A quasi-analytical solution is developed in this paper to investigate the mechanism of one-dimensional longitudinal wave propagating in inhomogeneous viscoelastic pile embedded in layered soil and subjected to a transient axial loading. At first, the pile-soil system is subdivided into several layers along the depth direction in consideration of the variation of cross-sectional acoustic impedance of the pile or differences in soil properties. Then, the dynamic governing equation of arbitrary soil layer is established in cylindrical coordinates and arbitrary viscoelastic pile segment is modeled using a single Voigt model. By using the Laplace transform and boundary conditions of the pile-soil system, the vertical impedance at the top of arbitrary pile segment is defined in a closed form in the frequency domain. Then by utilizing the method of recursion typically used in the Transfer Function technique, the vertical impedance at the pile top can be derived in the frequency domain and the velocity response of an inhomogeneous viscoelastic pile subjected to a semi-sine wave exciting force is obtained in a semi-analytical form in the time domain. Selected numerical results are obtained to study the mechanism of longitudinal wave propagating in a pile with a single defect or double defects.
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