On the Theory of Acoustic Scanning of Damage to Underground Pipelines

The paper studies the evolution of a pulsed signal initiated by the pushing of a cylindrical piston and propagating through a stationary fluid filling a buried pipeline with an extensive damaged section. The adopted mathematical model is based on linearized equations for a one-dimensional flow of a weakly compressible fluid. The spatial extent of the scanning pulsed signal is assumed to be significantly less than the length of the pipeline and length of the damaged section, but more than the diameter of the channel. When obtaining reflection conditions at the boundaries of the damaged section and calculating the evolution of the signal in this area, it is assumed that the intensity of fluid leakage is completely limited by the soil permeability. The problem is solved numerically by fast Fourier transform. For this, dispersion expressions are obtained for the phase velocity and attenuation coefficient of the harmonic signal in the damaged section, and the reflection and transmission coefficients at the boundaries of this section. These were then used to analyze influence of the geometric parameters of the channel, soil permeability, and rheological properties of the fluid on the behavior of harmonic waves. The problem of the evolution of a pulsed signal is solved in several stages: propagation of a pulsed signal through the medium filling the channel; signal dispersion in the damaged section with the formation of reflected and transmitted perturbation waves; and propagation of pulsed perturbations reflected and transmitted through the damaged section to model signal analyzers.