Engineering Rock Mechanics

391

A20.7 (a) When A is very small, the expression (ac)pILLAR = 10+45e-'
tends to a value of 55 MPa - this is the laboratory compressive strength.
Similarly, when A becomes very large, the strength tends to 10 MPa,
which is the super-REV pillar compressive strength.
(b) Room-and-pillar designs are usually produced using the tributary
area theory, and the formula

(20.9)

where a, is the vertical stress which, for this case, is given by

yz = 0.027 x 100 = 2.7 MPa. Also, the maximal stress that a square

pillar can be subjected to is given by

(20.10)

where F is the factor of safety.

Eqs. (20.9) and (20.10) can be combined to find a pillar width for a

given set of parameters, but the resulting equation has to be solved by

iteration. It is more instructive to plot a series of curves for the opening

width in terms of the pillar stress and the pillar width. Rearranging

Eq. (20.9) gives

and hence

The resulting curves of opening width in terms of pillar width and

factor of safety are as shown below.

0 2 4 6 8 10 12 14 16 18 20 22

pillar width, m