A rapid prediction of track deterioration states under earthquakes for random complex structure scenarios is identified as a core task for post-earthquake emergency command and train speed limit scheme formulation. In this paper, the continuous prediction of seismic track irregularity is reduced to the discrete prediction of girder end misalignment, and the complex response prediction for random structures is reduced to the single response prediction combination of characteristic structures. Based on dual dimensionality reduction, the rapid construction of seismic track irregularity under random complex structure scenarios is realized using a bidirectional long short-term memory neural network. The conclusions indicate that the girder joint area of track alignment irregularity is the main factor causing wheel-rail impact, and both the girder joint and girder deck areas contribute to the lateral vibration of car body; the continuous seismic track alignment irregularity can be regarded as a spliced body of a series of mutually decoupled sub-segments, and the train response excited by continuous irregularity can be approximately decomposed into the superposition of the independent train response to each sub-segment; by aggregating seismic responses from multiple characteristic structures and applying an equivalent correction factor, the equivalent structural scenario can yield girder misalignments that envelope those of random structural scenarios at the 99 % confidence level.

This study proposes a multi-parameter seismic fragility (MSF) modeling framework for high-speed railway trackbridge system (HRTBS) that couples a multi-task Bayesian neural network (MTBNN) with fractional logit regression. The MTBNN acts as a probabilistic surrogate to jointly predict seismic demands of key HRTBS components from ground-motion intensity measures and structural parameters, while quantifying epistemic and aleatory uncertainties via a heteroscedastic Gaussian negative log-likelihood and Monte Carlo dropout inference. Results show that the MTBNN model achieves R2 = 0.913-0.972 on the test set, exhibiting more robust generalization and maintaining comparable or superior prediction accuracy than a tuned deterministic XGBoost model, while providing prediction intervals with near or exceeding nominal coverage and stable interval widths to effectively quantify uncertainty. Then, this study develops an MSF model by introducing fractional logit regression and quantifies uncertainty for component- and system-level fragility by constructing the fragility mean and quantile curves. Results indicate that structural parameter uncertainty significantly impacts the fragility confidence intervals of the track subsystem components and the system-level, and that continuous bridges are more sensitive to input parameter uncertainty than simply-supported bridges. This proposed framework provides uncertainty-aware failure probability models for safety-critical HRTBS infrastructure, supporting risk-informed design and rapid post-earthquake decision-making.

A prerequisite for defining post-earthquake speed is to develop a representation framework for seismic track vertical irregularities that incorporates both seismic and structural uncertainties. This study examines the mechanism of damage progression and deterioration of track irregularity under longitudinal seismic action. Target seismic track vertical irregularities are generated, and serve as an intermediate link to formulate a damage evolution representation for the bridge-track-train system. Evaluation and design procedures are developed for assessing post-seismic train running performance on bridge. Findings reveal that the rails integrate the longitudinal motions of the girder and the piers into a coherent whole. Piers and girders at different locations exhibit consistent longitudinal vibration due to the track restraining effect, and the effect decreases the maximum response of taller piers while amplifying the minimum response of shorter piers. The rail vertical displacements situated on opposite sides of pier display antisymmetric, and a pronounced linear proportionality is observed between rail vertical displacements and longitudinal pier top displacements. A correlation exists between the upper bound of peak pier top displacement and the structural natural period, and the assessment process for post-seismic train operation capability can be streamlined through the correlation.

Irregular railway bridges may exhibit complex seismic responses due to abrupt changes in geometry, stiffness, and mass distribution, which can threaten train running safety during and after earthquakes. This study investigates train running safety on an irregular simply supported bridge with sudden changes in girder section and mass. A three-dimensional train-track-bridge coupled model is established by combining MATLAB and SAP2000, considering ballasted track modeling, wheel-rail interaction, bridge irregularity, and local nonlinear bearing behavior. The exported mass and stiffness matrices and the proposed local nonlinear force calculation strategy are verified by comparison with SAP2000 results. The results show that the wheel-rail lateral relative displacement remains below approximately 10 mm at PGA = 0.1 g, increases to about 30 mm at PGA = 0.3 g, and reaches approximately 40 mm at PGA = 0.5 g. Abrupt girder-section and mass transitions can further amplify wheel-rail responses, especially during the attenuation stage of ground motion, and may produce dangerous running states even under moderate seismic intensity. After earthquakes, residual rail deformation is mainly concentrated near girder-end transition regions, with maximum lateral rail dislocation and deformation reaching approximately 8 mm and 10 mm, respectively, and maximum vertical deformation reaching about 60 mm. Post-earthquake analysis indicates that the train remains relatively safe below 200 km/h, whereas the wheel-rail contact point moves toward the flange region above 200 km/h and derailment may occur at 400 km/h in the investigated cases. These findings highlight the importance of irregular girder-end transition regions in seismic design, post-earthquake inspection, and train operation control.

Continuous beam bridges and CRTS III track structures are widely used in China’s high-speed railway (HSR) network, yet targeted studies remain limited. To investigate the seismic damage characteristics of a typical continuous beam bridge and CRTS III track structure under near-fault earthquakes, this study develops a refined dynamic calculation model and performs nonlinear time-history analyses to obtain the seismic responses of key components. The results indicate that the fasteners are the most vulnerable components of the CRTS III track structure and the damage spatial distribution in continuous beam bridges differs significantly from that in simply supported beam bridges. Bearing damage exhibits a non-uniform distribution among different spans, which is primarily governed by the main girder boundary conditions and the bearing design parameters. Finally, a statistical approach is proposed to define a response error with a 95% guarantee rate, which quantifies the influence of the vertical ground-motion component on the seismic responses of key components under different earthquake types and intensity levels. A linear regression model is further shown to capture the influence pattern of the vertical component effectively. This study provides a detailed assessment of the seismic damage characteristics of continuous beam bridges with CRTS III track structures under near-fault earthquakes and offers quantitative support for simplified consideration of vertical ground-motion effects on key components.

In order to explore the response law of typical high-speed railway isolation bridges under near-fault earthquakes, this paper proposes the OpenSees-MATLAB co-simulation modeling method based on Client-Server technology for analysis, and carries out a large-scale full-bridge shaking table test. The co-simulation method provides a new idea for the refined modeling of high-speed railway isolation bridges, which can help researchers introduce the developed refined mechanical model into the bridge system. In this paper, the feasibility and accuracy of the co-simulation calculation are verified by comparing the numerical calculation results with the shaking table test results, and the seismic response law of the high-speed railway isolation bridge is analyzed based on the shaking table test and numerical calculation. The results show that the vertical ground motion component (VH) has a significant and random effect on the seismic response of different components of the high-speed railway isolation bridge with hyperboloid friction pendulum bearing and viscous damper. Based on the probability statistics method, this paper proposes a response error upper bound (REupper) value with a confidence level of 95 % to quantify the influence of VH. The logarithmic regression model proposed in this paper can quickly and accurately predict the REupperof the high-speed railway isolation bridge caused by the VH, which can help to correct the seismic response without considering the VH.

The double-spherical surface isolation (DSSI) bearing is an improved friction-pendulum bearing (FPB) that combines a flat sliding surface (FSS) in series with a curved-surface sliding (CSS) subsystem, and uses sacrificial shear pins to defer isolation activation. This study develops a DSSI constitutive model that accounts for the unavoidable as-installed clearance at the pin engagement interface and validates it using large-scale shakingtable tests and nonlinear simulations. Bridge-level nonlinear time-history analyses are then performed, and shear-pin capacity is iteratively calibrated to meet multi-level code objectives: locked response under service and minor earthquakes and CSS sliding activation under strong earthquakes. Results show that practical clearance ranges have negligible effects on bearing hysteresis, whereas the required shear-pin capacity is strongly dependent on pier height. For 32 m-span simply supported railway bridges, the recommended longitudinal shearpin strengths are 222-665 kN, 282-681 kN, and 317-453 kN for bridges with uniform-section solid, nonuniform-section solid, and hollow piers, respectively, with corresponding transverse ranges of 205-566 kN, 269-407 kN, and 316-482 kN. These findings establish a validated, practice-oriented workflow for calibrating shear-pin capacity and enable performance-based design of DSSI-isolated railway bridges.

Most existing seismic studies on high-speed railway track-bridge systems (HSRBTS) mainly consider a single mainshock excitation, while the additional damage induced by aftershocks is commonly neglected. To address this limitation, this study investigates the seismic response, fragility evolution, and failure-sequence transition of HSRBTS under mainshock-aftershock (MS-AS) sequences within a probabilistic framework. A refined finite-element model is developed in OpenSees, and a dual incremental dynamic analysis method is adopted. A total of 1500 nonlinear time-history analyses are performed in the vector-valued intensity-measure space to obtain the seismic responses of key components under different ground-motion intensity levels. On this basis, a bilinear probabilistic seismic demand model (PSDM) and a probabilistic aftershock demand model (PADM) are established, and three-dimensional fragility surfaces are developed for key components and the system. In addition, the earthquake-induced failure sequence of key components is identified based on the 50% iso-probability curves. The results indicate that the damage probability of HSRBTS under MS-AS sequences generally increases with increasing mainshock and aftershock intensities, while the aftershock effect exhibits pronounced threshold behavior. Only when the aftershock intensity reaches or exceeds the critical intensity PGAcrit does the damage probability gradually increase with aftershock intensity; otherwise, neglecting aftershocks may underestimate seismic risk. Moreover, the failure sequence of key components varies with the vector-valued intensity measure. These findings illustrate the necessity of accounting for aftershocks in the seismic design and performance evaluation of HSRBTS, and provide a probabilistic assessment framework for analyzing the fragility evolution and failure-sequence transition of HSRBTS under MS-AS sequences.

This paper takes the typical CRTS II track-continuous beam bridge system as the object and establishes a validated numerical model based on OpenSees. Based on this model, the damage distribution patterns of key components in the CRTS II track-continuous beam bridge system under different seismic intensities are systematically investigated. Through a statistical analysis on the response errors of different components under corresponding vertical seismic components, the influence of vertical seismic components is quantified based on a probabilistic framework, and it is further refined to the component level. Finally, a linear fitting method is used to describe the variation pattern of the response errors of each component in the CRTS II track-continuous beam bridge system under different earthquake types and earthquake intensities, and the fitting results show good agreement. Based on this research, the seismic input of the CRTS II track-continuous beam bridge system can be simplified while maintaining adequate reliability of the response results for the key components. This provides a valuable reference for improving the efficiency and accuracy of the seismic damage analysis of the system.

Addressing the challenges of the stability of structural calculations in co-simulation of high-speed train-track-bridge systems under seismic excitation, this study develops a tunable dissipative Newmark scheme (single parameter alpha) on a MATLAB-OpenSees co-simulation platform. Starting from the classical Newmark relations, we derive the dissipative variant, formulate an equivalent two-degree-of-freedom model, and construct amplification matrices for two interface-damping treatments-the pseudo-force method (DPF) and the diagonal method (DD). A stability criterion is established based on the spectral radius (closed-form expressions are provided in the Appendix). Taking a CRTS III slab track on a simply supported beam bridge as the example, we assess wheel-rail relative displacement, contact force, and running continuity under both normal operation and seismic conditions for varying alpha. The results show that DD markedly enhances co-simulation stability and prevents divergence, whereas DPF tends to diverge when numerical damping is low or absent and thus requires relatively high numerical damping to remain stable. The parameter alpha has a pronounced impact on peak responses, high-frequency noise attenuation, and wheel-rail contact robustness. Balancing stability and physical fidelity, we recommend alpha = 0.4-0.7, which not only suppresses derailment tendencies and improves the physical plausibility of responses, but also ensures efficient and stable computations.

Near-fault earthquakes seriously endanger the structural safety and operational performance of high-speed railway track-bridge systems (HSRT-BS). To address this issue, this study proposes a multi-component multilevel seismic design (MMSD) method and develops a reduced-order model for parameter design. Using a CRTS III track-continuous beam bridge as a case study, a finite element model is established based on the OpenSEES engineering seismic software to implement the MMSD and conduct numerical analyses. The seismic responses of key components in the MMSD system and the ordinary system are compared, while operational safety is evaluated using the velocity-related spectral intensity (VSI) index. Results indicate that the MMSD markedly reduces seismic responses of the track, girder, rail, bearings, and piers, showing stable behavior under earthquake, and lowers the VSI index by nearly 50 %, demonstrating its effectiveness and feasibility for HSRT-BS.

Due to the insufficient longitudinal continuity in unit slab ballastless track systems, high-speed railway bridges are vulnerable to longitudinal seismic damage. This study investigates dynamic responses and proposes a method to construct track vertical irregularities. Results show that rail vertical displacement linearly correlates with pier-top displacement, with coefficients of 0.0905 for 10 m piers and 0.0755 for 14 m piers (R & sup2;=0.99). Irregularities are mainly caused by pier displacement. For random pier heights, the peak pier-top displacement upper bound follows a cubic function of the fundamental period (R & sup2;=0.94). The proposed pier-top displacement spectrum facilitates rapid post-seismic running safety assessment.

Combining the distribution characteristics of seismic hazard data in the log-log space and the features of the classical power-law model, a new seismic hazard model based on quadratic polynomials was proposed, and its application on actual seismic hazard data of various cities was briefly discussed. Then, by analyzing the composition of the analytical solution of the power-law model, a semi-analytical solution based on the new hazard model was derived to solve the engineering demand parameter (EDP) demand hazard and seismic risk probabilities, and the accuracy of the solution was verified by numerical integration. Next, the case study proved that the proposed semi-analytical solution has higher computational accuracy compared to the classical power-law model. Finally, the proposed new seismic hazard model and semi-analytical solution were used to conduct seismic risk analysis of a high-speed railway bridge.

Steel shock absorbers have attracted growing attention for their role in seismic energy dissipation in railway bridges. However, the absence of systematic investigations into their adaptation for various bridge configurations, coupled with an incomplete understanding of the underlying mechanisms of critical design parameters-such as stiffness, yield displacement, and initial gap-has constrained their widespread engineering implementation. To address these challenges, a simply supported girder railway bridge was selected as a representative case. A finite element model was developed using OpenSees and validated through large-scale shaking table experiments. Based on this model, the seismic impact of steel shock absorber design parameters was systematically analyzed for bridges with 8 m and 25 m piers respectively, through which optimal parameter ranges and corresponding configuration schemes were identified. The results demonstrate that: (1) There exists an optimal stiffness range for steel shock absorbers. When stiffness falls within 7000-10000 kN/m, seismic damping efficiency in terms of tensile strain reduction in longitudinal reinforcement can exceed 50%. (2) The initial gap must balance energy dissipation with operational smoothness. (3) Recommended design parameters are as follows: for an 8 m pier, stiffness of 7000-10000 kN/m, yield displacement of 7-10 mm, and initial gap of 20-23 mm; for a 25 m pier, stiffness of 6000-8000 kN/m, yield displacement of 14-16 mm, and initial gap of 13-15 mm. These findings provide practical configuration guidelines for implementing steel shock absorbers in railway bridges with typical spans and varying pier heights, serving as a theoretical reference for performancebased seismic design.

Accurately assess the post-earthquake functional recovery function (PFRF) and quantify the seismic resilience are essential for resilience design of engineering structures. Conventional methods are mainly focused on the component-level damages in railway bridges, however, the damages of high-speed railway track-bridge systems (HSRTBS) are complex and relate to bridge structures as well as track structures. Thus, this paper proposes a novel system-level framework for PFRF and resilience assessment of HSRTBS taking basis of the product of conditional marginal method for functions (PCMMF) method. Firstly, seismic fragility analyses are conducted for obtaining component-level recovery function of ten key components using cloud analyzing method and the expert surveys-based damage-state-dependent functional recovery paths. Then, the PCMMF method is employed to integrate the component functions to obtain system-level PFRF and resilience indexes. Finally, the effects of different components and energy-dissipating devices on seismic resilience of the system are quantified. The results indicate that: (1) Except for the responses of bridge structure, the responses of track structures also exhibited significant effects on system-level function recovery as well as seismic resilience; (2) By integrating component correlations into assessment framework, the nonlinear accumulation and smoother trajectories of the recovery process are presented in proposed function model compared to conventional independent-based step-function one. (3) The proposed U-shaped energy dissipation devices (UEDDs) enhance the system-level seismic resilience of HSRTBS by reducing system-level responses and shortening functional recovery time, where the residual functionality improves from 0 to 0.4, and the recovery duration to exceed 0.9 reduced by approximately 30 days meanly.

Earthquake-induced derailment of high-speed train-track-bridge (TTB) systems is dominated by strongly nonlinear wheel-rail contact and rapid separation-impact transitions, yet the full-process evolution from guided running to post-derailment impact demand is still rarely quantified in an event-consistent manner. This study presents a full-process, multi-scale framework combining an explicit LS-DYNA model (CRH2 train, CRTS-III slab track, continuous welded rails, and a six-span simply supported bridge) with automated MATLAB post-processing. Derailment is resolved through a geometry-based, irreversible event definition using the wheel vertical displacement relative to the railhead crown as a wheel-drop measure, Delta z (positive downward). A unified threshold (Delta z = 158 mm) with persistence identifies three instants: peak wheel lift t 0 (minimum Delta z), derailment onset t 1, and first wheel-slab impact t 2. Wheel-rail contact forces are converted into comparable envelopes using a zero-phase Butterworth low-pass filter, with the cutoff selected to retain 85% of cumulative PSD energy. After validation against published field and laboratory evidence, the framework is applied to 36 earthquake-speed scenarios (nine motions; 120-300 km/h). Results show that span-end amplification of lateral deck drift drives rail-end plastic bending across expansion gaps, governing derailment initiation in the examined cases. Although absolute triggering times vary among ground motions, the t 0-t 1-t 2 sequence remains near-linear, providing an interpretable event clock for pacing and sensitivity attribution. Conventional force-based indices (Y/Q and unloading ratio U) typically trigger after t 1. After guidance loss, lateral velocity continues to accumulate to the first wall impact, reaching 1.77 m/s, which constrains protective-wall demand and provides transferable impact-onset states for refined analyses.

Engineered Cementitious Composite (ECC) has excellent toughness and crack resistance, and carbon fiber reinforced polymer (CFRP) can significantly improve the tensile strength of ECC, enhance its deformability and reduce the risk of brittle failure. Therefore, based on the performance of ECC and CFRP, this paper proposes a bridge pier reinforcement method, that is, coating CFRP fiber-reinforced ECC around the high-speed railway bridge pier, thereby significantly improving its seismic capacity. In this paper, the dynamic response of the unreinforced full-bridge model is verified based on the shaking table test data, and the CFRP-ECC material model parameters are checked by the impact test results. On this basis, the influence of reinforcement measures on the seismic performance of high-speed railway piers is evaluated. The numerical results show that the high-speed railway bridge piers using this reinforcement measure can absorb more seismic energy and significantly reduce the dynamic response of the bridge structure. These research results provide strong theoretical support and practical guidance for seismic reinforcement of high-speed railway piers.

In seismic and isolation design of railway bridges, component material capacities are usually taken as design thresholds, yet trains may derail before these limits are reached. To avoid underestimating derailment risk on high-speed railway bridges, this study examines a high-speed train-CRTS III slab track-simply supported beam bridge system under a large set of strong ground motions. Damage correlations among bearing displacement, relative vibration between adjacent bearings, girder-end shift and fastener displacement are quantified. The lateral displacement at the wheel-rail contact is adopted as the core indicator of running state, and its three regimes-normal running, wheel climb and derailment-are characterized using a Gaussian mixture model. Bootstrap resampling with KS/CVM/AD statistics is employed to verify the goodness-of-fit. Conditional probabilities are then used to derive traffic-bearing capacity thresholds for key components, and, within a probabilistic seismic demand model, fragility curves based on these thresholds are compared with those based on conventional material limits. Results show that: once sliding bearings become nonlinear, girder-end shift markedly amplifies fastener displacement, forming a "bearing-girder-end-fastener" damage chain; wheel-rail lateral displacement exhibits a clear tri-modal pattern that is well captured by the Gaussian mixture model; traffic-bearing thresholds are substantially lower than traditional material damage limits, especially for bridges with longer fundamental periods, leading to significant underestimation of derailment risk if only the latter are used.

A known limitation of traditional Design Response Spectrum (DRS) is its tendency to underestimate design forces in the long-period range. Although the multi-period DRS mitigates this problem by directly predicting pseudo-spectral acceleration (PSA) ordinates at 22 discrete periods using site-specific Ground Motion Models (GMMs) and Probabilistic Seismic Hazard Analysis (PSHA), its application is often constrained by practical limitations in some regions. This study proposes a more accurate and physically meaningful method for calculating the long-period transition period (Access is denied) based on Berlage Waveform (BW) decomposition and the spectral correlation between decomposed components and recorded ground motions. Furthermore, this study develops simple empirical equations for TD and its normalized spectral ordinate as functions of site condition and magnitude based on 1370 Turkish ground motions. These relationships enable construction of an improved DRS for seismic design in Turkey. To evaluate the efficacy of the improved DRS, a case study is conducted on a three-tower long-span cable-stayed bridge in mountainous terrain. Ground motions are selected using either the classic two-period DRS or the improved DRS (DRSBW 2500), both at a 2500-year return period. Results show that DRSBW 2500 provides more accurate and conservative spectral estimates in the long-period range (T >>= 2s) for seismic design in Turkey.