Page 237 - Rock Mechanics For Underground Mining

SUPPORT AND REINFORCEMENT OF MASSIVE ROCK

Figure 7.20 Stress distribution
around a circular opening in a hydro-
static stress field, due to development
of a fracture zone.

The strength of fractured rock is taken to be purely frictional, with the limiting state
of stress within the fractured rock mass defined by

f
(1 + sin )
1 = 3
f
(1 − sin )
or
(7.10)
1 = d 3
f
where is the angle of friction for fractured rock.
Since the problem is axisymmetric, there is only one differential equation of equi-
librium,

d rr

− rr
= (7.11)
dr r
This condition is to be satisfied throughout the problem domain. In the fractured rock,

and rr are related through equation 7.10, since limiting friction is assumed in
the fractured medium. Introducing equations 7.10 into equation 7.11, gives

d rr rr
= (d − 1)
dr r
Integrating this expression, and introducing the boundary condition, rr = p i when
r = a, yields the stress distribution relations
r
d−1
rr = p i
a
(7.12)
r
d−1

= dp i
a
Equations 7.12 are satisfied throughout the fractured domain and on its bound-
aries. At the outer limit of the fractured annulus, fractured rock is in equilibrium
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