Page 544 - Rock Mechanics For Underground Mining

BLASTING MECHANICS

means that no circumferential tensile stresses can be sustained in the cracked zone.
At any point within the cracked zone of radius r c , the state of stress at any point r is
defined by

rr = p 0 a/r,

= 0

and at the perimeter of the cracked zone by

rr = p 0 a/r c ,

=−p 0 a/r c (17.4)

The implication of equations 17.4 is that existing radial cracks around a hole may
extend so long as the state of stress at the boundary of the cracked zone satisfies the
macroscopic failure criterion for the medium.
A third possible case of quasi-static loading involves radial cracks, but with full
gas penetration. If the volume of the cracks is negligible, the state of stress at the
boundary of the cracked zone is given by

rr = p 0 ,

=−p 0 (17.5)
In practice, the degree of diffusion of gas into the fractures is likely to lie somewhere
between the second and third cases, described by equations 17.4 and 17.5. In any
event, the existence of circumferential tensile stresses about the blast hole provides a
satisfactory environment for radial fracture propagation.
Analysis of high-speed photographs of surface blasts suggests that radial fractures
propagate to the free face, and that the elapsed time for generation of these fractures
may be about 3 ms/m of burden (Harries, 1977).

17.4.3 Release of loading
Field observations of blasts suggest that the elapsed time between charge detonation
and the beginning of mass motion of the burden may exceed ten times the dynamic
phase of loading. At that stage, the burden is rapidly accelerated to a throw velocity
−1
of about 10–20 m s . In the process of displacement, disintegration of the rock mass
occurs. It has been suggested by Cook, M.A. et al. (1966) that impulsive release of
the applied load may lead to over-relaxation of the displacing rock, generating tensile
stresses in the medium. Some evidence to support this postulated mechanism of final
disintegration is provided by Winzer and Ritter (1980). Their observations, made on
linearly scaled test blasts, indicated that new fractures are generated in the burden
during its airborne displacement. There is no similar evidence from full-scale blasts to
support the mechanism, and attempts to generate fractures by impulsive unloading in
laboratorytestshavebeenunsuccessful.However,thereisoneaspectofblastingwhich
can be explained most satisfactorily by the over-relaxation mechanism. Overbreak,
illustrated in Figure 17.6, is readily comprehensible in terms of the rebound of the
solid following rapid release of the blasthole pressure.
The preceding discussion was concerned with blasting in a medium at low states
of stress. In underground mines, the state of stress at a blast site may be high. In such
a situation, illustrated in Figure 17.7, where the local maximum principal stress is
parallel to the free face, crack generation and propagation occur preferentially parallel
to the free face. Crack propagation perpendicular to the free face is impeded.
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