Theoretical and Numerical Analysis of Soil-Pipe Pile Horizontal Vibration Based on the Fractional Derivative Viscoelastic Model

To describe the mechanical properties of the system of pipe pile-soil reasonably and accurately, the constitutive relations of the soil around pile and pile core soil are characterized by the fractional derivative viscoelastic model. We assume that the radial and circumferential displacements of the soil around the pile and pile core soil are the functions of r, θ, and z. The horizontal dynamic control equations of soil layers are derived by using the fractional derivative viscoelastic model. Considering the fractional derivative properties, soil layer boundary condition, and contact condition of pile and soil, the potential function decomposition method is used to solve the radial and circumferential displacements of the soil layer. Then, the force of unit thickness soil layer on the pipe pile and the impedance factor of the soil layer are obtained. The horizontal dynamic equations of pipe pile are established considering the effect of soil layers. The horizontal dynamic impedance and horizontal-swaying dynamic resistance at the pile top are obtained by combining the pipe pile-soil boundary conditions and the orthogonal operation of trigonometric function. Numerical solutions are used to analyze the influence of pile and soil parameters on the soil impedance factor and horizontal dynamic impedance at pile top. The results show that the horizontal impedance factors of the soil layer and horizontal dynamic impedance of pipe pile by using the fractional derivative viscoelastic model can be degraded to those of the classical viscoelastic model and the elastic model. For the fractional derivative viscoelastic model of soil layer, the influence of soil around pile on the dynamic impedance is greater than that of pile core soil. The model parameter TOa, the inner radius of pipe pile, and the pile length have obvious effects on the horizontal impedance of the soil layer and pipe pile, while the influence of the pile core soil on the pile impedance is smaller.