Page 292 - Rock Mechanics For Underground Mining

ENERGY, MINE STABILITY, MINE SEISMICITY AND ROCKBURSTS

Figure 10.3 (a) Dynamic loading of
a pillar, and (b) the corresponding
load–deflection diagram.

diagram. It is observed that the pillar load P z is constant throughout the pillar axial
deformation. The maximum axial compression is given by
u z max = ε zz L = ( zz max /E)L

and the strain energy increase is given by

U d = work done by the loading system

i.e.

(10.6)
( zz max /2E)AL = P z u z max
or

zz max = 2P z /A = 2 zz

Also

u z max = 2u z st (10.7)
where zz max and u z max are the peak static values of axial stress and compression.
It is useful to examine the partitioning of energy in the pillar as it passes through the
static equilibrium state on rebound from maximum axial compression. The problem
geometry is illustrated in Figure 10.4. Since energy is conserved in the system, the
total strain energy, U d , is distributed, at passage through the static equilibrium state,
among the other forms of energy according to

U d = (increase in gravitational P.E.) + K.E. + U st

Figure 10.4 Problem geometry for
examining energy partitioning in a pil-
lar under dynamic load.

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