AbstractA systematic approach was proposed to assess vehicle accident risk over sea-crossing bridges under strong winds. The annual frequency of an accident was evaluated as a risk index using the information on daily traffic volumes, the ratio of high-sided vehicles, and the long-term distribution of the speed and direction of the wind at the bridge site. The approach considered the effect that deck shapes and road alignments exert on vehicle stability. The risk index was estimated by accounting for the entire road sections of the examined bridge, including approach spans. The proposed method successfully identified the vulnerable positions along the bridge and the vehicle types. The application on a sea-crossing bridge demonstrated the usefulness of the proposed risk-assessment approach in determining a preferable mitigation strategy with less traffic intervention or minimized windscreen installation by quantitative comparisons between risk indices of several possible measures.IntroductionSea-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.Risk-Assessment ProcedureThe 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.Evaluation of the Aerodynamic Characteristics of VehiclesCalculating 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) (1) Fi=12ρCiVa2A;Mj=12ρCjVa2Ahwhere Ci (i=D,S,L) = drag, side, and lift force coefficients; Cj (j=R,P,Y) = rolling, pitching, and yawing moment coefficients of a vehicle on a bridge deck; Fi and Mj = corresponding six aerodynamic loads in the Cartesian coordinates; ρ = air density; A and h = reference vehicle area and height, respectively; and Va and ψ =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) (2) Va2(t)=(v+(U+u(t))cosβ)2+(U+u(t))2sin2β(3) ψ(t)=tan−1((U+u(t))sinβv+(U+u(t))cosβ)where U and u(t) = mean and fluctuating components of upcoming wind speed, respectively; v = vehicle speed; and β = upcoming wind incident angle measured clockwise from the direction of vehicle movement.The aerodynamic coefficients of vehicles on a bridge deck Ci can be expressed using two additional parameters Bi and CiU as shown in Eq. (4) (4) where CiU = aerodynamic coefficient of a vehicle under undisturbed wind conditions on a flat plate, which is the univariate function of the apparent wind direction, ψ (Baker 1987; Batista and Perkovič 2014); and Bi = 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 β 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, Bi and CiU, can be estimated from wind-tunnel testing. First, CiU 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, FiU and MjU, 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 similar (5) CiU=2FiUρUT2ACjU=2MjUρUT2Ahwhere UT = wind speed in the tunnel section. Once the six coefficients, CiU, are estimated for all wind directions, the DIFs, Bi, should be assessed using a deck-section model. Considering v=0 (accordingly, ψ=β and Va=UT) during the wind-tunnel test, the DIFs can be obtained using Eq. (6), derived from Eqs. (1), (4), and (5). Aerodynamic loads of vehicles, Fi and Mj, can be measured on a deck-section model using a force-balanced sensor (6) Bi(β)=2Fi(β)ρCiU(β)UT2A;Bj(β)=2Mj(β)ρCjU(β)UT2AhBecause 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) (7) Fi=12ρBi(β)CiU(ψ)Va2A;Mj=12ρBj(β)CjU(ψ)Va2AhEq. (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.Estimation of Fragility CurvesThe 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.Criteria for Wind-Induced AccidentsThe criteria for a wind-induced accident should be defined based on a vehicle’s response, and specified criteria are used to calculate the critical wind speed. In this study, the criteria were determined based on the tire reactions of vehicles. Two accident types of overturning and sideslip were considered. The thresholds were defined as follows: An index proposed by Liu (1999) for RSF was adopted to determine overturning accidents. The RSF indicates the transfer ratio of vertical wheel loads from the windward to the leeward side. The RSF can be calculated using Eq. (8) (8) RSF=|∑k=1nFzkl−Fzkw∑k=1nFzkl+Fzkw|where Fzkw and Fzkl = vertical reaction forces on the windward and leeward tires of the kth axle; and n = total number of axles of a vehicle. The RSF increases when the overall reaction forces of the windward tires approach zero and reach one when the windward tires are entirely lost. A threshold value of 0.9 was selected to determine the occurrence of overturning accidents.Sideslip accidents are supposed to occur when the friction force applied to one of the axles exceeds the friction limit, as shown in Eq. (9) (9) Fyk2+(Tk−fR(Fzkw+Fzkl))2>μ(Fzkw+Fzkl)where Fyk and Tk = lateral friction and traction forces of the kth axle, respectively; fR = rolling friction coefficient; and μ = friction coefficient.Calculating the Critical Wind SpeedA series of vehicle analyses were conducted for 100 different wind-speed histories to obtain a stochastic distribution of critical wind speed. The critical wind speed was obtained for each wind history according to the algorithm shown in Fig. 3, as suggested by Kim et al. (2021). A set of random phase angles was defined before the algorithm started. One-dimensional time histories of horizontal wind velocity fluctuations were artificially generated via the wave superposition method (Shinozuka 1971) to satisfy the target Von-Karman spectrum using predefined random phase angles. The algorithm in Fig. 3 began with an initial mean value of the wind speed U(=5 m/s) and the interval dU(=5 m/s). Wind fluctuation was artificially generated for a given mean wind-speed value based on the determined phase set. The wind data were then generated at a reference height for a bridge using the corresponding turbulence intensity and length scale.Next, the wind load histories were calculated via the obtained wind history and the DIFs using Eq. (7). The tire reaction forces were estimated by considering the aerodynamic, gravitational, and centrifugal forces. In the case of no accident, the average wind speed was increased via the dU, and the vehicle analysis was performed again. Once the reaction forces reached the limiting state, the analysis was performed by decreasing the average wind speed by dU/2. This iteration was repeated until the dU became smaller than 0.2 m/s (Kim et al. 2021). This allowed us to obtain the critical average wind speed, Uc, which was determined as U for the examined wind-speed history.Estimating the Fragility CurveThe stochastic distribution for the critical wind speed was obtained using 100 different sets of random-phase angles. Fig. 4 shows two examples of critical wind-speed distributions in a cumulative form obtained for the same truck, albeit for different turbulence intensities of 11.8% and 14.4%. The wind direction was 90°, and the truck was moving at 80 km/h. As shown in Fig. 4, the critical wind speed for turbulence intensity, 14.4%, had a smaller averaged critical wind speed and a higher standard deviation. This is because high-intensity turbulence resulted in greater amplitude for the fluctuation in wind speeds and larger maximum instantaneous wind loads on vehicles.The obtained critical wind-speed distribution can be expressed by a probabilistic function. In the present study, a Gaussian function was applied, and the solid line and dotted red line in Fig. 4 mark the estimated probabilistic distribution functions for each wind condition. These functions provide the accident probability of a single-vehicle trip for a specific mean wind speed. The estimated functions can be regarded as a fragility curve Fvi(U) where the superscripts i and v represent the ith wind direction and the vehicle speed, respectively.Risk AssessmentThe 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.Wind Environment AnalysisThe first step in the wind environmental analysis involved measuring the probability density functions for the wind speed. Long-term wind-speed data were collected from an anemometer on a bridge. The use of data measured at the height of the girder is preferred, but if not possible, data obtained from the top of the pylon can also be used via multiplication with a correction factor. The correction factor, CU, is calculated according to the power law in Eq. (10) (10) where zpyl = height of the anemometer on a pylon.Next, the probability density functions of wind speed were obtained for various wind directions. Weibull or generalized extreme value (GEV) functions were usually utilized to estimate the probability density functions of wind speed (Kim et al. 2011, 2016; Baker 2015). These functions were a good fit for the overall wind-speed distribution; however, the goodness of fit for the right-tail side of the wind distribution could be low due to a lack of measured data, which could result in a considerable error in probabilities for high wind speeds. Therefore, a histogram was adopted to obtain empirical probability density functions. Using Eq. (11), the empirical density was obtained for each wind-speed bin and direction (11) fUi(Uj)=P(U∈[Uj−ΔU/2,Uj+ΔU/2])ΔUwhere i and j = wind direction and bin number; ΔU = bin size; Uj = median wind speed of the jth bin; and P(U∈[Uj−ΔU/2,Uj+ΔU/2]) = probability that a wind speed is between Uj−ΔU/2 and Uj+ΔU/2. This probability is calculated by dividing the number of measurements in the jth bin by the total number of measurements. The empirical density accurately reflects the relative frequency of each bin for the wind speed, thus minimizing the loss of strong wind information.Estimating Accident ProbabilityThe accident probability for a single-vehicle trip on a bridge, PE, can be estimated by incorporating the estimated probability density functions of the wind speed and fragility curves. To reflect an actual traffic situation during strong winds, the probability was calculated by considering the traffic-control strategy of a particular bridge.First, the PE|dir=i was calculated. This is the conditional accident probability when the wind blows from the ith direction. Because the vehicle speed limit on a bridge changes according to the traffic-control strategy, the probability PE|dir=i can be expressed based on the total probability rule using Eq. (12) (12) PE|dir=i=∑k=1NlevelPE|dir=ikwhere Nlevel = total number of control levels of the wind speed in the strategy; superscript k = each level; and PE|dir=ik = conditional probability for level k that is calculated by using the fragility curve Fvki(Uj) and Eq. (13) (13) PE|dir=ik=∑Uj∈[Umink,Umaxk]Fvki(Uj)·fUi(Uj)ΔUwhere Umink and Umaxk =lower and upper boundaries for wind speed at control level k in the strategy; and vk = corresponding vehicle speed limit. Based on Eq. (12) and (13), the conditional accident probability, PE|dir=i, can be obtained for the ith wind direction, which reflects the traffic-control strategy of an examined bridge.Finally, considering all 16 wind directions, the accident probability of a single-vehicle trip on a bridge, PE, can be estimated using Eq. (14) (14) where Pi = probability of wind blowing from the ith direction, obtained via frequency analysis of the wind data.Two assumptions were made to calculate this probabilistic model. First, each wind data sample is independent, and the second assumption was that all vehicles are fully compliant with a particular traffic-control strategy. If the vehicle speed limit is 40 km/h, all vehicles were assumed to move at 40 km/h for a conservative risk assessment. These assumptions allow us to define wind-induced accidents as a Bernoulli process wherein the accident probability PE is applied equally to all vehicle trips. This probability must be estimated for each traffic lane and vehicle type.Estimating the Risk IndexThe annual frequency of wind-induced accidents can be evaluated using available statistical traffic data. Two traffic databases were used: the annual average daily traffic (AADT) and the vehicle composition ratio. Because we defined an accident event using the Bernoulli process, the risk index can be calculated using Eq. (15) (15) where NE = annual frequency of wind-induced accidents for the examined vehicle type and traffic lane; Qd = AADT of the examined bridge; RL = ratio of traffic volume that the interested traffic lane occupies; and Rv =composition ratio of the interested vehicle type. If we assume that RL is constant for all traffic lanes, Eq. (15) can be rewritten as Eq. (16), where NL = number of traffic lanes on the examined bridge. The risk index NE should be estimated for all lanes and vehicle types, and by adding all results, the total number of accidents per year for a specific bridge can be measured (16) To consider the effects of a payload on vehicle stability, two identical vehicle models were regarded as different vehicle types if the loading rates (payload/capacity) were different. For example, two identical trucks with 0% and 80% loading rates were considered to be different vehicle types.Mitigation MeasuresModifying a Traffic-Control StrategyThe risk can be effectively reduced by modifying a traffic-control strategy. Five main control factors can be considered: vehicle speed and type, wind speed and direction, and traffic lane. A traffic-control strategy can be divided into several levels, and each level can implement certain aspects of these five control factors.There have been several approaches in the literature to determine the control factors (Baker 1987; Imai et al. 2002; Kim et al. 2021). For example, Imai et al. (2002) calculated the critical wind speed for each wind direction. They established a train control strategy by applying wind-speed restrictions to a westerly wind (240°–300°) that differed from other wind directions. Kim et al. (2021) estimated fragility curves for vehicle types, speeds, and wind directions. Then, they selected a representative wind speed from each fragility curve corresponding to a specific accident probability (e.g., 5%). They established a four-level strategy according to vehicle type and wind speed, referencing existing control wind speeds. The effectiveness of these strategies must be evaluated using the proposed risk index to ensure the safety of vehicles traveling on the bridge.Most traffic-control strategies have been implemented by controlling vehicle speed, wind speed, and vehicle type. Operational personnel, feasibility, and monitoring capability need to be considered to avoid complexity. Although an optimum design should provide an adequate safe operating situation for any bridge, other aspects such as mobility and economic loss, among others, must also be considered.Windscreen InstallationWindscreen installation is an optional risk-mitigation method. This method can physically protect vehicles from wind hazards without modifying an existing traffic-control strategy. However, this can cause some deficiencies in terms of the aerodynamic characteristics of a girder, such as increasing the drag coefficient of the girder section or reducing the flutter stability of the bridge. Such steps can also result in high costs for installation and maintenance. Therefore, finding an optimized installation location is essential to reduce the risk level at minimum expense efficiently. To this end, the five-step procedure listed here is suggested to evaluate the effectiveness of windscreens and determine installation locations. •Step 1. Determine the configuration of a windscreen.•Step 2. Perform wind-tunnel testing for girders with windscreens installed.•Step 3. Select candidate locations on the bridge for windscreen installation.•Step 4. Calculate the risk index for each installation scenario.•Step 5. Determine final installation location based on the estimation results.Numerical ExampleA 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.Bridge CharacteristicsThe total road length of the bridge is 4,447 m. This bridge consists of one main and two approach spans, as shown in Fig. 5. The orientation of the main span is tilted about 37° from the north. Each approach span has a curved section with a radius of about 450–500 m. The highest elevations of the upper and lower deck of the bridge reach 44 and 35 m, respectively. Assuming that the anemometer for traffic control is located 5 m from the main span, 50 m was selected as the reference height. The corresponding turbulence intensity and length scale were determined as 11.7% and 162 m, respectively, according to Korean Society of Civil Engineers (KSCE) (2006) and Strømmen (2010). Table 1 summarizes the geometric parameters of all road sections used for vehicle analyses. As shown in Fig. 6, the traffic lanes of the upper and lower decks are southbound and northbound, respectively. There are eight traffic lanes on the bridge, and each has a width of 3.5 m. For simplicity, the lanes of the upper and lower decks were numbered from the land side to the sea side.Table 1. Geometric parameters of the main and the approach spansTable 1. Geometric parameters of the main and the approach spansGeometric informationApproach span (south)Main spanApproach span (north)Road length (m)1,2041,6801,563Road length for curved section (m)384—480Radius of curved section (m)500—450Cant (%)222Cant of curved section (%)5—5Slope (%)101Wind DataField-measured wind data were obtained from an anemometer located at the top of the pylon at 120 m. The recorded period spanned 11 years (2003–2013), and all wind data were multiplied by a correction factor of 0.9 based on Eq. (10) by considering the bridge site to be a coastal area (α=0.12). The 10-min averaged wind data were used for the analysis.Fig. 7(a) demonstrates the wind rose at the bridge site, and it depicts winds blowing mainly from south-southwest (SSW) to northwest (NW). Fig. 7(b), however, shows a wind rose for wind data exceeding 20 m/s, which is in contrast with that in Fig. 7(a) with a strong wind direction from north-northeast (NNE) to south-southeast (SSE).Traffic Data InformationAADT data from the upper and lower decks of the bridge were collected separately for 18 years (2003–2020) and are plotted in Fig. 8. According to the results, the AADT value for the lower deck is almost three times higher than that of the upper deck. From 2003 to 2017, the AADT of both decks increased linearly, but there was a significant decrease in traffic volumes during the recent 3 years. Therefore, we used the average AADT value for the last 5 years to reflect only the current traffic trends in the risk assessment (27,641 per day for the upper deck and 82,312 per day for the lower deck).According to the Ministry of Land, Infrastructure, and Transport (2020), the composition ratio of vehicle types in Busan city was classified into three large categories: cars (64.4%), buses (0.7%), and lorries (trucks and tractor-trailers) (34.9%). The ratio of the lorry class was further classified into three categories according to capacity: small-sized (56.4%), medium-sized (31.7%), and large-sized (11.8%) (Korea Transport Institute 2016). Small-sized lorries are two-axle trucks with a loading capacity of 1–2.5 t, and medium lorries are trucks with a 2.5–8-t capacity. Large-sized lorries are tractor-trailers that have a capacity of more than 8 t. According to the reports, the ratios of the loaded and empty lorries were 57.9% and 42.1%, respectively, and the average loading rate of the laden lorries was 79.1%. The loading rate information for sedans and buses was not available.Vehicle Model InformationThree vehicle types, namely a sedan, a truck, and a tractor-trailer, were selected for the present case study. These are considered the most common vehicle types in South Korea, and the vehicle parameters provided by Kim et al. (2021) were utilized in the analysis. The sedan and truck were modeled as a single body, whereas the tractor-trailer was modeled as a multibody. This was because tractor-trailers are two bodies that are connected at a hitch point by a roll spring. The payload capacities of the truck and the tractor-trailer were assumed to be 5,000 and 11,000 kg. The aerodynamic coefficients of vehicles under undisturbed wind conditions, CjU, were provided by Kim et al. (2020).In this analysis, the composition ratio of sedans was assumed to be 64.4% based on the traffic data information. They were considered to have crossed the bridge with only the driver as an occupant. The composition ratios of empty and loaded trucks were 13.2% and 18.2%, and those of empty and loaded tractor-trailers were 1.8% and 2.4%, respectively. Because the average loading rate was 79.1%, the payloads were assumed to be 3,955 and 8,701 kg for loaded trucks and tractor-trailers, respectively.As a vehicle analysis method, we adopted an enhanced quasi-static approach developed by Kim (2020), which could consider the effect of road alignments, including cant and curvature, and additional rolling moment induced by lateral deflection of the sprung mass along the roll center. The interactions between bridge–wind and bridge–vehicle were not considered in the analysis because the wind-induced or vehicle-induced vibration of the example bridge seemed not to affect the vehicle instability under the traffic-operating wind speeds.Wind-Tunnel TestThe DIFs of the vehicle models were estimated for the main and approach spans through a series of wind-tunnel tests at Seoul National University. The length scale of the girder models was 1/70, and the tunnel wind speed was set to 10 m/s. The aerodynamic loads on the vehicles were measured at the center of gravity using a small-size six-axis load cell.Figs. 9(a and b) show the experimental setups for each span. The factors of the main span were estimated for perpendicular wind, the most critical direction in wind-induced accidents. However, in the case of the approach span, additional measurements were taken for the directions plus or minus 15°, 30°, and 40° using a particular jig system. This consideration reflected that the lower deck in the approach span was exposed to a high-level vulnerability, as Kim et al. (2020) reported.Fig. 10 shows the DIFs of the side force and the rolling moment for trucks on the approach span as an example because these are the most critical factors in vehicle safety. Here, the wind was considered to blow from the land-side to the sea-side as such lane one would be the windward lane. According to Fig. 10, the DIFs reflect the wind distribution on the deck. First, based on the wind direction and vehicle position, the DIFs of side-force provided information regarding either the wind speed acceleration or deceleration. On the lower deck in the approach span, the DIFs of side-force always exceeded 1.0, which indicated the acceleration of wind speed. According to Kim et al. (2020), this phenomenon was explained as a wind-tunneling effect caused by the reduced gap between the upper and lower decks.This tunneling effect was not observed on the main span, as shown in Fig. 11(b), because the truss members blocked the wind flow and decreased the wind speed on the lower deck. The factor was maintained at around 0.8 on all traffic lanes on the lower deck of the main span. In the case of the upper deck, the factors were lower than 1.0, as shown in Figs. 10 and 11(a), which reflected the wind deceleration. Also, the factor decreased rapidly as the truck moved to the leeward. This was caused by the disturbance from the guardrail that spreads the wind flow into the open space. Accordingly, wind speeds dramatically decreased according to the vehicle’s position.Second, the DIFs of rolling-moment provided information regarding the wind-speed variation over the deck. On the upper deck, the factors of the rolling moment were much larger than those of side force. For example, it was doubled on lane four when the wind direction was 90°. This indicated that the wind speed over this traffic lane increased rapidly according to height, which induced the significant DIF of the rolling moment compared with the side force. Sharp wind profiles on the upper deck were also reported by Kim et al. (2020) due to the disturbance from the guardrail.On the other hand, the DIFs of the rolling moment on the lower deck were similar to those of the side force, except for Lane1. This translated to a nearly uniform wind profile for all traffic lanes and wind directions. These comparable results were due to the existence of the upper deck, which prevented the wind flow from spreading into the open space.Applying these new parameters, the wind-speed distribution over the deck could be evaluated considering a vehicle’s height with no need to measure the wind speed, which was the case in previous research (Kim et al. 2020). At the same time, the effects of wind distribution on the wind loads of vehicles were successively assessed according to the vehicle position and wind direction.Fragility CurvesFragility curves were estimated based on the algorithm shown in Fig. 3. Vehicle speeds of 40 and 80 km/h were examined considering the two-step speed-reduction strategy. It was assumed that all vehicles move on the bridge at the specified speed in evaluating fragility curves. In this way, the control effectiveness at the specified speeds was examined. Dry road conditions with a coefficient of friction of 0.85 were chosen. Fig. 12 shows the fragility curves of the five vehicle types in lane four on the upper and lower decks for the NE direction at a vehicle speed of 40 km/h.According to Fig. 12, the fragility depends highly on the vehicle type. Two high-sided vehicles, i.e., trucks and tractor-trailers, showed higher levels of fragility than the sedan. The fragility of the sedan was extremely low on the upper deck due to protection by the guardrail. In the case of loaded vehicles, fragilities were smaller than those of empty vehicles because the payloads prevented the vehicles from overturning. There were also considerable differences in the fragility curves between the upper and lower decks because of the wind-tunneling effect. The fragility of all vehicle types was higher on the lower deck due to the wind-speed acceleration.Risk Assessment ResultsRisk indexes were calculated for each vehicle type using the estimated fragility curves. First, based on Eqs. (12)–(14), accident probabilities per single-vehicle trip, PE, were estimated by considering the traffic-control strategy of the example bridge. The strategy of the examined bridge appears in Table 2. This strategy controlled traffic on the bridge based on a 10-min average wind speed.Table 2. Traffic-control strategies for the example bridgeTable 2. Traffic-control strategies for the example bridgeControl levelWind speed (m/s)Response110Limit vehicle speed to 40 km/h215Close all lanes for tractor-trailers320Close the upper deck for all vehicles425Close all lanes for all vehiclesFig. 13 shows the estimated PE for five vehicle types. As the results show, the accident probability of an empty truck was higher than other vehicle types in all traffic lanes. The difference between empty tractor-trailers and trucks was more than 108-fold, even though they had a similar level of fragility (Fig. 12). This large gap was due to the different limits that regulators implemented for tractor-trailers (15 m/s) and trucks (25 m/s). These results show that early traffic closure can significantly reduce the risk of accidents. Sedans also had smaller accident probabilities because of the protection by the guardrail. The accident probabilities of high-sided vehicles with payloads were more than 106-fold less than those of empty vehicles due to higher levels of rolling resistance.The probabilities on Lane 4 were generally higher than other traffic lanes because it was the windward lane for wind directions from NNE to SSE. Also, the accident probabilities were higher on the lower deck due to the tunneling effect and the different restrictions on wind speed. For example, the probability of empty trucks on Lane 4 was 5.34×10−16 on the upper deck, whereas it was 1.50×10−6 on the lower deck. According to the results, empty trucks on Lane 4 moving on the lower deck had the highest accident risk.According to Eq. (16), the annual frequency of wind-induced accidents was evaluated for each vehicle and traffic lane. Table 3 summarizes the estimated risk indexes of all vehicle types. According to the results, empty trucks were prone to 1.79 times per year on the lower deck, whereas the risk index was zero for other vehicle types or positions. As a result, the total risk index of the bridge was calculated to be 1.79 times per year. Empty trucks moving on the lower deck of Lanes 3 and 4 contributed the most to the total risk index due to the wind-tunneling effect and to the overall wind environment at the bridge site.Table 3. Estimated risk index for each vehicle typeTable 3. Estimated risk index for each vehicle typeVehicle positionSedanTruck (empty)Truck (loaded)Tractor-trailer (empty)Tractor-trailer (loaded)Upper deck0.000.000.000.000.00Lower deck0.001.790.000.000.00Only dry road conditions were considered during the risk assessment in this study. Because the probability of sideslip accidents increases as the friction coefficient decreases, it is necessary to consider the various type of road conditions, such as icy and wet roads, for a more accurate risk assessment. To this end, however, a statistical relationship among road conditions, road friction coefficients, and other environmental factors such as temperature and precipitation should be investigated, which is beyond the scope of this paper. These additional factors could be incorporated in future works.Modifying Traffic-Control StrategiesThe bridge operation agency has implemented a new form of traffic control as a mitigation strategy since 2020. Also, Kim et al. (2021) suggested a new traffic-control strategy for this bridge based on the vehicle analysis results. In this section, the effectiveness of these two strategies (Table 4) in reducing the risk level of the bridge was evaluated. The agency has applied Strategy 1 to the bridge since September 2020, and Strategy 2 was suggested by Kim et al. (2021). In Strategy 1, a speed limit of 64 km/h was enforced, and the bridge closure wind speed was reduced from 25 to 20 m/s. However, in the second strategy, the lower deck lanes were closed only for high-sided vehicles at wind speeds of 18 m/s without changing the vehicle speed limit.Table 4. New traffic-control strategiesTable 4. New traffic-control strategiesControl levelWind speed (m/s)ResponseWind speed (m/s)Response17Limit vehicle speed to 64 km/h16Limit vehicle speed to 40 km/h210Limit vehicle speed to 40 km/h18Close the lower deck for high-sided vehicles315Close all lanes for tractor-trailers21Close the upper deck for high-sided vehicles420Close all lanes for all vehicles25Close all lanes for all vehiclesThe risk index of the bridge was estimated for the two strategies and is presented in Table 5. The results show that the two strategies effectively reduced the risk index by more than 98%. Both approaches effectively reduced the risk by closing the lower deck for winds of 20 and 18 m/s, respectively, which prevented the overturning of the high-sided vehicles. Based on the second strategy, sedan vehicle types can be excluded from all the enforced closings because the risk of overturning for sedans was much lower than that for high-sided vehicles.Table 5. Risk assessment results for the new strategiesTable 5. Risk assessment results for the new strategiesStrategyRisk indexPrevious strategy1.79Strategy 10.00Strategy 20.03Windscreen InstallationAs another mitigation method, the installation of windscreens was also examined. Fig. 14(a) shows the windscreen configuration. The screen height was about 4 m on a prototype scale, which could cover the trucks, and the ventilation ratio was 47.3%. The windscreen model was attached on both sides of the lower deck in the approach span model during the wind-tunnel test, as shown in Fig. 14(b).Fig. 15 shows the six different locations on the bridge that were picked to check the windscreen performance. Overall, the risk index decreased as its installation point was changed (Fig. 16). The results show a maximum reduction of 42% was the risk index when the windscreen was installed at road section five. The average risk index reduction was about 10%–25% for the other sections. This can be explained by the onsite wind distribution when the strong wind frequently came from NNE, northeast (NE), and east-northeast (ENE) directions, which created a vulnerable wind angle for vehicles in road section five. In addition, road section five featured a curved road where the heading direction of vehicles continually changed. Therefore, vehicles moving on this section were more prone to facing vulnerable wind conditions. When the windscreens were installed on road sections four and five together, the risk index was estimated as 0.49 times per year, which was 72% lower than when there were no mitigation measures.In this case study, we made several assumptions to simplify the problem. For example, all vehicles were classified into one of five types. Also, the traffic ratio in all lanes was considered constant. These results could be improved by using more detailed information on vehicle types and traffic conditions. Despite the mentioned limitations, the case study showed that the proposed method provides useful quantitative information for risk assessment. In particular, the process reflects the geometric characteristics of vehicles and bridges and onsite wind and traffic data. In addition, the estimated risk indexes were consistent with the real-world accident data collected for this particular bridge. Therefore, the proposed method could provide helpful insight into the wind-hazard analysis and risk assessment and aid the decision-making process for mitigation strategies.ConclusionsThis 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: •The risk index and annual accident frequency were evaluated for each vehicle type and location. This index enabled us to quantitatively compare the relative effectiveness among the potential measures for risk reduction and resulted in a more systematic decision-making process.•The proposed method successfully estimated the risk level by considering the effect of deck shape and road alignment on vehicle stability. The change of wind distribution over a girder according to wind direction was reflected through wind-tunnel tests. The relative angle between the main wind direction and the vehicle heading direction on bridges was also reflected in the risk index, which significantly affected the frequency of vehicle exposure to vulnerable wind directions.•The application of the proposed method to the examined bridge demonstrated that the risk to a vehicle was maximized on the lower deck in the approach span. The estimated risk indexes were consistent with the three accident cases observed over the last decade, which showed the effectiveness of the proposed method for assessing the risk level of bridges.•The mitigation strategies examined in the case study showed that road closure of the lower deck or the limited windscreen installation in a critical position could significantly reduce the risk level by 98% and 72%, respectively.•The proposed procedure provides a general approach for assessing the risk of wind-induced accidents and determining mitigation actions, which could account for the unique features of each bridge. Considering the increasing importance of risk management for social infrastructure, the proposed method is expected to play an essential role in managing the vehicle-accident risks in sea-crossing bridges against strong winds.Data Availability StatementSome or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.AcknowledgmentsThis 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.References Baker, C., and N. Humphreys. 1996. “Assessment of the adequacy of various wind tunnel techniques to obtain aerodynamic data for ground vehicles in cross winds.” J. Wind Eng. Ind. 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