Page 155 - Rock Mechanics For Underground Mining

BEHAVIOUR OF DISCONTINUOUS ROCK MASSES

Figure 4.51 Applicability of the
Hoek–Brown empirical rock mass
strength criterion at different scales
(after Hoek and Brown, 1988).

be isotropic with elastic constants E and , let the discontinuities have normal and
shear stiffnesses K n and K s as defined in section 4.7.5, and let the mean discontinuity
spacing be S. By considering the deformations resulting from the application of unit
shear and normal stresses with respect to the x, y plane in Figure 2.10, it is found that
the equivalent elastic constants required for use in equation 2.42 are given by

E 1 = E
1 1 1
= +
E 2 E K n S
1 =
E 2
2 =
E
1 1 1
= +
G 2 G K s S
−1
If, for example, E = 10 GPa, = 0.20, K n = 5GPa m , K s = 0.1GPa m −1 and
S = 0.5 m, then G = 4.17 GPa, E 1 = 10 GPa, E 2 = 2.0GPa, 1 = 0.20, 2 = 0.04
and G 2 = 49.4MPa.
Similar solutions for cases involving more than one set of discontinuities are given
by Amadei and Goodman (1981) and by Gerrard (1982). It is often found in practice
that the data required to apply these models are not available or that the rock mass
structure is less regular than that assumed in developing the analytical solutions. In
these cases, it is common to determine E as the modulus of deformation or slope
of the force–displacement curve obtained in an in situ compression test. There are
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