Analysis of Longitudinal Guided Wave Propagation in a Liquid-Filled Pipe Embedded in Porous Medium

Abstract

To study the leakage situation of a liquid-filled pipe in long-term service, a model of a liquid-filled pipe embedded in an infinite porous medium as well as in a finite porous medium is designed. The principal motivation is to perform detailed quantitative analysis of the longitudinal guided wave propagating in a liquid-filled pipe embedded in a saturated porous medium. The problems of pipeline leakage and porosity as well as the media outside the pipe are solved to identify the characteristics of the guided wave in a more practical model. The characteristics of the guided wave are investigated theoretically and numerically, with special emphasis on the influence of porous medium parameters on the dispersion properties. Assuming the pipe is a cylindrical shell buried in an isotropic, homogeneous, and porous medium, the dispersion equations are established based on the elastic-dynamic equations and the modified Biot liquid-saturated porous theory. The characteristics of dispersion, time-domain waveform and attenuation curves varying with porous medium parameters, wrapping layer material, and thickness, are all analyzed. The increase in porosity decreases the partial mode phase velocity in the liquid-filled pipe embedded in the finite porous medium. The characteristics of attenuation are in good agreement with the dispersion curves and the time-domain waveform results.