Elastic Wave Motion in a Cracked, Multi-Layered Geological Region under Transient Conditions

Abstract

A hybrid boundary element method (BEM) for transient problems in elastodynamics is developed here [1] 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 (SCF) that develops around cracks buried within the deposit for the same type of loading. The present method combines both displacement and regularized traction BEM in the Laplace transformed domain [2] 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 BEM, 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 some conclusions regarding the relative influence of various key parameters of the problem (such as layering, surface canyon, crack interaction, etc.) on the scattered displacement field and on the SCF. Further extension of the method to cover mildly inhomogeneous continua is also planned [3].