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The fatigue performance of the bridge deck significantly affects the safety and durability of the overall steel-concrete composite beam bridge. Based on the vehicle flow information of the highway within 10 years, the fatigue performance of a two-way four-lane steel-concrete composite continuous beam bridge deck is studied in this research. The results indicate that the effect of the wheel track position is negligible for two-way four-lane bridge when the wheel track sways laterally, and the fatigue stress of bridge deck concrete is the most unfavorable while the loading position is 7.0 m away from the bridge center line. The fatigue damage decreases by 30%–40% when the centerline of the lane deviates from the most unfavorable stress position by 1 m. The punching fatigue of the concrete is more sensitive to the changes in slab thickness, and the thickness of the deck concrete slab is recommended to be ≥35 cm.

Compared with concrete bridges, steel-concrete composite structure bridges have the advantages of a lower self-weight and a larger span; compared with steel bridges, they have the advantages of less steel consumption, better structural stability, higher bending rigidity, and higher ductility [

According to the existing research results, there is no relatively mature crack calculation theory for composite beams, and the test data about cracks of composite beams are also limited [

In current research, structural fatigue assessment methods are mainly divided into two categories. The first category is assessment methods that do not calculate fatigue damage [

The second type of the assessment method is the one that requires calculating the degree of fatigue damage [

The bridge deck directly bears vehicle loads; thus, its design affects the safety and durability of the overall bridge structure [

At present, research on the effect of the wheel position on the fatigue performance of bridge decks mainly focuses on steel decks [

Previous studies indicated that the reinforcement ratio of the bridge deck significantly affects the fatigue of the bridge deck [

Thus, in the present study, the fatigue performance of the deck of the Dazhenggang steel-concrete composite continuous beam bridge on the Shanghai-Hangzhou Expressway was investigated. First, the fatigue assessment process of the bridge deck was determined. Second, a finite-element analysis model was established, and the fatigue evaluation parameters of the bridge deck were determined according to traffic flow data of the expressway for 10 years. Finally, the effects of the wheel transverse position, steel and concrete damage, lane location, deck reinforcement ratio, and deck thickness on the fatigue performance of steelconcrete composite beams were analyzed.

Various fatigue assessment methods are also applicable to punching fatigue of bridge decks [

Fatigue damage assessment procedure for the bridge deck.

As shown in Figure

Location of Dazhenggang Bridge.

The Dazhenggang steel-concrete composite beam bridge (2 × 75 m) of the Shanghai-Hangzhou Expressway is located between the Songjiang and Dayun toll stations. A total of 163,369,169 passenger cars and 65,998,076 trucks passed the Dayun toll station of the Shanghai-Hangzhou Expressway in the 10-year study period. To facilitate the calculation and analysis, the vehicles are classified, as shown in Table

Vehicle type classification.

Vehicle classification | Model sketch | Vehicle type description | |
---|---|---|---|

Model 1 | Two-axle vehicle weighing <3 tons | ||

Model 2 | Two-axle vehicle weighing >3 tons | ||

Model 3 | Single axle and two wheels + single axle and two wheels + single axle and four wheels | ||

Model 4 | Single axle and two wheels + single axle and two wheels + two axles and four wheels | ||

Model 5 | Single axle and double wheel + double axle and four wheels + double axle and four wheels | ||

Model 6 | Single axle and double wheel + double axle and four wheel + three axle and four wheels |

Proportions of different vehicle models.

The bridge deck slab not only bears the local action of the vehicle but also participates in the force of the whole part as part of the composite beam. It is difficult to consider the effect of transverse beam on the supporting stiffness and shear lag of bridge deck when the simplified model is adopted, so it is impossible to accurately simulate the coupling effect of the first and second system models. The spatial finite-element model can reflect the actual stress state of the bridge [

The spatial force characteristics of the structure cannot be reflected accurately through the simplified method of effective distribution width [

Finite-element model.

According to a traffic investigation and statistical analysis of Jiangyin Bridge over the Yangtze River, the Third Bridge of the Nanjing Yangtse River, Humen Bridge, and the Second Nanjing Yangtze Bridge, the fatigue design loads were determined, as shown in Figure

Fatigue design load model. Note:

To better reflect the characteristics of the vehicle load on the Shanghai-Hangzhou Expressway, the traffic load of the Dazhenggang continuous composite beam bridge was converted into the fatigue design load, as shown in Figure

Let _{ti} represent the proportions of different vehicle types, and _{di} represent the probability of the axle load distribution.

According to the vehicle weight statistics for 474,660 vehicles that traveled on Jiangyin Bridge over the Yangtze River, the distribution and statistical characteristics of the vehicle weight for different vehicle types are presented in Figure

Weight distribution of vehicles that traveled on Jiangyin Bridge over Yangtze River.

Statistical characteristics of the vehicle weight.

Vehicle type | Average vehicle weight (tons) | Variance of vehicle weight (tons) |
---|---|---|

Two-axle vehicle | 8.89 | 4.92 |

Three-axle vehicle | 21.54 | 6.93 |

Four-axle vehicle | 32.25 | 8.85 |

Five-axle vehicle | 39.87 | 10.42 |

Six-axle vehicle | 38.71 | 12.87 |

Equivalent number of vehicles corresponding to fatigue design load for different vehicle types.

Vehicle weight | Vehicle type 2 | Vehicle type 3 | Vehicle type 4 | Vehicle type 5 | Vehicle type 6 |
---|---|---|---|---|---|

0–5 | 0.001 | 0.000 | 0.000 | 0.000 | 0.000 |

5–10 | 0.004 | 0.001 | 0.000 | 0.000 | 0.000 |

10–15 | 0.009 | 0.010 | 0.004 | 0.001 | 0.000 |

15–20 | 0.017 | 0.025 | 0.012 | 0.012 | 0.017 |

20–25 | 0.008 | 0.072 | 0.023 | 0.013 | 0.036 |

25–30 | 0.001 | 0.155 | 0.054 | 0.024 | 0.059 |

30–35 | 0.000 | 0.092 | 0.158 | 0.056 | 0.046 |

35–40 | 0.000 | 0.013 | 0.454 | 0.144 | 0.086 |

40–45 | 0.000 | 0.001 | 0.389 | 0.491 | 0.217 |

45–50 | 0.000 | 0.000 | 0.057 | 0.941 | 0.615 |

50–55 | 0.000 | 0.000 | 0.004 | 0.393 | 0.766 |

55–60 | 0.000 | 0.000 | 0.000 | 0.046 | 0.238 |

60–65 | 0.000 | 0.000 | 0.000 | 0.003 | 0.048 |

65–70 | 0.000 | 0.000 | 0.000 | 0.002 | 0.036 |

70–75 | 0.000 | 0.000 | 0.000 | 0.004 | 0.008 |

Number of vehicles with equivalent fatigue | 0.038 | 0.369 | 1.156 | 2.131 | 2.173 |

In this study, the distribution of vehicle types passing through the Dayun toll station is used to approximately replace the distribution of vehicle types passing through the Dazhenggang composite girder bridge in the Shanghai-Hangzhou Expressway. The vehicle distribution is as follows: Model 1, 78.1%; Model 2, 9.8%; Model 3, 2.5%; Model 4, 1.1%; Model 5, 6.4%; Model 6, 2.1%; and vehicles weighing >3 tons, 21.9%. Neglecting the effects of vehicles weighing <3 tons on the bridge fatigue, the equivalent vehicle conversion coefficient of the fatigue design load for vehicles weighing >3 tons can be obtained as follows:

For developing the axle load spectrum model, Jiangyin Bridge over Yangtze River, the Third Bridge of Nanjing Yangtse River, Humen Bridge, and the Second Nanjing Yangtze Bridge were taken as the research objects. The vehicle flow, vehicle axle load, wheelbase, and lane flow distribution were investigated and statistically analyzed. The axle load spectra for various vehicles (single axle and double wheel, single axle four-wheel, double axle, and triple-axle) were obtained, as shown in Figures

Single-axle and double-wheel load spectrum.

Single-axle four-wheel load spectrum.

Double-axle load spectrum.

Triple-axle load spectrum.

The total axle load spectrum for all types of axles obtained from the statistical data is shown in Figure

Total axle load spectrum.

In this study, single-axle double-wheel, single axle four-wheel, double-axle, and three-axle units were converted to equivalent single-axle units according to the axle load. Models 1 and 2 are two-axle vehicles, while models 3–6 can be regarded as three-axle vehicles. According to the vehicle survey of the Dazhenggang Bridge, the number of axles (as shown in Table

Annual traffic volume and axle number for Dazhenggang Bridge.

Years | Annual traffic volume | Number of axles | Remarks |
---|---|---|---|

2010 | 25,710,725 | 57,052,099 | |

2020 | 43,460,505 | 96,438,861 | |

2030 | 61,210,285 | 136,000,000 | Forecast |

The fatigue failure of the RC bridge deck is mainly caused by the direct action of the wheels, and the stresses of the bridge deck at different transverse positions under the wheel load are not identical. To determine the most unfavorable position of the bridge deck, unit loads were arranged as close to each other as possible along the transverse direction of the bridge. The loading area was selected according to the provisions of the “General Design Specification for Highway Bridges” (JTGD60-015). A concentrated load of 100 kN was applied, and the spacing was 0.5 m along the transverse direction of the bridge. The stress of the concrete slab under the wheel load was calculated under loading, and the accuracy was sufficient to satisfy the calculation requirements. The transverse load distribution is shown in Figure

Transverse load distribution.

The bridge deck at the top of the bearing in the negative-bending moment area was selected as the research object, as shown in Figure

Checking the calculation position of the bridge deck in the negative-bending moment area.

Vehicles do not drive exactly along the track line. Additionally, the distribution of the wheel track line along the transverse direction varies significantly among different countries; thus, it cannot be simply applied [

Lateral loading position of the wheel.

Lateral distribution frequency of vehicles.

Effect of the wheel transverse position on the stress amplitude of the bridge deck.

The influence lines of different positions of the wheels, i.e., the influence surface of the bending moment of the concrete slab, were used for calculation. To compare the effects of various wheel lateral distribution models on the roof stress amplitude, we refer to the calculation method for the equivalent stress amplitude [^{th} wheel path (Figure ^{th} wheel path (Figure

To better understand the differences between various wheel lateral distribution models and determine whether the effect of the bridge deck pavement on the lateral distribution effect of the wheels should be considered, the ratio of the equivalent stress amplitude calculated using the lateral distribution of the wheels to that calculated using the most unfavorable loading position was examined, as shown in Table

Equivalent stress-amplitude ratio.

Equivalent stress-amplitude ratio | |
---|---|

Midspan | 0.913 |

Beam | 0.907 |

The traffic volume used for the fatigue checking of the reinforcing bars was the predicted traffic volume in Table

The fatigue life of the bridge-deck reinforcement at different locations is presented in Table

Fatigue life of reinforcement bars.

Check position of reinforcement | Distance between loading position and bridge centerline (m) | Fatigue life | |
---|---|---|---|

ECCS100 [ | BS5400 [ | ||

Midspan | 1.0 | >100 | >100 |

Beam | >100 | >100 | |

Midspan | 7.0 | 15 | 7 |

Beam | >100 | 44 |

For checking the punching fatigue of the concrete, the axle load spectrum used was the number of axle loads converted from the traffic volume predicted in Table

Here,

According to the S-N curve of formula (

The fatigue life of the bridge-deck concrete at different locations is presented in Table

Fatigue life of the bridge-deck concrete.

Checking calculation position of bridge-deck concrete | Distance between loading position and bridge centerline (m) | Fatigue life |
---|---|---|

Midspan | 1.0 | >100 |

Beam | >100 | |

Midspan | 7.0 | 37 |

Beam | >100 |

According to the analysis presented in Section

Transverse distribution frequency of wheels for different lane arrangements. (a) The distance between the left tire and lane one is 0.96 m; (b) the distance between the left tire and lane two is 0.96 m; (c) the distances between the left tire and the center line of bridge structure, the left tire and lane two both are 0.96 m.

The wheel positions and wheel distribution ranges for various working conditions are presented in Table

Distribution ranges of lanes and wheels under various working conditions.

Distance from bridge centerline (m) | |||
---|---|---|---|

Working condition 1 | Working condition 2 | Working condition 3 | |

Lane 1 | 0.5∼4.25 | 1.5∼5.25 | −0.5∼3.25 |

Lane 1, left wheel | 0.725∼2.225 | 1.725∼3.225 | −0.275∼1.225 |

Lane 1, right wheel | 2.525∼4.025 | 3.525∼5.025 | 1.525∼3.025 |

Lane 2 | 4.25∼8.0 | 5.25∼9.0 | 3.25∼7.0 |

Lane 2, left wheel | 4.475∼5.975 | 5.475∼6.975 | 3.475∼4.975 |

Lane 2, right wheel | 6.275∼7.775 | 7.275∼8.775 | 5.275∼6.775 |

According to the analysis presented in Section

Distance between the maximum frequency position of wheel and the centerline of the bridge under various working conditions.

Distance between maximum frequency of wheel and center line of bridge (m) | |||
---|---|---|---|

Working condition 1 | Working condition 2 | Working condition 3 | |

Lane 2, right wheel | 6.875∼7.175 | 7.875∼8.175 | 5.875∼6.175 |

The fatigue damage at the most unfavorable transverse position of the bridge deck, that is, 7.0 m from the centerline of the bridge, and that at the highest frequency of wheels were compared. The results are presented in Table

Damage degrees under various working conditions.

Year | On the beam 7.0 m from the centerline of the bridge | On the beam with the highest wheel frequency | ||||

Cumulative damage degree | Cumulative damage degree | |||||

Working condition 1 | Working condition 2 | Working condition 3 | Working condition 1 | Working condition 2 | Working condition 3 | |

2010 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 |

2020 | 0.16 | 0.09 | 0.10 | 0.16 | 0.09 | 0.11 |

2030 | 0.39 | 0.22 | 0.24 | 0.39 | 0.22 | 0.26 |

2040 | 0.65 | 0.37 | 0.40 | 0.65 | 0.37 | 0.43 |

2050 | 0.92 | 0.52 | 0.57 | 0.92 | 0.52 | 0.60 |

2060 | 1.18 | 0.66 | 0.73 | 1.18 | 0.67 | 0.78 |

2110 | 2.49 | 1.40 | 1.54 | 2.49 | 1.42 | 1.64 |

Year | Midspan of 7.0 m from the centerline of the bridge | Midspan at the highest wheel frequency | ||||

Cumulative damage degree | Cumulative damage degree | |||||

Working condition 1 | Working condition 2 | Working condition 3 | Working condition 1 | Working condition 2 | Working condition 3 | |

2010 | 0.11 | 0.06 | 0.07 | 0.11 | 0.07 | 0.06 |

2020 | 1.57 | 0.89 | 0.97 | 1.57 | 1.11 | 0.94 |

2030 | 3.77 | 2.13 | 2.33 | 3.77 | 2.66 | 2.26 |

2040 | 6.29 | 3.55 | 3.89 | 6.29 | 4.44 | 3.77 |

2050 | 8.82 | 4.98 | 5.45 | 8.82 | 6.22 | 5.28 |

2060 | 11.34 | 6.40 | 7.01 | 11.34 | 8.00 | 6.80 |

2110 | 23.97 | 13.53 | 14.81 | 23.97 | 16.91 | 14.36 |

In working condition 1, the fatigue damage was high owing to the overlap of the lane centerline and the most disadvantageous position of the deck. However, in working conditions 2 and 3, the probability of driving in the most unfavorable position was reduced because the distance between the centerline of the lane and the most unfavorable position of the deck under stress was approximately 1.0 m, which significantly reduced the fatigue damage of the reinforcement. At the position 7.0 m from the centerline of the bridge, the damage degrees of conditions 2 and 3 were 56.2% and 61.8% of that of condition 1, respectively. The amount of damage at the most disadvantageous position under the static stress of the bridge deck was smaller than the amount of fatigue damage at the highest wheel frequency. Therefore, if the influence of lane position on fatigue is considered, the service life of bridge deck can be significantly improved.

The tensile fatigue of the steel bar in the deck and the punching fatigue of the concrete are significantly affected by the thickness of the deck and reinforcement ratio of the steel bar [

Selected calculation parameters.

Reinforcement ratio (%) | 1.76, 2.50, 3 |
---|---|

Slab thickness (cm) | 25, 30, 35 |

As shown in Figures

Fatigue damage of bridge-deck reinforcement under three reinforcement ratios with a slab thickness of 25 cm.

Fatigue damage of bridge-deck reinforcement under three reinforcement ratios with a slab thickness of 30 cm.

Fatigue damage of bridge-deck reinforcement under three reinforcement ratios with a slab thickness of 35 cm.

Reinforcement life of the deck under different slab thicknesses and reinforcement ratios.

Slab thickness (cm) | Reinforcement ratio (%) | Life (years) |
---|---|---|

25 | 1.76 | 3 |

2.5 | 10 | |

3 | 28 | |

30 | 1.76 | 7 |

2.5 | 33 | |

3 | 52 | |

35 | 1.76 | 25 |

2.5 | 59 | |

3 | 101 |

The relationships between the punching fatigue life of the bridge deck and the reinforcement ratio and slab thickness are presented in Table

Punching fatigue life of the bridge-deck concrete under different slab thicknesses and reinforcement ratios.

Slab thickness (cm) | Reinforcement ratio (%) | Life (years) |
---|---|---|

25 | 1.76 | 5 |

2.5 | 18 | |

3.0 | 34 | |

30 | 1.76 | 37 |

2.5 | >100 | |

3.0 | >100 | |

35 | 1.76 | >100 |

2.5 | >100 | |

3.0 | >100 |

In conclusion, when the slab thickness of the bridge deck is <30 cm, the effects of increasing the reinforcement ratio on the fatigue life of the bridge-deck reinforcement and the punching shear fatigue life of the concrete are not obvious, and the increase in fatigue life is negligible in comparison with the 100-year design life of the bridge. For a 35 cm thick bridge deck, even a reinforcement ratio of 1.76% will not cause fatigue damage. Therefore, the concrete slab thickness of the bridge deck is recommended to be ≥35 cm, which complies with the strict requirement for the thickness of the concrete bridge deck in the Japanese Road specification [

According to a load investigation, a fatigue assessment method for a composite beam bridge deck was proposed, and the fatigue damage and life for steel bar tension fatigue and concrete punching shear fatigue of a composite beam RC bridge deck were calculated. The following conclusions are drawn:

When the centerline of the wheel track swings laterally on the same lane for approximately 1.5 m, it has little influence on the force of the deck. The effect of the wheel track position can be ignored in the fatigue checking of the deck.

For the deck of the steel-concrete composite beam, the fatigue properties of the steel bar and concrete in the deck depend significantly on the transverse loading position. The fatigue life of the deck at different positions is >100 years when the loading position is 1.0 m from the centerline of the bridge. The fatigue life of the concrete across the middle span is only 37 years when the loading position is 7.0 m from the centerline of the bridge. Therefore, the fatigue stress of the concrete on the bridge deck is the most disadvantageous when the loading position is 7.0 m from the centerline of the bridge.

The lane arrangement significantly affects the fatigue damage of the bridge deck; thus, the overlap of the lane centerline and the most unfavorable stress position should be avoided to the greatest extent possible. The fatigue damage is reduced by 30%–40% when the centerline of the lane deviates from the most unfavorable stress position by 1 m.

The reinforcement ratio and thickness of the deck have similar effects on the fatigue life of deck reinforcement, and the punching fatigue of the concrete is more sensitive to changes in the thickness of the deck. When the deck thickness is <30 cm, the effects of increasing the reinforcement ratio on the fatigue life of the deck reinforcement and the punching fatigue life of the concrete are not obvious, and the increase in fatigue life is negligible in comparison with the 100-year design life of the bridge. For 35 cm thick decks, even a reinforcement ratio of 1.76% will not cause fatigue damage. The thickness of the concrete slab of the bridge deck is recommended to be ≥35 cm.

The data used to support the findings of this study are not available.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (no. 51878623), Innovative Research Team (in Science and Technology) in University of Henan Province (no. 20IRTSTHN009), Program for Young Backbone Teachers in Colleges and Universities in Henan (no. 2018GGJS005), and Foundation for Postdoctoral Students in Henan Province (no. 1901024).

^{th}Edition, 2007