ELSEVIER GEO-ENGINEERING BOOK SERIES VOLUME 5 Part 9 pdf

Integrated method of tunnelling 441

The short-term support pressure in roof may be assessed by the following correlation

(equation (4.6)) for arch opening given by Goel and Jethwa (1991).

proof =

7.5B

0.1 H

0.5 − RMR

20 RMR

=

7.5 × 160.1 × 1650.5 − 73

20 × 73

= 0.037 MPa

The ultimate support pressure is read by the chart (Fig. 5.2) of Barton et al. (1974)

as follows (the dotted line is observed to be more reliable than correlation).

proof = 0.9 × 1 × 1 kg/cm2

or 0.09 MPa

(The rock mass is in non-squeezing ground condition (H < 350 Q1/3) and so f

′ = 1.0.

The overburden is less than 320 m and so f = 1.0.)

It is proposed to provide the steel fiber reinforced shotcrete (SFRS) [and no rock bolts

for fast rate of tunnelling]. The SFRS thickness (tfsc) is given by the following correlation

(equation (28.1)).

tfsc =

0.6Bproof

2qfsc

=

0.6 × 1600 × 0.09

2 × 5.5

= 8 cm

= 16 cm (near portals)

The tensile strength of SFRS is considerd to be about one-tenth of its UCS and so its

shear strength (qsc) will be about, 2 × 30/10 = 6.0 MPa, approximately 5.5MPa (UTS is

generally lesser than its flexural strength). Past experience is also the same.

The life of SFRS may be taken same as that of concrete in the polluted environment

that is about 50 years. Life may be increased to 60 years by providing extra cover of SFRS

of 5 cm. If SFRS is damaged latter, corroded part should be scrapped and new layer of

shotcrete should be sprayed to last for 100 years. So recommended thickness of SFRS is

tfsc = 13 cm

= 21 cm (near portals)

The width of pillar is more than the sum of half-widths of adjoining openings in the

non-squeezing grounds. The width of pillar is also more than the total height of the larger

of two caverns (18 m), hence proposed separation of 20 m is safe.

The following precautions need to be taken:

(i) The loose pieces of rocks should be scrapped thoroughly before shotcreting for

better bonding between two surfaces.

(ii) Unlined drains should be created on both the sides of each tunnel to drain out the

ground water and then should be covered by RCC slabs for road safety.

442 Tunnelling in weak rocks

(iii) The tunnel exits should be decorated by art and arrangement should be made

for a bright lighting to illuminate well the tunnels to generate happy emotions

among road users.

REFERENCES

Barton, N. (2002). Some new Q-value correlations to assist in site characterisation and tunnel design.

Int. J. Rock Mech. and Min. Sci., 39, 185-216.

Barton, N., Lien, R. and Lunde, J. (1974). Engineering classification of rock masses for the design

of tunnel support. Rock Mechanics, Springer-Verlag, 6, 189-236.

Bischoff, J. A., Klein, S. J. and Lang, T. A. (1992). Designing reinforced rock. Civil Engineering,

ASCE, 72, January.

Bhasin, R., Singh, R. B., Dhawan, A. K. and Sharma, V. M. (1995). Geotechnical evaluation and a

review of remedial measures in limiting deformations in distressed zones in a powerhouse

cavern. Conf. Design and Construction of Underground Structures, New Delhi, India,

145-152.

Duddeck, H. and Erdmann, J. (1985). On structural design models for tunnels in soft soil.

Underground Space, 9, 246-259.

Goel, R. K. and Jethwa, J. L. (1991). Prediction of support pressure using RMR classification.

Proc. Indian Getech. Conf., Surat, India, 203-205.

IS 15026:2002, Tunnelling Methods in Rock Masses-Guidelines. Bureau of Indian Standards,

New Delhi, India, 1-24.

Samadhiya, N. K. (1998). Influence of anisotropy and shear zones on stability of caverns.

PhD thesis, Department of Civil Engineering, IIT Roorkee, India, 334.

Singh, Bhawani,Viladkar, M. N., Samadhiya N. K. and Sandeep (1995). A Semi-empirical method

for the design of support systems in underground openings. Tunnelling and Underground

Space Technology, 10(3) 375-383.

Zhidao, Z. (1988). Waterproofing and water drainage in NATM tunnel. Symp. Tunnels and Water,

Ed: Serrano, Rotterdam, 707-711.

29

Critical state rock mechanics

and its applications

“All things by immortal power near or far, hiddenly to each other are linked.”

Francis Thompson

English Victorian Post

29.1 GENERAL

Barton (1976) suggested that the critical state for initially intact rock is defined as the

stress condition under which Mohr envelope of peak shear strength reaches a point of zero

gradient or a saturation limit. Hoek (1983) suggested that the confining pressure must

always be less than the unconfined compression strength of the material for the behavior

to be considered brittle. An approximate value of the critical confining pressure may,

therefore, be taken equal to the uniaxial compressive strength of the rock material.

Yu et al. (2002) have presented a state-of-the-art on strength of rock materials and

suggested a unified theory. The idea is that the strength criterion for jointed rock mass

must account for the effect of critical state in the actual environmental conditions.

The frictional resistance is due to the molecular attraction of the molecules in contact

between smooth adjoining surfaces. It is more where molecules are closer to each other due

to the normal stresses. However, the frictional resistance may not exceed the molecular

bond strength under very high confining stresses. Hence, it is no wonder that there is a

saturation or critical limit to the frictional resistance (Prasad, 2003). There should be limit

to everything in the nature.

Singh and Singh (2005) have proposed the following simple parabolic strength

criterion for the unweathered dry isotropic rock materials as shown in Fig. 29.1.

σ1 − σ3 = qc + Aσ3 −

Aσ

2

3

2qc

for 0 < σ3 ≤ qc (29.1)

Tunnelling in Weak Rocks

B. Singh and R. K. Goel

© 2006. Elsevier Ltd

444 Tunnelling in weak rocks

qc

σ1

− σ3

σ3

σ3

=qc

Fig. 29.1 Parabolic strength criterion.

where

A =

2 sin φp

1− sin φp

φp = the peak angle of internal friction of a rock material in nearly unconfined

state (σ3 = 0) and

qc = average uniaxial compressive strength of rock material at σ3 = 0.

It may be proved easily that deviator strength (differential stress at failure) reaches a

saturation limit at σ3 = qc that is,

∂(σ1 − σ3)

∂σ3

= 0 at σ3 = qc (29.2)

Unfortunately, this critical state condition is not met by the other criteria of strength.

It is heartening to note that this criterion is based on single parameter “A” which makes

a physical sense. Sheorey (1997) has compiled the triaxial and polyaxial test data for

different rocks which are available from the world literature. The regression analysis was

performed on 132 sets of triaxial test data in the range of 0 ≤ σ3 ≤ qc.

The values of the parameter A, for all the data sets were obtained. These values were

used to back-calculate the σ1 values for the each set for the given confining pressure. The

comparison of the experimental and the computed values of σ1 is presented in Fig. 29.2.

It is observed that the calculated values of σ1 are quite close to the experimental values.

An excellent coefficient of correlation, 0.98, is obtained for the best fitting line between

the calculated and the experimental values.

For comparing the predication of the parabolic criterion with those of the others,

Hoek and Brown (1980) criterion was used to calculate the σ1 values. The coefficient of

correlation (0.98) for Hoek–Brown predictions is observed to be slightly lower and poor for

weak rocks, when compared with that obtained for the criterion proposed in this chapter.

Critical state rock mechanics and its applications 445

10 100 1000 10000

10

100

1000

10000

Experimental σ1 (MPa)

Calculated

σ1 (MPa)

R

2

= 0.9848

Fig. 29.2 Comparison of experimental σ1 values with those calculated through the proposed

criterion (equation (29.1)) (Singh & Singh, 2005).

In addition to the higher value of coefficient of correlation, the real advantage of proposed

criterion, lies in the fact that only one parameter, A is used to predict the confined strength

of the rock and A makes a physical sense.

A rough estimate of the parameter A may be made without conducting even a single

triaxial test. The variation of the parameter, A, with the uniaxial compressive strength

(UCS), qc is presented in Fig. 29.4. A definite trend of A with UCS (qc) is indicated by

this figure and the best fitting value of the parameter A may be obtained as given below:

A ∼=

7.94

q

0.10

c

for qc = 7 − 500 MPa (29.3)

Fig. 29.3 compares experimental σ1 values with those predicted by using equa￾tion (29.3) without using the triaxial data. A high coefficient of correlation of 0.93 is

obtained. Thus, the proposed criterion appears to be more faithful to the test data than

Hoek and Brown (1980) criterion. This criterion is also better fit for weak rocks as the

critical state is more important for rocks of lower UCS. The law of saturation appears to

be the cause of non-linearity of the natural laws.

29.2 SUGGESTED MODEL FOR ROCK MASS

The behavior of jointed rock mass may be similar to that of the rock material at criti￾cal confining pressure, as joints then cease to dominate the behavior of the rock mass.