Vertical dynamic response of end-bearing piles embedded in two-layered soil

This paper presents a mathematical model for the dynamic analysis of axially loaded end-bearing pile embedded in two-layered viscoelastic soil. The soil layers surrounding the pile are treated as Tajimi-type continua, and the pile is modelled as one-dimensional elastic rod. This allows obtaining rigorous, closed-form expressions for the dynamic pile stiffness and the soil reaction acting along the pile shaft. Predictions of the model are validated against independent results, to demonstrate that the simplifications introduced in the formulation have trivial effect on predictions. The presentation concludes with an investigation on the effects of two-layered soil parameters on the vibration characteristics of end-bearing piles. There we identify under which conditions soil stratigraphy (and not just average soil stiffness) needs to be considered in the dynamic analysis of piles, and provide recommendations for practice.