Bench blast modeling: Consequences of crushed zone, wave front shape, and radial cracks.
A geometrical model for the rock crushed zone around a cylindrical charge is developed. The model is used to obtain empirical relationships between the scaled crushed zone diameter and some dimensionless ratios of explosive and rock properties. The ratios are velocity ratio, characteristic impedance ratio, medium stress ratio, and detonation pressure ratio. The empirical relations for granite, salt, and limestone in combination with a variety of explosives show that the scaled crushed zone diameter increases at a decreasing rate with increasing dimensionless ratios. The shape of the wave fronts around a cylindrical charge detonating in rock has been constructed for velocity ratios ranging from infinity to less than one. The shape of the wave front is not planar in the range of dimensions used in full scale bench blasting. The shape of the wave front is cylindrical in the middle and spherical at the top and bottom for infinite velocity ratio; sphero-conical for velocity ratios greater than one; spherical for velocity ratios ≤ 1. Quasi-static finite element models for a blasthole in a full scale bench blasting are analyzed using a 2-D finite element program written by the author. The models include a model neglecting radial cracks, models considering pressurized and non-pressurized radial cracks around the blasthole, and a model using an equivalent cavity to replace the pressurized radial cracks. Displacement fields, stress fields, and strain energy density distribution are studied. The analyses show that including radial cracks increases the levels of the strain energy density contours and the magnitudes of the displacement and stress fields several fold. The equivalent cavity gives much lower levels of strain energy contours and gives lower displacement and stress field magnitudes than those produced by the pressurized radial cracks. The scaled areas of the strain energy density contours increase at a decreasing rate with increasing the blasthole internal pressure and with increasing the ratio of the compressive strength to the tensile strength. These contour areas decrease at a decreasing rate with increasing tensile strength.
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