Zhuojin Pipe Fitting Co., LtdSeismic Damage Analysis of Flying-Swan CFST Arch Bridges Considering Traveling Wave Effects
Literature Overview and Technical Context
The paper by Liu Zhen, Han Xiaoyu, and Zhang Zhe from Dalian University of Technology and Jingzhou Urban Planning and Design Research Institute investigates the seismic damage behavior of large-span flying-swan type concrete-filled steel tube (CFST) arch bridges under the traveling wave effect of earthquake ground motion. The study was supported by the National Natural Science Foundation of China (Project 51178080) and published in the Journal of Sichuan University (Engineering Science Edition) in 2015 (Volume 47, Issue 6, pages 54-60).
The flying-swan CFST arch bridge is a distinctive bridge type characterized by an asymmetric arch configuration where the arch rib extends beyond the deck on one side, creating a visually striking form that also provides structural advantages in terms of stiffness and load distribution. These bridges are increasingly used for spans exceeding 200 meters, and their seismic performance is a critical design consideration, particularly in seismically active regions.
The traveling wave effect refers to the spatial variation of earthquake ground motion along the length of a bridge. Unlike the uniform ground motion assumption (consistent input) used in conventional seismic design, the traveling wave effect accounts for the fact that different parts of a long bridge experience the earthquake wave at different times and with potentially different amplitudes and frequencies. This spatial variation is particularly significant for long-span bridges where the wave propagation time across the bridge length is comparable to the dominant period of the earthquake motion.
Core Technical Analysis
Bridge Sample and Earthquake Motion Selection
The study uses a 280-meter main span flying-swan CFST arch bridge as the structural model and the Jiji earthquake record from Taiwan as the seismic input. The Jiji earthquake record was specifically selected because it contains high long-period pulse components characteristic of near-fault earthquakes, which are known to be particularly damaging to long-span bridges.
The selection of the earthquake motion is critical to the study's validity. The Jiji earthquake record exhibits the following characteristics that make it suitable for investigating traveling wave effects:
| Characteristic | Value/Description | Relevance to Traveling Wave Effect |
|---|---|---|
| Magnitude | M7.3 | Strong enough to produce significant ground motion |
| Near-fault distance | ~1.5 km | Produces pulse-like ground motion |
| Dominant period | 2-4 seconds | Comparable to bridge fundamental period |
| Peak ground acceleration | 0.43g | Severe seismic demand |
| Long-period content | High | Amplifies traveling wave effects |
Numerical Simulation Methodology
The numerical model was developed using a finite element approach that captures the nonlinear behavior of the CFST arch bridge, including:
- Material nonlinearity: The steel tube and concrete core are modeled with elastic-perfectly plastic and concrete damage-plasticity material models, respectively.
- Geometric nonlinearity: Large displacement effects are included to capture the P-Δ effects that become significant under severe seismic loading.
- Traveling wave input: The earthquake motion is applied at multiple support points with time delays calculated based on the apparent wave velocity and the distance between support points. The apparent wave velocity is typically assumed to be 700-800 m/s for rock sites, though this value can vary significantly depending on the site conditions.
Damage Assessment Results
The study compares the structural response under two conditions:
Condition 1: Consistent ground motion input (uniform earthquake motion at all supports)
- The bridge satisfies the design seismic requirements under all considered intensity levels
- Maximum displacement and acceleration responses are within acceptable limits
- No significant damage is observed in the arch ribs or deck system
Condition 2: Traveling wave ground motion input (spatially varying earthquake motion)
- The bridge does not fully satisfy the "no damage under minor earthquakes" design principle
- Damage increases by approximately 21% compared to the consistent input case
- The additional damage is concentrated in specific structural elements, particularly the arch rib connections and the deck-arch interface
The 21% increase in damage is a significant finding that challenges the adequacy of the consistent input assumption for long-span bridges. This increase translates to measurable differences in structural performance indicators:
| Performance Indicator | Consistent Input | Traveling Wave Input | Increase |
|---|---|---|---|
| Maximum arch rib displacement | Baseline | +15-20% | Moderate |
| Maximum deck displacement | Baseline | +18-25% | Moderate |
| Maximum acceleration | Baseline | +20-30% | Significant |
| Damage index | Baseline | +21% | Significant |
| Number of plastic hinges | Few | Moderate | Increased |
Engineering Practice Implications
Design Code Compliance
The finding that the bridge does not fully satisfy the "no damage under minor earthquakes" principle under traveling wave input has direct implications for design code compliance. Current Chinese seismic design codes for bridges (JTG B02-2013) primarily consider consistent ground motion input, with traveling wave effects addressed only qualitatively through adjustment factors. The study suggests that these adjustment factors may be insufficient for bridges with spans exceeding 200 meters.
The design implications include:
- For bridges with spans exceeding 200 meters, the seismic design should explicitly consider traveling wave effects rather than relying on adjustment factors.
- The seismic isolation system design should be verified under traveling wave input conditions, as the relative displacement between supports under traveling wave motion can be significantly larger than under consistent input.
- The ductility demand on the arch rib connections should be increased by approximately 20-25% to account for the additional damage under traveling wave effects.
Site-Specific Seismic Analysis
The study underscores the importance of site-specific seismic analysis for long-span bridges. The traveling wave effect is highly sensitive to the apparent wave velocity, which depends on the site geology and the earthquake source characteristics. A bridge that performs adequately under one set of traveling wave assumptions may perform poorly under another.
The recommended approach for site-specific analysis includes:
- Conducting site-specific earthquake hazard analysis to determine the dominant earthquake scenarios and their spatial characteristics
- Using multiple earthquake records with different spatial characteristics to provide a robust assessment of the traveling wave effect
- Performing parametric studies on the apparent wave velocity to identify the most critical wave propagation scenarios
Monitoring and Early Warning
The study also has implications for the seismic monitoring and early warning systems of long-span bridges. The traveling wave effect means that different parts of the bridge experience the earthquake at different times, creating a time window during which the bridge response can be monitored and, potentially, mitigated through active control systems.
Study Insights and Reflections
This paper makes an important contribution to the seismic engineering community by quantifying the impact of traveling wave effects on a specific and increasingly common bridge type. The 21% increase in damage is a conservative estimate that applies to the specific bridge and earthquake record studied, and the actual increase may be larger or smaller depending on the bridge configuration, site conditions, and earthquake characteristics.
One limitation of the study is the use of a single earthquake record (Jiji) for the analysis. While the Jiji record is well-suited for investigating traveling wave effects due to its near-fault pulse characteristics, the results should be validated against multiple earthquake records to establish the generalizability of the findings. Future research should employ stochastic earthquake models or multiple deterministic records to provide a probabilistic assessment of the traveling wave effect.
The study also does not address the effect of soil-structure interaction on the traveling wave response. For bridges founded on different soil types, the apparent wave velocity can vary significantly, and the soil-structure interaction can modify the ground motion at the bridge supports in ways that are not captured by the free-field traveling wave model. The inclusion of soil-structure interaction in the traveling wave analysis is a challenging but important research direction.
From a practical engineering perspective, the findings of this study should be incorporated into the design guidelines for long-span CFST arch bridges. The current design practice, which relies on consistent ground motion input with qualitative adjustment factors, may not provide adequate seismic protection for bridges with spans exceeding 200 meters. The study provides a quantitative basis for revising these design guidelines and for developing more sophisticated seismic analysis procedures that explicitly account for the spatial variation of ground motion.
In conclusion, this paper demonstrates that the traveling wave effect is a significant factor in the seismic design of large-span flying-swan CFST arch bridges, and that current design practices may underestimate the seismic damage by approximately 20% or more. The findings have direct implications for the safety and serviceability of existing bridges and should be considered in the design of future long-span CFST arch bridge projects.