Page 594 - Rock Mechanics For Underground Mining

APPENDIX C ROCK–SUPPORT INTERACTION ANALYSIS

Figure A.6 Axisymmetric tunnel
problem showing the development of
a plastic zone around the tunnel.

Calculation sequence

1/2

1 m 2 mp m
(1) M = + + s −
2 4 c 8
E
(2) G =
2(1 + )
(3) For p i p − M c , deformation around the tunnel is elastic,

(p − p i )
i
=
r i 2G
(4) For p i < p − M c , plastic deformation occurs around the tunnel

u e M c
=
r e 2G

1/2
p − M c s r
(5) N = 2 +
m r c m 2
r
" #
1/2

r e p i s r
(6) = exp N − 2 + 2
r i m r c m r
"
f +1 #
( f − 1)
i M c r e
(7) = +
r i G( f + 1) 2 r i
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