Page 127 - Rock Mechanics For Underground Mining

STRENGTH CRITERIA FOR ISOTROPIC ROCK MATERIAL

Figure 4.27 Griffith envelopes for
crack extension in plane compression.

During the 1960s, a number of attempts were made to apply these results to the
peak strength envelopes for rock. Quite often, 2 in the plane stress criterion was
simply replaced by 3 so that the criterion could be applied to triaxial test results.
For a number of reasons, the classical Griffith criterion did not provide a very good
model for the peak strength of rock under multiaxial compression. Accordingly, a
number of modifications to Griffith’s solution were introduced (see Paterson, 1978
and Jaeger and Cook, 1979 for details). The most important of these modifications
was probably that introduced by Cook (1965) who developed equations for the
Griffith locus for instability, or the post-peak stress-strain curve, for rock in com-
pression by assuming shear displacement or sliding on an array of variably inclined
cracks.
Using Cook’s approach, Martin and Chandler (1994) developed equations for the
Griffith locus for rock in triaxial compression which they fitted to triaxial test results
obtained for the Lac du Bonnet granite from the Underground Research Laboratory
at Pinnawa, Manitoba, Canada. Figure 4.28 shows a comparison of the calculated
Griffith locus (solid line) and the measured Griffith locus at confining pressures of 2,
15 and 30 MPa. It was found that as crack-induced damage accumulated in the sample,
the stress level associated with crack initiation remained essentially unchanged but
that the stress level required to initiate sliding reduced dramatically.

Figure 4.28 Comparison of calcu-
lated Griffith locus (solid line) and
measured Griffith locus for Lac du
Bonnet granite (after Martin and
Chandler, 1994).

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