Page 602 - Rock Mechanics For Underground Mining

APPENDIX D LIMITING EQUILIBRIUM ANALYSIS

D.2 Calculation sequence

The following sequence of calculations allows angles of failure and angles of break
to be estimated using the equations derived above. For dry conditions, U = V = 0.
If the upper surface is horizontal, = 0. Positive values of are as shown in Figure
16.19. The equations listed also apply for negative values of . The sequence of
calculations is:

(1) Calculate K from equation D.4.
1
(2) Let p2e = ( p1 + )

2
Z 2
(3) Calculate from equation D.16
c
(4) Calculate a from equation D.14.
(5) Calculate b from equation D.15.
H 2
(6) Calculate from equation D.13.
c
(7) Calculate X from equation D.18.
(8) Calculate Y from equation D.19.
(9) Calculate the estimated value of p2 from equation D.17.
(10) Compare p2 from step 9 with p2e from step 2. If p2 = p2e , substitute p2
for p2e in steps 3, 4 and 5 and repeat the calculation cycle until the difference
between successive values of p2 is < 0.1%.
(11) Calculate b from equation D.20.

584