A full-field solution to predict vibrations in the presence of a free surface

Blasting is a common activity in mining that can cause significant damage in the remaining rock mass. The most commonly used method for predicting vibrations is the Swedish or Holmberg-Persson approach. It is a simple and fast method that uses empirical formulation to estimate the vibration levels based on the explosive charge weight, distance to the source, and other parameters. However, it has limited accuracy and does not consider the effect of free surfaces or other boundary conditions. On the other hand, recently developed methods as the full-field solution (FFS) can provide more accurate predictions of vibrations due to excitations provoked by cylindrical columns of explosive, but the inclusion of free surfaces in analytical methods is a challenging problem. This paper presents a new approach that includes free surfaces in the FFS to predict vibrations analytically in the near-field. The main obstacle to including free surfaces in the FFS was the belief that the solution was non-decoupleable in P- and SV-waves separately. The Heelan's approach was previously used to decouple them, but it only provides valid radiation patterns in the far-field and does not account for intrinsic attenuation. In this paper, we address this problem successfully, allowing for the inclusion of free surfaces in the FFS.