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Vehicles are extremely vulnerable to single-vehicle accidents under some hazardous driving conditions (i.e. strong wind, icy or snowy road surface). An integrated framework is proposed to assess single-vehicle traffic safety performance of stochastic traffic flow under hazardous driving conditions. Different from most existing studies focusing on a single vehicle moving at a constant speed, for the first time, the proposed work evaluates individual vehicle safety performance based on the time-dependent simulation results of stochastic traffic flow, including instantaneous speeds and positions of each vehicle as a part of simulated traffic flow. Simultaneously, complex geometric and other environmental conditions of the highway system are also considered realistically, not only during the safety assessment process, but also in quantifying the wind loads applied on the vehicles. Finally, with the safety information of each individual vehicle, an overall safety performance index of the whole traffic flow on the highway system is further introduced, which serves as a potential traffic safety performance measure and resilience indicator of transportation infrastructure systems under various hazards. This study has potential applications to not only regular vehicles, but also advanced traffic management and control algorithms for connected and autonomous vehicles in hazardous driving environments.

A wind tunnel experimental study is conducted to study the wind loads acting on a moving vehicle model on a bridge installed with a solid wind barrier. The repeatability of the tests is verified by the cases with different wind and vehicle speeds. For comparison purposes, the difference of the results between the static and moving vehicle models are discussed. The effects of different heights of wind barriers and wind directions on the wind loads acting on the vehicles are analyzed. Finally, the wind loads acting on the vehicles are further evaluated to assess the potential impact of wind barriers on traffic safety. The results show that the relative movement between the vehicle, bridge and solid wind barriers affects the aerodynamic characteristics of the vehicle. The variation patterns of aerodynamic characteristics with different yaw angles are altered by the solid wind barriers with different heights, and there is a most unfavorable yaw angle for the protective effect of solid wind barriers in terms of side force. The wind direction has some impact on the five-component coefficients of vehicles after installing a solid wind barrier. However, the solid wind barrier has similar protective efficiency in terms of the side force acting on the vehicle under different wind directions.

Devising effective post-hazard recovery strategies is critical in enhancing the resilience of transportation networks (TNs). However, existing work does not consider the multiclass users’ travel behavior in network functionality quantification and the metaheuristic solution procedures often suffer from extensive computational burden due to the exploration need in large solution space and the expensive functionality quantification. This study develops a bilevel decision-making framework for the resilience-based recovery scheduling of the TN in a mixed traffic environment with connected and autonomous vehicles (CAVs) and human-driven vehicles (HDVs). The lower level quantifies the TN's functionality over time considering different travel behavior of CAV and HDV users arisen from their different levels of information perception. The upper level presents a novel deep-ensemble-assisted active learning approach to balance optimization performance and computational cost. This framework can help decision makers better quantify the TN's functionality to support effective recovery scheduling of TN with different mixed traffic scenarios ranging from HDV-only to future CAV-dominant traffic. The optimization approach bears the potential to be extended to solving general large-scale network recovery scheduling problems effectively and efficiently. The proposed methodology is demonstrated using a real-world traffic network in Southern California under earthquake considering deterministic and stochastic repair durations.

Road traffic crashes threaten thousands of drivers every day and significant efforts have been put forth to reduce the number and mitigate the impacts of traffic crashes. Although the last decade has witnessed substantial methodological improvements in crash prediction modelling, several methodological challenges still remain in terms of predicting crash frequencies of different injury severity levels. These challenges include spatial correlation and/or heterogeneity, temporal correlation and/or heterogeneity, and correlations between crash frequencies of different injury severity level. A framework of Bayesian multivariate space-time model is developed to address these challenges. A series of multivariate space-time models are proposed under the Full Bayesian framework with different assumptions on the spatial and temporal random effects. In addition to the ability to consider both temporal and spatial trends, the proposed framework is also capable of addressing complex correlations between crash types. It allows the underlying unobserved heterogeneity to be better captured and enables borrowing strength across spatial units and time points, as well as over crash types. The proposed methodology is illustrated using one-year daily traffic crash data from the mountainous interstate highway I70 in Colorado, which is categorized into no injury crash and injury crash. The results show that multivariate space-time model outperforms other alternatives, including multivariate random effects model and multivariate spatial models. The model comparison results highlight the importance to properly account for spatial effects, temporal effects and correlations between crash types.

Wind effects on long-span bridges and moving vehicles have drawn considerable attention during the past years. Effectively considering the dynamic interactions between wind, vehicles and bridges and rationally assessing the bridge performance becomes essential to this type of critical infrastructure system. The impact of strong winds on long-span bridge transportation systems has received a lot of attention during the past decades. Meanwhile, low to moderate winds may serve as a type of important service load acting on the long-span bridge transportation system, along with other extreme or hazardous loads. In addition to the structural integrity, it is also important to appropriately assess the vehicle performance, such as safety and comforting issues, under wind so that the associated risks can be identified and mitigated. This paper summarizes some recent advances on the research of wind effects on long-span bridge and traffic systems with a focus on the efforts from a system and multi-hazard perspective.

A new experimental investigation approach of a moving vehicle device is proposed to investigate the aerodynamic characteristics of moving vehicles on bridges under crosswinds. The new moving vehicle device, which can adjust the incoming wind directions and wind attack angles, consists of a vehicle, bridge segment, and motion system etc. The motion system includes a linear module propelled by a servo motor and it can realize bidirectional motions and rapid acceleration and deceleration. The five-component coefficients of the moving vehicle model were tested with the force balance equipment, and the sensitivity of some parameters on the aerodynamic characteristics of moving vehicles is studied. The results show that the proposed moving vehicle device can provide a rather smooth guideway. The measured time histories of aerodynamic force and moment are stable after filtering and the identified aerodynamic characteristics of moving vehicles have a good consistency over different wind speeds.

An efficient and safe transportation system is essential to communities during the long-term recovery period after earthquakes. A disrupted transportation network due to infrastructure damage or failure affects the functionality of the traffic system and poses increased traffic safety risks. A rational assessment of the traffic network performance in terms of both traffic efficiency and safety cannot only provide comprehensive quantification of system resilience, but also enable more risk-informed post-hazard recovery planning. A new methodology to assess the resilience performance of transportation networks during post-earthquake long-term recovery period is developed in this study with two main innovative contributions: (1) modeling the traffic performance of partially closed road segments in the network simulation and optimization, which offers useful tool to capture the time-progressive recovery process; and (2) integrating both traffic efficiency and safety into the resilience assessment and recovery prioritization. After a resilience indicator is introduced to characterize the overall traffic efficiency and safety of the transportation network using probabilistic sampling method, a new restoration priority measure is proposed to support post-earthquake restoration of damaged bridges. A demonstrative study is conducted on a hypothetical network system located in an earthquake-prone area.

Vehicle ride comfort issues for the drivers are related to not only individual satisfaction of driving experience, but also driving safety and long-term health of the drivers. A new methodology of ride comfort analysis is presented for typical vehicles driven on long-span bridges considering realistic traffic and environmental loads such as wind excitations. Built on the simulation framework developed previously by the writers, complex interactions among the long-span bridge, all the vehicles in the traffic flow and wind excitations are appropriately modeled. Vehicle ride comfort condition is evaluated by extending the advanced procedures as currently recommended in the ISO 2631-1 standard to the scenarios of multiple vehicles in the stochastic traffic flow, including obtaining the whole-body vibration response, frequency weighting the original response and determining the Overall Vibration Total Value (OVTV). The proposed methodology is then applied to a prototype long-span cable-stayed bridge and traffic system to demonstrate the proposed ride comfort evaluation methodology. The study starts with the baseline scenario when the vehicles are driven on the rigid road without considering the interactions with the supporting structure and wind excitations, followed by the scenarios of vehicles driven on the bridge. The influences of dynamic interactions, presence of other vehicles and wind excitations on the ride comfort are also numerically evaluated.

Accidents, such as deflections, side slips, and even rolls, can easily occur when road vehicles moving on the bridge deck at high speed are subjected to sudden changes owing to strong crosswinds. Wind barriers are an effective way to ensure the driving safety of vehicles on the bridge but with potential negative influences on the aerodynamic performance. Therefore, it is critical to evaluate the shielding effect of wind barriers on road vehicles by assessing the overall impact on the vehicle–bridge system. To optimize the wind-barrier scheme, a series of wind tunnel tests is conducted to evaluate the effects of barrier parameters on the aerodynamic characteristics of the wind-vehicle-bridge system. In this study, the aerodynamic force coefficients of the wind–vehicle–bridge system installed with wind barriers with four different heights and three ventilation ratios were investigated. With wind barriers installed on the bridge deck, dynamic responses of the wind–vehicle–bridge system were simulated with the proposed prediction procedures as those used in an earlier study. Results show that wind barriers on the bridge deck have significant influences on the aerodynamic force coefficients of the bridge, especially on the side-force coefficients, and on the dynamic responses of the wind–vehicle–bridge system. Additionally, the increase of the barrier height and the decrease of the barrier ventilation ratio considerably increase and decrease the lateral and torsional displacements of the bridge and the vehicles, respectively, but with only minor influence on the vertical displacements of both bridges and vehicles. Therefore, it is necessary to include the wind barrier in both experimental and numerical simulations of the wind-road vehicle-bridge system to explore the effect of different barrier parameters on the wind-vehicle-bridge system.

Cable breakage (loss) events can be disastrous to cable-stayed bridges because of potential risks of progressive collapse following the initial failure of stay cables. To avoid turning a cable-breakage hazard into a disaster, it is important to rationally assess the risk through accurately predicting the nonlinear dynamic behavior of the bridge subjected to various types of cable-loss events. With a recently developed advanced finite element (FE)-based nonlinear dynamic simulation platform, a comprehensive numerical investigation of cable-loss incidents on a long-span cable-stayed bridge is conducted by focusing on post-breakage performance. Parametric studies are carried out to evaluate the impacts from various important parameters related to cable-breakage process and service loads from stochastic traffic and wind. Several parameters associated with cable-breakage processes, such as the breakage duration, time-transient curve and initial state, are found to influence the dynamic performance of the bridge notably. The results also indicate that service traffic and wind loads as well as complex coupling effects with the bridge are important to the bridge response following cable-loss events. In the final part of the study, response envelope analysis is made and a comparative investigation is also conducted between the results from the advanced FE-based nonlinear dynamic approach and those from the equivalent static approach as suggested by the Post-Tensioning Institute (PTI).

Rational representation of seismic demand based on realistic characterization of earthquake ground motion is essential for seismic bridge design. Realization of the impact of vertical ground motion has led to an initiative to better characterize and simulate the seismic scenario for typical bridges in near-fault regions, such that structural design practices may improve. Current structural design provisions either do not account for effects of vertical ground motion or specify a simplistic equivalent-static-load based methodology. An assessment of the effect of vertical ground motions on a horizontally skewed and curved highway bridge is presented for a moderate-to-high seismic region. A numerical model of a skewed and curved, three-span bridge located in Tacoma, Washington is subjected to a suite of horizontal and vertical ground motions using non-linear time-history analysis. The ground motions selected are composed of a range of near-fault earthquake records with varying component characteristics such as site condition, fault distance, and vertical-to-horizontal acceleration ratios. The scenario represents a bridge with a short vibrational period in a moderate seismic zone where vertical ground motion effects may be applicable, yet are not considered by structural codes. The results of the numerical simulations depict a considerable impact from vertical ground motion to the substructure and superstructure, including behavior typically not documented in existing studies. The numerical simulations show amplification from the vertical component of ground motion in the demand on components of the substructure, particularly for vertical-to-horizontal peak ground accelerations exceeding one. The effects of vertical ground motion on skewed and curved bridges are also evaluated against a straight counterpart with comparable overall configuration. For structural designers, the results of this study indicate that excluding the vertical ground motion component from analyses may impose a larger margin of risk than previously perceived. This is particularly the case for moderate-to-high seismic regions where shorter period bridges may resonate with predominant frequencies of vertical ground motion.

High-sided vehicles often experience considerable single-vehicle accident risks under crosswinds. Long-span cable-supported bridges are usually flexible, wind-sensitive and support considerable amount of vehicles on a daily basis. When vehicles are driven through a long-span bridge, the complex dynamic interactions among wind, vehicles and the bridge significantly affect not only the safety of the bridge members, but also passing vehicles. Therefore, realistic modeling of the bridge–traffic system by characterizing these critical coupling effects becomes essential for rationally assessing traffic safety of passing traffic through a long-span bridge. In most existing studies about traffic safety study on bridges, vehicle safety was assessed for only one single vehicle or uniformly distributed vehicles at a constant driving speed. It is known that the traffic flow on a long-span bridge is typically stochastic and vehicle speeds vary following some traffic rules. Based on the stochastic traffic flow simulation, two new analytical frameworks, one using mode superposition and the other using the finite element (FE) formulation, were proposed recently for the bridge–stochastic traffic system. By considering the full-coupling effects among all the vehicles of the traffic flow, bridge and wind, the dynamic response of each individual vehicle of the stochastic traffic can be accurately obtained for the first time. Built based on the recent advances made by the authors, an integrated dynamic interaction and safety assessment model of the fully-coupled bridge–traffic system is further developed without considering vehicle aerodynamic interference and shielding effects. Traffic safety of vehicles in the stochastic traffic through the prototype long-span cable-stayed bridge is investigated as a demonstration.

To ensure the safety and normal working performance of both road vehicles and the bridge, it is important to study the dynamic interaction between the bridge, road vehicles, and wind loads. The wind–vehicle–bridge dynamic analysis has been extensively developed in the past decades. Recent studies highlighted the importance of predicting the dynamic responses of the vehicle–bridge system by considering the aerodynamic interference between the bridge and vehicles. However, the aerodynamic forces on vehicles in the previous studies were either calculated from the empirical formulae built on the work of vehicles running on roadway or obtained from wind-tunnel tests, which did not consider the interaction of the aerodynamic forces between the road vehicles and the bridge. Based on the wind tunnel tests, first, the aerodynamic force coefficients of the vehicle are fitted considering the aerodynamic interference between vehicles and the bridge, and a more effective and accurate approach to estimate the performance of vehicles and the bridge is provided in this study. Then, the application of the proposed methodology on the Jiangshun Bridge in China is presented as a numerical example. Effects of the coherence of the buffeting forces of the bridge and the aerodynamic parameters of the vehicle and the bridge on the dynamic performance of both the bridge and the vehicles are discussed. It is found that the coherence of buffeting forces of the bridge has obvious effects on the dynamic responses of the bridge and the vehicle, which should be considered in the analysis of the coupled vibration of wind–vehicle–bridge system. The aerodynamic parameters of the bridge have significant effects on the dynamic responses of the bridge, but slight impacts on the dynamic responses of the vehicle. Meanwhile, the aerodynamic parameters of the vehicle have essentially no impact on the responses of the bridge and have a great impact on the responses of the vehicle.

A number of skewed and curved highway bridges have experienced damage or collapse due to seismic events, and has most recently been observed during the Chile earthquake in 2010. In the Mountain West region, bridges integrating skew and curvature are becoming an increasingly prominent component of modern highway transportation systems due to their ability to accommodate geometric restrictions imposed by existing highway components. There is however very little information available on the combined effects of skew and curvature on the seismic performance of Reinforced Concrete (RC) bridges. A comprehensive performance analysis is performed on eight bridge configurations of various degrees of skew and curvature with low-to-moderate seismic excitations which are characteristic of the Mountain West region. Nonlinear time-history analysis is carried out on each bridge configuration using detailed finite element (FE) models. The results show a considerable impact on the seismic performance due to the effects of skew and curvature, with stacking effects observed in the combined geometries. Insights on the complexities of curvature, skew, loading direction and support condition are also made, which may lend themselves to more informed design decisions for practicing engineers in the future.

Characterizing the interdependencies among highly interconnected critical infrastructure systems with adequate details is critical in devising cost-effective resilience improvement strategies. This study presents a bi-level, stochastic, and simulation-based decision-making framework for prioritizing mitigation and repair resources to maximize the expected resilience improvement of an interdependent traffic-electric power system under budgetary constraints. The upper level seeks to find the optimal resource allocation plan to maximize the expected attainable functionality gain. The lower level characterizes the functionalities of the traffic and electric power systems considering three types of interdependencies based on network flow analysis methods. The dynamic traffic assignment algorithm, rather than the static traffic assignment algorithm, is used in order to capture more realistic traffic dynamics in the congested urban roadway networks. Uncertainties in disruptions, traffic demands, and costs of mitigation and repair actions are also considered in the problem formulation. The problem is solved by the binary particle swarm optimization algorithm initialized with the knapsack-based heuristic, and the priority indices of disrupted components for mitigation and repair are then established based on the solutions. The proposed decision model is demonstrated using a portion of the traffic-electric power system in Galveston, Texas.

Stay cables of cable-stayed bridges often experience vibrations with large amplitudes induced by wind or jointly by both wind and rain. To understand the aerodynamic characteristics of the stay cables and excitation mechanics of rain–wind-induced vibration (RWIV), an inclined and yawed circular cylinder with and without an artificial upper rivulet is studied through a series of wind tunnel tests. The impacts of upper rivulet and axial flow on the aerodynamics of the cylinder are investigated. It is found that for an inclined and yawed cylinder without rivulet there exists a non-zero lift force at large wind angle. Furthermore, the wind pressures and aerodynamic forces acting on both the cylinder and the upper rivulet are obtained, which can be used to develop more rational theoretical models for RWIV of stay cables. Results show that the upper rivulet can both enhance and depress Karman vortex shedding depending on the position of the rivulet. As a result, dramatic variations of the aerodynamic forces acting on the cylinder and the rivulet will occur, which may eventually result in RWIV. Also axial flow may have a noticeable influence on the aerodynamic characteristics of the inclined and yawed cylinder. And the presence of the rivulet can enhance such influence from the axial flow.

A probabilistic assessment model of vehicle safety under various driving conditions based on reliability method is developed. This model is built according to the advanced transient dynamic vehicle simulation models which can consider the coupling effects between vehicles and various driving conditions, such as wind gust, snow- covered or icy road surface and/or curving. By considering uncertainties of critical variables, the safety index is introduced to provide rational assessment of accident risks. In order to consider the complicated implicit limit state functions, the response surface method (RMS) is adopted to provide an efficient estimation of accident risks. Finally, the impacts of different critical variables on accident risks of a typical truck under several representative hazardous scenarios are investigated.

The presence of traffic on a slender long-span bridge (SLB) deck has two types of primary impacts: (1) modification of the bridge cross-section profiles, which may influence the flutter derivatives and in turn, wind-induced aeroelastic loads acting on the bridge and (2) additional dynamic loads acting on the bridge including dynamic interactions from the vehicles. As compared to the investigations on the impact of traffic as external dynamic loads, those on the impact from the modification of bridge cross-section profiles are rather rare. A scaled bridge section model with vehicle models distributed on the bridge deck has been tested in the wind tunnel laboratory following the simulated stochastic traffic flow. With the flutter derivatives obtained from the wind tunnel experiments of various modified bridge cross-section profiles by traffic, the present study is to numerically evaluate the impact on the wind-induced performance of the long-span bridge, such as the aeroelastic performance, buffeting response and potential fatigue accumulation.

In addition to moderate wind and normal traffic scenarios, it is known that some extreme events may also occur on long-span bridges. These extreme events may include complex traffic congestion on the bridge, coupled with moderate or even strong wind. It is known that the excessive dynamic response and stress level of the bridge under these rare but critical scenarios, even for a very short period, may cause critical damage initiation or accumulation on some local bridge members. In addition to accelerating damages, the extreme events (e.g. heavy traffic) may even trigger the hazardous collapse of a whole bridge in some rare cases, especially when some hidden damage or design flaw has not been detected. Therefore, even though the extreme cases associated with congested traffic and/or windy weather are relatively rare, it is important for bridge engineers to appropriately look into these unusual extreme events during design and life-time management. By applying the general Bridge/Traffic/Wind coupled analysis methodology, the present study focuses on (1) conducting the cellular automaton (CA)-based traffic flow simulation of a long-span bridge and connecting roadways under incidental situations, (2) defining representative scenarios for the extreme events, and (3) numerically studying the bridge performance under these possible extreme events. By conducting studies on a comprehensive set of possible scenarios, it is anticipated that better understanding of extreme events of long-span bridges from the perspectives of strength and serviceability design will be achieved, which may contribute to the future design specification about long-span bridges. The proposed methodology will also offer a reasonable framework to replicate probabilistic traffic flow, characterize dynamic interaction and assess structural performance under those rare but critical situations integrally.

A general framework of modeling the stochastic live load from traffic for a long-span bridge is developed. The cellular automaton (CA) traffic flow simulation technique is adopted to develop the analytical basis of the framework. Based on the traffic flow simulation results, the live load on a long-span bridge from the stochastic traffic is studied with a focus on the static component. Parametric studies of major variables of the framework, such as the length of the connecting roadways, the speed limit, and the vehicle combination, are conducted.

The framework of a reliability-based assessment model of vehicle safety under adverse driving conditions is developed. Such a framework is built based on the advanced transient dynamic vehicle simulation models which can consider the coupling effects between vehicles and adverse driving conditions, such as wind gust, snow-covered or icy road surface and/or curving. The single-vehicle safety index is introduced to provide rational assessment of accident risks by considering uncertainties of critical variables. In order to consider the complicated implicit limit state functions, the response surface method (RMS) is adopted to provide an efficient estimation of accident risks. Finally, a parametric study is conducted to demonstrate the methodology and the impacts of different critical variables on accident risks of a typical truck under several representative hazardous scenarios are investigated.

A long-span bridge infrastructure system (BIS) consists of a long-span bridge, traffic on the bridge, and a natural environment, such as wind. As a type of slender structure, long-span bridges usually experience strong dynamic vibration under both wind and busy traffic loadings, which act on the bridge simultaneously most of the time. However, just like traditional long-span bridge dynamic analyses, existing structural control studies of a long-span bridge usually consider either only wind loading or moving vehicles, but not both at the same time. In addition to causing the bridge to vibrate, a strong crosswind on the bridge deck also endangers the stability of moving vehicles on the bridge. An integrated analytical model was thus developed for a long-span bridge, with moving vehicles under windy conditions, to which is attached tuned mass dampers (TMDs). Since TMD control shares similar fundamental mechanisms with many other structural control measures, the proposed analytical model based on TMD control can also be used for various control studies of long-span bridges as well as with vehicles as a coupled system. First, with this framework considering the vehicles, wind, the bridge and the control system integrally, the structural control of long-span bridges can be designed and evaluated on a more realistic basis; second, the performance of the bridge-vehicle system with tuned mass dampers under windy conditions is parametrically studied for several different control schemes such as when TMDs are installed on the bridge, on a truck and on both; finally some observations of the coupled control system are discussed and the feasibility of developing a temporary control measure to protect unloaded or partially-loaded high-sided trucks from rollover accidents in windy conditions is studied.

The present study investigates the effect of approach span conditions on a bridge’s dynamic response induced by moving vehicles. After developing a 3D bridge–vehicle interaction model for numerical prediction, a dynamic test on a full scale slab-on-girder bridge is conducted with dump trucks to validate the developed numerical methodology. A wooden plank is used to simulate the large faulting between the bridge deck and the approach slab. With consideration of the road surface profile and approach span condition, the predicted dynamic response of the bridge is compared to the experimental results, and they show a satisfactory agreement. The numerical model is also applied to investigate the effect of the approach span condition on the dynamic behavior of the bridge induced by the AASHTO HS20 truck. A parametric study is eventually conducted by changing the road surface condition and the faulting value. The faulting condition of the approach span is found to cause significant dynamic responses for the slab-on-girder bridges and to have a considerable effect on the distribution of impact factors along the transverse and longitudinal directions. Furthermore, impact factors obtained from the numerical analyses are compared with those values specified in the AASHTO codes.

A transportation system includes transportation infrastructures and transportation vehicles. In most key transportation routes, bridges, especially long-span bridges, play an extremely important role in keeping the whole transportation line smooth and effective. Wind, as a common environmental phenomenon, exists in the nature almost all the time. In addition to the interaction between vehicles and supporting structures (e.g. roadways or bridges), the joining of the natural wind into the already coupled vehicle/supporting structure system makes the problem more complicated. The performance of the transportation system under complicated environmental conditions (e.g. wind) is critical to the hazard resistance capability of the whole transportation system, and thus should be well assessed. Long-span bridges, due to their flexible natures, are prone to exhibiting excessive vibrations caused by wind. So a suitable control scheme is sometimes necessary to improve the performance of the bridge under wind. An integral dynamic assessment and improvement scheme for the transportation system, including bridges, vehicles and roadways, is introduced for Luling Bridge in the South of the United States. With the fully coupled vehicle/bridge/wind model, the overall dynamic performance and accident risks of the vehicles can be assessed, followed by temporary control measures designed to improve the performance of Luling Bridge.

A reliability analysis method is proposed in this paper through a combination of the advantages of the response surface method (RSM), finite element method (FEM), first-order reliability method (FORM) and the importance sampling updating method. The method is especially applicable for the reliability evaluation of complex structures of which the limit state surfaces are not known explicitly. After the accuracy and efficiency of the method are demonstrated through numerical examples, the method is used to estimate the flutter reliability of a suspension bridge. The uncertainties such as material properties, geometric parameters, structural damping ratio, flutter derivatives and extreme wind velocity at the bridge site are considered. The example suspension bridge is the Jiang Yin Bridge with a main span length of 1385 m built in China. The results show that the proposed method based on an empirical formula in which the limit state function is explicitly represented as a function of variables overestimates the flutter reliability of suspension bridges. The actual flutter reliability should be more accurately analyzed using the proposed method based on the deterministic finite element method in which the limit state function is implicitly represented as a function of variables. Finally, the most influential random variables on flutter reliability of suspension bridges are identified by using a sensitivity analysis.

Long-span bridges undergoing wind excitation exhibit complex dynamic behaviors. Buffeting vibrations induced by wind turbulence happen throughout the full range of wind speed. As the wind speed increases, aerodynamic instabilities such as flutter may occur at high wind speed [1]. Much research effort has been made in mitigating excessive buffeting vibrations and improving aerodynamic stabilities for long-span bridges during construction [2,3] and at service [4–6]. Among all of the control procedures, dynamic energy absorbers such as tuned mass dampers (TMDs) have been studied in suppressing the excessive dynamic buffeting [7] or enhancing the flutter stability of bridges [4,8]. As traditional control devices, the dynamic energy absorbers dissipate external energy through providing supplemental damping to the modes of concern [9–11]. In a conventional TMD control design, the TMD frequency is designed or tuned to the modal frequency of the fundamental mode [12] in order to reduce the so-called resonant vibration and this method is thus called resonant-suppression approach here. When the modal coupling among the modes is weak, the bridge can be regarded as a simple combination of many single degree-offreedom (d.o.f.) systems and single mode analysis is usually applicable [13]. It is well-known that wind-induced aeroelastic effects result in additional aerodynamic damping and stiffness for long-span bridges [14]. The TMD control efficiency decreases with the increase of modal damping ratio. This implies that, for coupled mode vibrations of long-span bridges, the control efficiency of buffeting response of bending mode decreases with the increase of wind velocity since the aerodynamic damping of bending modes usually increases with the wind speed. Since bending modes usually contribute significantly to the overall buffeting response among all of the modes, the decreased control efficiency in bending modes may deteriorate the overall control efficiency of the bridge vibration. ARTICLE IN PRESS

Currently, there are very few systematic analyses of vehicle performance on bridges in windy environments. There are thus no scientific data to support bridge management in this regard, such as when to close traffic on bridges. This paper presents a framework of vehicle accident analysis model on long-span bridges in windy environments. In the accompanying paper, a three-dimensional analysis of the coupled bridge–vehicle–wind system is developed. Each vehicle is modeled as a combination of several rigid bodies, axle mass blocks, springs, and dampers. Dynamic interaction analysis is then conducted on the vehicle–bridge system to predict the “global” bridge and vehicle dynamic responses without considering accident occurrences. The results of the global bridge–vehicle vibrations serve as the basis for the present accident analysis of the “local” vehicle vibrations. With the global vibrations as inputs of the accident model, the lateral response, yaw response of the vehicle, and the reaction forces of each individual wheel are obtained and the stability condition of the vehicles are analyzed. The vehicle accidents on long-span bridges are then identified with given accident criteria. The developed framework can be used in not only analyzing the vehicle performance on highways and on bridges, but also in predicting useful information for emergency preparedness agencies in developing evacuation plans.

Despite the massive population growth in the south and southeast along the hurricane coast of the United States, the transportation infrastructure has not increased its capacity accordingly. Long-span bridges are usually the backbones of transportation lines along the coastal areas. When a hurricane is approaching, these long-span bridges sometimes have to be closed in order to ensure the safety of the bridge as well as the transportation on them due to excessive wind-induced vibrations, which however greatly reduces the capability of hurricane evacuation through the bridges. To date, bridge vibration controls in high wind speeds have not been adequately addressed. Most previous control work dealt with the bridge buffeting under moderate wind speeds, along with some cases of flutter controls in high wind speeds. While active control devices may provide satisfactory multi-objective control performance in a full range of wind speeds, their dependence on external energy supply has hindered their applications to the disaster evacuations. Recently, some aerodynamic controls using flaps were proposed to control flutter instability. However, their applicability to buffeting control has not been reported and established. Vehicles on bridges act as a sort of Spring-Damper-Subsystems (SDSs) to the bridge. The SDS is used here as a general terminology to differentiate with Tuned Mass Dampers (TMDs). The former may or may not be pre-tuned, while the latter is pre-tuned to the "optimal" value (usually the fundamental frequency of the structural system) for efficient vibration control. The objective of the present study is to investigate the effects of different SDSs (with different vibration frequencies) on the bridge performance during hurricane evacuations and develop a truck-type of movable passive SDS. The passive nature makes the control approach more reliable than the active one, considering the reality that power may not be available during the hurricane disasters. The temporary/movable SDS can be conveniently driven on the existing bridges when necessary, and be removed when it is not needed. It has been reported that the gust wind speed during hurricanes could be up to 60-80 m/s or more in the United States and other areas. Though the duration may be short, the consequence of such strong winds may be catastrophic for both the safety of the bridge and the safety of traffic on the bridge.

This paper presents a framework of dynamic analysis of coupled three-dimensional vehicle-bridge system under strong winds. A general formulation of this system is introduced to simulate a series of vehicles consisting of different numbers and different types of vehicles running on bridges under hurricane-induced strong winds. Each vehicle is modeled as a combination of several rigid bodies, axle mass blocks, springs, and dampers, considering wind and road roughness loads. With this vehicle-bridge model, coupled dynamic analysis of vehicles running on bridges is conducted with a numerical example. Effects of driving speeds on the dynamic performance of the vehicles as well as the bridge are discussed. It is found that the driving speeds mainly affect the vehicle's vertical relative response while they have insignificant effect on the rolling response of vehicles. Vehicle's absolute response is dominated by the bridge response when wind speed is high, while it is dominated by road roughness when the wind speed is low. Detailed accident analysis of vehicles on bridges under strong winds will be reported in an accompanying paper.

Flutter and buffeting are two important phenomena of long-span bridges susceptible to wind actions. When the wind velocity increases to the bridge flutter velocity, an initial or self-excited multi-frequency vibration in laminar flow becomes single-frequency flutter instability. Similarly, in turbulent flow, the multi-frequency buffeting vibration develops into a single-frequency dominated divergent vibration that can also be interpreted as flutter instability. Even though this transition from buffeting to flutter was observed in wind tunnel tests, the mechanism of transition from multi-frequency type of buffeting to single-frequency type of flutter has not been well demonstrated numerically. Some existent explanations on the occurrence of flutter are very generic and even somewhat confusing. An attempt to reinvestigate numerically the transition of these two phenomena was made in the present study. The established procedure demonstrates numerically how a pre-flutter multi-frequency free vibration and a multi-frequency buffeting vibration merge into a single-frequency dominated flutter at the flutter critical wind velocity. It is concluded that the modal coupling effect forces all modes to vibrate mainly in a frequency close to the oscillation frequency of the critical flutter mode. The oscillation frequency of each mode itself does not merge to that of the critical mode. As a result, some confusing concepts in flutter vibrations are clarified and the mechanisms of the vibration transition process are better understood. Numerical analyses of the Humen suspension bridge with a main span of 888 m were conducted to facilitate the discussions.

A study on buffeting control of the Yangpu Bridge using a multiple tuned mass damper (MTMD) system is performed in this paper. The MTMD system consists of a set of TMDs which are attached to the center region of the bridge's main span and are symmetrical about the center of the main span as well as about the central line along the bridge span. It is found that the control efficiency of the MTMD system is sensitive to its frequency characteristics, namely, the central frequency ratio and the frequency bandwidth ratio. On the other hand, the damping ratio of the TMDs has less significant effects on the control efficiency. A total of seven MTMD systems with different mass ratios are designed. Each one of these seven MTMD systems can be used for the buffeting control of the Yangpu Bridge, depending on the required control efficiency and the available budget.