The mathematical modelling of rock blasting

Abstract

This thesis presents a mathematical model for the motion of high pressure turbulent gas in the radial cracks generated around a borehole during rock blasting. The model equations are solved analytically for certain special cases of the blast parameters and the general solution is obtained numerically. The model solutions show that the initial mechanism for containing the high pressure gas is the clamping force from the natural in-situ stress in the rock. After a sufficient time, however, the borehole gas pressure will substantially decrease as gas is lost to the cracks. The gas will then flow much more slowly than at the start of the rock blast or than in other calculations, Erhie 88, where a constant borehole pressure throughout the blast was assumed. The gas front is in general distinct from the crack tip. As the gas pressure along the cracks decreases then the gas front will catch up with the crack tip. This agrees with the observation that low pressure magma flow in rock tends to have only a small gap between the magma front and the crack tip.

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