Analysis of wave propagation in piles

When piles are subjected to the disk loadings, there are the dilatational (P), transverse (S), and Rayleigh (R) waves in the surface wave field. Three-dimensional effects are obvious in the near field. The numerical results show that the waves in the longitudinal far field are insensitive to the loading distribution. Based on dispersion of the longitudinal waves in rods and displacement distribution of the modes in the radial direction, effects of the pile radius to wavelength ratio on wave propagation in the far longitudinal field are analyzed. Effects of the frequency and the loading distribution on the wave field of the top are discussed from the analytical surface displacement of a half-space under harmonic disk loadings. The surface wave field is controlled by the characteristic length of pulse and the radius ratio of the disk to piles. When the characteristic length is long, the maximum destructive interference occurs at the surface positions of about 3/5R from the center axis and the head waves (corresponding to the first hump) are approximate to the down traveling waves in the far longitudinal field. If the ratio of the characteristic length of pulse to the pile radius is significantly large and the receiver is placed at the positions of about 3/5R from the center axis, the reflections from the far field can be roughly analyzed by one dimensional wave theory.