Three-span Continuous Bridge Research Articles

Seismic Fragility Analysis of the Aging RC Columns under the Combined Action of Freeze–Thaw Cycles and Chloride-Induced Corrosion

The combined action of freeze–thaw cycles and chloride-induced corrosion are generally recognized as one of the main causes of the degradation of the mechanical properties and seismic performance of reinforced concrete (RC) structures in the northern frozen coastal regions. To investigate the degradation mechanisms of the seismic performance of RC columns subjected to the combined action of freeze–thaw cycles and chloride-induced corrosion, the impact of freeze–thaw cycles on the chloride diffusion coefficient of concrete was studied through concrete deterioration tests and theoretical analysis. This paper proposed a time-dependent deterioration model for RC columns, which is suitable to consider the combined action of freeze–thaw cycles and chloride-induced deterioration. The proposed deterioration model could be applied to the investigations of time-dependent seismic performance and the seismic fragility of RC columns. Based on the established deterioration model, this paper proposed a time-dependent seismic fragility analysis framework for the aging RC columns, considering the combined action of freeze–thaw cycles and chloride-induced corrosion. In addition, a representative three-span RC continuous T-shaped girder bridge that is located in the high-latitude northern frozen coastal regions of China was taken as the case study, and the time-dependent seismic fragility analysis of RC columns was conducted considering the involved uncertainties in geometric parameters, the deterioration mechanisms of the materials, and ground motions. The time-dependent seismic fragility curves of RC columns were obtained at different service time points. The results indicated that the combined action of freeze–thaw cycles and chloride-induced deterioration had a significant influence on the time-dependent seismic responses of the deteriorating RC columns. Under the combined action of freeze–thaw cycles and chloride-induced corrosion, when the RC bridge was in service for 75 years, the stirrup strength decreased by 3.88% and the cross-sectional area decreased by 30.03%. The peak stress of the confined concrete decreased by 52.1% and its peak strain increased by 12.2 times, respectively. Moreover, the time-dependent seismic fragilities of the aging RC columns under different damage states exhibited a nonlinear increase as the service life increased.

Seismic design and shaking table test of continuous girder bridges with winding rope fluid viscous dampers

In order to decrease the seismic response of continuous girder bridges, a winding rope fluid viscous damper (WRFVD) was proposed, which is installed on sliding piers, and connected to the deck by winding ropes. In this paper, the mechanical properties of WRFVD were derived and verified by the dynamic performance test. The direct displacement-based seismic design (DDBD) method of WRFVD was developed. Then, a scaled three-span continuous girder bridge was designed for the shaking table test to investigate the seismic performance of WRFVD and validate the seismic design method. The test results showed that WRFVD can effectively reduce the internal force of the fixed pier and the deck displacement. Additionally, the corresponding numerical simulations were carried out to compare with the test results, which are in good agreement with experimental data with acceptable difference. Then a series of nonlinear time history analyses based on the test model was conducted to evaluate the effectiveness of the DDBD method of WRFVD. The test and numerical results reveal that the DDBD method of WRFVD can effectively calculate the seismic response of continuous girder bridges with WRFVD.

Damage mechanism and experimental study of continuous bridges equipped with Sc-FSB

To improve the aseismic performance of continuous bridges, control the residual deformation of the girder and the damage of their fixed piers under strong earthquakes, we propose a new design idea: a continuous bridge equipped with self-centering function-separated bearing (Sc-FSB) located between the fixed pier and the girder. The Sc-FSB would be composed of a sliding bearing (for supporting vertical loads), a friction rope (for bearing horizontal seismic forces and dissipate the seismic energy input to the superstructure), and a spring (for ensuring its self-centering capability). A shaking table test based on a three-span continuous bridge (scale 1:30) and a finite element model analysis were conducted to study the aseismic effect of the Sc-FSB. The shaking table test results showed that the Sc-FSB can significantly reduce the internal force of the fixed pier and the acceleration response of the girder, as well as control the residual displacement of the girder. The spring stiffness and the friction coefficient of the Sc-FSB had a great influence on the seismic performance of the continuous bridge. If reasonable friction coefficients (μ) and spring stiffnesses (K) are selected, the above Sc-FSB can effectively control the residual displacement of the girder, leading to a good reduction of the fixed pier internal force response and of the displacement response of the girder to seismic events.

Seismic risk to beam end corner in railway bridges

The beam end of the railway bridge is the crucial part of the whole bridge, and the earthquake will cause damage to the beam end. In order to ensure the safety of the bridge and track system. To investigate the risk of seismic deformations at the beam end in railway bridges, a three-span continuous rigid frame bridge was taken as a case study and a three-dimensional finite element model of the whole bridge was established in ABAQUS. The deformation angle of the beam end was selected as the damage index, and the seismic vulnerability and risk curves of the beam end were calculated by the incremental dynamic analysis (IDA) method using 22 scaled ground motion time histories. The results show that in the same range of peak ground accelerations (PGAs), the influence of cross-bridge ground motion on the corner deformations of the beam end was much greater than that of the along-bridge ground motion. Under the along-bridge seismic excitation, the damage probabilities for the rotation angles in X, Y and Z-directions did not exceed 50 %. In different damage states, increasing in PGA correlated positively with the beam end damage probability. The vulnerability curves for PGA can be used for the seismic risk assessment of the beam end and can also provide decision support for prioritizing the seismic reinforcement of bridges.

An Algebraic Elimination by Substitution Algorithm for Vehicle–Bridge Interaction Problems

This paper proposes an algorithm to solve vehicle–bridge interaction (VBI) problems. It describes the VBI system in a linear second-order differential-algebraic equation (DAE) manner, incorporating the motions of both the vehicle and the bridge subsystems, together with the contact forces. On account of the conjugation between the VBI system’s motions and contact forces, the key feature of the proposed algorithm is to solve the DAE with the the algebraic method of elimination by substitution, avoiding the singularity of the differential operator. It enables a versatile and consensus solution scheme for different types of contact mechanisms, including the rigid contact model with constraints, the elastic contact model with the compliance method, and the creep tangential contact model, as well as different wheel–rail profiles. Combined with an appropriate numerical integration scheme, it allows an explicit expression of the contact forces, subsequently leading to the partitioned non-iterative analysis of the motions of both the vehicle and the bridge subsystems. In addition, by incorporating the dynamic condensation of wheels’ degrees of freedom into those of upper components in a matrix form, i.e. a reduced system approach, the proposed algorithm can avoid the numerical drift associated with the kinematic constraints on the acceleration level. To demonstrate the accuracy of the proposed approach, this study first examines a benchmark example of a single degree of freedom sprung mass model traversing a simply supported bridge. Further, it considers a more realistic problem of one and eight train vehicles crossing three three-span continuous bridges. The comparisons and the agreements with existing algorithms prove the accuracy and computational efficiency of the proposed analysis scheme.

Safety Monitoring of Bearing Replacement for a Concrete High-Speed Railway Bridge Based on Acoustic Emission

As an important part of a bridge, bearings easily suffer damage when exposed to various loading and environmental changes during their lifetime. Bearing replacement should be performed in a timely manner if damage occurs to high-speed railway (HSR) bridges. The unique structural form and strict operation requirements mean that bearing replacements of HSR bridges are much more difficult than those of highway bridges. However, compared with bearing replacements of highway bridges, far fewer scientific and engineering studies have been conducted to guide the bearing replacement of HSR bridges. In this paper, based on a three-span continuous concrete box girder HSR bridge, an innovative bearing replacement method using reverse disassembly and assembly techniques is proposed and was implemented at a location under operating HSRs. In addition, safety monitoring measures were undertaken to guarantee the safety of the bridge during bearing replacement. In contrast to the usual monitoring practice focusing on the displacement and the external strain of the structure, this monitoring work adopted the acoustic emission (AE) detection technique to explore the internal structural damage formed in the process of construction. The results suggest that the proposed bearing replacement method, which requires the girder to be jacked up by no more than 9 mm, is a promising practice for this complicated construction, and the start time and evolution of damage in the concrete of a bridge during construction can be captured accurately by AE detection with a parameter-based analysis method. All practices presented in this case study can guide future bearing replacements in similar projects.

A channel-spatial-temporal attention-based network for vibration-based damage detection

Structural health monitoring (SHM) is extremely vital for the diagnosis and prognosis of civil structures. As an important part of the SHM system, vibration-based damage detection (VBDD) methods have become a research hotspot with the development of sensor technologies. These methods are utilized to assess structural conditions or localize and classify damages. Recently end-to-end deep learning architectures have been widely used in VBDD tasks and achieved state-of-the-art results. However, there are seldom investigations on the attention mechanism in VBDD, which has been demonstrated as an effective module to extract features in other domains. In this paper, we propose a channel-spatial-temporal attention-based network to refine and enrich the discriminative sample-specific features in three dimensions, namely, channel, space, and time simultaneously. Specifically, the local and global block we designed is to extract the local and global spatial features adaptively, and the grouped self-attention is presented to extract the long- and short-term temporal features. Moreover, the squeeze-and-excitation block is selected to emphasize vital channels. Extensive experiments are conducted on three-span continuous rigid frame bridge scale model and IASC-ASCE benchmark datasets, and the results prove that the proposed method is superior to the existing state-of-the-art methods.

Damping enhanced novel re-centering seismic isolator incorporating superelastic SMA for response control of bridges under near-fault earthquakes

To enhance the bridge resilient performance, a novel re-centering seismic isolator (RSI) is developed by incorporating damping enhanced (DE)-sliding-lead rubber bearing (LRB) with superelastic shape memory alloy (SMA), which functions with the yielding-sliding hysteretic mode. The numerical model of the novel RSI is developed in OpenSees platform and validated by comparing the numerical and experimental hysteretic loops of the superelastic SMA and DE-sliding-LRB. A parametric design procedure is proposed to determine the optimum parameters of the novel RSI system. A three-span continuous girder bridge is selected to investigate the response mitigation efficiency of the novel RSI system compared with LRB system under near-fault ground motions. A systematic parametric study is conducted to design the optimal parameters of the novel RSI system for bridges. Case study is conducted to investigate the effectiveness of the proposed design procedure and the novel RSI system for response mitigation of bridges. Results show that the damping capability is effectively enhanced by designing the friction coefficient of the sliding element. The novel RSI system can achieve dual mitigation of the displacement responses and base force in piers for bridges. Case study demonstrates the effectiveness of the novel RSI and parametric design procedure.

Behavior of steel girder bridges damaged by vehicular collision

Vehicles often collide with girders of low-clearance bridges, yet there is a knowledge gap in understanding the behavior of damaged steel girders. This paper addresses this gap by performing non-destructive field testing on four damaged steel girder bridges. The focus is on two- and three-span continuous multi-girder steel bridges for which an exterior girder has sustained Category T damage, i.e., torsion about the longitudinal direction. The behavior of damaged girders, symmetric undamaged girders, and adjacent girders under quasi-static truck loading is monitored using digital image correlation (DIC). Specifically, the measured strains of damaged girders are compared to the strains of corresponding symmetric undamaged girders to investigate the effect of the damage on behavior for each bridge. Strain gauges were used to monitor the behavior of one bridge under quasi-static truck loading, as well as speed and crawl tests. The strain gauge readings are also used to validate DIC strain measurements for field monitoring of bridges. The measured strains are used to validate finite element (FE) numerical models. A parametric study investigates the effect of varying shapes and locations of damage on the load-deflection behavior of a single girder as well as two- and three-span continuous bridges. Overall, this study found that measured strains in all girders are less than 200 microstrain or approximately 40.0 MPa (5.80 ksi). Results indicate that vehicular damage may affect composite behavior, bridge railings participate in carrying live load, damaged girders may have increased live load amplification factors, and damage at the center of a span with a large rotation angle of the web results in the greatest loss of stiffness.

Seismic response of horizontally curved bridges in combination with skewed abutments

A bridge having in-plan curvature in combination with the skewed abutments is termed as skew-curved bridge. Present study explores upon the seismic response of a three-span continuous RC skew-curved concrete box-girder bridges under free and forced vibrations for which 3-D models of the bridge with varying configurations are generated in the CSiBridge. The curvature angle for the parametric study has been varied as 0°,30°,60° and 90° in combination with skew angles of 0°,15°,30°,45° and 60°. Modal analysis and response spectrum analysis for all the bridge models has been performed. Modal response of the various bridge configurations has been presented in graphical form in order to have knowledge of the mode shapes, time periods and fundamental frequencies of the bridges. Based on guidelines of AASHTO 2007 response spectrum analysis has been performed considering 0.3 g acceleration in longitudinal and transverse direction and an acceleration of 0.2 g in vertical direction. In-plane bending moments, longitudinal torsion and out-of-plane bending moments are monitored for all skew curved bridges under longitudinal, transverse and vertical excitations and it is observed that especially in-plane moments in longitudinal and transverse direction are significantly affected by inclusion of skewness and curvature in bridges.

Optimal selection of scalar and vector-valued seismic intensity measures based on Gaussian Process Regression

Intensity measure (IM) represents the power of ground motion, and its ability to describe the characteristics of ground motion plays a vital role in seismic risk and damage assessment. Therefore, the selection of optimal IM has always been one of the focuses of researchers in seismic engineering. The performance metrics based on regression or non-parametric methods, including efficiency, sufficiency, proficiency, and practicality, have been widely applied to select the optimal IM in past studies. This paper proposes a new procedure for performance evaluation of IM based on the Gaussian Process Regression (GPR), which can deal with the linear or nonlinear demand-IM relationship, and scalar or vector-valued IM. Two novel criteria, including G-Precision and G-Sufficiency, have also been developed to present the prediction accuracy and sufficiency of IM, combined with the concept of generalization performance in machine learning to update the existing metrics. A practical algorithm called Sequential Floating Feature Selection (SFFS) is proposed to automatically find the optimal vector-valued IM from a set of candidates. The proposed method can be integrated with multi-dimensional seismic fragility analysis to determine the optimal IM input, either scalar or vector-valued. Finally, the proposed procedure is demonstrated and discussed on a three-span continuous girder bridge.

Seismic response control of bridges with nonlinear tuned vibration absorbers

The paper investigates seismic response control of bridges with nonlinear tuned vibration absorbers (n-TVAs). A three-span continuous bridge is used as case study. The n-TVAs are designed to act in both longitudinal and transverse directions of the bridge. The n-TVAs are modelled as inelastic springs with bilinear hysteretic behavior. A simple and effective method to design the parameters of the n-TVAs for controlling structural displacement is presented. The performance of the proposed n-TVAs is compared with the optimum linear TVAs (o-TVAs) and elasto-plastic bilinear TVAs (bn-TVAs). The results show that the n-TVAs are at least as effective as o-TVAs in controlling structural response. Because the n-TVAs do not require additional dashpots like the o-TVAs, they provide a more economical solution. It is observed that although effective in controlling structural response, their stroke is of the same order as that of o-TVAs. Addition of a viscous dashpot to the device is found to reduce their stroke, although accompanied by an inherent detrimental effect on the structural control performance.

Stiffness Estimation of Girder Bridges Using Influence Lines Identified from Vehicle-Induced Structural Responses

The influence line is an important static property in bridges. The shape and magnitude of the girder bridge influence line contain stiffness information for the bridge supports and beam. This research sought to directly identify the rotational stiffness of bridge supports and the flexural stiffness of beams from extracted influence lines, which provides a quantification method for bridge damage and performance degradation. The paper first reviews the influence line identification method from vehicle-induced bridge responses. Then, the complete theoretical formulations of the deflection, rotation, and strain influence line for a general girder bridge are derived. Based on these derivations, the rotational stiffness at two supports and the equivalent flexural stiffness value of the beam are identified. Next, a certain span of a continuous girder bridge is converted to an equivalent simply supported system, and the flexural stiffness distribution of the beam is estimated based on the bending moment-curvature relationship and Betti’s law. The paper then presents a three-span continuous girder bridge verification example. The stiffness estimation results under different test conditions combined with the bridge influence line identification algorithm are presented to verify the reliability of the proposed method. This stiffness estimation method can be applied to baseline-free bridge performance evaluations based on vehicle-induced bridge responses.

Nonlinear Dynamic Analysis of Multi-vehicle Vehicle-bridge Coupling System

By analyzing different nonlinear models of vehicle-bridge coupling vibration when multiple vehicles travel on a bridge, this paper proposes the nonlinear vibration equation of multiple vehicle vehicle-bridge coupling. A comprehensive analysis is conducted on the quarter vehicle model, the nonlinear motion model of the bridge, and the coupled coupling equation of the vehicle and bridge. The vehicle-bridge coupled nonlinear analysis model of a single vehicle is established, and the correctness of the results calculated by the model is verified by calculation examples. In addition, taking the three-span continuous beam bridge with equal cross section and equal span as an example, this paper studies the driving conditions of multiple vehicles respectively from the influence of vehicle number, vehicle spacing and vehicle speed on the dynamic response value of the bridge. The results show that vehicle speed, vehicle number and vehicle spacing have significant influence on the dynamic response value of the bridge.

Maximum deflection of three span continuous bridge using rotation data based on 3 dimensional model

The Structural Health Monitoring System on the bridges continue to develop to ensure that the bridge being monitored is in good condition to serve traffic. One of the main bridge’s parameter observed is deflection of the bridge. Various methods has been developed to be able to monitor deflection accurately and economically. This study presents a method of determining the maximum deflection of a three-span continuous bridge using rotation data obtained from a tilt meter with linear regression. Initial data were obtained from FEM simulations under various load conditions to obtain the maximum deflection value and the rotations. Furthermore, linear regression was carried out to obtain the relationship between the four rotational data and the maximum deflection. The accuracy of the maximum deflection value is then compared with the results of the analysis using FEM. The accuracy rate obtained in this study is about 93.6%.

Comprehensive Study of Moving Load Identification on Bridge Structures Using the Explicit Form of Newmark-β Method: Numerical and Experimental Studies

Bridge infrastructures are continuously subject to degradation due to aging and excess loading, placing users at risk. It has now become a major concern worldwide, where the majority of bridge infrastructures are approaching their design life. This compels the engineering community to develop robust methods for continuous monitoring of bridge infrastructures including the loads passing over them. Here, a moving load identification method based on the explicit form of Newmark-β method and Generalized Tikhonov Regularization is proposed. Most of the existing studies are based on the state space method, suffering from the errors of a large discretization and a low sampling frequency. The accuracy of the proposed method is investigated numerically and experimentally. The numerical study includes a single simply supported bridge and a three-span continuous bridge, and the experimental study includes a single-span simply supported bridge installed by sensors. The effects of factors such as the number of sensors, sensor locations, road roughness, measurement noise, sampling frequency and vehicle speed are investigated. Results indicate that the method is not sensitive to sensor placement and sampling frequencies. Furthermore, it is able to identify moving loads without disruptions when passing through supports of a continuous bridge, where most the existing methods fail.

Efficient flexibility identification method using structured target rank approximation and extended Prony's method

An accurate estimation of the structural flexibility is crucial in applications such as deflection prediction, damage detection, and finite element model updating. By introducing a unit impulsive response function (UIRF) matrix estimated from noisy input and output signals collected through impact testing, this paper proposes a new method for estimating the structural flexibility matrix from a noisy UIRF. The advantages lie in the way the noise and decoupling modes of the impulse response signal are handled in the time domain. The proposed method consists of three steps: (1) Constructing an enhanced unit impulse response function (EUIRF) from the UIRF by utilizing the orthogonality of the displacement mode shapes for mode decoupling, (2) Noise removal from the constructed EUIRF to obtain a filtered one by implementing the improved Cadzow's algorithm for the structured target rank approximation (STRA) of the Hankel matrix constructed from the EUIRF, and (3) Structural flexibility identification from the EUIRF using the extended Prony's method to identify the basic modal parameters and modal scaling factors for a single-mode impulse response function with one degree of freedom. To validate the applicability of the proposed method, numerical and laboratory case studies were performed. A noisy impact test was simulated for a three-span continuous beam bridge, and the identified modal parameters and structural flexibility matrix were found to be accurate. Moreover, an impact test was conducted on a simply supported beam in a laboratory, and the results showed that the deformation predicted from the identified flexibility matrix and the one measured from the static load test are in good agreement.

Fire response of horizontally curved continuous composite bridge girders

This paper presents an approach for investigating fire response of horizontally curved continuous composite bridge girders under localized hydrocarbon fire exposure conditions, considering flexural-torsional-shear coupling effect. A three-dimensional nonlinear finite element model, established using computer program ANSYS and validated through experimental data generated from fire tests, is utilized to analyse the effects, including curvature radius, fire position along bridge span and fire exposed different steel girders, on fire response of a typically horizontally curved three-span continuous composite bridge girder. The predicted results including mid-span deflection, axial displacement and web out-of-plane displacement in different steel girders, are used to quantitatively evaluate fire resistance of horizontally curved continuous composite bridge girders. Findings from analysis results show that curvature radius, fire position along bridge span and fire exposed different steel girders have a significant influence on fire resistance of horizontally curved continuous composite bridge girders. Horizontally curved composite bridge girder with smaller curvature radius presents a lower fire resistance. The outer steel girder governs failure of horizontally continuous composite curved bridge girders subjected to simultaneously hydrocarbon fire and structural loading. Web buckling-based failure criterion is suited to determine failure of horizontally curved continuous composite bridge girders under fire conditions. Therefore, prevention of the outer steel girder from fire can highly improve fire resistance of horizontally curved continuous composite bridge girders.

Bridge structural damage identification based on parallel CNN-GRU

Structural damage identification has been the focus of engineering fields, while the existing damage identification methods heavily depend on extracted “hand-crafted” features. Recently, due to the powerful feature learning capability of deep learning, it has been widely used in structural damage identification. However, those methods only consider the local dependence or temporal relation of data. Thus, in this paper, a structural damage identification method by combining the convolutional neural network (CNN) and gated recurrent unit (GRU) is proposed. The CNN model is used to extract the local dependence of data, and the GRU model is used to extract the temporal feature of data. These two extracted feature matrices are spliced horizontally to a fused eigenvector. The eigenvector is input to the final softmax classifier layer to identify the structural damage state. Experiments on a scale model of the three-span continuous rigid frame bridge shown that the CNN-GRU model performs significantly better than CNN, LSTM, and GRU models for structural damage identification.

Analysis on load distribution of beam-arch combination system bridge

Many prestressed concrete beam-arch combination system bridges have been built in China, but the research on the mechanical characteristics of beam-arch combination system bridges is insufficient. By adopting the structural mechanics and taking the three-span continuous beam-arch combination bridge as the research object, a theoretical formula for calculating the load distribution of the beam, arch and boom of the beam-arch combination system is put forward. By comparing the theoretical calculation with the finite element calculation, the theoretical calculation formula is verified, and the factors affecting the load sharing ratio and the bending moment distribution ratio are analysed. The results show that the load sharing ratio is less affected by the beam-arch bending stiffness ratio, and more affected by beam-to-boom equivalent stiffness ratio. The load sharing ratio increases with the increase of rise-span ratio and the decrease of side-to-span ratio. The beam-arch bending moment distribution ratio is related to the beam-arch bending stiffness ratio, the side-to-span ratio and the rise-span ratio, and beam-to-boom equivalent stiffness ratio.