support pressure assessment in arched underground openings through poor rock masses

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E L S E V I E R Engineering Geology 48 (1997) 59-81

ENGINEERING GEOLOGY

Support pressure assessment in arched underground openings through poor rock masses

B h a w a n i S i n g h a, R . K . G o e l b , . , J .L . J e t h w a c, A . K . D u b e b

a Department o f Civil Engineering, University ofRoorkee, Roorkee 247 667, India b CMRIRegional Centre, CBRI Campus, Roorkee 247 667, India

c CMRI Regional Centre, 54 B Shankar Nagar, Nagpur 440 010, India

Received 30 May 1996; received in revised form 13 February 1997; accepted 13 February 1997

Abstract

Himalayan tunnels provide challenging opportunities for working on the problem of assessment of support pressure in tunnels. A resume of the efforts by Indian researchers on this topic is presented in this paper, with a brief review and comparison with the approaches of Bieniawski (1979) and Barton et al. (1974; Analysis of Rock Mass Quality and Support Practice in Tunnelling, and a Guide for Estimating Support Requirements, Report by NGI, June). It is noted that Goel's classification of tunnelling conditions (Goel, 1994; Correlations for Predicting Support Pressures and Closures in tunnels. Ph.D. Thesis, Nagpur University, India, p. 308) is complementary to the Q-system. Contrary to Terzaghi's theory, support pressures are observed to be independent of opening size. © 1997 Elsevier Science B.V.

Keywords: Classification; Pressure; Tunnel; Squeezing; Supports; Weak rocks

1. Introduction

Reliable prediction of tunnel support pressure is a difficult task. Starting with Terzaghi's rock load concept (Terzaghi, 1946), several classification systems have been developed for estimating tunnel support pressures. Most of these systems classify tunnelling conditions into several distinctly different groups and correlate these groups with stable support capacities.

In fact, the quantitative classification approach serves as the only practical basis for the design of complex underground structures on many projects

* Corresponding author. Tel. : +91 1332 72196 (0)/73720 (R); FAX: +91 1332 75998.

0013-7952/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0013-7952 (97)00019-7

(Bieniawski, 1984). The construction engineers and the geologists generally prefer the empirical approaches over the theoretical and the numerical approaches mainly due to their simplicity. However, no classification has found universal acceptance because none has been adequately backed by measured tunnel support pressures. Thus, the degree of uncertainty in any of the classification systems is not known.

This paper presents the state-of-art on assessment of support pressure on the basis of Indian tunnelling experience of over 20 years in more than 60 instrumented tunnel sections in the Himalayas and in other parts of the country, and also experiences of the Norwegian Geotechnical Institute (NGI) .

60 B. Sinjzh el al. EngineermL, Geo/@,,y 48 t 1997~ 5~ ,W

Approaches for assessment of support pressure vary with the ground conditions and, therefore, firstly an approach for the assessment of ground conditions is presented for arched underground openings.

2. Prediction of ground conditions for tunnelling

It is known that tunnelling through squeezing ground conditions is relatively slow and problem- atic because the rock mass around the opening fails and looses its inherent strength under the influence of cover pressure. Underground excavation, under such conditions, may mobilise high support pressures. Tunnelling under non-squeezing ground conditions, on the other hand, is compara- tively easy because the inherent strength of the rock mass is not lost. Therefore, an advance knowledge of the ground conditions (squeezing or non- squeezing) plays an important role in designing the support system and for obtaining a good advance rate.

Non-squeezing ground conditions are common in the majority of tunnelling projects. Squeezing ground conditions, on the other hand, have generally been encountered during tunnelling through the lower Himalayas in India, where the rock masses are weak, highly jointed, faulted, folded and tectonically disturbed and the overburden is high. The combination of the weak rock mass and the high in-situ stress is responsible for squeezing. Various ground conditions generally encountered in tunnelling are given in Table 1. In this paper approaches for predicting the self-supporting, non- squeezing and squeezing ground conditions are discussed.

Various approaches developed so far can be grouped broadly into two categories as follows: ( 1 ) the theoretical approach, and (2) the empirical approach.

2.1. The theoretical approach

The squeezing conditions around a tunnel opening are encountered if,

ao > q . . . . . . ( 1 )

where or0 is the tangential stress and q,. mass is the uniaxial compressive strength of the rock mass. Eq. (1) can be written as follows lbr a circular tunnel under hydrostatic stress field

2P > q . . . . . . . ( 2 )

where P is the magnitude of in-situ stress and approximately equal to the overburden pressure.

Use of Eq. (2) for predicting the squeezing ground condition poses practical difficulties as the measurement of the in-situ stress and determination of the mobilized compressive strength of the rock mass are both time consuming and expensive.

The research group of Prof. Jiri Nedoma has studied in-situ stresses due to interaction between tectonic plates in North-East Himalaya (Nedoma, 1996). Their study shows that there are compression zones in the lower and upper Himalayas causing high horizontal stresses resulting into the uplift of mountains. The high in-situ stresses in younger and weak rock masses in the lower Himalayas has caused a high degree of squeezing in tunnels. Research by Prof. Nedoma (1996) has shown that compression zones exist at upper plate boundaries. Such proposed empirical correlations (Table 2) may be applicable for tunnels in other mountain ranges.

The above research may also explain the horizontal stresses near surface in the undergoing tectonic plate reducing due to downward plate bending. Therefore the chances of squeezing may be less at shallower depths, and the suggested correlations may not be applicable in such ten- sion zones.

2.2. Empirical approaches for arched underground openings

The philosophy of empirical approaches, based on the classification systems, is that a maximum overall rating suggests that all the parameters are favourable and, similarly, a minimum rating indi- cates that all the parameters are unfavourable. Moreover, the role of each parameter increases as rock mass condition or situation tends to be poorer. These are probably the reasons why classification systems have proved successful and, there- tore, became popular all over the world.

B. Singh et al. / Engineering Geology 48 (1997) 59-81 61

Table 1 Classification of ground conditions

Sr. no. Ground Sub-class Rock behaviour classification

1 Elastic Self-supporting

Non-squeezing

2 Ravelling

3 Squeezing

4 Swelling

5 Running 6 Flowing

7 Rock burst

Mild squeezing (u/a = 1-3%) Moderate squeezing (u/a = 3 5%) High squeezing (u/a > 5%)

Massive or competent rock mass requiring no support for tunnel stability Massive and competent rock mass requiring supports for tunnel stability Chunks or flakes of rock mass begin to drop out of the arch or walls due to loosening, sometimes after the rock mass is excavted Rock mass squeezes plastically into the tunnel. Rate of squeeze depends upon the degree of overstress. Occurs at shallow depths in weak rock masses like clay (after Singh et al., 1973), etc. Hard rock masses under high cover may move in combination of ravelling of face and squeezing behind the face. Rock mass absorbs water, increases in volume and expands slowly into the tunnel, e.g., montmorillonite clay. Granular material becomes unstable when exposed to steeper slopes. A mixture of soil-like material and water flows into the tunnel. The material can flow from invert as well as from the face, crown, and wall and can flow for large distances completely filling the tunnel in some cases. A violent failure in hard and massive rock masses when subjected to high overstress.

u = radial tunnel closure; a = tunnel radius.

Table 2 Prediction of ground conditions using rock mass number N (after Goel et al., 1995)

Sr. no. Ground conditions Correlations

1 Self-supporting 2 Non-squeezing 3 Mild squeezing 4 Moderate squeezing 5 High squeezing

H<23 .4N °'s8" B -°1 and 1000B -°'1 23.4NO.SS. B-O.l < H <275NO.33. B-O.~ 275N °'33. B -°1 < H < 450N °33. B o.1 450N0.33. B-0.t < H<630NO.33. B-O.1 H > 630NO.33. B-0.~

2.3. The approach of Singh et al. (1992)

Singh et al. (1992) proposed an empirical approach using Barton's rock mass quality Q and overburden H. Incidentally, a plot between these two parameters (Fig. 1) provided a clear-cut demarcation between the squeezing and the non- squeezing cases with the following equation for this line of demarcation

H = 3 5 0 Q °'33 (3)

where H = tunnel depth in metres; Q = rock mass quality (Barton et al., 1974) (Q=(RQD/J,)" (J,/Ja)" (Jw/SRF)); RQD = rock quality designa-

tion > 10 even if RQD=0; J ,=joint set number; J, =joint roughness number for critically oriented joints; Ja=joint alteration number for critically oriented joints; Jw =joint water reduction factor; and SRF = stress reduction factor.

In the lower Himalayas, RQD was found to be generally low (0-20%). However, according to Barton et al. (1974), a minimum value of 10 should be taken for RQD.

Eq.(3) suggests that a tunnel will experience squeezing ground conditions when H > 350Q°'33 m, Fig. 2 shows the plot between H/Q °'33 and uniaxial compressive strength (UCS) of rock material qc. It may be seen that there is

62 B. Singh et al. / Engineering Geology 48 (1997) 59-81

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o - MANERI BHALI PROJECT b - SALAL PROJECT c - TEHRI DAM PROJECT • - KOLARGOLD MINES f - CHIBRO KHODRI TUNNEL g - GIRl HYDEL TUNNEL h - LOKTAK HYDEL TUNNEL i - KH,I~RA HYDEL PROJECT

-159- BARTON'S CASE HISTORIES

xf

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Fig. 1. Criterion for predicting ground condition (after Singh et al., 1992).

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no effect of qc on criterion of squeezing ground conditions (Eq. (3)). Grimstad and Barton ( 1993, 1995) and Bhasin and Grimstad (1996) have also recommended this criterion.

2.4. Effect of thickness of the weak band on squeezing ground conditions

Limited experience along the 29-km long tunnel of the Nathpa-Jhakri project, H.P., India suggests that squeezing does not take place if the thickness of band of weak rock mass is less than 2Q °'4 m. However, more project data is needed for a better correlation.

2.5. Difficulties in estimating SRF

Although Eq. (3) is quick and easy to use in the field, the authors have experienced that estimating a correct value of SRF is difficult in some cases. Incorrect selection of SRF values may lead to

unreliable prediction. There are problems in obtaining a correct value of SRF near zones of weaknesses intersecting an excavation. Further, a large range of SRF values are suggested by Barton et al. (1974) when a shear zone only influences but does not intersect the excavation. For "competent rock masses" the determination of SRF is based on 0-1, 03, qc and q, values (where 0", and c~ 3 are major and minor principal stresses, qc is unconfined compressive strength, and qt is tensile strength of rock material ) and the suggested values of SRF have wide ranges. For "squeezing and swelling rock masses", it is practically difficult to even identify the category. Further it has been experienced that the SRF does not adequately represent the stress conditions of a rock mass, at least for the squeezing ground conditions in the Himalayas (Goel, 1994).

For example, two tunnels at depths from surface of 100 and 300 m, indicating different magnitudes of cover pressure, are being excavated through the


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e •

• • m ......

l • " U l n

• l

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Fig. 2. Plot between H/Q °'33 and UCS of rock material qc (H= overburden in metres).

same rock mass with, say, a single zone of weak- ness containing clay or chemically disintegrated rock. For both tunnels, the SRF value will be 2.5, because the depth of excavation is more than 50 m. This clearly shows that precise weightage to stress conditions is missing from SRF, thereby indicating inadequacy in the Q-system in the complex Himalayan region.

Grimstad and Barton (1993) have suggested to increase SRF to virtually (SRF) 2 for competent rock masses. Further research is under progress at NGI.

Because of these problems, an easy to use empirical approach for predicting ground conditions, developed by Goel et al. (1995), is presented below.

2.6. The approach of Goel et al. (1995)

The parameters selected for developing the empirical approach are: ( I ) rock mass number, N

N=(RQD/J,)(Jr/Ja)Jw (4)

definition of various parameters in Eq. (4) is the same as given in Eq. (3); (3) tunnel depth or rock cover above tunnel roof H in metres to account for in-situ stress condition; and (3) tunnel width B in metres for strength reduction of rock mass.

The squeezing ground conditions have been divided into three sub-classes using the approach of Singh et al. (1995b). These are: (i) mild squeezing-closure of 1-3% of tunnel size; (ii) moderate squeezing-closure of 3-5% of tunnel size; and (iii) high squeezing-closure of > 5% of tunnel size.

Tangential strain e0 is equal to the ratio of tunnel closure and diameter. If it exceeds the failure strain e I of the rock mass, squeezing will occur. It may be added that mild squeezing may not begin even if the closure is 1% and less than e I.

2. 7. Criteria for ground conditions

All the 98 data points are plotted on a log-log graph between rock mass number N and H . B °'1


and are shown in Fig. 3, wherein the various ground conditions have been demarcated by straight lines. The equations of these lines are given in Table 2. The tunnel depth H and the tunnel width B in the correlations of Table 2 are in metres. These correlations may be used reliably for predicting the ground conditions.

It is to be noted that equations given in Table 2 are valid for a tunnel depth of up to 800 m and a tunnel diameter or width of up to 12 m.

Table 2 is found to be complementary to the Q- system. Table 2 should be used first to predict the ground conditions, and then SRF may be estimated from the SRF table of the Q-system. Fig. 4 shows the plot between H - B ° ' I / N 0'33 and uniaxial compressive strength (UCS) of rock material qc. It may be seen in Fig. 4 that the criterion of squeezing in Table 2 is independent of q,..

3. Prediction of support pressure in tunnels

3.1. Non-squeezing and squeezing ground conditions

The predicted support pressures from the approaches of Terzaghi (1946), Deere et al. (1969), Barton et al. (1974) and Unal (1983) have been compared with the measured values of support pressures under both non-squeezing and squeezing ground conditions, see Figs. 5 and 6, respectively. It has been observed that none of the approaches are applicable under squeezing ground conditions, whereas the approach of Barton et al. (1974) provides a reasonable estimate of support pressure in non-squeezing ground conditions and for smaller tunnels under squeezing ground conditions.

113000

T--

o II1

1000

1017

Rock burst

/

Maximum recommended tunnel depth

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- . / •

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Rock Mass Number N

Self- supporting

10 i 0.01 100 1000

i ' • NON-SQUEEZING • SELF SUPPORTING • SQUEEZING (~) ROCK BURST

Fig. 3. Prediction of ground condit ions (after Goel et al., 1995; H = overburden in metres, B = tunnel width in metres and N = Q. SRF ).


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(

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n . I t *' Ncm- Squeezing ' u ' , . , • u 0

0 50 100 150 qe, MPa

Fig. 4. Plot between H. B°': /N °'33 and UCS of rock material qc (B=tunnel width in metres).

200

The reliability of quantitative classification systems for estimating tunnel support pressure has increased with the passage of time. The recent work in India on the development of correlations for predicting support pressures and experiences on the use of the Q-system of Barton et al. (1974) and the RMR-system of Bieniawski (1973) are presented in this paper.

3.2. Correlations o f Singh et al. (1992)

A stiffer tunnel support system undergoes smaller deformations and attracts higher support pressure. A flexible support system, on the other hand, permits greater deformations and attracts smaller pressure. The support stiffness is therefore an important parameter in any correlation for tunnel support pressure. Since steel arch supports with a variety of back-fills, such as tunnel muck, concrete blocks, lean concrete, etc., have been used in most of the tunnel test-sections, tunnel closure was considered to represent the influence of support stiffness.

Experience with the application of the Q-system in tunnelling under squeezing ground conditions has shown that the stress reduction factor SRF

does not adequately represent the squeezing effect probably due to lack of sufficient number of case histories. Therefore, tunnel depth was considered as an additional parameter to give adequate weightage to the in-situ stress. Finally, the "time factor" was introduced as the third parameter because tunnel closure and, therefore, the support pressure increases with time under squeezing conditions.

Considering the above three parameters, in addi- tion to the original six of the Q-system, Singh et al. (1992) proposed correction factors f, f ' and f " for tunnel depth, tunnel closure and time after supporting, respectively. They modified Barton's correlation for short-term support pressure as follows:

Pi = [0.2.( 5Q)-°'a3 /J,] " f " f ' " f " (MPa) (5)

The correction factor f for tunnel depth is same for both the non-squeezing and squeezing ground conditions and is given as

f = 1 + ( H - 320)/800 > 1 (6a)

in which H is the tunnel depth in metres. Eq. (6a) implies that the correction for tunnel depth should be applied only when the tunnel depth exceeds

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68 R S&gh et al. / Engineering Geology 48 (1997) 59 81

320m. Grimstad and Barton (1993, 1995) have accepted a proposed correction factor for overburden also. Experiences in Himalayan tunnels suggest that f adequately accounts for the stress conditions for both non-squeezing and squeezing ground conditions. Therefore, there is no need for using increased SRF values as suggested by Grimstad and Barton (1993).

The correction factor f ' for tunnel closure after Singh et al. (1992) is given as

jr', = P o b s d / f " Pi ( 6b )

where, p~ = short-term support pressure of Barton et al. (1974) (pi=O.2(5Q)-°33/jr) in MPa.

The variation of Pobsa/J"Pi was plotted against normalized tunnel closure (u,,/a) in Figs. 7(a) and 7(b) to obtain roof and wall correction factors, i.e., froof and f ' au , respectively. The normalized tunnel closure is the ratio of tunnel closure and tunnel width expressed in percent. It may be seen in Fig. 7 that values off'roof and fwaU are almost equal and, therefore, both are denoted as f" and presented in Table 3. It can be seen that f ' was higher for low tunnel closure. It decreased grad- ually with rise in tunnel closures and attained a minimum value at 5% normalized closure. However, the correction factor f ' again increased when the normalized closure exceeded 6%. The cause of rapid increase in support pressure is the onset of sympathetic failure within the broken zone. Thus, it may be noted that the curves for f ' in Figs. 7(a) and 7(b) represent normalized ground

response curves for the squeezing ground conditions.

3.3. Effect of tunnel size on support pressure in non- squeezing ground conditions

Singh et al. (1992) have studied the effect of tunnel size on support pressure. Fig. 8 shows the variation of normalized roof support pressure pobsd/p . f . f , . f , , with the width of tunnel opening (2a or B). The ordinate represents the normalized observed roof support pressure corrected for the overburden, the tunnel closure and the time after excavation. It may be seen in Fig. 8 that the support pressure is independent of tunnel size and between 2 and 22 m.

It may be noted that rock mass quality Q estimated from a larger tunnel would be smaller than that obtained from small drifts in a similar rock mass. This is due to the possibility of intersecting more geological discontinuities and intrusions in a larger opening. So, in a wider cavern, the range of Q values is observed to be larger and the geometrical mean value reduces with the size of cavern.

3.4. The Bhasin and Grimstad (1996) correlation Jbr squeezing ground conditions

Using the cases of Scandinavian tunnels and the data of Singh et al. (1992) and Goel et al. (1995),

Table 3 Correction factors)'" for tunnel closures (after Singh et al., 1992

Ground condition Support stiffness Tunnel closure Correction factor, f '

Non-squeezing Very stiff < 1 1.0 Squeezing Very stiff I 2 > 1.8 Squeezing Stiff 2 4 0.85 Squeezing Flexible 4 6 0.70 Squeezing Very flexible 6 8 1.75 Squeezing Extremely flexible > 8 1.80

Note: the correction factor for tunnel closure, f ' , does not take into account the method of excavation and construction. For large tunnels (dia .>9 m) under high squeezing ground conditions, full face excavation will not be possible and therefore heading and benching methods of excavation would have to be adopted. In heading and benching methods the tunnel wall closure would be excessive, and therefore the value o f / " would be very high.

7 0 B. Singh et al. ,' Engineering Geology 48 (1997) 59 81

(3,.

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] {

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D I A M E T E R OF O P E N I N G ,rn

Fig. 8. Support pressure v i r tual ly independent o f tunnel size (after Singh et al., 1992).

Q} Ul q~ ql

0 n.

• ,,4 $.4 ~ 0

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Bhasin and Grimstad (1996) suggested a new correlation for poor qualities of brecciated rock mass experiencing squeezing ground conditions (H> 350Q °'~3 or H. B °'l >275N °'33) as follows:

p =(40' B/Jr) Q-O.3S (kPa) (7)

where B is the span of the opening in metres. Eq. (7) suggests that the support pressure p

increases with the increase in tunnel span B for poor qualities of brecciated rock masses.

3.5. The modified rock load theory of Terzaghi

The rock load theory of Terzaghi (1946) and wedge theory show that support pressures are proportional to the tunnel size. Terzaghi's theory of arching for tunnelling through soils is not applicable for rock masses because rocks have pre- existing planes of weaknesses unlike soils. Theory of rigid rock wedges does not give realistic predic- tions, as the in-situ stress along the axis of tunnels and caverns pre-stress rock wedges. Only small wedges tend to fall down due to the blasting vibrations. If openings are supported well and timely, interlocking of rock blocks with rough and dilatant joints also arrests falling of the rock

blocks. Consequently, observed support pressures are not higher for wider arched openings in non- squeezing ground conditions. However, there is need for improvement in understanding the mechanics of rock mass.

It is, therefore, suggested that in-situ stress along the tunnel axis should be accounted for in the wedge analysis for the prediction of support pressures.

Recently Singh et al. (1995a) have compared support pressures measured from tunnels and caverns with estimates from Terzaghi's rock load concept. They found that the support pressure in rock tunnels and caverns does not increase directly with excavation size as assumed by Terzaghi (1946) and others due mainly to dilatant behaviour of rock masses, joint roughness and prevention of loosening of rock mass by improved and modern tunnelling technology. They have subsequently recommended modified ranges of support pressures as given in Table 4. However, the support pressure is likely to increase directly with the excavation width for tunnels through slickensided shear zones, thick clay filled fault gouges, weak clay shales and running or flowing ground conditions where interlocking of blocks is likely to be missing as in Terzaghi's trap door experiments.

Tab

le 4

R

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dati

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995a

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port

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zagh

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lass

ific

atio

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lass

ific

atio

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f S

ingh

et

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Cat

egor

y R

ock

cond

itio

ns

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ad

Cat

egor

y R

ock

cond

itio

n R

ecom

men

ded

supp

ort

pres

sure

(k

gcm

-2)

Rem

arks

fa

ctor

, H

p

Pv

Ph

1 H

ard

and

inta

ct

2 H

ard,

str

atif

ied

or s

chis

tose

3

Mas

sive

, m

oder

atel

y jo

inte

d 0-

0.5B

4

Mod

erat

ely

bloc

ky,

seam

y an

d jo

inte

d 5

Ver

y bl

ocky

and

se

amy,

sha

tter

ed

Com

plet

ely

crus

hed

but

chem

ical

ly

inta

ct

Sque

ezin

g ro

ck

at m

oder

ate

dept

h

8 Sq

ueez

ing

rock

at

grea

t de

pth

9 Sw

ellin

g ro

ck

0 1

Har

d an

d in

tact

0

0 0-

0.25

B

2 H

ard,

str

atif

ied

or

0.0-

0.4

0 sc

hist

ose

3 M

assi

ve,

mod

erat

ely

0.4-

0.7

0 jo

inte

d 0.

25-0

.35B

(B

+H

t)

4 M

oder

atel

y bl

ocky

, 0.

7 1.

0 0-

0.2p

v In

vert

s m

ay b

e se

amy,

ver

y jo

inte

d re

quir

ed

0.35

-1.1

(B

+H

t)

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ery

bloc

ky a

nd s

eam

y,

1.0-

2.0

0-0.

5pv

Inve

rts

may

be

shat

tere

d, h

ighl

y jo

inte

d,

requ

ired

, ar

ched

th

in s

hear

zon

e or

fau

lt

roo

f pr

efer

red

1.1

(B+

Ht)

6

Com

plet

ely

crus

hed

but

2.0-

3.0

0.3-

1pv

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rts

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ntia

l, ch

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ally

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lter

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thic

k ar

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of

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d fa

ult

zone

es

sent

ial

1.1

2.1

(B+

Hi)

7

Sque

ezin

g ro

ck c

ondi

tion

D

epen

ds o

n pr

imar

y In

vert

s es

sent

ial

stre

ss v

alue

s Ph

in

exc

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ion,

m

ay e

xcee

d Pv

ar

ched

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of

esse

ntai

l

2.1-

4.5

(B+

Ht)

(A)

Mil

d sq

ueez

ing

3.0-

4.0

(u/a

up

to 3

%)

(B)

Mod

erat

e sq

ueez

ing

4.0

6.0

(u/a

= 3

-5%

)

(C)

Hig

h sq

ueez

ing

6.0-

14.0

(u

/a>

5%)

up t

o 80

m

8 Sw

ellin

g ro

ck

Dep

ends

on

orie

ntat

ion

Inve

rts

esse

ntia

l ir

resp

ecti

ve

of

swel

ling

mat

eria

l, P

h in

exc

avat

ion,

o

f B

+ H

t m

ay e

xcee

d Pv

ar

ched

ro

of

esse

ntia

l (A

) M

ild

swel

ling

3.0

8.0

(B)

Mod

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g 8.

0-14

.0

(C)

Hig

h sw

ellin

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.0-2

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o

~

t.~

Pv =

ver

tical

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port

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ssur

e; P

h =

hor

izon

tal

supp

ort

pres

sure

; B

= w

idth

or

span

of o

peni

ng; H

t = h

eigh

t o

f op

enin

g; u

= r

adia

l tu

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sure

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= B

/2; t

hin

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r zon

e =

up

to

2 m

thi

ck.

72 B. Singh et al. / Engineering Geology 48 (1997) 59 81

3.6. Correlation with rock mass number N (after Goel et al., 1995)

tories pertaining to 9-m diameter sections from the Chhibro-Khodri tunnel.

Considering tunnel depth, tunnel span, tunnel closure and rock mass number N defined as stress- free Q (SRF = 1 ), the following set of correlations have been developed for predicting ultimate support pressure: ( 1 ) for non-squeezing conditions

P e l ( N ) = ( 0 . 1 1 H ° ' l B ° ' l / N ° ' 3 3 ) - 0 . 0 3 8 (MPa) (8)

and (2) for squeezing conditions

Psq(N) = [f(N)/30] [ 10 (H°'6B°~/53'5N°331] (MPa) (9)

where pe~(N)=ultimate support pressure in non- squeezing ground in MPa; psq(N)=ultimate support pressure in squeezing ground in MPa; f (N)= correction factor for tunnel closure (see Table 5); H=tunnel depth in metres; B=tunnel span in metres; and N=rock mass number given as (RQD" J," Jw)/(J," J~).

The variation o f f (N) was plotted against the normalised tunnel closure in Fig. 9 which has subsequently been used to prepare Table 5.

Estimated support pressures from Eqs. (8) and (9) for tunnel sections under non-squeezing and squeezing ground conditions have been compared with the measured values in Figs. 10(a) and 10(b), respectively. Eqs. (8) and (9) have good correlation coefficients of 0.95 and 0.97, respectively. It can be seen in Fig. 10(b) that Eq. (9) provides reliable support pressure values even for case his-

3. 7. Correlations with rock mass rating (RMR)

Goel and Jethwa ( 1991 ) have proposed a correlation for estimating the support pressure using Bieniawski's RMR. The advantage of this correlation is that it can be applied for both non-squeezing and squeezing ground conditions without an advance knowledge of the ground conditions. The correlation is as follows:

p = (7.5BO.1.//0.5 - RMR)/20RMR (MPa) (10)

where tunnel depth H and tunnel span B are in metres and support pressure p is in MPa.

3.8. Correlation with rock condition rating (RCR)

Considering tunnel depth, tunnel span, tunnel closure and rock condition rating RCR (parameter-wise equivalent to rock mass number N and defined as Bieniawski's RMR, free from ratings of joint orientation and crushing strength of rock mass), Goel (1994) suggested the following set of correlations for predicting ultimate tunnel support pressure: (1) for non-squeezing conditions

peI(RCR) =(46.6H°'15B°'1/RCR 1"98) (MPa) ( 11 )

Table 5 Correction factory(N) for tunnel closure

Sr. no. Degree of squeezing (using Table 2) Normalised tunnel closure (%) Correction factor, J (N)

Very mild squeezing I 2 270N °'33- B -°'1 < H < 3 6 0 N °33. B ol)

Mild squeezing 2 3 360N °33 .B - ° ' I < H < 4 5 0 N °'33.B 0.1~

Mild to moderate squeezing 3 4 450N °33. B o.1 <H<540NO.33. B o.1)

Moderate squeezing 4 5 540N °33. B 0.~ <H<630NO.33. B ol)

High squeezing 5 7 630N °33. B -°1 < H < 8 0 0 N 0"33. B o.1)

Very high squeezing > 7 800NO.33 • B o . l > H )

1.5

1.2

1.0

0.8

1.1

1.7

Note: normalised tunnel closure is defined as radial tunnel closure expressed in terms of percent of tunnel width.

B. Singh et al. / Engineering Geology 48 (1997) 59-81 7 3

I Z

w , .

u

,,,..

u

o

L..

t, ( J

2'5

2"0

1"5

I '0

0.=,

0"0 0

1 I 1 2 4 6 El

Norma l i sed funnel closure (44/a~ " / . ) "

Fig. 9. Correction factor for tunnel closure f(N) under squeezing ground conditions (after God et al., 1995).

and (2) for squeezing conditions

p~q (RCR) = [f(RCR)/30]

[10 (0.93.//0.6. BO.1/RCR 1.2)] (MPa) (12)

where, pel(RCR)=ultimate support pressure in non-squeezing ground in MPa using RCR; psq(RCR) = ultimate support pressure in squeezing ground in MPa using RCR; f (RCR)=correct ion factor for tunnel closure (see Table 6); H=tunnel depth in metres; and B = tunnel span in metres.

Table 6 has also been prepared by using the same method as for Table 5.

Estimated support pressures from Eqs. ( 11 ) and (12) for tunnel sections under non-squeezing and squeezing ground conditions have been compared with the measured values in Figs. 11 (a) and 11 (b), respectively. Figs. l l(a) and l l ( b ) show that Eqs. (11) and (12) have good correlation coefficients of 0.93 and 0.94, respectively.

For obtaining ultimate support pressure using Eqs.(8), (9), (11) and (12), the relationship between ultimate and short-term support pressures suggested in the later part of the paper may be adopted.

It can be seen that the two parameters, tunnel depth H and tunnel span B, have little influence on support pressure for tunnels under non-squeezing ground conditions (Eqs.(8) and (11)).

Although tunnel span B continues to have less influence on the support pressure under squeezing ground conditions (Eqs. (9) and (12)), the tunnel depth H has a significantly higher influence.

A rise in the value of correction factor f (N) for tunnel closures beyond 5% is attributed to the increase in the loosening pressure which is reflected in a rising "ground reaction curve" (Figs. 7 and 9). Tunnel closures should normally not be allowed to exceed 5% of the tunnel size. However, in cases of soft rock masses with depths exceeding 500 m it may be necessary to permit higher closures to bring down temporary support requirements to manageable levels for ease of supporting at the face which is necessary for faster drivage. Such higher tunnel closures will be associated with larger plastic zones which will be mobilising relatively higher ultimate support pressures requiring higher ultimate support capacities (Jethwa et al., 1981). In other words, attempts to reduce support requirements closer to a tunnel face will be associated with a thicker tunnel lining.

Effect of tunnel size on support pressure obtained by Goel et al. (1996) is presented in Table 7. In the case of squeezing ground conditions, Table 7 shows that the support pressure depends significantly upon the tunnel size. The reason is that tunnel closures were high in tunnels

74 B. Singh eta/. Engineering Geology 48 (1997) 59 81

015

0~0

g

~a. 005

(a)

0 0

.,o

1 3 / Non - Squeez in~ [

l o.. ._ J

f I 1

0 05 0 iO 015

P obtd . , M Po

t 2

O 8 g

z

C 4

0 0

9

4 6 C a l e l

t __ I,,~ r -" 0 9 7

0-4 0 8 12

(b) P ' ) b t d , MP0

Fig. 10. (a) Comparison of measured support pressures with estimated support pressure using Eq. (8) under non-squeezing ground conditions. (b) Comparison of measured support pressures with estimated support pressure using Eq. (9) under squeezing ground conditions.

larger than 6 m diameter due to heading and benching method of excavation. So there is size effect.

In squeezing ground conditions, steel rib supports failed by buckling leading to more closure.

However, buckled ribs became stable after some closure as the support pressure was also reduced with enlargement of broken zone (Fig. 13). Thus it was possible to re-use these tunnels by replacing failed ribs with new stiffer ribs one by one. It is

B. Singh et al. / Engineering Geology 48 (1997) 59-81

Table 6 Correction factorf(RCR) for tunnel closure

75

Sr. no. Degree of squeezing Normalised tunnel closure (%) f(RCR)

1 Very mild squeezing 1-2 2.0 2 Mild squeezing 2-3 1.7 3 Mild to moderate squeezing 3-4 1.2 4 Moderate squeezing 4-5 0.8 5 High squeezing 5-7 1.2 6 Very high squeezing >7 1.7

Note: normalised tunnel closure is defined as radial tunnel closure expressed as percent of tunnel radius.

essential that steel ribs must have inverted struts at the bottom to enable ribs to take very high wall support pressures. The recent trend, of course, is to use steel fibre-reinforced shotcrete and closely spaced rock bolts in the squeezing ground which should also form the complete ring.

3. 9. Elasto-plastic theory for squeezing ground conditions

Daemen (1975) suggested the following equation for obtaining short-term support pressure in the tunnels in squeezing ground

Pi = [e( 1 -- sin ~bp) - cp cos ~bp + c, cot ~b,]M,

- c, cot q~, +_ 7(b - a)M~ (13)

where, Pi = short-term support pressure; P = overburden pressure or cover pressure, cp and c ,=peak and residual cohesion values of rock mass, respectively; ~bp and ~br=peak and residual angle of internal friction, respectively; Jr and Ja = Barton's parameters; My = [a ( 1 - sin q~r)/(b - a) ( 1 - 3 sin ~br)]. [(a/b)~ -1 _ 1 ];

M~ = (a/b)'; ~ = (2 sin ~br)/( 1 - sin ~br); a = radius of tunnel opening; b=rad ius of broken zone (< 5a); 7=un i t weight of rock mass (g cc-~).

Jethwa (1981 ) extended Eq. (13) to account for face advance. He also found that a compaction zone of radius of about 0.37b is developed around support system within the broken zones.

The experience suggests that the strength parameters of rock mass may be estimated as follows for

rock mass with qc > 2 MPa, Jw = 1 and Q < 10.

q . . . . . = 7. ~. QI/3 (MPa, derived from Eq. (3))

(14a)

~bp = t a n - ' (J,/Ja) (14b)

cp =q . . . . . (1 - s i n ~bp)/2 cos ~bp (14c)

c, =0.1 MPa (14d)

~b r = ~v - 10 > 14 ° (14e)

Aydan et al. (1993) studied squeezing phenomena and its mechanics and also proposed a method of predicting the squeezing. They have also proposed a few correlations for estimating various engineering properties of rocks using uniaxial strength. The correlation for frictional angle ~bp (°) with qc (MPa) considering about 35 data points from laboratory tests is as follows:

~bp = 20- qO.25 > 10 o (15)

Fig. 12 shows the plot between uniaxial compressive strength (UCS) of rock material qc and Q0.33. It is interesting to note that Eq. (14a) is lower bound of the data points for various projects worldwide (qc>2 MPa) in Fig. 12. For massive rock masses, q~ mass tends to be nearly equal to q¢. It should be realised that very high strength is mobilized in the tunnels due to the constrained fracturing unlike slopes.

The strength enhancement in tunnels is due to pre-stressing of rock wedges, both in roof and walls, by the in-situ stress along the axis of tunnels and caverns. Constrained fracturing is another reason for higher strength. Whereas in slopes,


0 t 6

0'12

g ~E

g re

0'08

n

0-04

0 b

0

(a)

1'2

0"8

u n~ v

0.,I

O k

o

(b)

I Non - sques zln Colos g )

r = 0 .94 =7

B

= 4

44

6

s t 3 /

'L n 2

0-04 0 0 8

Pob.d, , MPo

0'12

I Squ ee zing I Cales

r = 0 '93

I 8 m u

7= s 3

1 1 1 1

0 4

~ob~d_ , MPo

I 1

0"0

0"16

10

12

B. Singh et al. / Eng&eering Geology 48 (1997) 59-81

Table 7 Effect of tunnel size on support pressure in arched roof underground openings (Goel et al., 1996)

77

Sr. no. Type of rock mass Rise in support pressure due to increase in tunnel size (%)

A. Arched roof opening 1 2 (a) (b)

B. Rectangular opening

Non-squeezing ground conditions <20 Squeezing ground conditions Fractured, jointed and weak rock masses (N=0.5 10) 20-60 Soft-plastic clays, running ground, flowing ground, clay-filled 100 joints, fault gouges, and slickensided shear zones (N=0.1-0.5)

100

i000

¢g

¢S

100

10

0.1 0.001

I : i B m

[]

J f

D ; B I l l • []

[] ee ~

II

B

[I IJ I~n [] i [ ] I j

I i

..-- '~Q "0.33

0.01 0.1 I0 R o c k Mass Qual i ty Q

B N o n - s q u e e z i n g . Squeez ing

Fig. 12. Plot between QO.33 and UCS of rock material qc.

100 1000

in-si tu stress is re leased and is negligible and, therefore, there is no enhancement o f strength. In the b lock shear test, also, in te rmedia te pr inc ipa l stress is negligible and these tests underes t ima te the cohesive s t rength o f the rock mass mobi l ized in tunnels. Thus, s t rength pa rame te r s suggested by Bieniawski (1973) are val id for slopes only. I t m a y also be men t ioned tha t in-si tu stress also increases

modu lus o f de fo rma t ion o f weak and jo in ted rock masses jus t like soil (Singh et al., 1997).

The res idual cohes ion cr is no t zero until tunnel c losure exceeds 6% of tunnel d iamete r due to sudden sympathe t i c fai lure o f rock mass within entire b roken zone (Fig . 13). Therefore , tunnel c losure should no t be a l lowed to exceed this l imit and suppor t s should not be instal led too late.

Fig. 11. (a) Comparison of measured support pressures with estimated support pressure using Eq. ( 11 ) under non-squeezing ground conditions. (b) Comparison of measured support pressures with estimated support pressure using Eq. (12) under squeezing ground conditions.

78 B. Singh et al. /' Engineering Geology 48 (1997) 59-81

.o

0

\ \ ............................ ]i::~- ........ -.

\ . . . . . . . . . . . . . . . . . ,~ .......... .~ ",

\ \ 2b 2rc 2a: ~ - - ~ :

~-- onset of sympathetic failure

Failure or broken zone

Compaction zone

(2re = 0.37.2 b)

Cr = 0

Cr~ 0

6%

tunnel closure

Fig. 13. Effect of sympathetic failure of rock mass on theoretical ground response curve of squeezing ground.

However, concrete lining should be done beyond a distance of 4b from the tunnel face so that tunnel closure is stabilised. It is thus suggested that a tunnel in highly squeezing ground conditions should be less than 6 m in size to allow full face tunnelling.

3.10. Prediction of support pressure Jor tunnels in swelling ground conditions

The difference between squeezing and swelling ground conditions is that, in the latter case, the tunnel wall closure is due to swelling of the rock mass on account of the presence of the minerals which are prone to swelling when it comes into contact with moisture. Barton et al. (1974) has given due attention for assessing the support in swelling ground conditions by considering the swelling conditions in SRF. However, its applicability could not yet be checked because of the lack of measured support pressure values under swelling ground conditions. Field tests and laboratory test should, therefore, be conducted for proper assess-

ment of swelling support pressures, respectively, for swelling rocks with swelling minerals. On the contrary, Terzaghi (1946) has recommended very high values of support pressure. Verman (1993) has suggested increase in support pressure due to post-construction saturation as follows:

Psat <[1 -(Esat/Edry)].),H (16)

where Esat = modulus of deformation of saturated rock mass; Edry =modulus of deformation of dry rock mass; and H = overburden in metres.

In a rock mass with water-sensitive minerals, Esat<<Edry and the support pressure may increase drastically after post-construction saturation around pressure tunnels and penstocks. More research is needed on the effect of saturation on support pressure.

3.11. Prediction of support pressure Jbr tunnel walls in non-squeezing ground conditions

Experiences have shown that the approach of Barton et al. (1974) gives too high values of the


wall support pressures. Measured values of wall support pressure are negligible in non-squeezing ground conditions (Singh et al., 1992).

3.12. Prediction o f support pressure for caverns

The caverns are generally designed through good rock masses, i.e., the ground conditions would be either self-supporting or non-squeezing. It has been experienced that, for assessment of roof and wall support pressures, the approaches of Barton et al. (1974) and Singh et al. (1992) are reliable. The approach of Goel et al. (1995) has been developed for tunnels of up to 12m and, therefore, its applicability for caverns with a diameter of more than 12 m is yet to be checked.

It may be noted that the reinforced rock wall column has a tendency to buckle due to tangential stress (Bazant et al., 1993), because of the possibility of a vertical crack propagation behind the reinforced rock wall. So the length of anchors/rock bolts should be adequate to prevent buckling and vertical crack propagation.

3.13. Prediction of support pressure in shear and weak zones

Rock mass classifications consider only the homogeneous units, and so downgrading the rock quality adjacent to shear zones may be difficult. It is envisaged that the rock mass affected by the shear zone is much larger than the shear zone itself. Hence, this rock mass must be downgraded to the quality of shear zone so that a heavier support system in relation to the regular one can be installed. A method has been developed at NGI (Norwegian Geotechnical Institute) for assessing support requirements using the Q-system for rock masses affected by shear zones (Grimstad and Barton, 1993). In this method, weak zones and the surrounding rock are allocated their respective Q value from which a mean Q value can be determined taking into consideration the breadth of weak zone. The following formula may be employed in calculating the mean Q value from the two Q values (after Bhasin et al., 1995)

log Qm = (b- log Qwz + log Qsr)/(b + 1 ) (17)

where Qm =mean value of Q in deciding the support; Q,~= Q value of the weak zone; Qsr= Q value of the surrounding rock; and b = breadth of the weak zone in metre.

The strike direction (0) and thickness of weak zone (b) in relation to the tunnel axis is important for the stability of the tunnel, and therefore the following correction factors have been suggested for the value of b in the above Eq. (17):

if 0 =9 0 -4 5 ° to the tunnel axis then use lb; if 0 =45-20 ° then use 2b; if 0 = 10-20 ° then use 3b; if 0 < 10 ° then use 4b.

Hence, if the surrounding rock near the shear zones can be downgraded with the use of the above formula, a heavier support can be chosen for the whole area instead of the weak zone alone.

Fig. 14 shows a typical treatment method for shear zones. This strategy is very urgently needed if NATM or N TM (Norwegian Tunnelling Method) are to be used in the Himalayan region, as seams/shear zones/faults/thrusts/intra-thrust zones are frequently found along tunnels and caverns in the Himalayas. A case history showing the recurrence of thrusts and their effect on the tunnelling has been presented by Jethwa et al. (1980).

SHEIIII ZONE /

Z.~HOICREI~ Fig. 14. Typical treatment of a narrow shear zone (after Lang, 1961 ).

80 B. Smgh et al. / Engineering Geology 48 (1997) 59-81

3.14. Ultimate support pressure

Ultimate support pressure could be estimated from the short- term support pressure values obtained from the above correlations. The ratio between the ultimate support pressure after about 100 years and the short- term support pressure for various types o f g round conditions is given as follows: ( 1 ) Pult/P = 1.75 for non-squeezing ground ( = f " in Eq . (5 ) ) ; ( 2 ) p u l t / p = 2 - 3 for squeezing rock conditions (Jethwa, 1981); (3 )pu~t /p=6 for water-charged rock masses with erodible joint fill- ings (Mitra, 1991 ).

(4) Assessment o f support pressures in shear zones and walls o f caverns should be made cau- tiously. Shear zones t reatment should be done properly.

( 5 ) Under swelling ground conditions, the reliability o f any of the approaches is yet to be established and, therefore, labora tory tests and field instrumentat ion are suggested.

(6) Relationships between long-term or ultimate support pressure and short- term pressure also vary with the g round conditions, and the estimated values are given in the paper.

3.15. Effect o/seismicity on support pressure References

For tunnels located near faults/thrusts (with plastic gouge) in seismic areas, the ultimate support pressure may be about 25% to account for accumu- lated strains in the rock mass along the fault (Mitra, 1991 ). This has been estimated f rom the 10-year moni tor ing o f the Chhibro-Khodr i underground powerhouse, India.

4. Conclusions

(1) Assessment o f support pressure in arched underground openings depends upon the ground conditions. The ground conditions can be safely predicted using the approaches discussed in the paper. The approach of Goel et al. (1995) is complementary to the Q-system and one can predict the degree o f squeezing and other g round conditions for getting SRF (Fig. 3).

(2) Correlat ions presented for estimating the support pressures can also be used reliably. Suppor t pressures are found to be independent o f the size o f arched excavations (for tunnel diameter f rom 2 to 22 m) in the non-squeezing ground conditions. However, support pressure may increase with tunnel size in squeezing ground (Table 7).

(3) The support pressures in squeezing ground conditions are observed to decrease with tunnel closure significantly and increase rapidly beyond 6% closure.

Aydan, O., Akagi, T., Kawamoto, T., 1993. The squeezing potential of rocks around tunnels; theory and prediction. Rock Mech. Rock Eng. 26 (2), 137-163.

Barton, N., Lien, R., Lunde, J., 1974. Analysis of Rock Mass Quality and Support Practice in Tunnelling, and a Guide for Estimating Support Requirements, Report by NGI, June.

Bazant, Z.P., Lin, F.B., Lippmann, H., 1993. Fracture energy release and size effect in borehole breakout. Int. J. Numerical Analyt. Methods Geomech. 17, 1 14.

Bhasin, R., Grimstad, E., 1996. The Use of Stress-Strength Relationship in the Assessment of Tunnel Stability. Proc. Recent Advances in Tunnelling Technology, New Delhi, India.

Bhasin, R., Singh, R.B., Dhawan, A.K., Sharma, V.M., 1995. Geotechnical Evaluation and a Review of Remedial Mea- sures in Limiting Deformations in Distressed Zones in a Powerhouse Cavern. Conf. on Design and Construction of Underground Structures, New Delhi.

Bieniawski, Z.T., 1973. Engineering classification of jointed rock masses. Trans. S. African Inst. Civil Engineers 15 (12), 335 344.

Bieniawski, Z.T. (1979). Tunnel design by rock mass classification. Tech. Rep. No. GL-79-19, Sept. 1979, Prepared for Office of Chief Engineers, U.S. Army, Washington, D.C.

Bieniawski, Z.T., 1984. Rock Mechanics Designs in Mining and Tunnelling, Text book Published by A.A. Balkema, Rotter- dam, p. 272.

Daemen, J.J.K., 1975. Tunnel Supprt Loading Caused by Rock Failure, Ph.D. Thesis, University of Minnesota, Minneapo- lis, USA.

Deere, D.U., Peck, R.B., Monsees, J.E., Schmidt, B., 1969. Design of Tunnel Liners and Support System, Highway Research Record No. 339, US Department of Transporta- tion. Washington. DC.

Goel, R.K., 1994. Correlations tbr Predicting Support Pressures and Closures in tunnels. Ph.D. Thesis, Nagpur University, India, p. 308.

Goel, R.K., Jethwa, J.L., 1991. Prediction of Support pressure


using RMR Classification. Proc. Indian Geotechnical Conf., Surat, India, December 1991.

Goel, R.K., Jethwa, J.L., Dhar, B.B., 1996. Effect of tunnel size on support pressure. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33 (7), 749-755.

Goel, R.K., Jethwa, J.L., Paithankar, A.G., 1995. Indian experiences with Q and RMR systems. Tunnelling Underground Space Technol. 10 (1), 97 109.

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