Vortex-induced vibration performance and mechanism of long-span railway bridge streamlined box girder

Abstract

To investigate the vortex-induced vibration (VIV) characteristics of a narrow-streamlined railway box girder and optimize its VIV performance, a long-span railway cable-stayed bridge was analyzed. Based on sectional model wind tunnel tests, the influence of the wind attack angle and the damping ratio on the VIV performance of the girder was investigated. The main inducing factors of the VIV of the narrow railway box girder were explored and a series of corresponding optimization schemes was put forward. The results show that there is no VIV when the wind attack angles are −5°, −3° and 0°, and the damping ratio is 0.2%. The non-dimensional maximum amplitudes 1000y/D of the girder at wind attack angles of +3° and +5° are 14.4 and 19.4, respectively. The maximum amplitudes decrease with the increase of the damping ratios. The railing base is the influence factor that induces the vertical VIV, because the separation vortices between the railing base and ballast wall, as well as behind the railings, cause the VIV of the railway steel box girder. Compared with that of the girder section with the ballastless track board, the non-dimensional maximum vertical VIV amplitude of the girder without the ballastless track board greatly increases from 19.4 to 63.5, which could effectively suppress the VIV of the main girder. Lastly, in the construction state, vertical VIV occurs for girder sections I and II, which have respective aspect ratios of 4.3 and 4.6, at wind attack angles of +3° and +5°. Girder section III, which has a 6.7 aspect ratio and is more streamlined, does not have a VIV. The greater the aspect ratio of the bridge girder, the better the VIV performance. The relevant results could serve as a guide for wind resistance design of railway streamlined box girders.

Keywords

narrow streamlined box girder aspect ratio between width and height railing base vortex-induced vibration sectional model wind tunnel testing virtual model wind tunnel testing

Highlights

• The railing base is the influence factor that induces the vertical VIV, because the separation vortices between the railing base and ballast wall, as well as behind the railings, cause the VIV of the railway steel box girder.

• The ballastless track board could effectively suppress the VIV of the main girder.

• The larger the aspect ratio of the bridge girder, the better the girder’s VIV performance, relatively.

Introduction

In recent years, more and more railway lines have been constructed in China. Railway bridges are faced with increasingly severe challenges, such as complex wind environment conditions and greater span demands. Unlike cars running on highway bridges, railway vehicles are faced with higher requirements for running safety and comfort. The vortex-induced vibration (VIV) performance of long-span bridge railway girder sections under crosswind becomes a key control factor. Because VIV could affect driving safety and ride comfort. Continuous vibration phenomena can even cause structural fatigue damage to the bridge, although VIV is not divergent vibration and will not directly lead to structural damage (Chen, 2005). The VIV phenomenon has appeared in many long-span highway bridges at home and abroad, such as in the Humen Bridge in 2020, when the maximum vertical VIV amplitude reached up to 30 cm (Ge, 2022; Zhao, 2020), causing significant social impact. The Xihoumen Bridge, Yingwuzhou Yangtze River Bridge and Second Severn crossing have also been subjected to the VIV phenomenon. In recent years, some railway long-span bridges, e.g., Shanghai-Suzhou-Nantong Yangtze River Bridge and the Quanzhou Bay Bridge of Fuzhou-Xiamen Railway, have been appeared. To avoid similar VIV events in long-span railway bridges, it is necessary to conduct targeted research on this subject.

A variety of innovative work has been carried out on large-span railway bridges. Common steel truss girders are no longer used for the main girder sections. Many cable-stayed railway bridges have adopted the streamlined box girder (Li, 2021; Zeng, 2020; Chen, 2022), as shown in Table 1, due to its perfect wind resistance characteristics. The line spacing of a double-line railway is about 5 m. To ensure the stiffness of a long-span railway bridge meets the requirements, the aspect ratio of bridge girder width and height is generally about 4∼6, which is smaller than that of common long-span highway bridge girder sections. Generally, the smaller the aspect ratio of the width and height, the blunter the girder sections, and girder sections are more and more sensitive to crosswind action, and more prone to VIV. However, at present, there are few specialized studies of the VIV performance of long-span railway bridges with narrow streamlined steel box girders. To ensure the safety of human life and property, it is necessary to study the VIV performance of narrow streamlined steel box girders under crosswind.

Table 1.

Some long-span cable stayed railway bridges with streamlined steel box girders.

Number	Bridge name	Main span(m)	Main girder (m)
Number	Bridge name	Main span(m)	Width	Height	Aspect ratio
1	Anqing-Jiujiang high-speed railway Bianyuzhou Yangtze River bridge	672	32.20	4.79	6.70
2	Fuzhou-Xiamen high-speed railway Wulongjiang bridge	432	29.10	4.00	7.27
3	Fuzhou-Xiamen high-speed railway Quanzhou Bay Cross-sea bridge	400	21.00	4.25	4.90
4	Nanning-Yulin Intercity railway Baihe Yujiang bridge	330	18.40	5.00	3.68
5	Nansha Port railway Xijiang bridge	600	21.00	4.50	4.70
6	Ningbo railway Yongjiang River railway bridge	468	21.00	5.00	4.20
7	Qianjiang railway Branch line Yuekou Hanjiang railway bridge	260	13.00	3.50	3.71

Many scholars have studied the VIV characteristics of bridge main girders. Li (2021) conducted a series of sectional model wind tunnel tests to study the VIV performance of rectangular box girders, and proposed optimization measures involving wind fairings with platforms. Huang (2021) experimentally determined that triangular wind fairings with platforms could both reduce vortex sizes at the upper and lower surfaces of the main girder, and reduce the vortex-induced forces on the main girder, which could effectively suppress VIV. By wind tunnel tests and numerical simulation, Meng (2011) found wind fairing angle would influence the VIV performance of main girders. The slender the wind fairing, the better the VIV performance.

For streamlined box girder sections with relatively large aspect ratios, Larsen (2015) found that the separation vortex strength generated at the shorter bottom plate of the main girder is higher, which is the main factor that affects VIV. For rectangular sections with aspect ratios of 4:1, Nakamura (1975) found that the airflow separates at the leading edge and is impinged at the section. The velocity field changes in phase, causing a corresponding change in the vortex-induced forces. The negative damping of the system then leads to the VIV phenomenon (Tang, 2022).

The important facilities and attachments of main girder, such as railings and maintenance tracks, exert an aerodynamic influence on the VIV performance of girders and should not be ignored. Nagao (1997) and Guan (2014) experimentally found that handrails could change the aerodynamic shape of girder sections and enlarge the VIV amplitude, around which there has been a consensus. The area between the anti-collision railing and the curb may also be the main factor that causes VIV (Zhou, 2016). As opposed to that of a long-span highway bridge, the main girder of a railway bridge is arranged with attached facilities such as maintenance tracks and ballastless track boards, which could affect the flow structure around the bridge deck. It is necessary to study the VIV performance of streamlined railway box girders in both the service and construction states.

Smaller section aspect ratios could affect the flow structure around a girder section. Nakamura (1975) found that under the same test conditions, the smaller the aspect ratio of the rectangular section, the greater the vibration strength of the structure. Some scholars conducted further classification of instability-induced excitation concerning the type of wake formation behind prismatic bodies (Naudascher, 1993; Shang, 2019). These include four typical forms: leading-edge vortex shedding (LEVS), impinging leading-edge vortices (IEVS), trailing-edge vortex shedding (TEVS) and alternate-edge vortex shedding (AEVS). The first two correspond to the single shear layer mechanism, and the latter two are for the double shear layer mechanism. The type of rectangular section with an aspect ratio between 3∼9 mainly experiences IEVS.

Two-dimensional Delayed Detached Eddy Simulation (DDES) was carried out to investigate the uniform flow over rectangular sections with different chamfered-corner ratios, and the bad inner corner-cutting angle was proposed. Through numerical simulation, the flow structure around the main girder could be better presented. Frandsen (2000) simulated the VIV characteristics of a bridge through the discrete vortex method, which proved the feasibility of the numerical simulation method in developing VIV response prediction and mechanism analysis. Meng (2011) found that wind fairing could change the flow structure around girders. When the airflow passes through a streamlined box girder section with a small wind faring angle, it cannot easily form vortices with low frequency and high energy. Based on the VIV performance of a streamlined box girder, the flow structure and corresponding mechanism have some engineering application value (Duan,2022; Liu 2022).

Taking a cable-stayed bridge as the engineering background, the VIV performance of a narrow-streamlined steel box girder with an aspect ratio of 4.3 is experimentally and numerically considered. The influence of the wind attack angle and damping on the VIV and the inducing factors was explored. The numerical simulation method was then applied to the mechanism of VIV and corresponding suppression measures were proposed. The results could provide a specific reference for the wind resistance design of similar long-span railway bridges.

Experimental setup

Girder model

A railway bridge is a long-span mixed girder cable-stayed bridge with a high-low tower. The main girder is a single-box five-chamber streamlined steel box girder with wind fairing. The width and height of the main girder are 19.5 m and 4.5 m, respectively. The aspect ratio is 4.3. The railway bridge deck is arranged with a ballastless track board, ballast wall, cable groove, maintenance track, railing and so on, as shown in Figure 1. The railing has a rectangular base which is 0.26 m in height and 0.25 m in width (Figure 1(a)–(c)).

Figure 1.

Girder section (unit: m).

After consideration of the required simulation details, the geometric scale of the sectional model is set as 1:30 and the blockage is less than 4%. The length of the model is 2.095 m. The sectional models were designed and manufactured using conventional stiff model technology. The models are made of high-quality lightweight wood frames, deck surfacing, stringers and steel transverse beams. The wood frames and high stiff deck surfacing ensures the stiffness of the models. The coat of the model simulates the thin wood plates of the bridge girder. The railings and other auxiliary components on the bridge deck are made of plastic plate. The porosity of railing model is consistent with that of the porotype. The sectional model is shown in Figure 1(d) and (e).

Sectional model wind tunnel testing

The sectional model wind tunnel tests are conducted in the XNJD-1 industrial wind tunnel at Southwest Jiaotong University. The dimensions of the test section are 2.4 m × 2.0 m × 16.0 m (width × height × length), with a wind velocity of 0.5∼45.0 m/s.

The aspect ratio of the length and width of the girder model is 3.2. Generally, when the ratio is less than 4, the three-dimensional effect exerts influence on the sectional model wind tunnel results (Wang, 2021). To ensure the two-dimensional characteristics of the flow field around the bridge girder model, end plates are set at both ends of the model. The end plates in the wind tunnel test are roughly (D+B+D) in width and (D+D+D) in height. B and D are the width and height of model, respectively. Influence of end plates on VIV performance would be investigated later. And, the end plates in these wind tunnel tests are same to ensure that the end plate is not a variable during the test. The girder model is suspended by 4 pairs of springs. Meanwhile, the girder model and springs are connected by two brackets located at either side of the model in the longitudinal direction. The model can vibrate freely in the vertical and torsional directions. The springs and brackets are mounted on the outside walls of the wind tunnel to minimize the aerodynamic influence (Figure 2).

Figure 2.

Girder model in wind tunnel.

As the onset wind speed of VIV is low, rigid springs are adopted to increase the frequency of vibration and decrease the wind speed ratio of the prototype and model. Additional masses of soft lead were installed at each end of the model suspension system to ensure mass similitude. The testing parameters are shown in Table 2. Additional damping was provided by the oil damper and the rubber string. The actual damping ratio of the spring-suspended sectional model generally varies around the nominal ones with the change of the vibrating amplitude, a fact which has been studied by many experts (Gao, 2015; Zhang, 2018). Therefore, during the wind tunnel tests, the damping ratios are obtained according to the maximum VIV amplitudes.

Table 2.

Main parameters of sectional wind tunnel testing.

Mode	Frequency/Hz		Equivalent mass m/kg·m⁻¹		Equivalent mass I_m/kg·m²·m⁻¹
Mode	Prototype	Model	Prototype	Model	Prototype	Model
First order vertical	0.430	2.688	31,231.5	34.7	/	/
First order torsional	2.105	10.625	/	/	1,668,000	2.059

Virtual wind tunnel testing

To investigate the VIV phenomenon of the narrow-streamlined steel box girder, the flow structure around the girder section is analyzed. The calculation domain is shown in Figure 3(a), where B is the width of the girder. The distances from the girder’s vertical center to the front and rear boundaries of the calculation domain are 14B and 24B, respectively. The distances to the upper and lower boundaries are both 4B. When the grid is divided, the sparse grid is used in the area further from the girder section, while the grid used around the girder section is dense. Near the bridge girder, the minimum mesh size is 2 × 10⁻⁵ m and the growth rate for the cell height is less than 1.05. The y+ value is less than 5. The total number of grids is 5 × 10⁵. The Reynolds numbers coincide with the porotype.

Figure 3.

Virtual wind tunnel testing.

The surface boundary of the girder is a non-slip wall boundary. Other boundaries are shown in Figure 3(a). For the two-dimensional incompressible flow, the k-w SST-DDES turbulence model is adopted and the SIMPLE algorithm is used to solve the equations. The convergence value is set to 1 × 10⁻⁶ and the time step is set to 2 × 10⁻⁴ s to ensure that the Courant number is less than 1. Each calculation step is completed within 20 iterative steps.

While, two different meshing strategies are adopted to make sure the grid independence. The first one is called basic condition, and the second one is the refined condition. For the refined condition, the number of nodes on girder surfaces is twice as many as that of the basic and the cell number is 7.5 × 10⁵. Table 3 lists the numerical results Strouhal number S_t of the two meshing strategies. Thus, the basic mesh is adopted in this study. In addition, the time-step independence is also checked. As Table 1 show, the results of two time-steps have no distinct difference. Therefore, the time step 2 × 10⁻⁴ s is adopted to balance the computing cost and result accuracy.

Table 3.

The numerical results.

Condition	Grid number	Time step (s)	S _t
Basic condition	5.0 × 10⁵	2 × 10⁻⁴	0.1402
Refine condition	7.5 × 10⁵	2 × 10⁻⁴	0.1380
Basic condition	5.0 × 10⁵	1 × 10⁻⁴	0.1400

To obtain more comparative results, the numerical study mainly aims to investigate the flow field structure around the bridge deck. The present simulation can be validated by comparing the numerical and experimental values of the Strouhal number S_t of the bridge deck (Figure 3(b)). The Strouhal number S_t is calculated by fD/U, where f is the frequency in the vertical or torsional direction, D is the height of the girder and U is the wind speed. The results show that the numerical simulation results are aligned with the experimental results. The experimental result of Strouhal number S_t is 0.134. The difference between the numerical simulation results is aligned with the experimental results was 4.5%.

It should be noted that although the two-dimensional stationary analysis cannot study the flow field structure around the girder section during the VIV, the mechanism and corresponding differences between the VIV of the main girders can be obtained, which also has significance for long-span railway bridge girders.

Results and discussion

Influence of wind attack angle

The vertical and torsional damping ratios of the sectional model wind tunnel test were set as 0.20% and 0.25%, respectively. The sectional model test was conducted at 0°, ±3° and ±5° wind attack angles. The test results are shown in Figure 4. In the figure, the horizontal axis is the dimensionless wind speed U/f D, where U is the wind speed, f is frequency including the vertical frequency or the torsional frequency, and D represents the bridge deck height. The vertical axis is the dimensionless VIV amplitude (1000y/D) normalized by the bridge deck height D, where y represents the VIV amplitude of the prototype bridge girder.

Figure 4.

VIV amplitudes of main girder.

There is a vertical VIV region at wind attack angles +3° and +5°, respectively. The nondimensional wind speed regions are at 7∼9, which are basically the same. The maximum vertical VIV amplitudes at wind attack angles +3° and +5° are 14.4 and 19.4, respectively. The result at wind attack angle +5° is 34.7% higher than that at wind attack angle +3°. There is no torsional VIV phenomenon for the main girder at wind attack angle 0°, ±3° and ±5°. The vertical VIV performance at wind attack angle +5° and +3° will be discussed infra.

The first vertical and torsional frequency is 0.430 Hz, 2.105 Hz. The reduced wind speed for vertical VIV ranged from 0 to 15. However, the reduced wind speed for torsional VIV ranged from 0 to 3.5. The wind speeds corresponding to the real bridge is 29 m/s and 33 m/s, respectively. Maybe, the lock-in wind speed of torsional VIV is larger than 33 m/s, which is large enough within the common range of wind speeds. Therefore, the torsional vortex shock vibration of the main beam is not considered. The investigation is mainly focus on the vertical VIV. The corresponding wind tunnel test and numerical is also focus on the vertical VIV.

Influence of damping ratio

To investigate the effect of damping on the vertical VIV performance of main girder, vertical VIV amplitude was tested at 0.20% and 0.45% at wind attack angles +3° and +5°. The results are shown in Figure 5.

Figure 5.

Vertical VIV amplitudes of main girder at different damping ratios.

It could be known that the vertical VIV amplitudes decrease with the increase of the damping ratio. When the damping ratio increases to 0.45% from 0.20%, the dimensionless maximum vertical VIV amplitude is reduced to 9.0 and 12.1 from 14.4 to 19.4 at wind attack angles +3° and +5°, which represent respective reductions of 37.7% and 37.6%. Meanwhile, at wind attack angles +3° and +5°, influence of damping on the vertical VIV amplitudes of main girder is basically the same. That is, the slopes of the lines in Figure 5(b) are almost identical. At different damping ratios, the vertical VIV regions remain roughly unchanged.

Analysis of inducing factor

To explore the main inducing factor of the vertical VIV of main girder, the +5° wind attack angle condition is taken as an example, and three working conditions are shown in Figure 6. Figure 6(a)–(c) corresponds to working condition I, II and III. Detailed working condition settings are as follows:

Figure 6.

Working condition I, II and III.

Working condition I: original section without maintenance track.

Working condition II: original section without maintenance track and railing.

Working condition III: original section without maintenance track and railing base.

It could be seen from Figure 7 that, after removing the maintenance track, the maximum vertical VIV amplitude of the girder is reduced by only 5.6% compared to that in the original design scheme. The effect of maintenance track on vertical VIV performance is relatively small. Because the distance between the maintenance track and the bottom plate of the girder (a distance of 0.8 m on the real bridge) is relatively large, the aerodynamic effect of the maintenance track is relatively small. In other words, vertical VIV performance of main girder could be optimized by increasing this distance.

Figure 7.

Vertical VIV amplitudes of main girder.

After removing the railing and maintenance track, vertical VIV completely disappears. Meanwhile, in case of girder without maintenance track and railing base, there is still no VIV phenomenon. It could thus be seen that railing base is the main inducing factor of the vertical VIV of main girder.

To further analyze the influence of the railing base on the flow structure around main girder, Figure 8 shows the instantaneous vorticity diagram corresponding to the maximum and minimum lifting moment of the girder before and after removing the railing base at +5° wind attack angle. Influence of maintenance track was not considered here, because influence of which could be neglected from results (working condition I) in Figure 7.

Figure 8.

Instantaneous vorticities around the original and optimized sections.

In Figure 8, there is a relatively large separation vortex between the railing base and the ballast wall, and there are several obvious separation vortices after the railing. After removing the railing base, the separation vortices between the railing base and the ballast wall are greatly reduced in size, and there are still several separation vortices after the railing. The ballastless track board still causes a certain degree of disturbance in the airflow. The size of the separation vortices is significantly reduced, and they move to the leeward side of the bridge deck. Due to the influence of the railing base, the large vortex that appears behind the railing is shed at the wake region of the girder.

Influence of ballastless track board

To investigate the aerodynamic effect of the ballastless track board on the VIV performance of a narrow girder section, working conditions IV and V are enacted. In working IV and V (Figure 9), girder sections are both without ballastless track board. The corresponding parameters in the wind tunnel test are the same as those in Table 1. The detailed working condition setting is shown as follow:

Figure 9.

Working condition IV and V.

Working condition IV: without board, railing with the base.

Working condition V: without board, railing without base.

The non-dimensional vertical VIV amplitude results are shown in Figure 10.

Figure 10.

Vertical VIV amplitudes of main girder.

In Figure 10(a), the dimensionless maximum vertical VIV amplitudes at wind attack angle +5° are respectively 63.5 and 11.7 in working conditions IV and V, which represents a reduction of 81.5% from working condition IV to V. It is proven again that the railing base could worsen the VIV performance. Meanwhile, compared with that of the girder section with ballastless track board, the non-dimensional maximum vertical VIV amplitude of the girder without the ballastless track board increases greatly from 19.4 to 63.5. The maximum result is about 3.3 times that of the ballastless track board. For the railing without base in the working condition, there is still vertical VIV, and the maximum vertical VIV amplitude is 11.7.

In Figure 10(b), at wind attack angle +3°, the dimensionless maximum vertical VIV amplitude is respectively 40.5 and 8.3 in working conditions IV and V, which is reduced 37% and 29% than that at wind attack angle +5°. In short, the ballastless track board and the railing base can both effectively suppress the vertical VIV of the girder. Meanwhile, the girder without ballastless board is corresponding to the highway bridge and the VIV characteristics is not investigated at other wind attack angles, which will be investigated in detail further.

Figure 11 shows the instantaneous vorticity diagram around the original main girder (Figure 1) at moment that corresponding to the maximum and minimum lift in working conditions IV and V, at +5° wind attack angle. The maintenance track is connected to the main girder by the interval arranged support, and the support of the maintenance track is not simulated in the CFD simulation.

Figure 11.

Instantaneous vorticities around girder section I under condition one.

In Figure 11(a) and (b) (working condition IV), the airflow exhibits continuous vortex separation on the leeward side of the railing and on the windward side of the bridge deck. Meanwhile, due to the influence of the rectangular railing base, a large vortex is formed on the bridge deck after the airflow separation. As the vortex moves to the leeward side of the bridge deck, the airflow sheds above the inclined web of the section after passing through the railing. The lower airflow separates through the maintenance track, and continuous vortex shedding is produced in the rear of the track, forming a typical Kármán vortex street.

In Figure 11(c) and (d) (working condition V), the airflow separates at the windward side of the bridge deck. As the vortex moves along the bridge deck, it becomes larger and separates and sheds at the leeward side of the railing. The flow structure around the maintenance track at the bridge’s bottom plate is basically the same as that in condition IV, and has little influence on the bottom plate due to the large distance.

Comparing the instantaneous vortex structure around the girder section in conditions IV and V, it can be seen that, after removing the railing base, the airflow separation vortex disappears, and the vortex above the bridge deck reduces in size. The strength of the vortex around the main girder structure is weakened. When the bridge deck does not have the base railing, the larger vortex of the bridge deck is scattered into some vortices of small size, and the strength of the vortices is significantly weakened. This is the reason why the maximum amplitude of the vertical VIV is slightly lower for bridge decks without a railing base.

Influence of narrow girder aspect ratio

To investigate the influence of the aspect ratios of girder sections on the VIV performance, two other girder sections with aspect ratios of 4.6 and 6.7 are shown in Figure 12.

Figure 12.

Girder sections in working conditions VI and VII (unit: m).

The three girder sections, including the original girder section in the construction state in Figure 1(a) (described as girder I), girder II and girder III. Three girder sections have a width of 19.5 m. Their heights are 4.5 m, 4.2 m and 2.9 m, respectively. The wind fairing angle of girder III is the smallest among the three girder sections. The wind fairing angle of girder I in Figure 1 is 77°. With the decreased height of the girder sections, the wind fairing angle also decreases, being 65° and 54° for girders II and III, respectively. For girders I to III, the angles between the inclined web and horizontal plane are 21°, 26° and 16°, respectively. Larsen (2012) experimentally found that the VIV performance of a girder is better when the angle of the incline web is smaller than 16°. The main reason for this is that an incline web with an angle smaller than 16° can effectively weaken the separation effect of the airflow.

In Figure 12(c), girder section I, II, III, are respectively represented by the black line, the blue line and the red line. Changes in the three section profiles are shown. Differences between the three sections are mainly concentrated in the inclined web and the wind fairing angle. There is also a difference in the width of the bottom plate. Obviously, girder section III is more streamlined.

In view of the differences between the mass and damping parameters for the main girder sections, Figure 13(a) shows the relationship between the Scruton number S_c (S_c = 4πmξ/ρB²) and the maximum dimensionless vertical VIV amplitude. m is the equivalent mass, ξ is the damping ratio and B is the characteristic size. The width of main girder is taken here, because the three girder sections have widths of 19.5 m and the variables of the horizontal and vertical axes in Figure 13 are normalized by the width of the girder section.

Figure 13.

Influence of S_c on vertical VIV of main girder.

In Figure 13(a), the fitting curves of girder I and II at wind attack angle +5° are also presented, and the VIV amplitude of the girders corresponding to S_c at wind attack angle +5° could be obtained. The maximum amplitude of vertical VIV of girder section II is slightly smaller than that of section I. The vertical VIV performance of section II is relatively better than girder section I. The wind tunnel test results of Marra (2015) (0° attack angle) and Wu (2022) (0° and +5° wind attack angles) are also presented in Figure 13(a). The result for section I is slightly less than that of the rectangular section. Girdersection I, which is with an aspect ratio of 4.3, could be regarded as a rectangular section with chamfered corners. And, it could weaken the airflow separation and optimize VIV performance. VIV performance of girder section I is slightly better than that of a 4:1 rectangle. There is no vertical VIV for girder III, and the results are not shown here. The corresponding reasons will be discussed later.

Figure 13(b) shows the relationship between the S_c and the VIV regions of the girder sections. It is known that with the increase of S_c, the VIV regions of girder sections I and II gradually shorten, and the onset wind speed of girder section II is slightly higher than that of section I.

Figure 14 shows the instantaneous vorticity around girder sections I, II and III. Figure 14(a), (c) and (e) correspond to the moment of maximum lift force; And, Figure 14(b), (d) and (f) correspond to the moment of minimum lift force. Generally, the airflow is separated at the wind fairing. A part of the airflow moves along the upper inclined web and separates at the windward side of the bridge deck. The other part of the airflow moves along the lower inclined web and the bottom plate at the windward side of bridge deck, forming the upper and lower vortices, respectively.

Figure 14.

Instantaneous vorticities around girder sections.

According to Figure 14(a) and (b), after the airflow is separated at the windward side of the bridge deck for girder section I, the vortex increases in size and sheds at the leeward side of the bridge deck. The other part of the airflow moves along the bridge bottom plate. The vortex shedding is in the single vortex mode.

According to Figure 14(c) and (d), there are several vortices around girder section II, but compared with girder section I, the vortex size is significantly reduced. The airflow moves along the bottom plate and sheds at the wind fairing on the leeward side of the girder. The vortex shedding is in vortex pair mode. In other words, there are a pair of vortices with opposite directions on the same side of the wake zone.

According to Figure 14(e) and (f), although there are still a certain number of vortices around girder section III, their size is even smaller. Due to the relatively small angle of the oblique web, the vortex size at the lower oblique web of the leeward side is also significantly reduced. Compared with girder sections I and II, the wake vortex shedding strength of girder section III is weakened, and is not enough to cause the VIV of the main girder.

Conclusion

To better understand the VIV characteristics of steel streamlined railway box girder sections, a series of investigations was conducted through wind tunnel tests and numerical simulation. The major conclusions of this study are summarized as follows:

1. The vertical VIV of a narrow-streamlined box girder with an aspect ratio of 4.3 occurs at +3° and +5° wind attack angles. The maximum vertical amplitude at the +5° wind attack angle was 34.7% larger than that at the +3° wind attack angle. The wind speed regions are both about 7∼9.

2. The vertical VIV amplitudes decrease with the increase of the damping ratio. When the damping ratio increases from 0.20% to 0.45%, the dimensionless maximum amplitude of the vertical VIV at wind attack angles of +3° and +5° is reduced to 14.4 and 19.4 from 9.0 to 12.1.

3. The railing base is the main inducing factor of vertical VIV. There is a relatively large separation vortex between the railing base and the ballast wall. After removing the railing base, the size of the separation vortices between the railing base and ballast wall vortex is greatly reduced.

4. Compared with the girder section with the ballastless track board, the non-dimensional maximum vertical VIV amplitude is greatly increased from 19.4 to 63.5, and is reduced by 81.5%. For the railing without base, vertical VIV still occurs for the girder without the ballastless track board. The ballastless track board can effectively suppress the vertical VIV.

5. With the increase of S_c, the maximum amplitude of the vertical VIV decreases linearly. The maximum amplitude of the vertical VIV of girder section II, whose aspect ratio is 4.6, is slightly smaller than that in section with an aspect ratio of 4.3.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research described in this article was financially supported by the Natural Science Foundation of China (grant no: 52078438) and the China Postdoctoral Science Foundation (grant no: 2019M663897XB) and Natural Science Foundation of Southwest University of Science and Technology (grant no: 21ZX7148). Key research base of Humanities and Social Sciences of Sichuan Education Department of Chengdu Information Engineering University (grant no: ZHYJ22-ZD02).

ORCID iDs

Qingsong Duan

Cunming Ma

Qiusheng Li

References

Chen

(2005) Bridge Wind Engineering. Beijing: China Communications Press.

Chen

Yan

(2022) Achievements and prospects of railway bridge construction technology in China. High speed railway technology 13(4): 1–7.

Duan

, et al. (2022) Vortex-induced vibration characteristics of two open girders: a comparison of experimental and numerical investigation. Advances in Structural Engineering 25(14): 2844–2856.

Frandsen

(2000) Comparison of numerical predictions and full-scale measurements of vortex-induced oscillations. In: The 4th International Colloquium on Bluff Body aerodynamics and Applications, Bochum, 08 Sep.

Gao

Zhu

(2015) Nonlinearity of mechanical damping and stiffness of a spring-suspended sectional model system for wind tunnel tests. Journal of Sound and Vibration 355: 369–391.

Zhao

Cao

(2022) Case study of vortex-induced vibration and mitigation mechanism for a long-span suspension bridge. Journal of Wind Engineering and Industrial Aerodynamics 228(1): 104866.

Guan

, et al. (2014) Effects of railings on vortex-induced vibration of a bridge deck section. Journal of Vibration and Shock 33(3): 150–156.

Huang

Dong

Wang

, et al. (2021) Vortex-induced vibration performance of a cable-stayed railway bridge with rectangular steel box girder and its aerodynamic countermeasure. Journal of Vibration and Shock 40(6): 23–32+85.

Larsen

Larose

(2015) Dynamic wind effects on suspension and cable-stayed bridges. Journal of Sound and Vibration 334: 2–28.

10.

Larsen

Wall

(2012) Shaping of bridge box girders to avoid vortex shedding response. Journal of Wind Engineering & Industrial Aerodynamics. Industrial Aerodynamics 104-106: 159–165.

11.

Huang

Gao

, et al. (2021) Vortex-induced vibration performance of Bianyuzhou Yangtze river bridge with rectangular steel box girder and aerodynamic countermeasure research. Journal of Railway Science and Engineering 18(7): 1790–1797.

12.

Liu

Zou

, et al. (2022) Experimental investigation on vortex-induced vibration of a long-span rail-cum-road bridge with twin separated parallel decks. Journal of Wind Engineering and Industrial Aerodynamics 228(9): 105086.

13.

Marra

Mannini

Bartoli

(2015) Measurements and improved model of vortex-induced vibration for an elongated rectangular cylinder. Journal of Wind Engineering and Industrial Aerodynamics 147: 358–367.

14.

Meng

Guo

Ding

, et al. (2011) Influence of wind fairing angle on vortex-induced vibration and flutter performances of closed and semi-closed box decks. Engineering Mechanics 28(S1): 184–188+194.

15.

Nagao

Utsunomiya

Yoshioka

, et al. (1997) Effects of handrails on separated shear flow and vortex-induced oscillation. Journal of Wind Engineering and Industrial Aerodynamics 69-71: 819–827.

16.

Nakamura

Mizota

(1975) Unsteady lifts and wakes of oscillating rectangular prisms. Journal of the Engineering Mechanics Division 101(6): 855–871.

17.

Naudascher

Wang

(1993) Flow-induced vibrations of prismatic bodies and grids of prisms. Journal of Fluids and Structures 7: 341–373.

18.

Shang

Zhou

Alam

, et al. (2019) Numerical studies of the flow structure and aerodynamic forces on two tandem square cylinders with different chamfered-corner ratios. Physics of Fluids 31(7): 075102.

19.

Tang

Hui

(2022) LES study on variation of flow pattern around a 4:1 rectangular cylinder and corresponding wind load during VIV. Journal of Wind Engineering and Industrial Aerodynamics 228: 105121.

20.

Wang

Zhang

(2021) VIV properties of π-shaped bridge sectional model: dependence on torsional-Bending frequency ratio. Journal of Bridge Engineering 26(6): 06021003.

21.

Zhang

(2022) Experimental investigation on the vortex-induced vibration of a rectangular 4:1 cylinder under skew winds. Journal of Wind Engineering and Industrial Aerodynamics 229: 105114.

22.

Zeng

(2020) Design of stee-concrete composite girder of main bridge of Quanzhou Bay sea-crossing bridge on Fuzhou-Xiamen high-speed railway. World Bridges 48(S1): 12–16.

23.

Zhang

(2018) Nonlinear vibration characteristics of bridge deck section models in still air. Journal of Bridge Engineering 23(9): 04018059.1−04018059.13.

24.

Zhao

Liu

(2020) Vortex-induced vibration sensitivity of bridge girder structures. Acta Aerodynamica Sinica 38(4): 694–704.

25.

Zhou

(2016) Mitigation measures and mechanism for vortex-induced vibration of box girder with long cantilever in Qingzhou channel bridge of Hong Kong-Zhuhai-Macao bridge. China Journal of Highway and Transport 29(12): 17–24.