Page 399 - Rock Mechanics For Underground Mining

ELEMENTARY ANALYSIS OF PILLAR SUPPORT

Figure 13.11 Definition of mining
variables associated with a paral-
lelepiped shaped pillar (after Galvin
et al., 1999).

should be the minimum width, w, for R < 3 and w eo for R > 6. In the intermediate
range of R, the effective width varies according to the relation
w e = w (R/3–1) = w (13.11)
o
Equation 13.6 was then re-written as

S = S o h w (13.12)
and equation 13.8 as

a b ε
S = S o v R {(b/ε)[(R/R o ) − 1] + 1} (13.13)
o
For the revised South African database, Galvin et al. (1999) found that S o = 6.88
MPa, =−0.60 and = 0.42. For the Australian database, S o = 8.60 MPa, =
−0.84 and = 0.51, and for the combined South African and Australian databases,
S o = 6.88 MPa, =−0.70 and = 0.50.
For pillar design in hard rock mines, Lunder and Pakalnis (1997) proposed a method
of estimating pillar strength which integrated the results of tributary area and boundary
element analysis in the so-called confinement formula. It sought to reconcile the
highly empirical expressions for pillar strength with those derived from more rigorous
principles based on conventional rock strength criteria, as discussed in Chapter 4, and
the states of stress and confinement which develop in a pillar. It drew on a large data
base of observations of pillar behaviour in Canadian mines, and also results reported
by Brady (1977) for the Mount Isa Mine, Australia, Krauland and Soder (1987)
for the Black Angel Mine, Greenland and Sj¨oberg (1992) for the Zinkgruvan Mine,
Sweden.
Starting from the assumption that pillar strength S can be represented by

S = S( c , size, shape)
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