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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 report deals with the dynamic behavior of corrugated steel culverts underrailways. The main objective is to investigate the feasibility of these structures forhigh-speed trains. A combination of experimental testing and numerical simulationsis presented. Experimental testing is reported for three bridges, all built for conventional railways.The main novelty of the work is a method for forced vibration tests. Thisis performed using a 50 kN load actuator from inside the culverts. The forcedvibration tests enables experimental estimates of the frequency response functionsat all sensor locations, both in the culvert and the adjacent track area. For thetested bridges, the first resonance frequency is in the range of 15-20 Hz and thedamping is estimated to 4-8%. Tests with increased load amplitude generally showa decrease in natural frequency but increase in damping, possibly due to nonlineareffects of the soil-structure system. Numerical models have been developed, mainly focusing on the largest of the studiedbridges. The parameters of the numerical model is fitted using a model updatingalgorithm together with the experimental data. A full 3D model of the bridgeis rather computationally demanding, especially when simulating passing trains.Therefore, a simplified 1D track model with modified parameters has been developed.Relatively good agreement is found between the 1D and 3D model. Bothmodels show that the studied bridge is likely to fulfill the dynamic requirementsfor high-speed trains, according to EN 1990. The 3D model also shows relatively good agreement with experimental data of realtrain passages. At the centre crown point, the model somewhat underestimate theresponse. QC 20200910

This report present results from simulations of simply supported concrete slab bridges for railway traffic. The geometry follows the Swedish standard deck models according to design drawing B2447-2 and B2447-8, with span lengths ranging from 2-8 m. For each bridge four different configurations are studied; straight or skewed bridge deck and short or long edge beams. In addition, a case of higher mass due to increased ballast depth is studied. In total 78 different bridge configurations are included. According to the numerical models the first natural frequency range from about 15-80 Hz depending on span length and configuration. In all simulations the first three modes of vibration are included. The limit criteria is a peak deck acceleration of 3.5 m/s2 when loaded by the HSLM-A train model. Including a speed safety factor 1.2 according to EN 1991-2 results in an allowable speed that range from 175-350 km/h depending on the bridge configuration. The allowable speed is somewhat higher for the skewed bridges compared to straight bridges. Increased mass results in lower acceleration but also lower resonance speed. An increase in ballast depth from 0.6 to 1.2 m generally results in lower allowable speed, except for the shortestbridges in the study. It should be noted that the above conclusions are based only on simulations. Before upgrading these bridges to speeds higher than 200 km/h experimental validation is recommended. On the other hand, most existing real trains are likely to result insignificantly lower dynamic response compared to the HSLM-A trains. QC 20191025

In this report the analysis of 278 existing railway bridges is presented. The aim is to investigate how many of these bridges that potentially can be upgraded to higher speeds, with a target of 250 km/h. Due to the vast amount of bridges and the limited resources, the analyses are performed using simplified 2D models. The analysis is afflicted with several uncertainties, both regarding input parameters as well as model uncertainties. The results should therefore be interpreted carefully and primarily serve as an indicator for which bridges that may or may not meet the requirements. Large uncertainties are especially expected for portal frame bridges due to its inherently large interaction with the surrounding embankment and 3D behaviour. The results from the analysis show that a total of 22 bridges theoretically fail to meet the dynamic requirements. A combination of refined analysis and experimental validation is recommended to better assess the dynamic response for these bridges. Among the most critical cases are several steel-concrete composite bridges, that due to a combination of low mass and low natural frequency may be prone to resonant loading. Retrofitting with external dampers may for some bridges be a viable solution. QC 20181221

This report contains a comprehensive parametric study on the coupled dynamic train–track–bridge interaction (TTBI) system for non-ballasted railway bridges. The existing design limits in Eurocode EN 1990 A2 regarding vertical deck acceleration and vertical deck displacement is compared with the wheel–rail forces and car body acceleration from simulations. The simulations are based on a 2D TTBI model with linear Hertzian contact that allows for loss of contact. The model has been verified against both other numerical simulations as well as experiments, all with good agreement. The parametric study consists of a large number of theoretical bridges, all optimized to reach the limit of either vertical deck acceleration or vertical deck displacement. The study comprises both single- and double track bridges. The track irregularities are found to be of paramount importance. Two different levels are therefore studied; “higher track quality” corresponding to a well-maintained track for high-speed railways and “lower track quality” corresponding to the Alert Limit in EN 13848-5. The final conclusions are based on the “lower track quality” in order not to underestimate the risk of running safety and passenger comfort. Simulations with the bridge excluded show that the additional contribution from the bridge is low, especially for the lower track quality. The existing limit for vertical deck acceleration is set to 5 m/s2 in EN 1990 A2 and is based on a very simple assumption of the gravity acceleration reduced by a factor 2. The results in this report show that this likely is a too conservative measure of the running safety. Based on the wheel–rail forces from the simulations, the resulting wheel unloading factor and duration of contact loss does not reach critical values before the deck acceleration is beyond 30 m/s2. In EN 1990 A2, a vertical car body acceleration of 1 m/s2 is stipulated as “very good level of comfort” and is indirectly limited by the vertical deck displacement. Good agreement is generally found in the simulations between deck displacement and expected car body acceleration. In the simulations, the limit for car body acceleration is always exceeded before the running safety is compromised. QC 20180604 TRV 2016/56769

This paper presents some recent research on railway bridge dynamics with application to buried flexible structures. Based on a combination of simulations and full-scale testing, current research indicates that a rather comprehensive numerical model is required to accurately describe the response from passing trains. QC 20191213

This report contains a parametric study on the dynamic response of railway bridges on flexible supports. The results are based on simulations using 2D and 3D models. The dynamic stiffness of the supports is described by separate models of the foundation, including relevant stress and strain dependent soil properties from permanent loading that is linearized in a subsequent dynamic analysis. The complex-valued dynamic stiffness constitutes the boundary conditions in a separate analysis of the bridge superstructure that is solved in frequency domain. Two different foundation types are studied; shallow slab foundation with relatively good ground conditions, and pile group foundations with relatively poor ground conditions. In both cases, the foundation slab and the pile group have fixed geometry. In the parametric study, the corresponding vertical static foundation stiffness range from 2 – 20 GN/m for the slab foundation and 5 – 25 GN/m for the pile group foundation. For the slab foundations, both the stiffness and damping highly depends on the properties of the soil, foundation depth and geometry of the foundation slab. For the pile group foundations, the stiffness is mainly governed by the pile group and the damping by the soil. Based on the simulations, the additional damping from the slab foundation is in most cases negligible. Only for relatively soft foundations and short-span bridges significant additional damping is seen. For the pile group foundations, the additional damping is in some cases significant, especially for deeper foundations and short-span bridges. Considering a lower bound of the parametric study does however result in a negligible contribution. The dynamic response from passing trains show that the assumption of fixed supports in most cases is conservative. However, the flexible supports may result in a lower natural frequency that should be accounted for in order to not underestimate the resonance speed of the train. If flexible supports are included in a dynamic analysis, both the stiffness and damping component needs to be included. The frequency-domain approach presented in this report is a viable solution technique but is not implemented in most commercial software used in the industry. QC 20180618

I följande rapport redovisas så kallade designdiagram för dynamisk kontroll av järnvägsbroar. Syftet är att dessa ska kunna användas i tidiga skeden som en första bedömning om en given bro har möjlighet att klara kraven på komfort och trafiksäkerhet enligt SS-EN 1990, avsnitt A2.4.4. Kraven baseras på vertikal acceleration och vertikal nedböjning av brodäcket samt vinkeländring vid upplag. Baserat på spännvidd och brons lägsta egenfrekvens kan erforderlig massa samt styvhet läsas av direkt i diagrammen. Diagrammen gäller endast för broar med ballastfria spårsystem och största hastighet sth = 320 km/h. Diagrammen är framtagna baserat på en 2D balkmodell med konstant massa och styvhet samt fasta upplag och är giltiga endast under dessa förutsättningar. In this report, so called design charts for dynamic assessment of railway bridges are presented. The aim is to use these diagrams in early stage design of bridges, to determine if they are likely to comply with the requirements for riding comfort and traffic safety stated in SS-EN 1990, section A2.4.4. The requirements are based on vertical acceleration and vertical displacement of the bridge deck, as well as end rotation at supports. Based on the span length and the fundamental natural frequency, the required mass and stiffness can be obtained directly from the diagrams. The diagrams are only valid for bridges with ballastless track systems and an allowable speed sth = 320 km/h. The diagrams are developed based on a 2D beam model with constant mass and stiffness and fixed supports. The diagrams are only valid under these assumptions. QC 20160223

I föreliggande rapport redovisas dynamiska analyser av järnvägsbroar för höghastighetståg. En jämförelse i dynamisk respons mellan 2D- och 3D-modeller har utförts för ett mindre urval av plattbroar, balkbroar och lådbroar. Varje tvärsnitt har först optimerats att precis klara de dynamiska kraven avseende 2D-dynamik, utan beaktande av den statiska dimensioneringen. I många fall skulle tvärsnitten troligen behöva ökas för att klara den statiska bärförmågan. Plattbroar med spännvidder från 10 – 25 m och 1 – 4 fack har analyserats. I flertalet fall, främst vid kortare spännvidder, är egenfrekvensen för böjning lägre i 3D-modellen jämfört med 2D-modellen. Detta beror på mindre medverkande tvärsnitt i böjning i 3D (shear-lag). Detta resulterar i en lägre resonanshastighet och därmed ofta en större dynamisk respons för samma hastighetsintervall. I övrigt överensstämmer det dynamiska verkningssättet väl mellan 2D och 3D. Inverkan av vridning synes inte vara styrande för de studerade fallen. På motsvarande sätt har balkbroar med spännvidder från 20 – 40 m och 1 – 4 fack analyserats. På samma sätt som för plattbroar ger balkbroar lägre böjfrekvens i 3D jämfört med 2D. För dubbelspårsbroar är skillnaden i respons mellan 2D och 3D liknande som för plattbroar. För enkelspåriga balkbroar visar 3D-modellen i några fall en avsevärt lägre respons utan utpräglade resonanstoppar inom samma hastighets­intervall som 2D-modellen. Orsaken tros vara en kombination av upplagens excentricitet och brons massa, vilket vid vertikal böjning bidrar till en horisontell masströghet. Detta visas i de flesta fall kunna beskrivas med en modifierad 2D-modell. Lådbroar med spännvidd 40 – 70 m i 1 – 3 fack har analyserats. P.g.a. hög vridstyvhet är egenfrekvensen för vridning mycket högre än första böjmoden och p.g.a. mindre shear-lag är egenfrekvensen för böjning likvärdig i 2D och 3D. Detta ger små skillnader i dynamisk respons mellan 2D och 3D-modellerna. I de fall dynamiska kontroller utförs med förenklade metoder enligt (Svedholm & Andersson, 2016) föreslås att följande beaktas: Första böjfrekvensen n0 bör beakta inverkan av shear-lag och upplagens excentricitet baserat på en 3D-modell, vilket används som indata i design­diagrammen. Då första vridmoden nT < 1.2n0 bör en fullständig dynamisk kontroll utföras i 3D. I de fall en 3D-modell visar flera närliggande egenmoder för böjning med samma form bör en fullständig dynamisk kontroll utföras i 3D. This report present result from dynamic analyses of railway bridges for high-speed trains. A comparison of the dynamic response in 2D vs. 3D has been performed for a limited selection of slab bridges, beam bridges and box girder bridges. Each cross-section has been optimized based on the dynamic requirements for dynamics in 2D, without any consideration of the static design. In many cases, the cross-section probably needs to be increased to fulfil the static load capacity. Slab bridges with a span length from 10 – 25 m and 1 – 4 spans have been analysed. In several cases, mostly for shorter spans, the natural frequency for bending is lower in 3D compared to 2D. The reason is due to a smaller contributing width, owing to shear-lag. This results in a lower resonance speed and therefore often a larger dynamic response within the same speed range. Apart from that, the dynamic response is found to be similar in 3D compared to 2D. The influence of torsional does not appear to be governing the response for the studied cases. Using the same method, beam bridges with span length from 20 – 40 m and 1 – 4 spans have been analysed. Similar to the slab bridges, the 3D-model of the beam bridges show lower natural frequency in bending compared to the 2D-model, owing to shear-lag. For double-track bridges, the difference in response between 2D and 3D-models are similar to the findings for the slab bridges. For single-track bridges, some cases of the 3D-model shows significantly lower response without pronounced resonance peaks in the same speed interval as the 2D-model. The reason is likely a combination of the support eccentricity and the mass of the bridge, which for vertical bending results in horizontal inertia. It is shown that this can be simulated with a modified 2D-model in most cases. Box girder bridges with span length from 40 – 70 m in 1 – 3 spans have also been analysed. Due to the larger torsional stiffness, the torsional mode is often much higher than the first bending mode. Also, the shear-lag effect seems to be smaller and the response from the 3D-model agrees well with the corresponding 2D-model. In the case dynamic assessment is performed using the simplified methods according to (Svedholm & Andersson, 2016), it is suggested that the following is considered: Shear-lag and the eccentricity at the supports should be considered when estimating the first natural frequency for bending, n0, preferably using a 3D-model. If the first torsional mode nT < 1.2n0, a full dynamic analysis in 3D should be performed. In the case a 3D-model shows several closely spaced bending modes with similar shape, a full dynamic analysis in 3D should be performed. QC 20160824

The inner lining concept is a method to prevent water leakage and the risk of icing inside tunnels and is frequently used in countries with cold climate. Blocks of falling ice may result is a severe safety risk in both road and railway tunnels. Although several established inner lining systems exist, finding the optimal solution considering function, maintenance- and investment cost is a challenging task. A new system has recently been used in Sweden and is due to its success planned to be used for the Stockholm Bypass, an 18 km road tunnel project in Stockholm. A set of design criterions has been stipulated for the inner lining system. In this paper, the case of impact loading from falling rocks is studied. The inner lining system is required to withstand the impact of a 600 kg block landing on a square surface of 0.2x0.2 m. The free fall height, i.e. the distance to the rock surface, is typically less than 0.5 m but may span up to 1.5 m in some cases. A too conservative design may result in an unnecessary thick structure and lack of knowledge of the impact phenomena may result in an unsafe design. An extensive experimental program has been performed, consisting of representative parts of the inner lining system. A mass of 600 kg is dropped onto the structure and the results are compared with numerical simulations. The experiments show that the current system is rather ductile but that local concrete fallouts may occur at extreme free fall heights. QC 20150617

Inner lining system in tunnels is a method to prevent water ingress and forming of ice in the traffic area. A solution that is common in Norway is based on stretching a sealing membrane between rock anchorages that forms a gap to the primary rock strengthening. The membrane is in turn protected by a layer of shotcrete towards the traffic area. The rock strengthening is designed to resist all loads from the rock mass independent of the inner lining system. A problem is however how to perform inspections and conditional assessment of the rock strengthening, since the gap is usually small. Other topics are what loads the inner lining system should be designed for. In TRVK Tunnel 11, the load of a local falling rock of 600 kg is stipulated, assuming to act on a surface of 0.2×0.2 m. Furthermore, the inner lining system should be designed to resist what is connoted as an extreme rock load of 6 metric ton, acting on a 1×1 m area, even when a primary rock strengthening is present. Similar inner lining systems have been used in e.g. Norra länken, parts of Citybanan in Stockholm and is planned to be used for the Stockholm Bypass project. In the present paper, results from a recent research project are presented, aiming at investigating the structural manner of action of the aforementioned inner lining system. A series of concrete slabs have been tested, both until static failure and with a 600 kg drop weight from different heights. All tested slabs resulted in flexural failure and showed a significant ductility. For several of the slabs tested for impact loading, significant spalling from the soffit was obtained, at the most corresponding to a mass of 16 kg. Three of the slabs tested for impact load were manufactured with an outer layer of steel fibre reinforced shotcrete. None of these slabs showed any significant spalling, despite a free fall height up to 2 m. Several FE-analyses have also been performed, accounting for the nonlinear material properties of concrete. The results showed good agreement with the conducted experiments, both regarding static loading, cracking and impact load. A similar analysis was also done for the whole inner lining system. The results showed a larger load capacity compared to the experiments, but still with a rather localised failure. QC 20150617

n this article, the use of external damping systems for vibration mitigation of railway bridge dynamics is studied. For a presented case study bridge, the performance of different tuned mass damper systems (TMDs) is studied. During train passage, the change in dynamic characteristics of the bridge may produce a significant detune to a passive TMD. Therefore, routines for a variable stiffness TMD using incremental frequency estimates are developed. Based on numerical simulations, the cumulative fatigue damage is calculated for different damper systems. Due to resonant behavior, the results are found to highly depend on the train speed. Based on an assumed probability density function for the train speed, fragility curves are produced to express the probability of fatigue failure as a function of the number of train passages. Updated from "Submitted" to "Published". QC 20150901 Long Life Bridges

In this report, the load capacity of concrete slabs subjected to concentrated loads is studied, considering both the static load capacity and the response due to impact of a falling mass. The purpose of the study is to gain more knowledge on the static and dynamic behaviour of the slabs and to use that knowledge in the assessment of the load capacity of inner lining systems in tunnels. The methodology involves experimental testing of a series of slabs, validation of numerical models and simulating the response of the inner lining system. A total of 18 slabs were manufactured, consisting of shotcrete and reinforcement mesh. Some of the slabs also included steel fibre reinforced concrete (SRFC). The size of the slabs were 1.75×1.75×0.12 m, suspended in four hangers #1.2 m and loaded centric on an area of 0.2×0.2 m. In addition, a series of core samples and beams were cut from two of the slabs for material testing and verification of numerical models. From the static load tests of the slabs, the load at cracking was obtained at 50 – 60 kN with a vertical midpoint displacement of 0.6 – 1.0 mm. The ultimate load ranged from 60 – 80 kN. The slabs showed significant ductility with a peak displacement of about 70 – 80 mm at post-failure. All slabs showed a two-way flexural failure. The concrete cover was in average 30 mm, measured from the compressive side, resulting in little difference between the crack load and the ultimate load. A vertical displacement of about 1 – 2 mm was required to obtain a crack width of 0.2 mm. Three slabs with only SRFC were tested until static failure, the ultimate load ranged from 85 – 90 kN but with less ductility compared to the slabs with rebar mesh. Impact load tests were performed using a steel mass of 600 kg. The free fall height was varied from 1 – 2 m. The peak impact load varied from 200 – 250 kN, without any clear correlation with the height. The corresponding impulse load varied from 4.0 – 5.5 kNs with a clear correlation to the height. All slabs subjected to impact load showed a one-way flexural failure, the residual strength after impact was sufficient to carry the static load of the steel weight. Several of the slabs showed significant fallout of concrete during impact, in one extreme case a total of 16 kg. Three slabs were tested with an outer layer of 30 mm of SRFC, none of these slabs showed any significant fallout. The static and dynamic response of the slabs have been simulated using nonlinear FE-models. The models generally show good agreement, both for static load, crack widths and response during impact. Similar models were used to simulate the response of the inner lining system. The results indicate a significant load capacity, both due to static and impact loading. The models are however not able to account for potential punching failure. QC 20150519

I föreliggande rapport har inventering och dynamiska kontroller utförts på 76 järnvägs­broar längs Botniabanan. Samtliga broar är byggda under perioden 1999 – 2009 och dimensionerade statiskt för tåglast BV2000. Broarna kan indelas i tre grupper; balk- och plattbroar, plattrambroar och samverkansbroar. Baserat på förenklade dynamiska analyser erhålls ett överskridande av den vertikala accelerationen för 75 % av alla plattrambroar och 40 % av alla balk- och plattbroar. Överskridande erhålls även för 4 av 9 samverkansbroar. Av totalt 76 analyserade broar motsvarar detta 41 broar som inte uppfyller kravet på sth 250 km/h. En sänkning till sth 200 km/h ger att 26 broar inte klarar de dynamiska kraven. Fyra broar har en nominell kritisk hastighet under 120 km/h. För plattrambroarna är accelerationsnivån i hög grad beroende på grundläggnings­förhållandena. Enligt tidigare BV Bro medräknades endast frekvenser upp till 30 Hz, vilket i kombination med antagande om oeftergivliga stöd ofta resulterade i att dynamiska kontroller inte utfördes för plattrambroar. Eftergivlighet hos grund­läggningen resulterar i vertikala stelkroppsmoder som i kombination med med­svängande massa av angränsande fyllning ger låga egenfrekvenser och därmed låga resonanshastigheter. För balkbroar beräknas mycket höga accelerationsnivåer då dessa är utformade med ändskärmar. Orsaken är att tåglasten inducerar en stötbelastning då den passerar änden på ändskärmen. Detta ger höga accelerationsnivåer även i angränsande spann, även utanför ett resonanstillstånd. Plattbroar ger ofta högre accelerationsnivåer jämfört med motsvarande balkbroar, beroende på att en lägre böjstyvhet ger lägre resonanshastighet. Detta förvärras kraftigt för plattbroar utformade med ändskärmar, vilket identifierats för t.ex. bro över Sidensjövägen. För samverkansbroarna beror de höga accelerationsnivåerna på en kombination av låg böjstyvhet och låg massa, vilket ger en låg resonanshastighet och hög accelerations­nivå. Problemet är störst för två fritt upplagda broar, Banafjälsån och Bryngeån. Förslag på fortsatta utredningar i syfte att påvisa att fler broar klarar de dynamiska kraven inkluderar mer avancerade analysmetoder i kombination med fältmätningar och kontrollerad excitering. Det bedöms i nuläget finnas stor potential att påvisa lägre accelerationsnivåer baserat på mindre konservativa antaganden om t.ex. dämpning och samverkan mellan bro och omgivande fyllning. QCV 20130529

In this paper, the performances of different external damping systems for stay cables are studied based on numerical simulations. Two types of dampers have been analysed; a near anchorage viscous damper and a tuned mass damper (TMD) mounted near the midspan of the stay cable. For the passive case, both dampers are tuned to the fundamental mode of vibration of the cable. The optimal viscous damping for the near anchorage damper is determined based on well-known equations for a taut string. For the TMD, parametrical studies have been performed to determine the optimal damping ratio as function of the damper mass. The resulting vibration mitigation from the two systems are also studied for higher modes of vibration and the potential increase in performance using an adaptive or semi-active vibration control system is studied. QC 20140609 Long Life Bridges

In this paper, dynamic analyses and field measurements of a tied arch railway bridge is presented. Excessive vibrations of the hangers were obtained, caused by resonance during train passages. The resulting increase of the stress level and number of stress cycles were shown to decrease the fatigue service life significantly. The most critical section is a threaded turnbuckle connection of the hangers. Due to low damping of the hangers, more than 50 % of the cumulative fatigue damage was related to free vibrations after train passage. Passive dampers were installed to attenuate the vibrations by means of increased damping. A combination of field measurements and numerical models are used to investigate the behavior of the bridge and the impact of increased hanger damping. QC 20120730

Long Life Bridges is a Marie Curie 7th Framework Project funded under the Industry and Academia Partnerships and Pathways call, Grant Agreement No. 286276. The Project commenced in September 2011 and is continuing for 4 years until August 2015. The project vision is to extend the service lives of bridges through development of advanced assessment methods. The author wishes to acknowledge the financial contribution by the European Commission in supporting the project and funding this research. The work presented in this report has been conducted at Roughan & O’Donovan Innovative Solutions, Dublin, Ireland, during the period of January to December 2012, under supervision of Associate Professor Alan O’Connor. The author has been seconded from the Royal Institute of Technology (KTH), Division of Structural Engineering and Bridges. Within the project, experimental work to develop a prototype damper has been carried out at Trinity College Dublin (TCD), Department of Civil, Structural and Environmental Engineering. A special thank goes to Dr. Kevin Ryan and the laboratory staff at the Department for the help in manufacturing and testing the prototype damper. Full-scale testing has been performed on a railway bridge in Sweden. The tests were funded directly by the Swedish Transport Administration (Trafikverket). The instrumentation and field measurements were performed by KTH in collaboration with the author. The work presented, denoted secondment 1.1b, deals with development of adaptive and semi-active damping systems for railway bridges. The aim of the project is to develop methods for structural vibration control with applications for railway bridge dynamics. Much of the work has been related to a case study bridge. There is constant demand on rail authorities to increase both the allowable axle loads and the allowable speed on existing railway lines. As an example, the Swedish Transport Administration has recently investigated the possibility of upgrading part of the main lines to allow for future high-speed trains. Some lines are also being investigated with the aim of allowing ore transports with higher axle loads and longer trains. A large portion of the bridge stock was designed for significantly lower axle loads and only very few have been designed to account for dynamic effects. Increased dynamic effects may result in exceedance of dynamic design criteria, reduced service life due to fatigue, or even failure. Through better quantification of risk, it is often possible to prove that speeds can be increased with no adverse effect. However, for bridges where the level of risk is too high, a cost-effective means of reducing dynamic effects on bridges are active and semi-active control system. Semi-active control is well established in other fields and could prove to be a beneficial technique to allow train speeds to be increased. The concept of structural vibration control is to attenuate the dynamic response of a structure by means of an external damping device. Due to changes in either loading or structural behaviour, the properties of the damper device may need to be changed to efficiently mitigate vibrations. Two main principles of damper devices are commonly used; tuned mass dampers and shock absorbers. Tuned mass dampers consist of a suspended mass mounted on the main structure. Due to a phase-shift, the vibration of the suspended mass partly counteracts the corresponding motion of the main structure. Changing the stiffness of the suspended mass results in a variable adaptive tuned mass damper. Shock absorbers rely on producing the counteracting force by means of increased viscous damping. Devices with variable viscous damping are often categorised as semi-active. Fully active systems rely on producing the counteracting force by means of a load actuator. Adaptive and semi-active systems generally require much less energy to operate compared to fully active systems. QC 20131028 Long Life Bridges

In this paper, a semi-active control system for vibration mitigation of railway bridges is presented. The real time frequency response is estimated using a short-time Fourier transform, employing curve fitting to relevant peaks for increased accuracy. A control algorithm developed in Matlab® is linked to a commercial FE-software, facilitating application on arbitrary structures. A numerical study of an existing tied arch railway bridge is presented. From earlier field measurements and numerical analysis, resonance of several hangers during train passage was observed. This was shown to significantly reduce the fatigue service life of the hangers and for the most critical section about 50% of the cumulative damage was related to free vibrations. A system of passive dampers was later installed and the increase in resulting damping was measured. Within the present study, the previous results are reanalysed and compared with a semi-active approach. The natural frequencies of the hangers vary as a result of the variation in axial force. A semi-active control system has the potential to improve the vibration response of the structure when compared to the installed passive system. QC 20121005 Long Life Bridges

In this paper, results from full-scale tests on a corrugated soil-steel flexible culvert for railway traffic are presented. The bridge was instrumented with strain gauges, accelerometers and displacement gauges, measuring the response from passing trains. The aim of the measurement campaign was to gain knowledge of the dynamic behaviour due to train induced vibrations, both of the bridge structure and the overlying railway embankment. From the measured data, the load distribution and soil-stiffness can be estimated. The results also serve as input for calibration of numerical models that are used for predicting the behaviour due to high-speed trains. QC 20120613

I föreliggande rapport har omfattande dynamiska analyser av järnvägbroar utförts, i syfte att ge en översiktlig uppskattning av möjligheten att tillåta höghastighetståg på befintliga banor. Aktuella sträckor som studerats är Västra stambanan mellan Stockholm och Göteborg, Södra stambanan mellan Stockholm och Malmö samt Västkustbanan mellan Göteborg och Malmö. Totalt omfattar detta mer än 1000 broar. Eftersom detaljerade analyser av samtliga broar ej varit möjlig med givna resurser och tid, har en kombination av detaljstudier och sannolikhetsbaserade metoder valts. Analyserna har begränsats till balk- och plattbroar samt plattrambroar, vilka utgör ca. 90 % av tillgängligt underlag. Förutsättningarna för de dynamiska kontrollerna baseras på kraven enligt Eurokod EN-1990 samt EN-1991-2 och utgör främst vertikal acceleration av brokonstruktionen, begränsad till 3.5 m/s2. Förutsättningarna inom utredningen har varit att undersöka tåghastigheter upp till 250 km/h (sth). Baserat på omfattande parameteranalyser har ett antal faktorer identifierats som viktiga för en bros dynamiska respons. Många av dessa parametrar är svåra att entydigt bestämma och påverkar ofta strukturresponsen på ett oregelbundet sätt. Omfattande Monte-Carlo simulering har utförts baserat på förenklade 2D-modeller. Resultaten visar att ca. 70 % av balk- och plattbroarna samt ca. 50 % av plattram­broarna förväntas överskrida de dynamiska kraven enligt Eurokod, baserat på sth 250 km/h. Även om tillåten hastighet sänks till sth 150 km/h ger detta ett förväntat värde på 15 % för balk- och plattbroar samt 30 % för plattrambroar. Förväntat värde för varje bro redovisas i Bilaga F, vilket kan användas som underlag för kostnads­kalkyl. Resultaten är en konsekvens av de höga krav som ställs i Eurokod, vilka är samma som vid dimensionering av nya broar. Andra förutsättningar avseende t.ex. lastmodell eller frekvensband för utvärdering av accelerationer är helt avgörande för resultaten. En av de största kvarstående frågeställningarna är det dynamiska verkningssättet för korta broar med höga egenfrekvenser. Den dynamiska responsen från dessa broar utgörs ofta av stötvis belastning istället för resonans. Enligt tidigare BV-Bro begränsades frekvensbandet till 30 Hz, i Eurokod anges att de 3 första egenmoderna ska medräknas, vilket ofta resulterar i betydligt högre frekvensband. Giltigheten av dessa krav måste utredas. The following report comprises extensive dynamic analyses of railway bridges, with the aim of presenting an initial estimate on the feasibility to allow future high-speed trains on existing bridges. The lines studied are the West main line between Stockholm and Gothenburg, the South main line between Stockholm and Malmö and the West coast line between Gothenburg and Malmö. This comprises more than 1000 bridges. Detailed studied of all bridges is beyond the scope of the present study. Instead, a combination of detailed studies and probability-based methods has been chosen. The analyses have been limited to beam- and slab bridges and portal frame bridges, constituting about 90 % of the total included bridge stock. The requirements for the dynamic analyses follow Eurocode EN-1990 and EN-1991-2 and are mainly related to the vertical acceleration of the bridge deck, limited to 3.5 m/s2. The aim of the study is to investigate allowable speeds up to250 km/h. Based on extensive parametric analyses, a number of factors have been identified as decisive for the dynamic bridge behaviour. Many of these parameters are difficult to properly estimate and often influence the structural response in a non-regular manner. Extensive Monte-Carlo simulations have been performed based on simplified 2D-models. The results show that about 70 % of the beam- and slab bridges and about 50 % of the portal frame bridges are expected to exceed the design criterions stated by the Eurocode. Even if the allowable speed would be decreased to150 km/h, 15 % of the beam- and slab bridges and 30 % of the portal frame bridges are expected to exceed the criterions. Expected probabilities for each bridge are presented in Appendix F, to be used for further investment cost estimates. The presented results are a consequence of the strict criterions stated by the Eurocode, also valid for design of new bridges. Other conditions regarding e.g. train load model or frequency range for evaluation of accelerations will be critical for the results. One of the main remaining questions is the dynamic behaviour of short span bridges appertaining high natural frequencies. The dynamic response from such bridges often constitutes of transient loading rather than resonance. According to the previous Swedish bridge design code BV-Bro, the frequency range was limited to 30 Hz. In Eurocode the frequency range is limited to the third mode of vibration for each studied structural member. This often results in significantly higher frequency ranges, especially for short span bridges. The validity of these criterions must be investigated further. QC 20120227