Page 112 - Rock Mechanics For Underground Mining

ROCK STRENGTH AND DEFORMABILITY

Figure 4.8 Principle of closed-loop
control (after Hudson et al., 1972b).

The essential features of closed-loop servocontrol are illustrated in Figure 4.8.
An experimental variable (a force, pressure, displacement or strain component) is
programmed to vary in a predetermined manner, generally monotonically increasing
with time. The measured and programmed values are compared electronically several
thousands of times a second, and a servo valve adjusts the pressure within the actuator
to produce the desired equivalence.
Modern servocontrolled testing systems are used to conduct a wide variety of tests
in rock mechanics laboratories. The key to the successful use of these systems is the
choice of the control variable. The basic choice is between a force (or pressure) and a
displacement (or strain) component. Figure 4.9 shows why it is not feasible to obtain
the complete uniaxial force–displacement curve for a strain-softening specimen by
programming the axial force to increase monotonically with time. When the peak
strength of the specimen is reached, the program will attempt to continue to increase
the axial force, but the load-carrying capacity can only decrease with further axial
displacement. However, the test can be successfully controlled by programming the
axial displacement to increase monotonically with time.
The post-peak portions of the force–displacement curves obtained in compression
tests on some rocks may be steeper than, or not as smooth as, those shown in Figures
4.7 and 4.9. In these cases, better control can be obtained by using the circumferential
displacement rather than the axial displacement as the control variable. Figure 4.10
shows the complete axial stress ( a )–axial strain (ε a ) and circumferential (or radial)
strain (ε r )–axial strain curves obtained in such a test on a 50 mm diameter by 100 mm
Figure 4.9 Choice between force
long specimen of an oolitic limestone (Portland stone) in which a wrap-around trans-
and displacement as the programmed
ducer was used to monitor circumferential displacement. Although the possibility of
control variable (after Hudson et al.,
1972a). extracting energy from the machine–specimen system offered by this technique is
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