Page 336 - Rock Mechanics For Underground Mining

ROCK SUPPORT AND REINFORCEMENT

of stress in the elastic and fractured rock are given by

(7.8)
1 = b 3 + C 0
and
(7.9)
1 = d 3
The principal stresses within the fractured zone are
r
d−1
3 = rr = p i
a
and
r
d−1
1 =

= dp i (7.11)
a
and the radius of the fractured zone is
1/(d−1)

2p − C 0
r e = a (7.15)
(1 + b)p i
The radial stress transmitted across the elastic-fractured zone interface at radiusr = r e
is
Figure 11.5 Idealised elastic-brittle
stress–strain model (after Brown 2p − C 0
et al., 1983). p 1 = 1 + b (7.14)
In the elastic zone, the radial displacement produced by a reduction of the radial
stress from p to p 1 is
(p − p 1 )r e 2
u r =−
2Gr
At r = r e
(p − p 1 )r e
u r =−
2G
If no fractured zone is formed, the radial displacement at the periphery of the
excavation (r e = a)is

(p − p i )a
u i =− (11.1)
2G
Note that the radial displacement, u, is positive outwards from the centre of the
excavation.
Within the fractured zone, for infinitesimal strain and with compressive strains
positive, considerations of the compatibility of displacements give
u
ε 1 = ε

=− (11.2)
r
and
du
ε 3 = ε rr =− (11.3)
dr
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