Analytical solution of ground and underground vibration subject to spherical charge

Considering the geological bodies as a viscoelastic medium, rather than an elastic medium, is more reliable for the issues of blasting vibration because of the damping characteristic of the geological bodies. However, the analytical solution for ground vibration subject to spherical charge in a viscoelastic medium has never been reported yet. In this study, an approximate analytical solution is first proposed to address such a problem. Its accuracy and validity are verified by direct numerical simulation (finite difference method) and extensive experiences in construction. Based on the present analytical solution, the ground and underground vibration characteristics are systematically studied. The results show that both blasting parameters and medium parameters affect the blasting vibration, especially, the viscosity modulus of the medium will significantly change the waveform and amplitude of blasting vibration. The attenuation coefficients for underground and ground vibration vary from 1.4 to 2.0 and 0.7 to 2.0 with the increasing viscosity modulus. This analytical solution provides reliable prediction and analysis for blasting vibration.