The u-p analytical solution for impedances of saturated soil to a laterally vibrating pile considering radial inhomogeneity

Abstract

Neglecting the inertial forces associated with the relative acceleration of pore fluid, this paper presents a u-p analytical solution of the dynamic impedances of a horizontally vibrating pile embedded in a saturated soil layer whose boundary region is radially inhomogeneous. To facilitate the analysis, we further divided the inhomogeneous boundary region into a set of concentric annular sub-region, and the material properties of each sub-region are assumed to be constant. The impedances of radially inhomogeneous saturated soil are calculated by making use of transfer matrix method. The present solutions are compared with the existing u-w analytical solution. The influence of the shear modulus, permeability coefficient, soil porosity, pile radius and radial inhomogeneity on the errors between u-p form and u-w form are investigated. Then, the applicable range of the u-p approximation is given. • A u-p analytical solution for the horizontal dynamic impedances of saturated soil layer is presented. • The horizontal impedance of radially inhomogeneous saturated soil is obtained by transfer matrix method. • The errors between u-p solution and u-w solution under different conditions are discussed. • The applicable range of the u-p approximation is given.