# Development of an equation describing signature waveform based on the Fourier series for blast vibration prediction

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Transactions of the Society for Mining, Metallurgy, and Exploration
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, 2012, Vol. 332, No. 1, pp. 440-449

Silva Castro, J.J.; Lusk, B.T.

ABSTRACT:

Currently, there are several methodologies to assess ground vibrations from blasting. Of all available methodologies, one that is becoming more important is the waveform superposition or signature hole technique. This technique is based on a signature waveform assigned to each hole to build the complete waveform for the whole production blast, using the convolution between the time initiation sequence and the signature hole waveform. In the basic methodology of the signature hole technique, the waveform hole-to-hole is assumed to be the same. Several studies and field tests have proven that the waveform hole-to-hole, even in ideal rock mass conditions (rock mass with little or no joint system), changes. In addition to distance or confinement, other factors that could change the waveform hole-to-hole include different geologic paths from the source to the monitoring point and a different energy output of each hole, due to hole loading, explosive composition and/or contamination, priming, etc. These factors result in varying waveforms generated for each hole, making the waveform produced by each hole a somewhat random process. There is available in the literature some proposals to include variability in the waveform hole-to-hole, but the parameters involved are complex and difficult to estimate. In this paper, the variability in the signature waveform hole-to-hole in a blast event was recorded through a field test, and a proposal to include signature waveform variability to develop an equation based on the Fourier series is presented. This methodology is the basis for a future signature hole analysis using a Monte Carlo scheme, taking into account the variation of the amplitude and the frequency content of the waveform hole-to-hole in a production blast event.