Design Of Long-span Bridges Research Articles

Assessment of the Aerodynamic and Aeroelastic Performance of Long-Span Twin-Box Bridges Based upon Multidimensional Surrogate Models

Twin-box decks are being extensively used in the design of long-span bridges due to their superior flutter performance. Although the significant role played by the gap distance has been previously addressed in the frame of experimental studies, there is still a lack of understanding about the complex interplay between box geometry, gap distance and the aerodynamic force coefficients and flutter derivatives. In the present work, firstly, a surrogate model is developed, considering three design inputs for the geometry of the deck along with the angle of attack, providing the force coefficients as output. Afterwards, the work is then extended by developing another surrogate model, considering as inputs the reduced velocity and the same geometric variables of the deck, with the outputs being the flutter derivatives. The methodology, comprising the selection of the design domain, the definition of the samples, the CFD-based evaluation of the samples' response and the construction of the surrogate through the application of the neural network-based radial basis method, is reviewed. The surrogate models enable a quantitative description of the impact caused in the force coefficients and the flutter derivatives by modifications in the geometry of the twin-box deck. It has been found that flutter derivatives H1*, H2* and A2* are strongly dependent on the gap distance.

Influence of non-uniform grid plates on the vortex-induced vibration performance of twin-box girder section

The wind resistance design of long-span bridges necessitates addressing the issue of vortex-induced vibration (VIV) and implementing appropriate counter measures to mitigate it. The present study focused on the examination and comprehensive analysis of a self-anchored suspension bridge. Wind tunnel tests were conducted on sectional models to analyze the effect of wind attack angles on the VIV performance of the girder. Moreover, the investigation examined the impact of opening slot ratio and the configuration of grid plates on the trigger mechanism and performance of VIV. From the results, it is observed that the main girder displays vertical VIV when the damping ratio reaches 0.25%. At wind attack angle of − 3°, 0°, and + 3°, the dimensionless maximum amplitude of the vertical VIV normalized by the height of the girder section, represented as ymax/D, is measured to be 0.032, 0.033, and 0.023 correspondingly. When the opening slot ratio of the grid plates reaches 50%, and the grid plates are non-uniformly arranged on the opening slot, that is the sides of the opening slot position, the vertical VIV becomes non-existent. Furthermore, it is observed that when the grid plates are arranged uniformly with the same opening slot ratio, the suppression effect on VIV is relatively worse and the dimensionless maximum amplitude of the vertical VIV is reduced to 0.013 from 0.032. The flow structure mechanism is that the upside airflow is separated at the windward edge of the girder section, leading to the formation of a large upper vortex. The upper vortices interact with the airflow passing through the upper and lower portions of the central slot, colliding with the top and bottom surfaces of the downstream section. Eventually, the vortices are shifted towards the tail side of the girder section and eventually shed, causing VIV. After implementing grid plates, vortices with a certain size still form at the gap. The grid plate effectively separates the vortices from the upper and lower sections of the girder, reducing their impact on the downstream section and optimizing the VIV performance of the main girder. These research findings could serve as a guide for designing the two-box girder section.

Full-scale monitored wind and response characteristics of a suspension bridge compared with wind tunnel investigations at the design stage

Structural health monitoring of long-span bridges makes it possible to assess the assumptions and considerations in the design stage of the structures through measurements of their structural response and environmental conditions. In wind-resistant design of long-span bridges, the wind-induced dynamic buffeting response is difficult to assess as the uncertainty in the loading and the structural and aerodynamic characteristics is high. In that case, one of the best sources of information is wind tunnel tests, in addition to field measurements and analytical considerations. However, it is unclear if such methods can provide reliable information for the designer since, typically, many uncertainties and assumptions are involved in such a process. Here, we evaluate the scaled full aeroelastic and terrain model tests carried out during the design stage of the Gjemnessund Bridge in Norway through comparisons with full-scale monitoring data spanning five years. The monitoring system and the data are presented along with the wind tunnel study. The results from both campaigns are analyzed and critically discussed, emphasizing implications for the wind-resistant design of long-span bridges.

Analyzing Wind Effects on Long-Span Bridges: A Viable Numerical Modelling Methodology Using OpenFOAM for Industrial Applications

Aerodynamic performance is of critical importance to the design of long-span bridges. Computational fluid dynamics (CFD) modelling offers bridge designers an opportunity to investigate aerodynamic performance for long-span bridges during the design phase as well as during operation of the bridge. It offers distinct advantages when compared with the current standard practice of wind tunnel testing, which can have several limitations. The proposed revisions to the Eurocodes offer CFD as a methodology for wind analysis of bridges. Practicing engineers have long sought a computationally affordable, viable, and robust framework for industrial applications of using CFD to examine wind effects on long-span bridges. To address this gap in the literature and guidance, this paper explicitly presents a framework and demonstrates a workflow of analyzing wind effects on long-span bridges using open-source software, namely FreeCAD, OpenFOAM, and ParaView. Example cases are presented, and detailed configurations and general guidance are discussed during each step. A summary is provided of the validation of this methodology with field data collected from the structural health monitoring (SHM) systems of two long-span bridges.

A study on stabilizing mechanism of flap countermeasures mitigating VIV of a box girder bridge section

As bridge spans stretch, the structure becomes more flexible and susceptible to dynamic wind effects causing harmful wind-induced vibration. The biggest issue with the design of long-span bridges is the possibility of vibration caused by vortices. This study examines the mechanism of the decrease in the amplitude of vortex-induced vibration for the box girder using a flap countermeasure. Aerodynamic countermeasures such as a flap have successfully increased bridge deck aerodynamic stability. However, their stabilizing mechanism has yet to be fully understood. Based on the proposed approach, a wind tunnel experiment and a CFD technique are used to investigate the aerodynamic instability of the bridge girder in the presence of aerodynamic countermeasures. The flow fields surrounding the bridge deck, both with and without the flap, are examined, and the experiment outcomes are compared. Flow imagery is utilized to explain and understand the modified flow properties surrounding the bridge girder in the presence of aerodynamic countermeasures that minimize vibration amplitude. Indeed, installing flaps on a girder leads to increased turbulence over the surface and at the leeward side, which disrupts vortex formation and decreases lift forces on the structure. In addition, the results revealed that the efficiency of the flap is related to the installed location of the flap and the flap length. This research provides a reliable framework for designing the flap countermeasure and significantly improves the aerodynamic stability of a deck-flap system.

Modeling Nonlinear Aeroelastic Forces for Bridge Decks with Various Leading Edges Using LSTM Networks

With the rapid increase in bridge spans, the mitigation of risk to flutter (aeroelastic instability) is of critical importance in the design of long-span bridges, especially considering the more frequent intense hurricanes under climate change. Although the strong nonlinearities of the aeroelastic (self-excited) forces in wind–bridge interactions can be well captured through either numerical simulations or experimental tests, both are expensive and time consuming. Hence, it is important to develop an efficient reduced-order model for the simulations of nonlinear aeroelastic forces on the bridge decks. This study proposes a reduced-order model based on the long short-term memory (LSTM) network to simulate the nonlinear aeroelastic forces on bridge decks with various leading edges, and thus rapidly predict the corresponding post-flutter behaviors of long-span bridges. To generate the training datasets, computational fluid dynamics (CFD) was employed to simulate the nonlinear aeroelasticities of bridge decks with a wide range of leading-edge configurations and wind speeds. Trained on the high-fidelity CFD datasets, the LSTM network takes the motion of a bridge deck, leading-edge angles and wind speeds as inputs and outputs the nonlinear aeroelastic forces on the bridge decks. A hybrid loss function utilizing the prediction errors of both aeroelastic forces simulated by the LSTM network and the bridge deck responses calculated by the Newmark-β algorithm was introduced into the training process to improve the network performance. The prediction results of the trained LSTM model were compared with the CFD simulations, which demonstrated that the nonlinear aeroelastic forces of the bridge deck with various leading edges can be accurately and efficiently acquired by the proposed LSTM model.

Full long-term buffeting analysis of suspension bridges using Gaussian process surrogate modelling and importance sampling Monte Carlo simulations

Recent findings from full-scale measurements campaigns and analytical investigations of the design buffeting response of long-span bridges suggest that the assumptions adopted in most wind-resistant design guidelines are not strictly conservative. In such cases, a full long-term analysis is the most accurate alternative for reliability-based design. However, the application of such methodology becomes unfeasible due to the corresponding computational demand. Notably, many evaluations of the buffeting response are required, and time-consuming numerical integration is traditionally used to evaluate the long-term response. To overcome these drawbacks, this paper proposes a framework to increase the computational efficacy of long-term analyses for the wind-resistant design of long-span bridges by combining two strategies. First, the buffeting response is estimated with a Gaussian process regression that requires less time than the traditional multimodal buffeting response estimation. Then, long-term analysis is carried out using importance sampling Monte Carlo simulations that converge faster than the traditional analysis based on numerical integration. The computational framework is demonstrated in a case study of a proposed super-long suspension bridge subjected to loads induced by wind buffeting. The advantage of the proposed framework is verified, as it requires less than 1% of the computational demand of the traditional full long-term analysis.

Wind load assessment with the JPDF of wind speed and direction based on SHM data

The calculation of basic wind speed (wind load) in return period is directly related to the wind resistance design of long-span bridge, high-rise building and etc. Nowadays, the calculation of basic wind speed in Chinese codes (GB50009-2012) mainly depends on the probability distribution function (PDF) of extreme wind speed, that is, univariate Gumbel PDF. However, this method doesn’t consider the influence of wind direction and the finite mixture (FM) of Gumbel PDF. In this paper, we use the Angular-linear (AL) model to characterize the extreme wind speed and wind direction, that is, joint PDF (JPDF). Specially, the FM Gumbel PDF is used to model the extreme wind speed and FM von Mises PDF is used to model the wind direction based on structural health monitoring (SHM) data. Then, the Genetic algorithm (GA) method is applied to solve the multi parameter solution in FM-AL model. Finally, the results of basic wind speed with return period of 100 years are compared based on the univariate Gumbel PDF (GB50009-2012 of Chinese code), FM Gumbel distribution, univariate Gumbel distribution + FM von Mises distribution and FM Gumbel distribution + FM von Mises distribution.

IABSE Task Group 3.1 Benchmark Results. Numerical Full Bridge Stability and Buffeting Simulations

Aerodynamic stability and buffeting response due to turbulent wind have a fundamental importance for long-span bridge design. However, there are no benchmark cases that can be used as a reference estimate for an independent validation of the numerical methods and theoretical approximations. Therefore, the IABSE Task Group 3.1 proposal is to fill this gap by defining a reasonably well predicted set case for the response to wind of long-span bridges, both in terms of aerodynamic stability and buffeting. Specifically, a statistical analysis was performed on the numerical results collected by the task group participants, who used their own methodology and tools (either in time domain and/or frequency domain) to predict the bridge stability to flutter and buffeting response to wind, sharing the same input data (wind conditions, bridge structural properties, and deck aerodynamic coefficients). The benchmark results presented in this paper can be used as a point of reference for other numerical codes, and they include the onset of flutter speed, damping ratio variation with mean wind speed and the root mean square of the displacements as a function of mean wind speed, power spectral density values, and time histories of displacements.

Numerical investigation of the nonlinear interaction between the sinusoidal motion-induced and gust-induced forces acting on bridge decks

With the increasing spans and complex deck shapes, aerodynamic nonlinearity becomes a crucial concern in the design of long-span bridges. This paper investigates the nonlinear interaction between the gust-induced and motion-induced forces acting on bridge decks using the Vortex Particle Method (VPM) as a Computational Fluid Dynamics (CFD) method. This nonlinear interaction is complex and intractable by the conventional linear semi-analytical models that employ the superposition principle. To excite such interaction, a sinusoidally oscillating bridge deck is subjected to sinusoidal vertical gusts. Two distinct aspects are studied: The influence of large-scale sinusoidal vertical gusts on the shear layer of a moving body and the nonlinear dependence of the aerodynamic forces on the effective angle of attack. For the latter, the resultant aerodynamic forces based on a linear semi-analytical and a CFD model are compared for the same effective angle of attack due to sinusoidal gust and motion. The methodology is first employed to verify the linear behavior of a flat plate and then study the nonlinear behavior of two bridge decks. The results show that the linear superposition principle holds for streamlined bridge decks with minimal shear layer instability. However, this principle may not be valid for bluff bridge decks due to strong separation vortices that dictate the shear layer, which induces nonlinearity in the aerodynamic forces manifested through amplitude difference in the first harmonic and emergence of higher-order harmonics. The outcome of this study aims to provide a deeper understanding of the complex nonlinear fluid–structure interaction occurring for bluff bodies subjected to motion and free-stream gusts.

Research status and prospect of wind-vehicle-bridge coupling vibration system

To promote and develop the theoretical basis and application of the wind-vehicle-bridge coupling vibration system, the corresponding research status and prospects are reviewed and discussed from five aspects, i.e., the analytical framework, the aerodynamic interference, the evaluation criteria, the design loads of long-span bridge and the double-deck rail-cum-road bridge. The refining process of analysis system is reviewed from the aspects of simulation wind load, vehicle load and bridge structure, and the corresponding coupling relationship. For aerodynamic interference, the development process is summarized from the simulative precision of the elements (wind, vehicle and bridge), the load cases and the object of interference. For evaluation criteria, the corresponding development course is summarized from the certain evaluation method to uncertain one. For long-span bridge design load, the wind and vehicle loads are reviewed and summarized from current multinational codes and theoretical research. For double-deck rail-cum-road bridge, the mechanism of multi-element coupling relationship and corresponding aerodynamic interference are both reviewed. By comprehensive review and summary, the analytical framework is in the process from simplification to refinement. The simulation and consideration of the objects of structural interference gradually become complex. The corresponding simulation theory, wind tunnel scale, test equipment and technology are the key factors to limit its development. For systematic evaluation of vehicle and bridge, the structural and systemic security are the basis of the evaluation, and the auxiliary components and functional evaluation need to be paid more attention. The evaluation criterion will be developed from certain method to reliability assessment. For design load of long-span bridge, the vehicle load is gradually transferred from the simple application of the design load of small-medium span bridge into a complex model considering the load characteristics. For double-deck rail-cum-road bridge, the basic theory and experimental study on coupling mechanism and aerodynamic interference need to be developed.

An advanced particle swarm optimization algorithm and its application to search flutter critical velocity of bridges

Flutter may lead to collapse of long-span bridges and need to be avoided, which makes the estimation of the onset flutter essential for long-span bridge design. However, the efficiency of traditional solution methods of predicting onset flutter is not high. In this study, it is converted into an optimization model, which is solved by a proposed advanced particle swarm optimization (APSO) with a novel inertia weight strategy and mutation mechanism. Two well-known benchmark functions are firstly employed to validate the performance of APSO. Compared with other existing PSO methods, APSO not only has high accuracy, but also has the fastest convergence speed. Then, APSO is used to find the flutter critical wind speed of bridges. A good agreement is obtained comparing predictions on the onset flutter by the proposed methods and available tests on several study cases. In addition, the value range of APSO variables is discussed in depth. It is confirmed that the proposed APSO algorithm has excellent stability, robustness and fast convergence, which is suitable for searching onset flutter of bridges.

Environmental contours for wind-resistant bridge design in complex terrain

Accurate estimation of the extreme wind fields is crucial for long-span bridge design. The current practice is focused on estimating the extreme mean wind speed, neglecting the inherent uncertainty in the turbulence model parameters. However, full-scale measurements on bridges show that such uncertainties are significant and should be considered in design. Here, the environmental contour method (ECM) is used to obtain long-term extreme wind fields considering uncertainties from the mean wind speed, turbulence intensities and spectral parameters measured at the Sulafjord Bridge site. Design contours of combinations of wind field parameters are obtained for target return periods of 4, 50 and 100 years. The contours are based on a proposed probabilistic modeling strategy that combines hindcast mesoscale simulations and field measurements. The contour estimates are also compared with state-of-the-art design values from the design recommendations. It is concluded that the environmental contours provide a more complete and yet intuitive description of the wind field at the bridge site compared to the current design methodology. The ECM is found suitable for obtaining design wind fields at new long-span bridge sites as it makes use of the limited site data more efficiently and it is still easy-to-use for the practicing engineer.

Aero-structural optimization-based tailoring of bridge deck geometry

The deck cross-section is usually identified in engineering practice as the most important design variable in the wind-resistant design of long-span bridges. This is certainly true in most cases since it controls the aerodynamic and mechanical contribution of the deck to the global bridge performance. However, the effectiveness of deck shape modifications to handle the aeroelastic constraints is highly influenced by the aeroelastic performance requirements. This paper seeks to delve into the aero-structural design optimization of long-span bridges by analyzing possible design scenarios depending on the ability of the deck shape to meet the imposed aeroelastic requirements. A long-span cable-stayed bridge is optimized focusing on the buffeting response and considering different sets of limit values for the design constraints. According to the effectiveness of the deck shape design variables and other size design variables to manage the aeroelastic design constraints, three types of aero-structural optimization problems are identified: type I, aeroelastic constraints are not active and structural constraints drive the design; type II, aeroelastic constraints are active and effectively controlled by deck shape modifications; and type III, aeroelastic constraints are active and demand both shape and size modifications. The engineering significance for practical design is discussed.

Tropical-cyclone-wind-induced flutter failure analysis of long-span bridges

Continuously growing number and span length of long-span bridges in coastal region of China require a robust aeroelastic design to against the tropical-cyclone (TC) -induced flutter instability. Instead of using the deterministic approach, this study presents a Monte-Carlo-technique-based framework to analyze the flutter reliability of a long-span suspension bridge subjected to TC winds. A limit state function formulated as the difference between the flutter capacity and the extreme gust wind, termed as the product of a random gust factor and the TC mean wind hazard is employed. The flutter fragility curve in terms of the critical wind speed is derived using 2D and 3D flutter analysis models accounting for the structural modal and damping randomness as well as experiment-induced errors of aeroelastic flutter derivatives. The TC wind hazard curves at the height of the bridge deck described as the probability of exceedance at any given years of interest versus the extreme 10-min mean wind speed are estimated through generating a large quantity of synthetic tracks around the bridge site. The probabilistic solutions of the gust factor associated with any gust duration of interest are determined utilizing the statistics of observed TCs coupled with a theoretical model. The TC-induced flutter failure probabilities of present bridge are then predicted in different combinations of gust duration, surface roughness length and flutter analysis models, which enables the assessment of flutter risk subjected to TC winds as compared to code-suggested target reliability indices. The present reliability analysis provides some basic information to assist and enhance the flutter-resistant design of long-span bridges due to TC winds during the preliminary stage.

Dual lidar wind measurements along an upstream horizontal line perpendicular to a suspension bridge

Remote wind sensing can complement traditional anemometry at a bridge site and contribute to an improved wind-resistant design of long-span bridges. This study examines wind lidar measurement data recorded along a 168-meter-long horizontal line perpendicular to the main span of a suspension bridge in complex terrain. The velocity data records are obtained by a pair of continuous-wave Doppler lidars (short-range WindScanners) installed on the bridge deck. The measurement data are explored in terms of the mean wind speed and mean wind direction upstream of the bridge. The spectral characteristics of turbulence along the line are also investigated in relation to the increasing sampling volumes of a continuous-wave lidar system at increasing distances from the monitored area. Wind characteristics observed by the lidars are compared to those derived from sonic anemometer data recorded above the bridge deck at midspan. The results provide new insight into the wind flow characteristics in a fjord and demonstrate the potential of lidar measurements in charting the wind flow around a bridge. A slight monotonic increase of the wind speed, as well as a decrease in the yaw angle, is observed as the distance to the bridge reduces from 160 m to 20 m, while lower wind velocities are accompanied by a more stable wind direction. Within 15 m from the bridge deck, the adopted lidar setup gives unreliable information due to the large angle between the lidar beams.

Phase-Structure in Conditional Simulation of Spatially Varying Ground Motion and Possible Influence on Structural Demand

Recorded ground motion is nonstationary in both intensity and frequency contents. Two methodologies were reported by the authors elsewhere for generating spatially varying ground motion (SVGM), namely, (i) auto-spectral density (ASD)-based framework, and (ii) evolutionary power-spectral density (EPSD)-based framework. While the former framework imparts nonstationarity through a uniform modulation (that accounts for nonstationarity only in intensities), the latter framework accounts for nonstationarity in both intensity and frequency contents. Reported EPSD-based framework was modeled through a decay function and a random component and was investigated only in the context of horizontal ground motion. Reported EPSD-based framework made two strong assumptions that need further investigation: (i) spatial variation of the random component was assumed to be frequency independent; and (ii) phase-structure of the ground excitation simulated around the reference station (with seed motion) was assumed to be same as that of the seed motion. This paper investigates the possible impact of these two assumptions on the simulated SVGM through appropriately revising the framework and introducing the phase-structure accordingly. Possible effects of the phase-structure on structural demand are investigated through an idealized long-span bridge. Revised EPSD-based framework is next assessed against the vertical recordings of SMART1 array along with the auto-spectral density (ASD) framework. Though spectral representation is nearly identical in both the frameworks, the acceleration time series simulated using the revised EPSD-based framework matches the recorded data better when compared with the ASD-based framework. Possible effect of spatially varying vertical ground motion on the seismic design is investigated through the same idealized bridge model. Significant increase in the demand of axial force in piers and mid-span moment in the deck are observed. Although these inferences are contingent on the idealized example considered for illustration, the spatially varying vertical ground motion is expected to contribute significantly to the seismic design of long-span bridges.

Field measurement study of wind characteristics in mountain terrain: Focusing on sudden intense winds

Due to the local terrain and temperature, various types of intense wind, such as sudden intense winds, thermally developed winds, and thunderstorms, will occur in mountainous areas of different regions and periods of time. The identification and separation of intense wind events into different families are key topics in wind engineering to study the characteristics of intense winds in mountainous areas, which are essential to investigate the wind-excited response of structures. This research presents a systematic field measurement study on intense wind events in a deep-cut canyon situated in a mountainous area of southwestern China and identifies a series of sudden intense wind events whose wind speed, direction, ambient temperature, and other characteristics change rapidly. To distinguish and isolate such events, an automatic classification method was proposed, and 11 sudden intense wind events were captured. Additionally, it was also found that the sudden intense wind had relatively strong nonstationary characteristics. Finally, the average and fluctuating wind characteristics of sudden intense winds were investigated, and the time-variant characteristics were discussed in detail. These varying characteristics at high wind speeds, which will make the loads acting on bridges more complex, should be considered in the wind-resistant design of long-span bridges.

Incremental dynamic analysis of the long-span continuous beam bridge considering the fluctuating frictional force of rubber bearing

In the seismic design of long-span bridges, the classic bi-linear model was used to simulate the frictional restoring force of the rubber bearings. However, in actual earthquake, the rubber bearing suffered fluctuating axial pressure in earthquake, even separated from the beam when vertical component of the earthquake was too strong. Employing the bi-linear model for the bearing may incorrectly estimate the seismic response of the bearings, as well as the whole bridge. This paper developed a nonlinear frictional bearing model, which can consider the variation of the frictional restoring force in the bearings, even the separation with the beam in vertical directions. A typical continuous beam bridge was modeled in ABAQUS, and incremental dynamic analysis was conducted for the quantitative comparison of the seismic responses using different bearing models. The intensity measure was selected as the ratio of the peak ground acceleration (PGA) in the vertical direction to the PGA in the horizontal direction. The analysis results indicated that the different bearing model led to the significant different seismic response for the bearings and piers, even the vertical component was small. The bi-linear bearing model would underestimate the seismic demand of the bearing and piers.

Optimization of bridges with short gap streamlined twin-box decks considering structural, flutter and buffeting performance

While it is well known that the gap between twin-box decks is a key design variable that impacts the onset flutter velocity of a bridge, further research is required to ascertain how modifications in several bridge design variables affect other aeroelastic responses. This paper utilizes aero-structural optimization techniques for the design of long-span bridges with short gap twin-box decks considering simultaneously structural, flutter and buffeting constraints. The optimization helps to reduce the material volume of the structure while maintaining all the performance and safety requirements below the imposed thresholds. It has been found that the geometry of the individual box cross-section is an important feature for the control of the buffeting response, particularly the vertical acceleration. On the other hand, flutter and torsional buffeting constraints require designs with larger gap distance and alternative box geometries, leading to a trade-off between conflicting design demands. Hence, depending on the expected wind load conditions and the specific requirements of a particular project, an optimum aero-structural bridge design with a particular deck shape can be identified. The framework presented in this study is an effective tool to achieve sustainable and safe bridge designs that seeks a most efficient balance between all the design constraints.