Page 259 - Rock Mechanics For Underground Mining

ROOF BEAM ANALYSIS FOR LARGE VERTICAL DEFLECTION

8.5.7 Shear failure at the abutments
As in the small-deflection analysis, the possibility of shear failure of the roof beam
by slip at the abutments can be assessed from the abutment stresses and the beam
geometry. Referring to Figure 8.7b, the lateral thrust, T , at the abutment must mobilise
a frictional resistance to slip sufficient to balance the abutment shear force, V , acting
on the vertical joints. The maximum frictional resistance F that can be mobilised by
thrust T is

1
F = T tan = xx nt tan (8.45)
2
where is the angle of friction of the cross joints of the rock bed.
The abutment shear force is given by

1
V = st (8.46)
2
and the Factor of Safety against abutment shear failure, FoS slip , is then defined by
xx n tan
FoS slip = (8.47)
s
In summary, equations 8.42, 8.44 and 8.47 provide the means of determining the
factors of safety against the three modes of roof beam failure under conditions of
large vertical deflections of the beam. In addition to rock strength and joint friction
parameters, the in situ deformation modulus plays an important role in roof bed
deformation mechanics and consequently in roof stability. Both the vertical deflection
and the longitudinal stresses mobilised in the beam are directly proportional to the
deformation modulus. Therefore it is necessary to measure or estimate the roof bed
deformation modulus in the direction parallel to bedding. In doing so, proper account
must be taken of the frequency and compressibility of cross joints, as compressible
joints may constitute the most deformable component of the rock mass.

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