Rock Mechanics.pdf - Mining and Blasting

Figure 10.12 Distribution of radial
and circumferential stress after
elapsed times of (a) a/Cp and (b)
2a/Cp, around a sphere suddenly excavated
in a hydrostatic stress field.
Figure 10.13 Effect of excavation of
a narrow slot in a medium subject to
pure shear stress.
ENERGY, MINE STABILITY, MINE SEISMICITY AND ROCKBURSTS
the excess energy mobilised at the excavation surface. Further, consideration of the
sudden development of a spherical cavity showed that excess elastic strain energy is
propagated radially as a stress wave, at the P-wave velocity. For arbitrarily shaped
excavations, the nature of the energy propagation must be more complex. This can
be readily inferred from the case of development of a narrow excavation in a medium
subject to pure shear stress, as illustrated in Figure 10.13. It can be readily appreciated
that sudden creation of the slot will cause transverse displacement of the long surfaces
of the excavation. The excess energy in this instance would be generated exclusively
by transverse tractions and displacements, and it is suggested that energy propagation
would occur via transverse, or S waves.
Calculation of the excess energy and energy released by excavation, for arbitrarily
shaped openings, requires the use of a suitable computational method. The boundary
element method is ideal for this purpose, since the solution procedure is formulated in
terms of tractions and displacements induced at excavation surfaces by the mining process.
Its other advantage is that no arbitrary surfaces, such as occur with finite element
and finite difference methods, are introduced in the solution domain. The calculated
energy changes are thus truly appropriate for an infinite or a semi-infinite body.
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