Study Note on Seismic Vulnerability Analysis of Large-Span CFST Stiffening Skeleton Arch Bridges

Literature Overview

The paper by Wang Zhiyuan and colleagues from Southwest Jiaotong University, published in Journal of Vibration and Shock in 2023, presents a comprehensive seismic vulnerability analysis of large-span concrete-filled steel tube (CFST) stiffening skeleton arch bridges. Using a high-speed railway arch bridge as an engineering case study, the research employs nonlinear numerical modeling on the OpenSEES platform, nonlinear dynamic time-history analysis, incremental dynamic analysis (IDA), and Copula function-based system vulnerability assessment. This work addresses a critical gap in the seismic assessment methodology for CFST stiffening skeleton arch bridges, which are increasingly used in high-speed railway infrastructure due to their large span capability and structural efficiency.

Numerical Modeling Approach

The nonlinear numerical model was established on the OpenSEES platform, which is widely recognized for its capabilities in nonlinear structural analysis. The model accounts for material nonlinearity in both the steel tubes and the concrete core, geometric nonlinearity including large displacement effects, and potential debonding between the steel tube and concrete core.

Component	Modeling Approach	Key Parameters
Steel tube	Fiber-section model with bilinear or multilinear hardening constitutive law	Yield strength, hardening ratio, ultimate strain
Core concrete	Fiber-section model with confined concrete constitutive law	Compressive strength, tensile strength, confinement factor
Outer concrete	Concrete fiber model with cracking and crushing	Cover thickness, reinforcement ratio
Steel-concrete interface	Interface elements or bond-slip model	Bond strength, slip capacity
Connections	Spring elements or rigid links	Connection stiffness, yield moment

Component Damage Assessment

The study assessed seismic damage at three levels: the main arch rib sub-components, the interface piers, and the arch barrel columns. The main arch rib was further divided into steel tube sections and outer concrete sections, allowing for differentiated damage evaluation.

Damage Indicator	Steel Tube Section	Outer Concrete Section	Interface Pier	Arch Barrel Column
Damage measure	Plastic hinge rotation	Crack width, spalling	Drift ratio	Drift ratio
Damage states	Slight, Moderate, Severe, Collapse	Slight, Moderate, Severe, Collapse	Slight, Moderate, Severe, Collapse	Slight, Moderate, Severe, Collapse
Most vulnerable location	L/4 to L/2 transition	L/4 section	Pier base	L/4 column

Key Findings

The research revealed several important findings regarding the seismic behavior of CFST stiffening skeleton arch bridges. Under three-dimensional seismic excitation, the outer concrete damage probability and damage severity were significantly greater than those of the CFST core. This is attributed to the lower ductility and brittleness of the outer concrete compared to the ductile steel tube. The vulnerability location of the CFST core shifts from the mid-span to the arch foot as the peak ground acceleration (PGA) increases, indicating a transition in the failure mode from flexural yielding at mid-span to shear yielding at the arch foot under severe seismic loading.

System Vulnerability Using Copula Functions

Two types of Copula functions were introduced to establish the system vulnerability curve for the main arch rib component system under a series system assumption. The series system assumption means that the system fails if any single component fails, which is a conservative approach for safety assessment.

Method	System Vulnerability	Conservative Level
Sub-component vulnerability	Based on individual component IDA	Baseline
First Reliability Principle system vulnerability	Based on FOSM	Moderate
Gaussian Copula system vulnerability	Accounts for correlation between components	Lower
Clayton Copula system vulnerability	Captures lower-tail dependence	Lower than Gaussian

The results showed that the system vulnerability of the main arch rib was more biased toward the outer concrete. The L/4 arch rib section exhibited the maximum damage probability. For the interface piers and arch barrel columns, the cover concrete vulnerability level was significantly higher than that of the longitudinal reinforcement and core concrete. The L/4 column location showed the maximum damage probability.

Engineering Implications

The findings have direct implications for seismic design and retrofitting of CFST stiffening skeleton arch bridges. The design should prioritize strengthening measures at the identified vulnerable locations, particularly the outer concrete at the L/4 section of the arch rib and the cover concrete of the interface piers and arch barrel columns. Potential strengthening measures include increasing the cover concrete confinement reinforcement, adding fiber-reinforced polymer (FRP) wrapping to the outer concrete sections, and enhancing the ductility of the steel tube connections.

The use of Copula functions for system vulnerability assessment represents a methodological advancement over traditional component-level assessments. By accounting for the statistical correlation between component responses, the Copula-based approach provides a more accurate representation of the system behavior. The Clayton Copula, which captures lower-tail dependence, is particularly suitable for seismic assessment where the concern is the joint probability of severe damage events.

Study Insights

This paper demonstrates the importance of integrating component-level and system-level vulnerability analysis for comprehensive seismic assessment of complex bridge structures. The shift in vulnerability location with increasing PGA is a critical finding that has implications for performance-based seismic design. Engineers should not assume that the most vulnerable location under moderate seismic loading remains the same under severe loading. The application of Copula functions to bridge seismic assessment is still relatively new and represents a promising direction for more accurate system reliability analysis. The emphasis on outer concrete vulnerability highlights the need for better confinement design in CFST stiffening skeleton arch bridges, particularly in the arch barrel columns and interface piers.