Page 254 - Rock Mechanics For Underground Mining

EXCAVATION DESIGN IN STRATIFIED ROCK

Figure 8.10 Normalised arch thick-
ness versus normalised span (after
Sofianos, 1996).
between load depth fraction, n, and normalised room span, s n (given by s/t, where
t is the roof bed thickness). The plot shown in Figure 8.8 shows good consistency
between the finite element and UDEC results.
It was found that, for a wide range of roof beam geometries, the values of n at
equilibrium lie between 0.12 and 0.30, and fit the expression

n = 1/(0.22 s n + 2.7) (8.15)

It should be noted that this equation returns magnitudes of the equilibrium value of
n that are considerably less than the value of about 0.75 reported by Diederichs and
Kaiser (1999a).

8.5.1 Beam deflection
In roof beam formation, an arch of undeflected height z o is shortened by an increment
L during a vertical deflection to form an arch of height z. The relation between
arch height and deflection, and some associated relations required in the following
analysis, are given by

= z 0 − z (8.16)
z
z n = = z on − n (8.17)
t
2
z on = 1 − n (8.18)
3
1 2
M R = xx nt z n (8.19)
2
where subscript n represents normalisation of geometric parameters with respect to
the roof thickness t.
8.5.2 Arch geometry
In its deflected position, the lateral thrusts T mobilised in the compression arch
are associated with axial stresses which satisfy equation 8.13. The relation between
mobilised thrust and beam deflection exploits the assumption of the shape of the
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