Bridge Model Research Articles

A method for reconstruction of structural health monitoring data using WGANGP with U-net generator

Data loss issue often occurs in structural health monitoring (SHM), which can undermine the reliability of structural condition diagnosis and prognosis. Neural networks are commonly employed for reconstruction of missing SHM data by modeling the correlation between intact and missing signals. The existing neural network methods use deeper architectures to capture complex data correlations. As network depth increases, the ability to preserve both low- and high-level features diminishes, and network training becomes challenging, which reduces data reconstruction accuracy. This study proposes a data reconstruction method that utilizes a Wasserstein generative adversarial network containing a gradient penalty term with a U-net generator. Multiple improvements are made to the generative adversarial network to enhance the reconstruction performance. First, the U-net is used as a generator, and the signal features at low and high levels are preserved based on the skip-connection technique. The U-net is pre-set with multiple layers to enhance the reconstruction accuracy. Second, a mean square error (MSE) term is added to the loss function. The MSE coefficient is proposed to balance adversarial training and reconstruction feature learning. Third, the Wasserstein distance is introduced to replace the cross-entropy loss function of traditional generative adversarial networks, avoiding gradient vanishing and exploding. The reconstruction performance of the proposed method is evaluated on a computational bridge model and Canton Tower, and the influence of reconstruction parameters on the accuracy of reconstruction results is discussed in detail. The reconstructed data by the proposed method closely matches the original data in both the time domain and frequency domain. The time–frequency characteristics of the acceleration data can be accurately reconstructed, demonstrating the effectiveness of the reconstructed signals in data analysis. By comparing with typical neural network methods, it is found that the proposed method has higher reconstruction accuracy.

Research on calculation of transverse bending moment of deck of box girder with long-span and long cantilever

To investigate the reasonable calculation value of the transverse design bending moment of a long-span cantilever box girder bridge deck under vehicle load, the plate beam model and beam element frame model were established according to the concept of load effective distribution width in the Chinese highway specifications. The local finite element model and full bridge model of a long-cantilever plate were established using the plate-shell element. The practical calculation formula and finite element analysis of the transverse bending moment of a bridge deck were studied. The results showed that the transverse bending moment of the long-cantilever plate calculated using Baider Bahkt formula slightly deviated from the calculated value of the plate-shell element, and the deviation between the calculated values of Baider Bahkt formula and Sawko formula was 7.72%. Baider Bahkt formula is more accurate than Sawko formula, which is recommended by the Chinese highway specifications.

Vehicle–Bridge Coupling Vibration Analysis of a Highway Pile–Slab Bridge Based on the Contact Constraint Method

To investigate the impact of vehicle load on highway pile–slab bridges, the contact constraint method is employed to treat the vehicle and the bridge as two independent subsystems. Through the formulation of point-to-surface contact and constraint equations, a vehicle–bridge coupling vibration analysis is performed, incorporating the effects of bridge deck roughness. The finite element method is utilized to construct the pile–slab bridge model, while the five-axis heavy vehicle model is developed based on the multi-rigid-body dynamics method. The analysis and computational results of the model reveal the effects of pier height, vehicle number, and the friction coefficient on the dynamic response of the pile–slab bridge. The results indicate that pier height significantly influences the dynamic response, and the appropriate pier height should be carefully determined during the design phase. The vertical displacement impact coefficient surpasses the design value derived from the specification, highlighting the need to consider the vehicle’s impact on the bridge. Furthermore, vehicle number and the friction coefficient significantly affect the longitudinal dynamic response and transverse acceleration response of the pile–slab bridge.

Seismic fragility, loss, and resiliency of old railway masonry arch bridges under near-field ground motion

ABSTRACT Iran’s historic railway arch bridges, many over a century old, face seismic risks due to their original design neglecting lateral loads. As they are often situated in seismically active zones near fault lines, understanding their seismic vulnerability is crucial. The goal of this study is to assess the seismic fragility and loss estimation of such bridges under various seismic events. To this end, the seismic performance of two masonry arch bridges, specifically a bridge with two long spans, named 2LS20, and a bridge featuring five small spans, named 5SS06, along the old Tehran-Qom railway line, is assessed under a set of 28 near-field and 22 far-fault earthquake records. Throughout the nonlinear incremental dynamic analysis, seismic fragility analyses were performed to ascertain the likelihood of damage across distinct limit states for each bridge model under the action of near and far-fault ground motions. Subsequently, throughout the resiliency analysis, the recovery process was simulated to assess the progress of bridge functionality with time. Moreover, seismic loss analyses were conducted to assess the comparative economic viability of the studied models. The results indicate the 5SS06 bridge for lower vulnerability and repair costs with near-fault motions posing higher risks, particularly for extreme damage conditions. Resilience varies significantly based on recovery models, with the 5SS06 bridge showing more effortless recovery under far-fault motions and higher resilience factors under near-fault records. Additionally, predictive equations were proposed for managing seismic risks in similar bridge infrastructures, particularly in Iran’s railway network, aiding resilience and risk mitigation planning.

Solving Multi-Point Boundary Value Differential Equations with a Novel Semi-Analytical Algorithm

To address the general multi-point boundary value problems, we present a novel semi-analytical algorithm. This scheme is applicable to both linear and nonlinear fractional-order and integer-order differential equations under multi-point boundary value and/or initial value conditions. The proposed algorithm involves the introduction of auxiliary fractional equations derived from the main equation. Subsequently, a linear combination of the solutions to the auxiliary equations is formed to meet the boundary conditions of the main equation. The combination includes some unknown coefficients. In respect with these unknown coefficients, we optimize the relevant residual function to achieve its minimum value. This is done by using the method of weighted residuals. The convergence of the method is established and proved. The algorithm is employed to obtain approximate solutions for multi-point boundary and initial value problems. Additionally, it effectively addresses problems with solutions that exhibit weak singularities at the origin. Numerical results, including solving two bridge models, reveal that the proposed method demonstrates a substantial improvement in performance over existing methods.

A Novel Analytical Model for Structural Analysis of Long-Span Hybrid Cable-Stayed Suspension Bridges

The hybrid cable-stayed suspension bridge is used to combine the advantages of cable-stayed and suspension bridges and hence has a broad prospect for application. The conventional simplified analytical models of the hybrid bridge are usually developed based on a schematic with the cable-stayed and suspension systems working separately without any overlapping zone, which cannot represent the modern hybrid bridge system. In this study, a novel analytical model is proposed based on the modified suspension–elastic foundation beam theory to estimate the mechanical performance and deflection of the hybrid bridge system with the consideration of the overlapped section between the suspension and stayed cables. The governing equations of the hybrid bridge system are developed based on the elastic foundation beam theory and the deflection theory, which are derived separately in the hybrid section, the pure suspension section and the cable-stayed section. The general solution of each section is presented. The Transfer Matrix Method is then employed to solve the unknowns from one end to the other, which are in turn used to solve the internal forces of the hybrid bridge system caused by the concentrated load. In addition, in view of no variation in the unstressed length of the main cable, the compatibility equation of the main cable is established with consideration of the longitudinal displacement of the main tower, which is used to derive the formulas for the internal force and deflection of the hybrid system. The model can be easily complied in any programming platform, such as Matlab, with simple input parameters, which can eliminate the complex finite element modeling process. Hence, it can be easily used in the preliminary design stage to determine the optimal size and layout of the bridge. Then, a case study is presented for the verification of the proposed model under a vertical load, which is simplified from the Xihoumen Bridge, a combined highway and railway bridge with a main span of 1488 m. Good agreement is obtained between the proposed model and the finite element method. Meanwhile, it is found that there exists a negative deflection zone for the main beam at a distance from the concentrated vertical load, which is mainly caused by the deflection of the main cables, leading to the cambering of the beam.

Evaluation of stress patterns in teeth with endodontic treatment and periapical lesions as abutments for fixed prosthesis: a finite element analysis study

BackgroundExamining stress distributions in abutment teeth with periapical lesions is essential for understanding their biomechanical impact on dental structures and tissues. This study uses finite element analysis (FEA) to evaluate these stress patterns under occlusal forces, aiming to enhance treatment strategies and prosthetic designs.MethodsThree FEA models were created: a healthy mandibular premolar (Model 1), a premolar with a single crown and a lesion repaired using a fiber-post (Model 2), and 3) a premolar with a lesion repaired using fiber-post to support a four-member bridge (Model 3). A 300 N occlusal static stress was given to each model at a 45° angle to the long axis of the tooth, namely at the lingual inclination of the buccal-cusp. Deformation behaviour and maximum equivalent stress distributions were simulated on the all components, including the bony structure for each model.ResultsThe study showed a reduction in equivalent stress levels in trabecular and cortical bone, crown, cementum, and PDL under occlusal force, from Model 1 to Model 3. The Von Mises yield criteria values of the tooth models differed depending on the prosthetic restorations, with the highest value seen in Model 2 (133.87 MPa). Similar locations in all models showed concentrated equivalent stresses for all components. The periapical lesion area exhibited relatively low stress values for Models 2 and 3, at 0.061 MPa and 0.039 MPa, respectively. The largest level of stress was seen in the cervicobuccal areas of the tooth in all models.ConclusionProsthetic restorations on teeth with periapical lesions resulted in varying stress and biomechanical responses in the tooth and surrounding bone tissue. These teeth can serve as abutments in a four-unit bridge when subjected to optimal occlusal stresses, based on the findings.

Review of Condition Rating and Deterioration Modeling Approaches for Concrete Bridges

Concrete bridges are the most prevalent bridge type worldwide, forming critical components of transportation infrastructure. These bridges are subjected to continuous deterioration due to environmental exposure and operational stresses, necessitating ongoing condition monitoring. Despite extensive research on condition rating and deterioration modeling of concrete bridges, a comprehensive and comparative understanding of these processes remains underexplored. This paper addresses this gap by conducting a critical scientometric and systematic review of condition rating and deterioration modeling approaches for concrete bridges to highlight their strengths and limitations. Accordingly, most of the condition rating methods were found to have a heavy reliance on qualitative visual inspections (VI) and inherent subjective assumptions. Techniques such as fuzzy logic and non-destructive evaluation (NDE) methods were identified as promising tools to mitigate uncertainties and enhance accuracy. Moreover, the performance of most deterioration models was dependent on the quality of the historical condition data. The advancement of hybrid deterioration models, such as integrating artificial intelligence (AI) with stochastic and physics-based approaches, has proven to be a powerful strategy, combining the strengths of each method to deliver enhanced condition predictions. Finally, this study offers key insights and future research directions to assist researchers and policymakers in advancing sustainable concrete bridge management practices.

A method for uniform upgrading of isolated bridges with complex root devices

An experimentally proved method for efficient seismic upgrading of isolated bridges exposed to very strong multi-directional near-field and far-field earthquakes is presented in this paper. The advanced capability of the upgraded bridge system was achieved by application of the developed uniform complex root (CR) energy dissipation devices. The new uniform complex root (UCR) bridge system was fully validated based on seismic tests on experimental models and analytical response simulation studies. The UCR system integrates the advances of seismic isolation and energy dissipation and represents an advanced technical solution for efficient protection of bridges located in seismic areas of the highest seismicity. The tested large-scale model of the UCR bridge system had double spherical rolling seismic bearings (DSRSB) as seismic isolation devices, while qualitative improvement of the seismic performances was achieved through the use of the created uniform CR energy dissipation devices. Extensive seismic testing of the UCR bridge model was conducted under simulated effects of near-field and far-field earthquakes, respectively.

Dynamic Responses of Long‐Span Steel Truss Girder Cable‐Stayed Bridge With a Single Pylon

The study investigates the seismic response of long‐span single‐tower and single‐cable steel truss girder cable‐stayed bridges, which structurally differ from traditional bridge types, and there is limited research on the influence of cable arrangement on the seismic response of long‐span single‐tower steel truss girder cable‐stayed bridges. Therefore, based on the engineering background of the world’s largest span single‐tower and single‐cable steel truss girder cable‐stayed bridge, a finite element model of the entire bridge is established to study the effect of cable arrangement on the seismic response of the bridge. The results indicate that although a double‐cable plane arrangement can slightly reduce the torsion of the main girder, it cannot completely eliminate the occurrence of torsional vibration modes. However, by employing structural measures such as sufficient stiffness and reasonable width of the steel truss girder, the negative impact of single‐cable plane arrangement on the dynamic characteristics of the bridge can be mitigated. It is suggested to adopt a single‐cable plane arrangement when the standard width of the main girder is narrow, while a double‐cable plane arrangement is more suitable when the standard width of the main girder is wide. These findings provide an important reference for the design of similar structures in the future.

Seismic Fragility Assessment of Steel Rigid‐Frame Bridges Exposed to Marine Corrosion

Corrosion is one of the main concerns in different industrial sectors, leading to millions of dollars lost every year worldwide. Hence, the study of deterioration due to corrosion and its effects on the seismic performance of steel structures, especially those located in corrosive regions, is essential. In the present study, the influence of marine corrosion has been considered to reduce the section area of the bridge’s immersion piers using Melchers’s corrosion model. Several models of corroded steel rigid‐frame (CSRF) bridges have been made, and nonlinear static analysis (pushover) and nonlinear incremental dynamic analysis (IDA) have been done on corroded bridge models to estimate capacity loss and predict seismic fragility at certain times during their service life. To validate the nonlinear analysis method, the experimental and numerical results are compared. The analysis results indicate that the bridge’s capacity and energy dissipation under a corrosive environment have been considerably decreased, and the probability of collapse has increased. After 90 years of the structure’s service life, the results of the seismic evaluation of the behavior of steel bridges in severe corrosive environments show that the bridge’s base shear has decreased by 33%, and the probability of collapse has increased by 15%. Based on the results of this study, some recommendations and strategies have also been suggested for the seismic design of new bridges and the rehabilitation of existing bridges in corrosive areas.

Effect of steam curing temperature on performance of high ductility cementitious composites (Part I: Modified fiber bridging model, performance and mechanism)

Effect of steam curing temperature on performance of high ductility cementitious composites (Part I: Modified fiber bridging model, performance and mechanism)

Interoperability level for bridge structural analysis from the IFC data interpretation

Importing IFC (Industry Foundation Classes) data from bridge structural models into structural analysis software is common in the BIM (Building Information Modeling) workflow. However, some software tools still do not import IFC data in the extended version that covers bridge models. In addition, there is a lack of a holistic framework for determining indicators that effectively represent the interoperability level for bridge structural analysis. To prevent data loss in bridge models, this work proposes a tool for interpreting IFC data related to the semantics of bridge elements, geometry, and material properties. A new methodology was developed to quantitatively evaluate an interoperability level for bridges structural analysis, considering the relevance of the imported information by defining numerical weight values. Then, a new framework was proposed for determining each data flow’s Interoperability Level for Bridge Structural Analysis (ILBSA). The interoperability level results showed that commercial bridge structural analysis software requires significant advances in interpreting IFC data.

AI-Enhanced IoT System for Assessing Bridge Deflection in Drive-By Conditions.

The increasing traffic on roads poses a significant challenge to the structural integrity of bridges and viaducts. Indirect structural monitoring offers a cost-effective and efficient solution for monitoring multiple infrastructures. The presented work aims to explore new sensing strategies based on digital MEMS sensors integrated into an intelligent IoT infrastructure to predict the bridge deflection behaviour for indirect Bridge Structural Health Monitoring purposes. An experimental setup comprising a bridge model and vehicle equipped with a smart sensing node has been used to generate the dataset. Various models for bridge deflection estimation are deployed on the sensorized vehicle, exploiting edge AI capabilities of smart sensors. This study shows the potential of leveraging data-driven technologies to enhance the performance of low-cost sensors. Additionally, it demonstrates the viability of assessing static deflection shapes of bridges through indirect measurements on board vehicles, underlining the potential of this approach to make SHM more cost-effective and scalable.

Study on Sensitivity of Uncertainty Factors in Seismic Demand Analysis of Continuous Girder Bridges with Seismic Isolation Design

In order to clarify the influence of the uncertain parameters of a bridge numerical model for seismic isolation design on the calculation results of structural seismic demand and to improve the accuracy of bridge seismic isolation design, a refined numerical model of a seismic isolation continuous girder bridge was established. The uncertainty of the model parameters was sorted out at two classification levels of the seismic isolation device system and the non-isolated system, and the sensitivity of the structural parameters was systematically analyzed by using the tornado diagram and the first-order second-moment method. The uncertain factors that have a great influence on the seismic response of the bridge structure in the seismic isolation design are bulk density coefficient, bearing friction coefficient, clay ultimate resistance, damping ratio, elastic modulus, clay ultimate deformation, and isolation bearing fusing force. The impact of the seismic isolation bearing’s melting force is particularly significant during periods of low peak acceleration. It was observed that the selection results remained largely unchanged despite the consideration of the collision effect. This finding serves as a valuable reference for the design and calculation of seismic isolation measures in continuous beam bridges.

Analysis of numerical models of an integral bridge resting on an elastic half-space

Abstract The paper presents three methods of the numerical modeling of a 60 m long integral bridge structure resting on an elastic half-space. For the analysis, three bridge models were built using Abaqus FEA software. Models A and C represent complex three-dimensional numerical models consisting of the bridge structure and the soil layer beneath it. The soil layer on which the bridge is resting was modeled as a homogeneous, isotropic, continuous, and elastic semi-infinite body elastic half-space. Model B represents a simple three-dimensional numerical model consisting of just the bridge structure. The stiffness of the soil layer beneath the structure in model B was modeled with spring constants derived for shallow footing foundation based on the theory for an elastic half-space. This model represents an engineering approach to the design of an integral bridge. In all models, the bridge deck is monolithically connected with abutment walls and intermediate piers. The bridge is made of cast-in-situ reinforced concrete. All material constants used in the analysis are presented in the table. Self-weight, uniformly distributed load, and thermal longitudinal expansion of the bridge deck were applied to the bridge models. Due to the nonlinear boundary condition used in the supports of the bridge model A, such as contact and friction, the superposition principle cannot be used in the calculations of this model. For this reason, all the loads involved in all bridge models were combined into a single load case and the large displacement formulation was used in the static analysis. The self-weight of the soil layer beneath the structure was omitted in the analysis. The author is focused on the method of modeling an integral bridge structure resting on elastic soil. For the purpose of this paper, only two piers from each model were selected, from which the internal forces and displacements were compared. Based on the analysis, it was concluded that it is possible to design an integral bridge by building its simplified numerical model, once the conditions given in the conclusions are met.

Seismic Response Analysis of Continuous Girder Bridges Crossing Faults with Assembled Rocking-Self-Centering Piers

Under the action of cross-fault ground motion, bridge piers can experience significant residual displacements, which can irreversibly impact the integrity and reliability of the bridge structure. Traditional seismic mitigation measures struggle to effectively prevent multi-span chain collapses caused by the tilting of bridge piers. Therefore, it is of practical engineering significance to explore the effectiveness of rocking self-centering (RSC) piers as seismic mitigation measures for such bridges. In this paper, cross-fault ground motion with sliding effects is artificially synthesized based on the characteristics of the fault seismogenic mechanism. A finite element model of a cross-fault bridge is established using the OpenSees platform. The applicability of RSC piers to cross-fault bridges is explored. The results show that RSC piers can significantly reduce residual displacement during cross-fault ground motions, facilitating rapid recovery after an earthquake. RSC piers significantly reduce residual displacement in cross-fault bridges, with the most notable vibration reduction effects observed in piers adjacent to the fault. When an 80 cm fault displacement occurs, the vibration reduction rate reaches 48%. Additionally, when the fault’s permanent displacement increases the risk of pier toppling, the vibration reduction effect of the RSC pier is positively correlated with the degree of fault displacement. However, the amplification effect of RSC piers on the maximum relative displacement of bearings in cross-fault bridges cannot be ignored. In this study, for the first time, RSC piers were assembled on bridges spanning faults to investigate their seismic damping effect. When the degree of fault misalignment is greater than 60cm, the seismic damping effect of RSC abutments is positively correlated with the degree of fault misalignment, and its amplifying effect on the maximum relative displacement of the bearing becomes more and more obvious with the increase of permanent displacement. For example, when the fault misalignment degree is 60cm, the vibration reduction rate is 39%, and when the fault misalignment degree is 90cm, the vibration reduction rate is 54%. Designers should rationally configure RSC piers according to the specific bridge and site conditions to achieve optimal vibration reduction effects.

Investigation of Separating Temperature-Induced Structural Strain Using Improved Blind Source Separation (BSS) Technique.

The strain data acquired from structural health monitoring (SHM) systems of large-span bridges are often contaminated by a mixture of temperature-induced and vehicle-induced strain components, thereby complicating the assessment of bridge health. Existing approaches for isolating temperature-induced strains predominantly rely on statistical temperature-strain models, which can be significantly influenced by arbitrarily chosen parameters, thereby undermining the accuracy of the results. Additionally, signal processing techniques, including empirical mode decomposition (EMD) and others, frequently yield unstable outcomes when confronted with nonlinear strain signals. In response to these challenges, this study proposes a novel temperature-induced strain separation technique based on improved blind source separation (BSS), termed the Temperature-Separate Second-Order Blind Identification (TS-SOBI) method. Numerical verification using a finite element (FE) bridge model that considers both temperature loads and vehicle loads confirms the effectiveness of TS-SOBI in accurately separating temperature-induced strain components. Furthermore, real strain data from the SHM system of a long-span bridge are utilized to validate the application of TS-SOBI in practical engineering scenarios. By evaluating the remaining strain components after applying the TS-SOBI method, a clearer understanding of changes in the bridge's loading conditions is achieved. The investigation of TS-SOBI introduces a novel perspective for mitigating temperature effects in SHM applications for bridges.

A Time-Frequency-Based Data-Driven Approach for Structural Damage Identification and Its Application to a Cable-Stayed Bridge Specimen.

Structural damage identification based on structural health monitoring (SHM) data and machine learning (ML) is currently a rapidly developing research area in structural engineering. Traditional machine learning techniques rely heavily on feature extraction, where weak feature extraction can lead to suboptimal features and poor classification performance. In contrast, ML-based methods, particularly deep learning approaches like convolutional neural networks (CNNs), automatically extract relevant features from raw data, improving the accuracy and adaptability of the damage identification process. This study developed a time-frequency-based data-driven approach aiming to improve the effectiveness of traditional data-driven structural damage identification approaches for large complex structures. Firstly, the structural acceleration signals in the time domain were converted into two-dimensional images via the Gram angle difference field (GADF). Subsequently, the characteristic feature in the image data was studied by convolutional neural networks (CNNs) to predict the structural damage conditions. An experimental study on a scale model of a cable-stayed bridge was conducted to identify the damage of stay cables under the moving vehicle load on the main girders. The CNN was employed to extract the characteristic features from the time-varying monitoring data of vehicle-bridge interactions. The CNN parameters were optimized to conduct the structural damage classification task. The performance of the proposed method was evaluated by comparing it with various traditional pre-trained networks. The effect of environmental noise on the prediction accuracy was also investigated. The numerical results show that the ResNet model has the best performance in terms of damage identification accuracy and convergence speed, achieving higher accuracy and faster convergence compared to the other four traditional networks. The method can accurately identify damage on bridges using insufficient sensors on the bridge deck, which has valuable potential for application to real-world bridges with monitoring data. As the Signal-to-Noise Ratio (SNR) decreases from 20 dB to 2.5 dB, the prediction accuracy of ResNet decreases from 86.63% to 62.5%, which demonstrates the robustness and reliability in identifying structural damage.

Theoretical Research on Suspension Bridge Cable Damage Assessment Based on Vehicle-Induced Cable Force

As one of the most critical load-bearing components in suspension bridges, cables require accurate damage assessments. Contemporary research methodologies primarily rely on cross-validation across multiple cables, which can present challenges in identifying damage under certain conditions. To address this limitation, this study proposes an evaluation method utilizing the cable force of individual cables. A damage index is introduced by the ratio of vehicle-induced cable tension (defined as the ratio of vehicle-induced cable force without weight to its baseline value), and the finite element model of a suspension bridge is used to verify this index. Initially, the finite element model of a suspension bridge is established, and a large number of datasets are generated using this model. These datasets include vehicle weight and vehicle-induced cable force. Subsequently, Gaussian Mixture Model (GMM) clustering is employed to categorize the dataset according to lanes, thereby establishing baseline values for each lane. Finally, damage assessments are conducted using data from individual cables and are validated against the outcomes obtained from the upstream–downstream cable force ratio method. The results show that the data trend of the damage index is clearly visible in six lanes, with the most pronounced trend occurring in the lane farthest from the cable (the sixth lane). The robustness of the index is also verified by adding 2% Gaussian white noise data, providing a research basis for related engineering projects.