Page 238 - Rock Mechanics For Underground Mining

EXCAVATION DESIGN IN MASSIVE ELASTIC ROCK

with intact, elastic rock. If p 1 is the equilibrium radial stress at the annulus outer
boundary, r e ,
d−1

r e
p 1 = p i
a
or
1/(d−1)

p 1
r e = a (7.13)
p i
Simple superposition indicates that the stress distribution in the elastic zone is
defined by

r e r e
2
2

= p 1 + − p 1
r 2 r 2
(7.14)
2
2
r e r e
rr = p 1 − + p 1
r 2 r 2
At the inner boundary of the elastic zone, the state of stress is defined by

= 2p − p 1 , rr = p 1

This state of stress must represent the limiting state for intact rock, i.e. substituting
for

( 1 ) and rr ( 3 ) in equation 7.9 gives

2p − p 1 = bp 1 + C 0

or

2p − C 0
p 1 = (7.15)
1 + b
Substitution of equation 7.15 in equation 7.13 yields

1/(d−1)
2p − C 0
r e = a (7.16)
(1 + b)p i
Equations 7.12, 7.14, and 7.16, together with the support pressure, field stresses and
rock properties, completely define the stress distribution and fracture domain in the
periphery of the opening.
A numerical example provides some insight into the operational function of in-
f
stalled support. Choosing particular values of and of 35 , p i = 0.05p and
◦
C 0 = 0.5p, leads to r e = 1.99a. The stress distribution around the opening is shown
in Figure 7.20b. The main features of the stress distribution are, first, the high and in-
creasing gradient in the radial variation of

, both in an absolute sense and compared
with that for rr ; and secondly, the significant step increase in

at the interface
between the fractured and intact domains. These results suggest that the primary role

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