Phase Wave Velocities and Displacement Phase Differences in a Harmonically Oscillating Pile
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Analytical solutions are developed for the harmonic wave propagation in an axially or laterally oscillating pile embedded in homogeneous soil and excited at the top. Both fixed-head and free-head piles are considered. Pile-soil interaction is realistically represented through a dynamic Winkler model, the "springs" and "dashpots" of which are given values based on results of finite-element analyses with the soil treated as a linear hysteretic continuum. Closed-form expressions are derived for the phase velocities of the generated waves; these are compared with characteristic phase wave velocities in rods and beams subjected to compression-extension (axial) and flexural (lateral) vibrations. The role of radiation and material damping is described; it is shown that the presence of such damping radically changes the very nature of the wave propagation, especially in lateral oscillations where an upward propagating ("reflected") wave is generated even in a semi-infinite head loaded pile. Solutions are also developed for the phase differences between pile displacements at various depths. It is shown that for most piles, such differences would not be significant, and therefore, waves would emanate nearly simultaneously from the periphery of an oscillating pile. This conclusion is useful in analyzing dynamic pile-to-pile interaction, the consequences of which are illustrated in the report.