastic finite element
analysis of broken rock may perhaps leads to the
estimation of a reliable failure height. Accordingly,
in order to determine the extent of the failure zone
(plastic zone) developing around non-circular
tunnels due to stress release, a Finite Element
Analysis (FEA) has been utilized in this part.
In addition, the effects of a number of parameters
(i.e., shape of tunnel, rock mass quality, roof span,
and anisotropy in field stress) to the extent of failure
height were examined. For this purpose, rock
masses ranging in quality were selected (GSI= 20,
45, and 85) to stimulate the very poor, fair, and
good quality rock masses, respectively.
Furthermore, the tunnels with arch-shaped and
rectangular sections having spans of 5m, 10m, and
15m were examined in a state of field stress with
stress ratio “k” varying between a minimum of 0.3
and a maximum of 2.5. The rock-load heights,
estimated by the newly proposed empirical
approach were then compared to the failure heights
determined from the finite element analysis and a
satisfactory agreement was obtained. The
specifications of the selected numerical analysis and
its results analysis have been discussed in greater
detail elsewhere [1].
The last but most significant objective of the
numerical analysis was to determine the stress
correction factor used for the proposed empirical
formula. Let
“h
t
”: the rock-load height of the proposed
expression , and
“h
f
”: the failure height of numerical analysis.
Seeing that the effect of the stress ratio is taken into
account in the numerical modeling, the ratio of h
f
/h
t
is called the stress correction factor “C”, whose
value can then be multiplied in the empirical
formula to correct the stress effect.
4.3.
Correction factor for horizontal to vertical
stress ratio
Finite element analysis of broken zone around the
tunnel implied that the extension of failure height
above tunnels is dependent 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 k changes 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.
The ratio of the failure height (obtained from
numerical methods) to rock-load height (determined
by the proposed formula) yields a value called the
stress correction factor “C”. This correction factor
has to be applied while using Equations 3 and 5.
However; findings indicated that for a wide variety
of k values, the rock-load height form an upper limit
to the data points obtained from analytical and
numerical studies. In other words, the ratio of h
f
to
h
t
in most cases is less than 1. For reliability, the
minimum C for the proposed formula is always
suggested as 1 for k=0.5. Figure 6 aims at choosing
the stress correction factor.
It should be noted that the horizontal dotted line in
the figure shows the limit where the failure height,
obtained from the numerical modeling, is equal to
the rock-load height.
5.
THE ROCK REINFORCEMENT DESIGN
APPLIED TO NO: 7 MALATYA RAILROAD
TUNNEL
No: 7 Malatya railroad tunnel, situated in the South
-Eastern part of Turkey, was excavated through the
toe of a paleo-landslide material in 1930. Ever
since, the horseshoe shaped tunnel 5 meters wide
and 6 meters high has struggled with severe
squeezing ground conditions. Due to the fact that
the stress has exceeded the strength of such a poor
rock mass over the years, and the periodic effect of
surface and underground water, a large amount of
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
0 0,5 1 1,5 2 2,5 3
Horizontal to vertical stress ratio (
k
)
C=hf/ht
0.3
Figure 6. Suggested value for stress correction factor
used in proposed formula
deformation (170cm) has developed, resulting in the
tunnel being misaligned as well as causing
inadequate support conditions in the tunnel. A
detailed site characterization and reinforcement
design of the tunnel has been published elsewhere
[21]. Here, we intended to use the proposed
empirical approach as a preliminary integrated
design- approach for a reinforcement system. The
design stages of the rock reinforcement procedure
are summarized in the following.
5.1.
Rock mass characterization
The rock mass surrounding the Malatya No: 7
tunnel is composed of very poor rocks such as
metasiltstone, clayey and silty sandstone, shale and
phyllite. The core specimens taken from 67
boreholes were evaluated in classifying the rock
mass according to the M-RMR system [7] and Q-
system [9], and in determining the Modified GSI-
Index.
Worked example:
BSTR = 2 for the rock mass considered ( Figures 1
and 2)
Joint Condition Index for completely weathered
rock mass I
jc
= 2+ (2/2) +4=7 (Table 1)
Modified GSI-Index = 13 -15 (Figure 3)
5.2.
Support pressure (rock load) estimation
The expected rock-load height and support pressure
were determined using the proposed empirical
approach as follows:
mh
t
25.1056.13.1
100
14
100
1
)
2
0
1(100
=×××
×−−
=
where:
D=0 (Table 2) S=1.6 (Table 3)
C=1.3 (Figure 6) σ
ci
=1 MPa
MPamhP
m
MN
t
2255.0022.025.10
3
=×=⋅=
γ
where γ
rock mass
=0.022 MN/m
3
5.3.
Rock reinforcement design
These days, rock-bolting is used in almost all types
of underground structures due to its performance,
cost-effectiveness, and safety. For the Malatya
tunnel, MAI-bolts, which are self-driving full
column cement-grouted bolts, were chosen to be the
most suitable for the poor quality rock mass because
drill holes usually close before the bolt has been
installed, and the injection operation associated with
rock-bolting make the ground better in terms of
engineering parameters like strength, modulus of
deformation, and Hoek-Brown constants. In other
words, since the extent of yielding or broken zone is
directly related to the material properties, any
improvement of the strength and frictional
parameters must reduce the extent of overstressed
rock. The MAI-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 [25].
In order to obtain the optimum rock-bolting pattern,
the proposed empirical formula was incorporated
with the closed-form solution of rock-bolt design
undertaken by Osgoui [1]. The bolt density
parameter
β
, which reflects the relative density of
bolts with respect to the tunnel parameter and the
convergence reduction of the tunnel walls, can be
expressed as follows [1]:
b
C
BdP
λ
π
β
=
(9)
where,
P= support pressure, d= bolt diameter,
λ=friction factor for bolt/ground interaction relates
the mobilized shear stress acting on the grouted bolt
to the stress acting normal to the bolt,
B= tunnel
span or radius,
C
b
= yield load capacity of bolt.
Using MAI-bolts having diameter of
32mm and
yield capacity of
280 kN; respectively, the value of
β was obtained as:
2024.0
280
5.2133232255.0
=
××
−
×
×
=
ee
π
β
The obtained bolt density implied that a design with
high bolt density had to be carried out to control and
reduce the convergence of the tunnel. For a very
high bolt density (β=0.3), a convergence reduction
of about 60% has been reported by Indraratna and
Kaiser [25].
The bolt spacings were then calculated by the
following [1]:
β
λπ
ad
s =
(10)
For the same data,
ms 1.1= or mmss
lt
1.11.1
×
=× for a square
pattern ( s
t
,s
l
= circumferential and longitudinal
bolt spacing, respectively)
In order to sustain minimal yielding around the
tunnel, the bolt has to be long enough to ensure that
the neutral point of the bolt is located out side the
broken zone [1]. However, Ünal [10, 11] has
recommended that the rock-bolt length be at least
half of the rock-load height. Details about bolt-
length calculation are given by Osgoui [1].
6.
CONCLUSIONS
The method for estimating GSI-Index for poor and
very poor rock mass has been presented. This
resulting approach adds quantitative measures to
render the system more objective.
Using the concept of rock-load height and a
Modified GSI-Index, a convincing approach to
estimate the support pressure (rock load) for tunnels
has been developed. Not only does the proposed
approach take into account the rock mass quality
and quantity, but it also takes into account the
squeezing ground condition and anisotropy in field
stress.
The rock–load heights of the proposed approach
have been compared with failure height of
analytical methods (closed-form solutions).
Although those closed-form solutions are restricted
with circular tunnels, the results represent a
reasonable compatibility.
Numerical analyses were carried out so as to be able
to determine the failure heights for non-circular
tunnels and to compare the rock-load heights and
failure heights. The differences between rock-load
height and failure height give rise to stress
correction factor being used in estimating support
pressure. The proposed approach can also be
considered as an integrated approach to support
design. To be more precise, a sequential procedure
of rock-bolt design for No: 7 railway tunnel, which
was excavated through extremely weak rock mass,
has been presented.
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