Modeling variations of Rayleigh wave velocity due to distributions of one-dimensional surface-breaking cracks

Abstract

A model describing changes of Rayleigh wave velocity caused by distributions of one-dimensional, surface-breaking cracks is presented. The concept of effective medium and the assumption of noninteracting cracks are used in the model. This approach is developed in the low-frequency limit. A real cracked surface is modeled by a homogeneous, anisotropic layer on top of an isotropic substrate. The substrate’s elastic properties are those of the original isotropic half-space, whereas those of the layer are modified by the presence of the crack distribution. Distributions are considered where parameters such as crack density, crack depth, crack depth distribution, and crack orientation are varied. Variations of surface acoustic wave (SAW) velocity are reported for all these cases. SAW velocity is shown to be most sensitive to changes in crack density and crack depth. Negative variations of Rayleigh wave velocity are predicted to be up to 3% even for distributions of rather shallow cracks. These results show that variations of SAW velocity caused by crack distributions are much larger than those due to other forms of surface damage such as surface roughness or residual stresses.