Engineering Rock Mechanics

Questions and answers: rock masses 135

These materials may not be amenable to either standard rock mechanics

or standard soil mechanics approaches because they exhibit transitional

behaviour between the two modes described above.

48.9 The peak strength of a poor-quality, closely iointed and
weathered granite may be represented by the Hoek-Brown cri-
terion, (rl = u3 + ,/mucu3 +suo, with m = 1.3 and s = 0.00001.
The uniaxial compressive strength of the intact rock material is
estimated as Q, = 40 MPa, and the residual strength of the fractures
is given by cr = 0, & = 15O.
(a) Plot, in t--6 space, the expected peak shear strength envelopes
for the intact rock material, a fracture at residual strength, and the
jointed rock mass for normal stresses up to 10 MPa.
(b) The Hoek-Brown criterion is to be used for the analysis of
potential circular slopes cut in the rock mass. Determine values of
instantaneous cohesion and friction angle for normal stresses up to
10 MPa.

A8.9 In order to determine the instantaneous values of friction angle
and cohesion we must convert the principal stress form of the Hoek-
Brown criterion into a shear stress-normal stress space form. During the
development of the Hoek-Brown criterion many techniques have been
proposed for doing this (Hoek and Brown, 1980, 1988; Hoek, 19906),
but for the basic Hoek-Brown criterion of a1 = 03 + a,,/m(a~/a,) + s,
the simplest method is to use the following relations (Hoek and Brown,
1988 6,
h=l+-( 16 ma+sac )
3 m2ac

ma, (1 - sin 4;)

8 tan+;

In Eq. (8.2), if the angles are evaluated in degrees then Q = 90°, and if

Finally, substitution of 4; and r from Eqs. (8.3) and (8.4) into the linear

r=- (8.4)

the angles are evaluated in radians then Q = n/2.

Mohr-Coulomb criterion gives the instantaneous cohesion as

ci = r - a tan&. (8.5)

Hoek E. and Brown E. T. (1980) Underground Excuuations in Rock. Institution of Mining

and Metallurgy, London, 527pp. See also Hoek E. (1990) Estimating Mohr-Coulomb

friction and cohesion values from the Hoek-Brown failure criterion. Int. J. Rock Mech.

Min. Sei., 27, 3, 227-229, and Hoek E. and Brown E. T. (1988) Hoek-Brown failure

criterion - a 1988 update. Droc. 15th Canadian Ruck Mech. Symp. University of Toronto,

ON, pp. 31-38.