Surface displacements accompanying the propagation of acoustic waves within an underground pipe

Theoretical expressions for surface displacements accompanying the propagation of acoustic waves in a buried gas-filled pipe are derived. It is shown that the radiated field consists of both shear and compressional components of comparable amplitude which interfere with one another because of the large difference in the respective propagation velocites. This is manifested at the surface by a series of maxima and minima in the vertical and horizontal displacements. Comparing the theoretical calculation to experimental data on vertical surface displacements generated by plane progressive waves at frequencies ranging from 200 to 2000 Hz within an underground pipe shows that only axisymmetric radial and longitudinal vibration of the pipe wall is important. This stands in marked constant to experiments carried out by others in an air medium in which the contribution of bending mode excitation was shown to be significant, particularly at lower frequencies. The theory can be fitted to the experimental data only if the compressional and shear velocities α and β, respectively, are narrowly specified, leading to α = 259 m/s and β = 164 m/s, the latter being in reasonable agreement with the results of other investigators for clay soil.