Experimental Study of Wind Characteristics at a Bridge Site in Mountain Valley Considering the Effect of Oncoming Wind Speed

Abstract

The topography of mountainous areas is characterized by large undulations, which lead to a very complex wind field at bridge sites in mountain valleys. The influence of oncoming wind speed on long-span bridges built in mountain valleys is quite pronounced. To investigate the wind characteristics at a bridge site in a mountain valley under different oncoming wind speeds, a wind tunnel test of a terrain model with a scaling ratio of 1:1000, where a long-span bridge would be built in the V-shaped canyon, was conducted. Uniform and atmospheric boundary layer (ABL) inflows were both applied, and the effect of different oncoming wind speeds (basic wind speeds of 6 m/s, 8 m/s, 10 m/s, 12 m/s, and 14 m/s) under three wind directions (0°, 30°, and 180°) on the wind characteristics at the main beam and two bridge towers were studied. The results indicate that increasing oncoming wind speed leads to decreased wind profiles and wind speed amplification factors and increased wind attack angles, while wind yaw angles remain largely unchanged. In addition, compared to ABL inflow, the variation of fluctuating wind characteristics is more pronounced with the oncoming wind speed under uniform inflow. Under uniform inflow conditions, increasing the oncoming wind speed causes decreased turbulence intensity, reduces the peak frequency of the power spectrum, and slows down the high-frequency decay rate. Under ABL inflow conditions, turbulence intensity and the power spectrum remain unchanged with different oncoming wind speeds. Additionally, the turbulent integral scale derived from fitting with the von Kármán wind spectrum is sufficiently accurate, and the variation in the turbulent integral scale is greatly influenced by the terrain. Furthermore, higher wind speeds result in stronger coherence between two points. When two points are at different locations but with the same spacing, the coherence function remains roughly the same. Locations with higher kurtosis and skewness values exhibit steeper probability density functions, with larger kurtosis and skewness coefficients typically found on the leeward side. High wind speeds are more detrimental to bridge safety, and appropriate preventive measures should be implemented in advance to address extreme conditions that may arise at high wind speeds.

1. Introduction

Transportation is the foundation of economic development, and it enhances connectivity between regions and improves travel efficiency for residents [1]. Bridges play a pivotal role in transportation infrastructure, particularly the long-span bridge, which is able to cross natural obstacles and significantly improve transportation efficiency [2]. Meanwhile, due to the complex terrain and numerous natural obstacles, it is very inconvenient to travel for those living in mountain valleys. Therefore, the construction of bridges in mountain valleys is urgently needed. The bridges in mountain valleys are often characterized by long spans and low stiffness, which make them highly susceptible to wind disasters [3]. The current bridge design specifications [4] primarily cater to flat terrains such as plains, while for mountain valley terrains, the continued adoption of specifications solely applicable to flat terrains may result in the structural design of bridges being insecure. Therefore, it is necessary to refine the analysis of the wind characteristics at the bridge site in a mountain valley to enhance bridge safety.

To better control variables and obtain the pattern of turbulence development over terrain, the complex mountains and canyons are simplified to an ideal hill or ridge in many studies, and preliminary analysis and prediction of the wind characteristics near the simplified terrain are conducted [5,6,7]. Ishihara et al. [8] employed a wind tunnel test to study the wind characteristics near a simplified three-dimensional hill with a maximum slope of 30°, and the flow separation at the hilltop and the formation of a recirculation zone on the leeward side of the hill were observed. Yang et al. [9,10] and Liu et al. [11,12] adopted a numerical simulation approach to investigate the influence of slopes, wind directions, and sub-grid scale models on the wind characteristics over simplified hills. However, the influence of different oncoming wind speeds on the wind characteristics was not considered in their studies. Zhou et al. [1] used the large-eddy simulation (LES) approach to study the wind characteristics in simplified U-shaped and V-shaped canyons. The result indicated that the wind speed amplification effect was gradually diminished when the V-shaped canyon angle exceeded 160° or the width-to-height ratio of the U-shaped canyon was approximately 5:1. It is evident that the selection of model parameters such as the slope of simplified hills, the width-to-height ratio of U-shaped canyons, and the opening angle of V-shaped canyons has a significant influence on wind characteristics. Similarly, Abdi et al. [13] pointed out that there is a considerable difference between the simplified terrain and the actual mountain canyon terrain. Consequently, studying the wind characteristics only on the simplified terrain is insufficient.

With the improvement of experimental equipment and computer hardware, the wind characteristics of actual mountainous and canyon terrains are being established by more and more scholars [14,15,16]. Liao et al. [17] conducted a field measurement of the wind characteristics at a bridge site in an L-shaped mountain valley and found significant differences between parameters such as turbulence intensity, probability density function, and spatial coherence at the bridge site compared to the standard values in existing specifications. Boonterm et al. [18] used meteorological balloon measurements and numerical simulation methods to study the airflow characteristics over complex terrain. The measured and simulated results were compared, and the results indicated that the accuracy of numerical simulation software in modeling mountainous and adjacent terrains is sufficiently accurate. Ren et al. [19] employed the LES approach to study the spatial wind field in complex terrain. A spatial correlation analysis of the fluctuating wind speeds over complex terrain was conducted, and a spatial wind field prediction model was established to predict natural wind characteristics. Song et al. [20] investigated the wind characteristics at a bridge site in a Y-shaped canyon under different oncoming wind directions using a combination of field measurement and wind tunnel testing. The results indicated that the form of the terrain plays a significant role in the variation in wind directions, with the sheltering and channeling effects of the terrain found to contribute to wind deceleration and acceleration at the bridge site, respectively. Li et al. [21] adopted a wind tunnel test method to study the influence of oncoming wind directions on the wind characteristics at a bridge site in a deep-cut canyon, and a recommended value range for wind attack angles necessary for wind-resistant bridge design in mountain canyon terrain was provided. The decay factor of the coherence function as it changes with location was also investigated. Yamaguchi et al. [22] conducted a wind tunnel test of a coastal cliff terrain in Japan with a model scale of 1:2000. The results indicate that it is inappropriate to directly apply power laws to estimate wind speed or turbulence intensity in complex terrain, and significant changes in wind direction and increases in wind force around the river channel of the canyon were also observed.

In summary, although some progress has been made in the research on wind characteristics in mountain valleys, previous studies have primarily focused on research variables such as wind direction, slope, and canyon cross-section. Moreover, these studies have only investigated the wind characteristics at bridge sites in mountain valleys under a single wind speed, with the influence of different oncoming wind speeds on wind characteristics not being considered.

The remainder of this paper is structured as follows. In Section 2, detailed information about Jinqi Bridge and the topographical features of its vicinity is presented. The wind tunnel and experimental equipment used, as well as the model information, are described in Section 3. A comprehensive discussion of the mean wind characteristics and fluctuating wind characteristics on the main beam and two bridge towers of Jinqi Bridge is provided in Section 4. Finally, the main conclusions of this study are summarized in Section 5.

2. The Topography and Research Strategy

Jinqi Bridge is a controlling project on the entire stretch of the expressway from Wudang District to Changshun County in Guizhou Province. A double-pylon, double-cable-plane, and composite beam cable-stayed bridge structure was employed. The bridge crosses the Maotiao River, and the surrounding terrain is highly undulating and complex. The bridge is flanked by high mountains on both sides, which have formed a typical deep-cut “V”-shaped canyon due to the long-term erosion by the river, as shown in Figure 1. The bridge crosses both sides of the deep-cut “V”-shaped canyon, with the specific coordinates of the bridge center being 26.82° N and 106.44° E. The bridge is designed at an elevation of approximately 1150 m, with a total length of the main beam (L) of 672 m, a main tower height of 300 m, and a concrete usage exceeding 17,200 cubic meters, which makes it one of the tallest cable-stayed bridges in the world.

The airflow perpendicular to the axis of the main beam (southeast wind direction) is defined as the 0° wind direction. The definition of wind direction and selection of this terrain are particularly ingenious. When the oncoming wind direction is 0°, it flows along the river channel, and the overall terrain is low and relatively flat, with the airflow essentially unobstructed by the canyon terrain before reaching the bridge site. Taking the 0° wind direction as the reference, a 30° deflection to the left is defined as the 30° wind direction. When the oncoming wind direction is 30°, the airflow will be partially obstructed by the terrain. Considering upstream and downstream, the northwest wind direction is defined as 180°. When the oncoming wind direction is 180°, the oncoming airflow will encounter strong obstruction due to the presence of towering mountains in the northwest. The specific terrain features and wind directions are shown in Figure 2.

3. Wind Tunnel Test Setup

The wind characteristics at the bridge site under different oncoming wind speeds at 0°, 30°, and 180° wind directions were comprehensively investigated in this study. Additionally, the influence of different wind field conditions, including uniform and turbulent wind fields, on the wind characteristics at the bridge site was also examined. When the oncoming wind is uniform, the oncoming wind speeds U₀ at each wind direction are 6 m/s, 8 m/s, 10 m/s, 12 m/s, and 14 m/s, respectively. However, the oncoming flow cannot always be uniform in practice, as buildings and vegetation in the actual terrain are considered to affect wind speed. To render the research results more relevant to engineering, roughness elements are also placed in the wind tunnel to conduct a comparative study of the wind characteristics at the bridge site under turbulent atmospheric boundary layer (ABL) wind field conditions. The wind profile and turbulence intensity profile of the ABL inflow in the empty wind tunnel (taking the case of U₀ = 10 m/s as an example) is shown in Figure 3.

The wind tunnel test was conducted within the low-speed test section of the STU-1 wind tunnel laboratory. The test section is 4.4 m wide, 3.0 m high, and 24.0 m long, with a turntable diameter of 3.0 m. The wind speed range in the test section is 0 to 30 m/s, with a turbulence intensity of less than 0.4%.

A circular area with a diameter of 2.4 km around the midspan of Jinqi Bridge was selected as the terrain range. To prevent the formation of artificial cliffs, a sloped terrain transition section was used, which provided a good transitional effect on the wind characteristics, allowing the wind to maintain essentially the same properties as the oncoming wind when it reaches the terrain [23,24]. The transition section is 600 m long, and the total diameter of the model is 3.6 km. A scale ratio of 1:1000 was chosen to seat the terrain model onto the turntable. A circular plywood board with a diameter of 3 m was crafted to serve as the base of the model. Foam boards with a thickness of 2.5 cm were used to layer and cut the terrain until the highest location within the terrain range is reached. A layer of gypsum was evenly applied to the surface of the completed model and painted green.

The wind speed data were monitored by a Series 100 J-Cobra probe, which was manufactured by Turbulent Flow Instrumentation Pty Ltd., an Australian company. This Cobra probe has a wind speed measurement range of 2 to 100 m/s, a measurement accuracy of ±0.5 m/s, a data collection frequency of 10,000 Hz, an output frequency (f_s) of 625 Hz, and a data collection time of 60 s. The experimental equipment is capable of meeting the requirements for the measurement of wind speed range and the necessary precision. Two J-Cobra turbulence meters were employed in the experiment. The simultaneous measurement of wind speeds at two points in each set of conditions is allowed, which enables a better understanding of the coherence between the two sets of wind speed data. A movable measuring frame was used to suspend the J-Cobra turbulence meters. The movable measuring frame was installed within the test section, which primarily consists of two rigid supports on either side and a central horizontal bar. Bolt and sleeve connections are present at the joints, allowing for the vertical and horizontal movement of the J-Cobra turbulence meter, thereby obtaining wind speed data at different monitoring points on Jinqi Bridge. When the oncoming wind direction is 0°, the final model installations for uniform and ABL oncoming wind are shown in Figure 4a,b, respectively. A total of 7 monitoring points were arranged along the main beam at locations x/L = 0, 1/6, 1/3, 1/2, 2/3, 5/6, and 1. Five monitoring points were placed at each bridge tower, located at y/H = 0, 1/4, 1/2, 3/4, and 1, where H is the distance between the lowest and highest monitoring points on the bridge tower. The specific locations of the 15 monitoring points are shown in Figure 5.

4. Results and Discussion

4.1. Mean Wind Characteristics

Mean wind characteristics refer to the average state and behavior of the wind within a certain period and spatial range, serving as a crucial basis for the quantitative analysis of wind fields. By analyzing the mean wind characteristics of structures, a better understanding and analysis of wind behavior can be achieved. The mean wind characteristics include wind profiles, wind speed amplification factors, wind yaw angles, and wind attack angles, which are indispensable factors in bridge structural design. The distribution of mean wind characteristics at the bridge site forms the foundation for calculating wind loads. A precise analysis of mean wind characteristics could enhance the safety of bridge design while maintaining economic efficiency.

4.1.1. Wind Profiles and Wind Speed Amplification Factor

The distribution of wind speed along the vertical direction is referred to as the wind profile. Influenced by the terrain, the mean wind speed may exhibit different patterns in the vertical direction. The definition of mean wind speed is given by Equation (1). The bridge damage due to excessive wind speeds can be prevented by understanding the distribution of the wind profiles. The wind speed amplification factor is defined as the ratio of the wind speed at a certain height above the ground to the mean wind speed at a reference height [25], and the calculation expression is shown in Equation (2).

$$U=\sqrt{U_x^2+U_y^2+U_z^2}$$

(1)

where U is the total mean wind speed; U_x, U_y, and U_z are the mean wind speeds in the x, y, and z directions, respectively.

$$C_u={\displaystyle \frac{U_b}{U_{\mathit{ref}}}}$$

(2)

where C_u represents the wind speed amplification factor; U_b is the mean wind speed at the main beam; and U_ref is the mean wind speed at the height of the main beam when the oncoming wind reaches the terrain.

The wind profile and wind speed amplification factor are both normalized by U_ref (the mean wind speed at the height of the main beam when the oncoming wind reaches the terrain). The distribution of wind profiles on the southwest bridge tower is shown in Figure 6 and Figure 7. It can be observed that the wind speed generally increases with height. The mean wind speed on the southwest bridge tower is highest when the oncoming wind direction is 180°, followed by the 0° direction, and the 30° direction is lowest. The reason for this phenomenon is that when the oncoming wind direction is 180°, although there are high mountains around, there is a narrow gully between the mountains, as shown in Figure 2. The lateral movement of the wind is limited by the two mountains, which cause the wind to accelerate as it passes through this narrow gully. The highest wind speeds appear in the wind direction of 180° owing to the southwest bridge tower being located on this gully. When the wind direction is 0°, the wind flows along the river channel, and the terrain is more open without the canyon wind acceleration effect. Thus, the wind speed is lower than that of the 180° wind direction. When the wind direction is 30°, the obstruction effect of the high mountains on the oncoming wind is more significant, resulting in the lowest wind speed. Additionally, when the oncoming wind is uniform, although there is some difference in the wind profile with the oncoming wind speeds, the degree of the difference is small. For example, at the midpoint of the bridge tower under 180° wind direction, the dimensional wind speed difference between an oncoming wind speed of 6 m/s and 14 m/s is only 0.04, as shown in Figure 6c. When the oncoming wind is ABL inflow, due to the varying wind speeds at different heights under ABL inflow, significant differences with uniform inflow in the wind profile at the bridge site are caused. The wind profile decreases with increasing oncoming wind speed. Additionally, the higher the wind speed, the smaller the decrease extent in mean wind speed, and when the oncoming wind speed reaches above 12 m/s, the wind profile remains largely unchanged.

The distribution of wind profiles on the northeast bridge tower is shown in Figure 8 and Figure 9. When the oncoming wind direction is 180°, the wind speed on the northeast bridge tower is the lowest, which is due to the tower on the leeward side of the high mountains, and the wind is significantly reduced by the obstruction of the mountains. When the oncoming wind direction is 0°, the wind speed is the highest. Owing to the wide river channel and the lower terrain in front of the bridge, the two towers are less affected by the interference from the terrain. Thus, the distribution of wind profiles at the northeast tower is very similar to that at the southwest bridge tower. When the oncoming wind direction is 30°, although the wind is obstructed by the mountains, the mountains are relatively low, and the obstruction effect is not as significant as when the wind direction is 180°. Therefore, the mean wind speed at the 30° wind direction is lower than at 0° but higher than at 180°. When the oncoming wind is uniform, the northeast bridge tower is less affected by the wind speed, and the wind speed profiles essentially overlap. When the oncoming wind is ABL, the mean wind speed at different locations on the northeast tower decreases with increasing oncoming wind speed. This distribution pattern is consistent with the southwest bridge tower.

The wind speed amplification factors on the main beam are shown in Figure 10 and Figure 11. When the oncoming wind is uniform, the wind speed amplification factors on the main beam at the 0° and 30° wind directions are both greater than 1. This indicates that the wind accelerates as it passes over the terrain and reaches the main beam. Additionally, the wind speed amplification factors on the main beam remain largely consistent regardless of the oncoming wind speed. When the oncoming wind is ABL inflow and the wind directions are 0° and 30°, the relatively flat terrain of the river channel also leads to acceleration at the main beam, with the wind speed amplification factors being greater than 1 at the entire main beam. When the wind direction is 180°, the wind speed amplification factor on the main beam decreases in the direction of the northeast, which is influenced by the presence of mountains in the northeast. As the oncoming wind speed increases, the wind speed amplification factor on the main beam gradually decreases. When the wind speed reaches 12 m/s or above, the wind speed amplification factor remains unchanged.

4.1.2. Wind Yaw Angle

The wind yaw angle α represents the horizontal angle between the direction of the wind reaching the bridge and the oncoming wind direction, as defined by Equation (3). The wind yaw angle is a fundamental parameter for studying the wind-induced vibrations of bridge components in different directions. The wind acting on the bridge from different directions is clearly reflected by the wind yaw angle; thus, the wind loads in each direction can be determined. The distribution of wind yaw angles on the southwest bridge tower is shown in Figure 12 and Figure 13. When the oncoming wind is uniform, the wind yaw angle shows a trend of first decreasing, then increasing, and then decreasing again with height, which is related to the undulations of the terrain. The wind yaw angle exhibits minimal variation with the oncoming wind speed, with the obtained curves largely overlapping. When the oncoming wind is ABL inflow, at the locations y/H = 0.25, 0.5, and 1 under the 180° wind direction, there is a trend for the wind yaw angle to decrease with increasing oncoming wind speed, and the change is relatively small. There is only about a 1° difference in the wind yaw angle between oncoming wind speeds of 6 m/s and 14 m/s.

The distribution of wind yaw angles on the northeast bridge tower is shown in Figure 14 and Figure 15. Influenced by the irregular terrain, the distribution of wind yaw angles on the northeast bridge tower is also very complex. Overall, the wind yaw angles on the northeast bridge tower are relatively small and affected by the oncoming wind speed. When the oncoming wind is ABL inflow and the wind direction is 180°, the wind yaw angle tends to decrease with the increase in incoming wind speed, as shown in Figure 15c.

The distribution of wind yaw angles on the main beam is shown in Figure 16 and Figure 17. When the oncoming wind directions are 0° and 30°, the wind yaw angles on the main beam remain unchanged with the oncoming wind speed for both uniform and ABL oncoming inflow. However, when the oncoming wind is on the leeward side of the mountain, which corresponds to the 180° wind direction, the wind yaw angle tends to decrease with an increase in oncoming wind speed. This may be due to the flow field structure on the leeward side of the mountain being altered with the increase in oncoming wind speed, resulting in different distributions of wind yaw angles on the main beam.

$$\alpha =\arccos \left({\displaystyle \frac{U_x}{\sqrt{U_x^2+U_y^2}}}\right)$$

(3)

4.1.3. Wind Attack Angle

The wind attack angle β is a critical parameter to describe the state of structural elements such as the main beam and towers, which is used to assess the influence of the wind on bridges. A significant change in the velocity and pressure fields results in different attack angles. The attack angle is of great significance for studying the wind-induced vibration performance of components. The definition of wind attack angle is given by Equation (4).

The distribution of wind attack angles on the southwest bridge tower is shown in Figure 18 and Figure 19. It can be observed that the wind attack angle is the largest at the 180° wind direction, and this indicates that significant upward airflow exists at the southwest bridge tower. The wind attack angle is significantly influenced by the oncoming wind speed, with the angle increasing as the wind speed increases, whether the oncoming flow is uniform or the ABL inflow. Overall, when the oncoming wind is ABL inflow, the value of the wind attack angle is lower than uniform inflow. This is due to the obstruction of the wedges and rough elements in the wind tunnel, which reduces the wind speed as it reaches the bridge, resulting in a lower overall value than that of the uniform inflow. This is consistent with the conclusion that the higher the wind speed, the larger the attack angle.

The distribution of wind attack angles on the northeast bridge tower is shown in Figure 20 and Figure 21. When the oncoming wind is uniform, the wind attack angles are relatively small at the northeast tower under the 0° and 30° wind directions. The reason for this phenomenon is that the measuring points are higher and the obstruction effect of the mountains is smaller. Additionally, the higher the oncoming wind speed, the greater the wind attack angle at the same measuring point. For the 180° wind direction, the bridge site is located on the leeward side, and the distribution of wind attack angles is more complex, initially decreasing and then increasing with height. The wind attack angle changes very little with the oncoming wind speed.

The distribution of wind attack angles along the main beam is shown in Figure 22 and Figure 23. For both uniform and ABL inflow, the variation in wind attack angle with locations is essentially the same, and the values for the ABL are slightly lower. When the oncoming wind is uniform inflow, the wind attack angle of the main beam is relatively small, influenced by the oncoming wind speed. When the oncoming wind is ABL inflow, the wind attack angle shows an increasing trend with the increase in oncoming wind speed. The wind attack angles at the bridge site are all positive, indicating the presence of significant upward airflow throughout the bridge site, which typically increases the lift component in the bridge and possibly affects the structural stability. The influence of this aspect should be given due attention in engineering design.

$$\beta =\arcsin \left({\displaystyle \frac{U_z}{\sqrt{U_x^2+U_y^2}}}\right)$$

(4)

4.2. Fluctuating Wind Characteristics

The fluctuating wind characteristics are concerned with the short-term random fluctuations in wind speed and direction. Fluctuating wind characteristics refer to the rapid and random changes in wind speed and direction within a short period, representing the turbulent component of the wind. These characteristics include turbulence intensity, the fluctuating wind power spectrum, the turbulent integral scale, the coherence function, the probability density function, kurtosis, and skewness, among others. By analyzing the fluctuating wind characteristics, a more accurate prediction of the dynamic response of bridge components can be achieved, enhancing the comfort and safety of bridges.

4.2.1. Turbulence Intensity

Turbulence intensity (I_i) is a dimensionless parameter that characterizes the intensity of fluid motion. It is expressed as the ratio of the standard deviation of the fluctuating wind speed to the mean wind speed, as indicated in Equation (5). An intuitive reflection of the strength of the turbulent flow field relative to the mean flow field is provided by the turbulence intensity [26].

$$I_i={\displaystyle \frac{{\sigma }_i}{U}},(i=u,v,w)$$

(5)

where u, v, and w represent the fluctuating wind speed components in the longitudinal, transverse, and vertical directions, respectively; σ denotes the standard deviation of the fluctuating wind speed; and U is the mean wind speed at the monitoring point.

In wind engineering, the dominant flow direction is typically represented by the longitudinal wind. Consequently, the turbulence characteristics of the longitudinal wind have the most significant influence on wind flow behavior. Thus, an analysis of the longitudinal wind turbulence intensity at various locations on the bridge is conducted in this study. The turbulence intensity on the southwest bridge tower is shown in Figure 24 and Figure 25. The results indicate that when the oncoming wind is uniform, the turbulence intensity decreases with increasing height. This is due to the primary influence factor of turbulence intensity in uniform flow being the undulations of the terrain. The higher the location, the less the blocking effect of the terrain, which leads to a lower turbulence intensity. Additionally, the turbulence intensity continuously decreases with the increase in oncoming wind speed. This may be attributed to a more uniform airflow at high wind speeds, resulting in a reduction in turbulent fluctuation components. When the oncoming wind is ABL inflow, the degree of variation in turbulence intensity with height and oncoming wind speed is relatively small. Due to the presence of rough elements and wedges in front of the terrain, the ABL inflow inherently possesses a certain level of turbulence intensity, whereas the uniform inflow lacks any turbulence components. Consequently, after passing through the same terrain disturbance, the turbulence intensity at the bridge site of ABL inflow is higher than that of uniform inflow.

The turbulence intensity on the northeast bridge tower is presented in Figure 26 and Figure 27. When the oncoming wind is uniform, the turbulence intensity decreases with the increase in oncoming wind speed, which is consistent with the pattern observed on the southwest bridge tower. When the wind direction is 180°, the turbulence intensity first increases and then decreases with the increase in height, reaching a maximum at y/H = 0.25, which is approximately 40%, as shown in Figure 26c. This phenomenon is caused by the northeast bridge being located on the leeward side of the mountain, where the mean wind speed is low (as shown in Figure 8c), resulting in a higher turbulence intensity. When the wind is ABL inflow, the turbulence intensity for the 0° and 30° wind directions shows no significant variation with oncoming wind speed, while for the 180° direction, the turbulence intensity decreases with the increase in oncoming wind speed.

The turbulence intensity on the main beam is depicted in Figure 28 and Figure 29. The variation in turbulence intensity with wind speed on the main beam is consistent with the patterns observed on the two towers, showing a decrease as the wind speed increases. This result indicates that with the variation in wind speed, the turbulence energy spectrum may change, with the energy of high-frequency turbulence components relatively reducing, leading to an overall decrease in turbulence intensity.

4.2.2. Fluctuating Wind Power Spectra

The fluctuating wind power spectrum is used to describe the distribution of energy at different frequencies, clearly reflecting the dynamic wind characteristics, and is an important parameter in bridge buffeting. The peak of the power spectrum refers to the maximum value of the power spectral density, which can reflect the degree of fluctuation in wind turbulence [27,28]. The high-frequency decay of the power spectrum refers to the rate at which the power spectrum decreases in the high-frequency region. A faster decay indicates less high-frequency energy in the turbulence [29,30]. The peak value and high-frequency decay of the longitudinal fluctuating wind power spectrum at various locations on the bridge are focused on in this section.

The longitudinal fluctuating wind power spectrum of the southwest bridge tower is shown in Figure 30 and Figure 31. When the oncoming wind is uniform, the power spectrum peak with the increase in height is increased under the 0° wind direction, as shown in Figure 30a. The power spectrum for the 30° and 180° wind directions shows a smaller degree of variation with height. Additionally, the peak of the power spectrum significantly decreases with the increase in wind speed. This indicates that the wind fluctuations are smaller, which is consistent with the conclusion in Section 4.2.1 that the higher the wind speed, the smaller the turbulence intensity under uniform inflow. With the increase in oncoming wind speed, the high-frequency part of the power spectrum decays more slowly. This result suggests that there is more high-frequency energy in the turbulent vortices, and there may be more small-scale vortices in the flow field. When the oncoming wind is ABL inflow, compared to uniform inflow, the peak frequency of the power spectrum decreases, and the high-frequency part decays significantly faster. The power spectrum hardly changes with the variation in oncoming wind speed. Therefore, in Section 4.2.1, the turbulence intensity remains largely unchanged with the change in oncoming wind speed under ABL inflow.

The longitudinal fluctuating wind power spectrum of the northeast bridge tower is presented in Figure 32 and Figure 33. When the oncoming wind is uniform, the variation in the power spectrum with wind speed follows the same pattern as observed on the southwest bridge tower; that is, the higher the wind speed, the smaller the power spectrum peak and the slower the high-frequency decay rate, and there is an increase in peak frequency. This pattern is most evident in Figure 32c. However, unlike the southwest bridge tower, the power spectrum of the northeast bridge tower is essentially unchanged with the increase in height. When the oncoming wind is ABL inflow, the power spectrum shows no significant variation with the oncoming wind speed, and the power spectrum curves under different wind speeds are largely coincident.

The longitudinal fluctuating wind power spectrum of the main beam is shown in Figure 34 and Figure 35. The variation in the power spectrum with oncoming wind speed on the main beam is consistent with the patterns observed on the two towers. When the oncoming wind is uniform, the higher the wind speed, the smaller the peak value, and the slower the high-frequency decay rate. When the oncoming wind is ABL inflow, the power spectrum is essentially unchanged with the variation in wind speed.

4.2.3. Turbulent Integral Scale

The turbulent integral scale refers to the characteristic length scale at which two turbulent fluctuating velocity vectors are spatially correlated, reflecting the range of energy transfer and momentum exchange in turbulence. The methods currently used to obtain the turbulent integral scale generally include the von Kármán spectral fitting method and the correlation function integration method based on the Taylor frozen turbulence hypothesis. The von Kármán wind spectrum is conducted in the frequency domain, and information about the distribution of turbulent energy across different frequencies is provided. In contrast, the auto-correlation function method, which analyzes in the time or space domain, may not reveal the spectral characteristics of turbulence. Therefore, when the power spectrum satisfies the von Kármán wind spectrum, the turbulent integral scale results obtained through von Kármán spectral fitting are considered superior [31]. The expression for the longitudinal wind von Kármán wind spectrum is given by Equation (6) [32]. During the analysis of the power spectrum at various points on the bridge, it was found that the von Kármán wind spectrum aligns well with the power spectra. The fitting results for some cases at the midspan of the bridge under a 0° oncoming direction for both uniform and ABL inflows are demonstrated in Figure 36. Consequently, the turbulent integral scales at various locations on Jinqi Bridge are obtained through fitting the von Kármán spectrum.

The turbulent integral scale at the southwest bridge tower is shown in Figure 37 and Figure 38. When the oncoming wind is uniform, the turbulent integral scale increases with the increase in height. The higher the oncoming wind speed, the larger the turbulent integral scale, indicating that the formation of large-scale vortices may be promoted by the higher wind speeds. When the oncoming flow is ABL inflow, the turbulent integral scales for the 0° and 30° directions also tend to increase with the rise in wind speed. However, when the wind direction is 180°, the variation in the turbulent integral scale with wind speed is not significant.

The turbulent integral scale at the northeast bridge tower is illustrated in Figure 39 and Figure 40. When the oncoming flow is uniform, the turbulent integral scales at the northeast bridge tower for 0° and 30° wind directions decrease as the oncoming wind speed increases. Combined with the result in Figure 26 that higher wind speeds correspond to lower turbulence intensity, this indicates that at this location, the processes of airflow mixing and diffusion primarily occur at smaller scales under high-wind-speed conditions. When the oncoming flow is ABL inflow, the turbulent integral scale at the northeast bridge tower increases with height. The variation in the turbulent integral scale with the oncoming wind speed is not remarkable for oncoming flows from all directions.

The turbulent integral scale at the main beam is shown in Figure 41 and Figure 42. It is noted that when the oncoming wind is uniform and the wind directions are 0° and 30°, with the midspan of the main beam as the dividing line, the turbulent integral scale increases with the wind speed in the left half-section while decreasing with the increase in the right half-section, as shown in Figure 41a,b. This result indicates that the variation in the turbulent integral scale with oncoming wind speed is greatly influenced by the topography. When the oncoming wind direction is 180°, the turbulent integral scale is basically unchanged with the variation in wind speed. When the oncoming wind is ABL inflow, due to the blocking effects of roughness elements, wedges, and terrain, the distribution of turbulent integral scales at the main beam is complex, and the variation with oncoming wind speed is inapparent.

$${\displaystyle \frac{f{S}_u(f,z)}{{\sigma }_u^2}}={\displaystyle \frac{4f{L}_u}{{\left[1+70.8{\left(\frac{f{L}_u}{U}\right)}^2\right]}^{5/6}}}$$

(6)

where S_u, (f,z) is the fluctuating wind spectrum at a height of z, L_u is the longitudinal turbulent integral length scale, ${\sigma }_u$ is the standard deviations of the longitudinal components of the fluctuating wind speed, and U is the mean wind speed.

4.2.4. Coherence Function

The fluctuating wind coherence function is used to assess the correlation of wind loads at different locations on a structure, which aids in predicting the vibration behavior of bridges under wind action. The coherence function is defined as the ratio of the cross-spectral density to the auto-spectral density of fluctuating wind speeds, as expressed in Equation (7) [33]. By fitting the experimental values with the modified coherence function Equation (8), the values of parameters K and C can be obtained, where K represents the coherence at a reduction frequency of zero and C is the decay coefficient.

Under uniform inflow conditions, the variation in wind speed across space is very minimal. After investigation, the correlation between fluctuating wind speeds at different locations is low, and the coherence function between two measurement points on the bridge is very weak in uniform inflow cases. When the coherence function is weak, the effectiveness of formula fitting is also poor. Therefore, only the coherence at various locations on the bridge under ABL inflow conditions is displayed in this section.

When the wind direction is 0°, the coherence functions between two points with the same spacing but at different locations on the main beam under different oncoming wind speeds are presented in Figure 43. It can be observed that as the wind speed increases, the value of K gradually increases, and the value of C also increases. The increase in K indicates that the coherence between the two points strengthens with the increase in wind speed. A strong coherence function means that different locations of the structure may be simultaneously influenced by wind loads, leading to a more significant overall structural response. The larger decay coefficient C indicates that the coherence decreases more rapidly with increasing distance, implying that the two points must be very close for the coherence to be significant. In engineering practice, special attention should be given to areas with strong coherence but a high decay coefficient, and a severe local impact can be caused on the bridge. Additionally, it is noted that when two points are at different locations but with the same spacing, the results of the coherence function are quite similar, which suggests that in the flow field of mountain valleys, the size of turbulent vortices for two points at a fixed distance may be consistent.

When the wind direction is 30°, the coherence function at the same locations is investigated, as shown in Figure 44. Notably, at the oncoming wind speed of 14 m/s, the two points on the main beam exhibit strong coherence and significant decay, and the variation in the coherence function with wind speed is essentially consistent with that at 0° wind direction. However, for two points at the same distance, the decay coefficients at half span and five-sixths span are much higher than those at one-third span and two-thirds span. This phenomenon is caused by the obstructive effect of the mountains in a 30° wind direction, which affects the effective distance of coherence.

The coherence functions at different wind speeds under the 180° wind direction are illustrated in Figure 45. The coherence function between the two points also increases with the increase in the oncoming wind speed. Since the main beam is completely on the leeward side of the mountain in the 180° wind direction, the coherence between the two points is very weak, and the decay coefficient is also high. This may be due to the strong turbulence on the leeward side of the mountain, which leads to a reduction in wind coherence between different locations, thereby weakening the coherence function.

$${\mathrm{C}}_{\mathit{xy}}\left(f\right)={\displaystyle \frac{{\left|P_{xy}(f)\right|}^2}{P_{xx}(f)P_{yy}(f)}}$$

(7)

where C_xy represents the coherence estimate between two fluctuating wind speeds; P_xx(f) and P_yy(f) are the auto-power spectral densities of the two fluctuating wind speeds, respectively.

$$\mathit{coh}\left(f\right)=K\cdot \exp \left(-C\cdot {\displaystyle \frac{f\Delta }{U}}\right)$$

(8)

where K and C are the parameters to be fitted; Δ is the distance between the two points, and U is the mean wind speed.

4.2.5. Kurtosis, Skewness, and Probability Density Function

Kurtosis and skewness are statistical measures that describe the shape and symmetry of the fluctuating wind speed distribution. When fluctuating wind speeds follow a Gaussian distribution, the kurtosis value is 3, and the skewness value is 0 [34]. The further these values deviate from the standard, the stronger the non-Gaussian characteristics of the wind speed. Additionally, kurtosis and skewness can reflect the probability of the occurrence of extreme wind speeds, which can aid in preventing bridge damage due to extreme wind loads.

The kurtosis and skewness coefficients for the southwest bridge tower are presented in Figure 46 and Figure 47. It can be observed that when the oncoming wind is uniform, both the kurtosis and skewness coefficients at the midpoint of the southwest tower are quite large. Particularly when the wind direction is 180°, the kurtosis coefficient reaches as high as 60. This is due to the fact that the southwest tower is located on the leeward side of the mountain, making it very susceptible to the influence of extreme wind speeds, which leads to a higher kurtosis value in the 180° wind direction. Additionally, there is a clear trend of the kurtosis coefficient increasing with wind speed at the southwest tower, and the skewness coefficient also deviates significantly from the Gaussian value. When the oncoming flow is ABL inflow, the kurtosis and skewness values are generally close to those of the Gaussian distribution, indicating that the probability of extreme wind speeds occurring under ABL inflow is smaller.

The kurtosis and skewness coefficients for the northeast bridge tower are shown in Figure 48 and Figure 49. When the oncoming wind is uniform, both the kurtosis and skewness coefficients deviate more from the Gaussian values as the oncoming wind speed increases. The higher kurtosis and skewness values are observed at the midpoint of the tower. When the oncoming wind is ABL inflow, the 0° and 30° wind directions approximate a Gaussian distribution. However, when the oncoming wind direction is 180°, owing to the obstruction of the mountain, both the kurtosis and skewness coefficients are higher, with the highest values still occurring at the midpoint of the bridge tower. Extra precautions should be taken at this location in engineering.

The kurtosis and skewness coefficients for the main beam are shown in Figure 50 and Figure 51. When the oncoming wind is uniform, the variation in the kurtosis and skewness coefficients along the main beam with wind speed follows the same pattern as that for the two towers. As the wind speed increases, the kurtosis coefficient gradually increases, and the skewness coefficient deviates more from the Gaussian value. Therefore, at higher wind speeds, the dynamic response of the bridge may be stronger due to the unsteadiness of fluctuating winds. When the oncoming wind is from ABL inflow, the kurtosis and skewness at the 0° and 30° wind directions basically conform to the Gaussian values. However, the skewness and kurtosis values at the 180° wind direction are significantly different from the Gaussian distribution, with the largest discrepancy observed at the midspan of the main beam. Consequently, the midspan is more susceptible to damage from strong gusts. To ensure structural integrity and safety under extreme wind conditions in engineering, special attention should be given to the design and maintenance of the main beam, particularly at the midspan.

The probability density function displays an intuitive representation of the distribution of fluctuating wind speeds, as expressed in Equation (9) [35,36]. The probability density function distribution of fluctuating wind speed is of critical importance for the safety of structures [37]. Based on the analysis results of the kurtosis and skewness coefficients, the probability density function of the midpoint of the two towers and main beam is further analyzed. The probability density functions at three locations under uniform inflow are illustrated in Figure 52. It can be observed that the probability density functions at each location exhibit a high degree of deviation from the Gaussian distribution, demonstrating a strong non-Gaussian nature, which corresponds well to the higher kurtosis and skewness values mentioned in the previous analysis. When the oncoming wind is ABL inflow, the probability density functions at each location basically conform to the Gaussian distribution, as shown in Figure 53. Only a slight non-Gaussian nature appears at the 180° wind direction, which is consistent with the patterns indicated by the kurtosis and skewness coefficients.

$$f\left(x\right)={\displaystyle \frac{1}{x\sigma \sqrt{2\pi }}}{e}^{{\displaystyle \frac{-{\left(\ln x-\mu \right)}^2}{2{\sigma }^2}}}, x\ge 0$$

(9)

where μ and σ denote the mean and the standard deviation of the logarithm of the variable x, respectively.

5. Conclusions

To investigate the influence of oncoming wind speed on the wind characteristics at a bridge site in a mountain valley, a wind tunnel test of a terrain model with a scaling ratio of 1:1000, where a long-span bridge would be built in the V-shaped canyon, was conducted. Uniform and ABL inflows were both applied in the wind tunnel test. The mean and fluctuating wind characteristics at locations of the main beam and two bridge towers under different oncoming wind speeds were comprehensively studied. The main conclusions are as follows:

(1) The trend in mean wind characteristics at the bridge site in the V-shaped canyon with the variation in wind speed is consistent under uniform and ABL oncoming wind, while the influence of oncoming wind speed is more pronounced under the ABL inflow. Wind profiles and wind speed amplification factors decrease as wind speed increases, while the wind yaw angles remain largely unchanged. Moreover, an increase in oncoming wind speed leads to an increase in wind attack angles, and all values are positive. Therefore, a significant upward air current is present across the entire bridge site, which typically increases the lift component of the bridge and affects the stability of the structure. Special attention should be paid to the influence of large attack angles on bridges in engineering projects.

(2) Under uniform inflow conditions, the fluctuating wind characteristics exhibit a significant variation with the oncoming wind speed: increasing oncoming wind speed decreased the turbulence intensity, reduced the peak frequency of the power spectrum, and slowed down the high-frequency decay rate. The variation in the turbulent integral scale with oncoming wind speed is greatly influenced by the terrain. The turbulent integral scale at the southwest tower increases with the oncoming wind speed, whereas at the northeast tower, it decreases with the increase in wind speed. When the oncoming wind is ABL, the turbulence intensity and the turbulent integral scale remain unchanged with variations in oncoming wind speed, and the power spectrum curves are essentially coincident. In additional, the power spectra at various locations of the bridge align well with the von Kármán wind spectrum, and the turbulent integral scale derived from fitting with the von Kármán wind spectrum is sufficiently accurate.

(3) As wind speed increases, the value of K gradually increases, and the value of C also increases, leading to an enhancement of the coherence between the two points. At high wind speeds, different locations of the bridge may simultaneously be affected by wind loads, resulting in a more significant overall structural response, which is highly unfavorable for bridge safety and necessitates the implementation of protective measures in engineering. Additionally, the coherence function is only influenced by the spacing between two points. When two points are at different locations but with the same spacing, the coherence function remains roughly the same.

(4) Locations with higher kurtosis and skewness values exhibit steeper probability density functions. When the main beam or bridge tower is on the leeward side of a mountain, the kurtosis and skewness coefficients tend to be larger. Furthermore, the kurtosis and skewness coefficients increased with the oncoming wind speed increases, causing the probability density function to deviate more from the Gaussian distribution. Appropriate preventive measures should be taken in advance in engineering to cope with strong gust conditions at high wind speeds.

Unfortunately, due to the bridge not yet being constructed, there are no field measurement data available. In future work, we will make every effort to conduct comparative studies between wind tunnel tests and field measurements.