Design-oriented equivalent impact pulse construction and interpretable response prediction for high-speed railway bridge piers under pier-top impact

Accurate and efficient representation of pier-top impact effects remains a challenge in whole-bridge seismic analysis. Contact-element-based approaches are often highly sensitive to the selected time step and contact stiffness, while existing equivalent dynamic load methods are frequently derived from static equivalence, empirical pulse assumptions, or local force-based criteria, and therefore may not adequately reflect the actual structural demand. To address this issue, this study develops a mechanics-informed and design-oriented framework for simplifying pier-top impact on high-speed railway bridge piers. A spring-mass-beam impact model (SMBIM), previously validated by scaled impact tests, is adopted as the computational backbone to generate a parametric database covering representative bridge and impact conditions. A displacement-based equivalent pulse strategy (DEPS) is then proposed to define the duration of an equivalent rectangular pulse by enforcing peak-displacement equivalence, so that the impact effect can be directly incorporated into structural analysis without explicitly simulating the full contact process. To identify the dominant mechanisms governing local and global response quantities, feature-ranking and partial-dependence analyses are performed for the peak impact force, maximum pier-top displacement, and equivalent duration. Based on these insights, explicit power-law formulas are established for transparent and rapid estimation of these key quantities. Validation against a held-out numerical testing subset shows that the proposed explicit formulas for the peak impact force, maximum pier-top displacement, and equivalent duration achieve coefficients of determination of 0.950, 0.898, and 0.904, respectively, with mean relative errors below 6.5%. Representative verification cases further indicate that the equivalent rectangular pulse reproduces the peak displacement of the SMBIM with errors generally below 2%. The proposed framework provides a computationally efficient and interpretable alternative to detailed contact-impact simulation for design-level assessment of impact effects within the investigated parameter range.