Transient Response of Float Pile Under Vertical Impact Loading in Unsaturated Soil

[Purposes] On the basis of the dynamic governing equation of three-dimensional porous media, the vertical transient response of float pile in unsaturated soil is analyzed with considering of the coupling effect of liquid and gas phases. [Methods] The vertical wave equation of transform domain in unsaturated soil under cylindrical coordinate system was established by using Laplace transform and method of normalization. Then, the method of separation of variables and operator decomposition theory were used to solve the dynamic equation. Thus, the form of displacement solution of the Laplace transform domain in unsaturated soil was obtained. According to the boundary conditions of pile and soil, the dynamic equilibrium equation of pile was solved and the analytical solutions of vertical displacement and internal force of pile in transformation domain were obtained. [Results] The model is verified through the comparison with the single-phase models and saturated models by Laplace inverse transformation of numerical calculation. Saturation and pile tip reaction coefficient on response of pile are investigated. The results show that: The saturation and pile tip reaction coefficient have certain influence on the pile displacement and internal force, and the larger saturation, a greater vertical displacement for the float pile. The lager pile tip reaction coefficient, the greater the pile displacement, and the later the peak displacement arrives. Besides, with the increase of pile-to-soil modulus ratio, the pile displacement decreases first and then increases along the pile depth.