Page 212 - Engineering Rock Mass Classification_ Tunnelling, Foundations and Landslides

174 Engineering Rock Mass Classification

triaxial tests. The shear stress along the line of intersection of joint planes will be

proportional to s1 À s3 because s3 will try to reduce shear stress. The normal stress
on both the joint planes will be proportional to (s2 þ s3)/2. Hence, the criterion for
peak failure at low confining stresses may be as follows (s3 < qc/2, s2 < qc/2, and
SRF > 0.05):

s1 À s3 ¼ qcmass þ A½ðs2 þ s3Þ=2Š, ð13:14Þ
ð13:15Þ
qcmass ¼ qcEEdr 0:70 Á d 0:20
,

Srock

D ¼ fp À fr , beyond failure ð13:16Þ
2

where qcmass ¼ average UCS of undisturbed rock mass for various orientation of principal
stresses; s1, s2, s3 ¼ final compressive and effective principal stresses equal to in situ
stress plus induced stress minus seepage pressure; A ¼ average constants for various
orientation of principal stress (value of A varies from 0.6 to 6.0), 2 Á sinfp/(1 À sinfp),
and Ai þ 2(1 À SRF) for rock mass with fresh joints; Ai ¼ a value for intact rock material;
SRF ¼ qcmass/qc (strength reduction factor); fp ¼ peak angle of internal friction of rock
mass, is ffi tanÀ1 [(Jr Jw/Ja) þ 0.1] at a low confining stress, is < peak angle of internal
friction of rock material, and ¼ 14 À 57; Srock ¼ average spacing of joints; qc ¼ average
UCS of rock material for core of diameter d (for schistose rock also); △ ¼ peak angle
of dilatation of rock mass at failure; fr ¼ residual angle of internal friction of rock
mass ¼ fp À 10 ! 14; Ed ¼ modulus of deformation of undisturbed rock mass
(s3 ¼ 0); and Er ¼ modulus of elasticity of the rock material (s3 ¼ 0).

The peak angle of dilatation is approximately equal to (fp À fr)/2 for rock joints
(Barton & Brandis, 1990) at low s3. This correlation (Eq. 15.8) may be assumed for
jointed rock masses also. It is assumed that no dilatancy takes place before the peak fail-

ure so that strain energy is always positive during the deformation. The proposed strength

criterion reduces to Mohr-Coulomb’s criterion for triaxial conditions.
The significant rock strength enhancement in underground openings is due to s2 or

in situ stress along tunnels and caverns, which pre-stresses rock wedges and prevents

their failure both in the roof and the walls. However, s3 is released due to stress-free
excavation boundaries (Figure 13.1d). In the rock slopes s2 and s3 are nearly equal
and negligible. Therefore, there is insignificant or no enhancement of the strength. As such,

block shear tests on a rock mass give realistic results for rock slopes and dam abutments

only, because s2 ¼ 0 in this test. Equation (13.14) may give a general criterion of
undisturbed jointed rock masses for underground openings, rock slopes, and foundations.

Another cause of strength enhancement is higher UCS of rock mass (qcmass) due
to higher Ed because of constrained dilatancy and restrained fracture propagation near

the excavation face only in underground structures. In rock slopes, Ed is found to be much
less due to complete stress release and low confining pressure because of s2 and s3 and
the long length of weathered filled up joints. So, qcmass will also be low near rock slopes
for the same Q-value (Eq. 13.13). Mohr-Coulomb criterion (Eq. 26.12) is valid for poor
rock mass where qcmass < 0.05qc or 1 MPa.

Through careful back analysis, both the model and its constants should be deduced.

Thus, A, Ed, and qcmass should be estimated from the feedback of instrumentation data at
the beginning of the construction stage. With these values, forward analysis should be