A surrogate-model-driven framework for rockfall impact assessment on high-speed railway bridge piers: Shape effects, hybrid retrofit, and fragility analysis

This study presents an integrated framework to assess rockfall-impact risk for high-speed railway bridges in mountainous regions by combining explicit dynamic simulations, Gaussian Process Regression (GPR) surrogate modeling, and probabilistic fragility analysis. A validated high-fidelity finite element model of a coupled Boulder–Train–Track–Bridge (BTTB) system is established to capture responses spanning local contact, global structural dynamics, and train running safety indicators. Using Augmented Uniform Design sampling, GPR surrogates are trained to efficiently predict key responses, enabling full-domain parametric investigation and global sensitivity analysis. Rockfall shape effects are systematically quantified: relative to spherical blocks, the ETAG-027 standard 26-faced polyhedral blocks (under the same nominal diameter) tend to develop stiffer and more concentrated contact, producing a steeper force rise and more severe system-level demands; consequently, the beam-end relative displacement and pier damage index increase by 15–40% on average, and the unfavorable impact-height interval expands to 5.2–8.0 m. To mitigate these adverse effects, a hybrid retrofit scheme combining an ultra-high-performance fiber-reinforced concrete (UHPFRC) jacket and shape memory alloy (SMA) longitudinal reinforcement is proposed; under severe impacts, it reduces rock penetration depth by approximately 80% and increases residual load-carrying capacity by 60–70%. Finally, a GPR-assisted fragility assessment constructs damage-probability surfaces in terms of rockfall kinetic energy and diameter and identifies critical diameter–velocity thresholds for multiple damage limit states, providing quantitative guidance for risk-informed design and management of rockfall-prone high-speed railway bridges.