Page 397 - Rock Mechanics For Underground Mining

ELEMENTARY ANALYSIS OF PILLAR SUPPORT

Table 13.1 Exponents determining pillar strength from its volume and shape (equations 13.5 and 6)
(from Salamon and Munro, 1967).
Source a b Subject medium
Salamon and −0.66 ± 0.16 0.46 −0.067 ± 0.048 0.59 ± 0.14 South African coal;
Munro (1967) in situ failures
Greenwald −0.83 0.50 −0.111 0.72 Pittsburgh coal;
et al. (1939) model tests
Steart (1954); −1.00 0.50 −0.167 0.83 West Virginia coal;
Holland and laboratory tests
Gaddy (1957)
Skinner − − −0.079 − hydrite;
(1959) laboratory tests

Salamon and Munro (1967) summarise some estimated values of the pillar strength
exponents for square pillars, determined from various sources. The values are pre-
sented in Table 13.1.
Equation 13.6 suggests pillar strength is a simple function of pillar width and
height. However, a study reviewed by Wagner (1980) indicated that the operating
area (defined by the pillar dimensions perpendicular to the pillar axis) is important.
Measurement of the load distribution in a pillar at various states of loading, as shown
in Figure 13.10, showed that failure commenced at the pillar boundary and migrated
towards the centre. At the stage where structural failure of the pillar had occured,
the core of the pillar had not reached its full load-bearing potential. Further, it was
proposed that the relative dimensions of the pillar operating area had a substantial
e
influence on pillar strength. This led to definition of the effective width, w , of a pillar
p
of irregular shape, given by
e
w = 4A p /C (13.7)
p
where A p is the pillar operating area and C is the pillar circumference.
In the application of this expression for pillar effective width, pillar strength may
e
be estimated from equations 13.5 and 13.6, with w p replaced by w . It is notable
p
e
that equation 13.7 indicates that, for long rib pillars, with l p w p ,w = 2w p . This
p
is consistent with the field observation that rib pillars are significantly stronger than
square pillars of the same width.
When equation 13.6 is applied to pillars with width-to-height ratio greater than
about four or five, pillar strength is underestimated substantially. For these pillars
with so-called squat aspect ratios, Wagner and Madden (1984) propose that equation
13.5 can be modified to incorporate terms which reflect more accurately the effect of
aspect ratio on strength. The modified pillar strength expression has the form

ε
a
b
S = S o v R {(b/ε)[(R/R o ) − 1] + 1}, R > R o (13.8)
o
In this expression, ε is a parameter with magnitude ε > 1 which describes the rate
of strength increase when aspect ratio R is greater than a nominal aspect ratio R o at
which equation 13.6 is no longer valid. Values suggested for R o and ε which lead to
conservative estimates of squat pillar strength are 5 and 2.5 respectively.
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