Load Test and Fatigue Life Evaluation for Welded Details in Taizhou Yangtze River Bridge

To study the fatigue performance of welded details in the orthotropic steel decks, the steel box girder for Taizhou Yangtze River Bridge is taken as the research object. Based on the field monitoring data obtained from the load test, the stress response test of the orthotropic steel box girder under wheel loads is performed and the correctness of the vehicle test data obtained from the field monitoring data also have been verified by the numerical results of the finite element model. Based on the Miner linear cumulative damage theory, the S-N curve of the Eurocode3 specification is referenced, and the fatigue life calculation formula of the welded details is determined according to the actual structural features. The fatigue life evaluation of the four typical welded details is obtained. The results indicate that: The load test data is compared and verified by the numerical result of finite element model. The local effect of stress distribution is remarkable. The stress measurement points on the four typical welded details are mainly based on low amplitude stress cycles. Most of the stress ranges are 2-10 MPa, among which the stress range of the welded details at the U-rib butt joint is larger. The fatigue life of welded details in the 14 mm thick top plate is smaller than that of the 16 mm thick top plate corresponding to the fatigue life of the welded details. The rib-to-rib butt welded joints and the openings of the diaphragms were prone to fatigue failure. Among them, the welding details of the 14 mm thick U-rib butt joints first appeared fatigue failure. The arrangement of the diaphragm can effectively increase the fatigue life of the top-U rib weld and improve the fatigue performance at this detail.


Introduction
The orthotropic steel box girders as the main structure of the stiffening girder have been widely used for long span suspension highway bridges due to their overall light weight, convenient construction and high bearing capacity [Fisher and Roy (2011)]. A typical modern orthotropic deck usually consists of a thin steel deck plate stiffened by longitudinal ribs and transverse diaphragms. Closed longitudinal ribs are prevalently used for lighter weight, fewer welds and higher torsional and flexural stiffness [Kozy and the number of stress cycles of the two types of welded details is linearly related to the vehicle flow and not to the ambient temperature. Deng et al. [Deng, Ding and Li (2013)] took long-term strain monitoring data of Runyang Bridge steel box girder as the research object, and studied the massive strain monitoring data analysis and fatigue assessment methods. Research suggested that the average strain caused by the temperature variation of the welded details is very small. Therefore, fatigue assessment of welded details can be made without considering the effects of temperature changes. Many weld joints in orthotropic deck are fatigue-sensitive parts. Many investigations and studies have shown that the following parts of the fatigue disease accounts for more than 90% of the total diseases, which is the fatigue vulnerable parts of the steel box orthotropic steel bridge deck [Gurney (2006); Song, Ding, Wang et al. (2013); Deng, Ding and Li (2013)]: ① U-rib ribbed slot; ② Diaphragm and U-rib welds; ③ Steel box girder deck and U-rib; ④ U-rib butt joint. At present, the fatigue life of the above four types of key weld details is less studied based on the real-bridge load test. In order to improve the anti-fatigue design of steel box orthotropic steel bridge decks, this article focuses on t the above 4 key welds of Taizhou Yangtze River Bridge, and evaluates the fatigue performance of each welded detail under 14 mm and 16 mm thick decks combined with the load test of Taizhou Yangtze River Bridge.

Fatigue stress monitoring of Taizhou Yangtze River Bridge under vehicle loads 2.1 Engineering background
The profile of Taizhou Yangtze River Bridge is shown in Fig. 1. Taizhou Yangtze River Bridge lies between Taizhou, Zhenjiang and Changzhou City in Jiangsu Province. The total length of Taizhou Bridge is 62.088 km. The whole line is designed by freeway codes with six lanes in two directions. The main bridge crossing the Yangtze River is a continuous three-pylon two-span suspension bridge with the main span of 1080 m. It is open to traffic in 2012.

Figure1: Profile of Taizhou Yangtze River Bridge (dimensions in m)
The typical box-girder segment of Taizhou Yangtze River Bridge is shown in Fig. 2. The girder, including wind fairing, is 39.1 mm×3.5 mm, the roof width is 36.7 m, the floor width is 21.25 m, the transverse spacing of straight webs is 33.2 m, the spacing of transverse diaphragm is 3.2 m, and the spacing of U-ribs is 600 mm. The outside of the middle lane roof within the range of 6 m is 16 mm thick, and the U-rib is 8 mm thick, the remaining area roof is 14 mm thick, and the U-rib is 6 mm thick. The main structure of the box girder is made from Q345-D steel. The main parameters are roof thickness (td), U-rib thickness (t), U-rib height (H) and U-rib opening size (a), respectively. The values of the parameters are as following: On the ordinary lane, td1=14 mm, t1=6 mm, H1=280 mm, a1=300 mm. On the heavy truck lane, td2=16 mm, t2=8 mm, H2=280 mm, a2=300.2 mm.

Fatigue stress monitoring
According to the load test of Taizhou Yangtze River Bridge, the stress distribution test and stress response test of welded details in the steel box girder were performed. The Five test sections in the N26 hosting girder section (two standard box-girder sections) near the L/4 side was selected in this load test. The strain monitoring was performed on the welding details of the rib-to-deck plate, U-rib butt joint, deck plate-to-rib-todiaphragm and diaphragm plate opening. Because of the different thicknesses of the deck and U-rib, the fatigue properties of the welded details in different deck thicknesses were compared and studied. The measurement points were symmetrically arranged on the 14 mm and 16 mm thick deck. Among them, the top plate-to-rib welded detail was arranged with one-way and two-way strain gages to monitor strains of the top plate-to-rib in both transverse and longitudinal directions. One-way strain gauges in longitudinal direction were arranged on U-rib butt joint. Due to the complicated stress distribution of the welding details at the diaphragm, in the position of the diaphragm, strain flowers were arranged on the diaphragm, and two kinds of strain gauges are arranged on the top plate, one-way and two-way. The location and number of the girder sections and measuring points in the steel box girder were located are shown in Fig. 3 ("S" represents Section, "L" represents Location). The details of the location of the measuring points were shown in Tab. 1. In Fig. 3 and Tab. 1, 1-1/1-2 show that the strain gauge is bidirectional point, along the bridge of 1-1, 1-2 for the transverse direction; 3-9/3-10/3-11 indicates that this position is a strained flower, and the cross-bridge strain is measured from 3-9, the oblique 45-degree strain can be obtained from 3-10, and the vertical-bridge strain from 3-11.  , vol.13, no.2, pp.205-225, 2019   . The structure size in the finite element model is consistent with the real bridge. Because of the thin wall structure of the flat steel box girder, a four-node plate/shell element in the ANSYS cell library called the shell63 with each node having six degrees of freedom is used in the finite element model. To accurately reflect the structural deformation, stress conditions and detailed effects (e.g., top plate longitudinal ribbed stiffener) in the temperature loads, such a structure is detailed and discretized according to the actual composition of the top plates, sloping webs, transverse diaphragms and U-ribs of the steel box girder. The plate/shell element thickness of each site is the actual thickness of the steel plate at such a site. Steel has a thermal expansion coefficient of 1.2×10 -5 W m -2 o C -1 , elasticity modulus of 2.1×10 -5 MPa and Poisson's ratio (v) of 0.3. The constraints along the bridge of the finite element model are applied to the cross section of the girder both ends to meet the actual boundary conditions. The finite element model of the box-girder is shown in Fig. 6.

Stress analysis of welded details under a vehicle test
There are many measuring points in this test. The same test item will have different sections for comparison, and the same law is obtained in the analysis. In order to save space, this article lists two typical measuring points. The stress distribution of measuring points 2-3 (Deck plate-to-rib welded detail) can be seen in Fig. 8. The stress distribution of measuring points 4-2 (U-rib butt joint) can be seen in Fig. 9. It can be seen from Fig. 8 that: In loading case 3, the wheel load center coincides with the measuring point 2-3; and the stress response at point 2-3 is the most obvious. In loading cases 2 and 4, the wheel center is closer to point 2-3. The stress response trend of the measuring point in loading cases 2 and 4 are relatively close with that in loading case 3. But the stress in loading cases 2 and 4 is smaller than that in loading case 3. In loading cases 1 and 5, the center of the wheel is far from the measuring point; and the stress response is smallest and the trend is not obvious. The local effect of the top deck plate stress distribution is remarkable under the wheel loads. The length of lateral stress lines of the top deck plate is short. The stress distribution of the top deck plate is affected by the longitudinal ribs. It is found from Fig. 9 that the stress distribution characteristics of U-rib butt joint is the same as that of the deck plate-to-rib welded detail under the wheel loads. The stress response of the longitudinal rib has strong local characteristics. The length of the lateral stress influence line is shorter. The stress distribution of U-rib butt joint is affected by the longitudinal ribs. Comparison of stress values at points 2-3 and 4-2 by FEM analysis and those recorded in the load test，as shown in Fig. 10. It can be seen that: The trend of the stress response curve measured by the real bridge test is consistent with the FEM results. The measured data is reliable. The local effect of stress distribution is remarkable. (2)

Stress(MPa)
In the formula: D is the total fatigue damage, L is the structural fatigue life, i n is the number of cycles generated by the variable amplitude stress cycle i S , i N is the fatigue life corresponding to stress cycle i S in constant N S − , i is the number of stress amplitude levels. Miner's linear cumulative damage criterion assumes that at 1 ≥ D , fatigue failure.

The S-N curve of Eurocode3
According to the S-N curve, the fatigue life of the material can be determined. For variable amplitude fatigue, when all stress cycles are greater than the constant fatigue limit CAFL (Constant Amplitude Fatigue Limit), the fatigue life of the structure can be accurately calculated according to the Miner criterion and the S-N curve; when the stress cycle number is smaller than CAFL, the structural life is considered to be infinite and the effect of the low stress cycle is not considered. However, there are generally both high stress cycles larger than CAFL and low stress cycles smaller than CAFL in bridges. In order to accurately calculate the fatigue life of the structure, the fatigue damage caused by the low stress cycle should be properly dealt with in the fatigue strength curve. In the S-N curve of Eurocode3 [EC3 (2004)], not only the stress state of the welded details in the orthotropic steel bridge deck is considered, but also the low-level stress cycle that is less than the constant fatigue limit CAFL is considered. In addition, for the classification of fatigue details, British BS5400 specification and China TB99 have not given specific classification of welded details in orthotropic steel decks. The detailed classification in the American specification is not comprehensive. The classification of welded details for closed orthotropic steel decks are given in detail in the Eurocode3 specification. The N S − curve in Eurocode3 specification is shown in Fig. 11 Here: R ∆σ is the stress range of welded details. R N is the fatigue life. D ∆σ is the constant amplitude fatigue limit for each welded detail. When the stress range S is greater than D ∆σ , the fatigue strength coefficient is KC. When the stress range S is less than D ∆σ , the fatigue strength coefficient is KD . In addition, the specification also determines the stress cutoff limit when the number of cycles is 10 8 : , it is assumed that the stress cycle does not cause fatigue damage. Therefore, L ∆σ can also be regarded as the variable amplitude fatigue limit (VAFL) [Deng, Li and Ding (2014)]. The classification of welded details can be obtained From Eurocode3 Part1-9. According to formula (5) and formula (6), each fatigue strength curve parameter of welded details can be calculated, as shown in Tab. 2.

Fatigue cumulative damage calculation method
The fatigue failure of the structure is mainly manifested as crack propagation. In the detailed weld, there are inevitably small cracks or defects. Under the repeated action of the high stress cycle, cracks will be generated and continue to expand. The low stress cycle before the cracks can be neglected, but after cracks appear, low stress cycles promote crack propagation and cause damage. Therefore, it is unreasonable to ignore the effect of low stress range when calculating the detail fatigue life. When the high stress range is present, the so-called "fatigue threshold" concept [Chan, Li and Ko (2001)] is not fully applicable and all stress cycles should be considered. In order to obtain accurate welding details of fatigue life, this paper takes into account the fatigue damage caused by the stress cycle below the cutoff limit

Test results
For the measured strain-time curve by the test, the fatigue stress spectrum of each measuring point is obtained through the simplified rain flow counting method [AASHTO LRFD (2005)], and the numbers of stress ranges cycles at each level is obtained. Sections 3 and 4 include the typical details. Due to space limitations, only the stress spectra and stress cycle numbers for each of Sections 3 and 4 are given. Fig. 12 shows the stress spectra at each measuring point of Section 3. Cross section 3 is at the position of the diaphragm. Mainly measured stresses of deck-to-rib welds, U rib butt joint, U-rib-to-diaphragm welds, and the diaphragm openings. In Figs It can be seen from Figs. 12 and 13 that there are many stress cycles with very small stress ranges, which basically reach 10 4 orders of magnitude. The number of stress cycles at each measurement point is concentrated in the range of 0 to 1 MPa. Since a large number of small stresses contain a large number of random disturbance signals, the fatigue stress range of 0 to 1 MPa can be directly ignored in the fatigue damage calculation of each weld. At the same time, studies have shown [Deng, Ding and Li (2013)] that discarding a stress cycle of less than 2 MPa has little effect on the calculation of fatigue life. Therefore, only the stress range greater than or equal to 2 MPa is considered in the fatigue life calculation in this paper.
Tab. 3 lists the number of stress cycles corresponding to the different stress ranges of Sections 3 and 4 measured by the rain-flow counting method. The numbers of cycles of the stress range of the weld from the position of each section measuring point can be found: ① On Section 3, the stress ranges of the deck plate-to-rib welds are mainly distributed in the range of 2 to 10 MPa, indicating that the deck plateto-rib welds in Sections 3 at most experience low-amplitude stress cycles. ② On Section 4, the stress range of U-rib butt joint is larger and is distributed in the range of 2 to 46 MPa. Tab. 3, Tab. 4 and Tab. 5 list the stress cycle numbers corresponding to the different stress ranges of Sections 1-5 measured by the rain-flow counting method. The cycle numbers of the stress ranges of the weld from the position of each section measuring point can be found: ① The stress ranges of the deck plate-to-rib welds are mainly distributed in the range of 2 to 10 MPa, indicating that the deck-U ribs welding detail most experience low-amplitude stress cycles. ② the U rib butt weld has a large stress amplitude and is distributed in the range of 2 to 46 MPa.

Fatigue life of welded details
From the cut-off limit L σ ∆ value of the welding details in Tab. 1, the stress amplitudes of the measured welding details at different measuring points of each monitoring section can be judged. Both the stress amplitude greater than the deadline and the stress amplitude less than the deadline. The stress amplitude less than L σ ∆ is included in the fatigue damage calculation and is classified in the range of the formula (7) which is smaller than the constant fatigue limit D σ ∆ . Formula (8) and Formula (9) are available as following: (1) Deck plate-to-rib welded details and diaphragm openings: The fatigue life of each detail is calculated from Eq. (7), as shown in Tab. 6. It can be seen from Tab. 6: (1) U-rib butt joints and the diaphragm opening welded details are susceptible to fatigue failure. Among them, the fatigue life of the U-butt weld of position 1 (14 mm top plate thickness) is the shortest, followed by position 2 (16 mm top plate thickness). The fatigue life of the openings of the diaphragms at positions 1 and 2 is comparable; (2) From the fatigue life of the cross-sections of Section 3 and Section 5, it can be seen that for the deck plate-to-rib welded details. The fatigue life of the detail using the diaphragm is significantly longer than that without the diaphragm. This shows that the arrangement of the diaphragm can enhance the fatigue performance of the welded joints between the top plate and the U-ribs, and improve their fatigue life.
(3) For each section, the fatigue life of the measured points at Location 2 is greater than that at the corresponding measured at Location 1, which can be used to predict that the U-rib butt weld at Location 1 will experience the first fatigue failure. It is advisable to pay special attention to the damage of the U-rib butt and the weld at the opening of the diaphragm during the operation of the bridge and carry out timely fatigue tests.

Conclusions
According to the measured strain data of the steel box girder test of Taizhou Bridge, this paper studies the fatigue life of welded details of flat steel box girders based on Miner linear cumulative damage theory. The following conclusions can be drawn: (1) The local effect of stress distribution is remarkable. The stress values obtained from the load test is consistent with the FEM result, indicating that the data measured by the load test is reliable. (2) The stress measured points are mainly based on low-amplitude stress cycles, and most of the stress amplitudes are in the range of 2 to 10 MPa, the welding details stress at the U-rib butt joint is larger among the stress amplitudes. (3) The fatigue life of each welded detail at 14 mm thick deck plate position is smaller than that at at 16 mm thick deck corresponding to the fatigue life of the weld. (4) U-rib butt joints, openings in the diaphragm is easy to fatigue damaged. Among them, the 14 mm thick U-rib butt joints first appeared fatigue failure. (5) The arrangement of the diaphragm can effectively increase the fatigue life of the top-U rib weld and improve the fatigue performance at this detail.