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The vertical vibration of a viscoelastic pile immersed in arbitrarily layered soil is investigated by taking the interaction among pile, pile surrounding soil (PSS) and pile end soil (PES) into account. Firstly, considering both the stratification and stress wave effect of soil, a mathematical model of the pile–soil system is established based on the fictitious soil pile (FSP) model. Then, utilizing the impedance function transfer method and Laplace transform technique, the analytical solutions of the vertical dynamic impedance of pile are derived in the frequency domain. The analytical solutions are validated by comparing them with other existing solutions. Finally, a parametric study is put forward to investigate the properties of PES on the vertical dynamic impedance of pile. The results reveal that the properties of PES have a significant effect on the vertical dynamic impedance of pile, but there is a critical influence thickness for this effect. For the cases of the PES thickness exceeding the critical influence thickness, further increase of PES thickness will not affect the dynamic behavior of the pile–soil system. [ABSTRACT FROM AUTHOR]

• A 3D dynamic torsional impedance solution is derived for offshore large-diameter pipe piles. • The impedances across the pile cross-section vary with the pile dimension and soil plug strength. • One-dimensional rod theory overestimates the overall impedance of the cross-section. • For common-size pipe piles, the impedance decreases from the pile outer radius to the inner radius. • For large-diameter pipe piles, the soil plug could play a dominant role in resisting torsional vibrations. Wind-induced or current-induced torsional vibration is a long-neglected issue for offshore engineering (e.g., offshore wind turbines, offshore oil platforms, etc.). As the dimension of the pipe pile implemented offshore increases dramatically, the one-dimensional rod theory can no longer precisely compute the dynamic torsional impedance. This paper proposes a novel 3D torsional soil-pile interaction model and derives the corresponding analytical solution for the 3D dynamic torsional impedance at the pile cross-section with the adoption of the Laplace transform, variable separation, and impedance transfer method. The solution is then validated by comparisons against some widely-accepted existing solutions. The main conclusions of this study can be drawn as follows: (1). Classic one-dimensional theory overestimates the impedance of the pipe pile, which could result in severe disasters if the dynamic design is radical; (2). Even for small diameter pipe piles, the impedance would vary in the radial direction at the pile cross-section. Usually, the impedance at the outer radius would be slightly larger than that at the inner radius; (3). For large-diameter pipe piles or pipe piles with high-strength soil plugs, the most significant impedance could appear at the inner radius, indicating the resistance provided by the soil plugs can not be overlooked for large-diameter pipe piles. [ABSTRACT FROM AUTHOR]