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Article

Research on Mechanism of Vortex-Induced Vibration Railing Effect of Double-Deck Large-Span Suspension Bridge

by
Gang Yao
1,
Yuxiao Chen
1,
Yang Yang
1,*,
Yuanlin Zheng
2,
Linjun Wu
1 and
Hongbo Du
1
1
Key Laboratory of New Technology for Construction of Cities in Mountain Area, School of Civil Engineering, Chongqing University, Chongqing 400045, China
2
Chongqing City Infrastructure Construction Investment Co., Ltd., Chongqing 400014, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(16), 9314; https://doi.org/10.3390/app13169314
Submission received: 2 August 2023 / Revised: 11 August 2023 / Accepted: 15 August 2023 / Published: 16 August 2023
(This article belongs to the Special Issue Aerodynamics and Its Applications)
Browse Figures
Versions Notes

Abstract

:
Large-span suspension bridges are susceptible to wind loads. Therefore, a more precise analysis of their wind-induced vibration response is necessary to ensure the structure’s absolute safety. This investigation conducted wind tunnel tests for the construction and completion stages to reveal the vortex-induced vibration (VIV) phenomenon of a double-deck suspension bridge. The results showed that no VIV occurred during the construction stage. However, the inclusion of railings significantly deteriorated the aerodynamic performance of the suspension bridge, leading to significant VIV at +3° and +5° wind angles of attack. Additionally, reducing the railing ventilation rate can significantly suppress the VIV amplitude. A new analysis method based on computational fluid dynamics (CFD) simulation is proposed to investigate the VIV mechanism of the double-deck truss girder. Twenty-nine measurement points were used to explore the vortex that causes VIV. The numerical simulations found that the area above and aft of the upper deck dominated the vertical VIV, while the aft of the lower deck dominated the torsional VIV. Furthermore, the intensity of the vortex in these areas was significantly lower during the construction stage. Moreover, reducing the railing ventilation rate significantly suppresses the torsional VIV by reducing the intensity of the vortex in the region behind the lower deck.

1. Introduction

The increasing frequency of wind-induced disasters caused by climate change is placing greater demands on the safety of buildings. Double-deck truss girder suspension bridges are widely used in cross-river and cross-sea engineering due to their excellent spanning and transportation capabilities [1]. However, as the span increases, the structural stiffness, mass, and damping of suspension bridges decrease, leading to light flexibility and increased sensitivity to wind-induced vibrations [2]. This problem is particularly prominent in the complex and variable wind environment, and large-span bridges often suffer from wind-induced vibration problems such as vortex-induced vibration (VIV), buffeting vibration, and galloping vibration [3,4]. Among them, VIV has become a primary concern [5]. Many bridges have already suffered severe VIV, such as the Tacoma Narrow Bridge [6], the Humen Bridge [7], the Kesssock Bridge [8], the Fred Hartman Bridge [9], and the Xihoumen Bridge [10]. Therefore, as a crucial infrastructure, ensuring the wind stability of bridges is of utmost importance.
VIV is a type of amplitude-limiting vibration with both forced and self-excited characteristics [11]. The incoming flow generates periodic vortex shedding on the surface of the bridge structure, resulting in a periodic vortex force. When the frequency of vortex shedding is close to the intrinsic frequency of the girder, it triggers VIV in the bridge structure [12,13]. Unlike fluttering and buffeting, VIV does not cause destructive damage to the bridge [14]. However, since it occurs at low wind speeds, persists for prolonged periods, and has a high probability of occurrence, long-term VIV can impact the comfort of traffic and pedestrians and can reduce the durability of the bridge [15,16,17]. Truss girders, unlike Π-girders and box girders, consist of numerous discrete components, with web members that change along the bridge axis, creating complex aerodynamic disturbances [18]. This leads to the generation of multi-frequency and multi-size vortex shedding after different members, making the evaluation of VIV performance more challenging. Therefore, analyzing VIV and studying measures to suppress vibration in large-span double-deck truss girder suspension bridges is of particular importance.
Aerodynamic measures modifying the cross-sectional shape of components or adding appendages that alter airflow patterns (e.g., stabilizer plates, deflector plates, and wind fairings) represent the most commonly employed method for suppressing bridge VIV [19]. This approach involves making small, cost-effective, highly reliable structural changes, making it the preferred method for VIV suppression [20,21,22,23]. Additional aerodynamic measures can be more effective at suppressing VIV but require more materials and can negatively impact bridge aesthetics. Optimizing bridge aerodynamic performance by changing the structural shape, such as adjusting the railing ventilation rate or modifying the dimension and location of the maintenance track, can address these issues and better align with the demands of sustainable development, even though it may result in slightly reduced vibration suppression. Furthermore, VIV can also be suppressed through structural and mechanical measures [24,25,26,27]. Structural measures involve enhancing the stiffness or mass of the structure and increasing internal or external constraints, which can carry a higher cost. Mechanical measures entail incorporating various dampers to suppress vibration, which can lead to a more complex structural design. Therefore, these measures are more suitable for special cases where aerodynamic measures are ineffective.
The VIV of double-deck truss girders has received relatively little attention. Only Yao et al. [28] have studied the effect and mechanism of fairing and deflector plates on truss girder VIV. Fang et al. [29] have investigated the VIV mechanism of a truss girder through wind tunnel tests and numerical simulations. Previous studies on box girders and Π-beams have demonstrated that modifying the railing design can effectively suppress VIV. Nagao et al. [30] found that both the installation location and shape of the railing can significantly affect bridge VIV. Zhan et al. [31] found that installing wavy railings on the upper surface edge of the box girder can entirely suppress vertical and torsional VIV. Xin et al. [32] discovered that inclined railings could completely suppress both vertical and torsional VIV by significantly reducing the spanwise correlation of the streamwise velocity in the wake. Ge et al. [33] and Zhao et al. [34] demonstrated that installing suppressor plates at the top of the railing or removing the maintenance rails under the girder significantly suppressed the VIV of steel box girders through wind tunnel tests. Li et al. [35] and Cui et al. [36] found that reducing the railing ventilation rate can significantly suppress VIV in box girders. In conclusion, these studies demonstrate that adjusting the railing ventilation rate can effectively suppress bridge VIV. However, there is a lack of research conducted on the railings of double-deck truss girders. Additionally, the VIV of double-deck truss girders suffers from insufficient research data, incomplete understanding of vibration mechanisms, imperfect design specifications, and scarce field monitoring data. This research aims to investigate the impact of railing ventilation rate on truss girder VIV, which will fill in the shortcomings of existing research and provide valuable insights for designing truss girder suspension bridges.
This research investigates the VIV characteristics of the Huangjuetuo Bridge, currently under construction in China, along with the impact of railing ventilation rates and the associated mechanisms. Wind tunnel tests and computational fluid dynamics (CFD) simulations are conducted to achieve these objectives. Section 2 focuses on calculating the structural dynamic characteristics of the bridge using the finite element method. In Section 3, wind tunnel tests are carried out to measure the VIV response of the sectional model under different railing ventilation rates during the completion stage and the VIV response of the construction stage cross-section. Section 4 investigates the mechanism of VIV occurrence and the influence of railing using numerical simulation. Figure 1 provides a visual representation of the technology roadmap employed in this research.

2. Basic Information of the Suspension Bridge

2.1. Engineering Background

The Huangjuetuo Bridge is a significant infrastructure project in Chongqing, and it will be the world’s longest-span road-rail double-deck steel truss girder suspension bridge after completion. The bridge’s upper deck comprises a six-lane freeway, while the lower deck serves as a railway for Chongqing Rail Transit Line 18, a four-lane city main road, and a pedestrian sidewalk. The suspension bridge has a single span of 765 m, a total length of 945 m, and a width of 36.5 m. Two reinforced concrete towers with rectangular hollow box sections support the bridge. The main cable is created using the prefabricated parallel steel wire rope strand method, and the suspension cables are made of parallel steel wire bundles. The anchorages on both banks are made of gravity anchor ingots. Apart from the web members, the bridge’s cross-section hardly changes along the bridge axis, leading to a relatively uniform aerodynamic profile. Figure 2 displays the elevation and cross-sectional view of the bridge.

2.2. Structural Dynamic Characteristics

The dynamic characteristics of a suspension bridge are typically computed through the finite element method or measured using the environmental excitation method [37]. To accurately model the combined beam-slab-shell unit and to obtain consistent dynamic characteristics with the actual bridge, this research employed ANSYS APDL 15.0 software to construct a 3D finite element model based on the design drawings and documents, as shown in Figure 3. The finite element model has the same dimensions as the actual bridge. The main girder and towers were modelled using 3D elastic beam units (Beam4 units), while the main cables and booms were modelled using 3D linear rod units (Link10 units). The railings, maintenance vehicle tracking, and other ancillary components were modelled using mass units (Mass21 units) that simulate only the mass, not the stiffness [38]. Each node was assigned three degrees of freedom. Furthermore, the nonlinear solver was utilized to calculate the vibration patterns of suspension bridges and fully considered the effects of material nonlinearity and geometric nonlinearity. By accurately modeling the nonlinear behavior of the material as well as the large deformations and displacements of the structure, we were able to more accurately predict the intrinsic frequency and mode shape of the suspension bridge. An ANSYS modal analysis was utilized to solve the dynamic characteristics of the bridge, and Table 1 shows the primary vibration modes and frequencies of the suspension bridge. These dynamic characteristics will serve as actual bridge values for designing the sectional model system in the wind tunnel test.

3. Wind Tunnel Tests

3.1. Experimental Details

Wind tunnel testing is the most commonly employed method to investigate wind-induced vibration problems [39,40]. This research experimented at the Experimental Center of Civil Engineering, Chongqing University, in a 15.0 m (long) × 1.8 m (high) × 2.4 m (wide) DC wind tunnel, as shown in Figure 4. The test section is equipped with a special device for dynamic testing of the bridge sectional model. Tests were performed in uniform flow with equal wind speeds across all locations in the wind tunnel. Wind speeds ranging from 0.50 to 35.00 m/s were continuously adjusted, with turbulence intensity less than 0.50% of the corresponding wind speed. Moreover, the airflow deflection angle, velocity field deviation, and velocity stability were less than 1.00%. To ensure that the test conditions are similar to the actual situation and to reduce the effect of friction on the incoming flow on the test wall of the wind tunnel, the tests were conducted at the middle height of the wind tunnel. To measure the vibration response of the sectional model, aerodynamic forces, and real-time wind speed in the wind tunnel, two laser displacement sensors [41], a high-frequency force balance [42], and a TFI series 100 cobra probe [43] were employed, respectively.
The sectional model used in this investigation was selected from the middle section of the truss girder and was constructed to a scale of 1:55, with a length of 2.2 m, as shown in Figure 5. To ensure accurate experimental results, the sectional model was designed to match the actual aerodynamic shape of the bridge [44]. A spring-suspended sectional model (SSSM) system was developed to simulate vertical and torsional vibrations precisely, as depicted in Figure 6. The sectional model was suspended from the angle-of-attack turntable using eight springs through two steel brackets, with independent vertical and torsional displacements. Additionally, the aspect ratio of the sectional model was 4.0, and the end plates were not installed according to the Chinese design specification [45]. The weight and distribution of the counterweight blocks were adjusted to achieve the required equivalent mass and mass moment of inertia. Adjusting the spring stiffness and spacing ensured the appropriate vertical and torsional vibration frequency and frequency ratio of the sectional model. Furthermore, the actual-to-experimental wind speed ratio was reduced by increasing the spring stiffness, which was 4.48 in this test. The wind speed for the force test was set to 10.0 m/s, while the wind speed for the vibration test was gradually increased from 0 to 10.0 m/s, with a wind loading range of 0.2 m/s. When VIV occurred, the wind loading range was reduced to 0.1 m/s. Table 2 shows the critical design parameters of the SSSM system.

3.2. Wind Tunnel Test Results of Original Cross-Section

3.2.1. Force Test Results

In this research, the body axis coordinate system was adopted, and the positive directions of the pitch moment FM, drag force FD, and lift force FL are shown in Figure 7. The aerodynamic coefficients are defined as follows:
CM = FM/(0.5ρU2B2),
CD = FD/(0.5ρU2D),
CL = FL/(0.5ρU2B).
where U represents wind speed; ρ represents air density; and D and B represent the width and height of the sectional model, respectively. The static aerodynamic coefficients of the sectional models in the construction and completion states are shown in Figure 8. These coefficients will be used to verify the accuracy of the numerical simulation results later.

3.2.2. Vibration Test Results

Wind tunnel tests were conducted to measure the VIV responses of the sectional model in the construction and completion states at five wind angles of attack, 0°, ±3°, and ±5°, and the results are presented in Figure 9 and Figure 10. No VIV was observed in the tests for the construction stage model, while significant VIV occurred in the completion stage model at +3° and +5°. The addition of various accessory elements such as railings, maintenance vehicle tracks, and sidewalk corbels significantly degraded the truss girder’s aerodynamic performance, resulting in significant VIV. The completion stage sectional model tests revealed two forms of VIV: vertical VIV appeared first, followed by torsional VIV. Unlike vertical VIV, which has only one locking range, torsional VIV has two locking ranges with significant differences in amplitude, named major locking range and minor locking range, respectively. With an increase in wind angle of attack from +3° to +5°, the maximum amplitude of vertical VIV and major torsional VIV increased significantly, while minor torsional VIV increased slightly. Furthermore, the length of the vertical VIV locking range and the starting wind speed did not change significantly, while the starting wind speed of the torsional VIV was significantly delayed. No obvious VIV phenomenon was observed under the three angles of attack of 0°, −3°, and −5°.
To investigate the vibration frequency of the truss girder subjected to VIV, displacement time-history curves at the peak response points were obtained using two laser displacement sensors, and the corresponding amplitude spectra were analyzed, as shown in Figure 11. The amplitude time-history curves displayed a clear single frequency of simple harmonic equal amplitude vibration. The laser displacement sensors recorded time-history curves with the same phase for vertical VIV, while for torsional VIV, the sensors recorded time-history curves in the opposite phase. Furthermore, the vortex shedding frequency will be locked during the VIV [46]. The characteristic frequencies of 2.23 Hz and 4.29 Hz for vertical and torsional VIV, respectively, were observed when the VIV occurred, and these frequencies were found to be close to the natural frequencies of the sectional model. The phenomenon indicates that different vortices with different shedding frequencies might drive the vertical and torsional VIV of the bridge.

3.3. VIV Characteristics with Different Railing Ventilation Rates

3.3.1. Working Condition Setting

In the original section, VIV occurred only at +3° and +5° wind angles of attack. Therefore, the impact of railing ventilation rates on the VIV of the truss girder was examined at these two angles. Three types of lattice railings with ventilation rates of 66.7%, 50.0%, and 33.3%, as well as an airtight railing with a ventilation rate of 0.0%, were utilized in this research. The pedestrian ventilation rate was decreased by increasing the horizontal bars. The original bridge design of the completion stage adopted a pedestrian railing with a ventilation rate of 66.7%. The ventilation rate of the anti-collision railing and the upper deck edge railing, which had a weak impact on VIV, was not altered [47,48]. Figure 12 displays the schematic diagram of the railings utilized in this investigation.

3.3.2. Test Results

Figure 13 illustrates the wind tunnel test results of the truss girder with various railing ventilation rates, where the values correspond to the actual situation.
Figure 13 demonstrates that as the pedestrian railing ventilation rates decrease, the maximum amplitude of both vertical and torsional VIV decreases. Specifically, the vertical VIV is only slightly affected by the change in railing ventilation rate, with a slightly reduced maximum amplitude and no change in the length of the locking range or starting wind speed. The airtight railing has the most significant effect on suppressing vertical VIV, with reductions of 22.7% and 24.8% at +3° and +5°, respectively. Decreasing the railing ventilation rate significantly reduces the maximum amplitude of both major and minor locking ranges of torsional VIV, slightly shortens the length of the major locking range, and increases the starting wind speed. Table 3 displays the different ventilation rates’ effects on torsional VIV. Similarly, the airtight railing has the most pronounced suppression effect, with the major and minor torsional VIV suppression effects at +5°, reaching 71.6% and 78.7%, respectively, and the minor torsional VIV being almost entirely eliminated.
To analyze the VIV occurrence mechanism, we calculated the Strouhal number of the truss girder when VIV occurred, defined as
St = fD/U,
and the results are presented in Table 4 [49]. The values show that changing the railing ventilation rate does not alter the Strouhal number of the girder section corresponding to the primary peak of vertical VIV, suggesting that the railing ventilation rate minimally impacts the primary vortex driving the bridge to vertical VIV. However, the primary vortex driving torsional VIV was influenced.

4. Vortex Shedding Characteristics by Numerical Simulations

With the advancement of computer technology, CFD simulation has become increasingly efficient and accurate. CFD simulation offers the ability to visualize fluid flow characteristics, to handle complex disturbance problems, and to explain the causes of various fluid phenomena. Consequently, it has been widely used in the study of wind-induced vibration of bridges [50,51]. Due to the difficulty of establishing an accurate 3D model of the truss girder, this research employed ANSYS Fluent 15.0 [52] to conduct 2D CFD simulations. A 2D CFD model with a scaling ratio of 1:55, identical to the experimental sectional model, was established. Although the truss girder section was simplified to some extent and discontinuous members such as stiffening ribs were neglected, the equivalent total area of wind action in the vertical direction and the flow field disturbance by the horizontal members were consistent with the experimental model. The simplification was appropriate and improved the calculation efficiency without compromising the accuracy of the results, which is still an effective method to investigate the VIV of bridges [53,54].

4.1. Solution Setting and Mesh Division

The CFD simulation utilized transient calculations, with the corresponding mathematical model being the Reynolds time-averaged Navier–Stokes equation. The SST k-ω model served as the turbulence model, while the Coupled algorithm was used for pressure–velocity coupling [55]. The second-order windward interpolation was employed as the discrete format, and the computational residual was controlled to 1 × 10−5. A sufficiently small time step was necessary to capture the more minor non-constant flow field characteristics and to ensure calculation accuracy. However, excessively small time steps would significantly reduce calculation efficiency. After conducting trial calculations, a time step of 1 × 10−4 s was selected to meet the Coulomb number requirement [28,29].
The computational domain mesh was generated using the preprocessing software ICEM 15.0, with the computational domain taking the form of an overlapping external and internal region [56]. The external region was 15B long and 15D high, with the inlet boundary being the velocity inlet located 5B from the center of the section and the outlet boundary being the pressure outlet located 10B from the center. The upper and lower boundaries were considered free-slip symmetric boundaries, positioned 7.5D from the center of the section. A structured mesh was employed, and the external region was large enough to minimize the boundary’s impact on the internal region’s flow field. The internal region was 2B long and 2D high, using an unstructured mesh. The outer wall of the truss girder section and accessory members were treated as smooth wall boundaries. Figure 14 shows the boundary conditions of the computational domain. The number of meshes significantly influenced the calculation results, with excessively sparse meshes affecting calculation accuracy and overly dense meshes significantly increasing the calculation volume and reducing calculation efficiency. This research set the maximum mesh size in the internal region to 6 × 10−3 mm. To meet the computational needs of the SST k-ω turbulence model, a boundary layer mesh was positioned at the wall surface. The boundary layer consisted of 12 layers with a linear growth rate of 1.2 for the section and accessory components, with the height of the first layer taken as 5 × 10−5 mm to ensure a smooth transition of the near-wall mesh [57]. The total number of meshes was 0.22 million, which was sufficient after the trial calculation [28,29]. Furthermore, the Y-plus values of the truss girder section were all less than one, indicating that the mesh division met the requirements of the SST k-ω model [58]. Figure 15 displays the computational domain mesh division.

4.2. Accuracy Verification of Calculation Results

Truss girders have a continuously changing cross-section with the length direction of the bridge, resulting mainly from the web member position changes. To investigate the impact of web member position on the calculation results, three cross-sections were selected for CFD simulations, with web members located at 0.25D, 0.5D, and 0.75D from the upper chord, as shown in Figure 16. The simulations were performed using wind angles of attack of +3° and +5°, and a wind speed of 2.23 m/s (equivalent to an actual wind speed of 10.0 m/s, consistent with the wind speed used in the force tests conducted in the wind tunnel). The aerodynamic coefficients were averaged over 5 s after the calculation converged, and the results are presented in Table 5. The findings indicate that the differences between the aerodynamic coefficients of the three cross-sections are within 5%. Moreover, the web member position does not produce significant differences in the calculation results. Consequently, subsequent calculations were conducted using 2-2 cross-sections.
To validate the model’s reliability, five different wind angles of attack were used to calculate the aerodynamic coefficients at a wind speed of 2.23 m/s (equivalent to an actual wind speed of 10.0 m/s, consistent with the wind speed used in the force tests conducted in the wind tunnel). The calculated results were compared with the wind tunnel test results, and the findings are presented in Table 6.
Table 6 shows that the maximum error between the simulation and test values is 9.14%, while the minimum error is 0.34%. The drag coefficient has an average error of 3.51%, the lift coefficient has an average error of 3.85%, and the moment coefficient has an average error of 6.15%. The overall average error is 4.50%, indicating that the simulation results have a small error. Therefore, the chosen algorithm and the mesh division of the CFD simulation are feasible and can be used to analyze the flow characteristics near the girder cross-section.

4.3. Numerical Analysis of VIV Performance

Figure 17 and Figure 18 depict the static flow around vortex distribution at the peak response point of the vertical VIV at +3° and +5° wind angles of attack for the cross-section during the construction and completion stages. The construction stage section demonstrates good aerodynamic performance, with the incoming flow producing a vortex only behind the lower chord. The remaining section does not produce a vortex of sufficient strength and scope. Hence, the wake cannot produce a sufficiently sizeable vortex-induced force, leading to the absence of the VIV phenomenon in the construction stage section. However, the presence of the railing, maintenance vehicle track, and sidewalk corbel causes non-negligible vortices near these accessory structures, which continue to shed to the wake. As a result, the intensity and range of wake vortices are significantly higher than those of the construction stage section. Among the vortex shedding of various frequencies and sizes, one vortex with a shedding frequency similar to the natural frequency of the truss girder drives the VIV at +3° and +5° wind angles of attack in the completion stage section.
In order to find these vortices that cause VIV in the truss girder, 29 measurement points were positioned at various locations close to the girder to record wind speed time-history curves. The placement of the measurement points is depicted in Figure 19. Specifically, measurement points P1–P13 were situated around the upper deck plate, while P14 and P15 were positioned behind the windward and leeward diagonal bracing members, respectively. Measurement points P16–P29 encircled the lower deck, with P23 and P29 behind the maintenance track. Table 7 presents the characteristic frequencies of wind speed time-history curves recorded at measurement points and their corresponding Strouhal numbers.
The Strouhal number of measurement points P1–P6 and P13 is 0.51, consistent with the Strouhal number of 0.47 observed at the peak response point of vertical VIV during wind tunnel tests. Similarly, the Strouhal numbers of measurement point P22 are 0.31 and 0.64, corresponding to the Strouhal numbers of 0.36 and 0.64 for minor and major torsional VIV in the tests, respectively. The above phenomenon indicates that the vortex shedding in the wake area of the upper deck or above the upper deck may cause the vertical VIV of the truss girder, while the vortex shedding in the wake area of the lower deck may cause the torsional VIV. Therefore, optimizing the sections in these areas should be prioritized when considering aerodynamic measures to suppress VIV in truss girder bridges.

4.4. Influence Mechanism of the Railing Ventilation Rate

Wind tunnel tests revealed that decreasing the pedestrian railing ventilation rate suppressed the torsional VIV response of the truss girder significantly. The wind speed time-history curve recorded by measurement point P22 indicates a frequency close to the first-order torsional fundamental frequency of the truss girder, suggesting that vortex shedding in the wake region of the lower deck may dominate the torsional VIV. Reducing the railing ventilation rate may disrupt this region’s original pattern of vortex shedding. In order to investigate the mechanism behind this vibration suppression, numerical simulations were conducted on the girder cross-section using various pedestrian railing ventilation rates, and the resulting flow fields were analyzed. The simulations were conducted with a wind angle of attack of +5° and a wind speed of 16.67 m/s (equivalent to an actual wind speed of 16.67 m/s, consistent with the major torsional VIV peak response point wind speed in the wind tunnel tests). This working condition produced the most significant torsional VIV in the wind tunnel tests. Figure 20 displays the variation in vorticity contours in the wake region of the lower deck in a complete vortex shedding cycle.
Reducing the pedestrian railing ventilation rate alters the vortex shedding mode in the wake region of the lower bridge deck significantly: the vortex intensity at the top of the railing decreases markedly; the blocking effect of the railing increases, and the vortices generated by the airflow passing through the gap of the railing were gradually decreased to zero; the vortex on the sidewalk surface also decreases significantly with the reduction in the gap of the railing until it vanishes when using an airtight railing; and the slowed airflow above the lower bridge deck reduces the pressure difference on the upper and lower sides of the bridge deck, leading to a marked reduction in the strength of the vortex behind the lower chord. Overall, the decrease in the railing ventilation rate reduces the vortex intensity and quantity in the wake region of the lower bridge deck, resulting in weak vortex shedding. Figure 21 displays the frequency spectrum analysis of wind speed time histories detected at the measurement point P22. The vortex shedding frequency at this point did not change significantly, consistent with wind tunnel tests, but the amplitude decreased considerably, indicating a marked reduction in vortex intensity. When the pedestrian railing ventilation rate was zero, the amplitude of the peak corresponding to the minor torsional VIV was almost zero, possibly due to the significant reduction in vortex because of the inability of flow to pass through the railing, resulting in the nearly complete disappearance of minor torsional VIV in wind tunnel tests. The torsional VIV of the truss girder at low wind speeds may be related to vortex shedding caused by flow passing through the railing gap and vortex shedding at the top of the railing. Furthermore, the torsional VIV at high wind speeds may be related to vortex shedding caused by flow being blocked by the lower chord. By reducing the railing ventilation rate, the vortex intensity and quantity in the wake region of the lower bridge deck decrease significantly, achieving the goal of suppressing VIV. Currently, Chinese design codes provide for the minimum height, railing form, and crashworthiness of bridge railings, but there are no recommendations for aerodynamic performance [45,59]. The findings of this investigation suggest prioritizing railings with a low ventilation rate during the design of railings for double-deck truss girder suspension bridges to mitigate potential VIV issues. However, it is necessary to further investigate whether reducing the railing ventilation rate causes other wind-induced vibration problems.

5. Conclusions

This article investigates the influence of railing ventilation rate on VIV in a double-deck truss girder through wind tunnel tests and CFD simulations and presents the following principal conclusions.
(1)
The construction stage sectional model did not exhibit any VIV during the wind tunnel tests. Conversely, the completion stage sectional model demonstrated significant VIV at +3° and +5° wind angles of attack, with one vertical VIV locking range and two torsional VIV locking ranges. The maximum vertical VIV amplitude was 98 mm, while the maximum torsional VIV amplitude was 0.21°. Moreover, the vertical VIV frequency was locked at 2.23 Hz, while the torsional VIV frequency was locked at 4.29 Hz.
(2)
Wind tunnel tests demonstrate that decreasing the railing ventilation rate has a suppressing effect on VIV, with the maximum suppression effect occurring at the railing ventilation rate of zero. Among them, the suppression effect on vertical VIV is weak, with maximum suppression rates of 22.7% and 24.8% at +3° and +5°, respectively. The suppression effect on torsional VIV is significant. At +3° and +5°, the maximum suppression of minor torsional VIV is 78.5% and 78.7%, respectively, and the maximum suppression of major torsional VIV is 71.3% and 71.6%, respectively.
(3)
Comparing the vorticity contours of the construction stage and completion stage sections, it is evident that the wake vortices’ intensity and range are significantly higher in the completion stage section, leading to VIV occurrence. Various vortices with different frequencies and sizes were generated after each discrete member of the completion stage section. It is plausible that the vortex shedding above the upper deck or in the wake area of the upper deck leads to vertical VIV, whereas the vortex shedding in the wake area of the lower deck leads to torsional VIV.
(4)
Numerical analysis of the truss girder cross-section with different railing ventilation rates found that minor torsional VIV may be related to vortex shedding from the railing gap and the top of the railing, and major torsional VIV may be related to vortex shedding from behind the lower chord. Decreasing the railing ventilation rate reduces vortex intensity and volume in the wake region of the lower deck significantly, thereby suppressing VIV.

Author Contributions

Conceptualization, G.Y.; methodology, G.Y., Y.C. and Y.Y.; software, Y.C. and H.D.; validation, G.Y. and Y.C.; formal analysis, G.Y.; investigation, G.Y. and Y.Y.; resources, Y.Z.; data curation, Y.C. and L.W.; writing—original draft preparation, Y.C.; writing—review and editing, G.Y. and Y.Y.; visualization, Y.C. and L.W.; supervision, Y.Y. and Y.Z.; project administration, Y.Y.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Chongqing City Infrastructure Construction Investment Co., Ltd., grant number CQCT-JSA-GC-2021-0140.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Technology roadmap.
Figure 1. Technology roadmap.
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Figure 2. Schematic diagram of the Huangjuetuo Bridge (unit: mm). (a) elevation of the bridge. (b) cross-sectional view of the bridge.
Figure 2. Schematic diagram of the Huangjuetuo Bridge (unit: mm). (a) elevation of the bridge. (b) cross-sectional view of the bridge.
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Figure 3. Three-dimensional finite element model.
Figure 3. Three-dimensional finite element model.
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Figure 4. DC wind tunnel at Chongqing University.
Figure 4. DC wind tunnel at Chongqing University.
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Figure 5. Construction and completion stage sectional model. (a) construction stage. (b) completion stage.
Figure 5. Construction and completion stage sectional model. (a) construction stage. (b) completion stage.
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Figure 6. The SSSM system used in the tests.
Figure 6. The SSSM system used in the tests.
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Figure 7. Positive directions of aerodynamic forces.
Figure 7. Positive directions of aerodynamic forces.
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Figure 8. Aerodynamic coefficient of the truss girder. (a) construction stage. (b) completion stage.
Figure 8. Aerodynamic coefficient of the truss girder. (a) construction stage. (b) completion stage.
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Figure 9. VIV responses of the construction stage (converted to actual bridge values). (a) vertical responses. (b) torsional responses.
Figure 9. VIV responses of the construction stage (converted to actual bridge values). (a) vertical responses. (b) torsional responses.
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Applsci 13 09314 g010
Figure 10. VIV responses of the completion stage (converted to actual bridge values). (a) vertical responses. (b) torsional responses.
Figure 10. VIV responses of the completion stage (converted to actual bridge values). (a) vertical responses. (b) torsional responses.
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Figure 11. VIV response time-history curves of completion stage.
Figure 11. VIV response time-history curves of completion stage.
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Figure 12. Schematic diagram of the railings. (a) edge railing. (b) anti-collision railing. (c) pedestrian railing.
Figure 12. Schematic diagram of the railings. (a) edge railing. (b) anti-collision railing. (c) pedestrian railing.
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Figure 13. VIV responses of the truss girder with different pedestrian railing ventilation rates (converted to actual bridge values). (a) vertical responses at +3°. (b) vertical responses at +5°. (c) torsional responses at +3°. (d) torsional responses at +5°.
Figure 13. VIV responses of the truss girder with different pedestrian railing ventilation rates (converted to actual bridge values). (a) vertical responses at +3°. (b) vertical responses at +5°. (c) torsional responses at +3°. (d) torsional responses at +5°.
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Figure 14. The computational domain boundary conditions.
Figure 14. The computational domain boundary conditions.
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Figure 15. The computational domain mesh division.
Figure 15. The computational domain mesh division.
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Figure 16. Three cross-sections of the truss girder for the trial calculation.
Figure 16. Three cross-sections of the truss girder for the trial calculation.
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Figure 17. Vorticity contour of construction stage at a certain moment. (a) α = +3°. (b) α = +5°.
Figure 17. Vorticity contour of construction stage at a certain moment. (a) α = +3°. (b) α = +5°.
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Figure 18. Vorticity contour of completion stage at a certain moment. (a) α = +3°. (b) α = +5°.
Figure 18. Vorticity contour of completion stage at a certain moment. (a) α = +3°. (b) α = +5°.
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Applsci 13 09314 g019
Figure 19. Layout of measurement points.
Figure 19. Layout of measurement points.
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Figure 20. Vorticity contours in the wake region of the lower deck in a complete vortex shedding cycle. (a) railing ventilation rate = 66.7%. (b) railing ventilation rate = 50.0%. (c) railing ventilation rate = 33.3%. (d) railing ventilation rate = 0.0%.
Figure 20. Vorticity contours in the wake region of the lower deck in a complete vortex shedding cycle. (a) railing ventilation rate = 66.7%. (b) railing ventilation rate = 50.0%. (c) railing ventilation rate = 33.3%. (d) railing ventilation rate = 0.0%.
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Figure 21. Variations in the wind speed characteristic frequency recorded at measurement point P22.
Figure 21. Variations in the wind speed characteristic frequency recorded at measurement point P22.
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Table 1. Primary vibration modes and frequencies of the suspension bridge.
Table 1. Primary vibration modes and frequencies of the suspension bridge.
Order NumberVibration Mode *Frequency (Hz)Vibration Mode (Front View)
31-S-V0.211Applsci 13 09314 i001
41-AS-V0.237Applsci 13 09314 i002
82-S-V0.402Applsci 13 09314 i003
111-S-T0.478Applsci 13 09314 i004
202-AS-V0.571Applsci 13 09314 i005
251-AS-T0.706Applsci 13 09314 i006
* S: symmetric; AS: antisymmetric; V: vertical; T: torsional.
Table 2. Parameters of the SSSM system.
Table 2. Parameters of the SSSM system.
ParameterSymbolUnitScaling FactorPrototypeModel
WidthBm1:5531.30.569
HeightDm1:5515.80.286
Radius of gyrationrm1:5513.830.251
Massmkg/m1:5526.85 × 10422.628
Mass moment of inertiaImkg·m2/m1:5541.31 × 1071.431
Vertical frequencyfhHz/0.2112.22
Torsional frequencyftHz/0.4785.03
Frequency ratiofh/ft//2.272.27
Vertical damping ratioξh%/0.50.27
Torsional damping ratioξt%/0.50.41
Table 3. Torsional VIV responses and vibration suppression amplitude for different pedestrian railing ventilation rates.
Table 3. Torsional VIV responses and vibration suppression amplitude for different pedestrian railing ventilation rates.
Ventilation RateMinor Peak at +3°Major Peak at +3°Minor Peak at +5°Major Peak at +5°
66.7%0.079°/0.181°/0.089°/0.211°/
50.0%0.060°24.1%0.154°14.9%0.066°25.8%0.177°16.1%
33.3%0.042°46.8%0.113°37.6%0.047°47.2%0.128°39.3%
0.0%0.017°78.5%0.052°71.3%0.019°78.7%0.060°71.6%
Table 4. St for the girder at different working conditions.
Table 4. St for the girder at different working conditions.
Railing Ventilation Rate66.7%50.0%33.3%0.0%
Wind Angle of Attack+3°+5°+3°+5°+3°+5°+3°+5°
St for vertical VIVMajor peak0.470.470.470.470.470.470.470.47
St for torsional VIVMinor peak0.640.600.630.590.630.590.620.58
Major peak0.360.330.350.330.350.320.340.31
Table 5. The aerodynamic coefficients simulation values of three cross-sections.
Table 5. The aerodynamic coefficients simulation values of three cross-sections.
Wind Angle of Attack 1-12-23-3
+3° C _ D 0.57950.58130.5917
C _ L 0.84160.86220.8498
C _ M 0.02790.02850.0291
+5° C _ D 0.63620.63910.6180
C _ L 1.05041.04721.0373
C _ M 0.04110.04190.0433
Table 6. Comparisons of test and simulation values of aerodynamic coefficients.
Table 6. Comparisons of test and simulation values of aerodynamic coefficients.
Wind Angle of Attack−5°−3°0°+3°+5°
C _ D Test value0.64040.63740.65310.63980.6672
Simulation value0.62330.62910.65090.58130.6391
Error2.67%1.20%0.34%9.14%4.21%
C _ L Test value−0.8520−0.42760.29890.89481.1012
Simulation value−0.8184−0.41280.28900.86221.0472
Error3.94%3.46%3.31%3.64%4.90%
C _ M Test value−0.1039−0.0889−0.01530.03100.0451
Simulation value−0.0998−0.0841−0.01450.02850.0419
Error3.95%5.40%5.23%9.08%7.09%
Table 7. Characteristic frequency and Strouhal number of measurement points.
Table 7. Characteristic frequency and Strouhal number of measurement points.
Measurement PointFrequency (Hz)St
P221.47, 3.080.31, 0.65
P1–P6, P132.390.51
P23–P294.941.04
P23, P297.361.56
P1~P12, P16–P21, P24–P298.561.81
P14, P1510.022.11
P11, P1211.642.47
P1–P3, P7–P9, P14, P16–P1915.023.18
P1–P3, P23–P2518.553.92
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Yao, G.; Chen, Y.; Yang, Y.; Zheng, Y.; Wu, L.; Du, H. Research on Mechanism of Vortex-Induced Vibration Railing Effect of Double-Deck Large-Span Suspension Bridge. Appl. Sci. 2023, 13, 9314. https://doi.org/10.3390/app13169314

AMA Style

Yao G, Chen Y, Yang Y, Zheng Y, Wu L, Du H. Research on Mechanism of Vortex-Induced Vibration Railing Effect of Double-Deck Large-Span Suspension Bridge. Applied Sciences. 2023; 13(16):9314. https://doi.org/10.3390/app13169314

Chicago/Turabian Style

Yao, Gang, Yuxiao Chen, Yang Yang, Yuanlin Zheng, Linjun Wu, and Hongbo Du. 2023. "Research on Mechanism of Vortex-Induced Vibration Railing Effect of Double-Deck Large-Span Suspension Bridge" Applied Sciences 13, no. 16: 9314. https://doi.org/10.3390/app13169314

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