Page 222 - Rock Mechanics For Underground Mining

EXCAVATION DESIGN IN MASSIVE ELASTIC ROCK

For the special case of a zone of influence defined by a 5% departure from the field
stresses, A is set equal to 10 in the preceding expressions.

7.3 Effect of planes of weakness on elastic stress distribution

In excavation design problems where major discontinuities penetrate the prospective
location of the opening, questions arise concerning the validity of elastic analysis in
the design process and the potential effect of the discontinuity on the behaviour of the
excavation periphery. It is now shown that, in some cases, an elastic analysis presents
a perfectly valid basis for design in a discontinuous rock mass, and in others, provides
a basis for judgement of the engineering significance of a discontinuity. The following
discussion takes account of the low shear strengths of discontinuities compared with
that of the intact rock. It assumes that a discontinuity has zero tensile strength, and is
non-dilatant in shear, with a shear strength defined by

= n tan (7.3)

As observed earlier, although the following discussion is based on a circular opening,
for purposes of illustration, the principles apply to an opening of arbitrary shape. In
the latter case, a computational method of stress analysis would be used to determine
the stress distribution around the opening.
Case 1. (Figure 7.6) From the Kirsch equations (equations 6.18), for
= 0, the
shear stress component r
= 0, for all r. Thus rr ,

are the principal stresses xx ,
yy and xy is zero. The shear stress on the plane of weakness is zero, and there is no
tendency for slip on it. The plane of weakness therefore has no effect on the elastic
stress distribution.

Case 2. (Figure 7.7a) Equations 6.18, with
= /2, indicate that no shear stress
is mobilised on the plane of weakness, and thus the elastic stress distribution is not

Figure 7.6 A plane of weakness,
oriented perpendicular to the major
principal stress, intersecting a circular
openingalongthehorizontaldiameter.

204