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Traditionally, regulations employ semi-probabilistic methods with partial safety factors to control design limits. Calibrating these partial safety factors involves estimating the target reliability level and optimizing the partial safety factor values in order to minimize the deviation of the safety index between the considered design scenarios and the target value. This procedure necessitates performing a demanding amount of reliability analyses and is often carried out for simplified design situations. Therefore, high computational costs must be accepted for design problems formulated with complex computational models. This study implements a meta-modeling approach based on active learning in the partial safety calibration procedure, enabling its application to computationally intensive problems. Subsequently, the approach is applied to the running safety of ballasted high-speed railway bridges. This limit state implicitly accounts for the phenomenon of ballast destabilization, the occurrence of which disturbs the load path from the rail level to the bridge structure. The dramatic increase in train operating speeds in recent decades has increased the possibility of this design limit state being violated due to resonance. Despite the evident safety concerns, the adopted safety factors appear to be solely based on engineering judgments rather than calibration through higher-level reliability analysis. Therefore, the proposed calibration method is employed to determine the corresponding partial safety factors for various maximum allowable operating train speeds. The newly calibrated partial safety factors allow for a permissible maximum vertical acceleration of the bridge deck approximately 25% higher than the conventional design approaches. Therefore, incorporating these factors into the design procedure may lead to the construction of lighter bridges., QC 20240115

The operational safety of high-speed trains traversing ballasted bridges is contingent upon the prevention of the ballast destabilization, which can interrupt load transfer from the rail to the bridge. Current design regulations indirectly address this limit-state by specifying a threshold value for the vertical acceleration of the superstructure. This value represents the condition at which the inertial forces induced by train passage exceed the resistive forces. However, this approach is based on limited experimental data and the influence of numerous parameters remains unexplored. As a result, reliability analyses pertaining to running safety are hampered by a lack of knowledge, leading to greater epistemic uncertainties. In this study, the impact of such uncertainties on this dynamic system is investigated using surrogate-based Imprecise Structural Reliability Analysis (ISRA). For this purpose, parametric probability boxes are used to represent lower and upper bounds of the cumulative distribution function for basic random variables with epistemic uncertainties and surrogate models are adaptively trained to reduce computational costs. The obtained results show that neglecting the influence of epistemic uncertainties can lead to permissible operating train speed higher than the speed corresponding to the desired reliability level. In this study, an overestimation of about 13% was observed on average. Furthermore, the rough analyses carried out show that taking epistemic uncertainties into account can lead to a reduction of the system characteristic safety factor by up to 30%. This significant reduction underlines the importance of expanding the available knowledge on the phenomenon of ballast instability., QC 20240108

In this study, the influence of Soil-Structure Interaction (SSI) on the dynamic behavior of a three-span concrete slab railway bridge with integrated retaining walls is investigated. The bridge is subjected to controlled excitations using a hydraulic actuator with different frequencies and load amplitudes. A 3D model of the railway bridge-soil system is implemented and calibrated using the experimental frequency response functions at each sensor location. A soil-free model is also created to compare with the calibrated model. It is observed that the dynamic behavior of the railway bridge is substantially altered by the presence of the surrounding soils, and neglecting SSI can lead to underestimation and inaccurate results. Additionally, the calibrated model is used for further train-passage analyses. For the studied bridge, neglecting SSI increases the maximum acceleration response of the bridge during high-speed train passages from 5.5 m/s2 up to 14.5 m/s2. It is also shown that the response of the bridge during train passage is predominantly influenced by its first bending mode, with higher modes inducing no discernible effect. Finally, parametric studies are performed in order to study the uncertainties related to the soil properties., QC 20240108

This paper presents an efficient 2D beam model of a continuous single-trackconcrete slab bridge considering the effect of surrounding soil conditions at the location ofthe retaining walls. A 3D model is used to investigate the backfill soil’s added flexibility fordifferent soil properties. It is shown that for the first bending mode, the additional dynamicstiffness of the backfill soil can be modeled using equivalent vertical and rotational springs.Various experimental tests have been performed on the studied railway bridge, including forcedvibration tests and train passage loadings. Good agreement is found between the 2D model andthe experimental data. It is shown that removing the soil causes both a shift in the structure’snatural frequencies (and their corresponding resonant speed) and a substantial increase inacceleration amplitude. This may give the impression that the bridge is not suitable for highspeedtrain passage. It is also shown that the bridge’s response to train passage is mainlygoverned by the first bending mode., QC 20240402

As far as the authors are aware, the threshold for vertical acceleration of the bridge deck was chosen based on the assumption that the induced dynamic loads would overcome gravity at higher accelerations, resulting in loss of contact between wheels and rail; however, the previous studies do not support this hypothesis. Considering these inconsistencies, a better understanding of the simplified design criteria is essential before conducting further studies suchas the calibration of partial safety factors. Therefore, this study considers a set of representative design scenarios to statistically compare wheel-rail contact loss with other criteria that can bederived from moving load models, such as vertical accelerations and bridge deck deflections. Based on the analyzes performed, deflection seems to be a better criterion than acceleration to control the running safety limit-state; although the results presented do not necessarily show avery strong correlation between these two criteria. Therefore, the k-means clustering approach isused together with 5% lower quantiles of the collected data to propose potential new thresholds. It should be noted that due to the limited number of analyzes, the approach presented in this study can be considered as a possible framework for further updates of the current design method rather than drawing general conclusions., Initially submitted with the title “New Running Safety Design Criteria For Non-ballasted Railway Bridges Based On Statistical And Probabilistic Investigations”QC 20231006

In this paper, the dynamic behavior of four railway bridges with integrated retaining walls, considering the effect of soil-structure interaction (SSI), is investigated both numerically and experimentally. Among these bridges, two are single-span, and the remaining two are three-span. Each bridge is equipped with numerous accelerometers and is excited by a hydraulic actuator across various frequencies. Full 3D solid Finite Element (FE) models incorporating the railway bridges and surrounding soils are developed and calibrated using the Frequency Response Functions (FRFs) from each accelerometer. Furthermore, simplified 3D solid and 2D beam models are created for each railway bridge, incorporating springs and dashpots to account for the effect of surrounding soils. The values for these springs and dashpots are obtained from simple equations, except for the impact of the backfill soil in the simplified 2D beam models, which are derived from the impedance functions of the soil medium. The performance of these simplified models is then compared to the calibrated 3D models in terms of modal properties of the first bending mode and the maximum acceleration response during highspeed train passages. The results indicate that the simplified models closely align with the calibrated models in terms of modal properties and high-speed train passage response and can be used as simple and efficient alternatives for practical usage in bridge design., QC 20240912

This study utilizes a 3D DEM sleeper-ballast bed model, comprising four sleepers interacting with the actual shape of the ballast, to comprehensively explore the impact of sleeper-ballast interaction and ballast aggregate friction coefficient on the lateral resistance of ballast bed. Based on the DEM numerical simulation, the following conclusion can be drawn: 1) The friction resistance between the sleeper and the ballast is crucial in determining the lateral resistance in railway tracks, with the base ballast contributing to more than 50% of the lateral resistance of the ballast bed on average; 2) The sleeper bottom resistance and sleeper side resistance of lateral force is derived from the sleeper-ballast friction mechanisms, while the friction coefficient between the sleeper end and the shoulder ballast has minimal impact on the sleeper end resistance; 3) The lateral resistance of the ballast bed is more significantly influenced by alterations in the ballast friction coefficient than by changes in the friction coefficient sleeper-ballast interface., QC 20240909

The assessment of running safety of railway bridges is conditioned by the Eurocode EN 1990 A2 by limiting vertical deck acceleration. On ballastless track bridges, this value is 5 m/s2. The background for this value is not clear, and it is believed that it originates in the application of an arbitrary safety factor of 2 on accelerations around 1 g to avoid loss of wheel–rail contact. However, studies show that the level of acceleration may not be directly related to the occurrence of derailment. In this work, this idea is expanded by assessing both vertical and lateral dynamics, comparing acceleration values with the Unloading and Nadal derailment criteria. The parametric study is comprised of a set of five representative single-track slab bridges with spans between 10 m and 30 m with two levels of track irregularities, corresponding to a well-maintained track and an Alert limit situation. A three-dimensional articulated FE model based on the load properties of the EN 1991-2 High-Speed Load Model A is presented, crossing the bridges at running speeds from 150 km/h to 400 km/h. Despite the complexity of the models, a large amount (1461) of full 3D train–track–bridge interaction dynamic analyses are performed, to produce a data set representative of the phenomenon. Results show a weak correlation between the criteria and deck acceleration (maximum r2 of 0.47 for Unloading and 0.15 for Nadal). Additionally, track quality is shown to be a more conditioning factor for derailment when compared to resonance. This work contributes to discussing the thesis of using deck acceleration as an indicator of running safety, considering lateral dynamics., QC 20240703

There is a growing intent among engineers, stakeholders, and decision makers to use probabilistic methods for infrastructure assessment or design objectives. However, the corresponding limit state for such problems usually requires the construction of complex computational models, usually using commercial software without parallelization capability. Such a requirement makes performing reliability analysis computationally prohibitive, which is even more challenging for dynamic problems, since a very short time step is required to obtain sufficiently accurate predictions. This concern has led to several methods being proposed to surrogate the limit state function with a generally black box called a meta-model. A variety of them, such as Kriging, Polynomial Chaos Expansion (PCE), Artificial Neural Networks (ANN), and response surfaces (e.g., polynomial, spline, or radial-base functions), have been adopted for this purpose. These meta-models are typically trained on a limited data set collected by computing the true responses of carefully selected input variables. Their applicability for assessing the probability of failure has been studied individually in the literature for both benchmark and practical problems. However, as far as the authors are aware, no comparison has been made between them for dynamic problems. This comparison needs to be made from the point of view of both accuracy and performance (number of calls to the limit state function). In this context, this paper takes a systematic approach to evaluate their performance under identical conditions, i.e., with similar training datasets. For this purpose, the dynamic response of railway bridges with different spans excited by the passage of trains with a wide range of speeds is used as a reference problem., QC 20231004

High-speed railway is expanding drastically in Sweden, necessitating new technology, and improve-ments of existing structures. End-shield bridges are a common and under-tested bridge type inSweden. Their dynamic performance is significantly impacted by their boundary conditions due to thesoil–structure interaction (SSI) and their large masses cantilevering beyond the footings. A specificend-shield bridge was tested under low (5 kN) and high (20kN) amplitude-forced hydraulic excitationfor a wide range of frequencies. Several train passages for typical passenger trains,‘X62’, were meas-ured with the same experimental setup. The results were analysed to isolate the significant modes ofthe system and the natural frequencies. A full 3D numerical model was calibrated and updated inAbaqus, along with a brief sensitivity study to determine the most influential parameters. Finally, theresponse to passing trains and Eurocode design HSLM trains was calculated. The experimental studyshowed that higher loading amplitudes resulted in higher damping and lower natural frequencies. Thenumerical analysis showed that for this bridge type the SSI cannot be neglected and can be success-fully introduced in the model., QC 20240228

This paper studies analytically the steady state response of the generalised coupled modulated pedestrian-beam system. Pedestrians are considered as modulated spring–mass–damper systems with and without a partially attached mass to the structural system. The governing non-dimensional parameters that defined the system's behaviour are found in an analytical framework. An application of the expression is developed, and a parametric analysis is presented considering a reference pedestrian. The frequency shift effect and the dynamic amplification factor, DAFHSI, of the coupled pedestrian-beam system are characterised. The main contribution of this paper is to provide a closed-form solution of the generalised coupled modulated pedestrian-beam system. This solution can consider any distribution of pedestrians and any definition of the pedestrian SDOF properties. A simple and representative example is presented to demonstrate the utility of the found expression in the context of footbridge dynamics., QC 20231006

Operating high-speed trains imposes excessive vibrations to bridges raising concerns about their safety. In this context, it was shown that some conventional design methods such as those related to the running safety suffer from a vague scientific background questioning their reliability or optimality. Therefore, the current article is devoted to updating the conventional design methodology, using Reliability-Based Design Optimization (RBDO) to propose the minimum allowable mass and stiffness which assures satisfying the target reliability. These proposed minimum design values can conceptually replace the conventional partial safety factor-based design method for running safety without the need for dynamic analysis. If the mass and stiffness resulting from the control of other limit states meet the proposed minimum values, the desired target reliability for running safety will be assured. This is achieved by adaptively training Kriging meta-models as a surrogate for the computational models decoupling the RBDO problem. In this regard, a new stopping criteria is proposed using mis-classification ratio of the cross-validated model; which reduces the generalization error of the trained meta-model and consequently the estimated failure probability. Moreover, due to the dependence of the design variables, the Copula concept is used to refine the augmented space and reformulate the RBDO problem., QC 20230710

This work presents the results from an experimental test on a 97 m long lightweight footbridge in Stockholm, Sweden. The modal properties were estimated based on impact hammer testing. The experimental results show that the lightweight steel footbridge presents damping ratios in accordance with the Sétra Technical Guide for footbridges. Furthermore, the work presents a 3D Finite Element (FE) model of the footbridge. The bridge model is first tested by performing a sensitivity analysis of the boundary conditions with respect to the modal properties of the system. Next, the model is adjusted using a frequency-based modal updating technique with a Genetic Algorithm (GA) to solve the optimization problem. Finally, the model results are compared with the experimental test, and the vicinity of the obtained solution is evaluated. The FE model shows a good agreement with respect to the experimental results in terms of bending natural frequencies and corresponding mode shapes., Part of ISBN 9781003348443QC 20230802

Structural damping is an important characteristic in railway bridges, which affects the performance of the structure, especially for bridges with train speeds higher than 200 km/h. The accurate evaluation of damping must be performed properly to correctly assess the structural performance of the bridge under dynamic loading conditions. The present article introduces an alternative methodology that contributes to the assessment of damping coefficients with application to railway bridges. The methodology is based in the Prony method with an energy-sorting technique for the identification of dominant frequencies of a free vibration signal of a passing train. The numerical validation of the method is based on a sensitivity analysis of the free vibration periods of signals through the evaluation of influence lines of displacement and numerically simulated receptance tests, and in the estimation of the damping coefficient from the free vibration period obtained in a train-bridge interaction dynamic analysis with a known imposed value. Finally, and in the scope of the In2Track2 and In2Track3 projects, the experimental assessment of damping coefficients using this methodology was carried out, considering four filler-beam bridges from the Portuguese Railway Network. The ambient vibration tests allowed the evaluation of the main frequencies and damping in these bridges, and the dynamic tests under railway traffic allowed the definition of the dynamic response of these bridges and subsequent application of the Prony method for two types of trains. The results of this work allow a new update of the database for damping coefficients of filler-beam railway bridges, contributing to future revisions of EN1991-2., QC 20230403

This paper present experimental testing of an in-service railway bridge where viscous dampers were installed near the roller support, with the objective to mitigate vibrations from passing trains. Forced vibration tests were performed before and after installing the dampers, which showed a significant increase in resulting modal damping. A long-term monitoring system was installed and more than 4000 train passages has been recorded to date. The system records both the response of the bridge and the resulting force in the dampers. Based on a Bridge Weigh-in-Motion system (BWIM), the train speed and train types are identified. The estimated train speed varies from 40 to 160 km/h for passenger trains, which enables to study the dynamic performance of the bridge under different loading frequencies. The variation in modal properties, e.g. natural frequency and damping is studied as function of the vibration amplitude. The bridge is located in the North of Sweden where the temperature is expected to range from +30°C in the summer to -30°C in the winter. Experimental data will be collected to further study any seasonal changes on the dynamic properties of the bridge, e.g. due to longitudinal stiffness of the continuous track system.

In this paper, a closed-form solution of the moving harmonic load problem for continuous Euler- Bernoulli beam systems is presented. The generality of the boundary conditions is taken into account by solving the characteristic equation of the system, obtaining its natural frequencies and mode shapes. The undetermined coefficient method is applied to solve the governing differential equation of motion, determining the base functions of the solution space of the problem. For vertical vibrations, three numerical examples of footbridges are presented. The main contribution of this paper is to provide the closed-form solution of the moving harmonic load problem applied to continuous footbridges including the phase angle in the load definition. In this way, it is possible to find the solution in the time domain of the harmonic component of any load spectra., QC 20220216

Increasing operating speeds and axle loads of trains may induce higher verticaldeck accelerations on bridges, which may subsequently lead to the occurrence of ballast instabilities.This phenomenon not only increases maintenance costs but also leads to speed restrictionsunder operating conditions. In severe cases, it can also cause train derailment. Thishas been shown to be the governing criterion for the design of short to medium span lengthhigh-speed railway bridges, especially from the dynamic behaviour point of view. Despiteits substantial importance in the design of railway bridges, the conventional deterministic approachescannot achieve the desired level of safety (Allahvirdizadeh et al. 2020). Therefore,this article is devoted to the evaluation of the probability of violating running safety usingsimulation-based methods. In this context, different variables, including those for the bridge(span length, flexural rigidity, and geometric properties), for the train (axle load, dominantfrequency and damping ratio) and for the boundary conditions (soil and foundation properties)are considered. Due to the high computational cost and complexity of the consideredperformance function, a low-cost meta-model is trained using stack modelling concept as acombination of support vector machines (SVM), k-nearest neighbours (k-NN) and decisiontrees. Then, the range of maximum and minimum probabilities of exceeding the verticalacceleration threshold are evaluated as a function of train speed and bridge span length. Comparingthese boundaries with corresponding results of simply-supported bridges showed thatneglecting soil-structure interaction effects in shorter span bridges may result an underestimatedsafety of the system; however, for longer span bridges it may result in overestimatedsafeties., QC 20211103

Excessive vertical acceleration of ballastless railway bridges subjected to vibrations induced by passing trains is one of the governing design criteria for bridges in high-speed lines. However, to the authors' knowledge, the corresponding design limit is not based on a solid theoretical or experimental background. Moreover, the traditionally applied safety factor also suffers from these concerns. Therefore, in the present study, a crude probabilistic approach is adopted to evaluate the consistency and reliability of this safety factor. For this purpose, deterministically designed bridges (using conventional methods) with short to medium spans are considered. Then, their reliability is evaluated using simulation-based techniques and extreme value theory, i.e., tail approximation. Then, the existing safety factor is calculated to evaluate the consistency of the current approaches, and possible new values are proposed based on the desired target reliabilities., QC 20230622

Railway bridges may experience large vibrations from passing trains if the load frequency of the train coincides with the natural frequency of the bridge. For long and slender bridges on high-speed lines, this may occur within the range of the operational speed. In combination with low inherent damping of the bridge, excessive vibrations during train passage may pose both safety risks and riding comfort issues. One approach to mitigate the response of railway bridges and ensure resilience is to install external damping devices. In this chapter, a generalized theoretical model of a bridge-viscous damper system is derived based on the rotation of the bridge deck around the neutral axis. The dampers are installed horizontally in the vicinity of the roller bearing. A setup for a real-time hybrid simulation is described, in which a numerical model of a bridge is connected to a large-scale magnetorheological damper. From both cases, it is found that the vertical bridge deck acceleration could be significantly reduced, indicating that the proposed installation of the damping devices is applicable., QC 20230523

This paper presents dynamic analyses of railway bridges traversed by heavy freight trains, with application to the iron ore line in the North of Sweden. The main objective is to show that the allowable axle load can be increased as a result of lower dynamic effects compared to current design codes, especially for short- and medium span bridges. Simulations are based on a 2D traintrack-bridge interaction model and a large set of sampled realistic track irregularities. Using a semi-probabilistic approach, the results show that for short span bridges the dynamic effects is less than 15% compared to more than 40% in current codes. For span lengths longer than 10 m the dynamic effects are less than 5% according to the simulations. A parametric study shows that the dynamic effects are proportional to the standard deviation of the track irregularities and that the main governing effects of the train is the un-sprung mass., Part of ISBN 9780784483886

One approach for upgrading existing high-speed railway bridges which are susceptible to excessive vibrations is to install damping devices. In this article, a model of a simply supported bridge with supplemental fluid viscous dampers installed between the superstructure and the abutments is derived based on an arbitrary mode of vibration. The aim is to ensure the robustness of the proposed vibration mitigation method by conducting Monte Carlo simulations including uncertainties associated with the bridge-damper system. From this statistical screening, it is possible to evaluate the probability of exceedance of a stipulated acceleration level, as well as studying the sensitivity of the ingoing random variables. This probabilistic evaluation highlights the necessity of conducting a statistical assessment to determine an estimate for the distribution of the acceleration limit and model uncertainty for dynamic analyses. The results show that the required damping coefficient could be multiply reduced, as compared to a deterministic analysis., QC 20210112

The information contained in this paper will be of interest not only to bridge engineers, but also to train manufacturers. The article provides practical insight into the degree of coverage of real articulated trains (ATs) that Eurocode EN1991-2 guarantees. In both the design of new railway bridges, as well as in the assessment of existing ones, the importance of a detailed knowledge of the limits of validity of load models cannot be overemphasised. Being essential components of the rail transportation system, the capacity of bridges to withstand future traffic demands will be determined precisely by the load models. Therefore, accurate definition of the limits of validity of such models reveals crucial when increased speeds and/or increased axle loads are required by transportation pressing priorities. The most relevant load model for a significant portion of the bridges in high-speed railway lines is the so-called HSLM-A model, defined in EN1991-2. Their limits of validity are described in Annex E of such code. For its singular importance, the effects of vibrations induced by HSLM-A are analysed in this paper with attention to the response of simply supported bridges. This analysis is carried out in a view to determine whether the limits of validity given in Annex E of EN1991-2 cover the largest part of cases of interest. Specifically, the vibration effects of HSLM-A are compared with those of the ATs described in such Annex E, and the response is analysed in depth for simply supported bridges, which are structures especially sensitive to passing trains at high speeds. New theoretical approaches have been developed in order to undertake this investigation, including a novel, simplified expression of the train signature for ATs that is convenient for its low computational cost. The mathematical proofs are included in the first part of the paper and two separate appendices., QC 20201210

The influence of dynamic soil-structure interaction (SSI) on simply supported railway bridges is investigated. Impedance functions are calculated considering shallow foundations in soil strata limited by bedrock. The impedance functions are coupled to bridge models, and the assembled soil-bridge systems are investigated addressing the modal properties. A parametric study is performed on a large set of soil-bridge systems. Finally, the response to train loading is analysed. The study shows that the effects of SSI are essentially different depending on whether radiation damping is active or not. Shorter bridges are often affected by radiation damping and the response due to train loading may be significantly reduced when SSI is considered. However, for longer bridges (>15 m) the effect of SSI is often small. Due to the stiffness reduction of the impedance, some bridges may even have a detrimental effect from SSI and a reduction of the traffic speed is obtained., QC 20211005

The dynamic response of railway bridges is important to consider, as the high velocity loading from the trains increases the risk of resonance. Increasing train speeds and loads result in a need for adaptable properties for railway bridges. One solution is to install magnetorheological dampers, as the response of the structure originating from moving loads could be controlled by alternating the input current to the damper. However, the complexity of such devices results in difficulties to accurately model their behaviour. From this context, real-time hybrid simulations, consisting of a numerical bridge model and a full-scale physical magnetorheological damper in a test frame, are presented in this paper. The novelty of the present paper is the application of RTHS in railway bridge engineering and the substructure combination with magnetorheological dampers. The results from the real-time hybrid simulations show that the bridge deck responses can be reduced to permissible levels. ., QC 20220427

Limiting the maximum vertical acceleration and deflection of the deck are two principal design criteriaof high-speed railway bridges. The former prevents ballast instability to ensure running safety, andthe latter attempts to limit the acceleration of the car-body below the level at which passengercomfort is disturbed. The previous studies are mainly concerned with the destabilization of the ballast,nevertheless the possibility of the maximum deflection occurrence should not be underestimated.Moreover, the literature indicates the need to improve the current design requirements including theminimum allowable mass and frequency of bridges, which requires solving optimization problems basedon modern requirements. Therefore, a probabilistic framework with simulation-based techniques is usedto evaluate the violation probability of the above limit states and distinguish dominant criteria underdifferent conditions, i.e., bridge span length and operational train speed. First, the performance of thesubset simulation method is compared with the Latin Hypercube-sampling based Monte-Carlo approachsupported by surrogate models. Polynomial chaos expansion (PCE) surrogate models are trained for thisobjective. Then, the resulting violation probabilities are evaluated for the two considered limit statesusing the approach with better performance., Priceedings ISBN: 978-981-18-2016-8, QC 20211011

This paper presents results from experimental testing of a railway bridge. Forced vibration tests was performed using a hydraulic actuator with variable load amplitude. The estimated modal properties show that the increased load amplitude results in lower natural frequency and higher damping, especially for the first mode of vibration. Despite this, even at relatively large amplitude of vibration the estimated damping is lower than proposed by Eurocode EN 1991–2. A simple 2D model is presented that shows good agreement with the experimental results, both regarding natural frequencies, mode shapes and the response from passing trains., QC 20210311

This paper presents dynamic measurements performed on two pedestrian bridges inSweden subjected to different loading scenarios. Using accelerometers, the natural frequencies,the experimental mode shapes and damping properties were determined for each bridge. Analysiswere performed using the generalized single degree of freedom theory, the finite elementmethod and the coupled system approach taking into account the flying phase of the runningload. Additionaly, a simplified sensitivity analysis is presented in terms of accelerations dueto the pedestrian transient event of a running load case. The results indicate that there is anexcellent agreement between the aforementioned modelling strategies and, that it is possible tohave human structure interaction under running load scenarios., QC 20210824

The operational speed of the trains is intended to be significantly increasedforthcoming; which consequently questions the safety level of the current design conceptsconcerning different performance limits. Thus, the reliability of the simply supportedsingle-span bridges is assessed in the current article adopting the first-order reliabilitymethod (FORM) approach. In this regard, the dynamic response of the aimed bridges isinvestigated under the passage of a series of moving loads using available closed-form solutions in the literature. Hereof, axle load, car body/train configuration, flexural rigidity,damping, mass and model uncertainties are considered as random variables; while traintrack-bridge interactions are neglected and the procedure is repeated for a wide range ofspan lengths and train velocities. Then, the safety index corresponding to each case isevaluated by considering running safety as the limit state function; where, the bridge deckvertical acceleration is taken as the capacity of the system. The outcomes are presentedas average probability of exceeding the limit state versus train speed and categorized basedon span lengths., Not duplicate with DiVA 1552464QC 20201216, Shift2Rail

The objective of this study is to evaluate the vibratory response of two-span continuous beams subjected tomoving loads and, in particular, to investigate the maximum resonance and cancellation of resonance phenomena.The main practical interest is the evaluation of the maximum acceleration response in railway bridges,which is one of the most demanding Serviceability Limit States for traffic safety according to current regulations.Two-span continuous bridges, in their simplest version (i.e. uniform identical spans), present antisymmetric andsymmetric modes with closely spaced natural frequencies, leading to a more involved dynamic behaviour thanthat of simply-supported bridges. First, the free vibration response of a Bernoulli-Euler two-span beam after thepassage of a single load at constant speed is formulated analytically, and non-dimensional speeds leading tocancellation or maximum response in free vibration are obtained for each mode. Then, these conditions areequated to resonant speeds induced by equidistant load series, and span length-to-characteristic distance ratioscausing cancelled out resonances, or remarkably prominent ones, are obtained. Based on the previous derivations,a methodology for detecting which could be the most aggressive trains for a particular structure based onpure geometrical considerations is discussed. Finally, the applicability of the theoretical derivations is shownthrough the numerical analysis of two real bridges belonging to the Swedish railway network., QC 20200916

The information contained in this paper will be of interest not only to bridge engineers, but also to train manufacturers.The article provides practical insight into the degree of coverage of real articulated trains (ATs) that Eurocode EN1991-2guarantees. In both the design of new railway bridges, as well as in the assessment of existing ones, the importance of adetailed knowledge of the limits of validity of load models cannot be overemphasised. Being essential components of therail transportation system, the capacity of bridges to withstand future traffic demands will be determined precisely bythe load models. Therefore, accurate definition of the limits of validity of such models reveals crucial when increasedspeeds and/or increased axle loads are required by transportation pressing priorities. The most relevant load model fora significant portion of the bridges in high-speed railway lines is the so-called HSLM-A model, defined in EN1991-2. Theirlimits of validity are described in Annex E of such code. For its singular importance, the effects of vibrations induced byHSLM-A are analysed in this paper with attention to the response of simply supported bridges. This analysis is carried outin a view to determine whether the limits of validity given in Annex E of EN1991-2 cover the largest part of cases ofinterest. Specifically, the vibration effects of HSLM-A are compared with those of the ATs described in such Annex E, andthe response is analysed in depth for simply supported bridges, which are structures especially sensitive to passing trainsat high speeds. New theoretical approaches have been developed in order to undertake this investigation, including anovel, simplified expression of the train signature for ATs that is convenient for its low computational cost. The mathematicalproofs are included in the first part of the paper and two separate appendices., QCR 20200923

The influence of model assumptions on the dynamic impedance functions of shallow foundations is investigated using finite elements in two studies. The first investigates the effects of model assumptions in different combinations including embedment of the foundation, variation of modulus with depth, and permanent load acting on the foundation. The second study is a parametric analysis investigating the effects of permanent load at varying soil depths and with different soil modulus coefficients. Shallow foundations in strata of frictional soil on top of bedrock are considered. Small-strain modulus and modulus reduction relationships are used in an iterative process to update the modulus due to the permanent load. The results show that model assumptions can have a large influence on impedance functions. The static stiffness coefficients differ, in some instances by more than 100%. The impedance functions, normalized with the static stiffness coefficients match each other well in the pre-resonance frequency range. However, in the frequency range above the fundamental frequency, the normalized impedance functions show a large variation. Further, the results show that the influence of the permanent load is largest in the case of shallow and stiff soil strata, both regarding normalized impedance functions as well as the static stiffness coefficient, which can be increased up to 67%. The change in fundamental frequency was however minimal., QC 20200922

The influence of dynamic soil-structure interaction (SSI) on simply supported railway bridges is investigated. Impedance functions are calculated considering shallow foundations in soil strata limited by bedrock. The impedance functions are coupled to bridge models, and the assembled soil-bridge systems are investigated addressing the modal properties. A parametric study is performed on a large set of soil-bridge systems. Finally, the response to train loading is analysed. The study shows that the effects of SSI are essentially different depending on whether radiation damping is active or not. Shorter bridges are often affected by radiation damping and the response due to train loading may be significantly reduced when SSI is considered. However, for longer bridges (>15 m) the effect of SSI is often small. Due to the stiffness reduction of the impedance, some bridges may even have a detrimental effect from SSI and a reduction of the traffic speed is obtained., QC 20200922Syskonpost till ID: diva2:1600518 (published)

To analyze the mesodynamic and macrodynamic performance of the track transitions more precisely, a bridge-embankment transition model has been established by combining the discrete element method (DEM) with the finite difference method (FDM). In this model, the DEM is utilized to model sleepers and ballast particles with complex shape, and the FDM is applied to simulate the abutment, transition section and embankment. The DEM/FDM coupled model is then achieved by exchanging displacements, velocities, and contact forces at the interface. Afterwards, the influence of the transition section parameters and transition forms on dynamic behaviour of the track-substructure system is studied under measured rail seat load. The numerical simulations indicate that the increase of the transition section elastic modulus, decrease of the backfill slope values and the transition form of trapezoid backfill following by inverted trapezoid backfill can provide a better displacement gradient between the abutment and the embankment. Additionally, the results show that the inverted trapezoid transition form can provide a better transition of the track dynamic performance than the trapezoid transition form and the embankment soil over the wedge-shape backfill has the tendency to propagate along the slope toward the embankment section under the moving train load for the trapezoid transition form., QC 20200427

In this work, the effect of the surrounding soil condition on the fundamental modal characteristics and dynamic response of railway bridges with integral abutments is studied. Due to the computational cost of the full FE models and the lack of reliable simplified models, the effect of the soil-structure interaction is usually neglected in the vibration analysis of the high-speed railway bridges. In the present study, an efficient simplified numerical model is employed to evaluate the modal characteristics of the railway bridge-soil systems. After verifying the accuracy of the simplified numerical model against rigorous models, the effect of the span length and abutment/soil stiffness on the dynamic response of the studied bridges is investigated through a comprehensive parametric study. Several case studies which covers different span lengths and abutment conditions are chosen. It is shown that the SSI has substantial effect on the dynamic response of the short and stiff bridges while its effect decreases as the ratio between the deck stiffness and the abutment/soil stiffness decreases. The results may lead to review the recommended modal damping ratios for this type of bridges in the code provisions and design manuals., QC 20211003

Corrugated steel culverts are sometimes used as an alternative to portal frame bridges for small and medium crossings under railway lines. From a static point of view, the corrugated steel culverts are rather flexible structures and the load capacity relies on the confinement from the surrounding soil. From a dynamic point of view, especially for potential use on high-speed lines, the structural manner of action is not yet fully explored. This paper presents the result from full-scale experimental testing of a corrugated steel culvert, including both forced vibration tests and response from passing trains. The aim is to estimate the dynamic characteristics of the bridge, especially the interaction with the surrounding soil and how that will influence the response at the track level. From the forced vibration tests, the results show that the structure has a high inherent damping owing to the surrounding soil and that both the natural frequency and damping change with load amplitude. The experimental frequency response functions are used for updating numerical models to further understand the dynamic behaviour of these structures., QC 20211001

This paper presents an analytical approximation to describe the vertical and horizontal vibrations of clamped-clamped beams subjected to a single pedestrian induced load. No intra—person variability is considered and only a single crossing is taken into account. This approximation is performed by choosing a suitable trigonometric function that well estimates the dynamic properties and mode shape of the system. Moreover, the approximation enables to find the relationship between the loading parameters such as the step frequency and velocity and, the dynamic properties of the system as the natural frequency and damping. Furthermore, approximation formulas are presented for peak displacements, velocities and accelerations in the damped, low damped and undamped cases. Finally, amplifications factors and minimum design mass curves are defined using non dimensional parameters, aiming to contribute to a fast pedestrian bridge dynamic assessment for systems whose mode shapes reassemble the mode shape of a clamped—clamped beam, for both walking and running pedestrian load cases., QC 20211001

The effects of model assumptions on the dynamic impedance junctions of shallow foundations are investigated using finite elements. The shallow foundations are considered massless and rigid and are positioned in strata of frictional soil on top of bedrock. Two studies are established. The first investigates the combined effects of model assumptions including the variation of modulus with depth, the embedment of the foundation, and permanent load acting on the foundation. The second study is a parametric analysis investigating the effects of permanent load considering strata with varying soil modulus coefficients and with varying soil depths. Functions describing the small-strain modulus and the modulus reduction of frictional soil are used in an iterative process to update the spatial modulus distribution of the soil due to the permanent load. The results show that model assumptions can have a large effect on the impedance functions. The static stiffness coefficients vary substantially, in some instances by more than 100 %. The impedance functions, normalized with the static stiffness coefficients, match each other well in the frequency range below the fundamental frequency. However, in the frequency range above the fundamental frequency, the normalized impedance functions differ substantially from each other. Further, the results show that the effect of the permanent load is largest in the case of shallow and stiff soil strata, both regarding normalized impedance functions as well as the static stiffness coefficient, which was increased up to 67 %. The variation in fundamental frequency is however small., QC 20210505

This paper deals with the dynamic response of railway bridges traversed by articulated trains, specifically the interaction effect between the coach length D and bogie distance dBA. Current design code EN 1991-2 stipulate that the ratio D/dBA should not be close to an integer value, but no further guidance is given. By using train signatures and a so-called bogie factor, the combined effect is illustrated in a non-dimensional domain. The results are also presented by realistic examples which show that integer ratios of D/dBA are not necessarily worse than non-integer ratios. This is further confirmed by a parametric study of simply supported beams and ranges of train parameters according to EN 1991-2 Annex E., QC 20210505

This paper presents an analytical approximation to describe the vertical and horizontalvibrations of clamped-clamped beams subjected to a single pedestrian induced load. Nointra—person variability is considered and only a single crossing is taken into account. Thisapproximation is performed by choosing a suitable trigonometric function that well estimatesthe dynamic properties and mode shape of the system. Moreover, the approximation enables tofind the relationship between the loading parameters such as the step frequency and velocityand, the dynamic properties of the system as the natural frequency and damping. Furthermore,approximation formulas are presented for peak displacements, velocities and accelerations inthe damped, low damped and undamped cases. Finally, amplifications factors and minimum designmass curves are defined using non dimensional parameters, aiming to contribute to a fastpedestrian bridge dynamic assessment for systems whose mode shapes reassemble the modeshape of a clamped—clamped beam, for both walking and running pedestrian load cases., QC 20210824

This paper presents the use of external dampers for vibration mitigation of railway bridges subjected to passing trains. A numerical model of the bridge combined with an experimental setup of a full-scale magnetorheological damper is used. The combined bridge-damper system is analyzed in real-time using a hybrid simulation technique. The approach is illustrated on a simply supported steel-concrete composite bridge. Due to the large eccentricity between the neutral axis and the roller support, the resulting displacement motivates the use of a near support damper. It is shown that sufficient vibration mitigation can be obtained with a single damper. A parametric study is performed to determine the optimal damper position and inclination., QC 20191104

The train running safety on non-ballasted bridges is studied based on safety indices from the vertical wheel-rail forces. A 2D train- track-bridge interaction model that allows for wheel-rail contact loss is adopted for a comprehensive parametric study on high-speed passenger trains. The relation between bridge response and vehicle response is studied for more than 200 theoretical bridges in 1-3 spans. The bridge's influence on running safety and passenger comfort is differentiated from the influence of the track irregularities. The Eurocode bridge deck acceleration limit for non-ballasted bridges is 5 m/s(2) based on the assumed derailment risk at 1 g from wheel-rail contact loss. This study shows that the running safety indices are not compromised for bridge accelerations up to 30 m/s(2). Thus, accelerations at 1 g do not in itself lead to contact loss and there is potential to enhance the Eurocode safety limits for non-ballasted bridges., QC 20190620

This paper presents the result from a parametric study of the dynamic response of railway bridges during train passage. A 2D coupled train-track-bridge interaction (TTBI) model is used to calculate the response from both the bridge and the vehicle. To assure traffic safety and riding comfort, Eurocode EN 1990/A2 gives a set of design limits for railway bridges on high-speed lines. The vertical bridge deck acceleration and displacement are often of main interest. For bridges with non-ballasted tracks the vertical deck acceleration is limited to 5 m/s2, simply obtained as the gravity divided by a safety factor 2, under the assumption that loss of wheel-rail contact will occur at 1g. The vertical bridge deck displacement is an implicit measure to assure riding comfort, based on a limited set of simulations carried out in the 1980ies and 1990ies. The main aim of this paper is to study the relation between the vertical bridge deck acceleration and the risk of derailment as well as the relation between the vertical deck displacement to the riding comfort. The risk of derailment is estimated both as a wheel-unloading factor based on the filtered wheel-rail contact forces or as the duration of contact loss based on the unfiltered wheel-rail contact forces. A large set of theoretical bridges are studied, all optimised to reach the design limits according to EN 1990/A2 for either vertical bridge deck acceleration or displacement. The results show that there is no risk of derailment until the deck acceleration exceeds 30 m/s2. Based on the present parametric study, it appears that the current limit for vertical deck acceleration of non-ballasted railway bridges is very conservative but that the limits for vertical deck displacement is in the correct order of magnitude. It is further concluded that the magnitude of rail irregularities is of great importance, often causing larger dynamic response in the vehicle than due to the vibration of the bridge., QC 20191104

This paper presents a full-scale dynamic testing on a simply supported railway bridge with integrated end-shields, by using a hydraulic exciter. Experimental frequency response functions are determined based on load controlled frequency sweeps. Apart from accurate estimates of natural frequencies, damping and mode shapes, the experimental testing also gives valuable information about the dynamic characteristics at resonance and amplitude dependent nonlinearities. Numerical models are used to simulate the dynamic response from passing trains which is compared to experimental testing of similar train passages. The results show that the bridge deck is partially constrained due to the interaction between the end-shields and the wing walls with the surrounding soil. Measurements at the supports also show that the flexibility of the foundation needs to be accounted for. An updated numerical model is able to accurately predict the response from passing trains. The response is lower than that predicted from the initial simulations and the bridge will fulfil the design requirements regarding vertical deck acceleration., QC 20190201

The vertical dynamic interaction between vehicle and railway track is simulated in the time domain using an extended state space vector approach. The track model includes a transition zone between slab track on a bridge and ballasted track on an embankment. By considering a multi-objective optimisation problem, solved using a genetic algorithm, selected vehicle and track responses are simultaneously minimised by optimising the distributions of rail pad stiffness and sleeper spacing in the transition zone. It is shown that the magnitudes of the maximum dynamic loads in the optimised transition zone can be reduced to be similar as the magnitudes far away from the transition zone., QC 20190125

This paper is devoted to identify the effect of soil-structure interaction on the dynamic response of,a portal frame railway bridge. The study aims to validate the accuracy of numerical models in evaluating the dynamic stiffness and modal properties of the bridge-soil system. To achieve this aim, a controlled vibration test has been performed on a full-scale portal frame bridge to determine the modal properties of the system through measuring Frequency Response Functions. The results of the dynamic test provide reference data for FE model calibration as well as valuable information about the dynamic behavior of this type of bridges. Using the experimental data, an FRF-based model updating procedure was used to calibrate a full 3D solid model involving the entire bridge track-soil system. Both measured and computed responses identify the substantial contribution of the surrounding soil on the global damping of the system and highlight the importance of the soil-structure interaction on the dynamic response of this type of bridges. The identified modal damping ratio corresponding to the fundamental bending mode of the studied bridge was nearly 5 times higher than the recommended design values. A simplified model for the surrounding soil was also proposed in order to attain a less complicated model appropriate for practical design purposes., QC 20180307