Full-field solution from an oblique shock to estimate ground motion from blasting

Abstract

The full-field solution (FFS) of the seismic radiation from a blasthole is refined with the use of a source function consistent with the shock physics on the detonation shock/rock interface. This source function accounts for the directionality of the flow in the detonation front, that is curved under the influence of the confining rock, inducing on it an oblique shock mostly on axial direction, contrary to current models that consider a radial source. The interaction of the explosive/confiner system is solved with the oblique shock local polar theory. From this analysis, pressure (p) versus deflection angle (Θ) polar curves are constructed and plotted in the p-Θ plane. The intersection of the explosive and confiner polar curves corresponds to the possible shock matching solution across the explosive/rock interface, which leads to a shock incident angle. A code has been written in MATLAB to perform the shock polar analysis. The resulting detonation front angle of the explosive with the confiner is considered to build a combined radial/axial source. For this, the displacement potentials for the axial component of the source are formulated and incorporated to the solution. Experimental data from quarry blasting are used to illustrate the application of the FFS model and the calibration of results in terms of attenuation coefficients. The effect of introducing the radial/axial combined source is also discussed.