Dynamic Stability Limit Bearing Capacity of CFST Arch Bridges Under Seismic Action

Literature Overview

The paper by Xu Yan and Hu Shide, published in the China Civil Engineering Journal (Vol. 39, Issue 9, 2006, pp. 68-73), investigates the dynamic stability limit bearing capacity of concrete-filled steel tube (CFST) arch bridges under seismic action. Funded by the National Natural Science Foundation of China (Grant No. 50078016), this research was conducted at Tongji University. The authors developed a methodology based on the B-R motion criterion combined with the incremental dynamic analysis (IDA) method, implemented through the ANSYS APDL programming language, to determine the dynamic stability limit bearing capacity of CFST arch bridges. The study examines the effects of seismic input direction, geometric nonlinearity, material nonlinearity, and initial geometric imperfections on the dynamic stability limit bearing capacity, and validates the methodology through shake table testing of a CFST model arch bridge.

Core Technical Findings

The study's principal conclusions are as follows:

• Seismic input direction: Transverse (lateral) input is the most unfavorable direction for the dynamic stability of the arch bridge.
• Material nonlinearity vs. geometric nonlinearity: The effect of material nonlinearity on the dynamic stability limit bearing capacity is greater than that of geometric nonlinearity.
• Initial geometric imperfections: Initial geometric imperfections reduce the dynamic stability limit bearing capacity of the arch bridge, with antisymmetric imperfection modes being the most unfavorable.
• Method validation: The proposed IDA-based methodology was validated through shake table testing of a CFST model arch bridge, demonstrating its correctness and engineering applicability.

Methodology: B-R Motion Criterion and Incremental Dynamic Analysis

The B-R (Bass-Rao) motion criterion is used to determine the onset of dynamic instability by monitoring the response characteristics of the structure under incrementally scaled seismic inputs. The incremental dynamic analysis (IDA) method involves subjecting the structural model to a series of seismic records scaled at different intensity levels and recording the structural response at each intensity level. The dynamic stability limit bearing capacity is identified as the seismic intensity level at which the structure exhibits unstable behavior, such as unbounded displacement growth or loss of equilibrium.

The implementation through ANSYS APDL (ANSYS Parametric Design Language) allows for automated execution of the IDA procedure, including the scaling of seismic inputs, the nonlinear dynamic analysis at each intensity level, and the post-processing of results to identify the stability limit. This automation is essential for the systematic investigation of multiple variables (input direction, imperfection mode, imperfection amplitude) that would be impractical to analyze manually.

Parametric Study Results

The finding that material nonlinearity has a greater effect than geometric nonlinearity is significant for CFST arch bridges because it highlights the importance of the constitutive behavior of both the steel tube and the confined concrete. In CFST members, the steel tube provides lateral confinement to the concrete, which enhances the compressive strength and ductility of the concrete. Under seismic loading, the steel tube may yield and the concrete may crush, and these material nonlinearities can significantly reduce the overall structural capacity. Geometric nonlinearity, which accounts for large displacements and P-Δ effects, is also important but has a secondary influence compared to material nonlinearity.

The observation that antisymmetric imperfection modes are the most unfavorable is consistent with the buckling behavior of arch structures. Antisymmetric imperfections correspond to the first asymmetric buckling mode, which typically has a lower critical load than the symmetric buckling mode. In the dynamic context, these imperfections provide a preferred path for instability development under seismic excitation.

Validation Through Shake Table Testing

The shake table test of a CFST model arch bridge serves as an important validation of the proposed analytical methodology. The test involves subjecting a scaled physical model of the CFST arch bridge to simulated seismic ground motions on a shake table and comparing the measured structural response with the predictions from the IDA analysis. The agreement between the test results and the analytical predictions confirms the validity of the B-R motion criterion and the IDA implementation for CFST arch bridge applications.

Shake table testing of CFST arch bridges is technically challenging due to the need to replicate the self-weight effects of the full-scale structure, which requires either large models or advanced gravity compensation techniques. The successful validation through shake table testing demonstrates that the proposed methodology can be applied to full-scale CFST arch bridge analysis with confidence.

Engineering Practice Implications

For engineers involved in the seismic design and assessment of CFST arch bridges, this study provides several important insights:

• The seismic assessment of CFST arch bridges should consider material nonlinearity in addition to geometric nonlinearity, as the former has a more significant effect on the dynamic stability limit.
• Initial geometric imperfections should be included in seismic analyses, with antisymmetric modes being the most critical. The imperfection amplitude should be based on construction tolerances and quality control records.
• The transverse seismic direction should be identified as the critical loading direction for stability assessment, although multi-directional seismic inputs should also be considered for comprehensive evaluation.
• The IDA-based methodology provides a systematic and repeatable approach for determining the dynamic stability limit bearing capacity, which can be incorporated into performance-based seismic design procedures.

Standards and Design Considerations

Study Insights and Reflections

This research represents a significant contribution to the understanding of dynamic stability in CFST arch bridges, which are increasingly used in modern bridge engineering for their high strength-to-weight ratio and aesthetic appeal. The development of a systematic IDA-based methodology for determining the dynamic stability limit bearing capacity fills an important gap in the seismic assessment tools available to engineers. The finding that material nonlinearity dominates over geometric nonlinearity in terms of its effect on dynamic stability is a valuable insight that should be reflected in seismic design codes and assessment procedures. The validation through shake table testing provides the confidence needed for practical application of the methodology. For future work, the study suggests extending the methodology to consider multi-hazard scenarios (seismic plus wind, seismic plus traffic) and to develop simplified design procedures based on the IDA results for routine engineering practice.