Page 220 - Rock Mechanics For Underground Mining

EXCAVATION DESIGN IN MASSIVE ELASTIC ROCK

Figure 7.3 (a) Axisymmetric stress
distribution around a circular opening
inahydrostaticstressfield;(b)circular
openings in a hydrostatic stress field,
effectively isolated by virtue of their
exclusion from each other’s zone of
influence.

excavations. Figure 7.3b illustrates the overlap of the zones of influence of two circular
openings. In the overlap region, the state of stress is produced by the pre-mining
stresses and the stress increments induced by each of the excavations I and II. In the
other sections of each zone of influence, the state of stress is that due to the particular
excavation.
Figure 7.4 illustrates a large-diameter opening (I) with a small-diameter opening
(II) in its zone of influence. Since excavation I is outside the zone of influence of
excavation II, a fair estimate of the boundary stresses around I is obtained from the
stress distribution for a single opening. For excavation II, the field stresses are those
due to the presence of excavation I. An engineering estimate of the boundary stresses
around II can be obtained by calculating the state of stress at the centre of II, prior to
its excavation. This can be introduced as the far-field stresses in the Kirsch equations
(Equations 6.18) to yield the required boundary stresses for the smaller excavation.

Figure 7.4 Illustration of the effect
of contiguous openings of different di-
mensions. The zone of influence of ex-
cavation I includes excavation II, but
the converse does not apply.

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