Unified Rigorous Solution for Kinematic Response of Pipe Piles Embedded in Unsaturated Soil Subjected to S Waves

ABSTRACT The dynamic response of pile foundations is critical for seismic design. This study employs the Timoshenko beam model for pipe piles and Biot's poroelasticity theory for wave propagation in unsaturated soils. Analytical solutions are derived for three displacement fields under S waves excitation: free‐field soil, pile–soil interface, and scattered soil displacements. By computing the relative interaction forces between the soil and pile using the scattered displacement field, a coupled vibration analytical model for pile–soil interaction under S waves is established. Based on principles similar to the dynamic beam on the Winkler foundation (BDWF) model by Makris and Gazetas, this approach eliminates empirical parameter selection, offering a more rigorous mathematical framework applicable to both end‐bearing and friction piles in saturated and unsaturated soils. Comparative analyses are conducted to assess the prediction accuracy of the BDWF method and continuum models. The results demonstrate that the BDWF model underestimates the resonant frequency of piles and overpredicts the corresponding amplification factor. In contrast, continuum models, which neglect pile–soil relative displacement differences, overestimate the bending moment distribution. Furthermore, the influences of soil saturation degree, void ratio, and internal soil plug formation on the pile dynamic response are systematically investigated. The analytical results show that the inner soil plug can improve the dynamic stability of the pile foundation.