Rock Mechanics.pdf - Mining and Blasting

BEHAVIOUR OF DISCONTINUOUS ROCK MASSES
illustrate the criterion’s application in practice. A further update was given by Hoek
et al. (2002). The summary of the criterion given here is based on these accounts and
those of Marinos and Hoek (2000) and Brown (2003).
In effective stress terms, the generalised Hoek-Brown peak strength criterion for
jointed rock masses is given by:
′ 1 = ′ 3 + mbc ′ 3 + s 2a c
(4.37)
where mb is the reduced value of the material constant mi (see equation 4.25) for the
rock mass, and s and a are parameters which depend on the characteristics or quality
of the rock mass. The values of mb and s are related to the GSI for the rock mass (see
section 3.7.4) by the relations
and
mb = mi exp{(GSI − 100)/(28 − 14D)} (4.38)
s = exp{(GSI − 100)/(9 − 3D)} (4.39)
where D is a factor which depends on the degree to which the rock mass has been
disturbed by blasting or stress relaxation. D varies from 0 for undisturbed in situ rock
masses to 1.0 for very disturbed rock masses. For good quality blasting, it might be
expected that D ≈ 0.7.
In the initial version of the Hoek-Brown criterion, the index a took the value 0.5 as
shown in equation 4.25. After a number of other changes, Hoek et al. (2002) expressed
the value of a which applies over the full range of GSI values as the function:
a = 0.5 + (exp −GSI/15 − exp −20/3 )/6 (4.40)
Note that for GSI > 50, a ≈ 0.5, the original value. For very low values of GSI, a →
0.65.
The uniaxial compressive strength of the rock mass is obtained by setting ′ 3 to
zero in equation 4.37 giving
cm = cs a
(4.41)
Assuming that the uniaxial and biaxial tensile strengths of brittle rocks are approximately
equal, the tensile strength of the rock mass may be estimated by putting
′ 1 = ′ 3 = tm in equation 4.37 to obtain
tm =−s c/mb
(4.42)
The resulting peak strength envelope for the rock mass is as illustrated in Figure 4.50.
Because analytical solutions and numerical analyses of a number of mining rock
mechanics problems use Coulomb shear strength parameters rather than principal
stress criteria, the Hoek-Brown criterion has also been represented in shear stresseffective
normal stress terms. The resulting shear strength envelopes are non-linear
and so equivalent shear strength parameters have to be determined for a given normal
stress or effective normal stress, or for a small range of those stresses (Figure 4.50).
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