ABSTRACT

Rocks, being so much stronger in compression than in tension, can effectively transmit potentially damaging disturbances to regions remote from the sources of the disturbances. Development of an appreciation of how small rocks break up under impact loads resolves itself primarily into the geometrical problem of tracing the peregrinations of these disturbances through the rock specimen of interest, particularly with respect to mutual interactions of incident and reflected stress waves. Completion of a number of exercises of this type suggest that comminution may to a large measure be controlled by the interferences of stress waves.

Comminution of rocks is an old and honorable art, an art which has been placed, during the past twenty years, on a sound basis as regards efficiency of operation. Although a number of excellent theoretical treatments have been made which describe statistically the end result of comminution processes, there is not a complete understanding of the details of the mechanics and dynamics of rock break up under dynamic loads. Indeed, it has only been in the past few years that we have begun to appreciate the very important role that stress waves play in the fracturing of impulsively loaded bodies( Rinehart and Pearson, 1954).

A body such as a small rock will break whether crushed under a static load or struck a blow with a hammer. The events leading to the breakage in the two instances are decidedly different. Under the static crushing load, the rock disintegrates because it cannot support the static strains to which it is subjected. The disintegration is a gradually occurring one in which all parts of the rock participate simultaneously. On the other hand, when a rock is struck a sharp blow, the fact that it has been struck this blow is not instantaneously transmitted to all parts of the rock: each individual part of the rock does not have a chance to cooperate leisurely with its remote neighbors in determining the specific reaction of the whole rock to the blow. Transmittal of the disturbance through the rock will be controlled by well defined physical laws, involving the elastic properties of the material out of which the rock is made.

An elastic material has the important property that it can transmit a disturbance only as either one of two types of waves: a dilitational wave, in which the particle motion at the front of the wave is parallel to the direction of propagation of the wave; and a transverse or shear wave in which the particle motion is perpendicular to the direction of propagation of the wave. No other disturbances can exist, although at times it is convenient to describe mass movements of complex interplays of these two kinds of waves as distinct waves such as the Raleigh, Love, or bar waves. The dilitational wave moves with a velocity, cl, given by Mathematical equation (Available in full paper) where K is the bulk modulus; p is the density of the material; and v is its Poisson's ratio.

FIGURE 1. Waves generated by impulsive load applied at a point. (Available in full paper)

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