An analytical model of ground surface vibration due to axisymmetric wave motion in buried fluid-filled pipes

Abstract

The axisymmetric (n=0) fluid-borne (s=1) wave has been exploited with varying degrees of success in practical surveys for determining the location of buried pipes. Difficulties are sometimes encountered in interpreting ground surface vibration data, whilst attempting to locate the pipes, due to the occurrence of abrupt changes in the phase response over the usable frequency range. Based on a wave propagation model developed recently, this paper presents an analytical model for predicting the ground surface displacements resulting from the radiated elastic waves in the soil medium. Two representative soils have been specifically considered, where the s=1 wave in the pipe will leak shear waves into the soil, but may or may not leak compressional waves. In each of these cases, numerical simulations are presented to predict the ground surface displacements. The model is used to demonstrate how, when both compressional and shear waves are radiated, they can interfere such that abrupt phase changes occur at the frequencies coincident with magnitude minima in the ground surface displacements; when only shear waves are radiated, such interference does not occur. Furthermore, for sandy soil, it is found that the horizontal displacement is dominated by the radiated shear wavenumber component whereas the vertical displacement is controlled by the radiated compressional wavenumber component. Using the analytical model, theoretical predictions of ground surface displacements are compared with experimental data from a dedicated MDPE pipe rig.