Probabilistic Seismic Sensitivity Analyses of High-Speed Railway Extradosed Cable-Stayed Bridges
Abstract
:Featured Application
Abstract
1. Introduction
2. Analysis of Structural Uncertainty Based on Probability Reliability
2.1. Latin Hypercube Sampling
2.2. Nataf Transformation of Model Parameter Correlation
3. Numerical Analysis
3.1. Background of the Bridge
3.2. Nonlinear Finite Element Model
3.3. Seismic Ground Motions
4. Analysis of Structural Uncertainty
4.1. Random Parameter Selection and Distribution of the Bridge
4.2. Sensitivity Analysis of Tornado Diagram
- (1)
- For high-speed railway bridge damage, the SFDP of an extradosed cable-stayed bridge are selected, such as angles of girder, support displacement, pier displacement, pier curvature, tower curvature and cable force;
- (2)
- According to the probability distribution characteristics of each random parameter in Table 4 and considering the correlation, the upper limit and lower limit values can be determined using Latin hypercube sampling. Then, the single random variable x is changed, and its upper limit and lower limit values are brought into the dynamic analysis model, while the other parameters remain unchanged. Subsequently, the difference between the upper limit and lower limit value of the SFDP can be calculated. Finally, the difference is divided by the maximum value of the SFDP of a benchmark model, and its ratio is defined as the sensitivity of the SFDP;
- (3)
- The sensitivity of the demand parameters to random variables can be analyzed after repeating step (2), and then the sensitivity as a “horizontal graph” of the random variable X can be drawn in the graph;
- (4)
- Finally, a “horizontal graph” of each parameter can be obtained by repeating step (3); these can be arranged in descending order to analyze the parameter sensitivity of dynamic damage of the extradosed cable-stayed bridge.
4.3. Analysis of Structural Uncertainty
5. Conclusions
- (1)
- SFDP are greatly affected by structural uncertainty. The sensitive parameters with the greatest influence on dynamic response are the friction coefficient of bearing, concrete bulk density, damping ratio, peak compressive strength of confined concrete, component size and peak strain of confined concrete. The secondary parameters are the strength and strain of unconfined concrete, the impact of which on the bridge cannot be ignored. The other parameters are insensitive to responses of high-speed railway extradosed cable-stayed bridges;
- (2)
- The effects of material properties and cross-section should be fully considered for nonlinear dynamic time-history analysis. Therefore, accurate calculation of material parameter characteristics and accurate simulation of structural characteristics are the prerequisites for ensuring accurate and reliable calculation results. In addition, the variation ratio of cable force is less sensitive than other SFDP, and it is difficult to quantify the seismic function damage;
- (3)
- Structural uncertainty has a great impact on the dynamic response of high-speed railway extradosed cable-stayed bridges, and it is quite different from traditional static parameter sensitivity analysis. Therefore, it is necessary to clarify the influence of random parameters on the bridge dynamic responses, and to explore the relationship between seismic demand and structural random parameters.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Component | Element Type | Material |
---|---|---|
Cable | Truss Element | Steel02 Material |
Pylon | Nonlinear Beam-Column Element | Concrete02 Material |
Steel02 Material | ||
Main girder | Elastic Beam-Column Element | Elastic Material |
Bearing | ZeroLength Element | Elastic-Perfectly Plastic Material |
Pier | Nonlinear Beam-Column Element | Concrete02 Material |
Steel02 Material | ||
Pile | Nonlinear Beam-Column Element | Concrete02 Material |
Steel02 Material | ||
Soil spring | ZeroLength Element | Elastic Material |
Connecting rigid arm | Elastic Beam-Column Element | Elastic Material |
No. | Model Parameter | Pylon/Pier/Pile | Unit | No. | Model Parameter | Pylon/Pier/Pile | Unit |
---|---|---|---|---|---|---|---|
1 | Peak compressive strength of confined concrete | 48.1/30.55/30.55 | MPa | 7 | Peak strain of unconfined concrete | 0.002/0.002/0.002 | |
2 | Ultimate compressive strength of confined concrete | 9.62/6.11/6.11 | MPa | 8 | Ultimate strain of unconfined concrete | 0.004/0.004/0.004 | |
3 | Peak strain of confined concrete | 0.0045/0.0045/0.0045 | 9 | Elastic modulus of concrete | 36000/33000/33000 | MPa | |
4 | Ultimate strain of confined concrete | 0.009/0.009/0.009 | 10 | Yielding strength of steel | 400/400/400 | MPa | |
5 | Peak compressive strength of unconfined concrete | 37/23.5/23.5 | MPa | 11 | Elastic modulus of steel | 200000/200000/200000 | MPa |
6 | Ultimate compressive strength of unconfined concrete | 7.4/4.7/4.7 | MPa | 12 | Thickness of cover layer | 0.035/0.04/0.06 | m |
13 | Elastic modulus of main girder | 36,000 | MPa | 16 | Friction coefficient of bearing | 0.02 | |
14 | Elastic modulus of cable | 195,000 | MPa | 17 | Damping ratio | 0.05 | |
15 | Yielding strength of cable | 1860 | MPa | 18 | Concrete bulk density | 26.5 | kN/m3 |
Calculation Parameters | Longitudinal Direction Soil Spring Stiffness | Transverse Direction Soil Spring Stiffness | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Soil Division | a | b1 | m | z | k | a | b1 | m | z | k |
(m) | (m) | (kN/m4) | (m) | (kN/m) | (m) | (m) | (kN/m4) | (m) | (kN/m) | |
1.0 | 2.0 | 1.6 | 21,425.1 | 1.0 | 69,631.6 | 2.0 | 1.4 | 21,425.1 | 1.0 | 60,847.3 |
2.0 | 2.0 | 1.6 | 21,425.1 | 3.0 | 208,894.8 | 2.0 | 1.4 | 21,425.1 | 3.0 | 182,541.9 |
3.0 | 2.0 | 1.6 | 21,425.1 | 5.0 | 348,158.0 | 2.0 | 1.4 | 21,425.1 | 5.0 | 304,236.5 |
4.0 | 2.0 | 1.6 | 21,425.1 | 7.0 | 487,421.1 | 2.0 | 1.4 | 21,425.1 | 7.0 | 425,931.1 |
5.0 | 2.0 | 1.6 | 21,425.1 | 9.0 | 626,684.3 | 2.0 | 1.4 | 21,425.1 | 9.0 | 547,625.7 |
6.0 | 2.0 | 1.6 | 21,425.1 | 11.0 | 765,947.5 | 2.0 | 1.4 | 21,425.1 | 11.0 | 669,320.3 |
7.0 | 2.0 | 1.6 | 21,425.1 | 13.0 | 905,210.7 | 2.0 | 1.4 | 21,425.1 | 13.0 | 791,014.9 |
8.0 | 2.0 | 1.6 | 21,425.1 | 15.0 | 1,044,473.9 | 2.0 | 1.4 | 21,425.1 | 15.0 | 912,709.5 |
9.0 | 2.0 | 1.6 | 21,425.1 | 17.0 | 1,183,737.1 | 2.0 | 1.4 | 21,425.1 | 17.0 | 1,034,404.1 |
10.0 | 2.0 | 1.6 | 21,425.1 | 19.0 | 1,323,000.3 | 2.0 | 1.4 | 21,425.1 | 19.0 | 1,156,098.7 |
11.0 | 2.0 | 1.6 | 21,425.1 | 21.0 | 1,462,263.4 | 2.0 | 1.4 | 21,425.1 | 21.0 | 1,277,793.3 |
12.0 | 2.0 | 1.6 | 21,425.1 | 23.0 | 1,601,526.6 | 2.0 | 1.4 | 21,425.1 | 23.0 | 1,399,487.9 |
13.0 | 2.0 | 1.6 | 21,425.1 | 25.0 | 1,740,789.8 | 2.0 | 1.4 | 21,425.1 | 25.0 | 1,521,182.5 |
14.0 | 2.0 | 1.6 | 21,425.1 | 27.0 | 1,880,053.0 | 2.0 | 1.4 | 21,425.1 | 27.0 | 1,642,877.1 |
15.0 | 2.0 | 1.6 | 21,425.1 | 28.0 | 1,9496,84.6 | 2.0 | 1.4 | 21,425.1 | 28.0 | 1,703,724.4 |
No. | Uncertainty Parameter | Radom Variables | Variables Distribution Type | Standard Deviation | Coefficient of Variation | Unit |
---|---|---|---|---|---|---|
1 | Peak compressive strength of confined concrete | fc,core | Normal distribution | 4.076/2.5889/2.5889 | 0.14 | MPa |
2 | Ultimate compressive strength of confined concrete | fcu,core | Normal distribution | 0.8217/0.5218/0.5218 | 0.14 | MPa |
3 | Peak strain of confined concrete | ec,core | Normal distribution | 0.0008/0.0008/0.0008 | 0.15 | |
4 | Ultimate strain of confined concrete | ecu,core | Normal distribution | 0.002/0.002/0.0019 | 0.15 | |
5 | Peak compressive strength of unconfined concrete | fc,cover | Normal distribution | 3.351/2.1283/2.1283 | 0.14 | MPa |
6 | Ultimate compressive strength of unconfined concrete | fcu,cover | Normal distribution | 0.71/0.4509/0.4509 | 0.14 | MPa |
7 | Peak strain of unconfined concrete | ec,cover | Normal distribution | 0.0003/0.0003/0.0003 | 0.15 | |
8 | Ultimate strain of unconfined concrete | ecu,cover | Normal distribution | 0.0006/0.0006/0.0006 | 0.15 | |
9 | Elastic modulus of concrete | Ec | Normal distribution | 2880/2640/2640 | 0.08 | MPa |
10 | Yielding strength of steel | fy | Normal distribution | 16/16/16 | 0.045 | MPa |
11 | Elastic modulus of steel | Ey | Normal distribution | 6600/6600/6600 | 0.10 | MPa |
12 | Component size | D | Log-normal distribution | / | 0.2 | m |
13 | Thickness of cover layer | C | Normal distribution | 0.0017/0.0019/0.0029 | 0.2 | m |
14 | Elastic modulus of main girder | Eg | Normal distribution | 2880 | 0.08 | MPa |
15 | Elastic modulus of cable | Eca | Normal distribution | 19,500 | 0.1 | MPa |
16 | Yielding strength of cable | fca | Normal distribution | 74.4 | 0.04 | MPa |
17 | Friction coefficient of bearing | m | Normal distribution | 0.002 | 0.5 | |
18 | Damping ratio | x | Normal distribution | 0.005 | 0.2 | |
19 | Concrete bulk density | g | Normal distribution | 1.75 | 0.1 | kN/m3 |
Correlation Coefficient | fc,core | fcu,core | ec,core | ecu,core | fc,cover | fcu,cover | ec,cover | ecu,cover |
---|---|---|---|---|---|---|---|---|
fc,core | 1 | 0.8 | 0.8 | 0.64 | ||||
fcu,core | 0.8 | 1 | 0.64 | 0.8 | ||||
ec,core | 1 | 0.8 | 0.8 | 0.64 | ||||
ecu,core | 0.8 | 1 | 0.64 | 0.8 | ||||
fc,cover | 0.8 | 0.64 | 1 | 0.8 | ||||
fcu,cover | 0.64 | 0.8 | 0.8 | 1 | ||||
ec,cover | 0.8 | 0.64 | 1 | 0.8 | ||||
ecu,cover | 0.64 | 0.8 | 0.8 | 1 |
Seismic Response in Longitudinal Direction | Seismic Response in Transverse Direction | |||||||
---|---|---|---|---|---|---|---|---|
10# Pier | 11# Pier | 12# Pier | 13# Pier | 10# Pier | 11# Pier | 12# Pier | 13# Pier | |
Displacement of pier Top (units: m) | 0.38 | 0.33 | 0.363 | 0.338 | 0.059 | 0.123 | 0.149 | 0.043 |
Main girder angle (units: ×10−3 rad) | 2.40 | 3.10 | 2.90 | 1.70 | 1.90 | 3.40 | 3.10 | 2.20 |
Curvature of pier bottom(/×10−3) | 3.80 | 4.70 | 3.30 | 7.60 | 0.12 | 1.10 | 1.30 | 0.11 |
Bearing displacement (units: m) | 0.015 | 0.048 | 0.043 | 0.025 | 0.016 | 0.123 | 0.13 | 0.016 |
11# Pylon | 12# Pylon | 11# Pylon | 12# Pylon | |||||
Curvature of pylon Bottom (/×10−5) | 4.10 | −2.40 | 110 | 140 | ||||
Cable force (units: KN) | 5905.6 | 6055.2 |
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Xie, M.; Yuan, J.; Jia, H.; Yang, Y.; Huang, S.; Sun, B. Probabilistic Seismic Sensitivity Analyses of High-Speed Railway Extradosed Cable-Stayed Bridges. Appl. Sci. 2023, 13, 7036. https://doi.org/10.3390/app13127036
Xie M, Yuan J, Jia H, Yang Y, Huang S, Sun B. Probabilistic Seismic Sensitivity Analyses of High-Speed Railway Extradosed Cable-Stayed Bridges. Applied Sciences. 2023; 13(12):7036. https://doi.org/10.3390/app13127036
Chicago/Turabian StyleXie, Mingzhi, Jinglian Yuan, Hongyu Jia, Yongqing Yang, Shengqian Huang, and Baolin Sun. 2023. "Probabilistic Seismic Sensitivity Analyses of High-Speed Railway Extradosed Cable-Stayed Bridges" Applied Sciences 13, no. 12: 7036. https://doi.org/10.3390/app13127036
APA StyleXie, M., Yuan, J., Jia, H., Yang, Y., Huang, S., & Sun, B. (2023). Probabilistic Seismic Sensitivity Analyses of High-Speed Railway Extradosed Cable-Stayed Bridges. Applied Sciences, 13(12), 7036. https://doi.org/10.3390/app13127036