Probabilistic Assessment of Running Safety for Deck Arch Bridges under the Dual Randomness of Track Irregularities and Train Meeting Positions

To address the vehicle–bridge coupled vibration induced by high-speed trains meeting on bridges, conventional deterministic analysis methods, which neglect the spatial randomness of train meeting positions, may lead to distorted structural safety assessments and excessive design redundancy. To this end, an analytical framework that simultaneously considers the dual randomness of track irregularities and train meeting positions is established. First, a single-randomness model is employed to investigate the spatial sensitivity of the system dynamic responses and accurately identify the regions associated with the most unfavorable responses. Subsequently, the train meeting position is introduced as a discrete random variable into the model, and the expected system dynamic responses over the entire bridge are efficiently and accurately determined using a probabilistic integration method. Numerical analysis indicates that the dynamic responses of deck-type arch bridges are highly sensitive to the train meeting position, with the most unfavorable position occurring at 3L/8 rather than at the midspan, as traditionally assumed. The results obtained using the dual-randomness model show a high degree of agreement with those from large-sample Monte Carlo simulations while significantly improving computational efficiency. Under the benchmark condition, the expected carbody acceleration obtained using the dual-randomness model (1.114 m/s 2 ) is approximately 8.5% lower than the deterministic extreme value at the 3L/8 position (1.217 m/s 2 ). The proposed dual-randomness model effectively smooths out local extreme responses associated with specific meeting positions, thereby reducing the overestimation (conservative bias) inherent in conventional deterministic assessments. This approach enables a transition from deterministic extreme-value envelope-based assessment to probabilistic expected-value quantification, thereby reducing excessive design conservatism and providing a scientific basis for the refined design of high-speed railway bridges.