Page 209 - Engineering Rock Mass Classification_ Tunnelling, Foundations and Landslides

Chapter 13 Strength Enhancement of Rock Mass in Tunnels 171

It may be inferred that s2 will enhance s1 at failure by 75–200% when s2 % qc.
Strength enhancement may be much more as propagation of fracture will be behind

the excavated face (Bazant, Lin, & Lippmann, 1993). Murrell (1963) suggested 100%

increase in s1 at failure when s2 ¼ 0.5 s1 and s3 ¼ 0. Thus, the effective confining
pressure appears to be an average of s2 and s3 and not just equal to s3 in the anisotropic
rocks and weak rock masses.

Hoek (1994) suggested the following modified criterion for estimating the strength

of jointed rock masses at high confining stresses (e.g., around s3 > 0.10 qc)

n
s3 s
s1 ¼ s3 þ qc m qc þ ð13:3Þ

where s1 and s3 ¼ maximum and minimum effective principal stresses, respectively;
m ¼ Hoek-Brown rock mass constant (same as mb in Chapter 26); s and n ¼ rock mass
constants; s ¼ 1 for rock material, n ¼ 0.5 and 0.65 À (GSI/200) 0.60 for GSI < 25

(or use Eq. 26.9 for any GSI); qc ¼ UCS of the intact rock core of standard NX size; and
GSI ¼ geological strength index % RMR’89 À 5 for RMR > 23 (see Chapter 26),

ðm=mrÞ ¼ s1=3 for GSI > 25 ðsee Chapter 26Þ ð13:4Þ

where mr ¼ Hoek-Brown rock material constant.
The Hoek and Brown (1980) criterion in Eq. (13.3) is applicable to rock slopes and

opencast mines with weathered and saturated rock mass. They have suggested values of

m and s for Eq. (13.3). The Hoek and Brown (1980) criterion may be improved as a poly-
axial criterion after replacing s3 (within bracket in Eq. 13.3) by effective confining
pressure (s2 þ s3)/2 as mentioned previously for weak and jointed rock masses. It
may be noted that parameters mr and qc should be calculated from the upper bound
Mohr’s envelope of triaxial test data on rock cores in the case of anisotropic rock

materials (Hoek, 1998).

According to Hoek (2007), rock mass strength is as follows (for disturbance factor
D ¼ 0):

qcmass ¼ ð0.0034 mr0:8Þqc f1:029 þ 0:025 expðÀ0:1mrÞgGSI ð13:5Þ

The Hoek and Brown (1980) criterion assumes isotropic rock and rock mass condition

and should only be applied to those rock masses in which there are many sets of closely
spaced joints with similar joint surface characteristics. Therefore, the rock mass may be
considered to be an isotropic mass; however, the joint spacing should be much smaller
than the size of the structure of the opening.

When one of the joint sets is significantly weaker than the others, the Hoek and
Brown criterion Eq. (13.3) should not be used, as the rock mass behaves as an anisotropic
mass. In these cases, the stability of the structure should be analyzed by considering a
failure mechanism involving the sliding or rotation of blocks and wedges defined by
intersecting discontinuities (Hoek, 2007). Singh and Goel (2002) presented software
for wedge analysis for rock slopes (SASW) and WEDGE and UWDGE for tunnels

and caverns.

Keep in mind that most of the strength criteria are not valid at low confining stresses

and tensile stresses, as modes of failure are different. Hoek’s criterion is applicable for

high confining stresses only where a single mode of failure by faulting takes place; hence
the quest for a better model to represent jointed rock masses.