Simplified dispersion relationships for fluid-dominated axisymmetric wave motion in buried fluid-filled pipes

Abstract

The dispersion characteristics of axisymmetric (n=0) waves offer a way to gain physical insight into the low-frequency vibrational behaviour of underground pipe systems. Whilst these can be found in the literature, they are generally calculated numerically. Coupled equations of motion for the n=0 waves that propagate in a buried fluid-filled pipe are presented in this paper and, from this, an analytical solution is developed for the fluid-dominated (s=1) wavenumber. The effect of the frictional stress at the pipe–soil interface on the dispersion behaviour of the s=1 wave is characterised by adopting a soil loading matrix. Overall, the fluid loading has a greater effect on the propagation wavespeed compared with the soil loading: for metal pipes, the effect of soil loading is negligible; for plastic pipes, however, simply neglecting the effect of soil loading can lead to a considerable underestimation in the calculation of the wavespeed. The wave attenuation increases significantly at higher frequencies regardless of pipe material resulting from the added damping due to radiation into the soil. Theoretical predictions of the s=1 wavenumber are compared with experimental data measured on an MDPE water pipe. The degree of agreement between prediction and experiment makes clear that, although the wavespeed is only slightly affected by the presence of the frictional stress, the frictional stress at the pipe–soil interface needs to be appropriately taken into account for attenuation predictions.