Management of Stresses in the Rails on Railway Bridges

This paper analyses the stresses in continuous welded rails on bridges including the aspect of fatigue of rail steel. Furthermore, it examines the possibility to avoid rail expansion joints, while simultaneously exploiting the permissible stress capacity of the rail profile 60E1. Accordingly, general application of permissible values of pressure and tensilestresses prescribed in the current European standards was critically analysed. Paper includes specific application aspects of the prescribed stress values for railway bridges in Serbia. General algorithm for reducing the stresses due to the vehicle/track/bridge interaction, which is presented in this paper, was developed by the authors.This algorithm includes all essential parameters of the bridge structure and railway superstructure, as well as the influence of climate conditions and railway route design.


INTRODUCTION
Sustainable rail traffic has to meet user requirements and maintain competitiveness with other modes of transport.Accordingly, the increase in speed and axle load on the modern railways is evident.Simultaneously, adapting the track to the topographic characteristics and the problems of routing through the urban environment are getting more complex and challenging.Application of shallow radius of horizontal curves and low railway grades for mixed traffic lines contribute to a large number and large length of railway engineering structures (including bridges, viaducts, overpasses etc.).According to current experience, engineering structures could comprise up to 70% (or more) of the length of railway line.
Railway bridges should provide the continuity of the track in order to ensure the same traffic safety and ride comfort along the entire length of railway line.Authors particularly investigated the possibilities to avoid rail expansion joints, in order to provide traffic safety and ride comfort on the railway bridges.This approach contributes to reduction of maintenance costs, as well as adverse environmental impact (noise and vibration).
Considering the dangerous consequences of derailment on the bridge (which could be expressed in human lives, injuries, environmental and material damage), importance of research in the area of bridge design and maintenance is obvious.This research includes the analysis of the vehicle/track/bridge interaction.The main assumption is multidisciplinary approach during design, construction and maintenance of railway bridges (Figure 1).Further considerations are primarily focused on the parameters of the track and bridge structure (blue and orange colour in Figure 1).Vehicle/track/bridge interaction leads to the occurrence of additional stresses in rails on the bridge.Figure 2 shows additional tensile stresses in CWR, including stresses due to temperature changes σ bT and bending of the bridge deck σ vb , as well as braking and acceleration of railway vehicles σ ba .
Similarly, Figure 3 shows additional pressure stresses in CWR including stresses due to temperature changes in the bridge deck.Pressure stress 290 N/mm 2 leading to track buckling is defined according to the results obtained in the previous researches [1,2].Paper includes critical analysis of tensile and pressure stress values in CWR prescribed by European standards for railway bridges.Furthermore, it presents a general algorithm for reducing the additional stresses in CWR due to the vehicle/track/bridge interaction.This algorithm, developed by the authors,could be applied by railway infrastructure designers and infrastructure managers throughout the entire lifetime of the track and bridge.
In addition, this paper presents climate conditions in Serbia, which should be considered in the design of railway bridges in order to ensure safety of railway traffic.We investigated the influence of tensile and pressure stress values in rail prescribed in [3][4][5][6][7][8][9][10][11] considering the specific Serbian climate conditions and presented the results.

EUROPEAN REGULATORY FRAMEWORK
Technical regulations for railway bridges should be based on the results of vehicle/track/bridge interaction analysis.Considering the complex requirements of rail transport, as well as long service life of railway bridges, the need for critical analysis of current technical regulations and its adaptation to in-service condition is obvious.
The problem of determining the stresses in CWR on the bridge and transfer of the longitudinal forces to the bridge bearings was considered by International Union of Railways (UIC).In 1995, the first edition of UIC Leaflet 774-3 provided recommendations for calculation of track/bridge interaction, which presented the basisfor development of relevant European standards.In 1999, European Rail Research Institute (ERRI) formed an expert commission to modify UIC Leaflet 774-3.The upgraded second edition of UIC Leaflet 774-3 was published in August 2001 [11].
In 2003, European Committee for Standardization (CEN) published EN 1991-2 [3], which is based on previously mentioned research by ERRI [11].European standard [3] defines loads (models and representative values) associated with road traffic, pedestrian actions and railway traffic, which include dynamic effects and centrifugal, braking/acceleration actions and actions for accidental situations.Section 6 of the standard [3] includes railway traffic actions and other actions that occur on railway bridges.Furthermore, Annex A2 in [4] provides calculation procedure, which contains the necessary factors for combination/frequent/quasi-permanent values of variable actions.In addition, CEN has published standards for design of concrete, steel, and composite steel/concrete bridges [5][6][7].
In addition, the railway bridges have to meet the interoperability requirements for the European railway system in accordance with Technical Specifications for Interoperability (TSI).TSI represents obligation for European railway system and basis for national rules and regulations.Resistance of new and existing railway bridges and embankments to traffic load is defined as basic parameter of the infrastructure subsystem and should meet the essential requirements defined in [11].
Railway bridges have to be designed to support vertical loads according to the load models defined in EN 1991-2.The mentioned load models should be multiplied by the factor alpha α [3].The minimal values of factor α for the design of new bridges are prescribed in [10].Dynamic analysis is required for railway bridges designed for maximum speeds over 200 km/h [3,10].
According to [3,10], calculation of railway bridge structure includes centrifugal force (for curved track over the whole or part of the bridge length), nosing force (frictional lateral force), and acceleration/braking forces (occasional longitudinal forces).

ANALYSIS OF TENSILE STRESSES INCWR USING SMITH DIAGRAM
European standard EN 1991-2 [3] prescribes permissible values of additional stressesin CWR on the bridge in accordance with [11,12], which refer to the technical properties of railway superstructure affecting lateral and longitudinal track resistance: -60E1 rail profile according to [13], -steel grade at least R260 according to [13](tensile strength of at least 900 N/mm 2 ), -rail fastening systems for ballasted track in accordance to European standard EN 13481series, -maximum spacing of heavy concrete sleepers (e.g.B70 sleeper type) up to 65 cm in ballasted track or equivalent ballasted track structure, -minimum 30 cm thickness of consolidated ballast under the sleeper contact surface (at rail placement).
Furthermore, permissible values refer to the technical properties of railway alignment on the bridge (including adjacent abutments) straight track, and/or minimum track radius 1500 m.
When the previous criteria are not satisfied, specific analysis and calculation should be carried out or additional measures defined.
An open point still remains -whether the prescribed values of the additional stresses [3,11,12] in CWR could be applied regardless of: (a) specific climate conditions (extremely low/high temperatures in CWR and bridge), (b) traffic requirements (high braking/acceleration frequency), and (c) rail manufacturing technology (wide range of residual stresses up to 250MPa according to [13])?
The decrease in permissible stress in the corroded rail compared to the new rail 60E1/900 (tensile strength 900 N/m 2 ) is presented in Smith diagram (Figure 4).Permissible additional tensile stresses in rail foot can be determined from Smith diagram for corroded rail steel.Corrosion of the rail foot occurs due to the chemical substances in air and/or water, or due to the electrolytic actions induced by stray current.Corrosion could result in a rail break due to the profile reduction and this is the reason to analyse permissible values for additional stresses in corroded rails.
Figure 4 shows permissible tensile bending strength in rail foot centre according to Smith diagram for new and corroded rails with a tensile strength 900 N/m 2 .If the estimated value of the stress due to bridge deck bending is σ vb =20 N/mm 2 , the free stress σ f * is112-20=92 N/mm 2 according to [3,11,12,14].If the value of stress due to bridge deck bending σ vb is determined by calculation, the free tensile stress in the rail foot σ f amounts 112 N/mm 2 according to the research presented in dissertation by Freystein [14].
In both above cases, it is assumed that the residual stress in rail foot is 80 N/mm 2 and the tensile stress due to the temperature change in CWR is 120 N/mm 2 .
In Figure 4, the total basic tensile stress is 358 N/mm 2 , representing the sum of the following: σ r =80 N/mm 2 , σ T =120 N/mm 2 ,and σ Q =158N/mm 2 .The additional free tensile stress amounts 470-358=112 N/mm 2 , whereby the available zone of dynamic stresses includes only the effects of bridge deck bending σ vb =20 N/mm 2 .Accordingly, influences due to braking and temperature changes in the bridge deck is 112-20=92 N/mm 2 (Figure 4).
Stress due to railway traffic load σ Q presents the part of basic tensile stress and significantly influences fatigue of rail steel.Value σ Q =158 N/mm 2 in Figure 4 corresponds to following technical properties of railway superstructure: 60E1 rail profile, B70W concrete sleepers with elastic rail fastening system, sleeper spacing up to 65 cm, and good track foundation (track modulus C=0.1 N/mm 3 ).Calculation was performed for light high-speed trains, as well as for heavy slow trains, usingreference combination, which implied speed up to 200 km/h [15].Furthermore, calculation considered unequal wheel load distribution in curves, as well as dynamic influences.
In Figure 4, value σ T =120 N/mm 2 corresponds to temperature change during winter conditions: where: ΔT RT -difference between minimum rail temperature T min and neutral temperature T n , E=210 GPa-Young`smodulus for rail steel, α=1,15•10 -5 1/K -coefficient of thermal expansion.Residual stress in Figure 4is presented as a part of basic tensile stress in rail.In the manufacturing process, generated in rails during hot rolling are uneven cooling, as well as roller straightening and levelling.For Vignole rails [13], the mass is concentrated in the rail head and the middle of the rail foot.In these areas, the cooling process takes a longer period than in the rest of rail profile (Figure 5).Furthermore, Figure 6 presents distribution of residual stresses in rail head, web and foot for new and used rails [16].

ANALYSIS OF PRESSURE STRESSES IN CWR
The permissible value of additional pressure in CWR due to vehicle/track/bridge interaction is σ P =72 N/mm 2 for ballasted track [3,11,12].
Track buckling on the bridge is a representative criterion for defining the permissible additional pressure in CWR.The critical temperature increases in the rail during summer conditions, which might lead to track buckling.This critical temperature is 122 K according to [1,2,17], or approximately 120 K according to [18].The critical temperature corresponds to the following technical properties of railway superstructure: 60E1 rail profile, B70W concrete sleepers with elastic rail fastening system, sleeper spacing up to 65 cm, and good track foundation (track modulus C=0.1 N/mm 3 ).Furthermore, the following should be met: (a) track alignment deviation of 4.5 mm for high-speed lines, (b) dynamic resistance to the lateral displacement of track w Q =10 kN/m.
The reserve of representative temperature change ΔT R could be obtained using the following equations: where: ΔT RP -difference between maximum rail temperature T max and neutral temperature T n , ΔT S -safety temperature change according to Table 1, ΔT RE -rail elongation under the influence of traffic load corresponding to the temperature change of 3 K.The difference of 30 K could be calculated and expressed through the additional pressure stress in the rail of 72 N/mm 2 , which ensures track stability against buckling.

DISCUSSION OF PERMISSIBLE VALUES FOR AXIAL STRESSES IN CWR ON THE BRIDGE
In accordance with design criteria for rails on the bridge and on the adjacent abutments [3], the permissible additional rail stresses due to the combined response of the bridge structure and ballasted track to variable actions should be limited to 72 N/mm 2 for the pressure stress and 92 N/mm 2 for the tensile stress.Moreover, the alternative requirements should be specified in the National Annex.Following discussion concerns specific requirements for vehicle/track/bridge interaction in Serbia.
Prescribed values for permissible tensile stresses in the rail foot [3,11,12], which are presented in Smith diagram (Figure 4) imply properties of railway superstructure and technical properties of railway alignment defined in Chapter 3, as well as the following: mixed traffic line for speed up to 200 km/h, temperature change in rails up to ΔT RT <50 K (σ T =120 N/mm 2 ), tensile stresses up to σ r =80 N/mm 2 .
It should be mentioned that value σ r =80 N/mm 2 corresponds to rail profile 49E1 (previous profile S49) according to German superstructure design regulation from 1992.On the other hand, results in dissertation [19] shown that rail profile 60E1 has significantly larger residual stresses due to larger mass.Furthermore, EN 13674-1 defines the maximum longitudinal residual stress in the rail foot up to 250 N/mm 2 for all steel grades, which has to be determined using destructive cutting method [13].Residual stress could be determined using non-destructive methods, such as X-ray diffraction, ultrasonic velocity, Barkhausen noise analysis etc. [18], but only for relative comparing to cutting method [13].
Rail manufacturing process (especially cooling) significantly influences residual stress distribution in rail profile (Figure 6).The rail market already provides rails which were manufactured using "optimal cooling, straightening and levelling technology" with residual stress σ r * =50 N/mm 2 (Figure 4).Free tensile stress value σ f =112 N/mm 2 (Figure4) is derived based onthe assumption that residual stress equals 80 N/mm 2 , which does not necessarily correspond to rail profile 60E1.In any case, calculation of CWR should include real value of residual stress in the foot of corroded and used rail profile 60E1 (Figure 6), considering current rail market.
Furthermore, local climate conditions and neutral temperature value significantly influence ΔT RT .Hence, ΔT RT =50 K cannot be prescribed in general.For example, Serbian Infrastructure Manager prescribed T n =22,5 o C.On the other hand, ΔT RT could have different values depending on climate region and considering global climate changes in Serbia.Figure 7 presents temperatures in rails for two monitoring places (SremskiKarlovci and Priboj) for last three years, which correspond to significant climate change in Serbia.Figure 4 shows that σ vb =20 N/mm 2 is an estimated value which refers to available zone of dynamic stresses.Furthermore, bridge deck bending stress σ vb and stress due to the traffic load σ Q have to belong to available zone of dynamic stresses.Exact value for σ vb could be calculated and it could be larger, equal or less than 20 N/mm 2 .Considering the starting assumptions in this Chapter, if σ vb >20 N/mm 2 , it is necessary to reduce permissible stress in rail thus enabling both σ Q and σ vb stresses to pertain in available zone of dynamic stresses.
In Figure 4, stresses due to braking/acceleration σ ba does not belong to available zone of dynamic stresses in Smith diagram.This means that braking/acceleration occurs exceptionally.In case when railway station is located on the bridge, or right before/after the bridge, σ ba , σ Q and σ vb have to belong to available zone of dynamic stresses in Smith diagram.This case demands calculation of appropriate permissible additional stress σ f ≠92 N/mm 2 .
According to equation ( 4), permissible value for temperature difference between maximum rail temperature T max and neutral temperature T n in CWR is: If it is considered that neutral temperature is 22,5°C, then maximum allowed temperature in CWR equals: which corresponds to permissible pressure stress of 72 N/mm 2 .Calculated T max coincides with values that are used on majority of European railway networks.For example, maximum temperature in rail measured in Germany is58°C [17].Considering that air temperatures measured in August were above 42°C during last several years in Serbia, it is necessary to reduce value of permissible pressure stress in railsσ P according to climate region.

PROPOSED ALGORITHM FOR MANAGEMENT OF THE STRESSES IN CWR DUE TO THEVEHICLE/TRACK/BRIDGE INTERACTION
This paper proposes general algorithm for management of the stresses in CWR on the bridge respecting the multidisciplinary approach (Figure 1).The main goal of managing the stresses in CWR is to avoid rail expansion joints on the bridge.The algorithm is developed by the authors of this paper and presented in Figure 9.
After defining the rail route, mutual adjustment of bridge and track structure contributes to the reduction in maintenance costs of railway infrastructure and vehicles, decrease in the negative environmental impact (noise and vibration), as well as increase of ride comfort due to the omitting of the rail expansion joints [20,21].
The developed algorithm for management of the stresses in CWR includes specific requirements discussed in Chapter 5 (residual stresses in rails according to manufacturing technology and temperature changes according to climate region).Furthermore, stress management has to include specific influence of the bridge position on the railway route, especially when railway station or signal is located on the bridge, or right before/after the bridge (frequent braking/ acceleration).In such circumstances, influence of the braking/acceleration has to be considered as dynamic load.This could lead to decrease in permissible tensile stress in the rail foot (Figure 4).
If applying the procedure from proposed algorithm (steps A-G in Figure 9) does not provide acceptable technical solution for vehicle/track/bridge interaction, ballastless track structure on the bridge could be considered (permissible pressure/tensile stress amounts 92 N/mm 2 -step H).
In the case when it is not possible to apply ballastless track structure, step I provides option to change railway route and bridge position in order to achieve shorter expansion length and, if necessary, larger curvature (1/R) of the bridge.
The last step of algorithm(stepJ in Figure 9) offers technical solution for exceeding the permissible pressure stress in CWR above the last movable bridge support -installation of the rail expansion joints(Figure 8).This solution could be applied regardless of the circumstances, but it is the worst solution regarding cost-effectiveness and ride comfort.Design of expansion capacity has to include temperature changes (according to climate region), as well as influence of braking/acceleration.
Analysing the vehicle/track/bridge interaction and using the developed algorithm, possible competitive technical solutions for track and bridge structure could be created.Optimal technical solution should be determined using multi-criteria analysis techniques.
Figure 9 presents appropriate comments for each algorithm step (A-K).In addition, step H includes option to ensure track stability using ballastless track instead of ballasted track.However, detailed considerations in this paper are limited to ballasted track.Due to the specific requirements, results of the analyses of ballastless track on reconstructed and new bridges require separate presentation.According to the structure of basic and additional stresses (Figures 2 and 3), this paper points out that the components of total stress in CWR depend strongly on: (1) type of railway line (design speed, axle load, pas-senger, freight or mixed traffic, number of tracks), (2) bridge position on the railway route (curvature 1/R, railway station located on the bridge, or right before/after the bridge, signal position), (3) climate zone (relevant temperature changes in bridge deck and CWR), and (4) rail manufacturing technology (residual stresses according to [13]).
For ballasted track on the bridge, the prescribed permissible values of tensile (92 N/mm 2 ) and pressure stress (72 N/mm 2 ) in the rail in accordance with EN 1990:2002 [4] were critically analysed in Chapters 3-5.According to the Smith diagram for corroded rail 60E1/900 and fatigue stress diagrams (Figure 4) it was pointed out that values of permissible stresses [4] in CWR cannot be used in case of frequent vehicle braking/ aceleration on the bridge (due to the station and/or signal).In such circumstances, the influence of vehicle braking/ aceleration has to be considered as fatigue stress (Figure 4), hence defining appropriate lower value of permissible rail stress.Furthermore, the paper points out that the analysis of additional stresses in CWR has to incorporate the influence of modern braking systems on track stability (Table 1).
Chapter 5 discusses permissible values for axial stresses in CWR on the bridge.Additionally, it presents the influence of climate regions in Serbia (Figure 7) on permissible stress values due to the temperature changes in bridge and rails.
The permissible additional rail stresses due to the combined response of the bridge structure and track (design criteria for track on the bridge and on adjacent abutments) have to strongly comply with real requirements of railway route, traffic regime, rail manufacturing technology, and climate change/region.Otherwise, uncritical application of design criteria defined in European standard EN 1990EN :2002 [4] [4] could jeopardise railway traffic safety.

Figure 1 .
Figure 1.Relevant engineering requirements for solving vehicle/track/bridge interaction Considerations in the paper refer to the track with continuous welded rail (CWR -Continuous Welded Rail) 60E1 in the ballasted track on the bridge.

Figure 4 .
Figure 4.Smith diagram for new and corroded rail 60E1/900 (left) and fatigue stress diagrams (right)

Figure 5 .Figure 6 .
Figure 5.The uneven cooling of rail profile and bending of the rails in cooling bed

Figure 7 .
Figure 7.Results of temperature monitoring in Sremski Karlovci (up) and Priboj (down) in Serbia

Figure 8 .
Figure 8.Referent influences for design of expansion capacity of rail expansion joint on the bridge This work was supported by the Ministry of Education, Science and Technological Development of Serbia through the research project No. 36012: "Research of technical-technological, staff and organization capacity of Serbian Railway, from the viewpoint of current and future European Union requirements".

Figure 9 .
Figure 9.General algorithm for reducing the stresses in rails due to vehicle/track/bridge interaction