Page 393 - Rock Mechanics For Underground Mining

ELEMENTARY ANALYSIS OF PILLAR SUPPORT

and subsequent relaxation of the elastic state of stress in the pillar, need only be of
elastic orders of magnitude. A pillar (or other rock remnant in a mine layout) with
a well-developed foliation or schistosity parallel to the principal axis of loading will
fail in a buckling mode, as illustrated in Figure 13.5e. This mechanism resembles the
formation of kink bands.
Field observations of pillars subject to biaxial loading are usually difficult, due to
the mine geometries in which they occur. However, observations reported by Brady
(1977), Krauland and Soder (1987), Sj¨oberg (1992) and Diederichs et al. (2002)
suggest that the modes of response for biaxially loaded pillars are consistent with
those for uniaxial loading. A similar conclusion is implied in the work by Wagner
(1974).

13.3 Elementary analysis of pillar support

In the analysis and prediction of the behaviour of a set of pillars in a mine structure,
the computational techniques described in Chapter 6 could be used for detailed deter-
mination of the state of stress throughout the rock mass. However, some instructive
insights into the properties of a pillar system can be obtained from a much simpler
analysis, based on elementary notions of static equilibrium. These are used to establish
an average state of stress in the pillars, which can then be compared with an average
strength of the rock mass representative of the particular pillar geometry. Notwith-
standing the limitations of this approach, Lunder and Pakalnis (1997) proposed that
it is possible to reconcile the analysis of pillar stress using the tributary area method
with more rigorous analysis using computational methods.
Figure 13.7a shows a cross section through a flat-lying orebody, of uniform thick-
ness, being mined using long rooms and rib pillars. Room spans and pillar spans
are w o and w p respectively. For a sufficiently extensive set of rooms and pillars, a
representative segment of the mine structure is as shown in Figure 13.7b. Consid-
ering the requirement for equilibrium of any component of the structure under the
internal forces and unit thickness in the antiplane direction, the free body shown in

Figure 13.7 Bases of the tributary
area method for estimating average
axial pillar stress in an extensive mine
structure, exploiting long rooms and
rib pillars.

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