Page 396 - Rock Mechanics For Underground Mining

PILLAR SUPPORTED MINING METHODS

stress field have no effect on pillar performance is not generally tenable. Finally the
effect of the location of a pillar within an orebody or mine panel is ignored.
The tributary area method provides a simple method of determining the average
state of axial stress in a pillar. Prediction of the in situ performance of a pillar requires
a method of assessing the strength or peak resistance of the pillar to axial compression.
Retrospective analysis of the in situ performance of pillars, using the tributary area
method to estimate imposed pillar stresses, suggests that the strength of a pillar is
related to bothitsvolume and its geometric shape. The effect of volume onstrength can
be readily understood in terms of a distribution of cracks, natural fractures and other
defects in the rock mass. Increasing pillar volume ensures that the defect population
is included representatively in the pillar. The shape effect arises from three possible
sources: confinement which develops in the body of a pillar due to constraint on its
lateral dilation, imposed by the abutting country rock; redistribution of field stress
components other than the component parallel to the pillar axis, into the pillar domain;
changeinpillarfailuremodewithchangeinaspect(i.e.width/height)ratio.Thesecond
of these factors is, in fact, an expression of an inherent deficiency of the tributary area
method.
The historical development of formulae for pillar strength is of considerable prac-
tical interest. As noted by Hardy and Agapito (1977), the effects of pillar volume and
geometric shape on strength S are usually expressed by an empirical power relation
of the form

a
a
b
S = S o v (w p /h) = S o v R b (13.5)
In this expression, S o is a strength parameter representative of both the orebody rock
mass and its geomechanical setting, v, w p and h are pillar volume, width and height
respectively, R is the pillar width/height ratio, and a and b reflect geo-structural and
geomechanical conditions in the orebody rock.
Examination of equation 13.5 might suggest that if strength tests were performed
3
on a unit cube of orebody rock (i.e. 1 m , each side of length 1 m), the value of the rep-
resentative strength parameter S o could be measured directly. Such an interpretation
is incorrect, since equation 13.5 is not dimensionally balanced. Acceptable sources
of a value for S o are retrospective analysis of a set of observed pillar failures, in the
geomechanical setting of interest, or by carefully designed in situ loading tests on
model pillars. The loading system described by Cook, N.G.W. et al. (1971), involving
the insertion of a jack array in a slot at the midheight of a model pillar, appears to be
most appropriate for these tests, since it preserves the natural boundary conditions on
the pillar ends.
An alternative expression of size and shape effects on pillar strength is obtained by
recasting equation 13.5 in the form

S = S o h w p (13.6)
For pillars which are square in plan, the exponents , , a, b in equations 13.5 and
13.6 are linearly related, through the expressions
1 1
a = ( + ), b = ( − 2 )
3 3
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