Tianyue Sun

Seismic pounding between bridge girders and pier-top restraining components can alter the global seismic demand and fragility of high-speed railway (HSR) bridges. Conventional contact-element models require prescribed contact parameters, and their predictions may be sensitive to contact stiffness and numerical integration settings. To address this issue, this study develops a displacement-equivalent pulse-loading method, termed DEPS-Load, for representing pier-top pounding in OpenSees bridge-system analyses. Pounding events are identified from the instantaneous relative displacement and velocity at potential contact locations, and an equivalent rectangular pulse is generated and applied to the corresponding girder-side and pier-side node pair as equal and opposite dynamic loads. The implemented procedure is evaluated using shaking-table tests of a one-span scaled HSR bridge and is benchmarked against a conventional ElasticPPGap-based contact model. For the two pounding cases considered, the errors in peak pier-base moment are below 5%, and the errors in peak pounding force and maximum girder-pier relative displacement remain within approximately 16%. The ElasticPPGap-based model shows strong sensitivity to prescribed contact stiffness, with peak pounding-force errors ranging from −89.32% to 286.08% over the examined stiffness range. DEPS-Load is further applied to the fragility analysis of a representative five-span prototype HSR bridge using 100 ground-motion records. The results show that pier-top pounding increases pier curvature-ductility demand and bearing displacement demand, leading to higher damage probabilities for both individual components and the bridge system, especially for moderate and extensive damage states. The proposed method provides a practical peak-demand-oriented framework for incorporating pounding effects into repeated whole-bridge fragility analyses without solving a high-stiffness contact element at each impact step.

Seismic pier-top pounding in high-speed railway bridges transfers short-duration girder-restraint contact forces into bridge piers, coupling local contact damage with global vibration and possible base yielding. This critical review evaluates how evidence and modelling strategies can be transferred from local contact mechanics to pier response and, ultimately, to whole-bridge seismic demand. The literature is synthesized across experimental and refined numerical characterization, reduced-order contact–structure modelling, response-equivalent-pulse construction, and nonlinear whole-bridge analysis. A qualitative evidence-confidence grading is introduced to distinguish the strength and transferability of the available evidence based on study independence, evidence type, and configuration similarity. The primary scope is high-speed railway bridges, while the underlying contact–structure modelling principles are transferable to conventional railway and highway bridges with comparable pier-top restraints, subject to bridge-specific calibration. Conventional spring-dashpot models are computationally efficient but sensitive to contact stiffness, damping, restitution, and damage assumptions, whereas refined finite-element models resolve local response at substantially greater computational cost. Static, impulse-equivalent, and prescribed pulse representations can reduce analysis effort, but agreement in force or impulse alone does not ensure equivalence in pier displacement, base moment, plastic rotation, or residual demand. Demand-oriented pulses can reproduce selected component-level responses within a calibrated applicability domain, while response-triggered loading remains a conditional system-level reduction requiring reliable event logic, state updating, and independent benchmark validation. Future research should prioritize realistic restraint tests, identifiable parameter ranges, multi-demand validation, uncertainty quantification and damage-updatable repeated-impact models. These advances can provide a mechanics-based basis for performance-oriented restraint assessment, while practical design application requires consistency with code-based seismic restraint provisions and post-earthquake track-system serviceability criteria.

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.