Page 219 - Rock Mechanics For Underground Mining

ZONE OF INFLUENCE OF AN EXCAVATION

used various numerical methods to show that an elastic analysis coupled with a simple
Mohr-Coulomb criterion for slip provided good approximations for estimation of
zones of slip on planes of weakness near excavations. These observations suggest that
the procedures are adequate for analysis of many mine excavation design problems.
The following examples deal with simple excavation shapes for which the stress
fields can be described by simple algebraic expressions. In practice, for general exca-
vation shapes, the methods of stress analysis described in Chapter 6 may be employed,
and the results used in the ways described in the following discussion.

7.2 Zone of influence of an excavation

The concept of a zone of influence is important in mine design, since it may provide
considerable simplification of a design problem. The essential idea of a zone of
influence is that it defines a domain of significant disturbance of the pre-mining stress
field by an excavation. It differentiates between the near field and far field of an
opening. The extent of an opening’s effective near-field domain can be explained by
the following example.
The stress distribution around a circular hole in a hydrostatic stress field, of mag-
nitude p, is given by equations 6.20 as

2
a
rr = p 1 −
r 2
a
2

= p 1 + (7.2)
r 2
r
= 0
Equations7.2indicatethatthestressdistributionisaxisymmetric,andthisisillustrated
in Figure 7.3a. Using equations 7.2, it is readily calculated that for r = 5a,

=
1.04p and rr = 0.96p, i.e. on the surface defined by r = 5a, the state of stress is not
significantly different (within ± 5%) from the field stresses. If a second excavation
(II) were generated outside the surface described by r = 5a for the excavation I, as
shown in Figure 7.3b, the pre-mining stress field would not be significantly different
from the virgin stress field. The boundary stresses for excavation II are thus those for
an isolated excavation. Similarly, if excavation I is outside the zone of influence of
excavation II, the boundary stresses around excavation I are effectively those for an
isolated opening. The general rule is that openings lying outside one another’s zones
of influence can be designed by ignoring the presence of all others. For example, for
circular openings of the same radius, a, in a hydrostatic stress field, the mechanical
interaction between the openings is insignificant if the distance D I,II between their
centres is
D I,II ≥ 6a

It is important to note that, in general, the zone of influence of an opening is related
to both excavation shape and pre-mining stresses.
Other issues related to the notion of zone of influence include the state of stress in a
medium containing a number of excavations, and interaction between different-sized
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