Vibrations induced by blasting in rock: a numerical approach

To describe the progressive effects of underground blasting on the surrounding site, a finite element approach is presented. The explosion energy is translated in a time history of pressure at the boundary of the blast hole. Cracking of the nearby rock mass is modelled according to a cohesive crack model, while elastic behaviour is assumed for the non cracked rock mass and soil deposits. Propagation of stress waves from the blast hole is simulated by a time domain 3-D finite element analysis, which is able to provide the time history of all the relevant quantities describing the motion at any given distance. The numerical results can be post processed in order to derive attenuation laws for the most relevant quantities to which the codes of practice usually refer to, i.e., peak particle velocity and principal frequency of the vibration. The model is energy-conserving, thus the energy supplied by the explosive is correctly partitioned into fracture energy of the rock mass close to the blast hole, elastic energy providing the stress wave propagation and kinetic energy of the fragmented rock blocks. Numerical simulations of two literature case-histories are presented, and the numerical results are compared to the available experimental data. Experimental peak particle velocity could be captured remarkably. Principal frequencies for the rock mass could be reproduced as well. In layered sites, the ratio between the stiffness of the different media where stress waves propagate seems to play a key role in the determination of principal frequencies, while less influence is observed on peak particle velocities.