Wavenumber prediction and measurement of axisymmetric waves in buried fluid-filled pipes: Inclusion of shear coupling at a lubricated pipe/soil interface

Acoustic methods have been widely used to detect water leaks in buried fluid-filled pipes, and these technologies also have the potential to locate buried pipes and cables. Relatively predictable for metal pipes, there is considerably more uncertainty with plastic pipes, as the wave propagation behaviour becomes highly coupled between the pipe wall, the contained fluid and surrounding medium. Based on the fully three-dimensional effect of the surrounding soil, pipe equations for n=0 axisymmetric wave motion are derived for a buried, fluid-filled pipe. The characteristics of propagation and attenuation are analysed for two n=0 waves, the s=1 wave and s=2 wave, which correspond to a predominantly fluid-borne wave and a compressional wave predominantly in the shell, respectively. At the pipe/soil interface, two extreme cases may be considered in order to investigate the effects of shear coupling: the “slip” condition representing lubricated contact; and the “no slip” condition representing compact contact. Here, the “slip” case is considered, for which, at low frequencies, analytical expressions can be derived for the two wavenumbers, corresponding to the s=1 and s=2 waves. These are both then compared with the situations in which there is no surrounding soil and in which the pipe is surrounded by fluid only, which cannot support shear. It is found that the predominant effect of shear at the pipe/soil interface is to add stiffness along with damping due to radiation. For the fluid-dominated wave, this causes the wavespeed to increase and increases the wave attenuation. For the shell-dominated wave there is little effect on the wavespeed but a marked increase in wave attenuation. Comparison with experimental measurements confirms the theoretical findings.