Page 598 - Rock Mechanics For Underground Mining

APPENDIX D LIMITING EQUILIBRIUM ANALYSIS

(6) For 12 > max 2 < max 1

max 2 (k 1 + k 2 )
p max 12 =
r i

Appendix D Limiting equilibrium analysis of

progressive hangingwall caving

D.1 Derivation of equations

The assumptions made, and the variables involved in the limiting equilibrium analysis
of the problem illustrated in Figure 16.19, are set out in section 16.4.2.

Weight of wedge. The weight of the wedge of rock BCDNML in Figure 16.19 is

"
2
2
H sin( + 0 ) sin( p2 + 0 ) H sin( + 0 ) sin( p1 + 0 )
W = 2 − 1
2
2
2 sin 0 sin( p2 − ) sin 0 sin( p1 − )
#
cos cos p1 2 cos cos p2
2
+ Z 1 − Z 2 (D.1)
sin( p1 − ) sin( p2 − )
Base area of wedge. The area of unit thickness of the surface LM (Figure 16.19)
on which failure takes place is
H 2 (sin cot 0 + cos ) − Z 2 cos
A = (D.2)
sin( p2 − )
Thrust due to caved material. The thrust acting on the wedge BCDNML due to
the caved material left in the crater is one of the most difficult parameters to estimate
with confidence in this analysis. A simplified system of forces used to calculate T is
shown in Figure 16.19. Resolving the forces W c , T c and T in the horizontal and vertical
directions and applying the equations of equilibrium of forces gives the solution

1
2
T = c H K (D.3)
2 c
where
S

(cot p1 + cot 0 ) + 2
H c
K = (D.4)
cos( p1 − w ) + sin( p1 − w ) cot( 0 − w )
580