Introduction
Bridges with two separated parallel decks have been built to accommodate increasing traffic flow, and it has been observed that aerodynamic interferences exist between the two neighboring decks and that the interference behavior depends on the distance between the two decks [
1-
5]. If the two bridge decks are close enough to each other, the surrounding flows around one bridge deck are influenced by another, and vice versa. Consequently, the vortex-induced vibration (VIV) of each deck, which is typically excited by cross winds at a relatively low velocity and is sensitive to the surrounding flows, is inevitably and significantly affected by another deck [
1].
Most of the relevant studies have focused extensively on revealing the complicated behavior of the aerodynamic interference phenomenon; however, few suggestions have been provided that describe how to mitigate the VIV amplitudes of two neighboring parallel decks; the aerodynamics of each deck is significantly affected by the other deck. Thus, using the two neighboring Haihe Bridges as an example, the influence of the aerodynamic interference between the two decks on the VIV responses and the corresponding aero-dynamic mitigation measures were initially investigated via a series of wind tunnel tests with a spring-suspended sectional model. The computational fluid dynamics (CFD) method was then employed to visualize the flow patterns around still decks, which were further utilized to explore the mechanisms of some aerodynamic interference phenomena observed in the tests.
Summary of the two adjacent Haihe Bridges
The existing Haihe Bridge in Tanggu of Tianjing, China is a single tower cable-stayed bridge with a main span of 310 m (Fig. 1) and a semi-closed steel box deck (Fig. 2). To accommodate the increasing traffic flow, a similar cable-stayed bridge with the same span length as the existing one and a fully closed steel box deck is now under construction, which is very close (11.3 m) to the existing bridge (Fig. 2). The deck widths (
B) of the existing and new bridges are, respectively, 24.17 m and 23.17 m in the original designs, and 23 m and 22 m barring two wind fairings. The central separation distance
X is 35.0 m, and
X/B is approximately 1.45-1.51, which is much less than 8. Therefore, the aerodynamic interference effect on the VIV performance of the two bridges is expected and should be taken seriously [
1].
Table 1 shows the modal properties of the existing and new bridges. The vertical fundamental natural frequencies of the existing bridge and the new bridge are 0.384 Hz and 0.386 Hz, respectively, which are very close to each other. The torsional frequencies are 1.110 Hz and 1.437 Hz. The latter is approximately 30% higher than the former.
Brief description of wind tunnel tests
All tests were carried out in smooth flows in the TJ-2 Boundary Layer Wind Tunnel at Tongji University (Fig. 3). In the test, two deck plans were considered for the new bridge to compare the influence of deck shape on the interference effect. The first design has a semi-closed box cross-section that is the same as that of the existing bridge and is referred to as “Plan A” in this paper. The second one has a fully closed box cross-section (Fig. 2), which was actually adopted for the new bridge and is referred to as “Plan B” in this paper.
Although many test cases of structural configurations were considered in the series tests, only 10 main cases are discussed in this paper. In Case 1, the single existing bridge was tested alone. In Case 2, the new bridge with the deck cross section of Plan A was put together and tested with the existing bridge at the specified relative position. The windward and leeward bridge decks were the same in this case. In Case 3 and Case 4, the new bridge with the deck cross section of Plan B was put together and tested with the existing bridge. The new bridge was located on the windward side in Case 3 and on the leeward side in Case 4. Case 5 through Case 10 were designed to investigate aerodynamic mitigation measures and are introduced below. The length scale of the sectional model test was 1/50 for Case 1‒Case 3 and 1/45 for the rest. The corresponding velocity scales were approximately 1/3.1 for Case 1‒Case 3 and approximately 1/4.3 for the remaining cases.
Results and discussions
Aerodynamic interference on vortex induced vibrations
The test results show that the maximum VIV responses occurred in the case of a+3° wind attack angle for the single bridge and the existing and new bridges at either of the leeward or windward positions. Figures 4(a) and (b) show, respectively, the measured curves of vertical and torsional VIV amplitudes vs. wind speed. The maximum amplitudes of both bridges in different conditions are illustrated in Fig. 5. It can be seen from the figures that the aerodynamic interference effect is notable in the vertical and torsional VIV responses of the leeward bridge but is not significant for the windward bridge.
For Case 1 with a single existing bridge, it is evident from Fig. 4 that the vertical VIV has two lock-in ranges of wind velocity between 9 and 11.5 m/s and 15 and 21.5 m/s, while the torsional VIV has two ranges of lock-in wind velocity between 21 and 23 m/s and 27 and 40 m/s. The corresponding two peak values are 0.076 m and 0.099 m for the vertical VIV and 0.083° and 0.338° for the torsional VIV.
For Case 2, in which the existing and new bridge decks are the same, the aerodynamic interference significantly amplifies the maximum VIV amplitudes of the leeward bridge deck by 141.1% for the vertical interference and 485.8% for the torsional interference compared to those of the single existing bridge (Case 1). However, the interference effect has relatively little influence on the maximal VIV amplitudes of windward bridges; the increase is only 18.6% for the vertical interference and 20.4% for the torsional interference. Moreover, it can be found from Fig. 4 that the variation of the lock-in ranges of wind velocity due to the interference is insignificant in this case for both the vertical and torsional VIV of the windward and leeward bridges.
For Case 3, in which the windward new bridge has the deck of Plan B, the two velocity lock-in ranges of the vertical VIV are minimally affected by interference. For the torsional VIV, the 1st velocity lock-in range observed in Case 1 and Case 2 almost vanishes for both the windward new bridge and the leeward existing bridge. The 2nd one, meanwhile, is narrowed to 26-30 m/s for the leeward existing bridge and increases to 36-47 m/s for the windward new bridge. The notable increase of the 2nd velocity lock-in range is not because of the interference but rather the significant increase in the torsional natural frequency of the new bridge by approximately 30% compared with that of the existing bridge. Furthermore, compared with the maximum VIV amplitudes in Case 1, the maximum VIV amplitude of the leeward existing bridge increases by approximately 26.0% for the vertical VIV and decreases by approximately 49.5% for the torsional VIV, due to the interference effect. However, the maximum vertical and torsional VIV amplitudes of the windward new bridge are close to those of the single bridge in Case 1.
For Case 4, in which the leeward new bridge uses the deck of Plan B, variations in the velocity lock-in ranges due to the aerodynamic interference are similar to those in Case 3 for the windward and leeward bridges. The aerodynamic interference does not significantly affect the maximum vertical and torsional VIV amplitudes of the windward existing bridge but reduces the maximum vertical VIV amplitude of the leeward new bridge by approximately 36% and almost completely eliminates the torsional VIV phenomenon of the leeward new bridge.
Therefore, the aerodynamic interference between two adjacent bridge decks does not significantly affect the VIV responses of the windward bridge, and adopting the same structural and aerodynamic configurations for the parallel neighboring bridges causes unfavorable VIV responses on the leeward bridge because the small vibration of the windward bridge can stimulate large vibration of the leeward bridge when the two bridges have the same or similar natural modal properties. However, if the two adjacent bridges are obviously different in their configurations and thus in their natural modal properties, the aerodynamic interference generally has a positive influence and reduces the VIV responses of the leeward bridge.
Aerodynamic mitigation measure for VIV
Although the VIV responses of the two neighboring bridges did not deteriorate when the deck of Plan B was adopted for the new bridge, the maximum vertical and torsional VIV amplitudes, 0.125 m and 0.39° for the existing bridge and 0.090 m and 0.30° for the new bridge, were still unacceptably large to the engineers of the bridge. Therefore, an effective and feasible aerodynamic mitigation measure was needed to sufficiently reduce the vertical and torsional VIV amplitudes of both bridges, whether they are on the windward side or on the leeward side. A combined aerodynamic countermeasure of adding wind barriers on two parapets of each deck (Fig. 6) and sharpening wind fairing noses of the two box decks (Figs. 7 and 8), which meet the requirement, were implemented after testing various countermeasures. The test cases of the combined countermeasures with different angles of faring noses (Case 5‒Case 10) and the corresponding response amplitudes are listed in Table 2 together with those of Case 3 and Case 4 without any countermeasures to demonstrate the efficiency of the proposed countermeasures.
It was found that the torsional VIV of both bridges, whether they were on the leeward side or on the windward side, disappeared for any wind attack angle between -3° and 3° after adopting the combined countermeasures listed in Table 2. However, the effects of the countermeasures on the vertical VIV responses were somewhat complicated. Figure 9 shows the vertical VIV amplitudes vs. wind speed of the two bridge decks with different countermeasures. It is interesting to note that both the nose shape of the wind fairing and the relative position between the two decks significantly affect the maximum amplitude of each deck and the lock-in range of the wind speed to some extent. For example, if the wind attack angle is -3° and the new bridge is on the windward side, the maximum amplitudes are 0.120 m and 0.109 m, respectively, for the existing and new bridges in Case 5, in which the nose angle of the new bridge deck was sharpened from 80.5° to 40° while that of the existing bridge deck was not changed. The lock-in ranges of wind speed were approximately 13-18 m/s for both bridges. If the nose angle of the existing bridge deck was also sharpened from 80.5° to 40° at the same time (Case 7), the maximum amplitudes are reduced to 0.054 m and 0.074 m, and the lock-in ranges of wind speeds are approximately 15-18 m/s. Furthermore, if the nose angle of the existing bridge deck was changed to 70° while that of the new bridge deck remained 40° (Case 9), the maximum amplitudes were reduced to 0.045 m and 0.021 m, and the lock-in ranges of wind speeds were approximately 15-19 m/s. Similar phenomena were also observed in other cases.
Figure 10 compares the VIV amplitudes of the bridges with and without the above-mentioned combined countermeasures. It can then be seen that the aerodynamic countermeasure of added wind barriers combined with sharpening the fairing nose angles to 40° for the new bridge deck with a fully closed box and to 70° for the existing bridge deck with a semi-closed box, which is adopted in the Case 9 and Case 10, can reduce the VIV amplitudes most efficiently for the winds from both sides for all the tested measures. With the combined aerodynamic measures, the maximum vertical VIV amplitudes of the existing and new bridges are 0.066 m and 0.065 m, respectively, which occurs in the case of a wind attack angle of -3° and the new bridge on the leeward side. Compared to those without any countermeasure (Case 3 and Case 4), which are 0.125 m and 0.090 m, respectively, and occur in the case of a+ 3° wind attack angle and the new bridge on the windward side, the best countermeasure reduces the VIV amplitudes of the existing and new bridges by 47% and 28%, respectively.
Numerical simulation results
To explain the phenomena observed in the wind tunnel tests, the flow pattern around the still bridge deck(s) was simulated numerically using FLUENT; the 2D large eddy simulation (LES) method with the Smagorinsky sub-grid scale (SGS) model was employed for the turbulence model.
Figures 11 and 12 show the visualized flow patterns around the single semi-closed box deck and single fully closed box deck without any countermeasure. For the semi-closed box deck, it can be seen that the flow separation occurs at the upper edge of the front wind fairing, which causes vortices to form that continue to grow while traveling to the leeward side of the bridge deck. Furthermore, large vortices are evident in the middle open cavity and beneath the lower oblique box web at the leeward side. Moreover, the windward overhaul rail mounted beneath the lower oblique box web can also generate a series of moving vortices along the deck.
For the fully closed box deck, a similar vortex distribution to that around the semi-closed box can be seen in Fig. 12, except that the large vortices circling in the middle open cavity disappear due to the closure of the deck. Moreover, the vortices generated by the fully closed box deck seem relatively large and fewer than those by the semi-closed box deck.
Figure 13 shows the visualized flow pattern around the double semi-closed box decks. It can be seen that the flow patterns around both the windward and leeward decks are significantly different from that around the single deck. The aerodynamic interference causes the vortices in the surrounding flow around the double decks to increase and become more regular than those surrounding the single deck and generates additional large eddies in the region between the decks. This interference inevitably increases the vortex-excited forces on both decks and consequently amplifies the VIV responses.
Furthermore, the vortex-excited forces on the leeward deck are composed of three interacting vortices because they are immerged in the wake flow of the windward deck. The first vortex is generated by the leeward deck itself. The second is inherently in the wake flow of the windward deck but is affected aerodynamically by the leeward deck. The third vortex is generated by the aerodynamic interaction between the two decks, such as that existing in the gap region between the two decks, which is not evident in the wake flow of a single deck. When the two bridges have the same aerodynamic configuration and natural frequencies, the frequencies of all three vortices are very close to the natural frequency of the bridge due to the lock-in effect. In this case, the VIV resonances of the two bridges are synchronous and magnified significantly, especially for the leeward bridge. In contrast, if the two bridges have different configurations and different natural frequencies, the frequencies of the second and third kinds of vortices, which are mainly controlled by the oscillation of the windward deck, deviate from the natural frequency of the leeward bridge. Thus, the VIV resonances of the two bridges are non-synchronous and weakened.
Conclusions
The following conclusions may be drawn based on the discussion provided in this paper:
The aerodynamic interference between two adjacent bridge decks can have a significant effect on the VIV responses of both bridges, and the extent of the interference varies with the shapes of the windward and leeward decks. The VIV amplitudes of the windward bridge are often fairly close to those of the single bridge. However, those of the leeward bridge are magnified substantially by aerodynamic interference if the same structural and aerodynamic configurations are adopted for the two bridges. Otherwise, if the two bridges have different configurations, the aerodynamic interference may not significantly amplify the VIV responses and can sometimes reduce the VIV responses.
The combined measure of adding wind barriers and sharpening the wind fairing noses of the two box decks is found to be very effective. It almost completely eliminates the torsional VIV of both bridges and reduces the maximal vertical VIV amplitudes of the existing and new bridges by 47% and 28%, respectively, compared to the original configuration of the new bridge with a fully closed box deck. It also changes the most unfavorable wind attack angle to the vertical VIV of both the windward and leeward bridges from+ 3°to -3°.
Higher Education Press and Springer-Verlag Berlin Heidelberg
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