Seismic Vulnerability Analysis of Steel Tube Concrete Rigid Frame Arch Bridge

Literature Overview

This paper by Wang Zhiyuan, Zhao Renda, Wu Xinrui, and Zhao Chenggong from the School of Civil Engineering at Southwest Jiaotong University, published in Vibration and Shock in 2023, Volume 42, Issue 16, presents a comprehensive seismic vulnerability analysis of a steel tube concrete (SRC) rigid frame arch bridge. Funded by the Sichuan Provincial Science and Technology Plan (2020YFH066), the study uses a specific high-speed railway rigid frame arch bridge as an engineering case to develop a more complete seismic damage assessment methodology. The research is classified under U442.5 and U448.22 and employs advanced computational tools including OpenSEES for nonlinear numerical modeling and Copula functions for system vulnerability analysis.

Methodology and Core Technical Approach

The research follows a systematic three-step methodology. First, a nonlinear numerical model of the arch bridge is established on the OpenSEES platform, which is a widely used open-source software for structural engineering analysis. Second, nonlinear dynamic time history analysis and incremental dynamic analysis (IDA) are conducted to evaluate the seismic damage of main arch rib sub-components, interface piers, and arch columns. Third, two types of Copula functions are introduced to establish the vulnerability curves of the main arch rib component system under a series system configuration, and these are compared with sub-component vulnerability and system vulnerability based on the first reliability principle.

The following table summarizes the key analytical methods and their purposes in this study:

Key Findings on Seismic Vulnerability

The study reveals several important findings regarding the seismic vulnerability characteristics of SRC rigid frame arch bridges under three-directional seismic excitation. The outer wrapped concrete of the main arch rib exhibits significantly higher damage probability and damage degree compared to the steel tube concrete core. Furthermore, the vulnerable location of the steel tube concrete shifts from mid-span to the arch foot as the peak ground acceleration increases, indicating a progressive damage pattern that is critical for seismic design considerations.

The following table presents the comparative vulnerability findings for different structural elements:

System Vulnerability Analysis Using Copula Functions

A significant contribution of this paper is the application of Copula functions to establish system-level vulnerability curves that account for the statistical correlation between component failures. The authors compare two different Copula functions and demonstrate that the system vulnerability of the main arch rib component system is more biased toward the outer wrapped concrete. The L/4 arch rib section exhibits the maximum damage probability, which is a critical finding for seismic design and retrofitting efforts.

The comparison between Copula-based system vulnerability and first reliability principle-based system vulnerability reveals important differences in predicted damage probabilities. The Copula function approach provides a more realistic assessment by accounting for the dependence between component failures, which is particularly important for series systems where the failure of any single component can lead to system failure.

Engineering Practice Implications

The findings of this study have direct implications for the seismic design and retrofitting of SRC rigid frame arch bridges. The following recommendations emerge from the analysis:

• Seismic design should prioritize strengthening measures for the outer wrapped concrete of the main arch rib, particularly at the L/4 arch rib section
• The transition of vulnerable locations from mid-span to arch foot with increasing PGA must be considered in performance-based seismic design
• Interface piers and arch columns require enhanced cover concrete protection, as their vulnerability significantly exceeds that of longitudinal reinforcement and core concrete
• Multi-directional seismic excitation should be used in design analyses, as it produces more severe damage than single-direction excitation
• System-level vulnerability assessment using Copula functions provides more accurate predictions than first-order reliability methods and should be adopted in future design codes

Study Insights and Reflections

This paper represents a significant advancement in the seismic assessment methodology for SRC rigid frame arch bridges, which are increasingly used in high-speed railway infrastructure across China. The integration of nonlinear numerical analysis, incremental dynamic analysis, and statistical correlation methods through Copula functions provides a comprehensive framework for evaluating structural vulnerability. For practicing engineers, the identification of specific vulnerable locations and the demonstration of damage progression patterns under increasing seismic intensity offer actionable guidance for seismic design and retrofitting. The findings emphasize that the outer wrapped concrete, rather than the steel tube concrete core, is the primary seismic vulnerability in these structures, which has important implications for material selection and detailing requirements in seismic zones. This research contributes to the ongoing effort to improve the seismic safety of critical transportation infrastructure and should inform future revisions of seismic design codes for bridge structures.