ELSEVIER GEO-ENGINEERING BOOK SERIES VOLUME 5 Part 3 ppsx

84 Tunnelling in weak rocks

6.5.1.1 Influence of shape of the opening

Some empirical approaches listed in Table 6.4 have been developed for flat roof and some

for arched roof. In case of an underground opening with flat roof, the support pressure

is generally found to vary with the width or size of the opening, whereas in arched roof

the support pressure is found to be independent of tunnel size (Table 6.4). RSR-system of

Wickham et al. (1972) is an exception in this regard, probably because the system, being

conservative, was not backed by actual field measurements for caverns. The mechanics

suggests that the normal forces and therefore the support pressure will be more in case

of a rectangular opening with flat roof by virtue of the detached rock block in the tension

zone which is free to fall.

6.5.1.2 Influence of rock mass type

The support pressure is directly proportional to the size of the tunnel opening in the

case of weak or poor rock masses, whereas in good rock masses the situation is reverse

(Table 6.4). Hence, it can be inferred that the applicability of an approach developed for

weak or poor rock masses has a doubtful application in good rock masses.

6.5.1.3 Influence of in situ stresses

Rock mass number N does not consider in situ stresses, which govern the squeezing or

rock burst conditions. Instead the height of overburden is accounted for in equations (6.9)

and (6.10) for estimation of support pressures. Thus, in situ stresses are taken into account

indirectly.

Goel et al. (1995a) have evaluated the approaches of Barton et al. (1974) and Singh

et al. (1992) using the measured tunnel support pressures from 25 tunnel sections. They

found that the approach of Barton et al. is unsafe in squeezing ground conditions and

the reliability of the approaches of Singh et al. (1992) and that of Barton et al. depend

upon the rating of Barton’s stress reduction factor (SRF). It has also been found that

the approach of Singh et al. is unsafe for larger tunnels (B >9 m) in squeezing ground

conditions. Kumar (2002) has evaluated many classification systems and found rock mass

number to be the best from the case history of NJPC tunnel, India.

6.5.2 New concept on effect of tunnel size on support pressure

Equations (6.9) and (6.10) have been used to study the effect of tunnel size on support

pressure which is summarized in Table 6.5.

It is cautioned that the support pressure is likely to increase significantly with the

tunnel size for tunnel sections excavated through the following situations:

(i) slickensided zone,

(ii) thick fault gouge,

(iii) weak clay and shales,

Rock mass number 85

Table 6.5 Effect of tunnel size on support pressure (Goel et al., 1996).

S.No. Type of rock mass

Increase in support pressure due to

increase in tunnel span or diam.

from 3 m to 12 m

A. Tunnels with arched roof

1. Non-squeezing ground conditions Up to 20 percent only

2. Poor rock masses/squeezing ground conditions

(N = 0.5 to 10)

20–60 percent

3. Soft-plastic clays, running ground, flowing

ground, clay-filled moist fault gouges,

slickensided shear zones (N = 0.1 to 0.5)

100 to 400 percent

B. Tunnels with flat roof (irrespective of ground

conditions)

400 percent

(iv) soft-plastic clays,

(v) crushed brecciated and sheared rock masses,

(vi) clay-filled joints and

(vii) extremely delayed support in poor rock masses.

Further, both Q and N are not applicable to flowing grounds or piping through

seams. They also do not take into account mineralogy (water-sensitive minerals, soluble

minerals, etc.).

6.6 CORRELATIONS FOR ESTIMATING TUNNEL CLOSURE

Behavior of concrete, gravel and tunnel-muck backfills, commonly used with steel-arch

supports, has been studied. Stiffness of these backfills has been estimated using mea￾sured support pressures and tunnel closures. These results have been used finally to

obtain effective support stiffness of the combined support system of steel rib and backfill

(Goel, 1994).

On the basis of measured tunnel closures from 60 tunnel sections, correlations have

been developed for predicting tunnel closures in non-squeezing and squeezing ground

conditions (Goel, 1994). The correlations are given below:

Non-squeezing ground condition

ua

a

=

H

0.6

28 · N0.4 · K0.35 % (6.11)

86 Tunnelling in weak rocks

Squeezing ground condition

ua

a

=

H

0.8

10 · N0.3 · K0.6 % (6.12)

where

ua/a = normalized tunnel closure in percent,

K = effective support stiffness (= pv · a/ua) in MPa and

H and a = tunnel depth and tunnel radius (half of tunnel width) in meters, respectively.

These correlations can also be used to obtain desirable effective support stiffness

so that the normalized tunnel closure is contained within 4 percent (in the squeezing

ground).

6.7 EFFECT OF TUNNEL DEPTH ON SUPPORT PRESSURE AND

CLOSURE IN TUNNELS

It is known that the in situ stresses are influenced by the depth below the ground sur￾face. It is also learned from the theory that the support pressure and the closure for

tunnels are influenced by the in situ stresses. Therefore, it is recognized that the depth

of tunnel or the overburden is an important parameter while planning and designing the

tunnels. The effects of tunnel depth or the overburden on support pressure and closure

in tunnel have been studied using equations (6.9) to (6.12) under both squeezing and

non-squeezing ground conditions which is summarized below.

(i) The tunnel depth has a significant effect on support pressure and tunnel closure

in squeezing ground conditions. It has smaller effect under non-squeezing ground

conditions, however (equation (6.9)).

(ii) The effect of tunnel depth is higher on the support pressure than the tunnel closure.

(iii) The depth effect on support pressure increases with deterioration in rock mass quality

probably because the confinement decreases and the degree of freedom for the

movement of rock blocks increases.

(iv) This study would be of help to planners and designers to take decisions on realigning

a tunnel through a better tunnelling media or a lesser depth or both in order to reduce

the anticipated support pressure and closure in tunnels.

6.8 APPROACH FOR OBTAINING GROUND REACTION

CURVE (GRC)

According to Daemen (1975), ground reaction curve is quite useful for designing the

supports specially for tunnels through squeezing ground conditions. An easy to use

Rock mass number 87

empirical approach for obtaining the ground reaction curve has been developed using

equations (6.10) and (6.12) for tunnels in squeezing ground conditions. The approach has

been explained with the help of an example.

For example, the tunnel depth H and the rock mass number N have been assumed as

500 m and 1, respectively and the tunnel radius a as 5 m. The radial displacement of the

tunnel is ua for a given support pressure pv(sq).

GRC using equation (6.10)

In equation (6.10), as described earlier, f (N) is the correction factor for tunnel closure.

For different values of permitted normalized tunnel closure (ua/a), different values of

f (N) are proposed in Table 6.3. The first step is to choose any value of tunnel wall

displacement ua in column 1 of Table 6.6. Then the correction factor f (N) is found from

Table 6.3 as shown in column 2 of Table 6.6. Finally, equation (6.10) yields the support

Table 6.6 Calculations for constructing GRC using equation (6.10).

Assumed ua/a (%) Correction factor ( f )

pv(sq) from equation

(6.10) (MPa)

(1) (2) (3)

0.5 2.7 0.86

1 2.2 0.7

2 1.5 0.475

3 1.2 0.38

4 1.0 0.317

5 0.8 0.25

0123456

0.2

0.4

0.6

0.8

1.0

Boundary Conditions

Tunnel depth = 500m

Tunnel radius = 5m

Rock mass number = 1

Ground Reaction Curve

from Eq. 6.10

Normalised Tunnel Closure (ua

/a), %

Support Pressure (pv), MPa

Fig. 6.3 Ground reaction curve obtained from equation (6.10).

88 Tunnelling in weak rocks

pressure in roof (pv) as mentioned in column 3 [Using Table 6.3 and equation (6.10), the

support pressures [pv(sq)] have been estimated for the assumed boundary conditions and

for various values of ua/a (column 1) as shown in Table 6.6]. Subsequently, using value

of pv (column 3) and ua/a (column 1) from Table 6.6, GRC has been plotted for ua/a up to

5 percent (Fig. 6.3).

It may be highlighted here that the approach is simple, reliable and user-friendly

because the values of the input parameters can be easily obtained in the field.

REFERENCES

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