Scattering of elastic waves by shallow elliptical cracks

Abstract

Comprehensive studies in engineering have dealt with diffraction phenomena in unbounded elastic domains containing cracks, while some others have been carried out to investigate diffraction by discontinuities located near a free surface. In this last case, the presence of cracks significantly affects wave motion and, in some cases, large resonant peaks may appear. In order to study these resonant peaks and describe how they respond, we propose the use of the Indirect Boundary Element Method to simulate 2D scattering of elastic P- and SV-waves. The geometry considered for the cracks is elliptical, but in some cases comparison of its behavior is made with that of planar cracks or cavities. This method establishes a system of integral equations that allows us to compute the diffracted displacement and traction fields. We present our results in the frequency domain. In the case of planar cracks located near the free surface, we validate the method by comparing our results to those of a previously published study. We develop examples of various elliptical crack configurations to show resonance effects, where one can observe important variations in the resonance peaks in the frequency domain. The results shown here can be used to detect the presence of subsurface cracks. Nevertheless, it is difficult to determine the shape (planar or elliptical) of the discontinuity that is embedded in the halfspace.