Revisiting the Serviceability of Long-Span Bridges under Vortex-Induced Vibrations Based on Human Body Vibration

. Vortex-induced vibrations (VIVs) have been frequently observed on long-span bridges (LSBs) in recent years. Unlike other destructive aerodynamic phenomena of LSBs, VIVs are self-limited in amplitude, primarily afecting the serviceability of LSBs through unpleasant users’ feelings characterized by human body vibration. Most existing studies discussed this issue based on a popular human body vibration measure, the human comfort index (HCI) in ISO 2631-1. However, the HCI is primarily concerned with vibration above 0.5Hz, which might be unsuitable for disclosing the infuence of VIV because of the low-frequency features of LSBs’ VIVs. To address this limitation, this study advocates using the motion sickness index (MSI) to revisit the serviceability of LSBs experiencing VIVs based on an innovative wind-trafc-bridge simulation platform. Diferent from current studies exclusively focusing on vehicle riders, this paper additionally incorporates a vibration model for standing persons to understand the feelings of the pedestrians on the bridge. On this basis, the infuence of VIV and trafc load is comprehensively examined. Te results indicate that the HCI is inappropriate for exploring the serviceability of LSBs under VIVs regarding users’ feelings, but the MSI is a good alternative. Moreover, the increasing trafc load can obviously mitigate the adverse efect of VIVs on the bridge’s serviceability, which may be utilized to control VIVs of LSBs in real-world engineering practice.


Introduction
Te rapid development of high-strength materials and construction technology has promoted the emergence of long-span bridges (LSBs) worldwide.Te inherent characteristics of high fexibility and low structural damping of LSBs render them highly susceptible to aeroelastic phenomena, such as vortex-induced vibration (VIV), coupled futter, torsional futter, and galloping [1].VIVs usually occur at modest wind environments (i.e., relatively low wind speeds), and the resulting aerodynamic forces acting on the bridge deck make the VIV self-limited in amplitude.For the other three typical aerodynamic phenomena, the bridge vibration amplitude tends to increase continuously and, therefore, can lead to aeroelastic instabilities [2].As a result, the VIV is commonly deemed less destructive than the other three and a potential serviceability threat for LSBs [3,4].Unfortunately, VIVs have been frequently observed on LSBs in recent years.Typical examples include the Trans-Tokyo Bay crossing bridge in Japan [5], Ewijk bridge in Netherlands [6], and Volgograd continuous bridge in Russia [7].Notably, two VIV events appeared successively on the Yingwuzhou Yangtze River Bridge [8] and Humen Bridge [9] in one week.Te feld inspection and theoretical analysis suggested that the oscillations (i.e., VIVs) on the above two bridges caused trivial structural deterioration/damage, but the oscillations make some people unpleasant when using the bridges [10,11].In particular, the VIV amplitude of Humen Bridge was so noticeable that the bridge managers promptly shut down the bridge for 10 days until no obvious VIVs to prevent bridge users from unpleasant feelings [12].Although closing the bridge is an efective way to avoid serviceability concerns, it is an expedient countermeasure and kind of overconservative.Tis makeshift adversely infuenced trafc mobility, which is unfavorable for a trafc bottleneck like a LSB.Actually, the defcient understanding of bridge users' feelings about VIVs, i.e., whether it is pleasant for bridge users to travel on the bridge under a specifc VIV, is blamed for this conduct.Terefore, a reliable evaluation framework of the serviceability of LSBs under VIVs is needed to be prepared for any future possible VIVs.
To ensure good serviceability, many bridge design codes and standards have established serviceability limit states for LSBs under VIVs, such as the AASHTO [13], Chinese code [14], and Japanese guide [15].However, most codes and standards were formulated in a very crude manner, which may be inadequate to meet the current requirement (or ft the current knowledge).As informed by research in the ergonomics arena, the bridge's serviceability regarding the users' feelings is increasingly discussed based on the vibration experienced by the users (i.e., human body vibration).For bridge VIV in particular, a number of studies have been conducted as prompted by the frequent VIV occurrences of LSBs in recent years.For instance, Yu et al. [16] examined the efect of bridges' VIVs on the ride comfort of a single vehicle crossing the bridge, revealing that VIVs could aggravate the dynamic vehicle responses and thereby cause more severe discomfort issues.Zhu et al. [11] assessed the drivers' ride comfort when traveling on a long-span suspension bridge under VIVs in the context of the wind-trafc-bridge system based on the criteria recommended in ISO 2631-1.Tey disclosed that the dynamic interaction between the stochastic trafc fow and the bridge can also afect the driver's ride comfort apart from the bridge's VIV, and trafc density and proportion can afect this interaction and the resulting ride comfort.More recently, Zhang et al. [17] considered the multimode lockin characteristics of the VIV of LSBs and studied the dynamic behavior and ride comfort of a single vehicle running on the bridge.
In general, the aforementioned studies focused more on developing methods to realistically simulate the human body vibration of the bridge users under a bridge VIV event, leading to a consensus that a realistic reproduction of realworld wind-trafc-bridge system is quite essential to understand the associated human body vibration of the bridge users and thus their feelings.However, most studies only provided vibration simulation methods for the users inside vehicles crossing the bridge but ignored the pedestrians standing on the bridge.More importantly, the ultimate human body vibration (or feelings) assessment was not considered seriously but simply followed a popular routine (i.e., using the overall vibration total value (OVTV) recommended in ISO 2631-1 [18] to identify the unpleasant feelings of the users of a bridge under VIVs).Actually, engineering practice has revealed that the frequencies (f ) of VIVs occurring on most LSBs are very low (e.g., f ≤ 0.5 Hz).Rather, the currently popular OVTV was designed for characterizing human's discomfort that is sensitive to vibration in the frequency range of 0.5∼80 Hz, which makes its ability to distinguish unpleasant users' feelings originating from the bridge's VIVs questionable.In view of this, this study attempts to revisit the serviceability of LSBs under VIVs in terms of human's motion sickness that has been found to be triggered by vibration below 0.5 Hz.Additionally, a comprehensive examination of the infuence of VIV and trafc fow on the bridge serviceability (users' feelings) is performed both from the perspective of vehicle riders and pedestrians.
Te remainder of this paper is organized as follows.Section 2 introduces the general computational framework of bridge users' human body vibration and the associated feeling assessment method.In Section 3, the serviceability of LSBs under VIVs is studied with a single vehicle crossing the bridge, trying to reveal the infuence of VIV itself.In Section 4, the serviceability is evaluated in the context of a windtrafc-bridge system to disclose how VIV and trafc load together afect users' feelings.Finally, Section 5 concludes the entire paper.

Evaluation Procedure of Human Body Vibration for Users of the Bridge under VIVs
Evaluating the bridge users' feelings on a subjected vibration based on numerical simulation requires two critical parts, which are a wind-trafc-bridge dynamic analysis framework to calculate the human body vibration of the users and a human body vibration assessment procedure to identify the users' feelings, respectively.As shown in Figure 1, the wind-trafc-bridge dynamic analysis involves the modeling of the coupled vehiclebridge system, VIV, and trafc loading scenario, each of which contains complex details.Since these details have been well reported in the authors' previous work [11,19], this study only provides a summarizing demonstration and accessible references of each ingredient in Section 2.1.
For the human body vibration assessment procedure that has been seldom reported in the literature, the authors presented a detailed demonstration of how to obtain the index for determining users' feelings based on the objective human body vibration of a user and the specifc feeling criteria in Section 2.2.

Wind-Trafc-Bridge Dynamic Analysis for the Bridge under VIVs.
Te general computational framework of the wind-trafc-bridge system with a bridge experiencing VIVs includes two major ingredients: the VIV modeling and vibration analysis shown in Figure 1.Specifcally, the vortexinduced force (VIF) model is adopted to replicate the VIV of the bridge.Since the main focus of this study is to build a general evaluation framework and to examine the efect of VIV on bridge users' feelings, the harmonic VIF model [20] that exclusively depicts the force caused by the shedding of vortices from the bluf body (i.e., the major excitation of VIVs) is considered for easy implementation, which can be expressed as 2 Structural Control and Health Monitoring in which ρ represents the air density; U denotes the wind speed; D is the deck depth;  C L is the root-mean-square (RMS) value of the lift aerodynamic force coefcient; ω is the circular frequency of the vortex shedding, which can be obtained as ω � 2πf b (f b is the VIV frequency); t denotes time in seconds; and θ is the phase diference between VIF and VIV.Te determination of the VIF model parameters often requires massive wind tunnel tests, which can be time-consuming and cost-prohibitive.Alternatively, an inverse identifcation method of the VIF model parameters based on dynamic analysis is recommended.Te idea is to compare the VIV amplitude caused by unit VIF (calculated by dynamic analysis) and the VIV amplitude of interest.Previous studies of the authors have demonstrated that the adopted VIF model and model parameter identifcation method have a good performance in simulating VIVs of LSBs according to feld monitoring data, and readers may refer to Zhu et al. [11] for more details.Note that, in the present study, the VIF model parameters will be calculated in terms of the condition that the LSB only sufers from the VIF, and several groups of parameters will be discussed to investigate the efect of VIV severities (i.e., the VIV amplitude) on human body vibration and users' feelings.Once the VIF model parameters are obtained, the VIF can be conveniently included in the subsequent coupled vibration analysis.Terein, the aerodynamic behavior of the bridge is simulated solely by the VIF, and the wind efect on the vehicle is reproduced based on the corresponding turbulent wind feld.
With explicit excitations from the wind, the governing equations of the wind-trafc-bridge system can be expressed as follows: where i denotes the ith vehicle on the bridge (n is the total vehicle amount); the subscripts b and v denote the bridge and vehicle; M, C, and K are the mass, damping, and stifness matrices, obtained from fnite element modeling for the bridge or multibody dynamics simulation for the vehicle; and a, v, and u are the acceleration, velocity, and displacement vectors.Te force term F vG,i represents the weight of the ith vehicle.F bv,i and F vb,i are the coupled vehiclebridge forces (i.e., interactions) at the contact points between ith vehicle and the bridge, which are related to the bridge and vehicle vibration status and the road roughness excitation [21].Te aerodynamic behavior of the bridge is determined by an elementwise force vector acting on the bridge girder as follows: where φ n (x) denotes the nth VIV mode shape of the bridge and L is the bridge span length.By applying specifc F bw to the bridge's model, diferent modes of VIV can be refected.As for the vehicle, the quasistatic aerodynamic forces are adopted to describe the associated wind efect (F vw ) according to [22].In this way, the complex interactions between wind, trafc (or vehicles), and the bridge can be rationally modeled.Equations ( 2) and (3) will be solved independently through the Newmark-β method based on the force and displacement equilibriums at the vehiclebridge contact points to obtain the ultimate system vibration.
Notably, the realistic trafc loading scenario is simulated by introducing an improved cellular automaton (CA) trafc model.CA trafc model can facilitate a spatiotemporal microscopic trafc simulation, assuming that time and space are discrete.By regulating the driving behavior (e.g., acceleration, deceleration, and lane change) of each vehicle in Structural Control and Health Monitoring the trafc fow and parallelly updating each vehicle's velocity and position, the real-world trafc phenomena can be realistically reproduced [23].More detailed explanations can be found in the authors' previous work [19], which are omitted herein for a succinct purpose.Besides, other excitations of the system include road roughness and turbulent wind, each of which can be assumed as a stationary Gaussian stochastic process and simulated in a pretty mature way [24].

Human Body Vibration Assessment
Procedure.Based on the vibration analysis, the dynamic responses of the bridge and vehicles can be obtained.As shown in Figure 1, the dynamic responses need to be further transformed for vibration assessment because the human is experiencing a compound vibration transmitted from the relevant supporting surfaces (i.e., whole-body vibration).In this case, the overall vibration measure needs to be calculated based on the vibration model of bridge users (Figure 2).Unlike the previous research focusing on the feelings of vehicle riders only, this study introduces a seated person and a standing person for the vibration (or feeling) assessment for vehicle riders and pedestrians, respectively.A seated person can experience motions from three supporting surfaces, i.e., the foor, seat, and backrest, and a standing person can only perceive the motion from the supporting foor [18].
With the whole-body vibration measure, the human feeling index can be examined with a typical routine as recommended in ISO 2631-1 [18].For the previously popular human comfort index based on OVTV [11,17,25], the routine is to frst get the whole-body vibration measure from vehicle/bridge responses according to the relative position between the person and the vehicle/bridge node (as the responses are calculated for discrete points).Ten, those human body vibrations that are related to the human comfort index need to be frequency-weighted to show the infuence of vibration frequency on human comfort.Finally, the OVTV is obtained as a human comfort indicator based on the RMS values of the frequency-weighted vibrations and some multiplying factors suggesting the infuence of vibrations from diferent directions on human comfort.It should be noted that the frequency weighting functions for the human comfort index (W k , W d , W c , and W e in Figure 3) have relatively small values in the interested frequency range of VIVs of LSBs (e.g., below 0.5 Hz).As a result, the human body vibration originating from VIV might be fltered out in calculating OVTVs, and the infuence of VIV on bridge users' feelings can be misunderstood if using human comfort (or OVTV) as an indicator.
Alternatively, this study advocates using the motion sickness index (MSI) to describe the users' feelings on VIVs of LSBs.As documented in ISO 2631-1 [18], the MSI is concerned with vibration with frequency contents below 0.5 Hz.Motion sickness generally happens when the movement that a person sees is diferent from what his/her inner ear senses, resulting in dizziness, nausea, and vomiting.Similar to the procedure of obtaining the human comfort index (OVTV), the calculation of MSI starts with transforming bridge/vehicle responses to the whole-body vibration measures based on the relative position.Te major infuencing vibration on the MSI includes vertical, pitching, and rolling accelerations, so the vertical accelerations from three supporting faces (a zf , a zs , and a zb ) and pitching (a ry ) and rolling (a rx ) accelerations are obtained as follows: in which € Z v , € θ v , and € φ v represent vertical, pitching, and rolling accelerations at the vehicle centroid and d s , y s , and h s are longitudinal, transverse, and vertical distances between the vehicle centroid and the vehicle rider's seat.As for the standing person, only the vertical vibration transmitted from the foor (a zf ) is involved in the MSI calculation, and it is obtained as the vertical bridge acceleration at the standing point.Subsequently, the decisive accelerations for MSI are frequency-weighted based on a fast Fourier transform (FFT) convolution.In detail, the original time-history acceleration x(k) (with N discrete time steps) is transformed into the frequency domain as X(r) using the discrete Fourier transform (DFT): where ω N � e −2πr/N ,r � 0, 1, . .., N − 1. Te frequencydomain acceleration will be weighted as a wi (t) (i denotes diferent acceleration components, e.g., subscripts zf and ry in equations ( 5) and ( 6)) according to the frequency weighting function for MSI (W f in Figure 3).Ten, the frequency-weighted acceleration is used to calculate the motion sickness dose value (MSDV) according to in which T is the duration of the time-history acceleration in seconds.Te total MSDV (MSDV T ) is obtained by adding MSDVs of all decisive accelerations for MSI (i.e., 5 acceleration components for a seated person and 1 acceleration component for a standing person), as the decisive accelerations are deemed as equally important to MSI.Finally, the MSI is calculated as follows [18]: where K m is a constant related to the characteristics of persons of interest, and it is adopted as 1/3 herein for typical bridge users, mainly consisting of adults.A larger MSI value suggests that more bridge users may sufer from motion sickness and have unpleasant feelings on the VIV.It should 4 Structural Control and Health Monitoring be noted that many existing studies developed motion sickness criteria in terms of structural vibration for the users of a particular structure (e.g., the occupants of wind-excited tall buildings in [26]).However, the associated outcomes can hardly be used in the present study, given the signifcantly diferent systems being studied.By focusing on the fundamental human body vibration, the adopted MSI from a reputable standard provides a reliable measure to characterize the motion sickness of the users of a bridge experiencing VIV, which is deemed suitable for the current research focus.

Vibration Characteristics and Feelings of Users of the Bridge under VIV and a Single Vehicle
Currently, very few endeavors have been made to understand the infuence of LSBs' VIVs on the vibration characteristics of the bridge users in the context of a windvehicle-bridge system, and the associated users' feelings did not receive deserved attention.In this regard, this section presents evaluations in the wind-vehicle-bridge system, where the bridge is experiencing VIVs and supports a single running vehicle.Accordingly, it can be deemed that the vibration of the seated person in the vehicle is primarily afected by the bridge's VIV and vehicle-bridge interaction, while the vibration of a standing person on the bridge is exclusively infuenced by the VIV, given that a single running vehicle can cause trivial infuence on the bridge vibration.
3.1.Prototype Bridge.Te Yingwuzhou Yangtze River Bridge (YWB), a three-tower four-span suspension bridge, is adopted as the prototype bridge in this study.It has a total

Vertical Axis
Floor Floor Vertical Axis   4(a)).As shown in Figure 4(b), the π-shaped steel-concrete composite stifening girder is used, with a cross section that is 38 m in width and 3 m in height.Besides, the YWB supports two-way (with four lanes in each way) highway trafc.
As stated previously, the proposed method requires a fnite element model of the bridge.To capture the overall dynamic characteristics and maintain acceptable computational eforts, the bridge's girder and pylon are idealized as 3D beam elements; the cable and suspender are simulated with 3D link elements; the stifness contribution owing to the pavement and railing is neglected, and their masses are equally distributed to the girder using the mass-only element.Consequently, a fnite element model (FEM) with 1548 nodes and 2236 elements is obtained.According to the real measurement reported in [11], the prototype bridge had a VIV event at the frequency of 0.244 Hz, which corresponds to the fourth vertical asymmetric mode (f � 0.242 Hz) obtained in the current fnite element analysis.Considering that VIVs of LSBs are likely to be excited in multiple loworder modes [17], a qualitative study of the infuence of VIV modes on the vibration characteristics and users' feelings will be performed based on several vertical asymmetric modes (including f � 0.242 Hz) as listed in Table 1.Notably, although torsional VIV modes with appreciable amplitudes can also cause unpleasant feelings in users, such VIVs are uncommon for real-world LSBs that have been carefully designed to avoid detrimental torsional vibrations and are, therefore, neglected in the present study.

Vibration Characteristics of the Bridge User.
As mentioned above, only a single vehicle is considered in this section, which is selected as the most common type of vehicle traveling on the bridge, i.e., a sedan car running at 40 km/h.Te sedan car is modeled as a combination of several rigid bodies and wheel axles connected by springs and dampers, which has been reported in [11] and is omitted herein.

Time-History Dynamic
Response.Te previously observed VIV (f � 0.242 Hz) with an amplitude of 0.5 m [11] is frst studied.To clarify the infuence of vehicle-bridge interaction (VBI), VIV, and road roughness on the human body vibration of bridge users, three scenarios are studied with and without considering road roughness: (1) vehicle travels on the road (condition 1); (2) vehicle travels on the bridge without VIVs (condition 2); and (3) vehicle travels on the bridge under VIVs (condition 3).For those scenarios with road roughness, a very good road roughness is considered according to ISO [27].Figures 5 and 6 depict the time-history dynamic responses of the vehicle (measured from the vehicle centroid) and bridge (measured from the vehicle-bridge (V-B) contact point) under given conditions.
As shown in Figure 5, when road roughness is neglected, there is no vibration for the vehicle traveling on the road, and the VBI in condition 2 causes trivial vehicle vibration (i.e., a maximum vertical acceleration (MVA) of 0.0339 m/ s 2 ).However, the VIV and VBI can cause signifcant vertical vehicle vibration in condition 3 (namely, a MVA of 1.3798 m/s 2 ), and the VIV is the primary excitation because the MVA at the V-B contact point is 1.1506 m/s 2 .Te difference between the time-history accelerations of the vehicle centroid and the V-B contact point suggests that the perceived vibration for vehicle riders and pedestrians can be diferent, but generally, the bridge vibration is a baseline for the vehicle vibration because of the displacement equilibrium.
When road roughness is considered (Figure 6), the vehicle vibration becomes more signifcant, and the MVAs at the vehicle centroid for condition 1 and 2 become 1.4135 and 1.4253 m/s 2 , respectively.In condition 3, the MVA at the vehicle centroid increases to 2.1331 m/s 2 .But for the vertical acceleration at the V-B contact point, the MVA just increases slightly after considering road roughness, which can be because the VBI caused by a single vehicle (even if it is aggregated by road roughness) has a trivial infuence on the vibration of LSBs.
Generally, it can be concluded that the bridge vibration is closely related to the VIV and VBI, which can further afect the vibration of the running vehicle on the bridge.Although the bridge vibration serves as a baseline of the vehicle vibration, the vehicle vibration is typically more signifcant than the bridge vibration at the V-B contact point.Hence, for vehicle riders and pedestrians, the associated feelings on the bridge expiring VIVs might be diferent.Moreover, road roughness can aggregate the vehicle and bridge vibration, but its infuence on users' feelings remains unclear.

Power Spectrum Density.
Te bridge users' feelings on a vibration are highly dependent on the frequency of the vibration.Tis section further examines the power spectrum density (PSD) of the vertical acceleration at the vehicle centroid for conditions 2 and 3 introduced in Section 3.2.1.Figure 7 describes the PSD features under no road roughness condition, in which the vehicle vibration in condition 2 exclusively originates from the VBI, and the vehicle vibration in condition 3 is caused by the VIV and VBI.It can be seen from Figure 7(a) that the VBI primarily excites the vehicle vibration in relatively high frequencies (e.g., above 3 Hz).Te two obvious peaks in Figure 7(a) are at frequencies of 2.968 and 3.7 Hz, which are close to the frequencies of two high-order vertical bridge modes (i.e., 2.971 and 3.705 Hz).However, for condition 3 in Figure 7(b), the major frequency contents of vehicle vibration are near the frequency of VIV (0.242 Hz).Notably, there are two peaks enclosing the VIV frequency, which can be attributed to the Doppler efect [28] caused by the vehicle moving in a coupling vehicle-bridge system.Tis phenomenon can ultimately make the feelings of bridge users on moving vehicles unique because the contribution of the bridge's VIVs becomes two major components acting on the human body, each of which may have a diferent signifcance on the feeling depending on the associated frequency.
When considering road roughness (Figure 8), the PSD of vehicle acceleration becomes more chaotic, but it can be seen that most vibration energy concentrates in the range that is

Comparison of Human Comfort Index and Motion
Sickness Index.As mentioned previously, the currently popular index for human body vibration (or users' feelings) assessment might be unsuitable to investigate the efect of VIV because of the low-frequency characteristics of LSBs' VIVs.In specifc, the VIVs can cause excitations on the bridge users' bodies primarily in a range with low frequencies (e.g., below 0.5 Hz) rather than in a conventional range that is within the scope of OVTV including the resonance frequency of the human body (e.g., 4-7 Hz).Hence, this section presents a very important discussion by comparing the human comfort index and motion sickness    Structural Control and Health Monitoring index based on conditions 1, 2, and 3 described before, and an additional road roughness condition (average road roughness) is considered.Te calculation procedure of MSI follows the one presented in this study, and that of the human comfort index (i.e., OVTV) can be found in the previous work [11,17].Te MSI and OVTV for diferent conditions are summarized in Table 2. Interestingly, it is found that the OVTV is indeed an inappropriate index for studying the infuence of VIVs on bridge users' feelings, especially in terms of vehicle riders.As listed in Table 2, the OVTV for the vehicle driver in the very good road roughness condition only increases from 0.3846 m/s 2 to 0.4185 m/s 2 after considering VIV.Diferent from the trivial infuence of VIVs on the OVTV, road roughness can afect the OVTV signifcantly.For the vehicle driver in condition 3, the OVTV increases obviously from 0.4185 m/s 2 to 1.1068 m/s 2 as road roughness gets worse.
Nevertheless, the MSI appears to be a pretty good index to characterize the infuence of VIVs on bridge users' feelings.As shown in Table 2, after considering the VIV, the MSIs of the vehicle driver and pedestrian increase signifcantly, and the MSI is nearly free from the infuence of road roughness.For the example with a very good road roughness condition, the MSI of the vehicle driver increases from 0.02% to 3.49% after considering VIVs, but the MSI remains 3.49% as the road roughness condition becomes average.Similar patterns can be found in the MSI of the pedestrian, but it can be seen that the MSI of the pedestrian is lower than that of the vehicle driver.
Terefore, it can be clarifed that using the OVTV (human comfort index) is suitable to distinguish the efect of road roughness on bridge users' feelings, while the potential serviceability issue caused by VIVs of LSBs might be neglected.In other words, as long as road roughness remains 8 Structural Control and Health Monitoring the same, one may always obtain similar OVTVs under diferent VIV events.Tis issue can also be found in a recent study discussing the efect of the multimode lock-in property of VIVs on vehicle riders' OVTVs [17].In that study, different VIV modes only cause trivial diferences in OVTVs (e.g., in 10 −2 -level), but a worse level of road roughness easily leads to a signifcantly larger OVTV (e.g., in 10 0 -level).
Rather, using the MSI can obviously identify the serviceability issue for LSBs under VIVs in terms of users' feelings, i.e., the unpleasant feeling of the users of the bridge under VIVs can be distinctly predicted from the calculated MSI.

Infuence of Vehicle Speed, VIV Amplitude, and VIV
Frequency.Having disclosed that the MSI is a proper index to identify people's unpleasant feelings on VIVs, the serviceability issue of LSBs under VIVs is discussed using the MSI hereafter.In this section, the infuence of vehicle speed, VIV amplitude, and VIV frequency (or mode) is studied.
Similarly, only a single sedan car crossing YWB at 40 km/h is considered.Since previous studies have implied that the MSI is nearly free from the infuence of road roughness, it is assumed that the bridge is smooth.Te infuence of vehicle speed and VIV amplitude on the MSI is investigated based on the previously adopted VIV with f � 0.242 Hz.As shown in Figures 9(a Structural Control and Health Monitoring on (or for crossing) the bridge experiencing VIVs.Te efect of VIV frequency and amplitude is exclusively studied on the sedan car running at 40 km/h, addressing all VIV modes listed in Table 1.It can be seen from Figures 9(c) and 9(d) that the MSI of bridge users frst increases with VIV frequency but will fnally decrease as the VIV frequency is beyond a specifc value.For instance, when adopting the VIV amplitude as 0.5 m, the MSIs of the vehicle driver are  Te results can be attributed to the following two reasons.Firstly, as shown in Figure 3, W f increases with the frequency in the range of 0-0.166Hz and then decreases until f = 0.5 Hz, indicating an inverting decrease in MSI results starting at 0.387 Hz for the adopted VIV frequencies is not surprising.Secondly, although the maximum W f is obtained at f = 0.166 Hz, the higher energy contained in a relatively high-frequency VIV leads to a maximum MSI at f = 0.378 Hz, given the same vibration amplitude for all frequencies under investigation.

Users' Feelings for the Bridge under VIV and Traffic
In addition to the single-vehicle loading scenario in Section 3, users' feelings for the bridge under VIV and realistic trafc are often of more interest for understanding the real-world serviceability issue.Hence, the stochastic trafc fow is incorporated, following the authors' recent work [11,19].In specifc, a 2500 m-long road-bridge-road system is utilized to simulate random trafc fows based on the improved CA trafc model in [19].Herein, a road-bridge-road system can ensure the vehicle entering the bridge in a vibrating status as caused by road excitations to reproduce real-world phenomena and can help to simulate trafc behavior from a transportation network perspective [23].Four types of vehicles, including sedan car, minivan, motor bus, and semi-trailer truck, are considered to replicate heterogeneous trafc compositions, and three typical trafc densities (12, 25, and 40 vehicles/km/lane) are studied.Te trafc fow is assumed to be equally distributed on all lanes of YWB, each of which consists of 70% sedan cars, 10% minivans, 10% motor buses, and 10% semi-trailer trucks.For diferent vehicle types, diferent model structures and parameters (e.g., mass, stifness, and damping) are adopted according to [29] to refect the associated dynamic properties, and specifc driving features (e.g., acceleration rate and deceleration rate) are included in the CA trafc model.Overall, realistic trafc phenomena, like trafc congestion and its propagation, can be reproduced from the improved CA trafc fow, resulting in a reliable trafc loading scenario.Subsequently, the system will be analyzed for 800 s in a time step of 0.04 s, which allows an adequate evolution of trafc fows to refect various trafc distributions on the bridge and helps generate enough samples for calculating MSIs (each one refers to one sample of the feeling on crossing the entire bridge experiencing VIVs) for a statistical pursuit.Similarly, the infuence of VIV frequency and VIV amplitude is discussed in terms of the values same as those in Section 3. Notably, an 800 s-long simulation can take around 20 hours on a workstation with AMD Ryzen Treadripper 3970 × 32-Core @ 3.69 GHz processor when involving a free trafc fow, and the computational cost increases with trafc density.

Vehicle Rider.
As mentioned above, a statistical evaluation of the MSI of vehicle riders under various conditions is preferred, considering the stochastic nature of trafc fows.
Specifcally, during the 800 s-long simulations, multiple vehicles can cross the entire bridge.It is, therefore, more rational to collect all MSI samples, each of which represents the feeling of a vehicle rider on crossing the entire bridge under VIVs in a unique trajectory and time duration.Herein, the MSI samples of the same vehicle type are grouped and separately studied.It is found that for the four types of vehicles under consideration, the statistical characteristics of MSIs are similar.So, the most common bridge user, i.e., the sedan car driver, is discussed in detail.Figure 10 presents the violin plot of MSI samples of sedan car drivers under diferent VIV frequencies, VIV amplitudes, and trafc densities, and the corresponding mean value and coefcient of variance (CoV) are listed in Tables 3 and 4. In terms of the infuence of VIV frequency and VIV amplitude, the following observations are obtained: the mean MSI for sedan car drivers consistently increases with the VIV amplitude, and the mean MSI increases gradually for VIV frequencies of 0.101, 0.128, 0.242, and 0.378 Hz but then decreases when the VIV frequency turns into 0.531 Hz from 0.378 Hz.For instance, the mean MSIs for sedan car drivers of the moderate trafc fow (i.e., with a trafc density of 25 vehicles/km/lane) on YWB experiencing VIVs at 0.378 Hz with 0.1, 0.3, 0.5, 0.7, and 0.9 m amplitudes are 0.38%, 0.97%, 1.59%, 2.21%, and 2.84%, respectively; the mean MSIs regarding VIVs with a 0.9 m amplitude at frequencies of 0.101, 0.128, 0.242, 0.378, and 0.531 Hz are 0.39%, 0.72%, 2.20%, 2.84%, and 2.83%, respectively.
More interesting fndings are about the infuence of trafc density.First, the trafc load is found to be able to mitigate the adverse efect of VIVs on the MSI (or the bridge serviceability).As the trafc density increases, the MSI of sedan car drivers tends to decrease, which can be seen both from the violin plot (Figure 10) and the mean MSI.For example, for VIV frequency � 0.378 Hz and VIV amplitude � 0.9 m, the mean MSIs are 3.94%, 2.84%, and 2.47% for free, moderate, and busy trafc fows (trafc density � 12, 25, and 40 vehicles/km/lane).Te larger MSI (9.07%) obtained in Section 3 (i.e., only one vehicle is loaded on the bridge) for the same VIV condition also proves this phenomenon.Secondly, the trajectories/time durations of sedan cars crossing the bridge are often more irregular, resulting in larger CoVs of the MSI.For VIV frequency � 0.378 Hz and VIV amplitude � 0.9 m, the CoVs of the MSI are 0.03, 0.03, and 0.18 for free, moderate, and busy trafc fows.Tis is because there is heavy congestion in the busy trafc fow, and diferent drivers can take signifcantly diferent time durations to cross the entire bridge, leading to pretty diverse MSIs.To show this, the mean value and CoV of time durations for sedan cars crossing the bridge are calculated as 105.48 s (0.002), 105.57s (0.004), and 167.00 s (0.417) for free, moderate, and busy fows.a bootstrapping strategy is adopted to improve the reliability of the result.In specifc, 10 4 records of vibration are obtained from bootstrapping: randomly extracting each record with the expected time duration from the totally 800 s-long vibration results.Ten, the MSI of pedestrians is calculated as the mean value of the 10 4 records (or MSIs).Notably, the location of the pedestrian on the bridge can also infuence the MSI, which is related to the mode shape of the VIV.Hence, the MSI is evaluated for several standing locations regarding VIVs of diferent frequencies (with a 0.9 m amplitude).
Figure 11 shows the MSIs evaluated at several typical locations of the frst main span of YWB under diferent VIV frequencies and trafc densities.Figures 11(a) and 11(b) show the evolution of the MSI along diferent locations other than crests/troughs of the VIV wave, and Figures 11(c)-11(e) depict the evolution among diferent wave crests, nodes (zero wave amplitude), and troughs.For a better illustration, the selected locations for diferent VIV frequencies are explained as follows: (1) for f = 0.101 Hz, there is only a half wave for the frst (left) main span, as shown in Table 1, so the 1/2 (4/8) span location suggests a wave trough; (2) for  Te results in Figure 11 imply that the standing location of the pedestrian has a signifcant infuence on the associated MSI.Generally, this is related to the wave amplitude in terms of the VIV mode shape at the specifc location, and the pedestrian standing on the wave crest/trough points has a relatively large MSI.For the example in Figure 11(a), the MSIs for pedestrians standing on 1/8, 2/8, 3/8, and 4/8 span locations under the busy trafc fow are 0.12%, 0.15%, 0.19%, and 0.23%, respectively.Te increasing trafc density is found to also be able to reduce the MSI, particularly for standing locations with relatively large wave amplitudes.For the example in Figure 11(d), the MSIs for pedestrians standing on the 1/12 span location under free, moderate, and busy trafc fows are 3.69%, 2.67%, and 2.31%, respectively.To comprehensively understand the infuence of trafc density, PSDs of the vertical bridge acceleration at the 1/12 span location under diferent trafc densities and VIV amplitudes for VIV frequency � 0.378 Hz are presented in Figure 12.It can be seen that a larger trafc density can result in a signifcantly smaller maximum PSD, and an increasing VIV amplitude can amplify the PSD.For instance, the maximum PSDs for VIV frequency � 0.378 Hz and VIV amplitude � 0.3 m under free, moderate, and busy trafc fows are 0.84, 0.62, and 0.43 m 2 /s 3 , respectively; as the VIV amplitude increases to 0.9 m, the maximum PSDs for free, moderate, and busy trafc fows become 2.54, 1.88, and 1.31 m 2 /s 3 .Tis phenomenon can be attributed to the additional structural damping introduced by the increasing vehicles, which causes a smaller VIV amplitude given the same VIV event.Besides, one can observe that the vehicle rider's feeling on VIVs remains worse than the pedestrian's feeling because the mean MSI for sedan car drivers under the same VIV event and free trafc fow as shown in Figure 11(d) is 3.94%.

Concluding Remarks
Tis study attempts to revisit the serviceability issue of longspan bridges (LSBs) under vortex-induced vibrations (VIVs) based on bridge users' feelings, which are usually characterized by human body vibration.An evaluation framework of human body vibration is proposed in the context of a wind-trafc-bridge system, particularly designed for LSBs experiencing VIVs.Notably, this study advocates using the motion sickness index (MSI) to study the infuence of VIVs rather than the currently popular human comfort index, and the human body vibration assessment method for a standing person (e.g., pedestrian on the bridge) is introduced.Several case studies are performed to comprehensively examine the bridge users' feelings on VIVs based on a prototype longspan suspension bridge.Te major fndings are summarized as follows: (1) Te vehicle vibration is closely related to and typically more signifcant than the bridge vibration, which is dominated by the VIV and vehicle-bridge interaction (VBI) in the current context.Te VIV mainly causes vehicle vibration in a low frequency range (typically below 0.5 Hz), and the VBI can excite the vehicle vibration in a relatively high frequency range (e.g., above 3 Hz).(2) Using the OVTV (human comfort index) is suitable to distinguish the efect of road roughness on bridge users' feelings, while the potential serviceability issue caused by VIVs might be neglected.Nevertheless, using the MSI can obviously identify the serviceability issue for LSBs under VIVs.Tese are because OVTV and MSI are concerned with human body vibration with diferent frequency contents.By using the MSI, one can flter out the infuence of VBI and road roughness to a large extent, only focusing on the vibration content in the VIV-sensitive range.On the contrary, using the human comfort index can flter out the infuence of VIV.(3) Te MSI of vehicle riders is typically slightly larger than that of pedestrians, resulting in a worse feeling on VIVs.Te infuence of VIV amplitude on MSI is intuitive, i.e., a larger VIV amplitude always causes a larger MSI (worse bridge serviceability).Te infuence of VIV frequency on MSI is more complex: a higher VIV frequency leads to a more signifcant human body vibration, but after the frequency weighting in calculating MSI, such a more signifcant human body vibration does not necessarily produce a larger MSI.(4) For the real-world engineering practice involving stochastic trafc loading, it is found that trafc loads can mitigate the adverse efect of VIVs on MSI (or bridge serviceability).As the trafc density on the bridge increases, the associated MSI for bridge users often becomes smaller.Tis phenomenon can be explained by the remarkable damping deduced from multiple vehicles.(5) For the pedestrians on the bridge, their feelings (or MSI) are highly dependent on their standing locations.Generally, this is related to the wave amplitude in terms of the VIV mode shape at the specifc location, and the pedestrian standing on the wave Structural Control and Health Monitoring crest/trough points has a relatively large MSI.Moreover, the increasing trafc density on the bridge is found to be able to reduce the associated MSI, especially when involving standing locations with relatively large wave amplitudes.
Despite the potential merits, future eforts are recommended to incorporate an advanced vortex-induced force (VIF) model that can well characterize aerodynamic damping behaviors (e.g., [30]).Such eforts are especially inducive for practical applications requiring accurate quantitative results (e.g., conducting trafc management for LSBs under VIVs).Nevertheless, the major fndings of this study are expected to be free from the infuence of a diferent VIF model because they are basically qualitative insights related to the VIV frequency.Meanwhile, the pedestrian's feeling is only assessed for persons standing at a constant point, considering most pedestrians on LSBs are specialized workers rather than regular pedestrians, and these workers mostly stay at a constant location to fnish their assignments.Nevertheless, further endeavors can be made to perform human-structure interaction analyses [31] to study the feelings of pedestrians walking through the bridge.Moreover, the temperature efect [8,32] is worth considering to accurately simulate the VIV event as well as provide predictive user's feeling assessments.In addition, the risk of single-vehicle crashes [33] on LSBs under VIVs is worth studying, given such a comprehensive modeling framework.Finally, the bridge users' MSI can be assessed from monitoring data as a supplement for the current numerical study, in which one may need to carefully deal with real-world disturbances in the collected vibration signal.In that case, some prior knowledge about the inherent physics and signalprocessing techniques might be helpful [34,35].

Figure 1 :
Figure 1: Evaluation procedure of human body vibration for users of the bridge under VIVs.

Figure 2 :
Figure 2: Vibration model for bridge users: (a) seated person model for vehicle riders; (b) standing person model for pedestrians.

Figure 3 :
Figure 3: Frequency weighting functions for human body vibration assessment.

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Structural Control and Health Monitoring near the most obvious peaks in Figure7(e.g., 2-5 Hz for condition 2 and 0.2-0.3Hz for condition 3).In particular, as shown in Figure8(b), even if the VIV is the major excitation in this condition, the infuence of road roughness can be observed in the frequency range of around 3-4 Hz.Terefore, it can be found that the vehicle vibration characteristics are closely related to the bridge vibration, which is dominated by the VIV and VBI in our context.Te VIV mainly causes vehicle vibration in a low frequency range (typically below 0.5 Hz), and the VBI can excite the vehicle vibration in a relatively high frequency range (e.g., above 3 Hz).Road roughness can make the vehicle vibration more chaotic, but the dominant frequency range remains the one originating from the V-B coupled vibration.3.3.Bridge Users' Feelings.Te vibration characteristic analysis helps to understand the infuencing mechanisms of VIV, VBI, and road roughness on users' human body vibration.On this basis, this section further examines users' feelings, following the same case setting in Section 3.2.Specifcally, the users' feelings are assessed for the driver of the sedan car running at 40 km/h and a pedestrian standing on the 3/8 span of the frst main span of YWB (i.e., one crest of this VIV (f � 0.242 Hz), which can lead to the maximum human body vibration for standing persons).Since the MSI is correlated to the time duration of the vibration (see (9)), the users' feelings are evaluated based on the entire process (T � 2100/(40/3.6)� 189 s) of the vehicle crossing the bridge both for the driver and pedestrian for a fair comparison.

Figure 4 :
Figure 4: Yingwuzhou Yangtze River Bridge: (a) elevation view of the entire bridge (m); (b) cross section of the main girder (mm).

Table 1 :Frequency
Typical low-order vertical asymmetric modes of YWB.

Figure 5 :
Figure 5: Vertical accelerations at the vehicle centroid and the vehicle-bridge contact point under given conditions without road roughness: (a) condition 1; (b) condition 2; (c) condition 3.

Figure 6 :
Figure 6: Vertical accelerations at the vehicle centroid and the vehicle-bridge contact point under given conditions with road roughness: (a) condition 1; (b) condition 2; (c) condition 3.

Table 2 :
Feeling indexes of users of the bridge under VIV and a single vehicle.

Table 3 :
Mean value of MSIs of sedan car drivers under diferent VIV frequencies, VIV amplitudes, and trafc densities (%).

Table 4 :
CoV of MSIs of sedan car drivers under diferent VIV frequencies, VIV amplitudes, and trafc densities.