Attenuation and dispersion of Rayleigh waves propagating on a cracked surface: an effective field approach

A new effective field approach describing the attenuation and dispersion of a Rayleigh wave propagating on a surface containing a distribution of one-dimensional, surface-breaking cracks is presented. Limited by the validity of the independent scattering approximation, the model utilizes the complex transmission coefficient of a single crack to build expressions for the phase velocity and attenuation coefficient of an effective Rayleigh wave. The model is shown to be able to accommodate the effect of compressive residual stresses that tend to close the distributed cracks at their mouth, and therefore substantially reduce the attenuation and the velocity change caused by an equivalent distribution of open cracks. Wherever possible, the predictions of the new model are compared with those of other approaches and critical remarks are offered which discuss the advantages of the effective field approach over the others. Finally, an extension of this approach to distributions of two-dimensional surface-breaking cracks is outlined.