Abstract
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.
Highlights
As a new viscoelastic constitutive model, the fractional derivative viscoelastic model has many advantages
On the basis of creep tests, Zhu et al [8] proposed a fractional Kelvin–Voigt model to account for the time-dependent behavior of soil foundation under vertical line load based on the theory of viscoelasticity and fractional calculus and derived an analytical solution of settlements in the foundation using Laplace transforms; the results indicated that the settlementtime relationship can be accurately captured by varying the fractional orders of differential operator and the viscosity coefficients
For the fractional derivative viscoelastic model, classical viscoelastic model, and elastic model of soil, the comparison curves of soil horizontal impedance factors are shown in Figure 3. e impedance factor curves of fractional derivative viscoelastic model can gradually degenerate to the classical viscoelastic model and elastic model, which verifies the correctness of the results
Summary
As a new viscoelastic constitutive model, the fractional derivative viscoelastic model has many advantages. Liu et al [19] studied the influence of soil plug effect on the dynamic response of large-diameter pipe piles during lowstrain integrity testing and derived an analytical solution that can consider the stress wave propagating both in the vertical and circumferential directions in the frequency domain using the transfer function method. To more reasonably describe the constitutive relationships of the pile-soil system and investigate the mechanical properties of the pile-soil system under the dynamic load, this paper adopts the fractional derivative viscoelastic method to derive the horizontal dynamic control equations of pipe pile and soil layers. The dynamic solutions of the pile around soil and pile core soil under the horizontal harmonic load are obtained by the fractional derivative viscoelastic model. For the soil layer under the harmonic load with different frequencies, the variations of horizontal stiffness factor and the horizontal damping factor can be analyzed and discussed by equation (30)
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