Bridge pier impact analysis faces significant challenges due to the complex coupling between local contact deformation and global structural vibration. Existing contact element models typically neglect plastic deformation at the contact interface, resulting in inaccurate impact force predictions. Additionally, when using simplified beam models to calculate the impact response of piers, it is essential to assess the rationality of such simplifications. In this study, a novel dual-plasticity spring-mass-beam impact model (DP-SMBIM) was developed to simultaneously incorporate contact interface plasticity and structural plastic hinge formation. This is achieved by dividing the contact process into three distinct phases based on contact mechanics, and considering the potential plastic hinge generated during impact process. Moreover, various contact element models and beam models were employed to simulate contact interaction and the dynamic responses of the column under top-impact loading, respectively. To evaluate the performance of these models, impact tests were conducted to validate the computational accuracy of maximum impact force and column-top displacement. The results indicate that the maximum impact force and column-top displacement calculated by the proposed DP-SMBIM exhibit good agreement with the experimental results from impact tests. This is because DP-SMBIM provides significant improvements over conventional models by simultaneously capturing contact stiffness degradation and the elastic-plastic behavior of the beam, especially under high impact velocities. In contrast, the analysis models based on existing contact element models cannot simultaneously predict both impact forces and column-top displacements accurately, particularly when the initial kinetic energy of the impactor is large.

The complex interaction between multiple cracks poses a major challenge for fracture analysis of structures, as they significantly complicate the prediction of crack propagation. The complex propagation of cracks may alter the local stress state of the structure. Both the interaction of cracks and contact behavior of crack surfaces is critical to make the accurate simulation of a structure with multiple cracks under tension and compression. This paper proposes a modified XFEM to predict the development of multiple cracks under tension and compression. In the modified XFEM, a new crack competition criterion is employed to consider the interaction between multiple cracks by the minimum total energy principle. Besides, a novel virtual hydraulic method is proposed to simulate frictional contact in multi-crack systems. This method employs a virtual viscous fluid layer between the crack surfaces to prevent interpenetration and simulate frictional resistance. The core of the proposed method is to adapt the contact stiffness when using the iterations to calculate the contact force. Compared to the traditional penalty method, the proposed method does not need to add any contact stiffness term in the global stiffness matrix and therefore has a well-conditioned stiffness matrix. Numerical examples verify that the a modified XFEM can effectively simulate the multiple cracks and prevent friction locking in contact problems.

Fluid viscous dampers (FVDs) have long been regarded as reliable and effective for reducing structural vibrations. However, their performance deteriorates due to gap issues and thermo-mechanical effects during operation. To assist in the maintenance of FVDs, this study introduces approaches for monitoring, identifying, and assessing their damping performance. A system integrating strain gauges and thermometers was implemented for damper condition monitoring. A Probability Density-Based Gap Identification (PDGI) method was proposed for gap detection. A restoring force model was established to replicate the gap-thermo-mechanical coupling effect on the FVD. Additionally, an Uncertainty-Based Active Learning with Gaussian Process Regression (UAL-GPR) model was developed to predict structural seismic responses. A seven-story building served as a case study to verify the accuracy of the surrogate model and to examine how changes in damper conditions impact the responses. The results show that the proposed monitoring system effectively captures the gap and thermal characteristics of the damper, matching data from thermal imagery and force sensors. The PDGI method remains stable despite variations in model parameters and external fluctuations, demonstrating high robustness. The UAL-GPR model predicts damper force with slightly greater accuracy than structural displacement. As damper conditions change randomly, upper and lower stories are more likely to exceed displacement limits, with top-story dampers also at risk of surpassing force limits. Among all factors, temperature has the most significant impact, followed by the upper-story damper gap, while the lower-story damper gap has the least influence.

Previous studies on bridge columns under impact were mainly focused on collisions near the bottom and/or middle positions. However, in real engineering, the columns may also suffer from impact at the top. An accurate estimation of the dynamic response of columns subjected to impact generally requires refined numerical simulations or experiments, which present significant challenges due to their complexity and high cost. In this study, an experiment on a concrete bridge column subjected to the impact at the top is conducted. Experimental observations reveal distinct damage patterns, including a noticeable plastic pit at the impact interface on the column cap and concrete spalling near the column base, which respectively verify the occurrence of contact plasticity and the potential formation of a plastic hinge. Based on experimental results, a novel dual-plasticity spring-mass-beam impact model (DP-SMBIM) is proposed to theoretically calculate the dynamic response of the columns, considering both plastic hinge formation and contact plastic deformation effects. Based on the DP-SMBIM, the impact process is revealed in detail, and the effects of impact mass and velocity on the structural response are investigated. The result indicates that the proposed DP-SMBIM can accurately calculate the dynamic response of a column subjected to impact at the column top, with an error of less than 10% for predicting the maximum impact force and column-top displacement. The increase in impact velocity and mass leads to greater indentation depth and impact force, and the effect of velocity is more significant than that of mass.

Fluid viscous dampers (FVDs) are extensively researched and utilized for the longitudinal seismic response mitigation of long-span suspension bridges. Nevertheless, serviced dampers are prone to degradation due to environmental and operational factors. This study aims to develop a parameter design framework for FVDs in suspension bridges that guarantees structural safety in the presence of performance deterioration caused by the gap-thermo-mechanical effect. Cyclic tests were conducted to characterize the mechanical behavior of FVDs under varying temperatures and gap conditions. A damping degradation (DD) model was established to simulate the gap-induced force loss and the temperature-dependent damping variations. A simplified beam-spring-mass (BSM) model was proposed to reproduce the girder-pylon longitudinal relative motion of the suspension bridge under seismic excitations. Based on this, a three-factor modification strategy for the FVD damping coefficient was suggested by integrating stochastic vibration analysis with the energy equivalence principle, taking into account the operation temperature, self-heating, and gap modifications. The results indicate that the damper force is negatively correlated with temperature, while the gap leads to incomplete hysteresis loops, which can be simulated by the proposed DD model. The BSM model can accurately reproduce the girder-pylon relative seismic responses while significantly reducing computational complexity. Gaps have the most significant impact on the damper performance, followed by operation temperature and self-heating. When experiencing degradation, the modified FVD achieves nearly identical vibration mitigation performance to that of the ideally designed damper, thereby ensuring structural safety. The findings can support the parameter design of FVDs considering life-cycle performance changes.

Accurate and efficient representation of pier-top impact effects remains a challenge in whole-bridge seismic analysis. Contact-element-based approaches are often highly sensitive to the selected time step and contact stiffness, while existing equivalent dynamic load methods are frequently derived from static equivalence, empirical pulse assumptions, or local force-based criteria, and therefore may not adequately reflect the actual structural demand. To address this issue, this study develops a mechanics-informed and design-oriented framework for simplifying pier-top impact on high-speed railway bridge piers. A spring-mass-beam impact model (SMBIM), previously validated by scaled impact tests, is adopted as the computational backbone to generate a parametric database covering representative bridge and impact conditions. A displacement-based equivalent pulse strategy (DEPS) is then proposed to define the duration of an equivalent rectangular pulse by enforcing peak-displacement equivalence, so that the impact effect can be directly incorporated into structural analysis without explicitly simulating the full contact process. To identify the dominant mechanisms governing local and global response quantities, feature-ranking and partial-dependence analyses are performed for the peak impact force, maximum pier-top displacement, and equivalent duration. Based on these insights, explicit power-law formulas are established for transparent and rapid estimation of these key quantities. Validation against a held-out numerical testing subset shows that the proposed explicit formulas for the peak impact force, maximum pier-top displacement, and equivalent duration achieve coefficients of determination of 0.950, 0.898, and 0.904, respectively, with mean relative errors below 6.5%. Representative verification cases further indicate that the equivalent rectangular pulse reproduces the peak displacement of the SMBIM with errors generally below 2%. The proposed framework provides a computationally efficient and interpretable alternative to detailed contact-impact simulation for design-level assessment of impact effects within the investigated parameter range.

To address the limitations of traditional passive dampers in controlling multi-level seismic excitations, the hybrid damping system, which typically incorporates various dampers, has attracted considerable interest owing to its enhanced performance. This study presents a comprehensive investigation of the Combined Viscous-Steel Damping System (CVSDS) specifically designed for the longitudinal seismic control of long-span suspension bridges. A novel dual-stage analytical model was developed to characterize the nonlinear mechanical behavior of the CVSDS, capturing the fuse-lock transition mechanism between the viscous and steel damping components. The simplified calculation approach for the supplementary damping ratio of the system was proposed and verified through numerical simulations. To validate the seismic mitigation performance of the CVSDS in realistic conditions, a series of shake table tests were conducted using a single-degree-of-freedom model that represents the longitudinal floating behavior of a suspension bridge. The results illustrate that the CVSDS can effectively reduce seismic-induced displacement by 37.9 %-60.2 % under various earthquake intensities. In particular, adjustment in the locking force allows control over the triggering sensitivity of the system, enabling tailored responses under different loading scenarios. Moreover, the proposed numerical model, which incorporates the clearance effect observed during tests, shows good agreement with experimental data, with a maximum deviation of approximately 15 %. The findings provide a practical framework for its application in long-span bridges.

Seismic pier-top pounding in high-speed railway bridges transfers short-duration girder-restraint contact forces into bridge piers, coupling local contact damage with global vibration and possible base yielding. This critical review evaluates how evidence and modelling strategies can be transferred from local contact mechanics to pier response and, ultimately, to whole-bridge seismic demand. The literature is synthesized across experimental and refined numerical characterization, reduced-order contact–structure modelling, response-equivalent-pulse construction, and nonlinear whole-bridge analysis. A qualitative evidence-confidence grading is introduced to distinguish the strength and transferability of the available evidence based on study independence, evidence type, and configuration similarity. The primary scope is high-speed railway bridges, while the underlying contact–structure modelling principles are transferable to conventional railway and highway bridges with comparable pier-top restraints, subject to bridge-specific calibration. Conventional spring-dashpot models are computationally efficient but sensitive to contact stiffness, damping, restitution, and damage assumptions, whereas refined finite-element models resolve local response at substantially greater computational cost. Static, impulse-equivalent, and prescribed pulse representations can reduce analysis effort, but agreement in force or impulse alone does not ensure equivalence in pier displacement, base moment, plastic rotation, or residual demand. Demand-oriented pulses can reproduce selected component-level responses within a calibrated applicability domain, while response-triggered loading remains a conditional system-level reduction requiring reliable event logic, state updating, and independent benchmark validation. Future research should prioritize realistic restraint tests, identifiable parameter ranges, multi-demand validation, uncertainty quantification and damage-updatable repeated-impact models. These advances can provide a mechanics-based basis for performance-oriented restraint assessment, while practical design application requires consistency with code-based seismic restraint provisions and post-earthquake track-system serviceability criteria.

A few bridges have been constructed with the capability to rock at their support to reduce the impact of earthquakes, e.g., the South Rangitikei Viaduct in New Zealand. Most research on rockable bridges has focused on the single-segment case, even though during strong earthquakes the interaction between adjacent segments can significantly affect the overall bridge response. In reality, a spatial variation of strong ground motions and the presence of abutments make poundings between bridge members unavoidable. However, experimental research that considers the simultaneous influence of spatially varying excitation, soil, and abutments on the seismic behaviour of a rockable bridge has not been reported. The objective of this work is to investigate the seismic response of a two-segment rockable bridge with subsoil and abutments using two shake tables. To elucidate the consequence of two-sided poundings, the results without pounding and with only girder-girder poundings were also considered. The results of the rockable bridge on a rigid base with that on soil support were compared to reveal the consequences of soil. This study reveals the complex interplay between girder-girder pounding, girder-abutment pounding and footing movement due to spatially varying ground motions.

Previous studies on columns subjected to impact load were mainly focused on the impacts occurring near the bottom and/or middle of the columns. In real engineering, the columns may also suffer from impact at the column top. In this study, an impact experiment on a reinforced concrete (RC) precast socket column is conducted. Based on the impact experiment, a numerical model for modeling the impact experiment is established by ANSYS/LS-DYNA and validated by the test results. The numerical model is further used to investigate the transmission of the internal forces and the damage mechanism of the socket column. Moreover, the influences of testing parameters on the dynamic responses of the columns are discussed. The result indicates that in the initial impact stage, obvious vibration can be found in the time histories of shear forces and bending moments developed in the column. In contrast, when the column-top displacement reaches its maximum value, the shear force and bending moment along the column (excluding the socket part) are respectively distributed in a rectangular shape and a triangular shape, i.e., the distribution of the internal forces under the impact load is very similar to that under the quasi-static load. When subjected to an impact load, the maximum bending moment appears at the bottom of the column (excluding the socket part), while the maximum shear force appears in the socket part. Consequently, damage to the socket column is manifested as bending damage at the column bottom and bending-shear damage in the socket part. With the increase of impact mass and velocity, a larger maximum impact force would be generated, and impact velocity has a more significant effect on the impact force than impact mass. Increasing the reinforcement ratio of the column will lead to more severe bending-shear damage to the socket part. In contrast, a larger bending moment will be generated in the case of the socket column with a larger embedment depth, resulting in more severe bending damage at the column bottom.

Velocity-dependent dampers are commonly used for the longitudinal vibration control of long-span bridges. Among these devices, traditional fluid viscous dampers (FVDs) suffer from performance degradation resulting from oil leakage during service, whereas newly developed electromagnetic-inerter dampers (EIDs) face cost issues, as well as efficiency problems for controlling under earthquake-induced vibrations. This study develops an Electromagnetic-Inerter-Fluid Hybrid Damping System (EIFHDS) that combines the benefits of both dampers while mitigating their drawbacks. In the EIFHDS, the low-output EID functions during the service stage of the bridge, whereas the high-output FVD is activated only when large vibrations induced by earthquakes occur. The gap and gap-lock mechanisms were suggested to release the constraints of the FVD during moderate vibrations and activate it during high-intensity vibrations. Cyclic tests were conducted to validate the suggested gap-lock device applied to FVD. A modification approach for the damping coefficient of the FVD was proposed, taking into account the gap and gap-lock effect. In light of this, a parameter optimization strategy for the EIFHDS was proposed based on stochastic seismic analysis. The dynamic performance was assessed using time history analyses on a suspension bridge subjected to white noise and seismic excitations. The results indicate that the proposed displacement-triggered gap-lock device accomplishes the inactivation and activation of the FVD. The seismic performance of the modified FVD is minimally affected by the gap length, validating the energy-based modification approach. The optimized EIFHDS outperforms the EID and nearly matches the performance of FVD in vibration control. Furthermore, the EIFHDS with the gap mechanism excels over that with the gap-lock mechanism in mitigating peak displacement, though it is less effective in reducing the RMS of displacement.

Bridge structures generally involve complex construction processes with potential multi-stage transformations of the structural system. Consequently, the safety verification of all the construction stages is imperative when designing a bridge. Optimization targeting only the operational state cannot guarantee the structural safety during construction processes. This study introduces an innovative optimization design method for concretefilled steel tubular (CFST) bridges, which can take the structural safety of both the construction and operation stages into account. The optimization problem incorporates 29 key design variables, including geometry parameters of the main arch rib and tie beam, prestressed tendon configuration schemes, and the tensioning parameters of hangers. 35 safety indicators throughout the construction and operation stages are selected as the optimization constraints. The comprehensive cost of the bridge is considered as the objective function. Genetic algorithm (GA) is used to solve the optimization problem. Based on the proposed optimization method, an optimization program of CFST tied-arch bridges is implemented, which integrates automated modeling, structural analysis, and optimization iteration. The optimum result of the case study bridge demonstrates a 9.17 % reduction in comprehensive cost for the optimized solution compared to the original scheme.

This study evaluates the longitudinal and transverse seismic fragility of a long-span bridge equipped with a novel integrated Horizontal Bidirectional Hybrid Damping System (HBHDS). The HBHDS is composed of eddy current dampers, metallic yielding dampers, fuse-lock devices and a spherical steel bearing. A total of 100 ground motions are selected and the damage states of critical components i.e., bearings, towers and piers are defined. Seismic fragility curves for the bridge equipped with the HBHDS are generated at both the component and system levels. Fragility mitigation effects are assessed and compared with those related to the damping system applied to the actual bridge. The results indicate that, at the component level, the proposed HBHDS can achieve a comparable seismic fragility control effect with respect to the as-built bridge configuration in the longitudinal direction. It is also less vulnerable to side pier and tower failure than the transverse fixed system. For the system-level seismic fragility, the HBHDS is the best performer in terms of mitigating the failure probability of a long-span cable-stayed bridge, highlighting superior performance in the longitudinal and transversal direction.

The fluid viscous damper (FVD) is a typical passive energy dissipation device applied to civil engineering structures for vibration control. However, the heat generated during its operation will alter the properties of the fluid, thereby affecting the damping force. This study explores the thermo-mechanical coupling effect on the performance of the FVD. A theoretical model is developed based on fluid dynamics and thermodynamics to reflect the interaction between the real-time damping force and temperature of the FVD. Computational fluid dynamics (CFD) simulations are performed to investigate the impact of the thermo-mechanical coupling effect on the hysteresis performance of the damper and validate the proposed calculation method. The dynamic behavior and vibration mitigation effectiveness of the FVD considering the thermo-mechanical coupling effect are examined based on time history analysis on a single-degree-of-freedom and a multi-degree-of-freedom system. The results indicate that the increased temperature will lead to a reduction in the damping force, while the degraded force will in turn slow the temperature rise. Long-duration and high-intensity excitations can significantly amplify the impact of the thermo-mechanical coupling effect, thus it is essential to be considered in designing dampers for loads in the service stage and major earthquakes. The thermo-mechanical coupling effect on the supplemental damping ratio of the damper is greater than that on structural response control effectiveness, thereby it cannot be neglected when the damping ratio is used as the design criterion for FVDs.

Fluid viscous dampers (FVDs) in long‐span bridges are prone to performance change, in which the gap effect caused by oil leakage and the parameter alteration induced by viscous material denaturation are two primary sources of change. These variations may negatively affect the safety of both the bridge and the damper, thus underlining the significance of performance assessment and abnormality detection. This study develops a Gap‐Maxwell (G‐M) model to simulate the restoring force characteristics of the FVD considering performance alteration and subsequently suggests identification methods for gap and parameter change to capture the condition variation of the damper. The G‐M model contains a gap–hook element group and a Maxwell element, where the gap length of the gap element represents the leakage, and the parameter change is achieved by setting different parameter values for the Maxwell element. Its feasibility is verified by comparison with the cyclic test results. The simplified longitudinal movement pattern for the railway suspension bridge during the operational stage is suggested. Based on the G‐M model and the movement pattern, the segmental gap identification (SGI) method is proposed to determine the gap length by segmenting the original data and identifying the gap in each segment. Numerical simulations illustrate its accuracy and robustness under different damper parameter settings and noise pollution. The G‐M model parameter identification (GMPI) procedure is raised to capture the parameter change, which follows a procedure of preprocessing, clustering, fitting, and optimization. It is numerically proved to be effective in identifying the damping coefficient and velocity exponent of the FVD.

This study develops a novel Horizontal Bidirectional Hybrid Damping System (HBHDS) for mitigating the vibration of long-span bridges. It consists of eddy current dampers (ECDs), metallic yielding dampers (MYDs), fuse-lock device (FLD), and a spherical steel bearing (SSB). The ECD and MYD are connected in series through the FLD along the longitudinal direction to form an integrated passive control system together with the SSB. This system can not only mitigate the vibrations caused by service and seismic loads in the longitudinal direction, but also reduce the bridge seismic response when experiencing an earthquake in the transverse direction. The mechanical model of the HBHDS is introduced, and the method for determining the parameters of the HBHDS is given. To verify the superiority of the proposed HBHDS, a case study is performed on a long-span cable-stayed bridge. The numerical results confirm that the HBHDS has an excellent multi-level vibration control capacity, i.e., it can effectively mitigate structural vibrations caused by moving vehicle as well as earthquakes.

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

This paper introduces a new integrated Horizontal Bidirectional Hybrid Damping System (HBHDS) incorporating eddy current dampers, metallic yielding dampers, fuse-lock device with a spherical steel bearing, for controlling the longitudinal and transverse vibrations of long-span bridges under near-fault pulse-like earthquakes. Based on the nonlinear time history analysis, the seismic response of a long-span bridge with HBHDS is investigated under different near-fault pulse-like earthquakes and compared to the installed damping system on the as-built bridge. The numerical results indicate that the HBHDS is an effective damping system against the near-fault earthquakes and exhibits a common tendency with similar or even better reductions of structural responses in comparison to installed damping system. Besides, a series of robustness investigations for HBHDS are carried out considering the out-of-service different HBHDS' components. It is found that HBHDS presents superior robustness to considering out-of-service dampers in terms of response reduction and energy dissipation capacity.

The hybrid damping device, which adopts a combination of various types of dampers, has received substantial interest from the structural seismic mitigation community due to its high performance. A hybrid device so-called the Combined Viscous-Steel Damping System (CVSDS) is proposed and evaluated in this paper, consisting of a viscous fluid damper (VFD), a steel yielding damper (SYD), and a mechanical fuse-lock device (FLD). It aims to alleviate the multi-level seismic vibrations by applying different dampers. The detailed configurations and operating mechanisms of the CVSDS are introduced, followed by the theoretical analysis to develop the simulation method. Shake table tests are conducted based on a single-degree-of-freedom (SDOF) system equipped with CVSDS. The results show that the proposed analytical model is feasible in describing the fuse-lock function and hysteresis performance of CVSDS. The fuse-lock device can be successfully triggered during seismic-induced movements when the generated damping force of FVD exceeds the preset locking force. The effectiveness of CVSDS in mitigating the vibration caused by seismic excitations is remarkable. The numerical result shows good consistency with the experimental data when considering the clearance effect caused by assembly and machining errors in the simulation.