Spring-Based Soil–Structure Interaction Modeling of Pile–Abutment Joints in Short-Span Integral Abutment Bridges with LR and RSM

Integral abutment bridges (IABs) are increasingly adopted in transportation infrastructure due to their durability, reduced maintenance needs, and cost-effectiveness compared to conventional bridges. However, their reliable performance under live loads is strongly influenced by the nonlinear soil–structure interaction (SSI) at the pile–abutment joint, which remains challenging to quantify using conventional analysis methods. This study develops simplified spring-based models to capture the SSI behavior of pile–abutment joints in short-span IABs. Predictive equations for joint rotation, deflection, moment, and shear are formulated using Linear Regression (LR) and Response Surface Methodology (RSM). Unlike prior studies relying solely on FEM or traditional p–y curves, the novelty of this work lies in deriving regression-based spring constants calibrated against FEM analyses, which can be directly implemented in standard structural software. This approach significantly reduces computational demands while maintaining predictive accuracy, enabling efficient assessment of pile contributions and global bridge response. Validation against finite element method (FEM) results confirms the reliability of the simplified models, with RSM outperforming LR in representing nonlinear parameter interactions.