Vertical impedance of a pile in layered saturated viscoelastic half-space considering radial inhomogeneity

A simplified analytical approach is presented to investigated the vertical impedance of a pile embedded in layered saturated viscoelastic half-space considering radial inhomogeneity. The vertical dynamic interaction between the soil and pile is simulated by the Beam-on-Dynamic-Winkler-Foundation (BDWF) model. To characterize the variation of the soil properties in the disturbed zone around the pile, an improved complex stiffness transfer model is developed to determine the Winkler moduli based on the wave propagation theory of saturated porous medium. Vertical impedance of the pile head is obtained by solving the differential equation for axial vibration of the pile, combined with transfer-matrix formulations to deal with the layered property of the soil along the pile shaft. The validity and accuracy of the analytical solutions are demonstrated through the comparison examples for the cases of different radial variations of soil properties. Parametric studies are performed to investigate the influences of the Darcy permeability coefficient, width ratio and shear modulus ratio of the disturbed zone on the vertical impedance of the pile. It is revealed that the permeability of the pore fluid has an influence on the impedance of the pile when the Darcy permeability coefficient is large than 1 × 10−3. In addition, the different disturbance degrees of the soil layers along the pile shaft are suggested to take into consideration in analysis of the vertical impedance of the pile embedded in layered saturated viscoelastic half-space.