Vertical vibration of a single pipe pile in saturated soil with 3D wave model

The vertical vibration of a single pipe pile in saturated soil is studied with 3D wave model. The soil around pile and in the pile core are regarded as two-phase porous medium, and the pipe pile is regarded as uniform circular tube unit. A dynamic model of saturated soil-pipe pile with coupled vertical vibration is developed with soil 3D wave effect model. Considering the boundary conditions of soil, the vertical vibrations of the saturated soil around the pile and inside pile core are solved by using potential functions and method of separated variables. The vertical vibration of a single pipe in saturated soil is solved and the vertical complex stiffness at pile head is obtained by using the orthogonality of trigonometric functions considering the boundary conditions at pile end. The results of soil 3D wave effect model and simplified model neglecting the radial displacement of soil are compared and analyzed by numerical examples. The influences of the main parameters of pile and soil on the vertical vibration of pipe pile in saturated soil are investigated. The results indicate that the radial displacement shouldn't be neglected when the pipe pile wall is thin and frequency is low. The liquid phase of the soil shouldn't be ignored at the peaks and valleys of the curves of dynamic stiffness factor and the equivalent damping varying with frequency. The pipe pile wall should not be too thin. The thickness of pipe pile wall, the ratio of length to diameter, density ratio and shear modulus ratio between the pile core saturated soil and saturated soil around pile, pile-soil modulus ratio have great effect on the vertical vibration of a single pipe pile in saturated soil. The relevant parameters should be considered synthetically in the design of pipe pile.