Remote pipeline assessment and condition monitoring using low-frequency axisymmetric waves: a theoretical study of torsional wave motion

Waves that propagate at low frequencies in buried pipes are of considerable interest in a variety of practical scenarios, for example leak detection, remote pipe detection, and pipeline condition assessment and monitoring. Particularly useful are the n=0, or axisymmetric, modes in which there is no displacement (or pressure) variation over the pipe cross section. Previous work has focused on two of the three axisymmetric wavetypes that can propagate: the s=1, fluid-dominated wave; and the s=2, shell-dominated wave. In this paper, the third axisymmetric wavetype, the s=0 torsional wave, is studied. Whilst there is a large body of research devoted to the study of torsional waves and their use for defect detection in pipes at ultrasonic frequencies, little is known about their behaviour and possible exploitation at lower frequencies. Here, a low-frequency analytical dispersion relationship is derived for the torsional wavenumber for a buried pipe from which both the wavespeed and wave attenuation can be obtained. How the torsional waves subsequently radiate to the ground surface is then investigated, with analytical expressions being presented for the ground surface displacement above the pipe resulting from torsional wave motion within the pipe wall. Example results are presented and, finally, how such waves might be exploited in practice is discussed.