Page 258 - Rock Mechanics For Underground Mining

EXCAVATION DESIGN IN STRATIFIED ROCK

Figure 8.11 Normalised deflection
and arch lever arm versus normalised
span, from numerical simulation for
3
E = 16 GPa and = 30 kN/m (after
Sofianos, 1996).
Using r = 1/2.6n from equation 8.25,
3 2 3 4
)
FoS b = 0.59/ Q n s z 1 + s ≈ 3.15/Q n s = 3.15 z on q n s (8.42)
16 z z z
This shows that the factor of safety against buckling instability is inversely pro-
portional to the fourth power of the roof span. Further, for a given room span, the
minimum roof bed thickness corresponding to a factor of safety of unity is given by
1/3

Q n
t min = s 3.15 (8.43)
z on
Comparison of UDEC numerical studies of the beam thickness at buckling with
results calculated from equation 8.43 (Sofianos, 1996) shows good correspondence
between the two different approaches.

8.5.6 Beam failure by crushing at hinges
The maximum values of compressive stress in the arch occur at the hinge points at
the top centre of the span and at the lower edges of the contacts of the beam with
the abutments. Although Sofianos (1996) proposes an analysis in terms of allowable
strains, the most direct method of assessing the possibility of local crushing of the
hinges is to compare the local compressive stress with a measure of rock strength. To
do this, equation 8.31 may be used to estimate a value of the arch deflection z , which
provides directly a value of and, from equation 8.16, a value for the equilibrium
moment arm of the arch, z. The required value xx may then be evaluted directly from
equation 8.14.
As noted previously, care must be taken in selecting a suitable value for the rock
mass compressive strength c to be used in assessing the potential for failure by local
crushing. The Factor of Safety against crushing at the beam hinge points, FoS crush ,is
given by

c
FoS crush = (8.44)
xx
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