Engineering Rock Mechanics

1 36 Rock masses: deformability, strength and failure

Evaluating these equations for a range of values of normal stress, with
values of a, = 40 MPa, m = 1.3 and s = O.oooO1, gives the following
results.

a (MPa) 0.0 0.5 1.0 2.5 5.0 7.5 10.0

h 1.000 1.051 1.103 1,256 1.513 1.769 2.026

0 (rad) 1.04 0.92 0.87 0.79 0.71 0.67 0.64

4 (rad) 1.43 0.93 0.83 0.68 0.57 0.50 0.45

#i (deg) 82.1 53.6 47.7 39.2 32.5 28.7 26.0

t (ma) 0.009 0.938 1.542 2.938 4.721 6.191 7.479

c; (ma) 0.00 0.26 0.44 0.90 1.54 2.09 2.60

In addition to the weathered granite, we can use values of m = 25 and
s = 1 to plot the criterion for the intact granite. The results of this are
shown in the following table.

a (ma) 0.0 0.5 1.0 2.5 5.0 7.5 10.0

h 1.009 1.011 1.014 1.022 1.035 1.049 1.062

0 (rad) 0.99 0.99 0.98 0.96 0.94 0.92 0.91

4i (rad) 1.15 1.12 1.10 1.05 0.99 0.94 0.91

IP~ (deg) 65.9 64.3 63.0 60.0 56.5 54.0 52.0

t (MPa) 4.852 5.929 6.938 9.692 13.719 17.319 20.637

ci (ma) 4.85 4.89 4.98 5.37 6.16 6.99 7.82

Finally, to plot the criterion for the fractures, we use the Mohr-Coulomb

strength parameters given. The results of these calculations are shown in

the plots below.

Intact granite

0.0 2.0 4.0 6.0 8.0 10.0

Normal stress. MPa

For the more general form of the Hoek-Brown criterion, i.e.

cl = a3 + 0c[[m(a3/c,) $- sIa, a more sophisticated analysis is required

than that presented here. This makes use of linear regression through

pairs of (a3,al) data that satisfy the Hoek-Brown criterion to generate

equivalent values of (a, t) for the Mohr-Coulomb criterion. Further

details of this technique are given in Hoek (1990).