Page 111 - Rock Mechanics For Underground Mining

BEHAVIOUR OF ISOTROPIC ROCK MATERIAL IN UNIAXIAL COMPRESSION

Figure 4.6 Spring analogy illustrat-
ing machine–specimen interaction.

in Figure 4.6, the specimen continues to compress, but the load that it can carry
progressively reduces. Accordingly, the machine unloads and its extension reduces.
Figure 4.7 shows what will happen if the machine is (a) soft, and (b) stiff, with re-
spect to the specimen. Imagine that the specimen is at peak strength and is compressed
by a small amount, s. In order to accommodate this displacement, the load on the
specimen must reduce from P A to P B , so that an amount of energy W s , given by
the area ABED in Figures 4.7 a and b, is absorbed. However, in displacing by s
from point A, the ‘soft’ machine only unloads to F and releases stored strain energy
W m , given by the area AFED. In this case W m > W s , and catastrophic failure
occurs at, or shortly after, the peak because the energy released by the machine during
unloading is greater than that which can be absorbed by the specimen in following
the post-peak curve from A to B.
If the machine is stiff with respect to the specimen in the post-peak region, the
post-peak curve can be followed. In Figure 4.7b, W m < W s and energy in excess
of that released by the machine as stored strain energy must be supplied in order
to deform the specimen along ABC. Note that the behaviour observed up to, and
including, the peak, is not influenced by machine stiffness.
For some very brittle rocks, generally those that are fine grained and homogeneous,
portions of the post-peak force–displacement or stress–strain curves can be very
steep so that it becomes impossible to ‘control’ post-peak deformation even in the
stiffest of testing machines. In these cases, the post-peak curves and the associated
mechanisms of fracture may be studied using a judiciously operated servocontrolled
testing machine.

Figure 4.7 Post-peak unloading us-
ing machines that are (a) soft, and (b)
stiff, with respect to the specimen.

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