Page 215 - Engineering Rock Mass Classification_ Tunnelling, Foundations and Landslides

Chapter 13 Strength Enhancement of Rock Mass in Tunnels 177

CRITICAL STRAIN OF ROCK MASS

The basic concept of structure design cannot be applied in tunnels, because stresses and
strains are not reliably known. Critical strain is a better measure of failure.

Critical strain (ecr) is defined as the ratio between UCS (qcmass) and the modulus of
deformation (Ed) of rock mass (Sakurai, 1997). He found that the critical strain is nearly
independent of joints, water content, and temperature. Singh, Singh, and Choudhari
(2007) reported the following correlation for the critical strain and verified the same

using 30 case histories:

ecr ¼ 5:84 qc0:88 ðpercentÞ ! 100 qc ð13:18Þ
Q0:12 Er0:63 Er

ecr ! ey ¼ 100 ua=a

where ecr ¼ critical strain of the rock mass in percentage; ey ¼ tangential strain around
opening in percentage, ¼ (observed deflection of crown in downward direction/radius of
tunnel), and ¼ 100 ua/a (Figure 13.2); Er ¼ tangent modulus of the rock material
(in MPa); qc ¼ UCS of rock material (in MPa); and Q ¼ rock mass quality.

In Japan there were few construction problems in tunnels where ey < emass or er.
Critical strain appears to be somewhat size dependent.

Predictions and actual observations differ greatly in tunnels, and joints need more

attention from engineers. It is easier to observe strains than stresses in the rock mass.

Sakurai (1997) classified the hazard warning level into three stages in relation to degree
of stability as shown in Figure 13.2. He observed that where strains in the roof (ey ¼ ua/a)
were less than the warning level I, there were no problems in the tunnels, but tunneling

problems were encountered where strains approached warning level III. Swarup, Goel,

and Prasad (2000) confirmed these observations in 19 tunnels in weak rocks in the

Himalayas.

FIGURE 13.2 Hazard warning levels for assessing the stability of tunnels. (From Sakurai, 1997)