Fragmentation of rock by geometrical simulation of crack motion—I: Independent planar cracks

Abstract

We employ numerical simulation and photographic reproduction of a manifold of cracks to study crack motion under stress, leading to fracturation. In our model (which is two-dimensional) the rock contains one planar crack, or a number of such cracks which may be randomly distributed in the medium, or else may be a set of radial cracks (such as would arise near a cylindrical borehole). The detonation is simulated by a time and stress varying wave emerging from one (or several) boreholes. The sense (tensile or compressive) and magnitude of the instantaneous pressure at each crack-tip determine the motion of the crack, in particular its direction. The finiteness of the rock is taken care of by the presence of a set of image-boreholes. Alternatively, a regular array of boreholes is “fired”, as in bench-blasting of rocks. Our technique of visual representation illustrates the motion of the cracks as the pressure waves progress in the rock and exhibits the development of “damage” up to the stage of fracture. One sees clearly the effect of spalling (i.e. formation of tensile waves by reflection of compressive waves from the boundary) on crack growth and the bending of cracks as a boundary is approached. In the vicinity of the borehole the strongly compressive wave causes in the initial stages of the detonation a violent zig-zagging of the cracks; this results in the observed crushed-zone near the borehole. Effects on crack-growth of boundaries, time-delays and variations in elastic constants of the medium are examined.