Transient seismic wave propagation in a multilayered cracked geological region

Abstract

A hybrid boundary integral equation method (BIEM) for transient problems is developed here as a means for investigating ground motion phenomena in geological regions with complex geometry, variable material properties and in the presence of both interface and internal cracks. Two different aspects of the problem are considered, namely computation of (a) ground motions in the form of synthetic seismograms that are manifested at the free surface of the geological region as it is swept by a seismically induced pressure wave and (b) evaluation of the near crack-tip stress concentration field that develops around cracks buried within the deposit for the same type of loading. The present method combines both displacement and regularized traction BIEM in the Laplace transformed domain for the crack-free and cracked states, respectively, while the transient nature of the wave scattering phenomenon is reconstructed through use of the numerical inverse Laplace transformation. Furthermore, plane strain conditions are assumed to hold and the response of the geological region remains within the linear elastic range. The basic strategy, whereby the aforementioned two states are superimposed, has been successfully used in the past for problems in fracture mechanics. Following numerical implementation of the hybrid BIEM, two validation-type examples serve to calibrate the methodology. Finally, the method is used for solving the seismic response of a complex geological region so as to reach a series of conclusions regarding the relative influence of various key parameters of the problem (layering, surface canyon, crack interaction) on the scattered displacement field and on the stress concentration factor.