Charge Weight Scaling Laws and the Superposition of Blast Vibration Waves

A detailed discussion is given on the relationship between the vibration waves from a single blasthole and the vibration waves from a full-scale blast. The relationship is not necessarily simple. In this regard, the full-scale blast may be considered as a linear or non-linear superposition of blast vibration waves from representative single blastholes. If linear superposition is assumed, then standard Monte Carlo techniques may be used to predict the complete vibration time history due to the entire blast. However, for non-linear superposition the problem is much more complex, and in many aspects remains unsolved. It is also shown that the traditional charge weight scaling laws used to predict the peak vibration levels of a blast are plagued with many problems. Two problems of particular concern are that such laws are dimensionally awkward, if not unsound, and they are also inconsistent with any notion of superposition. In light of the superposition problem associated with traditional charge weight scaling, a new, weighted scaled distance is proposed for use in vibration prediction of full-scaled blasts. Although this weighted scaled distance remains dimensionally awkward, it is more consistent with the notion of waveform superposition since it takes account of all the blastholes within a blast and also all the distances from each hole to a specified monitoring location. The current and ad-hoc method for selecting a single value of charge weight and distance to calculate a scaled distance for the entire blast makes no sense, especially for monitoring locations close to a blast. Use of the weighted scaled distance completely avoids this problem, and when it replaces the traditional scaled distance, less scatter is observed in the charge weight scaling plots.