Vertical impedance of a tapered pile in inhomogeneous saturated soil described by fractional viscoelastic model

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• A semi-analytical method is presented to analyse vertical impedance of a tapered pile considering soil disturbances. • Fractional viscoelastic model is applied to describe the stress-strain relationship of the saturated soil medium. • An improved complex stiffness transfer model is proposed to determine shear resistance of disturbed saturated soil. • Effects of fluid permeability , fractional order and tapered angle on vertical impedance of the tapered pile is analysed. Vertical impedance of a tapered pile embedded in the saturated viscoelastic half-space is theoretically investigated with the consideration of construction disturbances in radial direction. The constitutive behaviour of the soil is described by a fractional viscoelastic model. The tapered pile is divided to a series of stepping cylindrical segments to characterize its variable cross-section. An improved complex stiffness transfer model of the saturated soil is developed to determine the vertical reactions of the radially inhomogeneous soil on pile segments. The vertical impedance of the tapered pile is obtained by solving the differential equations for axial vibration of pile segments based on the Rayleigh-Love rod theory and recursive formulas. The validity and accuracy of the analytical solutions are demonstrated through the comparison examples for the cases of both soil compaction and soil softening. Parametric studies are performed to investigate the influences of tapered angle, fluid permeability and fractional order of soil constitutive model on vertical impedance of the tapered pile. The results indicate that the soil medium with high permeability, such as sandy and gravelly saturated foundation, has noticeable influence on the vertical impedance of tapered pile. In addition, it is suggested that the constitutive model of the soil should accurately describe the stress-strain experimental data to ensure the accuracy of the vertical impedance, especially for those tapered piles under excitations with high frequency.