Page 310 - Rock Mechanics For Underground Mining

ENERGY, MINE STABILITY, MINE SEISMICITY AND ROCKBURSTS

Figure 10.15 Problem geometry for
determination of released energy for
an incremental increase in a mined
void.

When the excavation is created suddenly, the surface S does no work against the
forces applied to it by the interior material, and the work potential W i is expressed
as excess energy at the excavation periphery. Therefore, for an excavation of arbi-
trary shape, the excess energy and the released energy are obtained directly from the
excavation-induced tractions and displacements, i.e.

1 %
W e = W r = (t x u xi + t y u yi )dS (10.72)
2 s

Also, since the excess energy is mobilised at the excavation surface, this acts as the
source for P and S waves, which radiate through the rock mass.
In mining small excavations, such as drives and crosscuts, the practice is to generate
thecompleteexcavationcrosssectionrapidly,inanincrementallongitudinalextension
of the opening. For the ore production excavations used in extracting an orebody, it
is unusual for a complete stope to be mined instantaneously. The interest then is
in the energy release rate for increments of extraction of the stope. Referring to
Figure 10.15, the surface of the volume increment of excavation acts as a source for
energy release. The area rate of energy release, dW r /dS, becomes a more appropriate
measure of the intensity of energy release. If the orebody is geometrically regular, e.g.
of uniform thickness, the volume rate of energy release, dW r /dV , is an index of the
specific energy available for local crushing of rock around the excavation boundary.
The value of this index is that it has the same dimensions as strain energy density,
and therefore the same dimensions as stress.
The computational determination of W r and its derivates is a simple matter using the
boundary element method of analysis. It is a trivial exercise to integrate, numerically,
the products of induced tractions and displacements over the surface of an excavation.
If this is repeated for the successive stages of excavation, the released energy W r
for an incremental increase in a mined void is obtained simply from the difference of
the successive total amounts of released energy. The incremental area S or volume
V of excavation is provided by the successive stages of the problem geometry, so
that the derivates dW r /dS or dW r /dV are obtained directly.

292