Analytical solution of vertical vibration of a floating pile considering different types of soil viscoelastic half-space

For penetrating investigating the effect of foundation characteristics on the vertical vibration of a floating pile, an analytical solution of vertical vibration of a floating pile considering different types of soil foundation under vertical dynamic loads is developed. The pile is considered as Euler-Bernoulli beam, and the soil is considered as a three-dimensional axisymmetric viscoelastic medium. The soil governing equation is decoupled by introducing potential function, and utilizing the separation variables method, given the expression of soil displacement and soil impedance function. Then, further based on the boundary conditions of displacement equilibrium and stress equality between pile and soil, the expression of pile displacement is created. In addition, the frequency-domain solution for the coupling interaction of soil-soil viscoelastic half-space is derived at the same time. Furthermore, when the present analytical solution is degraded to a rigid foundation and the top of system is only subjected to vertical dynamic load, the reasonableness of the present analytical solution has been predicted by contrast with software ABAQUS and the existing analytical solution, respectively. Finally, on the basis of the present analytical solution, the differences and similarities of dynamic response of several soil foundation types to pile and soil are revealed with emphasis. Moreover, the results can provide a theoretical support for numerical analysis.