Page 543 - Rock Mechanics For Underground Mining

PHENOMENOLOGY OF ROCK BREAKAGE BY EXPLOSIVES

Figure 17.5 Conditions of quasi- 17.4.2 Quasi-static loading
static loading around a blast hole.
The dynamic phase of loading is complete when the radial wave propagates to the free
face, is reflected, and propagates back past the plane of the blast hole. For an average
−1
rock mass (C p = 4000 m s ), this process is complete within 0.5 ms/m of burden.
(The burden is the perpendicular distance from the blasthole axis to the free face.)
Because mass motion of the burden does not occur for an elapsed time much greater
than the dynamic load time, it appears that pressure exerted in the blast hole by the det-
onation product gases may exercise a significant role in rock fragmentation. Sustained
gas pressure in the blast hole increases the borehole diameter, and generates a quasi-
static stress field around the blast hole. Gas may also stream into the fractures formed
by dynamic loading, to cause fracture extension by pneumatic wedging. An idea of
the action of the gases may be obtained by considering the stress distribution around a
pressurized hole, by applying the Kirsch equations (equations 6.18). In the following
discussion,theeffectoffieldstressesonthequasi-staticstressdistributionisneglected.
The simplest case of quasi-static loading involves a pressurized hole, of expanded
radius a, subject to internal pressure p 0 , as shown in Figure 17.5a. If the region
around the hole boundary is uncracked, the state of stress at any interior point, of
radius co-ordinate r,isgiven by

2
2
2
2
rr = p 0 a /r ,

=−p 0 a /r , r
= 0 (17.2)
and the hole boundary stresses are given by
rr = p 0 ,

=−p 0 (17.3)

Thus, if the state of stress represented by equation 17.3 is incapable of generating
fractures at the hole boundary, that represented by equation 17.2 cannot generate
fractures in the body of the medium. This suggests that the pattern of cracks produced
during the dynamic phase may be important in providing centres from which crack
propagation may continue under gas pressure.
Quasi-static loading may occur in the presence of radial cracks, as illustrated in
Figure 17.5b, with no gas penetration of the cracks. The presence of radial cracks
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