Page 593 - Rock Mechanics For Underground Mining

AN INFINITE LINE LOAD

B.2 An infinite line load

For a line load, of intensity p x per unit length, applied at the xy co-ordinate origin,
in the x direction, and tensile normal stresses reckoned positive, etc.

p x x 2x 2
xx =− (1 − 2 ) +
4 (1 − ) r 2 r 2
x 2y 2
p x
yy =− −(1 − 2 ) +
4 (1 − ) r 2 r 2
y 2x 2
p x
xy =− 2 (1 − 2 ) + 2
4 (1 − ) r r
2
p x x
u x = − (3 − 4 ) n r
8 G(1 − ) r 2
p x xy
u y =
8 G(1 − ) R 2
2
2
2
where r = x + y .

Appendix C Calculation sequences for
rock–support interaction analysis

C.1 Scope

The stepwise calculation sequences presented in this appendix permit rock–support
interaction analyses to be carried out for the axisymmetric problem defined in Figure
A.6. Further details of these analyses are given by Daemen (1975), Hoek and Brown
(1980), and Brown et al. (1983).

C.2 Required support line calculations

Solution using the elastic-brittle rock mass behaviour model of Figure 11.5
Input data

c = uniaxial compressive strength of intact rock pieces;
m, s = material constants for the original rock mass;
E, = Young’s modulus and Poisson’s ratio of the original rock mass;
m r , s r = material constants for the broken rock mass;
p p
f = gradient of −ε vs. ε line (Figure 11.5);
3 1
p = hydrostatic field stress;
r i = internal tunnel radius.
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