Skewed railway bridge decks cut vibration as train speeds climb

High-speed trains crossing a heavily skewed, multi-span bridge in central Spain generate smaller vertical vibrations than an equivalent straight deck, according to a detailed numerical study published in Advances in Bridge Engineering. The finding matters because vertical deck acceleration is one of the most stringent serviceability requirements for ballasted railway bridges, and the European standard EN 1990:2023 A2 caps it at 3.5 metres per second squared for ballasted track. As operators consider raising operating speeds on existing lines, understanding which structural features keep accelerations in check—and which modelling shortcuts inflate them—has direct consequences for safety assessments and upgrade costs.

The study, led by J. C. Sánchez-Quesada with E. Moliner, P. Galvín and M. D. Martínez-Rodrigo, focuses on the Jabalón Bridge, a structure built in the 1980s on the Madrid–Sevilla high-speed line. The bridge consists of three identical simply supported spans of 24.9 metres, each carrying a double-track reinforced concrete slab 11.6 metres wide on five prestressed concrete I-girders 2.05 metres deep. The spans cross the Jabalón River at a skew angle of 134 degrees, and the girders rest on laminated rubber bearings at two abutments and two wall piers. Because the spans are structurally independent but share a continuous ballasted track, a weak coupling develops between them through the rails and ballast alone.

The researchers built an unusually detailed three-dimensional finite element model of the bridge in ANSYS, explicitly representing the rails, sleepers, rail pads and ballast layer, including the transition zones near the joints between spans where the ballast is modelled as a transversely isotropic material. The model was calibrated against an experimental campaign conducted in May 2019, in which vertical accelerations were measured beneath the longitudinal girders under ambient vibration and operational train passages. Several natural frequencies below 30 hertz and their mode shapes were identified, revealing a pronounced three-dimensional behaviour with coupled flexural–torsional response, quite unlike the beam-like behaviour assumed for long straight viaducts.

Train excitation was represented with three models of increasing complexity. The simplest, the moving load model, treats axle loads as point forces travelling at constant speed. The second, a vehicle–bridge interaction model, represents the train as a three-dimensional multi-body system of rigid masses connected by springs and dampers, capturing the inertial effects of the vehicles and the energy dissipated by their suspensions. The third adds measured-class track irregularities with wavelengths between 3 and 25 metres, corresponding to the D1 class of EN 13848-5:2017, generated from analytical power spectral density functions. The generated profiles had a standard deviation of longitudinal level of 1.0142 millimetres, classifying the track as Type D under EN 13848-6. The authors stress that irregularities are stochastic and their results reflect a single realisation, so a full statistical analysis would be needed to quantify their effects rigorously.

The team first examined single-span, non-skewed versions of the bridge under the ten normative HSLM-A trains defined in EN 1991-2:2024, sweeping speeds from 144 km/h upward in increments of 3.6 km/h and progressively extending the upper limit of the speed window. At very low speeds the three excitation models gave nearly identical predictions, because the response is essentially quasi-static. When irregularities were neglected, vehicle–bridge interaction consistently produced lower bridge accelerations. When irregularities were included, which model produced the overall maximum response depended on the speed window and on the particular irregularity profile. The influence of unevenness was more pronounced near the supports, although the absolute response there remained relatively low.

Skewness emerged as a decisive factor. Comparing straight and 134-degree skewed single-span models under the HSLM-A moving load trains, the vertical acceleration decreased with increasing skewness at all post-processing points. The reason is that skewing the deck raises its natural frequencies: in the single-span model the first bending frequency rose from 5.76 to 6.07 hertz and the first torsional frequency from 7.60 to 7.93 hertz. Since resonant speeds are proportional to the bridge frequencies, the resonances shift to higher train speeds, and for the bridge studied some prominent resonances moved outside the operational range of current rolling stock. The difference between straight and skewed configurations grew as the speed window was extended, and vehicle suspensions consistently reduced the structural response in the skewed case, with a stronger effect at higher speeds where lower-order resonances dominate.

Analyses with real trains operating on the line—the articulated RENFE S100 and the regular RENFE S102—confirmed the picture. The S100, with shared bogies 18.7 metres apart, produced its largest peaks at the mid-span external border, with resonances of the fundamental longitudinal mode predicted at about 408.6 km/h and 204.3 km/h and a torsional resonance near 267 km/h amplifying the response at the deck edges. The S102, a Talgo-type train with a shorter characteristic distance of 13.14 metres, excited the first resonance of the fundamental mode at roughly 287.1 km/h, with a further torsional amplification near 375 km/h. For both trains, vehicle–bridge interaction played only a minor role, lowering accelerations mainly at resonance, while irregularities slightly increased predictions at moderate speeds but left the moving load model conservative at the most prominent resonances for this particular track realisation.

The full three-span model revealed the role of the weak span connection. Softening the degraded ballast properties at the joints—reducing the relevant elastic and shear moduli by up to a factor of 25—had little effect away from resonance, but shifted resonant speeds slightly lower as the bending and torsion frequencies dropped. Near the supports, the maximum response increased as the ballast connection relaxed, while away from the supports the response tended to rise in the first and third spans and fall in the central span, particularly at higher speeds. In the central span the stiffest, nominal connection always produced the overall maximum response, whereas for the external spans the governing model depended on the speed window, with softer connections dominating at high speeds.

Perhaps the most consequential result concerns the simplified analyses prescribed by design codes. Because of the bridge’s skewness and design speed, Eurocode 1 requires an explicit dynamic analysis including three-dimensional modes, and the researchers replicated a standard consultancy approach: a single skewed orthotropic plate simply supported at its ends, with nominal properties, no explicit track, and axle loads distributed over three rail supports. This code-based model proved overly conservative across every speed range, predicting cumulative accelerations close to twice those obtained with the detailed models. Under the code-based analysis the bridge would exceed the 3.5 metres per second squared limit at approximately 270 km/h, whereas the detailed model pushed that threshold up to about 350 km/h. The discrepancy stems largely from the normative axle load distribution over three sleepers, which is far more severe than the realistic load spreading that emerges when rail, rail pad and ballast flexibility are modelled explicitly.

The authors conclude that deck skewness is beneficial for serviceability compliance in the 200 to 300 km/h range, that vehicle–bridge interaction and track irregularities become key factors above 300 km/h, and that the weak ballast coupling between spans reshapes the spatial distribution of peak accelerations. For speed-upgrade assessments of bridges behaving like isotropic or orthotropic plates, they recommend simulating the axle load distribution through the ballast and the actual state of the track rather than relying on normative simplifications, ensuring both safety and rational use of infrastructure resources. Bridges with other deck typologies, they note, would require dedicated studies beyond the scope of this work.

Subject of Research: Vertical acceleration serviceability of skewed multi-span high-speed railway bridges under increasing operational speeds

Article Title: Maximum vertical acceleration patterns in skewed multi-span railway bridges under increasing operational speeds

Article References: Sánchez-Quesada, J. C., Moliner, E., Galvín, P., & Martínez-Rodrigo, M. D. (2026). Maximum vertical acceleration patterns in skewed multi-span railway bridges under increasing operational speeds. Advances in Bridge Engineering, 7(1), Article 28. https://doi.org/10.1186/s43251-026-00217-4

Image Credits: AI Generated

DOI: 10.1186/s43251-026-00217-4

Keywords: railway bridges, high-speed rail, deck skewness, vertical acceleration, serviceability limit state, vehicle-bridge interaction, track irregularities, ballast degradation, Eurocode, finite element model, resonance, speed upgrade