An Improved Model for Design Fatigue Load of Highway Bridges Considering Damage Equivalence
Abstract
:1. Introduction
2. Fatigue Damage Theory
3. Traffic Data Collection and Preprocessing
4. Data of Fatigue Load Spectrum
4.1. Derivation of Fatigue Load Spectrum
4.2. Lane Distribution Parameters
4.3. Fatigue Load Spectrum of Slow Lane
5. Fatigue Damage Calculation
- (1)
- the fatigue damage is not only affected by the shape of the influence line, but also closely related to the length;
- (2)
- the curve shows no regular pattern as the influence line length (L) is less than 30 m, while the REFD values seems to increase monotonously with ‘L’ increasing as ‘L’ exceeds 30 m and will basically close to an upper limit value when the length increases to 100 m.
6. Equivalent Coefficients and Equivalent Heavy Vehicle Flow
6.1. Equivalent Coefficients
6.2. Equivalent Average Daily Traffic Flow
7. Determination for Design Frequency
7.1. Calculation for Representative EC Values
7.2. Verification
7.3. Grades for Design Frequency
7.4. Procedure for Determining the Design Frequency
- (1)
- Necessary traffic investigation, analysis, and prediction;
- (2)
- Vehicle classification referring to Table 2;
- (3)
- The corresponding fatigue load spectra of the effective vehicles (with a GVW above 10 t) is obtained;
- (4)
- The representative EC values are determined referring to Table 9;
- (5)
- The EADTF can be calculated based on the representative EC values and ADTF
- (6)
- The corresponding level of design fatigue load is selected and the design frequency of the standard vehicle in the slow lane is finally determined based on the EADTF.
8. Conclusions
- (1)
- During the fatigue analysis for steel bridges, it was suggested that the vehicle’s damage contribution with a GVW that is less than 10 t should be ignored;
- (2)
- In view of fatigue damage equivalence, it was reasonable to utilize EADTF, which is defined as the product of the representative EC values and ADTF, rather than ADTF in the calculation of the design frequency of the standard vehicle in fatigue analysis;
- (3)
- A practical method was proposed to determine the representative EC values according to the number of axles and the GVW of the vehicle;
- (4)
- A total of three grades for design frequency of the standard vehicle were put forward based on the statistical analysis of EADTF at 35 locations;
- (5)
- The steps to determine the design frequency of the standard vehicle in slow lane were given based on the EADTF calculation and the fatigue design load grades.
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Location Number | Province | Expressway/ Toll Station | Location Number | Province | Expressway/ Toll Station |
---|---|---|---|---|---|
1 | Beijing | G2/Dayangfang | 11 | Hunan | G4/Yanglousi |
2 | Gansu | G30/Ganshan | 12-1 | Hebei | G4/Jiyu |
3-1 | Guangxi | G72/Guixiang | 12-2 | G20/Jilu | |
3-2 | G75/Guihai | 12-3 | G1/Jiliao | ||
4-1 | Jilin | G1/Lalinhe | 13-1 | Henan | G4/Anyangbei |
4-2 | G1/Wulihe | 13-2 | G 4/Yu’e | ||
5-1 | Liaoning | G11/Dalian | 13-3 | G36/Yuwan | |
5-2 | G1/Maojiadian | 13-4 | G 40/Yushan | ||
5-3 | G1/Wanjia | 14 | Heilongjiang | G1/Lalinhe | |
6-1 | Shanxi | G30/Chencang | 15-1 | Hubei | G4/Yu’e |
6-2 | G30/Tongguan | 15-2 | G4/Xiang’e | ||
6-3 | G20/Wangquan | 16-1 | Jiangsu | S26/Suhu | |
6-4 | G20/Wubu | 16-2 | G25/Sulu | ||
7-1 | Sichuan | G85/Yujian | 16-3 | G4211/Suwan | |
7-2 | G65/Sichuan | 17 | Jiangxi | G70/Xiongcun | |
7-3 | G42/Lindian | 18-1 | Shandong | G15/Fushan | |
7-4 | G76/Longnaquba | 18-2 | G20/Luji | ||
7-5 | G75/Sichuan | 18-3 | G15/Lusu | ||
7-6 | G93/Sichuan | 19-1 | Shanxi | G55/Deshengkou | |
8 | Zhejiang | G104/Fenshuiguan | 19-2 | G20/Jundu | |
9-1 | Fujian | G15/Minyue | 19-3 | G20/Jiuguan | |
9-2 | G15/Minzhe | 20-1 | Chongqing | G75/Chongxihe | |
9-3 | G70/Mingan | 20-2 | G75/Xiangxingshan | ||
10 | Guangdong | G4/Yuebei |
Axle Number | Axle Type | Representative Axle Configuration | Representative Vehicle | GVW | Serial Number |
---|---|---|---|---|---|
2 | 11 | | small passenger car | 3 t below | V1 |
11 | | minivan (2 t below) | V2 | ||
12 | | medium bus (11–30 seats) | 3 to 10 t | V3 | |
12 | | medium truck (2–8 t) | V4 | ||
12 | | Large bus (30 seats above) | 10 t above | V5 | |
12 | | dual-axle large truck (8–16 t) | V6 | ||
3 | 112 | | large truck | V7 | |
15 | | large truck | V8 | ||
4 | 115 | | large truck | V9 | |
125 | | dual-axle tractor +dual-axle semi trailer | V10 | ||
5 | 129 | | dual-axle tractor +tri-axle semi trailer | V11 | |
155 | | tri-axle tractor +dual-axle semi trailer | V12 | ||
6 | 1129 | | tri-axle tractor +tri-axle semi trailer | V13 | |
159 | | V14 |
Serial Number | Wheelbase (m) | ||||
---|---|---|---|---|---|
A1 | A2 | A3 | A4 | A5 | |
V3 | 3.6 | ||||
V4 | 3.8 | ||||
V5 | 6 | ||||
V6 | 5 | ||||
V7 | 1.9 | 5.3 | |||
V8 | 4.8 | 1.3 | |||
V9 | 1.9 | 4.5 | 1.3 | ||
V10 | 3.5 | 8.6 | 1.3 | ||
V11 | 3.6 | 6.8 | 1.3 | 1.3 | |
V12 | 3.3 | 1.3 | 6 | 1.3 | |
V13 | 1.7 | 2.7 | 7.3 | 1.3 | 1.3 |
V14 | 3.3 | 1.3 | 9.3 | 1.3 | 1.3 |
Statistical Values | Minimum | Maximum | Mean | Standard Deviation | Variability Coefficient | |
---|---|---|---|---|---|---|
Serial Number | ||||||
V3 | 5.1 | 8.4 | 7.0 | 0.9 | 0.13 | |
V4 | 6.3 | 7.7 | 6.9 | 0.3 | 0.04 | |
V5 | 14.4 | 18.3 | 16.2 | 0.8 | 0.05 | |
V6 | 14.6 | 19.1 | 16.5 | 1.2 | 0.07 | |
V7 | 19.3 | 28.8 | 24.2 | 2.2 | 0.09 | |
V8 | 19.0 | 28.1 | 24.5 | 2.0 | 0.08 | |
V9 | 27.2 | 43.6 | 34.3 | 3.8 | 0.11 | |
V10 | 26.2 | 38.9 | 32.7 | 3.0 | 0.09 | |
V11 | 32.9 | 47.9 | 42.2 | 3.8 | 0.09 | |
V12 | 26.5 | 49.7 | 40.0 | 5.7 | 0.14 | |
V13 | 33.2 | 60.2 | 48.5 | 6.4 | 0.13 | |
V14 | 37.5 | 55.7 | 48.8 | 4.9 | 0.10 |
Vehicle Type | 2 Axles | 3 Axles | 4 Axles | 5 Axles or More | |
---|---|---|---|---|---|
Lanes | |||||
2-way 4-lane | 70 | 100 | 100 | 100 | |
2-way 6-lane | 40 | 50 | 70 | 70 | |
2-way 8-lane | 25 | 45 | 60 | 65 |
Vehicle Type | Equivalent Axle Load (t) | Equivalent | ADTF | |||||
---|---|---|---|---|---|---|---|---|
1st Axle | 2nd Axle | 3rd Axle | 4th Axle | 5th axle | 6th Axle | GVW | ||
V3 | 2.4 | 4.1 | 6.4 | 35 | ||||
V4 | 2.7 | 4.5 | 7.2 | 147 | ||||
V5 | 6.4 | 10.9 | 17.3 | 223 | ||||
V6 | 5.3 | 11.8 | 17.1 | 221 | ||||
V7 | 4.8 | 4.8 | 15.2 | 24.7 | 227 | |||
V8 | 6.5 | 10.6 | 10.6 | 27.8 | 51 | |||
V9 | 5.7 | 6.1 | 12.3 | 12.3 | 36.4 | 435 | ||
V10 | 4.7 | 11.6 | 10.1 | 10.1 | 36.4 | 83 | ||
V11 | 5.6 | 14.2 | 8.7 | 8.7 | 8.7 | 45.9 | 315 | |
V12 | 5.6 | 8.8 | 8.8 | 12.9 | 12.9 | 48.9 | 14 | |
V13 | 4.7 | 4.8 | 14.9 | 9.9 | 9.9 | 9.9 | 54.2 | 1366 |
V14 | 5.5 | 9.8 | 9.8 | 9.6 | 9.6 | 9.6 | 53.9 | 1376 |
Location Number | Locations | Notes |
---|---|---|
21 | Xinyihe bridge, Jiangsu province | Large bridge |
22 | Inner Mongolia section of G6 Expressway | Main channel for coal transportation |
23 | Jiujiang Yangtze River Bridge, on the boundary between Jiangxi Province and Hubei Province | Large bridge |
24 | Zhejiang province | Port highway |
25 | Pingsheng Bridge, Guangdong province | Large bridge |
26 | Guangxi province | Highway toll station |
27 | Guizhou province | Highway toll station |
28 | Humen Bridge, Guangdong province | Large bridge |
Vehicle Type | Axle- Number | Representative EC Values | ADTF | EADTF | ||||
---|---|---|---|---|---|---|---|---|
5 m Below | 5 to 30 m | 30 m Above | 5 m Below | 5 to 30 m | 30 m Above | |||
V3 | 2 | 0.026 | 0.012 | 0.003 | 35 | 1 | 0 | 0 |
V4 | 2 | 0.034 | 0.017 | 0.005 | 147 | 5 | 2 | 1 |
V5 | 2 | 0.447 | 0.131 | 0.066 | 223 | 100 | 29 | 15 |
V6 | 2 | 0.514 | 0.202 | 0.074 | 221 | 114 | 45 | 16 |
V7 | 3 | 1.063 | 0.388 | 0.185 | 227 | 241 | 88 | 42 |
V8 | 3 | 0.781 | 0.817 | 0.31 | 51 | 40 | 42 | 16 |
V9 | 4 | 1.258 | 1.279 | 0.618 | 435 | 547 | 556 | 269 |
V10 | 4 | 0.907 | 0.7 | 0.41 | 83 | 75 | 58 | 34 |
V11 | 5 | 1.122 | 1.153 | 0.846 | 315 | 353 | 363 | 266 |
V12 | 5 | 1.459 | 1.211 | 1.04 | 14 | 20 | 17 | 15 |
V13 | 6 | 1.495 | 2.084 | 1.339 | 1366 | 2042 | 2847 | 1829 |
V14 | 6 | 1.725 | 2.53 | 1.23 | 1376 | 2374 | 3481 | 1692 |
Number of Axles | Length of Influence Line | ||
---|---|---|---|
5 m Below | 5 to 30 m | 30 m Above | |
2 | |||
3 | |||
4 | |||
5 | |||
6 (or more) |
Design Frequency of the Standard Vehicle | Cumulative Frequency | Length of Influence Line | ||
---|---|---|---|---|
5 m Below | 5–30 m | 30 m Above | ||
Level 1 | 50% | 100 | 130 | 80 |
Level 2 | 70% | 140 | 180 | 110 |
Level 3 | 90% | 230 | 265 | 155 |
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Fu, H.; Zhou, X.; Zhou, Q.; Xiang, P.; Zhou, Z.; Fu, Q. An Improved Model for Design Fatigue Load of Highway Bridges Considering Damage Equivalence. Buildings 2022, 12, 217. https://doi.org/10.3390/buildings12020217
Fu H, Zhou X, Zhou Q, Xiang P, Zhou Z, Fu Q. An Improved Model for Design Fatigue Load of Highway Bridges Considering Damage Equivalence. Buildings. 2022; 12(2):217. https://doi.org/10.3390/buildings12020217
Chicago/Turabian StyleFu, Huawei, Xuhong Zhou, Qishi Zhou, Ping Xiang, Zhibin Zhou, and Qiang Fu. 2022. "An Improved Model for Design Fatigue Load of Highway Bridges Considering Damage Equivalence" Buildings 12, no. 2: 217. https://doi.org/10.3390/buildings12020217