Analytical Solution to Horizontal Vibrations of Large-Diameter Piles in Layered Pasternak Soils

Abstract

A simplified mechanical model for investigating pile–pile horizontal vibration is developed by combining the Pasternak model and the Timoshenko beam theory, with the consideration of the influence of axial load at the head of the source pile. The expressions for horizontal displacements and internal forces of the source pile are obtained with respect to the differential transform method and pile–soil boundary continuity conditions. Additionally, considering that the vibration of the source pile affects the dynamic displacements of the receiver pile, the dynamic equilibrium equation of the receiver pile is established. Then, a closed-formed solution for the response of the receiver pile is derived from the obtained expressions. Further, the pile–pile horizontal dynamic interaction factor is derived based on its definition and validated by comparison with existing related analytical solutions. Finally, the effects of the shear deformations of soil and pile, pile slenderness ratio, and axial load on the pile–pile horizontal dynamic interaction factors are examined. It is indicated that a smaller pile-to-soil modulus ratio of the near-surface layer results in a more significant effect of shear deformation of the soil. In particular, when L/d is small (i.e., L/d < 5) or the pile cross section is annular, the effect of shear deformation of the pile is not ignorable.