Page 473 - Rock Mechanics For Underground Mining

SUBLEVEL CAVING

Figure 15.21 Janelid and Kvapil’s
flow ellipsoid concept.

Laboratory and field observations have shown that the ellipsoid of motion is not
always a true ellipsoid. Its shape is a function of the distribution of particle sizes
within the flowing mass and of the width of the discharge opening. The smaller the
particle size, the more elongated is the ellipsoid of motion for the same discharge
opening width. The upper portion of the ellipsoid of motion tends to be flattened or
broadened with respect to a true ellipsoid, particularly for large draw heights and
irregular particle sizes (Figure 15.22). Despite these observed complexities, Janelid
and Kvapil’s concept of the ellipsoid of motion provides a useful basis on which to
develop some understanding of the mechanics of the gravity flow of broken ore in
sublevel caving.
In the classical theory, the shape of a given ellipsoid of motion is described by its
eccentricity

1 2 2 1/2
ε = a − b
N N
a N
where a N and b N are the major and minor semi-axes of the ellipsoid, it being assumed
that the horizontal cross section of the ellipsoid is circular. Janelid and Kvapil (1966)
suggested that, in practice, ε varies between 0.90 and 0.98 with values in the range
Figure 15.22 Modified draw shape
for large draw heights and irregular 0.92 to 0.96 being found to apply most commonly. If E N is the volume of material
particle sizes (after Just, 1981). discharged from an ellipsoid of motion of known height h N , then the corresponding
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