Page 224 - Rock Mechanics For Underground Mining

EXCAVATION DESIGN IN MASSIVE ELASTIC ROCK

Figure 7.8 A flat-lying plane of
weakness intersecting a circular exca-
vation non-diametrically.
The limiting condition for slip under this state of stress is
= n tan

or, introducing equation 7.4,
2

sin
cos
=

cos
tan (7.5)
or
tan
= tan

Thus if
= , the condition for slip is satisfied on the plane of weakness. (This
conclusion could have been established by noting that the resultant stress, in this case

, is constrained to act within the angle to the normal to the plane.) It is observed
that the sense of slip, defined by the sense of the shear stress, involves outward
displacement of the upper (hanging wall) surface of the fault relative to the lower
surface. This implies boundary stresses lower than the elastic values in the crown of
the opening. A prudent design response would anticipate the generation of subvertical
tension fractures in the crown.
The equilibrium state of stress at the boundary-plane of weakness intersection can
be established from equation 7.5, which may be rewritten in the form

sin(
− )

= 0
cos
For
> , this condition can be satisfied only if

= 0. Thus the regions near the
intersection of the opening and the plane of weakness are either de-stressed, or at low
confining stress. They may be expected to be areas from which loosening of rock may
commence, and therefore deserve special attention in support design.

Case 4. (Figure 7.9) The problem illustrated in Figure 7.9a is introduced as a simple
example of an arbitrarily inclined plane of weakness intersecting an opening. The
far-field stresses are defined by components p (vertical) and 0.5p (horizontal). For
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