Fatigue Life Assessment of Intercity Track Viaduct Based on Vehicle–Bridge Coupled System
Abstract
:1. Introduction
2. Vehicle–Bridge Coupled System
2.1. Vehicle Model
2.2. Bridge Dynamics
2.3. Coupled System Dynamics
2.3.1. System Dynamic Formula
2.3.2. Mass Matrix
2.3.3. Damping and Stiffness Matrices
2.3.4. Force Vector
2.4. Dynamic Stress Calculation
2.5. Validation
3. Fatigue Assessment Theory
3.1. Reinforcement Corrosion Considered Carbonation
3.2. Fatigue Assessment Method
4. Case Study
4.1. Time–History Curves
4.2. Stress Amplitude
4.3. Cumulative Damage
4.4. Fatigue Life Evaluation
5. Conclusions
- (1)
- The vehicle speed has a significant impact on the bridge’s displacement and stress ergodic curve; when the vehicle passes through different span bridges, the displacement and ergodic curve trends are drastically different, with 30 m-span bridges having higher peak displacement and stress than 25 m-span bridges. However, the dynamic stress amplitudes of the two types of spans are close.
- (2)
- Vehicle speed has a significant impact on the stress amplitude and cycle times, with the majority of cycles concentrated in the small stress amplitude stage.
- (3)
- According to cumulative curves, material corrosion should be considered, and there is no evident law governing the impact of vehicle speed on the cumulative damage curve.
- (4)
- The bridge fatigue life is inconsistent at different speeds, and the fatigue life of bridges with different spans is vastly different. Based on this, the recommended vehicle speed is proposed from the standpoint of fatigue life. For bridges with a 30 m span, it is recommended that the speed be kept between 115 km/h and 70 km/h; for bridges with a 25 m span, the speed should be kept between 78 km/h and 116 km/h.
- (5)
- Under the long-term fatigue load, the structure will have stiffness degradation, which will increase the stress amplitude of reinforcement and concrete. In addition, the interlayer components may be damaged. How to reasonably consider the degradation and damage is a problem that needs to be paid attention to in the future.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Symbol | Value |
---|---|---|
Elastic modulus of concrete | Ec | 3.45 × 1010 Pa |
Sectional area | A | 3.6552 m2 |
Section moment of inertia about horizonal axis | Iy | 1.3514 m4 |
Section moment of inertia about vertical axis | Iz | 9.1108 m4 |
Line weight | ρ | 126.43 kN/m |
Damping ratio | ξ | 2% |
Span length | L | 30 m and 25 m |
Compression of cube concrete | fcu | 50 MPa |
Yield strength of steel reinforcement | fy | 400 MPa |
Elastic modulus of steel reinforcement | Es | 2.0 × 1011 Pa |
Local environmental coefficient | mef | 2.5 |
Environmental relative humidity | RH | 65° |
Fatigue coefficient of steel reinforcement | m | 1.7637 |
Fatigue coefficient of steel reinforcement | C0 | 1.4213 × 1010 |
L1/m | L2/m | dV/m | mc/kg | mt/kg | mw/kg |
---|---|---|---|---|---|
2.2 | 12.5 | 19.0 | 21,920 | 2550 | 1420 |
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Cui, C.; Feng, F.; Meng, X.; Liu, X. Fatigue Life Assessment of Intercity Track Viaduct Based on Vehicle–Bridge Coupled System. Mathematics 2022, 10, 1663. https://doi.org/10.3390/math10101663
Cui C, Feng F, Meng X, Liu X. Fatigue Life Assessment of Intercity Track Viaduct Based on Vehicle–Bridge Coupled System. Mathematics. 2022; 10(10):1663. https://doi.org/10.3390/math10101663
Chicago/Turabian StyleCui, Chenxing, Fan Feng, Xiandong Meng, and Xiang Liu. 2022. "Fatigue Life Assessment of Intercity Track Viaduct Based on Vehicle–Bridge Coupled System" Mathematics 10, no. 10: 1663. https://doi.org/10.3390/math10101663