Application of a particle method for estimating effective elastic properties in cracked media

We applied a Hamiltonian particle method, which is one of the particle methods, to simulate seismic wave propagation in a cracked medium. In a particle method, traction free boundaries could readily be implemented and the spatial resolution could be chosen in an arbitrary manner. The utilization of the method enables us to simulate seismic wave propagation in a cracked medium and to estimate effective elastic properties derived from the wave phenomena. We first describe our strategy to introduce free-surface inside a rock mass, i.e. cracks, and to refine the spatial resolution in an efficient way. We then model a 2D cracked media which contains randomly distributed, randomly oriented, rectilinear, dry and non-intersecting cracks, and simulate the seismic wave propagation of P- and SV-plane waves through the region. We change crack density in the cracked region and determine the effective velocity of the region. Our results show good agreement with the modified self-consistent theory which is one of the effective medium theories. Finally, we investigate the influence of the ratio of crack length to particle spacing on the calculated effective velocities. The obtained effective velocity becomes almost constant when the ratio of crack length to particle spacing is from 10 to 20. Based on this result, we propose to use at least 10 particles per crack length.