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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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