Zhuojin Pipe Fitting Co., LtdVehicle-Bridge Coupled Vibration Analysis of Large-Span CFST Arch Bridges
Literature Overview
This paper by Yao Dunrong and Deng Nianchun from Guangxi University investigates the vehicle-bridge coupled vibration response of large-span highway concrete-filled steel tube (CFST) arch bridges, using the Pingnan Third Bridge as a case study. The authors employ a coupled finite element method (ANSYS) combined with multi-body dynamics software (Universal Mechanism, UM) to improve computational efficiency. The study examines the effects of road surface irregularity, vehicle spacing, and bridge structural damping on the coupled dynamic response, with particular attention to the phenomenon of frequency coincidence between the vehicle and bridge systems. The findings provide practical recommendations for vibration mitigation in the operation and maintenance of CFST arch bridges.
Core Technical Approach and Coupled Dynamics Modeling
The vehicle-bridge coupled vibration problem is fundamentally a nonlinear dynamic system where the vehicle and bridge interact through the contact forces at the wheel-rail or wheel-road interface. The authors model the vehicle as a 20-degree-of-freedom (DOF) rigid-body system using the KAMAZ-55111 truck model in UM, which captures the suspension dynamics, tire stiffness, and mass distribution of a heavy-duty truck. The bridge model is constructed in ANSYS and exported to UM in MAC (Modal Analysis) format at various truncation frequencies to balance computational accuracy and efficiency.
The road surface irregularity is modeled according to ISO 8608 spectral density functions, which characterize the spatial frequency content of road roughness. The bridge structural damping is applied as a Rayleigh damping model with a damping ratio typically in the range of 2% to 4% for steel-arch bridges. The coupled equations of motion are solved iteratively, with the contact forces at each time step computed from the relative displacement between the vehicle tires and the bridge deck.
| Parameter | Symbol/Value | Typical Range | Effect on Dynamic Response |
|---|---|---|---|
| Road surface irregularity | ISO 8608 Class A–F | Class A (smooth) to Class F (very rough) | Most significant factor; higher class → larger dynamic response |
| Vehicle spacing | $d$ | 0–50 m | Larger spacing → smaller arch dynamic response; "peak-shaving" effect |
| Bridge damping ratio | $\zeta$ | 2%–4% | Higher $\zeta$ → reduced acceleration but minimal effect on displacement |
| Truncation frequency | $f_{tr}$ | 1–12 Hz | Higher $f_{tr}$ → more accurate but computationally expensive |
| Vehicle spring stiffness | $k_v$ | 100–300 kN/m | Governs vehicle natural frequency; affects resonance sensitivity |
Frequency Coincidence and Resonance Amplification
One of the most critical findings in this paper is the amplification of dynamic response when the natural frequencies of the vehicle and bridge approach each other. This phenomenon, known as frequency coincidence or parametric resonance, can lead to unexpectedly large dynamic amplification factors that exceed those predicted by static analysis or single-degree-of-freedom models. The authors identify two cases of frequency coincidence and observe that while both amplify the arch bridge response, the degree of amplification depends on how closely the frequencies actually match. In one case with truncation frequency 12, the frequencies were not closely matched, and the amplification was not pronounced.
From a steel pipe manufacturing perspective, the natural frequency of a CFST arch rib is governed by the flexural and axial stiffness of the steel tube, which in turn depends on the tube's wall thickness, diameter, and material grade. For a typical large-span CFST arch bridge with a span of 300–500 m, the arch rib may be fabricated from API 5L X65 or X70 grade steel pipe with diameters of 1.0–1.5 m and wall thicknesses of 20–40 mm. The welding quality of the longitudinal and circumferential seams directly affects the stiffness and damping characteristics of the arch rib. Poorly executed submerged arc welds (SAW) or flux-cored arc welds (FCAW) can introduce localized stiffness reductions and stress concentrations that alter the natural frequency distribution.
Process and Standards Analysis
The road surface irregularity is identified as the most dominant factor influencing both vehicle and bridge dynamic response. This finding has direct implications for the maintenance of bridge deck pavements, which are typically composed of asphalt concrete or polymer-modified bitumen layers bonded to the steel deck or composite deck of the CFST arch. According to ASTM D4264 and EN 13108-2, the smoothness of the bridge deck pavement should be regularly monitored using profile measurement methods such as the international roughness index (IRI). The paper demonstrates that even moderate increases in road roughness can significantly amplify the dynamic loads transmitted to the arch ribs and hangers, accelerating fatigue damage in the welded connections.
The vehicle spacing effect is also noteworthy: the authors observe that a moderate vehicle spacing produces a "peak-shaving" and "warping" effect on the displacement response of the arch, reducing the peak displacement. This suggests that traffic management strategies, such as spacing control on the bridge approach, can be an effective measure to reduce dynamic amplification. For the short hangers connecting the arch rib to the deck, the impact factor decreases with increasing bridge damping ratio, but the damping ratio has a more pronounced effect on mid-span acceleration than on displacement.
Integration with Engineering Practice
In the design and inspection of CFST arch bridges, the vehicle-bridge coupled vibration analysis provides a more realistic assessment of dynamic loads than traditional static load analysis. The Chinese standard JTG D60-2015 and the European standard EN 1990 incorporate dynamic amplification factors (impact factors) that are typically derived from empirical formulas rather than coupled dynamic analysis. The results of this paper suggest that these empirical factors may be insufficient for bridges where the natural frequency is close to the vehicle bounce frequency (typically 1.0–2.0 Hz for heavy trucks). Engineers should consider conducting coupled dynamic analysis for bridges with spans exceeding 300 m or where the arch rib natural frequency falls within the 0.5–2.5 Hz range.
For the welding quality control of CFST arch ribs, the dynamic response analysis highlights the importance of maintaining consistent weld quality along the entire length of the arch rib. Variations in weld toe geometry, weld penetration, and residual stress distribution can create localized stiffness variations that alter the natural frequency spectrum. Non-destructive testing (NDT) methods such as phased array ultrasonic testing (PAUT) and time-of-flight diffraction (TOFD) should be employed to detect volumetric defects and planar defects in the circumferential welds of the arch ribs, particularly in areas where the weld is subjected to high cyclic stress ranges.
Key Questions and Reflections
A key question that emerges from this study is whether the current design codes adequately account for the vehicle-bridge coupled vibration phenomenon in the fatigue assessment of CFST arch bridges. The paper demonstrates that frequency coincidence can significantly amplify dynamic loads, but the standard fatigue assessment procedures typically use static load spectra with empirical dynamic amplification factors. This discrepancy could lead to underestimation of fatigue damage in bridges where the natural frequency is poorly matched to the vehicle bounce frequency.
Another reflection is the role of bridge deck damping in mitigating coupled vibration. The paper shows that increasing the bridge damping ratio reduces the acceleration response but has limited effect on displacement. In practice, damping can be increased through the addition of tuned mass dampers (TMDs) or viscous dampers at the hanger-arch connections. However, the cost-effectiveness of such measures should be evaluated against the actual dynamic load amplification, which may be modest for bridges with well-maintained road surfaces and controlled traffic spacing.
Study Insights and Implications
This paper provides a comprehensive framework for analyzing vehicle-bridge coupled vibration in large-span CFST arch bridges, with practical recommendations that can be directly applied to bridge management and maintenance. The identification of road surface irregularity as the dominant factor underscores the importance of pavement maintenance in preserving the structural integrity of the arch ribs and hangers. For steel pipe engineers involved in the fabrication of CFST arch ribs, the study reinforces the need for rigorous welding quality control and consistent material properties to ensure predictable dynamic behavior. The coupled analysis approach should be adopted as a standard verification tool for bridges with spans exceeding 300 m, and the findings should inform the revision of dynamic load factors in future editions of bridge design codes.