Lateral kinematic response of single-pile bridge pier foundations under seismic waves: Linear versus non-linear soil behaviour

This paper analyses the kinematic response of single-pile bridge foundations subjected to vertically propagating seismic S-waves, considering both linear and non-linear soil behaviours. Two one-dimensional soil models are adopted to compute the free-field responses: (i) the conventional elastic propagation model for layered soils, and (ii) a non-linear lumped-parameter formulation incorporating the modified Kondner and Zelasko shear stress–strain relationship and extended Masing rules. Different Beam on Dynamic Winkler Foundation (BDWF) formulations are examined to model soil–pile interaction, including linear formulations proposed by Gazetas and Dobry, and non-linear expressions proposed by recommended practices. The degradation of soil stiffness derived from the non-linear soil site response is also incorporated into selected BDWF formulations. The seismic response of floating and end-bearing piles embedded in both homogeneous and non-homogeneous sandy soils, characterised by different stiffness levels, is considered. The soil–pile seismic response is analysed in terms of mean envelopes of bending moments and shear forces obtained from ten earthquakes. Results show that the soil behaviour under S-wave propagation considerably affects the free-field soil response, and consequently, the pile kinematic response. Overall, both non-linear soil models and BDWF formulations generally lead to greater internal forces, while neglecting soil stiffness degradation within the soil–pile interaction modelling proves to be a conservative assumption. The findings provide insight into the importance of modelling assumptions, offering guidance for selecting analysis strategies in the seismic assessment of deep foundations, particularly when site-specific data are unavailable and rigorous numerical models are not feasible, such as in parametric studies or preliminary design stages.