Vertical Vibration of Deep Foundations in Layered Deposits

An efficient analytical solution has been Developed for the analysis of harmonically vibrating vertical, linearly elastic of circular cross section. The pile is assummed to be infinitely long, compared to its diameter. The soil consists of a number of horizontal elastic strata that are homogeneous, isotropic, and the soil-pile interface.the pile is modeled as a number of cylindrical segments connected by nodes. the governing dynamic differential equation of each pile element is established and solved explicitly.