Application of the reciprocity theorem to scattering of surface waves by an inclined subsurface crack

In this paper the scattering of incident surface waves by an inclined subsurface crack in a homogenous, isotropic and linearly elastic half-space has been investigated in a two-dimensional plane strain configuration. The elastodynamic reciprocity theorem together with a virtual wave has been used to determine the amplitude of the scattered surface waves in the far field. It is found that the amplitude is in terms of the crack opening volume due to the incident surface waves. A special case of low frequency, for which the wavelength of the surface wave is sufficiently larger than the crack length, has been considered to illustrate the method. A specific expression of the amplitude has been obtained, which provides information on the angle, length and depth of the crack. It shows that the amplitude of the scattered surface wave increases first and then decreases as the crack angle changes from 0° to 90°. For the case of an inclined crack, the results of the numerical analysis together with the analytical solutions show excellent agreement when the crack length is much smaller than the wavelength. The results in this paper should be useful for the quantitative measurement of subsurface cracks.