The free surface influence on blast vibration

When a charged blasthole initiates it typically radiates P waves and shear-vertical (SV) waves. Furthermore, dependent upon the velocity of detonation (VoD), P-Mach and/or SV-Mach waves will form, which will contain a significant proportion of the blast vibrational energy. It is important to understand the influence of the free surface on such wave radiation when considering near field vibration monitoring for material damage/fragmentation and far field surface vibration monitoring for statutory compliance. The reflection characteristics of plane P- and SV-waves incident on a free surface are given by the well-known Zoeppritz equations. However, it is much more difficult to derive the reflection characteristics for the non-planar waves radiated from a blasthole. This work describes an analytical model in which the non-planar incident radiation from a blasthole is given by the Heelan solution and its reflection from the free surface is approximated using the Zoeppritz equations. Predictions of the free surface influence using this analytical model are in good agreement with the predictions from a dynamic finite element model. The analytical model also shows that as the VoD increases, the reflected vibrational energy is channelled further away from the near field. Thus the model predicts that the explosive VoD can be altered to control damage in specific near-field regions. In this regard, the present analytical method produces a complete near field vibration damage model in which the VoD and the free surface play crucial roles. At high VoD, the radiation approaches grazing incidence at the surface in the far field. This phenomenon is relevant to monitoring far field vibration.