Seismic Analyses of Rocking Bridges Considering Vehicle‐Bridge Interaction
Bibliographic record
Abstract
ABSTRACT Rocking piers have attracted increasing attention due to their promise to simultaneously reduce structural damage and residual displacement of the bridge during seismic shaking. However, the literature lacks a thorough investigation of the system rocking behavior when taking into account the vertical vibration of the deck and the presence of vehicles on the bridge. This study derives an advanced analytical model to fill this research gap. A vehicle model represented by a mass‐spring‐damping system is adopted to derive the dynamics equilibrium of the vehicle‐bridge system (VRB). The derivation is followed by coupling the system's rocking motion through the examination of rocking kinematics, initiation criterion, and energy dissipations during impacts. The analytical model investigates the rocking spectra and overturning stability of the VRB system under different vehicle masses, speeds, and vertical frequencies. It evaluates bridge responses under (1) Ricker wavelets representing pulse‐type excitations and (2) recorded spectrally equivalent long‐ and short‐duration ground motions. Results indicate that the pulse effects on the rocking response depend on its excitation frequency and type (i.e., symmetric vs. antisymmetric). Long‐duration seismic effect can significantly amplify or reduce the seismic responses of both piers and vehicles, although it has a minor effect on these responses on average. Conversely, heavier vehicles can mitigate the rigid‐body‐like displacement of the deck, while increasing its elastic deformation. In turn, bridge rocking also affects vehicle responses in vertical and driving directions, which will impair driving comfort and safety, and increase the potential risk of vehicle collision.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".