Analytical solution for the kinematic response of end-bearing piles subjected to SH waves in a homogeneous layer by an improved beam-foundation model

Abstract

This paper presents an analytical solution for evaluating kinematic response in piles subjected to shear waves. The proposed model treats the pile as a Timoshenko beam supported by a two parameter Winkler foundation, capturing both transverse and rotational ground reactions. Validation against both analytical and numerical solutions from the literature, particularly 3D finite element models, shows very good agreement. The proposed model generalizes different solutions currently applied in practice, covering various pile slenderness ratios and ground conditions. This approach addresses limitations in existing Euler-Bernoulli beam resting on Winkler or Vlasov-Pasternak foundation models, by incorporating shear distortions in the structure and ground friction at the interface. Shear stresses induced by the rotational springs are found to significantly influence the kinematic factors, as well as bending and, particularly, shear forces. Finally, simplified expressions for kinematic interaction factors and forces are provided for expedited analyses of practical engineering problems.