Page 221 - Rock Mechanics For Underground Mining

ZONE OF INFLUENCE OF AN EXCAVATION

Figure 7.5 (a) A practical prob-
lem involving semi-coupling between
a large excavation (a cut-and-fill
stope) and smaller access openings;
(b) nomenclature for definition of
the zone of influence of an elliptical
opening.

Problems related to zone of influence arise frequently in metalliferous mining.
Haulages, access and service openings must frequently be located, for reasons of
economy and practicality, in the zone of influence of the major production openings.
An example is shown in Figure 7.5a, with access openings on the footwall side
of an inclined orebody. In this case, a zone of influence could be defined for an
ellipse inscribed in the stope cross section, for any particular stage of up-dip advance
of mining. Suppose the stope is outside the zone of influence of each access drive.
Then, reasonable estimates of the access opening boundary stresses could be obtained
from the local stresses due to the pseudo-elliptical stope and the boundary stress
concentrations due to the shape of the access drive.
The preceding discussion suggests that it is useful to consider the zone of influence
of an elliptical excavation in the course of a design exercise. It is therefore appropriate
to formalise its definition. The general case of a zone around an elliptical excavation
in which the stresses depart from the maximum in situ stress (p or Kp) by more
than c% has been considered by Bray (1986). From this analysis, the zone may be
approximated by an ellipse with axes W I and H I equal to the greater of each of the
following sets of values:

W I = H[A | q(q + 2) − K(3 + 2q) | ] 1/2
or

2
2
W I = H[ {A(K + q ) + Kq }] 1/2
H I = H[A | K(1 + 2q) − q(3q + 2) | ] 1/2
or
2
H 1 = H[ {A(K + q ) + 1}] 1/2
where W and H are the width and height of the elliptical excavation, q = W/H, A =
100/2c and = 1, if K < 1, and = 1/K,if K > 1.
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