Elastic wave propagation in liquid filled buried pipes

The non-destructive testing of pipelines encounters many different environmental conditions, which includes pipelines that are buried in materials such as soil, sand and even concrete. In addition, these pipelines may carry gases or liquids, such as oil or water. The location of cracks or areas of corrosion in pipelines often encounters varied environmental conditions and this requires knowledge of the influence these conditions have on the propagation of elastic waves travelling down the pipe wall. This includes knowledge of modal group velocity, which is used to estimate the time-of-flight of a pulse scattered by a defect, as well as the reduction in inspection range caused by the attenuation of energy in the pulse. Accordingly, it is desirable to develop theoretical models to help in understanding the influence of different environmental conditions, and so in this article the semi-analytic finite element (SAFE) method is used to obtain the dispersion curves for buried liquid filled pipes. It is shown that through a Galerkin based formulation a governing eigenequation may be formulated in a way that delivers a fast and efficient solution. Crucially, this involves the utilization of a semiorthogonality relation so that modes can be sorted quickly and easily in order to focus on those modes relevant in commercial non-destructive testing.