Dynamic analysis of axially loaded end-bearing pile in a homogeneous viscoelastic soil

Abstract

A new approximate analysis technique is developed to obtain the steady-state response of axially loaded pile embedded in a homogeneous, isotropic soil, and resting on a rigid base. In the analysis, the soil is modeled as an axisymmetric linear viscoelastic continuum with frequency independent hysteretic material damping and the pile is modeled as an elastic Euler rod with a circular cross-section. The soil displacement in the vertical direction is expressed as a product of separable functions, while the radial displacement is assumed to be zero for mathematical simplicity; although the effect of the radial displacement is indirectly taken into account by modifying the soil modulus. The Extended Hamilton's principle in conjunction with the calculus of variations is used to obtain the differential equations governing pile and soil displacements and the relevant boundary conditions. The pile and soil displacement equations are solved analytically following an iterative algorithm. The accuracy of the analysis is ensured by comparing the pile responses obtained from this analysis with those obtained by other methods available in the literature. A parametric study is performed to investigate the influence of the pile and soil parameters on the axial dynamic pile-head impedances. The plots developed from the parametric study can be used in the design.