In engineering applications, various defects such as bulging, necking, slurry crappy, and weak concrete are always observed during pile integrity testing. To provide more reasonable basis for assessing the above defects, this paper proposed simple and computationally efficient solutions to investigate the vertical vibration characteristics of a variable impedance pile embedded in layered soil. The governing equations of pile-soil system undergoing a vertical dynamic loading are built based on

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... e plane strain model and fictitious soil pile model. By employing the Laplace transform method and impedance function transfer method, the analytical solution of the velocity response at the pile head is derived in the frequency domain. Then, the corresponding semianalytical solution in the time domain for the velocity response of a pile subjected to a semisinusoidal force applied at the pile head is obtained by adopting inverse Fourier transform and convolution theorem. Based on the presented solutions, a parametric study is conducted to study the vertical vibration characteristics of variable cross-section pile and variable modulus pile. The study gives an important insight into the evaluation of the construction quality of pile.