Non-linear superposition models of blast vibration

Current waveform models of blast vibration typically consider a linear superposition of characteristic (seed) waveforms. However, blasting produces large strains in the surrounding medium, which, in turn, implies a non-linear response of the material. It is therefore questionable to use a linear superposition scheme to add the contributions of individual charge masses. These individual charge masses could be the elements of charge within a single blasthole, or the separate charge masses associated with each blasthole within a full-scale blast. Within a single blasthole, each charge element is necessarily in the very-near-field of its neighbour. In this case, a simple non-linear superposition scheme can be devised such that the vibration due to the entire explosive column is consistent with charge weight scaling. If A is the traditional scaling constant, then non-linear superposition predicts that the vibration is less than that obtained using linear superposition provided A<1. However, if A>1, then non-linear superposition predicts a vibration greater than that predicted by linear superposition, which is in conflict with accepted theories of large strain non-linear attenuation. For a full-scale blast, each charge mass is clearly separated, which complicates the situation. In this case, two non-linear superposition approaches are given—one based solely on charge weight scaling, the other based on the distinct notion of blast damage. In principle, the damage model is more realistic than the charge weight scaling model, and this is also consistent with the predictions based on these two schemes when compared with measured results.