Numerical simulation using a Hamiltonian particle method for effective elastic properties in cracked media

Abstract

We apply a Hamiltonian particle method, one of the particle methods, to simulate seismic wave propagation in a cracked medium. In the particle method, traction free boundaries can be readily implemented and the spatial resolution can be chosen in an arbitrary manner. Utilisation 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. These features of the particle method bring some advantages of numerical efficiencies (e.g. calculation time, computational memory) and the reduction of time for pre-processing.We describe first our strategy for the introduction of free surfaces inside a rock mass, i.e. cracks, and to refine the spatial resolution in an efficient way. We then model a 2D cracked medium 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 the crack density in the cracked region and determine the effective velocity in the region. Our results show good agreement with the modified self-consistent theory, 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 effective velocity obtained becomes almost constant when the ratio of crack length to particle spacing is more than ~20. Based on this result, we propose to use more than 20 particles per crack length.