Risk Assessment of Wind-Induced Vehicle Accidents on Long-Span Bridges Using Onsite Wind and Traffic Data

Sea-crossing long-span bridges are essential in providing continuous mobility and minimizing logistics costs by accommodating daily traffic. However, because of their high location in an open space, vehicles are more likely to be exposed to strong side winds. Several risk-reduction plans have been adopted for most bridges, including traffic-control scenarios and windscreen installation. However, those strategies were implemented using a heuristic decision rather than a systematic assessment process with theoretical backgrounds. The technical components regarding vehicle safety include a wide range of engineering knowledge, such as vehicle dynamics, aerodynamic evaluation of wind loads on vehicles over bridge decks, and wind environment analysis for the specific bridge site.

Over the last 2 decades, extensive research has been performed for vehicle safety under strong crosswinds on a bridge. As mentioned by Reymert et al. (2022), who performed a systematic search and filtering process for recent technical articles, most literature focused on numerical simulation of vehicle motion (Chen and Cai 2004; Chen et al. 2015; Kim and Kim 2019; Kim et al. 2021) and wind-tunnel testing technique to measure aerodynamic forces on vehicles (Suzuki et al. 2003; Zhu et al. 2012; Dorigatti et al. 2012; Chen et al. 2015; Wang et al. 2018; Kim et al. 2020). In recent years, challenging technologies also have been reported, such as the wind-tunnel technique for moving vehicle tests (Wang et al. 2022; Xiang et al. 2018) and numerical dynamic analysis considering bridge–vehicle–wind interaction (Hou et al. 2019; Zhou and Chen 2016; Wang and Xu 2015). All those accomplishments enable us to estimate the critical wind speeds of vehicles on a bridge and determine when to close the bridge or lower the vehicle speed limit during windy conditions. Kim et al. (2021) also proposed a traffic-control strategy based on critical wind speeds obtained through wind-tunnel tests and numerical analysis.

However, most of these studies do not provide answers on how often bridges would be exposed to traffic-vulnerable conditions and whether or where risk-mitigation measures should be applied. To answer these questions, we need to estimate the risk level, which can represent the vulnerability of bridges to wind-induced accidents reflecting onsite wind and traffic environmental characteristics. Also, based on the obtained risk information, it should be able to identify the dominant factors of the risk level and determine practical and economic decisions to secure sufficient vehicle safety. Unfortunately, although previous studies have provided excellent ways to assess the key components of risk, i.e., aerodynamic coefficients and critical wind speeds of vehicles, they barely addressed the problem of how to calculate the risk level itself.

Various geometric and environmental factors contribute to the overall accident risk of bridges. Geometric characteristics of a long-span bridge, such as deck shape, elevation, curvature, and slope, change along the entire driving path, which results in varying wind conditions that vehicles experience according to their location. For example, Kim et al. (2021) reported a considerable reduction in the critical wind speed of a truck on a curved approach span compared with that on the cable-supported bridge in their case study due to the unique deck shape and road alignment. Also, two environmental factors, wind and traffic characteristics, can affect the risk. For example, even if the critical wind speed is low, the actual risk remains acceptable when traffic volume is low or strong winds are not frequent enough. Accordingly, the risk analysis needs an engineered procedure to accommodate all these uncertain factors that govern the risk evaluation and identify the dominant sources of vulnerability and their significance on the estimated risks. This information enables us to establish an effective risk-mitigation strategy via comparative risk analyses for potential measures.

As far as we can ascertain, available studies on the risk assessment of vehicle accidents on bridges are limited. For example, Baker (1987, 1991, 2015) and Coleman and Baker (1992) suggested several risk-assessment methods that consider the onsite wind environment; however, these studies focused on the interactions between vehicles and winds on flat ground and did not consider the geometric factors of road infrastructures. Therefore, these methods could not consider the aerodynamic impact on vehicle stability caused by the geometric characteristics of bridges such as deck shape, curvature, cant, road alignment, and exposed length. Kim et al. (2016) also discussed the vulnerability of wind-induced accidents on bridges, but the following points were not properly incorporated. First, data such as daily traffic volume and the ratio of heavy vehicles were not considered in estimating the risk of accidents. Second, the risk assessment focused only on the cable-supported spans of the sea-crossing bridge, although the approach spans also could increase the overall risk of accidents (Kim et al. 2020).

Therefore, this study proposed a quantitative risk-assessment methodology of vehicle instability to strong winds reflecting geometric characteristics of entire roadways of sea-crossing spans and onsite wind and traffic properties. Guidance was provided for selecting geometric parameters of a bridge roadway—deck shapes and road alignments—and reflecting them during wind-tunnel tests and vehicle analysis. The annual frequency of wind-induced accidents was adopted as a risk measure. Because the total risk index is calculated as the sum of component risks from each lane, span, and vehicle type, the risk-assessment procedure can provide information on vulnerable positions and contributing factors. Accordingly, by evaluating the risk indices for available mitigation strategies, the proposed methodology enables the bridge operator to decide on an optimal risk-reduction measure with a solid technical background. The proposed risk-assessment method was applied to the Gwangan Bridge, South Korea, where several overturning accidents were reported (Kim et al. 2020, 2021). The application successfully identified the source of vulnerability and compared the countermeasure effectiveness in terms of risk index, demonstrating the engineering significance of the proposed method.

The suggested risk-assessment procedure consists of four main parts shown in Fig. 1. The first part is a wind-tunnel test to evaluate the influence that deck shape exerts on the aerodynamic characteristics of vehicles. During the experiment, the cross sections of a cable-stayed bridge and the approach ramps of bridges were tested to measure the variable wind loads according to a vehicle’s location on the bridge. In the second part, a series of vehicle analyses were performed considering road alignments to obtain a vehicle’s fragility curve according to the wind speed. The third part uses onsite wind speed and statistical traffic data to compose a risk index and a fragility curve of vehicles, which could be used to predict the annual frequency of accidents. The probability density functions of wind speed were estimated through wind environment analysis using long-term wind data. In the last stage, risk-mitigation measures were applied, if necessary.

Calculating vehicle wind loads on a deck is essential for evaluating fragility curves. The wind forces and moments of vehicles on a bridge deck can be calculated by Eq. (1) (Dorigatti et al. 2015; Kim et al. 2020; Zhu et al. 2012; Chen et al. 2015)where $C_i$ ($i=D,S,L$) = drag, side, and lift force coefficients; $C_j$ ($j=R,P,Y$) = rolling, pitching, and yawing moment coefficients of a vehicle on a bridge deck; $F_i$ and $M_j$ = corresponding six aerodynamic loads in the Cartesian coordinates; $\rho$ = air density; $A$ and $h$ = reference vehicle area and height, respectively; and $V_a$ and $\psi$ =apparent wind speed (vectorial summation of upcoming wind speed and negative vehicle speed) and direction, respectively, as shown in Fig. 2. They can be estimated using Eq. (2) and (3)where $U$ and $u(t)$ = mean and fluctuating components of upcoming wind speed, respectively; $v$ = vehicle speed; and $\beta$ = upcoming wind incident angle measured clockwise from the direction of vehicle movement.

The aerodynamic coefficients of vehicles on a bridge deck $C_i$ can be expressed using two additional parameters $B_i$ and $C_i^U$ as shown in Eq. (4)where $C_i^U$ = aerodynamic coefficient of a vehicle under undisturbed wind conditions on a flat plate, which is the univariate function of the apparent wind direction, $\psi$ (Baker 1987; Batista and Perkovič 2014); and $B_i$ = deck influence factor (DIF), representing the influence of a deck shape on each aerodynamic coefficient of a vehicle according to the wind direction. The DIF was assumed to be the univariate function of the upcoming wind direction $\beta$ because the wind-speed profile and its distribution over a deck, which govern wind loads of vehicles, are highly dependent on the upcoming wind direction regardless of the vehicle’s movement.

These two aerodynamic characteristics, $B_i$ and $C_i^U$, can be estimated from wind-tunnel testing. First, $C_i^U$ can be measured by implementing an undisturbed wind application on a scaled vehicle model located on a flat plate in the wind tunnel. Using a force-balance sensor, the wind loads of vehicle models under undisturbed wind conditions, $F_i^U$ and $M_j^U$, can be measured. Then corresponding coefficients are calculated using Eq. (5). These coefficients can also be found in the literature without testing if the vehicle shape is similarwhere $U_T$ = wind speed in the tunnel section. Once the six coefficients, $C_i^U$, are estimated for all wind directions, the DIFs, $B_i$, should be assessed using a deck-section model. Considering $v=0$ (accordingly, $\psi =\beta$ and $V_a=U_T$) during the wind-tunnel test, the DIFs can be obtained using Eq. (6), derived from Eqs. (1), (4), and (5). Aerodynamic loads of vehicles, $F_i$ and $M_j$, can be measured on a deck-section model using a force-balanced sensor

Because the wind-speed profile and distribution significantly changes over the deck, the DIFs must be estimated for each traffic lane. In addition, the DIF should be obtained for each vehicle type because the influence of deck shape can be different according to the vehicle shape (Zhu et al. 2012; Kim et al. 2020). Based on the wind-tunnel test results, the wind loads can be estimated for a specific wind speed, direction, and vehicle speed, as shown in Eq. (7), which is derived from Eq. (1) and (4)

Eq. (4) assumes that the DIF is not significantly affected by a vehicle’s movement. Several studies have confirmed that the vehicle movement on a flat ground did not meaningfully affect the side force and rolling moment under the same apparent wind speed and direction, which are the governing factors of vehicle safety under strong-wind conditions (Baker and Humphreys 1996; Dorigatti et al. 2015; Sterling et al. 2010). Similar test results could be found in other experimental studies, which conducted moving vehicle tests on a bridge girder (Wang et al. 2022; Xiang et al. 2018). According to Wang et al. (2022), the difference between the two testing methods was less than 10% when the vehicle speed was lower than half the wind speed. However, the gap between the static and moving vehicle tests increased even for the side force and rolling moment when the vehicle speed became comparable to the upcoming wind speed. Therefore, an improvement in evaluating DIFs that consider vehicle movement needs to be made where necessary. In this study, however, Eq. (4) was applied to evaluate the aerodynamic characteristics of vehicles on a bridge deck, assuming the effect of the vehicle’s movement would be minor because the vehicle speeds were generally much lower than the wind speeds in severe weather conditions like typhoons.

The critical wind speed follows a probability distribution that is highly affected by the maximum gust due to the random fluctuating components of wind. Also, unlike flat ground, on a bridge, the heading direction of a vehicle continuously changes, which can cause significant variations in wind loads on a vehicle. Therefore, a fragility curve was calculated using a probabilistic approach that considers wind fluctuations and road alignment.

The annual frequency of wind-induced accidents was chosen as the risk index based on a probabilistic approach. The risk index can be evaluated using the fragility curves and onsite wind and traffic data.

A double-deck truss-type suspension bridge in Busan, South Korea, was selected to apply the proposed method. This bridge has two representative types of girders. The first is a double-deck truss girder that constitutes the main span of the bridge. The second is a simple double-deck girder for the approach spans with no truss members between the two decks.

According to the wind-tunnel testing results of Kim et al. (2020), wind acceleration was observed between the upper and lower decks in the approach span due to a tunneling effect. In fact, during the last 10 years, there have been three overturning accidents of high-sided vehicles on the lower deck in the approach span. These accidents indicate the necessity of a reliable risk assessment and proper mitigation measures.

This research focused on providing a systematic procedure that could assess the wind-induced car accident risk on bridges and manage the risk level by applying proper mitigation measures. The proposed method can estimate annual accident frequencies by considering deck shapes, road alignment, and onsite wind and traffic conditions. To this end, wind-tunnel tests, vehicle analyses, and probabilistic risk assessments were incorporated into the procedure. The effectiveness of the method was evaluated for an actual bridge. Based on the results, the following conclusions can be drawn:

Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

This research was supported by a Grant (21SCIP-B119963-06) from the Ministry of Land, Infrastructure, and Transport of the Korean Government. The authors are thankful to Principal Engineer Young-Kook Kim, the Bridge Management Team Leader of Busan Infrastructure Corporation, for field-measured wind data and his comments on this study.