Engineering Rock Mechanics

396

and at the centre it is
ocentre 18.8
ffp 7.7

Fcentre = - - - -- - 2.44

This shows that the effect of the confinement offered by the bulk of the
pillar is to produce a marked increase in factor of safety at the pillar
centres, in comparison to the pillar faces. However, given the uncertainty
that will surround the assessment of the geomechanical parameters,
both of these factors of safety are very low. Careful consideration would
need to be given to the acceptability of these values, and whether
reinforcement of the pillars should be considered.

420.10 A gold-bearing quartz vein, 2 m thick and dipping at 90°, is

to be exploited by a small cut-and-fill stoping operation. The mining

is to take place at a depth of 800 m, and the average unit weight

of the granite country rock above this level is 29 kN/m3. The strike

of the vein is parallel to the intermediate principal stress, and the

major principal stress is horizontal with a magnitude of 37.0 MPa.

The uniaxial compressive strength of the vein material is 218 MPa,

and the tensile strength of the country rock is 24 MPa. Poisson's

ratio and Young's modulus for the quartz are 0.2 and 48 GPa,

respectively. During mining, each blast will extend a stope up-dip by

about 2 m.

Assuming that no stress-induced failure is permissible, what is the

maximum height of a stope?

It is considered that the backfill will offer sufficient support to

prevent degradation of the side walls of a stope, and that the only

stress-induced failure of concern is that in the crown. What is the

maximum permissible height of a stope in these circumstances?

A20.10 We will assume that, in the cross-section of the excavation, the

stresses induced in the sidewall and the crown of the stope can be

approximated using the equations for an elliptical excavation. On the

basis that the sidewall stress can be computed using the inscribed ellipse,

we have

-- ffsidewall -1-k+2(:)

ffvertical

and if the crown is semi-circular we have

--k-l+k,/x ffcrown - =k-l+2k -.

Rearranging these gives the height of the excavation as the minimum of

ffvertical Pcrown

h= 2w orh=Z(=+l-k).^2

ffsidewall +k-1 4k2 overtical

ffvertical

The maximal stress that can be sustained by the crown and the

sidewall are 218 MPa and -5 MPa, respectively. Note that the sidewall

stress is negative because this represents the tensile strength.