Long-span Suspension Bridge Research Articles

Design and Static Analysis of Long-span Steel Truss Suspension Bridge

In order to effectively improve the structural safety status of suspension bridges, this paper proposes a design and static analysis method of long span steel truss suspension bridge based on Midas civil finite element calculation software. Taking the Guojiatuo Yangtze River Bridge as a case, the paper studies the mechanical characteristics of the key parts of the bridge in the completion state and operation stage, and determines the structural safety state. The results show that the minimum safety factor of main cable is 2.64, and the minimum safety factor of the suspender is 3.90, and the maximum downward deflection of the main beam is 1.231m < L/400. The structural strength and stiffness can meet the design requirements.

Effects of vertical central stabilizers on nonlinear wind-induced stabilization of a closed-box girder suspension bridge with various aspect ratios

The aerodynamic shape of a closed-box girder plays an important role in the wind-induced stabilization of long-span suspension bridges. The purpose of this study is to investigate the effects of the combination of five aspect ratios and a downward vertical central stabilizer (DVCS) on nonlinear flutter and aerostatic behaviors of a super long-span suspension bridge with closed-box girders. Through conducting a series of wind-tunnel tests and nonlinear finite element analysis, the results show that the nonlinear self-excited forces and the critical wind speed (Ucr) gradually increase as the increase of the aspect ratio (i.e. the width to depth ratios). Furthermore, the application of 20% deck depth DVCS could significantly increase the nonlinear self-excited forces and Ucr for small aspect ratios of 7.9 and 7.1. Particularly, the installation of the DVCS could change the flutter divergence patterns of the bridge from soft flutter to hard flutter, especially for a relatively small aspect ratio. In addition, the aerostatic force coefficients and torsional divergence critical wind speeds of the larger aspect ratio with DVCS are significantly larger than that without DVCS. A relatively small aspect ratio of the bridge has better aerostatic performance than that with a larger aspect ratio.

Parametric optimization of the Eddy current dampers applied to a suspension bridge considering bi-directional earthquakes

The Eddy Current Damper (ECD) is a velocity-based passive energy dissipation device that can be used for structural vibration control. This study aims to reveal the damper behavior and determine the optimal parameters of the ECDs applied to a suspension bridge suffering from bi-directional earthquakes. The influence of the bi-directional vibration interaction on the damping force is theoretically investigated. An optimization method is proposed combining the Sobol Sequence sampling method, the Coefficient of Variation (COV) method, and the Backpropagation neural network (BPNN) algorithm. A numerical model of a long-span suspension bridge with bi-directional ECDs is established and taken as a case study to verify the feasibility of the proposed optimization method. The results indicate that the ECD system with bi-directional interaction will produce a larger maximum force and less energy dissipation than one without bi-directional interaction. The proposed optimization method possesses the characteristics of objectivity, accuracy, and effectiveness. The obtained optimal bi-directional ECDs can significantly reduce the longitudinal and transverse vibration. Failing to consider bi-directional effects will lead to an overestimation of longitudinal damper parameters and an underestimation to transverse ones, as well as ignoring the influence of damper length on its mechanical performance.

Experimental Study of Influence Line–Based Damage Localization for Long-Span Cable Suspension Bridges

Influence line (IL)–based damage indices for long-span bridges are investigated in this study. Their effectiveness is experimentally validated for the first time through the scaled physical model of the Tsing Ma Bridge (TMB). First, the IL mechanism for damage detection and its corresponding damage indices are briefly introduced. Subsequently, the scaled TMB model instrumented with different types of sensors, including displacement sensors, strain gauges, and accelerometers, is introduced. The IL characteristics of different bridge components are compared. Two different damage cases with single- and double-damage locations at the bottom chord were tested. In the single-damage case, different ILs extracted from the nearby components were used for damage identification. These ILs can successfully locate damage visually. The strain IL (SIL) is more sensitive to local damage than deflection IL, but its detection performance degrades rapidly with the increasing distance between sensor and force locations. In the double-damage case, the SIL extracted from a single sensor cannot identify both damage cases because of the limited detectable range of each SIL; therefore, using multiple sensor information becomes necessary. For comparison, the modal parameters were also employed for damage detection. These experimental results validated the merits of the IL–based methods proposed for long-span bridges, indicating that IL–based damage indices are good indicators of local damage detection in long-span bridges. This finding contributes to the development of real-time techniques for damage localization in long-span bridges equipped with a structural health monitoring system.

Data-driven prediction of critical flutter velocity of long-span suspension bridges using a probabilistic machine learning approach

Among the consequences of wind-induced excitation on long-span cable-supported bridges, flutter instability is the most dangerous and can collapse bridge structures. Until now, the flutter velocity of long-span bridges can be computed after conducting an experimental wind tunnel test or by means of computational fluid dynamics (CFD). However, the approaches mentioned above are cost-prohibitive and time-consuming especially when there are many sampling designs to evaluate. Therefore, it is crucial to develop an alternative solution for evaluating the flutter performance of such structures while minimizing the associated cost and computation time without worsening the accuracy of the results. Scholars have proposed machine learning (ML) techniques to address this issue. Unfortunately, some ML techniques do not provide excellent generalization for small datasets and are prone to bias even when the accuracy is relatively high. Besides, conventional ML models do not consider the uncertainty in data. This study proposes a probabilistic machine learning approach to overcome the weaknesses of the conventional ML models. The dataset used to train the proposed model was generated from 73 sampling designs using a fully numerical approach that involved 2D URANS (Unsteady Reynolds-averaged Navier-Stokes) CFD simulations, quasi-steady flutter theory, finite element model, and multi-mode approach for critical flutter velocity computation. The deck cross-section's most influential parameters and the critical flutter velocity constitute the datasets used to build the proposed probabilistic machine learning model. Our finding substantiates that the probabilistic machine learning approach based on hierarchical Bayesian modeling (PML-HBM) overperformed the conventional machine learning models, including extreme gradient boosting regression (XGBR), random forest (RF), and the support vector regression(SVR). Therefore, PML-HBM can accurately predict the critical flutter velocity. This model is an interesting approach to circumvent the time and cost associated with wind tunnel tests and CFD simulations at the earlier design stage of long-span bridge aerodynamic study.

Analytical solutions for thermal effects of suspension bridges based on a surrogate model with longitudinal restraint stiffness

Ambient temperature variation has a significant influence on the deformation of main cables and the internal force of towers of long-span suspension bridges. Currently, the finite element method (FEM) is mainly used for these calculations. This paper intends to present an analytical solution of the thermal effects on suspension bridges. First, three typical temperature patterns are defined. Then, a surrogate model is established by replacing the longitudinal restraint stiffness of the main cable and the tower lateral stiffness with a set of equivalent horizontal springs. The stiffnesses of the suspended cables are formulated according to the energy conservation principle, while the tower lateral stiffnesses are obtained by incorporating the pure bending and Euler buckling solutions, namely considering the effect of the axial force placed on the tower top. Following the force equilibrium conditions, two governing equations are built, which can calculate the variations in the longitudinal displacement of the tower top caused by the temperature variation. After that, some other significant thermal effects, such as the horizontal force of the main cable, the sag of the main cable and the bending moment of the tower bottom, are obtained. Finally, the analytical solution is verified through the field test data of the Tsing Ma Bridge in Hong Kong and the FEM results of four typical examples. The proposed surrogate model offers a quick and easy approach for thermal effect analysis with acceptable accuracy. It is helpful to clarify the mechanical nature of temperature effects to facilitate the preliminary bridge design.

Role of moveable guide vane with various configurations in controlling the vortex-induced vibration of twin-box girder suspension bridges: An experimental investigation

The purpose of this paper is to investigate the effects of a moveable guide vane with various configurations (i.e., horizonal length and stiffness) in controlling the vortex-induced vibration (VIV) of a long-span suspension bridge with twin-box girder. First, a series of VIV tests of the 1:50 scaled ratio of sectional model with various guide vane configurations were performed. The vertical and torsional displacements of the twin-box girder as well as the vertical response of the windward and leeward guide vane measured to analyze the movement characteristics of the main girder and guide vanes, respectively. The test results show that, the moveable guide vane could significantly reduce the maximum vertical and torsional displacement responses of the main girder with an immovable guide vane or without a guide vane, especial under the most unfavorable wind attack angle of +3°. In addition, a moveable guide vane with relatively low stiffness could produce a better outcome of VIV control. Furthermore, the increase of the horizontal length of the guide vane could have a negative impact on the VIV control of the bridge. Importantly, the maximum vertical amplitude of the moveable guide vane is generally larger than that of the main girder, indicates that the leeward guide vane could play an important role in the VIV suppression when the stiffness of the guide vane is over certain threshold (e.g., 19 g/mm).

Temperature-induced response reconstruction method based on DL-AR model and attention mechanism

Data loss is unavoidable for structural health monitoring (SHM) systems due to various potential factors, such as equipment aging, radio interference. Previous studies have revealed that it is more challenging to extract structural state information from incomplete data. Therefore, it is important to develop high-precision response reconstruction methods for missing data. In this study, a hybrid deep-learning and autoregressive model with attention mechanism (DL-AR-ATT) framework is proposed to accurately reconstruct structural responses considering data correlations. The proposed model consists of the deep-learning (DL) and autoregressive (AR) components, which can simultaneously model the linear and nonlinear structure of data. To adaptively weight the contribution of the two components to the final result instead of directly summing, the study introduces a custom weighting layer into DL-AR-ATT. Moreover, the attention mechanism is introduced to eliminate redundant information caused by the data from multiple sensors as input. To verify the validity and feasibility of the proposed method, long-term SHM data from a long-span steel box girder suspension bridge and a prestressed concrete continuous box girder bridge are used. The results show that the reconstruction performance of DL-AR-ATT is superior to that of the one-dimensional convolutional neural network (1D-CNN)-based and hybrid DL and AR (DL-AR) models. Finally, the weights of the modules of DL-AR and DL-AR-ATT are visualized to verify the ability of the model to capture data correlations, and to explain how the attention and custom weighting layers improve the performance of DL-AR-ATT.

Load-bearing performance of caisson-bored pile composite anchorage foundation for long-span suspension bridge: 1-g model tests

Load-bearing performance of caisson-bored pile composite anchorage foundation for long-span suspension bridge: 1-g model tests

Point Cloud Registration Methods for Long-Span Bridge Spatial Deformation Monitoring Using Terrestrial Laser Scanning

In recent years, efforts have been devoted to utilizing terrestrial laser scanning for bridge spatial performance inspection, but they are still restricted to small or medium-span bridges, like some historical heritages. Due to the large-scale dimensional features of long-span bridges, applications of 3D point cloud techniques still remain challenging, such as the extra-long scan range and extreme-small incidence angle when scanning a bridge with a span over 1000 m. Moreover, rare attempts can be found for the performance evaluation of point cloud registration methods for long-span bridges as well, which is a critical basis for further spatial deformation recognition on the point cloud data. Hence, in this study, a cross-evaluation of three iterative closest point (ICP) registration methods is conducted for long-span suspension bridges, namely, traditional ICP, kd-tree-based ICP, and feature point-based ICP algorithms. We conducted field laser scanning on the Ma’anshan Yangtze Bridge, an 1880 m long suspension bridge located in China. The results show that the feature point-based ICP algorithm outperforms the other two in terms of convergence rate and execution time for a single iteration due to the smaller number of registration points compared to the other two algorithms. Moreover, it also gives more precise values in terms of bridge tower spatial deformation identification. Meanwhile, due to efficient data organization, the kd-tree-based ICP algorithm takes less time for a single iteration than the traditional ICP algorithm. Finally, two suggestions for algorithm improvement in terms of efficiency optimization and accuracy improvement of long-span bridge deformation analysis are proposed based on the assessment results.

Cost-Effective Maintenance Policy for Sliding Surfaces of Bridge Bearings Using a Gamma Stochastic Process for Forecasting

To determine the optimal alert threshold for sliding surface replacement of bridge bearings, a cost-effective maintenance policy is proposed in this paper using a gamma stochastic process. First, the sliding surface-triggered run-to-failure process of bridge bearings is discussed based on existing field inspection and maintenance records. Then, the wear thickness of sliding materials is estimated step-by-step based on the cumulative travel distance and wear rate. The gamma stochastic process is used to model degradation of sliding surfaces by using the indicator of wear thickness to depict uncertainties during the degrading process. Next, the optimal alert threshold for replacement of sliding surfaces is determined based on the cost-effective maintenance policy by minimizing the long-term expected maintenance cost rate. Finally, bearings of a long-span suspension bridge are employed to demonstrate the potential effectiveness of the proposed methodology. As a result, the wear thickness of sliding materials approximately follows a linear degrading law. Based on the gamma degrading model, the objective function subject to the long-term expected cost rate is formed. After optimization, the optimal alert threshold for replacement of sliding surfaces is 2.016 mm to achieve a minimum long-term expected maintenance cost rate of US$9,427 per day. In addition, the estimated service life subject to the alert threshold obeys a Gaussian distribution with a mean of 1278 days based on the one-year monitored displacement data.

Experimental study on the fire performance of prestressed steel parallel wire strands

Bridges are critical components of the transportation system and any damage to these structures can result in important social and economic consequences. The literature concerning design standardization for fire hazard in suspension bridges is limited. High strength prestressed steel cables serve as main load-bearing components for suspension bridges, and exposure to high temperatures may result in their prestress loss, leading to structural failure. This paper experimentally investigates the fire performance of 19-parallel wire strands (PWS cables) with a tensile strength of 1860 MPa used as suspender cables in long-span suspension bridges. PWS cables were prestressed and then subjected to UL1709 hydrocarbon fire and simulated open pool tanker fire scenarios in the gas furnace until failure. The load–deflection plots of PWS cables suggest that the cables at ambient temperature sufficiently withstood 95% of their ultimate load capacity. However, the unprotected PWS cables failed within 3–8 min in the fire tests but still sustained the load at 400 °C, which confirms the conservative estimation of 300 °C critical cable temperature mandated by the Post-tensioning Institute. The stress–strain data of tested steel wires correlated well with recently developed high-strength steel wire material models at elevated temperatures. The wire rupture surfaces indicated a brittle failure at ambient temperature and a ductile failure with visible necking under fire conditions. The ultimate (rupture) strain capacity of steel wires decreased from 5% to almost 1% during fire tests. Further, the post-fire strength of PWS cable was unchanged but the elasticity modulus increased by 19% and the rupture strain decreased by 20%. The experimental findings indicate the necessity of fire protection application on PWS cables to keep cable temperatures below the critical temperature of 400 °C in a fire hazard.

A Parallel Scheme of Friction Dampers and Viscous Dampers for Girder-End Longitudinal Displacement Control of a Long-Span Suspension Bridge under Operational and Seismic Conditions

Benefitting from economic development and technological progress, long-span suspension bridges, with their superior span capacity and good economy, have been built in large numbers in recent decades. However, the excessive cumulative longitudinal displacement at the girder ends in the process of bridge operation leads to the degradation of, and fatigue damage to, the connecting components. This study aims to solve the problem with an effective parallel damping scheme of friction dampers and viscous dampers. Firstly, the phenomenon that quasi-static longitudinal displacement accounts for the majority of cumulative displacement is confirmed by the decomposition of measured displacement data at the girder end, which is caused by the asymmetric geometric deformation of the main cable induced by the moving vertical loads of a long-span suspension bridge. An efficient control performance analysis method is proposed based on the formation mechanism of the quasi-static longitudinal displacement. Secondly, the friction damper with a continuous damping model is employed to achieve an effective control performance with respect to the quasi-static longitudinal displacement. Thirdly, in order to realize the target of operational and seismic dual control, a parallel scheme of friction dampers and viscous dampers is proposed, aiming to reduce the cumulative value in the operational state, and maximum value in the seismic state, for longitudinal displacement at the girder ends of a long-span suspension bridge.

Nonlinear Dynamic Analysis of the Wind–Train–Bridge System of a Long-Span Railway Suspension Truss Bridge

In order to study the coupling vibration between a bridge and a train under the action of crosswind loads, a dynamic interaction model of the wind–train–bridge system is established considering the geometric nonlinear factors of a long-span suspension bridge. A calculation frame is composed, and a corresponding computer program is written. A long-span highway–railway suspension bridge scheme is studied as an example. The linear and nonlinear vibration responses of the bridge under the simultaneous action of both train loads and wind loads are compared using the self-written program, and the influence of wind velocity and train speed on the dynamic responses of the bridge is studied. The results show that the large displacement nonlinearity of the structure does not influence the changing tendency of bridge displacement and acceleration time histories, but reduces the maximum values of the responses. The geometric nonlinear influence on the bridge accelerations is more obvious than that on the displacements. The natural frequencies of this long-span suspension bridge are very low and it is sensitive to wind action. The changes in train speed and average wind velocity have a great influence on the maximum value of bridge displacement, especially when the lateral deformation and acceleration increase sharply with the wind velocity, and the coupling vibration between wind, train, and the bridge can easily occur. The research results can provide references for the safe operation and maintenance of long-span bridges.

Corrosion Fatigue Degradation Characteristics of Galvanized and Galfan High-Strength Steel Wire.

Cables are the main load-bearing components of a cable bridge and typically composed of high strength steel wires with a galvanized coating or Galfan coating. Galfan steel wire has recently started to be widely used because of its better corrosion resistance than galvanized steel wire. The corrosion characteristics of the coating and the difference in the corrosion fatigue process of the two types of steel wire are unclear. To further improve the service performance and maintenance of cable bridges, this study investigated the corrosion characteristics of galvanized steel wire and Galfan steel wire through accelerated corrosion tests and established a time-varying model of uniform corrosion and pitting corrosion of high-strength steel wire. Then, a long-span suspension bridge was taken as the research object, and the corrosion fatigue degradation of the two kinds of steel wire under a traffic load was analyzed on the basis of traffic monitoring data. The results showed that the uniform corrosion of the two types of steel wire conformed to an exponential development trend, the corrosion coefficient of galvanized steel wire conformed to the normal distribution, and the corrosion coefficient of Galfan steel wire conformed to the Cauchy distribution. The maximum pitting coefficient distribution of the two kinds of steel wire conformed to the generalized extreme value distribution. The location parameters and scale parameters of the two distributions showed an exponential downward trend with the increase of corrosion duration. When the traffic intensity was low, the corrosion characteristics of the steel wire was the main factor affecting its service life, and the average service life of Galfan steel wire was significantly higher than that of galvanized steel wire. Under a dense traffic flow, the service life of the steel wire was mainly controlled by the traffic load, and the service life of Galfan steel wire was slightly improved. Effective anti-corrosion measures are a key factor for improving the service life of steel wire.

Influence mechanism of vertical dynamic track irregularity on train operation stability of long-span suspension bridge

The track needs to maintain sufficient foundation stiffness to ensure its smoothness and meet the operation stability requirements of high-speed trains. However, the train-induced deformation of flexible suspension railway bridge will inevitably induce the obvious vertical dynamic track irregularity and threaten train operation stability. Combined with a long-span suspension bridge with a main span of 1092 m, this paper provides a new analysis framework for evaluating the track smoothness on the long-span bridge from the perspective of train operation stability. The comprehensive train-track-bridge coupling vibration analysis is conducted to highlight the impact factors on train operation stability and identify the dynamic track irregularity. The simplified evaluation framework of dynamic track irregularity are then proposed to evaluate the track smoothness. The results show that the vertical dynamic track irregularity of long-span bridges is obviously affected by action of train, random track irregularity and overall temperature load. It is quite different from the static track irregularity in terms of alignment and spatial frequency. By separating the dynamic track irregularity according to the wavelength limit of 200 m, two alignment evaluation methods are proposed, namely the mid-chord measurement within 200 m wavelength and curvature method above 200 m wavelength, to reveal the different contributions of dynamic track irregularity component to the vertical car-body acceleration. The influence mechanism of dynamic track irregularity caused by different factors on the stability of train operation is finally identified from the perspectives of vibration acceleration and centrifugal acceleration.

Statistical characteristics of modal damping of long-span suspension bridge at different wind speeds

The present paper combined the natural environment excitation technology (NExT) with the eigen system realization algorithm (ERA) to identify the modal parameters of a suspension bridge. Firstly, the critical parameters in NExt–ERA, such as record length, window length, and ranks of the Hankel matrix, and their influence on identification accuracy have been discussed. Subsequently, based on the acceleration series obtained from the Xihoumen Bridge Health Monitoring System, 3015 sets of modal frequencies and modal damping ratios of the Xihoumen Bridge were identified under 7 sets of wind speeds by the NExt–ERA. Finally, the probability distribution and confidence interval of the structural modal damping ratios were analyzed. Besides, the dependence of identified frequencies damping ratios on wind speed was also discussed. The results show that at the same wind speed, the mean value, and variance of the torsional and lateral mode damping ratios are larger than those of the vertical mode, but this difference gradually decreases with the increment of wind speed. The modal damping ratios along three directions under different wind speeds all follow the generalized extreme value distribution, but wind speed affects the tailing properties of probability distribution of the vertical and torsional mode damping ratios. The estimated damping ratios could provide references for structural design and vibration control of similar long-span bridges.

Evaluation of Flexible Central Buckles on Short Suspenders’ Corrosion Fatigue Degradation on a Suspension Bridge under Traffic Load

Suspenders are the crucial load-bearing components of long-span suspension bridges, and are sensitive to the repetitive vibrations caused by traffic load. The degradation of suspender steel wire is a typical corrosion fatigue process. Although the high-strength steel wire is protected by a coating and protection system, the suspender is still a fragile component that needs to be replaced many times in the service life of the bridge. Flexible central buckles, which may improve the wind resistance of bridges, are used as a vibration control measure in suspension bridges and also have an influence on the corrosion fatigue life of suspenders under traffic load. This study established a corrosion fatigue degradation model of high-strength steel wire based on the Forman crack development model and explored the influence of flexible central buckles on the corrosion fatigue life of suspenders under traffic flow. The fatigue life of short suspenders without buckles and those with different numbers of buckles was analyzed. The results indicate that the bending stress of short suspenders is remarkably greater than that of long suspenders, whereas the corrosion fatigue life of steel wires is lower due to the large bending stress. Bending stress is the crucial factor affecting the corrosion fatigue life of steel wires. Without flexible central buckles, short suspenders may have fatigue lives lower than the design value. The utilization of flexible central buckles can reduce the peak value and equivalent stress of bending stress, and the improved stress state of the short suspender considerably extends the corrosion fatigue life of steel wires under traffic flow. However, when the number of central buckles exceeds two, the increase in number does not improve the service life of steel wire.

Development of a low-cost vision-based real-time displacement system using Raspberry Pi

Vision-based real-time displacement measurement systems can measure the structural displacements without contact and output the results immediately, overcoming some drawbacks of traditional contact-type sensors and off-line vision sensors in field applications. However, high cost and complexity of installation restrict the widespread application of the off-the-shelf vision-based real-time displacement systems. In this work, a fast image processing software is developed for operation in single board computers (SBC), firstly, based which a low-cost and portable vision-based real-time displacement measurement system using Raspberry Pi is constructed for civil structural health monitoring. To evaluate the performance of the system in field applications, a new method for validation of on-site measurement accuracy is proposed. The experimental results show that the constructed system accurately measured multipoint structural displacements of a long-span suspension bridge in real-time, with at least 1/17 pixel accuracy, providing a cost-efficient, convenient, high-precision, and contactless approach to obtain the displacement responses of infrastructures in the field.

Gradual Deterioration Behavior of the Load-Bearing Strength of Main Cable Wires in a Suspension Bridge

The main cable is the primary load-bearing component of a long-span multi-tower suspension bridge. The interaction between a dead load, vehicle load, wind load, and the corrosion environment leads the main cable wire to exhibit tribo-corrosion-fatigue behaviors. This behavior causes wire wear and deterioration, as well as a reduction in the effective cross-sectional area. This leads to the gradual deterioration of the wire’s load-bearing strength and seriously affects the load-bearing safety of the main cable. In order to ensure the safety of suspension bridges, it is critical to investigate the gradual deterioration behavior of the main cable wire’s load-bearing strength. A wire tribo-corrosion-fatigue test rig was established to test the wire under different friction pairs (saddle groove or parallel wires). The cross-sectional failure area of the wire with different pairs was obtained by super-depth electron microscopy and calculation. The damage degree evolution model and the deterioration model of the wire load-bearing strength were established by combining the theory of damage mechanics and the finite element method. The results show that, as contact and fatigue loads increase, so does the cross-sectional failure area of the fatigue steel wire. The fatigue wire’s damage degree has a good quadratic function relationship with fatigue cycles. The damage degree of the wire increases and the load-bearing strength decreases with increasing contact load and fatigue load. The load-bearing strength of the wire changes little at the beginning and decreases with increasing fatigue cycles. The results have fundamental significance for the life prediction of the main cable wires of suspension bridges.