Long-span Cable-stayed Bridge Research Articles

Response analysis of a long-span cable-stayed bridge with ultra-high piles subjected to near-fault ground motions considering deep-water, sedimentation, local site, and wave-passage effect

Response analysis of a long-span cable-stayed bridge with ultra-high piles subjected to near-fault ground motions considering deep-water, sedimentation, local site, and wave-passage effect

Optimizing vortex-induced vibration suppression in π-shaped girders using wind tunnel testing and CFD analysis

This investigation meticulously explores the vortex-induced vibration (VIV) characteristics in Π-shaped girders within long-span cable-stayed bridges, presenting novel VIV mitigation techniques. Employing detailed wind tunnel evaluations of a 1:50 scale model alongside computational fluid dynamics (CFD) analyses to model the two-dimensional flow around the girder, this study reveals the formation and shedding of vortices behind the railings and main steel girder, which significantly contribute to VIV in such structures. The introduction of horizontal splitter plates, one m in width, in conjunction with two-m-wide V-shaped guide vanes, was found to substantially reduce the VIV amplitude of the Π-shaped girder, minimizing vortex generation on the deck’s sides and dramatically reducing the maximum vertical VIV amplitude from 208.75 mm to only 5.56 mm. CFD simulations confirm the effectiveness of these measures in suppressing Karman vortex street formation, thereby significantly improving downstream airflow characteristics. These findings offer pivotal insights for the advancement of bridge design and the proactive management of VIV, showcasing the potential of integrated aerodynamic modifications to enhance structural resilience and performance.

Assessing running safety of high-speed trains on long-span cable-stayed bridges based on in-situ monitoring data

This paper presents a new method for assessing the running safety of high-speed trains passing through long-span cable-stayed bridges based on in-situ monitoring data. The monitoring data include the girder vertical deflection and girder-end rotation of bridges. Vertical deformation is utilized to derive the vertical acceleration formula of high-speed trains, and girder-end rotation is utilized to judge the arrival time of the train. According to the specified vertical acceleration limit of the train, the vertical deflection threshold of the bridge is derived from the vertical acceleration formula. The first derivative of the sinusoidal half-wave function of the side-span is utilized to obtain the girder-end rotation threshold, and the safety threshold system is established. The bridge deformation safety threshold system is then used to assess the running safety of the bridge. To verify the presented method, the bridge deformation thresholds calculated using the proposed method are compared with finite element analysis results. The proposed method avoids complex train-bridge coupling numerical simulation in acquiring the dynamic response of high-speed trains, largely improving computation efficiency and enabling real-time assessment of train safety.

Correlation analysis of long-span cable-stayed bridge strain response with environmental and operational variations based on feature selection

The structural response of large-span bridges is significantly influenced by environmental and operational conditions. This study employs a data-driven approach, which utilizes various techniques such as multiple linear regression, best subset regression, stepwise regression, Lasso regression, Ridge regression, and ElasticNet regression to analyze in detail the effects of environmental variables (temperature variables including temperature principal components, lateral temperature gradients, and vertical temperature gradients), and traffic loading on bridge strain response. Based on the analysis of 21 months of health monitoring data from a newly constructed cable-stayed bridge, Lasso regression is shown to perform best in predicting strains on the bridge deck and bottom slab. Furthermore, sensitivity analysis identifies several key influencing factors and quantifies their relative contributions to the strain. Although the 10-min average of the strain due to traffic loading has a minimal impact, the root mean square of the strain shows a significant correlation with the cumulative gross vehicle weight during busy traffic periods. The methodology proposed in this study helps to understand the strain response patterns of large-span bridges from a data perspective, and provides an effective approach to establishing a strain baseline model that eliminates environmental and operational variations.

Unified framework for stochastic dynamic responses and system reliability analysis of long-span cable-stayed bridges under near-fault ground motions

Long-span cable-stayed bridges are complex systems with numerous components, and prone to failures of multiple components under near-fault ground motions with long-period velocity pulses. The evaluation of dynamic system reliability of cable-stayed bridges is an important challenging issue. In this work, a unified framework for simultaneously determining both the stochastic dynamic responses and system reliabilities of long-span cable-stayed bridges under near-fault stochastic ground motions is proposed based on direct probability integral method (DPIM) with adaptive strategy. Firstly, the 3-dimensional finite element model of typical cable-stayed bridge and the stochastic synthesis model of near-fault ground motions are established. Based on probability density integral equation, new formulas in input probability space of time-variant moments of response are derived. Then, DPIM with adaptive strategy is suggested to calculate the mean value and standard deviation of response via new formulas. Dynamic system reliability of cable-stayed bridge under near-fault stochastic ground motions is evaluated by establishing failure criteria of extreme value mappings of multiple performance functions. Finally, numerical results indicate that the long-period velocity pulse of near-fault motions imposes an important effect, resulting in large mean responses and failure of cables. Failure probability of cables is significantly increased with the occurrence of velocity pulses, which causes the decrease of system reliability of cable-stayed bridge. Thus, the randomness and velocity pulse effect of near-fault ground motions should be seriously considered for reliability-based design and safety assessment of cable-stayed bridges.

Design and mechanical properties analysis of a novel CFRP tendons anchorage structure

To address the challenges of larger size, stress concentration at the loading end, and insufficient anchoring performance at the free end of traditional bonding-type anchors for Carbon Fiber Reinforced Polymer (CFRP) tendons, a novel anchor featuring a variable angle multi-stage cone is proposed. This solution is derived by analyzing the notch effect at the loading end caused by the wedging of the bonding medium in conventional cone-type anchors. A theoretical model for the stress distribution of the variable angle multi-stage conical anchor was developed using elastic deformation theory. The reliability of this model was validated through finite element analysis. Subsequently, a comparative analysis was conducted to evaluate the stress distribution and anchoring performance of the variable angle multi-stage conical anchor against several traditional anchor types. This analysis revealed the mechanical mechanisms and advantages of the variable angle multi-stage conical anchor in enhancing anchoring effectiveness. The study illustrates that the bonding medium between adjacent cone sections of the variable angle multi-stage conical anchor exhibits a specific gap under stress, leading to reduced stress in the tendon at the connection points. This ensures a smooth transition that prevents abrupt changes in stress due to sudden shape alterations, thereby guaranteeing uniform stress distribution within the anchor section. By incorporating a multi-stage cone structure and increasing the cone angle at the free end, compressive stress can be effectively transferred to the free end, mitigating the notch effect and enhancing anchoring performance. Compared to typical conical anchors, the maximum compressive stress of the variable angle multi-stage conical anchor is reduced by 53.5 %, the outer diameter of the anchor cylinder is decreased by 22.7 %, and the anchoring efficiency is improved by 12.2 %. These improvements result in a robust anchoring effect and significant size advantage. The anchor is suitable for multibar anchoring, providing a reliable solution for large tonnage and long-span cable-stayed bridges.

A New Method to Deduce the Mapping Relationship between A Track and A Long-Span Cable-Stayed Bridge Under Different Excitations

Urban rail transit is rapidly evolving, with long-span cable-stayed bridges becoming increasingly popular among engineers because of their adaptability. However, as the operation time of bridges with tracks increases, the combined effects of repeated wheel loads and various bridge system excitations, including temperature changes and shrinkage–creep, gradually alter the alignment of the main beam. Similarly, the track structure on the bridge deck also undergoes vertical displacement, leading to corresponding degradation in rail alignment. This study applies singular function theory and verifies its effectiveness in bridge mechanical analysis. For the steel spring floating plate track cable-stayed bridge system, the mapping relationship between the deformation of the bridge’s main beam and the track’s deformation under bridge system excitation is derived, integrating singular function theory with the theory of train–track–bridge dynamic interaction. By analyzing the force transfer mechanism of the track–bridge system under system excitation, this research examines the effects of different excitations on the coupled dynamic response of the train–track–bridge. These findings suggest that system excitations increase the dynamic response of the train–track–bridge system, which is crucial for improving the durability and reliability of urban rail transit infrastructure.

Dynamic response of high-speed trains under uneven temperature fields of slab tracks on cable-stayed bridges

The temperature deformation of a long-span cable-stayed bridge (LSCSB) could significantly deteriorate the smoothness of rails, thereby affecting the dynamic behavior of high-speed trains (HSTs). In this paper, based on the thermal-fluid-structure coupling theory and vehicle-track coupling dynamics theory, an analysis method was proposed to explore the influence of temperature deformation of LSCSBs on the dynamic behavior of HSTs. The temperature deformation of LSCSBs within a day was analyzed, and the dynamic behavior of HSTs passing through the LSCSBs at different times was revealed. The results showed that on a summer day, the temperature deformation of LSCSBs varied significantly and rapidly, and the variation experienced a significant increase of 23.46% within just 2 h. Due to the influence of structural temperature deformation, the wheel-rail interaction, train safety, and passenger comfort changed noticeably. The construction temperature of the bridge and track decisively affected the dynamic behavior of the train. Therefore, it was crucial to construct the structure under suitable temperature conditions to prevent further exacerbation of the dynamic behavior of HSTs due to violent temperature differentials. In summary, the method proposed in this paper could contribute to a comprehensive and in-depth understanding of the operational characteristics of HSTs on LSCSBs.

Temperature behavior of long-span cable-stayed bridges by using unified analysis

Varying temperatures significantly affect long-span cable-stayed bridges. However, previous studies on the temperature behavior of bridges were either limited by finite sensors, failing to capture the accurate relation between the temperature and responses, or constrained to a “divide-and-conquer” strategy, requiring considerable manual intervention. This study develops a unified approach to the investigation of thermal behaviors of cable-stayed bridges by integrating heat-transfer analysis and structural analysis based on the same refined global 3D finite element model. A navigation channel bridge of Hong Kong‒Zhuhai‒Macao Bridge is used as the testbed. First, the heat-transfer analysis is conducted based on thermal boundary conditions carefully determined from real-time ambient temperature, wind, and solar radiation, which are tailored for each surface to reflect the influence of the geometric configuration and temperature difference. Then, the detailed temperature distribution results are automatically converted to thermal loads, and thermal elements are changed to structural elements to calculate the temperature-induced responses. Results show that temperature has a significant effect on the structural responses of the bridge. The calculated temperatures and temperature-induced responses are in good agreement with their measured counterparts, verifying the effectiveness of the proposed unified approach to investigating the temperature behavior of cable-stayed bridges.

Simplified design of nonlinear damper parameters and seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers

Simplified design of nonlinear damper parameters and seismic responses for long-span cable-stayed bridges with nonlinear viscous dampers

Unsupervised quantitative structural damage identification method based on BiLSTM networks and probability distribution model

Current unsupervised structural damage identification methods mainly focus on unsupervised damage detection, i.e., detecting whether damage occurs, but rarely involve damage localization and quantification in practical civil engineering structures. Thus, based on bidirectional long short-term memory (BiLSTM) networks and a probability distribution model, i.e., generalized extreme value distribution (GEVD), this paper proposes an unsupervised structural damage detection, localization, and quantification method. The response correlations model among sensors under healthy conditions was built by employing the BiLSTM networks for reconstructing response data. Then, reconstruction error between reconstructed and true data is used as damage-sensitive features and thus is applied to detect and localized damage. In addition, a stable damage quantification result can be obtained based on the probability distribution model of damage-sensitive features. The proposed method is validated by using the data obtained from a numerical steel beam model and a practical long-span cable-stayed bridge. The research results demonstrate that the proposed method can effectively detect, localize, and quantify damage in an unsupervised manner, even with a limited number of sensors and low-order modal information in acceleration data. The proposed method possesses the capability to autonomously furnish alerts regarding structural damage location and severity under Environmental and Operational Conditions.

Evaluating the load-bearing capacity of corroded cables in long-span cable-stayed bridges: A stochastic corrosion field simulation approach

In cable-stayed bridges, cables are the primary load-bearing components. The corrosion of high-strength steel wires within these cables can degrade their bearing capacity, which in turn impacts the safety and durability of long-span cable-stayed bridges. To address this concern, a three-dimensional random field model was proposed in this study to evaluate the residual bearing capacity of corroded cables. This model considers the random distribution of the strength of high-strength wires along both axial and cross-sectional directions caused by corrosion. Subsequently, a three-dimensional spatial correlation model was developed based on field test results from two stay cables in service on an actual bridge. This model represents the strength distribution of corroded high-strength steel wires within the cable. Finally, the evaluation model developed in this study was employed to assess the bearing performance of two corroded cables with different degrees of corrosion. The results were then compared with test outcomes. The results show that the proposed evaluation model can accurately estimate the bearing performance of corroded cables.

Extraction and evaluation of cable forces of a cable-stayed bridge based on amplitude and phase estimation method

In order to identify the time-varying frequency and amplitude of structural vibration based on the bridge structural health monitoring data and obtain the cable force of cable-stayed bridges in real time, a spectrum analysis method based on amplitude and phase estimation (APES) was proposed in this study. The amplitude spectrum of the acceleration data is first calculated by the APES method, the real-time spectrogram of the cable is obtained by the sliding window method. Then the modal frequency and amplitude are automatically extracted from the real-time spectrum by using a frequency extrusion post-processing technique, which can be regarded as the average value of the instantaneous frequency and amplitude respectively. Next, the fundamental frequency of the cable is extracted by using an automatic identification method, and the performance of the proposed method is verified. Finally, real-time scoring of cable forces and structural condition assessment is achieved with consideration of the moderation index model as well as the material strength. The results show that the APES method can use shorter calculation samples than the traditional Fast Fourier Transform (FFT) to obtain higher resolution and more accurate amplitude, which provides a theoretical basis for the real-time identification of fundamental frequency based on short-term monitoring data. The frequency extrusion post-processing-algorithm can reduce the spectrum recognition delay and improve timeliness of the cable force evaluation. The time-varying cable force with an interval of 10 s can be used to reflect the health status of the cable in time. The research results can provide technical support for the real-time extraction of cable force of long-span cable-stayed bridges, and can also provide an effective basis for component condition evaluation and bridge maintenance decision-making.

Reynolds number sensitivity of the vortex dynamics around a long-span rail-cum-road bridge girder with three separated boxes

The novel separated three-box girder is gradually adopted for very long-span cable-stayed bridges due to its excellent flutter stability. Due to its special design of cross section, it exhibits notable Reynolds number effects in the flow patterns and vortex dynamics when subject to incoming flow. To explore its Reynolds number sensitivity, this paper performs a three-dimensional large eddy simulation (LES) on the flow around a static long-span rail-cum-road bridge girder with three separated boxes at different Reynolds numbers. The overall centre height H of the bridge model is chosen as the characteristic length, and the investigated Reynolds number regime falls into the regime of 1e2≤Re≤2.8e4. Through the analysis of the flow characteristics of three distinct regions in the flow field(the windward leading edge region, the gap region and the wake region), a successive transition of the wake flow, gap flow, and leading edge shear flow is observed with increasing Reynolds number. The surrounding flow patterns are divided by different Reynolds number regimes as: laminar separation at the trailing edge (Re<5e2); simultaneous instability of the gap shear layer and the wake (5e2≤Re<1e3); restabilisation of the upstream gap shear layer (1e3≤Re<3e3); secondary instability of the upstream gap shear layer and transition of the wake (3e3≤Re<8e3); transition of the separated shear layer at the leading edge (8e3≤Re≤2.8e4). This paper reveals in detail the complex vortex dynamics in the surrounding flow field of the special cross section with three separated boxes.

An Experimental Study of High-Damping Rubber Bearings (HDRB) and Their Implications for the Seismic Performance of Cable-Stayed Bridges

This article investigates the efficiency of high damping rubber bearings (HDRB), which are made of special rubber with excellent damping attributes and layers of steel. HDRB isolators have excellent flexibility, vibration reduction ability, and high restoring ability for controlling the seismic response of long-span cable-stayed bridge systems under near-fault ground motions. The seismic isolation of cable-stayed bridges is achieved using high-damping rubber bearings (HDRB). High-damping rubber bearings have excellent seismic effects during earthquakes. The elastic stiffness of the bearing depends on the degree of deformation. When the deformation is small, the stiffness will be large. Therefore, compressive stiffness is one of the key parameters in the design of seismic isolation bearings for cable-stayed bridges. For this reason, predicting the behavior of high-damping rubber bearings under compressive loads is highly important for their design. Therefore, the experimental verification of high-damping rubber bearings (HDRB) for compressive loading was tested according to the standard assumptions in STN EN 1337-3. Firstly, periodic vertical compression tests are performed, and the high damping rubber (HDRB) capabilities and energy dissipation are analysed, taking into account the effect of vertical compression and loading frequency. Secondly, a corrected calculation of the vertical stiffness for high-damping rubber bearings is proposed based on experimental data to provide a more accurate and realistic tool for measuring the vertical mechanical properties of rubber bearings. The test results prove that HDRB has the most advanced performance. For the fatigue property, the hysteresis curves of the HDRB plump both vertically, which provides a good energy dissipation effect. DOI: https://doi.org/10.52783/pst.431

Seismic behavior analysis of long-span cable-stayed bridge under bi-directional near-fault ground motions

In this paper, the seismic behaviors of a long-span cable-stayed bridge subjected to bi-directional near-fault ground motions are analyzed. The cable-stayed bridge with a main span of 432 m is selected as the research object and appropriately modeled using the OpenSees software. Ten sets of historical near-fault and far-field ground motions associated with the same earthquake event and site class are utilized as input excitations. Nonlinear time-history analyses are conducted to explore three key aspects: the influence of ground motion directionality, the effectiveness of the percentage rule and simplified Square-Root-of-Sum-of-Squares (SRSS) rule, and the main influential factors. The findings reveal that near-fault ground motions induce larger seismic responses compared to far-field ground motions. Moreover, the effects of ground motion directionality are more pronounced in near-fault scenarios than in far-field events. The percentage rule and simplified SRSS rule demonstrate minor significance in predicting the critical seismic responses. The bi-directional peak ground velocity (PGV) of seismic motions in the principal directions of the cable-stayed bridge may emerge as the primary factor influencing the seismic responses, making it a suitable intensity measure for bi-directional seismic fragility assessment.

A simplified weak coupling dynamic analysis method for running safety evaluation of train on bridges under earthquake excitation

This study proposes a simplified analysis method that couples the bridge and train-track subsystem in a weak form to facilitate the dynamic analysis of the train-track-bridge coupled system (TTBS) under earthquakes. The method includes three main steps: (i) performing dynamic analysis of the bridge under seismic conditions to obtain the response of the bridge deck; (ii) interpolating the bridge displacement beneath each wheelset based on the train's velocity, departure time, and the initial positions of the wheelsets; and (iii) assessing the running safety of the train by incorporating the interpolated bridge response as track irregularity into the train-track coupled system. Steps (i) and (iii) can be analyzed separately using finite element and multibody dynamics software, eliminating the need to create a complex TTBS model that is challenging to achieve within a single software platform. Additionally, based on the method’s assumptions, the earthquake excitation on the train can be separated into the seismic inertial effect and seismic-induced bridge deformation, enabling a quantitative analysis of the impact of these two types of excitations on train safety. Taking a 10-span simply supported bridge and a long-span cable-stayed bridge as examples, the proposed method’s assumptions are verified by comparing its results with those obtained from a complex TTBS model. Furthermore, the impact characteristics of inertial effects and seismic-induced bridge deformation on train safety for these two types of bridges are analyzed. The proposed method offers robust support for seismic design of bridges and facilitates a comprehensive analysis of the mechanisms through which seismic excitations affect train safety.

Novel long-span cable-stayed deck arch bridge: Concept and structural characteristics

To explore a cost-efficient bridge structure system and expand the options for long-span bridges in mountainous regions, we propose an innovative cable-stayed deck arch (CSDA) bridge with significant potential benefits. This paper discusses the conceptualization, structural design considerations, and implementable construction methods of this bridge-type. We trial designed two CSDA bridges with span arrangements of 268 + 350 + 268 m and 280 + 3 × 380 + 280 m to demonstrate the versatility of our proposal in different topographic situations and its ability to accommodate both single and multiple main spans. The finite element analysis confirms the mechanical properties and structural feasibility of the conceptual designs. A comprehensive comparison with other types of bridges under identical conditions reveals that this new hybrid bridge is not only lightweight in structure, excellent in performance, and elegant in form, but also cost savings and with minor environmental impact. The preliminary study indicates that the CSDA bridges are suitable for the construction demand of high-rise pier and long-span bridges in mountainous terrain, and also an economical option for the main span between 350 to 400 m.

Shake table test on support uplift force of long-span cable-stayed bridge under longitudinal ground motions

Since the excessive seismic support uplift force may cause the support failure of long-span cable-stayed bridges, this study focused on the support uplift force at the auxiliary pier for a double-tower cable-stayed bridge with a main span of 1088 m. A shake table test was designed and performed based on the 1/35-scale test model scaled from the prototype bridge. Details of the test model, including the scale factor, structural member configurations, boundary conditions, and the numerical validation were briefly presented. The test results show that although only the longitudinal ground motion was applied, significant seismic support uplift and compression forces would be generated in the bearings at the auxiliary pier, resulting in the bearing uplift. The vertical vibration of the deck contributed by the first vibration mode of the test model was one of the main causes of the bearing uplift, but no rigid-like pounding effect occurred due to the vertical nonlinear mechanical behaviour of the bearing. Furthermore, the effect of the bearing uplift on the main seismic responses of the test model was negligible.

Effect of uncertainties in cable corrosion and material strength on seismic fragility of long-span cable-stayed bridges in marine environments

This paper presents an investigation into the seismic fragility of cable-stayed bridges and considers the complex uncertainties in cable corrosion and material strength. Under certain assumptions and using the limited measured data available for steel corrosion, a cable corrosion model is established. The probability distribution of several parameters, including the corrosion rate, corrosion initiation time, chloride concentration, and cable replacement in the corrosion model, is considered. In addition, the influence of the stress level of cables is also considered in the model by the amplification coefficient of the corrosion rate. To consider the effect of the uncertainties in cable corrosion and material strength on the seismic fragility of this bridge, the uniform design (UD) method is used to generate reasonable bridge samples and to build probabilistic seismic demand models. The results indicate that cable corrosion has a significant impact on the seismic fragility of cable-stayed bridges. The seismic fragility of girders and piers are the smallest and the highest among all bridge components, respectively. The material strength uncertainties have a significant influence on the seismic fragility of bridge components. The coupling between the uncertainties in cable corrosion and material strength does not increase the seismic fragility of the bridge components in most cases because of the cancellation effect of the two uncertainties to some extent. In addition, cable replacement has a significant influence on the seismic fragility of bridge components. In order to correctly evaluate the performance of cable-stayed bridges in service, it is necessary to consider the uncertainties in cable corrosion and material strength in a seismic fragility analysis of long-span cable-stayed bridges with different service periods.