Rail Structure Interaction Design Guidelines-v11.pdf

RAIL STRUCTURE INTERACTION DESIGN GUIDELINES

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TABLE OF CONTENT 1. INTRODUCTION 2. TECHNICAL DESCRIPTIO 2.1 INTRODUCTION 2.2 BRIEF HISTORY OF THE 2.3 EXPLANATIONS ON 2.3.1 V 2.3.2 RAIL EXPANSION JOINTS 2.3.3 TURNOUTS AND CROSSOVERS 2.3.4 EXPANSION/CONTRACTION OF THE BRIDGE STRUCTURES 2.3.5 HORIZONTAL LOADS DUE TO BRAKING AND TRACTION 2.3.6 VERTICAL LOADS DUE TO RUNNING TRAINS 2.3.7 EARTHQUAKE LOADS 2.3.8 SUDDEN RAIL FAILURE 2.3.9 TRACK CONSTRUCTION AND MAINTENANCE 2.3.10 SPECIAL CASE OF A TRACK LAID IN TIGHT CURVE 2.3.11 OTHERS RAIL STRUCTURE INTERACTION EFFECTS 2.3.12 IMPACT OF LOCAL BRIDGE DEFORMATIONS ON TRACK INTEGRITY 2.4 SUMMARY OF THE MAIN REQUIREMENTS RELATED TO TRACK INTEGRITY

12 15 16 17 17 18 19 20 21 21 22

3. PRESENTATION OF TRACK SYSTEMS

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3.1 BALLASTED TRACK 3.2 SLAB TRACK 3.3 CONTINUOUS RAIL SUPPORT SYSTEM

24 25 31

4. PRESENTATION OF STANDARDS AND PRACTICES REGARDING RAIL STRUCTURE INTERACTION33 4.1 UIC 774-3 4.1.1 DESCRIPTION 4.1.2 LOADING 4.1.3 CRITERIA AND RANGE OF APPLICATION 4.1.3.1 Criteria 4.1.3.2 Range of application 4.1.4 CONCLUSION 4.2 UIC 776 4.2.1 DESCRIPTION 4.2.2 LOADING 4.2.3 CRITERIA 4.3 UIC RECOMMENDATIONS FOR DESIGN AND CALCULATIONS OF BALLASTLESS TRACK 4.3.1 DESCRIPTION XXXXXXXX

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4.3.2 LOADING 4.3.3 CRITERIA AND RANGE OF 4.4 UIC 720 4.4.1 P 4.4.2 DEFINITION OF RAIL TE 4.4.3 TYPE OF TRACK STUDIED 4.4.4 E 4.4.5 CONCLUSION 4.5 EUROCODE 1991-2 4.5.1 DESCRIPTION 4.5.2 LOADING 4.5.3 CRITERIA AND RANGE OF APPLICATION 4.5.3.1 Criteria 4.5.3.2 Range of application 4.5.4 CONCLUSION 4.6 EN 16432 “BALLASTLESS TRACK SYSTEM” 4.7 RDSO GUIDELINES FOR CARRYING OUT RAIL-STRUCTURE INTERACTION STUDIES ON METRO SYSTEMS (LUCKNOW) 4.7.1 DESCRIPTION 4.7.2 LOADING 4.7.3 CRITERIA AND RANGE OF APPLICATION 4.8 KOREAN CODE 4.9 ACI343.1R-12 4.10 JAPANESE CODE 4.10.1 RAIL STRUCTUREINTERACTION ANALYSIS 4.10.2 DISPLACEMENTS REQUIREMENTS RELATED TO TRACK INTEGRITY 4.11 CHINESE CODE 4.12 AREMA

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5. OTHERS TECHNICAL REFERENTIAL

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5.1 SNCF DESIGN DOCUMENTS

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6. GENERAL CRITERIA TO BE CHECKED REGARDING RAIL STRUCTURE INTERACTION

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7. FEEDBACKS FROM EXISTING PROJECTS

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7.1 HYDERABAD METRO PROJECT (INDIA) 7.2 VIADUCT ON VIENNE – SEA (FRANCE) 7.2.1 INTRODUCTION 7.2.2 DESCRIPTION OF THE BRIDGE 7.2.3 TRACK/BRIDGE INTERACTION 7.3 TRAMWAY LINE

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7.4 METRO LINES 1, 2 7.5 DELHI AIRPORT LINE 8. INTERACTION 9. 9.1 9.2 9.3 9.4 9.5

CWRBIA SOFISTIK CWR-BUCKLE/INDY CWERRI MIDAS

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10. CONCLUSION

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11. APPENDIX 1: SIMPLIFIED METHOD TO CALCULATE RSI RADIAL FORCE IN CURVE

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1. INTRODUCTION This technical guide presents the specifications related to rail structure interaction from codes and technical recommendations documentsused by Systra on its projects. Feedbacks from existing project are also provided. The members of the technical group involved in this technical guideare listed below: · · · · · ·

Bajpai Purnima (India – Civil) Girardi Marcel (Paris - Track) Gogny Eric (Paris - Civil) Lamouroux Guillaume (Paris - Civil) Targoula Ifra (Paris - Civil) Wouts Ivan (China - coordinator)

Improvement in computationcapabilities has allowed extensive useof finite element modelling (FEM) and refinement in the analysis, but to apprehend rail structure interaction analysis in the design of railway structure remains a challenge today. The main difficulty is not the FEM calculation itself,but is the understanding of the phenomenon and is selecting appropriate standards and criteria. As the reader may notice during its reading, there is a wide variety of approach from standards and each standard may cover some cases and not others. In conclusion, there isn’t a unified theory regarding rail structure interaction. This report focuses on existing standards and in which cases they can be used. Standardsare presented in chapters 4 and 5. Chapter 6 provides a synthetic table of the criteria related to rail structure interaction. Cases not covered by standards require dedicated study to assess which criteria can safely be applied. Methodology to define criteria for these cases is out of the scope of this guide and will be the subject of further technical guides.

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2. TECHNICAL DESCRIPTION OF THE PHYSICAL PHENOMENON 2.1 INTRODUCTION The rail structure interaction analysis (RSI) is used for the design of railway bridges. We present here the physical phenomenon. ContinuousWeldedRails(CWR) are nowwidelyusedfor newand upgrading railway projects, from light transit system (as tramway) to High Speed Railway lines. Fig. 1

Slab track under construction

It has many advantages in term of passenger comfort, maintenance cost and safety. Nevertheless, in case of track laid on viaduct, special cares in the design of both track and viaduct have to be taken. The interaction between the tracks and the bridges can generate high forces which may damage the bridges and the tracks. It is necessary for both ballasted and ballastless track to evaluate the intensity of these forces and to assess the track and bridge compatibility. It is calledthe 'Track Structure Interaction' or ‘Rail Structure Interaction’. The scheme below represents the link between the railsand the decks through the fasteners,sleepers and ballast. Fig. 2

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Simplified model of the link between the rails and the bridge structures

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A relative movement between the rails and the decks generates a transfer of forces from one to the other. The graph here below shows the longitudinal displacements of rails and decks under one train braking on a bridge for a simple case with three simplespans between two abutments Fig. 3

Longitudinal displacements under braking loads

In this example, there are two tracks on the bridges. The braking loads are applied on one track, represented by the blue line. They are applied only on the part of this track above the second span. The loads are transferred to the bridge below the braking train through the fasteners, sleepers and ballast, but they are also transferred to the adjacent bridges and abutments through the rails. Therefore, even though the loads are applied on one structure only, all the bridge structures are moving in the longitudinal direction and the unloaded track is dragged by the moving bridges. The maximum longitudinal displacement of the decks (the line in black) is around 1.7mm. Without taking into account the rail structure interaction, the maximum displacement wouldbe 12mm (7times higher). This example shows that the structural behavior of the bridge-track system is dependent mainly on the Rail Structure Interaction. A good understanding of this phenomenon is necessary to perform a safe and cost efficient design. Rail Structure Interaction is at the frontier between two design specialties: Civil engineering and track engineering. To be properly carried out, it requires a good knowledgein both domains. Due to the lack of calculation power and track engineering expertise by most of bridge design companies, bridges were generally designed in the past using simple but very conservative rules in order to avoid any problem for the bridge and the track during train operation. These rules require having relatively short bridges and very stiff piers, so to avoid excessive deformations and displacements of the bridge structure. Their disadvantages can be summed up as follow: · ·

They are very conservative and lead to expensive design They cannot be applied in all cases. They mainly apply in the case of one deck between two abutments. They are not adapted to the case of long succession of span of various length and pier stiffness, which are commonly found on the new railway projects. Also are not covered tight curve, low and medium axle weight rolling stock, …..

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·

Without RSI calculations, it is not possible to identify the critical point along the line and to design alternate solution that satisfied the RSI requirements. Even though the substructures are designed using the simplified rules and are very stiff, the design may remain unsafe.

Today, with the extensiveuse of computerizedcalculations and expertisein track and civil engineering fields, it is possible to model the interaction between the rails and the structure. This new approach leads to optimization of the superstructure and substructure design. The horizontal loads (as braking and traction loads) on the pier can be divided by a factor up to 3 compare to the simplified methods. The minimumstiffness of the piers and foundations can be reduced by a factor up to 4. In case of a project in seismic area, the reduction of the pier stiffness leads to a reduction of the seismic forces. The quantity savings for the piers and foundations are then even higher. Only the critical parts of the line have strengthened piers, foundations and deck (on the contrary to the simplified rules whereall the piers and foundations are very stiff, even when it is not necessary ). The expertise in the Rail Structure Interaction is today a clear asset on the market for the design companies who are able to carry out the calculations without impacting or delaying the bridge design production. Based on its expertise in both civil engineering and track engineering, SYSTRA has developed several software specially dedicated to the Rail Structure Interaction Analysis.

2.2 BRIEF HISTORY OF THE CONTINUOUS WELDED RAIL There are different ways of joining rails together to form tracks. The traditional way of doing thi s, was to bolt rails together in what is known as jointed track. In this form of track, lengths of rail, usually around 20 meters long are laid and fixed to sleepers, and are joined to other lengths of rail with steel plates known as fishplates. Fig. 4

Fishplates

Fishplates are usually60 centimeters long, and are bolted through each side of the rail ends with bolts. Small gaps are deliberately left between the rails to allow for expansion of the railsin hot weather, the holes through which the fishplatebolts pass are oval to allow for expansion. Because of the small gaps left between the rails, when trains pass over jointed tracks they make a "clickety clack, clicketyclack" noise. Unless it is very well maintained, jointed track gives a fairly bumpy and uncomfortable ride, and is unsuitable for high speed trains because it is too weak. However it is still used on lower speed lines,unimportant lines, and sidings.

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Fig. 5

Welded rail

Most modern railways use continuous welded rail (CWR). In this form of track the rails are welded together over several kilometers (there is no maximum limit), to form one long continuous rail. Because there are few joints, this form of track is very strong and gives a smooth ride, and also needs less maintenance. Due its strength, trains travelling on CWR can travel at higher speeds. Welded railsare more expensive to lie than jointed tracks, but are significantly cheaper to maintain (for the same type of traffic). Rails expand in hot weather and shrink in cold weather. Because welded track has very few expansion joints, if no special measures are taken, it could become distorted in hot weather or crack in cold weather and cause a derailment. Fig. 6

Rail buckling in curve

Cracks and rupture of the rail are mainly due to high tension stresses in the rail which can be combined with initial construction defect or fatigue of the rail. It occurs generally at the bottom of the rail where the tension stresses are maximum. On the opposite, when under a longitudinal compressi ve force, track geometrical defects can be amplified over time and track buckling may occur. When designing railway bridges withcontinuouswelded rails, it isnecessary to assess thecompatibility between the tracks and the bridges in order to provide a safe design.

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2.3 EXPLANATIONS ON THE RAIL STRUCTURE INTERACTION The purpose of RSI is to assess the track stability and integrity. Computer model of track and structures are made in order to assess rail stresses and displacements under various load cases.With the process of destressing,rails are setat a zero stress state under a defined air temperature(known as the neutral temperature). This means that, at this temperature, the only stresses in the rail are the residual stresses due to the rail construction process and no force are transmitted to the bridge. Additional rail stresses are then generated by: · · · · · · ·

Variation of temperature in the rails Variation of temperature in the bridges below the track Horizontal loads due to the braking and traction Train live loads Moderate earthquake occurring during train operation Sudden breaking of a rail Track maintenance and temporary stages of the track construction

In addition to these load cases, any singularityin the laying of the track may also amplified rail stresses and RSI effects, such as rail expansion joints, turn-outs or change in fastening system types. These effects are described in the following sub-chapters.

2.3.1 Variation of temperature in the rails Stresses in the rail come mainly from the variation of temperature of the rail itself. Under sunshine, the rail temperature increase dramatically. Considering that the continuous welded rail has no expansion joint, rail expansion/contraction is restrained and rail stresses increase accordingly. Generally, stress in the railsdue to its variation of temperature is constant along the track and there is no transfer of force between the rails and the bridges, except if rail expansion joints or turnouts are set on bridges. Fig. 7

Stress in the rail under temperature variation

In areas without nearby singularity,rail stress dueto temperature variation in the rail can be calculated using the formula (in MN/m 2) s = a DT E, with a: rail expansion thermal coefficient, DT: rail temperature increase (°C) and E: rail modulus of elasticity (MN/m2).

2.3.2 Rail expansion joints In case of rail expansion joint (REJ),rail movement is free at the REJ location, as one side of the rail can freely move in regards to the other side. The transition zone between the joint where the stress in the rail is zero (free movement) and the point where the rail stress is constant (rail fully restrained)

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depends on the track (and bridge) characteristics. The scheme below shows the rail stress decrease near a rail expansion joint. Fig. 8

Stress in the rail under rail temperature variation near a REJ

In case of REJ set on a bridge, there are large transfers of forces between the rails and the bridges due to the large displacements of the rails. The transition length can be calculated using the following formula (in m) L = srail A / (F / s) with srail: rail stress under temperature variationin the rail (seeprevious chapter), A: Area of one rail (m 2 ), F: one fastener longitudinal restraint force (in MN, for one rail) and s: distance between fastener (m).

2.3.3 Turnouts and crossovers Turnouts and crossovers allow the train to change direction or track. They are described below: ·

A railway switch or turnout is a mechanical installation enabling railway trains to be guided from one track to another, such as at a railway junction or where a siding branches off. The turnout consists of three major parts: - Set of switches (switch blades) - Common crossing - Closure rail Fig. 9

·

Standard right hand turnout

A crossover is a pair of switches/turnouts that connects twoparallel rail tracks, allowing a train on one track to cross over to the other.

Various combinations exist, as shown below, and depending on the combination,impact on rail stress may also vary. As turnouts are not generally set on viaduct structure on major railway line, the impact of turnout on rail structure interaction is not described in detail in standards.

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Fig. 10

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Various type of turnouts and crossings

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Fig. 11

Various type of cross-overs

The impact on rail stress due to a turnout is explained belowfor a simple case. In case of turn-out, two tracks are linked by the turn-out track. There is a transition between two rails (outside the turn-out) to 4 rails (inside the turn-out). Rail stress distribution is disrupted by this transition. The peak stress in the rail is located at this transition as shown on the graph below for a temperature variation in therail. Fig. 12

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Rail internal forces due to rail temperature increase in a turnout

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Fig. 13

Rail stresses at turnout location under rail temperature variation

At the location of the peak rail stress, a 40% rail stress increase typically occurs in turnouts under rail temperature variation. Conservative measuresare generallyimplemented in order to set turnouts and crossing at a safe distance to other singularity, so that stress increases due to turnouts and others effects (bridge expansion joint for example) are not added.

2.3.4 Expansion/contraction of the bridge structures Another major source of rail stresses is theexpansion/contraction of thebridge structures below tracks under variation of temperature. Tracks tend to resist to the bridge displacements and rail stresses increase. The longer the bridge, the longer the rail stresses built up and risk of reaching rail stress unacceptable level increases. Therefore, expandable length of bridgeis often limited in order to avoid unacceptable rail stresses,requiring setting up rail expansion joints.The graph below showsthe effect of the bridge expansion on the rail stress for one simple span bridge between two abutments. Fig. 14

Rail structure interaction effect under bridge temperature variation

Fig. 15

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Rail stresses under bridge temperature variation

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2.3.5 Horizontal loads due to braking and traction During train operation, rail stresses are also induced by braking or traction of the trains. The braking/traction forces are transmitted to the supporting structure through the rails and the tracks. Fig. 16

Rail structure interaction effect under train braking over a bridge structure

Part of the braking/traction forces is directlytransmitted to the deck below the train, but part of these forces is also transmitted to the adjacent decks/abutments through the rails. In case of braking/traction force,it is important not only to check that the rail stresses are in theallowablerange, but also to check the relative displacements between the bridge and the track to prevent the risk of ballast destabilization. We show on the graph below the rail stresses under braking load on one track in case of a track supported by a succession of simple spans. The maximum and minimum rail stresses are found at the front and end of the braking train. Fig. 17

Rail structure interaction effect under train braking/accelerating over succession of spans

A train may brake and accelerate at multiple different positions, it is necessary to consider separate load cases for all the possible train positions (generally at each bridge expansion joint).

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2.3.6 Vertical loads due to running trains The deck deflection under running train also generates interaction between rail and structure. Due to the flexure of the structure, the top of the deck tends to move in the longitudinal direction as shown on the figure below. Fig. 18

Rail structure interaction effect under train vertical loads

The graph below shows the rail stresses with two tracks loaded. As expected, rail tensile stresses are found at both bridge expansion joints. Fig. 19

Rail stresses under train vertical loads

It is to be noted that the rail stresses are due to the relative longitudinal displacements betweenthe top of the deck and rail due to deck rotation under live loads.It is not related to the rail bending under wheel loads or deck rotation at bridge expansion joint.

2.3.7 Earthquake loads Under major earthquakes (with an return period of around 500 years), bridge are designed with the capacity limit, i.e. the bridge shall not collapse under major earthquake, but there is no requirement to prevent train derailment, rail failure or track buckling. In case of railway line in high seismic area, it may be required to check the safety of the track and passengers under a moderate earthquake(which has a short return period - typically 50years - and is more likely to occur during train operation life). In that case, bridge structures and track shall remain at the serviceability state after a moderate earthquake and train derailment is not allowed. The earthquake risk should bestudied morein detail if the lineis long, as the risk of a moderate earthquake at one point along the line is higher than at one location. Therefore, an 50 years return period at one location may be equivalent to a lower return period for the entire line. Ideally, after a moderate earthquake, train operation could immediately restart without need of inspection and repair.

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The rail structure interaction analysis under earthquake is not addressed in most regulations. RSI calculations were performed on French Mediterranean High Speed Line and Taipei-Kaoshiung High speed railway and Japanese codes provides information on train safety and track integrity under earthquake. Fig. 20

Rail stresses under moderate earthquake (imposed displacements)

Under moderate earthquake, on the French Mediterranean line, maximum relative displacement between two spans was limited to 20mm. On the Taipei-Kaoshiung line in Taiwan, maximum relative displacement between two spans was limited to 25mm under moderate earthquake (one third of the maximum site nominal acceleration +one train braking).

2.3.8 Sudden rail failure Another risk for the track is the sudden failure of one rail due to crack or defect. The internal forces built up in the rail due to temperature loads are then released and transferred to the structure and to the remaining rails. It has to be checked that the track-structure system remains at the serviceability state under this accidental situation. Fig. 21

Rail stresses after rail failure

The maximum allowable rail gap varies according to standards and projects characteristics (from 25mm to 100mm). If track circuit is used for train location, then the system can detect broken rail and immediately reduce allowable speed. Therefore, high allowable rail gap may be acceptable. If axle counter equipment are used for train location, broken rail cannot be immediately detected and more

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conservative valueshould be selected. The valuefor one project should be defined with the track and system specialties.

2.3.9 Track construction and maintenance Finally, the effect on the rails and the superstructure of the temporary works as track maintenance or the track construction stages has to be studied. This part requires a good knowledge of the track construction and maintenance procedures. Fig. 22

Track construction on bridges

For ballast track, the key parameter to prevent track buckling isthe transverseresistanceof the sleeper in the ballast bed. This parameter is related to the ballast compaction. Ballast compaction reaches its nominal value after 100000TBC (traffic tonnage), unless specifics tamping methods are used. Therefore, lower allowabletemperature variation and train speed should be defined for maintenance and tamping operation until traffictonnagereaches thedesiredvalues or sufficient ballast compaction level is artificially achieved using tampering machine. It is to be defined in coordination with track specialty. In case of ballastless track, the full restraining capacity is reached immediately after the rail is fixed to the fastening system. The key issue are the forces transferred to the bridge structure in construction and maintenance (see hereafter). For both ballast and ballastless track (but more critical for ballastless track) , the construction and maintenance operation may lead to high forces on the bridge structure. During a typical construction and maintenance, the rail segments (25m long) are welded together in a yard next to the line to form 500m rail. These rails are then transported on the line and set in the fasteners. They are then welded to form 1500m long continuous rails. The process of rail destressing can then start. The purpose of destressing is to set the rail in the fastening system at rail neutral temperature. If the ambient air temperature is equal to the defined neutral temperature, then the rails are simply set on the fastener, welded on to the other and fixed to the fasteners. Nevertheless, this may not be the case on some project, as the air temperature differs from rail neutral temperatureand variesalong the day.

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on pulling on rail ends in order for the rail to reach

(10°C). Then, for a L (

theoretical Tn temperature, a equal to 1.2E-Ta) a E = Later on, the air temperature increases to 25°C, then the rail stress diminishes to 0MN/m2 at 25°C. Therefore, its neutral temperature is defined as 25°C even it is fixed in the fasteners at 10°C. As the two rails of one track are pulled at the same time,in order for therail to expand 450mm, it is necessary to apply a jacking forceof [(Tn-Ta) a E]*2*A =582kN with the rail section A equal to 7700mm2. On bridges, the jacks are connected to the adjacent rails fixed to the decks and the bridge structure are to be designed to resist the transferredforces. Coordination between track and civil specialty is necessaryto assess the forces transferred to bridge structure during rail destressing. Impact of staggered track construction on bridge should be checked, as the rail destressing on one track may lead to bridge movements and impact the already built adjacent track. Finally, during maintenance, the track may be cut and temporary acts as a rail expansion joint (and applies large forceson the bridge structure). In order to mitigatethis impact,maintenanceprocedures should be defined with coordination between the track, operation and civil specialties.

2.3.10

Special case of a track laid in tight curve

For railway in urban area, track tight curves are often found due to the limited space available. In that case, the stresses in the rail tend to generate radial forces which are applied to the substructure through the sleepers, ballast and superstructure. Fig. 23

Radial effects of rail compressive internal forces in curve

If FEM software for RSI calculations can model the structures and tracks in 3D, it is possible to obtain the RSI radial forces. A simplified method to obtain the RSI radial force is shown in Appendix1.

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2.3.11 Others rail structure interaction effects Others effects are mentioned in codes or have been studied on previous projects: · · ·

Creep and shrinkage Temperature gradient Settlement

They are generally of smaller influence onthe resultsthan temperature,braking/traction or train loads. Creep and shrinkage is a long term process. It is generally not included in the load cases for RSI, as it is assumed the built-up rail stresses dissipate over time due to vibration when passing train. If it is required to take these effects into account, they can be combined with temperature loads instead of carrying out separate calculations, which would lead to unfavourable results. Temperature gradient is sometimes taken into account in RSI calculations. It generallyacts oppositeto live loads and therefore is not governing the design. Settlement is generally not included in the load cases for RSI unless large longitudinal movement of the structure are expected (rotation at top of pier).

2.3.12 Impact of local bridge deformations on track integrity Rail Structure Interaction is generally understoodas the risk of excessiverail stressesor displacements for ballast and ballastlesstrack on bridge. Nevertheless, local deformation and displacements at bridge expansion joints should be checked in order to prevent local ballast destabilization, excessive rail bending and excessiverail forces on fastening system (uplift, rail pad compression,transverse forces). This aspect of RSI is not often properly described in standards. Either,detailed modelling of bridge and track can be performed to calculate displacements, forces and stresses (see document “UIC recommendations for design and calculations of ballastless track”) or allowable displacements and deformation criteria can be used (refer to Japanese standards). The main criteria defined in the various standards are (see figure below): · · ·

Rotation of bearings under live loads near expansion joint Relative vertical and transverse displacements between two adjacent structures Maximum uplift and compression forces on the fastening system Fig. 24

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Alignment irregularity and rotation checks in Japanese code

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Fig. 25 Compression/tension in fasteners, allowable transverse displacements and method to reduce vertical relative displacement at joint for track with grade (“UIC recommendations for design and calculations of ballastless track”)

2.4 Summary of the main requirements related to track integrity The main requirements to assess the track stability are given in the table below. Tab. 1

Track

Ballast track

Items checked for Rail Structure Interaction

Risk Maximum compressive rail stress

Check Track buckling

Maximum tensile rail stress

Rail yielding

Horizontal relative displacement between two adjacent bridge structures

Ballast destabilization

Horizontal relative displacement between the rail and the bridge structure Horizontal relative displacement between the top of two adjacent deck

Ballast destabilization Ballast destabilization

Vertical relativedisplacement between the top of two adjacent decks Horizontal relative displacement between the top of two adjacent decks

Rail yielding and excessive fastener uplift/compression Rail yielding, excessive fastener transverse loads and reduction of sleeper ballast resistance Vertical angular rotation between the top of Rail yielding and excessive two adjacent decks fastener uplift/compression Horizontal angular rotation between the top Rail yielding, excessive fastener of two adjacent decks transverse loads and reduction of sleeper ballast resistance

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Track

Ballastless track

Risk Maximum compressive rail stress

Check Rail yielding

Maximum tensile rail stress

Rail yielding

Vertical relativedisplacement between the top of two adjacent decks

Rail yielding and excessive fastener uplift/compression

Horizontal relative displacement between the top of two adjacent decks Vertical angular rotation between the top of two adjacent decks

Rail yielding and excessive fastener transverse loads Rail yielding and excessive fastener uplift/compression

Horizontal angular rotation between the top Rail yielding and excessive of two adjacent decks fastener transverse loads Other deformation criteria exist for railway bridge design, related to passenger comfort, dynamic behavior or running safety (derailment risks).

Fig. 26

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Measurement of transverse resistance of the track

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3. PRESENTATION OF TRACK SYSTEMS In this chapter, the main track systems are presented: · · ·

Ballasted track Slab track Embedded rail system

3.1 BALLASTED TRACK Ballasted track is the first type of railway track and can be considered the classical railway track. The principle of the ballasted track structure has not changed substantially since the beginning of railway, but it has been subjected to significant developments: continuous welded rail, concrete sleepers, heavier rail profiles, elastic fastenings, mechanization of maintenance and introduction of advanced measuring equipment and management systems. Ballasted track can comply with all type of railway from heavy fret to high speed rail. Fig. 27

Ballasted track

In terms of rail structure interaction, the track-bridge interaction depends mainly on the sleeper behavior in the ballast, as the fastening system tends to be significantly more rigid. A critical aspect of the rail structure interaction of ballasted track is the risk of track buckling under compressive stress in the rail. This aspect is studied in codes (such as UIC 774-3 and UIC 720), but it is reminded that these codes only covers certain types of ballasted track and it is necessary to check for each project if they are applicable. This is particularly critical in areas with high temperature variation, alignment with short radii curves and heavy train.

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3.2 SLAB TRACK Slab track has been developed since the 70s and is more and more common on project as it requires much less maintenance than ballasted track. For high speed railway, it is prevalent in Germany, China and Japan. Numerous slab track system have been developed in order to increase construction speed and reduce cost. We shortly present below the main system of slab track. Fig. 28

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Rheda system

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Fig. 29

Züblin system (left) and Heitkamp system (right)

Fig. 30

Fig. 31

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Stedef system

ATD system

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Fig. 32

Shinkansen system

Fig. 33

Fig. 34

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Bögl system

OBB-Porr system

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Fig. 35

Fig. 36

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Chinese CRTS III

Alstom Appitrack system

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The photos above illustrate the numerous types of slab track developed over the years by either private companies (ex. Rheda, Appitrack) or state (ex. CRTS III in China). New track slab system relies heavily on automatization and mechanization of the construction process in order to speed up construction and reduce cost. It is an innovative and competing market. For slab track, the main parameter related to the longitudinal restraint of the rail and the rail structure interaction is the type of fastening system selected, as there is no ballast. Most slab track systems can be adapted to various types of fastening systems. Slab track is not subject to track buckling, as the rails are firmly restrained transversallyin the fastening system. Nevertheless, due to the overall rigidity of the system compare to ballasted track, stringent criteria related to long term bridge deformations and relative deformations/displacements at bridge expansion joint between adjacent structures are defined. In terms of rail structure interaction, one slab track solution significantly differs from the others, as it avoids any form of rail structure interaction. It is the Bögl prefabricated slab track system for bridge (or its Chinese equivalent CRTS II). Bögl Slab track product is based on 9 tons precast slabs. It was developed by the German company Bögl and first used on the NBS Nuremberg–Ingolstadt line, a 70km high speed railway linebuilt in 2006. The line was mainly built at grade, with onlytwo small viaduct where a special type of precast slab was used (with shear key underneath). Fig. 37

Bögl typical slab track

The slab track system used on viaducts on the NBS Nuremberg-Ingolstadt lineis based on precast slab track with shear key, contrary to the slab on subgrade, without shear key.Each slab is anchored in the track bed. Therefore, construction on viaduct was complexand could not cope with the Beijing Tianjin High Speed Railway line schedule. A new construction method was implemented for this project.

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In order to use the same precast slab on bridge as on subgrade, Bögl developed in 2005 and 2006, for the Beijing Tianjin High Speed Railway line, a new concept: The support of the precast slab on bridge is made of a continuous reinforced concrete slab. It provides a continuous support over the entire length of the viaduct (i.e. no displacement of the support and expansion joints), similar to subgrade. The installation of the precast slab is then greatly facilitated. The precast slabs are laid on a continuous reinforced concrete layer that goes from one end of the viaduct to the other end without joint, as shown on the figures below. Fig. 38

Continuous concrete layer along a viaduct (profile and cross section)

If the design and installation of the precast slab are simplified, such design requires to build a highly reinforced continuous concrete layer over the viaduct, restrained at both ends in the embankments. This concrete layer is set on a three layers geotextilein order to reducefriction between concrete layer and deck. It is restrained in the decks at each pier fixed bearings. This reinforced continuous layer can extend over several tens of kilometers, depending on the length of the viaduct. Its design and construction methods are complex and difficult to implement. This design (named CRTS II in China) has been widely used in China for their high speed railway network. One unintended advantage is that there is no morerail structureinteractioneffect on viaduct (as the continuous concrete layer is restrained from extension and contraction), therefore there is no need of rail expansion joint in case of long bridge. The Bögl and equivalent CRTS II remain exceptions in the existing track slab systems, which for most of them requires studying the rail structure interaction in case of viaduct. In China, the more typical CRTS III track system is now preferred to CRTS II, as it is easier to build. Due to the wide range of slab track system existing today, it is important to check if the design to be implemented on the project may affect the way rail structure interaction studies are carried out. This can be only done on a case by case basis.

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3.3 CONTINUOUS RAIL SUPPORT SYSTEM When the continuous rail is continuously elastically supported by the concrete bearing layer either embedded or clamped then it belongs to the continuous rail support systems. The embedded rail structure (ERS) is a continuous elastically supported rail by means of a compound such as cork and polyurethane, as shown on the figure below. The rail fixation is established by an elastic compound surrounding the whole rail profile except the rail head. This system includes the full range from highspeed tracks to light rail. Fig. 39

Embedded rail structure (ERS)

As for slab track, this is a constantly innovative market with numerous proprietary systems. Contrary to slab track, the longitudinal restraint parameter is not govern by the fastening system, but by the compound mechanical behavior set in between the rail and the supporting concrete structure. UIC 774-3 provides longitudinal restraint parameters related to embedded rail systems, but it is necessary to check with the manufacturer selected for the project the exact values and requirements of its system. This is particularly relevant when new embedded rail system requires non-typical rail profile, as shown below. Fig. 40

Comparison between UIC 54 rail profile and new SA42 rail profile solutions

We present below various embedded rail systems. Fig. 41

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INFUNDO-EDILON system

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Fig. 42

Fig. 43

Fig. 44

BBERS system

Cocon track system

Vanguard & KES track system

Allowablebridgeexpandable lengths are expected to be shorter for embedded rail systemscompared to ballasted and slab track systems, as the longitudinal restraint created by the compound is higher than typical fastening system. Allowable relative angular rotations and displacements at bridge expansion joint shall be defined by the manufacturer. Therefore, prior to rail structure interaction studies, it is necessary to achieve a good understanding of the track system selected for the project.

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4. PRESENTATION OF STANDARDS AND PRACTICES REGARDING RAIL STRUCTURE INTERACTION A key issue related to rail structure interaction and compatibility between track systemand supporting bridge system is the lack of coherent theory governing all aspects of the problem. Codes and standards generally cover part of the issue and apply only to certain particular cases (for example minimum alignment curve radii). The following sub-chapters present the main codes used for RSI analysis. The purpose of the description for each code is not to replace the existingstandard but to provide a synthetic explanation of the standard criteria and limitations.

4.1 UIC 774-3 4.1.1 Description UIC 774-3 code is the document most referred for RSI studies. It presents CWR phenomenon and provides calculation methods, parameters and criteria to carry out RSI analysis. Simplified rules are also provided in case of typical bridge/track. Parameters affecting the phenomenon are detailed in the document: · ·

The bridge: expansionlength, typeof structural system (Deck bridge or Through girder bridge), height of the deck, support stiffness, etc. The track: type of the track (ballasted or ballastless), resistance of the track.

The loads relevant to interaction effects are specified in the chapter §1.4. The UIC leaflet provides various methods to calculate CWR effects, they are classified in two groups: · ·

Simplified methods, using diagrams and formula, General methods, based on FEM numerical analysis.

Simplified methods apply only in typical cases (one bridge in between abutments, viaduct with succession of identical structure without large variation of pier stiffness, …). They were defined for railway line projects in Europe, where number of bridge is limited and typical. They are considered conservative and may lead to very robust bridge structure. They are seldom used on new projects at Systra. Characteristics values of track resistance are provided in the standards for typical discrete fastening and embedded rail systems. For embedded rail systems, it is necessary to confirm with the manufacturer the exact characteristics and requirements of the system prior to rail structure interaction analysis.

4.1.2 Loading Actions to be taken into account for the rail structure interaction are : · Actions due to temperature In the case of CWR without rail expansion joint, variation of temperature in the rail does not cause any rail displacement and, therefore, does not generate any interaction between the

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track and the bridge. In that case, only actions due to bridge temperature can be taken into account. o Uniform variation in the deck: ΔTN o A varying temperature difference component about vertical axis in the bridge girder (temperature gradient)

·

When rail temperature needs to be considered, it is added to the above effects: o Uniform variation in the deck: ΔTN, o A varying temperature difference component about vertical axis in the bridge girder, o Uniform variation in the rail: ΔTR. Actions due to rail traffic The load model are based on the UIC load models LM71 and LM SW. For the track/bridge interaction, the dynamic factor φ has to be applied on vertical load model and the α factor has to be applied to horizontal and vertical load model as well. UIC 774-3 has been defined for railway project, hence the use of the load model UIC LM71. There is no mention of metro or tramway in the document. Nevertheless, it is customary to use the standard criteria with adapted traffic loading in case of metro or tramway. As metro and tramway wheel loads are lighter than UIC (250kN), it is assumed that this is a conservative approach in terms of rail stress.

The load combinations are: · · ·

For the calculation of the total support reaction: equivalent to a Ultimate Limit State with combination factors, For the calculation of the rail stresses: equivalent to an Ultimate Limit State with combination factors which are equal to 1, For the calculation of displacement of the deck or rail track: equivalent to a Service Limit State with combination factors which are equal to 1.

4.1.3 Criteria and range of application 4.1.3.1 Criteria The basic assumptions for the criteria are: · · · · · ·

Ballasted track UIC 60 rail track Straight Alignment or curve with R≥ 1500m Rail steel grade 900MN/m2 ΔTN ≤ 35°K ΔTR ≤ 50°K

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Tab. 2

Track criteria for Rail Structure Interaction

Criteria Additional compressive rail stress

Loads Temperature and rail (horizontal and vertical)

Additional tensile rail stress

Temperature and rail (horizontal and vertical)

traffic loads

Limit value ≤ 72 MN/m2

traffic loads

≤ 92 MN/m2

Relative displacement between the Rail Traffic loads (horizontal) deck and the rail

δh ≤ 4 mm

If different rail type than UIC 60 are be used on the project, specifications have to be defined for the limit stresses. It is to be noted that these limit values are valid only for track radius higher or equal to 1500m. Therefore, these limit values (specifically compressive stress related to track buckling) are to be reduced in case of lower radii. These criteria can be used with different bridge temperature variation if FEM analysis is carrying on, as bridge temperature variation is on load applied in the FEManalysis. The criteria above exclude the effect of rail temperature variation. In case the rail temperature variation exceeds 50°K, the remaining allowablerail stress (compressive and tensile) shall be reduced by (ΔTR-50) a E. As a, example, if on one project, positive rail temperature variation is 55°K, then the maximum allowable compressive rail stress is 72MN/m 2 – (55-50)x1.2E-5x210000 = 59.4MN/m2 . Tab. 3

Criteria Absolute horizontal displacement of the deck

Bridge criteria for Rail Structure Interaction

Loads Rail Traffic loads (horizontal)

Limit value δh ≤ 5mm with CWR δh ≤ 5mm with 1 REJ δh ≤ 30mm with 2 REJ and the ballast is continuous. δh ≥ 30mm with 2 REJ and the ballast is provided with a movement gap

Displacement between the top of the deck end

Rail Traffic loads (Vertical)

δθh ≤ 8mm with CWR δv no limit value in this UIC leaflet, refer to relevant authority δθh ≤ 8mm with 1 REJ, criteria at the deck end without REJ δv no limit value in this UIC leaflet, refer to relevant authority δθh no limit value with 2REJ δv no limit value in this UIC leaflet, refer to relevant authority

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Notes: REJ : Rail Expansion Joint CWR : Continuous welded rail. In the table, “CWR” means CWR and no REJ near to the bridge and “with REJ” means CWR and REJ.

4.1.3.2 Range of application As mentioned previously, the basic assumptions for the criteria are: · · · · · ·

Ballasted track UIC 60 rail track Straigth Alignment or curve with R≥ 1500m Rail steel grade 900MN/m2 ΔTN ≤ 35°K ΔTR ≤ 50°K

Two methods exist and can be used depending of the project characteristics. ·

Simplified methods (UIC 774-3 §1.6)

The simplified methods : Pre-dimensioning method (§1.6.1), Calculations without interaction (Point 2 §1.6.2.1) and Calculations with interaction (Point 3 §1.6.2.2), the limit of application is defined in the UIC leaflet. However one main condition can be applied on tempe rature load for all methods as follows: ΔTN ≤ 35°C ; ΔTR ≤ 50°C ; ΔT ≤ 20°C With ΔT is the Temperature difference between the track and the deck. Except the Pre-dimensioning method, which is limited to calculation of support reaction, the other methods allow to check each criteria to be met related to the track and to the deck and allow to calculate the support reactions. Only the method Point 3covers the case of consecutive decks, but it coversa narrow and limited range of bridge/track arrangement. The two others “Simplified methods” cover the case of an “one deck” (continuous or single deck). ·

General Methods

General recommendations for computer-assisted interaction analysis is given in the §1.7. The model should include a part of the track on the adjacent embankments over at least 100 m. A finite-element model includes track and the deck elements, modelled discretely.

4.1.4 Conclusion UIC 774-3 is the most referred standards for issues related to rail structure interaction. Nevertheless, it was written with standard railway, ballasted track and lack of powerful tool for FEManalysis in mind and only covered a limited range of cases. Therefore, it is necessary to adjust criteria when project characteristics deviate from the range of application (temperature vari ation, track radius, ….).

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4.2 UIC 776 4.2.1 Description The UIC 776 leaflet has three parts : · · ·

Part 1: Describes the loads to be taken into account in the design of railway bridges, Part 2: Specify the design requirements for rail bridges, as regards train/track/b ridge interaction phenomena, specifically related to train speed. Part 3: Bridge deformations

4.2.2 Loading Traffic load model are defined with the UIC model as UIC LM71, UIC SW and « unloaded train ». It is to be noted that acceleration and braking forces are not multiplied by the dynamic factor φ, but are multiplied by the α factor, which is related to the train weight.

4.2.3 Criteria Deformations and displacements criteria are based on static loading only. Tab. 4

Bridge criteria for Rail Structure Interaction

Criteria Expandable length Lt for ballasted track

Loads Temperature load

Limit value Lt ≤ 60m (steel bridge)

Displacement between the top of the deck end

Rail Traffic loads (Vertical)

δh ≤ 10mm with CWR

Absolute horizontal displacement of the deck

Rail Traffic loads (horizontal)

δh ≤ 5mm with CWR

Vertical displacement between the top of the deck end

Rail Traffic loads (Vertical)

Lt ≤ 90m (concrete / mixed bridge)

δh ≤ 30mm with REJ δv ≤ 3 mm ballasted track δv ≤ 1.5 mm slab track

These criteria are similar to UIC 774-3. The expandable length for ballasted track are based on the typical values used by the French SNCF when computerized analysis was not widely available. The UIC 776-3, dated 1989, presents some information on the criteria to be used at bridge joint in order to avoid excessive rail stress and fastener uplift. The criteria, to be complied with under traffic loads plus temperature gradient, are given in the table below.

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Tab. 5

Bridge criteria for Rail Structure Interaction

Ballasted track on both sides 0.010 rad

Ballastless track on one side 0.005 rad

Ballastless track on both sides

Uplift

6 mm

3 mm

Bending moment in rail

50kNm

50kNm

Specific calculations required

Angular variation

Rail stress due to bridge deformations at bridge expansion joint (see figure below) are limited to 80MN/m2. Fig. 45

Bridge deformation leading to rail stress at bridge expansion joint

It is to be noted that UIC 776-3 has not been updated since its first issue in 1989. For ballastless track, the “UIC recommendation for design and calculations of ballastless track” provides information regarding fasteners uplift and compression.

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4.3 UIC RECOMMENDATIONS FOR DESIGN AND CALCULATIONS OF BALLASTLESS TRACK 4.3.1 Description The “UIC - Recommendations for Design & calculation of Ballastless track” is based on German experiences for ballastless track. Criteria and calculation methods for this type of track, are described in this document. It can be considered as an addition to the UIC 774-3 which was mainly written with ballasted track in mind. The “UIC - Recommendations for Design& calculation of Ballastless track” provides information on the use of zero longitudinal restraint fastening system in case of long bridge in order to mitigate rail stress. In that case, it is necessary to limit broken rail gap (which increase with decreasing longitudinal restraint) in order to avoid traffic disruption in case of broken rail. Reference to SNCF practice (30mm gap) is provided. Allowable rail gap varies according to type of line, track, track radius and signalling system (track circuit or axle counter). The allowable rail gap should be defined in coordination with track and system specialty. A wide range of low longitudinal restraint fastening syste m exists today with varying restraint forces. The fastening system and the length of application on bridge should be defined in coordination with track specialty.

4.3.2 Loading For rail structure interaction calculations (rail stresses), the loads to be applied to the rail and the bridge are based on the Eurocode. For displacement check (uplift/compression), loads and load combinationsare given in the document. The loading to be considered are: · · · · · · ·

Real trains including dynamicfactor Individual wheel load including dynamic factor Traction and braking Temperature and temperature gradient Residual creep and shrinkage after completion of the track Residual settlement after completion of the track Additional permanent loads after completion of the track (SIDL)

4.3.3 Criteria and range of application Most of the criteria to be checked for a ballasted track are no more valid because they are related to the ballast stability. The criteria for ballastless track are given below.

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Tab. 6

Bridge criteria for Rail Structure Interaction

Criteria Additional compressive rail stress

Loads Limit value Temperature and rail traffic ≤ 92 MPa loads (horizontal and vertical)

Additional tensile rail stress

Temperature and rail traffic ≤ 92 MPa loads (horizontal and vertical)

Relative vertical displacement between the rail and the abutment or another bridge girder end. Uplift force in the rail fasteners must be checked

Rail Traffic loads (vertical), temperature difference inthe bridge girder or/and the piers.

3 mm, for maximum speeds on site of 160 km/h, 2 mm, for maximum speeds greater than 160 km/h.

UIC recommendations for ballastless track specifies additional checks to Eurocode 1991-2. Uplift/compression of fastening system and transverse relative displacements. Design method to mitigate unfavourable effects are also suggested (compensation slab). Fig. 46

Fig. 47

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Effect of rotation and settlement on fastening system compression and uplift

Restraining transverse relative displacement and case of viaduct in slope

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According to the UIC recommendations for ballastlesstrack, a key issue is the fastener uplift forceand rail pad compression force near bridge expansion joint. Fig. 48

Fastener uplift and rail pad compression force

They can be calculated by modelling the bridge track system and apply loadings. Typical fastening system parameters (Voosloh Innovia 300) are: · · · · ·

Static uplift rail fastening stiffness Cstat =30 kN/mm at -20°C Dynamic uplift rail fastening stiffness Cdyn =30 kN/mm at +20°C Dynamic uplift rail fastening stiffness Cdyn = 60 kN/mm at -20°C Permissible compression of the elastic pad Zul =2.5 mm Permissible uplifting force of rail fastening Z = 12 kN

The values of the vertical fastener stiffness and permissible uplift/compression force have to be given by the track specialty.

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4.4 UIC 720 UIC 720 title is “Laying and Maintenance of CWR track”. The document is not directly link ed to the issue of rail structure interaction, as it mainly intends to define allowable temperature variation for ballasted track to prevent track buckling. Themain purposeis to explain theparameters affecting track stability and to set out methodology for ensuring stability and safety of CWR. Nevertheless, it providesuseful information regarding the rail structure interaction issue and allowable compressive stress in the rail for various type of ballasted track and alignment curve.

4.4.1 Parameters affecting ballasted track stability The parameters listed in the UIC 720 impacting ballasted track stability are given below. More explanations are provided in the UIC 720. · · · · · · · · · · · · · · · ·

Rails Fastening system Type and spacing of sleepers Size, shape, granulometry, compaction and cleanness of ballast Track defect Track geometry Nominal temperature, stress free temperature Maximum and minimum temperature in the rail Subgrade characteristics Vehicle parameters Maintenance works (compacted state of ballast) Bridge (track on bridge or near abutment) Tunnel and deep trench (affecting rail temperaturelocally) Type of braking (Eddy current) Turnouts Track spacing variation

Based on the parameters above and the track buckling theory, it is possible to defined an allowable temperature increaseTall, which is related to the maximum allowable compressive stress in the rail, as defined inthe UIC 774-3. In case of new project, these information are generally not availableto define accurately the allowablecompressivestress in the rail. Therefore, UIC 720 refers to UIC 774-3 and UIC 717 to provide support for rail structure interaction. UIC 774-3 provides allowablecompressivestress for ballasted track for rail structure interaction studies,but it appliesonly for the most common cases. UIC 720 provides corresponding values for various cases and may be useful when the ballasted track characteristics deviates from UIC 774-3.

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4.4.2 Definition of rail temperatures UIC 720 provides definition of rail temperatures and method to calculate the maximum variations of rail temperature, useful for rail structure interaction analysis. Average temperature Tm: Tm = (Tmax+Tmin)/2 Note: the rail temperature Tmax and Tmin differ from air temperature (due to sunshine effect for example) Nominal temperature Ts: Optimal fixation temperature of the rails Ts = Tm + [additional temperature between 0°C and 10°C] Fixation temperature Tf: Rail temperaturewhen the rail is restrained by the fasteners Tf = Ts +/- 3°C Neutral temperature Tn: No rail stress temperature Tn = Tf – SFTN with SFTN (Stress FreeTemperature variation safetyfactor) chosen between5°C and 10°C Allowabletemperature Tall: maximum allowableincrease of temperature in the rail Tall > Tmax – Tn

4.4.3 Type of track studied in UIC 720 Based on the parameters defined above, UIC 720 provides the calculation methodology and suggests the use of dedicated software to calculate allowable temperatures (CWERRI and CWR-BUCKLE). For typical tracks and projects, the allowable temperature are provided in the UIC 720. The typical tracks studied are: Tab. 7

Studied track table

Radius in curve (m)

Sleeper (tan j)

Straight

Concrete 0.86

Main line

900

Concrete 0.86

Main line

900

Wood 1.2

No.

Type High speed

1

2

3

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Ballast trans. res. (kN/m’) 10/10 15/12 20/16 10/10 15/12 20/16 7/7 10/10 15/12

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75/150

Track defect (mm) 8/12/16

75/150

10/14/18

150/250

10/14/18

Fastener tors. Res.

(kNm/rad/m’)

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Radius in curve (m)

Sleeper (tan j)

Secondary line

600

Concrete 0.86

Secondary line

600

Wood 1.2

Freight line

300

Concrete 0.86

Freight line

300

Wood 1.2

No.

Type

4

5

6

7

Ballast trans. res. (kN/m’) 10/10 15/12 20/16

75/150

Track defect (mm) 14/18/22

7/7 10/10 15/12 10/10 15/12 20/16

150/250

14/18/22

75/150

14/22/30

7/7 10/10 15/12

150/250

14/22/30

Fastener tors. Res.

(kNm/rad/m’)

Refer to UIC 720 for more details. The allowable temperatures, calculatedwith various hypotheses and two different software, are given in the graphs below. Fig. 49

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Allowable temperatures for track type 1 to 3

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Fig. 50

Allowable temperature for track type 4 to 7

These allowable temperature Tall are the allowable temperature increased compared to the neutral temperature defined above.

4.4.4 Equivalent compressive allowable stress for rail structure interaction studies As the rail is considered infinitely continuous, there is a direct relationship between the allowable temperature Tall and the allowablecompressivestress. This relationship is defined by the formula sall = a E DTall, with a the expansion coefficient of the rail (1.2E-5/°C) and E the elasticity modulus of the rail (210000MN/m2). The allowable stress/temperature is to be checked under the following loadings: · · ·

Rail temperature variation (increase), including sunshine effect Additional rail temperatureincreasedue to Eddy current brakes Effects of Rail Structure Interaction

Based on the graph above, for the case 1 (High speed railway in straight alignment), the allowable temperature Tall is around 77°C (depending on hypotheses and software used). Considering a 50°K rail temperature variation (Chapter B.4 of the UIC 720 considers 40°K for the rail temperature variation,

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excluding Eddycurrent brake, but UIC 774-3considers 50°K) and absence of Eddy current brakes effect, the remaining allowable stress for Rail Structure Interaction in compression is: sRSI = 1.2E-5 x 210000 x (77-50) = 68MN/m2 This value is close to the UIC 774-3 compressive allowablestress (72MN/m2) typically used on railway project. Nevertheless, the hypothesis are different, as the calculation above is based on favorable hypotheses (High Speed Railway line in straight alignment) and UIC 774-3 applies for various type of track, train and alignment (1500m>900m). If case 2 (main line with radius of 900m), closer to UIC 7743 parameters, is used, then the allowable temperature Tall is only 68°C and the remaining allowable stress for Rail Structure Interaction is reduced to: sRSI = 1.2E-5 x 210000 x (68-50) = 45MN/m2 This illustrates a key issue of Rail Structure Analysis. Standards and codes criteria are not consistent and there is no unified approach of this issue. Depending on the focus of a standard or code (track for UIC 720 and bridge/track interaction for UIC 774-3), seemingly conflicting requirements are defined.

4.4.5 Conclusion UIC 720 is related to “Laying and Maintenance of CWR track” and specifically the buckling risk calculation of ballasted track depending on various parameters. It provides a calculation methods to assess the allowable stress for Rail Structure Interaction. Nevertheless, the use of UIC 720 to define allowablerail stress for Rail Structure Interaction should be carefully consider, as it is not consistent with the UIC 774-3.

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4.5 EUROCODE 1991-2 The part of the Eurocode 1991-2 related to rail structure interaction is based on the UIC 774-3.

4.5.1 Description The section 6 covers the Rail Traffic actions, and the track/bridge interaction is defined at the chapter §6.5.4. The general principles of combined response of structure and track to variable actions are shortly presented. The requirements are valid for conventional ballasted track. Parameters affecting the phenomenon are detailed, they are listed below: · ·

The bridge: expansionlength, type of structural system (Deck bridge or Through girder bridge), height of the deck, support stiffness, etc. The track: type of the track (ballasted or ballastless), resistance of the track.

The cases that could lead to interaction effects are specified in the chapter §6.5.4.3. The Eurocode suggests many methods to calculate CWR effects, they are classified in two groups: · ·

Simplified methods, based on formula (§6.5.4.6.1and the appendix G), General methods, based on numerical analysis, detailed in chapters 6.5.4.2.to 6.5.4.4.

As for the UIC 774-3, the simplified methods can be used only in some specific and typical cases. As bridge and track layout on new projects are more and more complex, they are less and less u sed.

4.5.2 Loading Loadings defined in the Eurocode are similar to the UIC 774-3. They are listed below: · · · · ·

Train live static loads Braking/traction Linear temperature variation in bridge and rail Creep and shrinkage Temperature gradient in bridge

Eurocode mentions that creep, shrinkage and temperature gradient are to be considered for calculation of deck rotation at ends and corresponding longitudinal displacements. UIC 774-3 also considered these loads (+settlement) to have “minor” effects on rail structure interaction. It remains matter of interpretation if they should be considered in the calculation of the rail stresses. The main loads are described below: ·

·

Actions due to rail traffic – vertical loads The load model are based on the UIC static load models UIC LM71 and UIC LM SW for the vertical loads, factored with the α factor defined in the Eurocode. Actions due to rail traffic – braking and traction loads Braking load is 20kN/m applied over an influence length to reach a total of 6000kN (In French National Appendix, the value is increased to 10000kN for freight line). Traction load is 33kN/m applied over an influence length to reach a total of 1000kN. For the track/bridge interaction, the α factor has to be applied to horizontal loads.

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·

For dedicated lines, these values can be adjusted to 25% of the real train static loads (with maximum of 6000kN and 1000kN respectively for braking and traction). Actions due to temperature The Eurocode refers to the EN 1991-1-5 for the Temperature loads. Then only the uniform variation of temperature is described: o Uniform variation in the deck: ΔTN, And combination factor ϒ and Ψ are equal to 1. Only in the simplified method is a variation of temperature in the rail given o Uniform variation in the rail: ΔTr =50°K And a maximum difference of temperature between the rail and the deck |ΔTN - ΔTr| ≤ 20 Kelvin

The rules of combinations are defined in the chapter §6.5.4.4 (4), as below: · ·

For the calculation of the total support reaction: equivalent to a Ultimate Limit State with combination factors, For the calculation of the rail stresses: equivalent to an Ultimate Limit State with combination factors which are equal to 1,

A linear superimposition of results of each action applied to the system Track/Bridge may be applied.

4.5.3 Criteria and range of application The rail structure interaction criteria apply to ballasted track. No detail information is provided for ballastlesstrack, and, on project, Eurocode istypically used with the document “UIC Recommendations for design and calculations of ballastless track”.

4.5.3.1 Criteria The basic assumptions for the criteria are: · · · ·

Ballasted track (at least 30 cm consolidated ballast) UIC 60 rail track Straight alignment or curve with R ≥ 1500m Rail steel grade 900MN/m2 Tab. 8

Bridge criteria for Rail Structure Interaction

Criteria Additional compressive rail stress

Loads Limit value Temperature and rail traffic ≤ 72 MPa loads (horizontal and vertical)

Additional tensile rail stress

Temperature and rail traffic ≤ 92 MPa loads (horizontal and vertical)

If different rail type than UIC 60 are be used on the project, specifications will be defined for the limit stresses.

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Tab. 9

Criteria Absolute horizontal displacement of the deck

Bridge criteria for Rail Structure Interaction

Loads Rail Traffic loads (horizontal)

Limit value δh ≤ 5mm with CWR δh ≤ 5mm with 1 REJ δh ≤ 30mm with 2 REJ and the ballast is continuous. δh ≥ 30mm with 2 REJ and the ballast is provided with a movement gap

Horizontal displacement between the top of the deck end

Rail Traffic loads (Vertical)

δH ≤ 8mm when the combined behaviour of structure and track is taken into account δH ≤ 10mm when the combined behaviour of structure and track is negleted.

Vertical displacement of deck at bridge ends

Variable actions

3mm for speed below 160km/h 2mm for speed below 160km/h

In case of ballastless track, Eurocode requires verification of uplift for fastening system due to the bridge rotation and vertical relative displacements at bridge expansion joint, but no methodology or criteria is provided.

4.5.3.2 Range of application ·

Simplified Method

The two « Simplified » Methods are presented in the document: Method described at §6.5.4.6.1 and AppendixG. Range of application are definedfor each. It is important to notice that they can be applied only if the following temperature variation conditions are in the range defined below: ΔTN ≤ 35°C ; ΔTR ≤ 50°C ; ΔT ≤ 20°C With

ΔTN is the bridge temperature variation ΔTR is the rail temperature variation ΔT is the Temperature difference between the track and the deck

Compliance with the RSI criteria is based on deformation, stiffness and other criteria, rail stresses are not calculated.

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One of the conditions is based on the bridge expansion length, for the Simplified Method (§6.5.4.6.1), the maximum expansion length is 100 m. Whereas the appendix G differentiates: · ·

Concrete or composite bridge, the maximum expansion length is 90m, Steel bridge, the maximum expansion length is 60m.

For the two methods, checks of the structure displacements and deformations are carried out without considering the track structure interaction. ·

General Method

The Eurocode does not provide any limitation of application of the numeric analysis. The approach is similar to UIC 774-3, and limitation of UIC 774-3 should also applied for Eurocode.

4.5.4 Conclusion As for UIC 774-3, which is the basis of Eurocode regarding rail structure interaction, the standard applies mainly to ballast track and covers longitudinal effects of rail structureinteraction. Effect of local deformations of bridge at bridge expansion joint are not covered or described in detail, especially for ballastless track.

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4.6 EN 16432 “BALLASTLESS TRACK SYSTEM” The EN 16432 “BALLASTLESS TRACK SYSTEM” defines the general requirements concerning the design and acceptance of ballastless track systems. It is applicable for high speed and conventional railway applications up to 250kN axle load. This standard applies to ballastless track systems including: · · ·

Booted systems Embedded rail systems Other fastening systems

The requirements of this standard apply to ballastless track systems including: · · · · ·

Plain line track as well as switches and crossings and rail expansion joints Various substructures like embankments and cuttings, tunnels, bridges or similar, with or without floating slabs Transitions between different substructures Transitions between different ballastless track systems Transitions between ballasted and ballastless track systems

It is mainly related to slab track design and does not cover the rail structure interaction. Nevertheless, some information are provided regarding the compatibility between bridge and track systems. An extract of the EN is provided below. Fig. 51

Extract of EN 16432

This first requirement ($5.2.3.2) is not related to rail structure interaction, but to the track geometry, passenger comfort and fastening system vertical adjustment capability. In case of bridge subjected to

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large vertical deformation (exceeding L/5000), special fastening system(with high vertical adjustment capability) or pre-camber of the rail vertical level along the bridge can be implemented. The following requirements ($5.2.3.3) are related to bridge movements: · · ·

Angular variation criteria to avoid excessive rail bending and fastener uplift at bridge end. Limitation of differential lateral movement between two adjacent spans in order to prevent excessivebending stress on the rail and forces on fasteners. Differential vertical bridgedeflection criteria to avoid excessiverail bending and fastener uplift at bridge end.

The criteria related to the differential lateral movement between two adjacent spans is often not checked on railway project, as this criteria is not clearly explained in several stan dards (such as Eurocode 1991-2). Nevertheless, it may have a significant impact on the bridge and bearings design and should be carefullyconsidered. Various solutions can be implemented to prevent excessivelateral relative displacement at joint between adjacent bridge, such as used of fixed bearing, shear key, bearing with high stiffness, ect… EN 16432 provides also information related to the minimum lateral and longitudinal resistance of the track, depending on the temperature variation. An extract of the EN 16432 is provided below. Fig. 52

Extract of EN 16432

These values should not be summed up along the bridgelength for bridgedesign, but the track/bridge interface (dowel, shear keys, …) shall be able to resist locally to these loads.

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4.7 RDSO GUIDELINES FOR CARRYING OUT RAIL-STRUCTURE INTERACTION STUDIES ON METRO SYSTEMS (LUCKNOW) 4.7.1 Description RDSO (Research designs and standards organization, Lucknow) guidelines provide a basis for carrying out RSI studies and thus to work out the forces induced in rail and bridge components due to interaction effects. the interaction effects includes actions of expansion/contraction of deck/rails under change of temperature, longitudinal deformation of substructure under braking/tractiveforces from rolling stock and vertical bending caused due to vertical loads. These guidelines explain the interaction phenomenon, parameters affecting RSI, provide guidance on choosing representative stretches for conducting RSI, special cases in RSI, useof computer program for carrying RSI and options available for modification in track if the RSI result indicate excessive stresses/deformations. These guidelines cover steel/concrete bridges with simply supported or continuous spans weather on straight or curved alignment and weather level or on gradient having any type of bearings on metro system in India.

4.7.2 Loading ·

· ·

Vertical train loads : the vertical train load shall be as per design loading or the heaviest train actually running on the route. The placement of load shall be donesuch as to create maximum rotation at ends. The loads shall be enhanced by CDA (coefficient of dynamic augment) as per IRS bridge rules. Breaking and tractive loads Temperature variation

4.7.3 Criteria and range of application 1) Additional stresses in rails: ·

·

For ballasted track : the permissible additional compressive stresses shall not exceed : For R ≥ 1500 m : 72N/mm2 For 1500 > R ≥ 700 m : 58 N/mm2 For 700 > R ≥ 600 m : 54 N/mm2 For 600 > R ≥ 300 m : 27 N/mm2 The permissibletensilestresses shall not exceed 92N/mm 2. For ballastless track : the permissible additional tensile as well as compressive stresses shall not exceed 92N/mm2.

2) Relative displacement between rail & deck or between rail & embankment: ·

The relative displacement between the rail and deck or between rail and embankment under tractive/breaking force should not exceed 4mm.

3) Vertical displacement of upper surface of deck with respect to adjoining structure : ·

The maximum vertical displacement are 3mm for maximum speed 160Km/h and 2mm for maximum speed greater than 160 Km/h.

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4.8 KOREAN CODE We refer in this chapter to the document KR C-8080 Rev. Dated January 2014 “궤도-교량 종방향상호작용 해석 – Track-Bridge – Longitudinal Interaction Analysis” and KR C-8090 Rev. Dated January 2014 “교량단부 콘크리트궤도사용성 검토 –Reviewof bridgetrack concrete track usability” from the Korea Rail Network Authority. The overall approach of rail structure interaction is based on and similar to the UIC 774-3 for ballasted track. Therefore, only major differences and addition are described below for ballasted track. For ballastless track, the document KR C-8090 provides additional information on the checking regarding uplift/compression of fasteners. Minimum pier stiffness are presented in chapter $3.2.1.. The ratio of rail stress relative to l imit value is given for expansion length varying from 20 to 60m and depending on pier stiffness. Fig. 53

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Minimum pier stiffness

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These tables can only be used for pre-dimensioning of high speed railway line, as the minimum pier stiffness obtained is conservativefor these relatively short span. Nevertheless, they show that shorter allowable expansion length are expected for ballastless track compare to ballasted track. Loadings and load combinations are similar to UIC 774-3, but with some adjustments for local characteristics (temperature variation, train loadings, ..). Main allowable tensile and compressive stress for ballasted track are defined for the same parameters as UIC 774-3: · · ·

Curve radius R > 1500m Rail UIC 60 Ballast depth > 0.3m

The allowable compressive and tensile stress for ballasted track are identical to the UIC 774-3: · ·

Allowablecompressive stress: 72MN/m2 Allowabletensilestress: 92MN/m2

The Korea codes provide additional allowable stressesfor ballasted track in case of curve radius below 1500m. They are provide below (intermediate values can be interpolated). Tab. 10

Load Temperature variations, Traction/braking loads, Train vertical loads

Allowable additional stress of rail per curve radius

1500

Maximum additional compressive stress (MN/m2) 72

700

58

92

600

54

92

300

27

92

Minimum curve radius (m)

Maximum additional tensile stress (MN/m2) 92

Similar criteria as UIC 774-3 exists in the code regarding allowable bridge/rail displacements for ballasted track: · · ·

·

4mm relative longitudinal allowable displacement between rail and top of deck under braking/traction load 5mm relative longitudinal allowabledisplacement between adjacent spans or span/abutment under braking/traction load 30mm relative longitudinal allowable displacement between adjacent spans or span/abutment under braking/traction load in case of rail expansion joint if ballast is laid continuously over the expansion joint Total longitudinal opening/closing at the upper edgesurfacedue to end rotation of bridge deck is limited to 8mm if track bridge interactionis considered and 10mm if track bridge interaction in not considered.

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·

Vertical relative deflection at bridge ends is limited to 3mm for speeds below 160km/h and 2mm for speeds higher than 160km/h under train vertical loads

For ballastless track, the maximum compressive and tensile allowable stress for rail structure interaction is 92MN/m2for track radius higher than 150m. Project specifics criteria regarding rail -track and bridge relative displacements, uplift/compression of fastener and precast slab stability are to be defined. Calculations for uplift/compression of fasteners as per KR C-08090 are based the theory of beam on elastic foundation or obtained using FEM software. Only a synthesis is presented below and refer to the original document for the full description of the method. The loading to be considered are: · · · · · · · · ·

Bridge deformation caused by creep and shrinkage after track installation Bridge deformation caused by gradient temperaturevariation Effect of settlement Rotation of bridge piers due to temperature difference between rail and bridgesuperstructure Rotation of piers at the top of the piers due to difference in temperature Train vertical load, including impact factor Rotation of bridge piers by braking load Vertical deformation in elasticbearing by vertical load of train Direct acting force due to wheel load, including impact factor

Factored coefficient are applied to each load cases. The uplift of fasteners is checked using the following formula:

With

Fd: Fastener uplift calculated value Zu: Allowable value of lift force of rail, i.e. fastener fastening force gM: Safety coefficient (gM= 1.0)

As the fastener stiffness varies according to the loading (static and dynamic stiffness) and the partial safety factor gF, used to calculateFd, also dependson the typeof loading,each load case are calculated individually and added as per load combinations. Refer to the code KR C-08090 for details. Regarding the fastener integrity under compression and fatigue, the compression deformation on the fastener pad is checked using the following formula:

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With

Fd: Fastener uplift calculated value sD: Allowablecompression deformation of rail pad compression for fatigue resistance (20% of rail pad thickness or value provided by manufacturor) kstat: Static stiffness of the fastener

As the fastener stiffness varies according to the loading (static and dynamic stiffness) and the partial safety factor gF, used to calculateFd, also dependson the typeof loading,each load case are calculated individually and added as per load combinations. Refer to the code KR C-08090 for details. For ballastlesstrack using prefabricated slab, thestability of precast track slab (Lift-off) ischecked using the formula below. It ensures that there is no lift-off of the slab:

With

e: Ls: Length of slab W: Weight per unit length Fd,i: Uplift/compressive force from fastener i di: Distance from slab centerline to fastener i Fig. 54

Precast slab over protection concrete layer

Finally, the code presents also a calculation method for the allowable rail gap when track circuit method is not used for broken rail detection. Typically, a fixed value is provided by the track designer (ACI343.1R-12 $4.4.3.3 provides gap values: 50mm for 400mm wheel diameter and up to 100mm for larger wheel). In the Korean code, the value is based on the wheel diameter and rail deflection, as described below. It applies for both ballasted and ballastless track.

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dall = [R^2-(R-d)^2)^0.5 with

R: Wheel radius d: vertical deflection of the rail at the broken part

Typical wheel radius are given below: · · ·

high-speed vehicles, multiple units and passenger coaches: 375 to 475mm locomotives: 500 to 650mm freight cars: 450 to 500mm

Vertical deflection d can be calculated as follow:

With

EI: Flexural stiffness of the rail K: Rail support factor per unit length (1 rail) P: Wheel load

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4.9 ACI343.1R-12 The ACI343.1-12 is titled “Analysis and design of reinforced and prestressed concrete guideway structure”. It is not a standard dedicated to rail structure interaction, but provides some information on American practices on this subject. The temperature variation range in the rail is defined in the ACI343.1as: Temperature increase T1+ + Ts - To Temperature decrease To – T1With

T1+: Maximum mean daily temperature over a 75 years period + 5°C T1-: Minimum mean daily temperature over a 75 years period - 5°C Ts: additional temperature increase due to sunshine(20°F = 12°C) To: Effective installation temperatureof rail

The ACI343.1R-12 reminds that, in case of vertical or horizontal radius, the effect of the rail curvature and the generated radial forces needs to be taken into account, using the following formula. Fradial = Frail / R With

Fradial: Radial force in the plane of the curvature Frail: Tensile/compressive force in the rail R: Radius of the curve

If FEM software for RSI calculations can model the structures and tracks in 3D, it is possible to obtain the RSI radial forces. A simplified method to obtain the RSI radial force is shown in Appendix1. ACI343.1R-12 provides also typical values for allowablegap under broken rail case: 50mm for 400mm wheel diameter and up to 100mm for larger wheel. Broken gap width can be calculated using FEM software or can be approximated using the following formula ( it does not consider bridge displacements): D = s2 A / [E (Ff / s)] With: D: Broken gap width (m) s: Stress in the rail before braking (MN/m2) E: Rail modulus of elasticity (MN/m2) A: Area of one rail (m2) Ff: Longitudinal restraining force of one fastener (MN) s: Fastener spacing (m)

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4.10 JAPANESE CODE The Japanese documents covered hereare: ·

鉄道構造物等設計標準・同解説 軌道構造 Design Standards For Railway Structures and Commentary 【Track】

·

鉄道構造物等設計標準・同解説 コンクリート構造物 Design Standards For Railway Structures and Commentary 【Concrete Structures】

·

鉄道構造物等設計標準・同解説【変位制限】 Design Standards For Railway Structures and Commentary【Displacement Limits】

As Systra does not have an in-depth knowledge of Japanesedesign practice and as Japanese standards have been written with Japan track in mind, it is important to refer to the original standards when design is carried on. This short explanation is for reference only. Two separate aspects of rail structure interaction in Japanese standards are presented here. · ·

Rail structure interaction analysis Displacements requirements related to track integrity

4.10.1 Rail structure interaction analysis The documents studied related to rail structure interaction focus mainly on three aspects: · · ·

Broken rail gap Forces on substructures Allowablecompressive forces in rail for ballasted track

General information are provided on rail structure interaction calculations and pier bearing type arrangement, but without detailed explanation. It is not a focus of the Japanese code. Broken rail gap: The maximum allowablebroken rail gap is 70mm. The typical formula for broken rail gap calculation is used. D = s2 A / [E (Ff / s)] With: D: Broken gap width (m) s: Stress in the rail before braking (MN/m2) E: Rail modulus of elasticity (MN/m2) A: Area of one rail (m2) Ff: Longitudinal restraining force of one fastener (MN) s: Fastener spacing (m) Forces on substructures:

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The temperature load case of rail structure interaction is equal to 10kN/m/track, with a maximum of 2000kN. It is mentioned in the standard that it can be reduced depending on the bridge expansion joint positions. No detailed information are provided. No information is provided on the allowable rail stress for rail structure interaction analysis, but it is mentioned in the commentary that, above 100m long rail bridge, rail structure interaction analysis is recommended (with details on methodology). Braking and acceleration loads on structure are based on the formula given in the table below. Tab. 11

Braking and acceleration loads for standard train

Parameter Braking

Force (kN) (0.27+1.00*L/Lv)*T

Acceleration

(0.25+0.95*L/Lv)*T

Tab. 12

Braking and acceleration loads for Shinkansen train

Parameter Braking

Force (kN) (0.20+0.80*L/Lv)*T

Acceleration

(0.19+0.76*L/Lv)*T

With: Lv: Length of one car (m) L: Length of bridge in between abutments (m) T: Weight of one car (kN) Allowablecompressive forces in rail for ballasted track: Allowablecompressive forces (buckling risk) in rail for ballasted track calculationmethodology follows the same general principal as UIC 720. It is based on the calculation of a critical minimum temperature in rail for which the risk of buckling is minimal (seefigurebelow). Fig. 55

Track lateral displacement versus temperature in ballasted track

Analytical formula are provided to obtain the allowable compressive forces and sleeper lateral resistance in ballast, based on Japanese railway parameters.

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4.10.2 Displacements requirements related to track integrity Japanese standards specifies strict deformation and displacements requirements in order to ensure: ·

· ·

Safety: o Running safety in ordinary conditions: the purpose is to ensure the railway runs smoothly under all actions during operation conditions. o Running safety in seismic conditions: Performance related to the reduction of derailment riskunder an earthquake(level 1earthquake with highrisk of occurrence). Serviceability: It is related to the riding comfort for passenger. Restorability o Track restorabilityin ordinary conditions: Performancefor maintaining track members in a sound or usable condition not requiring repair under all actions expected during the design life in ordinary condition. o Track damage in seismic conditions: Performance for maintaining track members in a sound or usable condition not requiring repair during an earthquake (level 1 earthquake with high risk of occurrence)or for minimizing damage so that repairs can be made in a short period of time.

The verifications are carried out according to the table below. Tab. 13

Performance items verification indices

The load combinations and number of track to be considered are listed in the tables below. Tab. 14

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Load combinations

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Tab. 15

Number of tracks to be considered

Verification of safety The verification of safety is defined to prevent derailment risks. It is based on train -track-bridge coupling dynamic analysis, as shown on the model below. Fig. 56

Model for verification of safety

Design limit values are defined in thestandards as maximum deflection and differential displacements and rotation of track surfaces at joint. It is no directly related to rail structure interaction (but to derailment risk) under normal and seismic condition, as it is not related to the track integrity assessment. Verification of serviceability The verification of serviceability coversthe riding comfort inordinary conditions.As for the verification of safety, design limit values are defined in the standards as maximum deflection and differential

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displacements and rotation of track surfacesat joint. It is no directly related to rail structureinteraction (but to riding comfort) under ordinary condition, as it is not related to the track integrity assessment. Verification of restorability The verification of safety is defined to ensure track integrity and maintenance in ordinary conditions and track reparability in seismic conditions. It is based on complete model of the track and bridge structure and on assigning design parameters and limits to each elements. De sign limit values are defined in the standards as maximum deflection and differential displacements and rotation of track surfaces at joint. These limits values are based on Japanesetrack characteristics and it may be needed to define specific values if different types of track are used. Tab. 16

Allowable angular rotation and alignment irregularity in ordinary conditions

It is to be noted that in the Japanese version of this table: · ·

The vertical direction angular rotation for ballast track and 50N rail is 3.5mm. The horizontal direction angular rotation for ballast track and 60kg rail is 5.5E-3. Tab. 17

Allowable angular rotation and alignment in seismic conditions

The parameters used in order to define these design limit values are: · · ·

Rail stresses Rail displacements Stresses of rail fastening system

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·

Reactions forces on rail pad

The parameters are defined for three levels for damage, repairing and maintenance: 1) Shinkansen lines 2) Conventional lines 3) Damage level The table above for ordinary conditions is based on level 1 and 2 and the table for seismic conditions is based on level 3. The parameters are given in the table below. Tab. 18

Direction

Vertical

Horizontal

Parameters used in Japanese standards to define design limits

Parameter Rail displacement

Level 1 0.5mm

Level 2 -

Level 3

Rail Stress

50N/mm2

100N/mm2

150N/mm2

Fastening reaction

-

Rail displacement

-

6kN (Slab) 10kN (Ballast) -

6kN (Slab) 10kN (Ballast) -

Rail Stress

50N/mm2

100N/mm2

150N/mm2

Fastening reaction (continuous model) Fastening reaction (discrete model)

8kN

16kN

32kN

16kN

32kN

64kN

-

It is reminded that this analysis in the standard is based on Japanese fastening characteristics.

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4.11 CHINESE CODE Information in this chapter are based on the Chinese code: ·

高速铁路设计规范- Code for Design of High Speed Railway - TB10621-2014/ J 1942-2014

There is no detailed description of rail structure interaction analysis. Requirements for rail structure interaction are based on pier stiffness minimum rigidity and displacements criteria. Vertical bridge deformation (creep/shrinkage) after track laying: The maximum vertical bridge deformation (creep/shrinkage)after track laying is: · · ·

20mm for ballasted track. 10mm for ballastless track and bridge below 50m. Minimum of L/5000 (L: span length in m) and 20mm for ballastless track and bridge longer than 50m

This criteria is not directly related to track structure interaction, but to the fastening system vertical adjustment capability. Transverse bridge deformation: The maximum transverse relative bridge deformation at expansion joint is 1mm for ballastless track in order to prevent excessive stresses on rail and fastening system. Rotations at end of bridge: Under Chinese ZK load model (around 80% of UIC LM 71), without impact, the maximum rotation at end of bridge are provided below. Tab. 19

Track Ballast

Allowable vertical rotation of bridge

Location Bridge - abutment

q <= 0.20%

Bridge - Bridge

q1 + q2 <= 0.40%

Bridge - abutment Ballastless Bridge - Bridge

Rotation

Comment

q <= 0.15%

d <= 0.55m

q <= 0.10%

0.55 < d <= 0.75m

q1 + q2 <= 0.30%

d <= 0.55m

q1 + q2 <= 0.20%

0.55 < d <= 0.75m

d: Distance end of beam to bearing center

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For ballast track, the rotation criteria are define to avoid ballast destabilizationand excessiverail stress. For ballastless track, if the criteria is not met, specific studies are to be carried out to ensure the compatibility between ballastless track and bridge deformations. Pier stiffness: The minimum pier stiffness are provided for singletrack and double track bridges in the table below. Tab. 20

Type

Minimum pier stiffness (kN/cm)

Span length (m) <= 12

Double track 100

Single track 60

16

160

100

20

190

120

24

270

170

32

350

220

40

550

340

48

720

450

3000

1500

Bridge pier

Abutment

These criteria are based on rail structure interaction for high speed railway lines, with the following parameters (ballast track): · · · · ·

Bridge deflections under static train load: L/5000 (L: Length of span in m) Loads: Temperature (T), Braking/traction (B) and Deck flexure (F) Load combinations: maximum of T+B and B+F Maximum additional stresses in rail: 81MN/m2(tensile)and 61MN/m2 (compression) Maximum allowabledisplacement between rail and deck under braking/traction load: 4mm

Pier settlement: The maximum pier settlement (due to permanent loads) after track construction are provided in the table below for ballast and ballastless tracks. Tab. 21

Type Absolute settlement Differential settlement

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Maximum allowable settlement (mm)

Type of track Ballast

Settlement (mm) 30

Ballastless

20

Ballast

15

Ballastless

5

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Other items: In the commentary of the standard, it is mentioned that the maximum relative vertical displacement between adjacent spans is to be limitedto 1mm in order to avoid excessive strain on fastening system and rails. In case of track profile in slope, vertical relative displacements due to bridge horizontal displacements should also be considered, as shown on the figure below. Fig. 57

Vertical differential displacements at expansion joint

4.12 AREMA There is no dedicated chapter in the AREMA related to rail structure interaction. There is no mention of rail structure interaction under bridgetemperature variation load case. In the AREMA 2012 Volume 2 Chapter 8.2.2.3(j), the longitudinal force for E-80(EM-360) loading is defined in the Design Basis Report as: ·

Force due to braking, as prescribed by the following equation Longitudinal braking force (kN)

·

: 200+17.5L

Force due to traction, as prescribed by the following equation Longitudinal traction force (kN)

: 200√L

Where ‘L’ is the length of the viaduct from one abutment to the other (with continuous welded rail). Nevertheless, these formula are not applicableon our project for rail structure interaction analysisfor the following reasons: ·

·

The forces obtained are pier reactions and not the braking and traction forces applied at rail level (which are the input data required for rail structure interaction analysis), as shown in the article “Longitudinal Forces in Bridges Due to Heavy Haul Freight Operations” issued for the “7th International Heavy Haul Conference, 2001”. These formula are based on AREMA 2012 Volume 2Chapter 8.2.2.3(j). They are based on field tests performed on short viaduct (120m long with 4 spans: 13m beam span, 12m beam span, 33m truss and 64m truss), as shown in the article “Longitudinal Forces in Bridges Due to Heavy Haul Freight Operations” issuedfor the “7th International Heavy Haul Conference, 2001”. Such tests differ significantly from theverylong viaduct consideredin thisproject. It can be assumed that, for short viaduct, a significant portion of the braking and traction forces are resisted by the track set on the near backfill. But, for long viaduct, these forces are almost fully resisted by the bridge structures, as backfill are too far to have significant influence.

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Other information can be found in the commentary of AREMA and literature: · ·

·

The longitudinal force from braking and traction are 15% of train static load each, as explain in “Longitudinal Forces in Bridges Due to Heavy Haul Freight Operations”. The drawbar design load (around 2200kN) limits the maximum tractive force, which is transmitted from one freight car to the next, as explain in AREMA 2012 Volume 2 Chapter 2.2.3(j) Commentary (d). The design approach is to considered that all bridges in between abutments have the same longitudinal movement due to track. Therefore, the train braking and traction loads are distributed over the pier relatively to the pier stiffness.

Rail structure interaction effect is not detailed in the standard and no detailed criteria or method are provided. The maximum longitudinal displacements under braking and acceleration is to be checked as per the following requirements (AREMA 2012 Volume 2Chapter 8.2.2.3(j)(3)): “The longitudinal deflection of the superstructure due to longitudinal force computed in (1) above shall not exceed 1 inch (25 mm) for E-80 (EM 360) loading. For design loads other than E-80 (EM 360), the maximum allowable longitudinal deflection shall be scaled proportionally. In no case, however, shall the longitudinal deflection exceed 1-1/2 inches (38 mm).”

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5. OTHERS TECHNICAL REFERENTIAL 5.1 SNCF DESIGN DOCUMENTS This chapter is based on SNCF’s practice for Continuous Welded Rail and Rail Expansion Joint on bridges. It is based on the IN04190 related to Rail Expansion Joint UIC 60 on bridge (document in French). Bridges are classified in 5groups (Group A to E), based on: · · · · · ·

Type of bridge Length of bridge Number of fixed thermal point Skew angle Bridge height Regularity of spanning and position of fixed points

Depending on the group, requirements are defined regarding: · · · ·

Bridge expandablelength Minimum distance between bridgemoveableends to singular point (Rail Expansion Joint, …) Strengthening track/ballast lateral resistance Specific rail structure interaction studies

The IN02915 regarding track and alignment for Continuous Welded Rail defines the requirements regarding minimum distance between singularities. A bridge’s end with moveable bearing can be considered a singularity. Tab. 22

Minimum distance between singularities

Track Rail profile

Ballasted

Ballastless

36E2/46E2/50E6/50E1

60E1

36E2/46E2/50E6/50E1

60E1

End of CWR

100m

120m

50m

60m

Turnout

50m

Rail expansion joint

50m

Based on the bridge group, sleeper type and rail profile, maximum expandable length are defined for various track radii (for ballasted track). The SNCF’s design document are mainly used in France, where the number of bridge is generally very limited.

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6. GENERAL CRITERIA TO BE CHECKED REGARDING RAIL STRUCTURE INTERACTION The table below provides, for each standard, code and technical document presented in chapters 4 and 5, a short description, the range of application and the main criteria related to rail structure interaction. Based on the project characteristics, it is possible to select the most appropriate document, or to define, in coordination with the track specialty, rail structure interaction criteria adapted to the project. Tab. 23

Codes/standards

UIC 774-3

Summary of existing standards, codes and technical documents related to RSI

Description

Range of application

Criteria

The UIC 774-3 i s the most referred code related to rail s tructure interaction. It was developed for ra ilway lines wi th ballasted track in mi nd.

It covers ballasted tra ck with track radius higher than 1500m, 900MN/m 2 ra i l s teel gra de and UIC 60kg ra il type. For ba llastless track, i t can be us ed i n combination with “UIC Recommendation for des ign and calculations of ba l lastless track”.

For cal culation carried out us i ng FEM a nalysis, rail s tresses and rail/bridge l ongitudinal displacements a nd deformation are ca l culated under temperature va riation a nd tra i n horizontal a nd vertical l oads.

It covers only the global effect of rail s tructure i nteraction.

For ba llastless track, only a l lowable rail s tresses are to be checked.

It ca n be used with UIC774-3 and covers similar cases. It provi des more information on the l ocal rail s tructure i nteraction effect a t bridge expa nsion joint (such as rail bending).

In a ddition to UIC774-3, cri teri a related to deck verti ca l relative deformation a t bri dge expansion joint is provided for ballast and bal lastless tra cks.

The rail s tructure i nteraction chapter in the Eurocode i s directly based on the UIC 774-3. As for UIC 774-3, i t was developed for rai lway lines with ballasted track i n mind.

Si milar to UIC 774-3. In case of l i ne with dedicated traffi c, braking a nd accel eration forces can be s elected as 25% of the tra in s ta tic l ive loads, instead of more conserva tive UIC bra king/acceleration.

Compa red to UIC 774-3, the cri teri a of relative di s placement between top of deck and rail under braking/acceleration is not menti oned. Criteri a of maximum vertical rel ative displacements at bri dge end i s provided for bal last track a nd fastener upl ift calculation a nd checki ng is mandatory for bal lastless tra ck (without ca l culation method provided).

UIC 774-3, UIC 776 a nd Eurocode 1991-2 have been wri tten with ballast tra ck and French experience in

The document describes pa ra meter and cri teria for ba l lastless track. Regarding tens ilerail stress in tension,

For ba llastless track, only ra i l s tresses a re checked and cri teri a for ballastless tra ck a re provi ded. Displacements

The UIC 776, l a st updated i n 1989, i s related to rai lway bridge deformations and track/bridge compatibility. UIC 776

Eurocode 1991-2

UIC Recommendation for des ign and calculations of bal lastless tra ck

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Angul ar va riation, uplift and bending moment i n rail cri teri a at bridge expansion joi nt a re also provided for bal last tra ck.

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Codes/standards

UIC 720

Eurocode EN16432

Description

Range of application

mi nd. This document adds German expertise i n ballast l ess tra ck.

as the va lue provided in the document is i dentical to UIC 774-3 for ba llast track, it can be assumed that i t is applicable for track radius above 1500m.

checks of UIC 774-3 apply onl y for ballast tra ck.

UIC 720 is not directly rel a ted to rail s tructure i nteraction, but provi de us eful information on al lowable equivalent temperature i n rail for di fferent type of railway, track a nd train. The code provides also methods to obtain the rail temperature va riation, ba s ed on envi ronment pa rameters a nd other hypotheses.

Va ri ous cases are cons idered, from freight rai lway line to high speed rai lway line.

Bas ed on the allowable temperature i n rail obtained wi th UIC 720, i t i s possible to deduct the allowable rail s tresses under RSI load combi nations. This criteria ca n then be used for the RSI a na lysis. The code can be us ed when project cha racteristics deviates from UIC774-3 or Eurocode ra nge of a pplication (such as mi nimum tra ck ra dius).

The Eurocode EN16432 i s rel a ted to ballastless tra ck des ign. It provides general cri teri a and method to des ign ballastless track. It is not di rectly related to rail s tructure interaction, but provi des information on the compatibility of ballastless track a nd bridge s tructures.

Al l type of ballastless tra ck.

Requirements on long term deformation of bridge, a l lowable deformations and di s placements of bridge are provided. If bridge s tructures do not comply wi th these requirements, tra ck s ys tem shall be modi fied accordingly.

The document is based on European approach of RSI, but a dd some lacking pa rameters a nd criteria rel a ted to i mpact of tra ck radi us and ballastless tra ck.

Ba l last track wi th UIC 60kg rai l, 0.3m depth of ballast and tra ck radius higher than 300m.

For ba llast track, cri teria rel ated to rail s tress and di s placements a re provi ded.

Korean Code C-8090

Ba l lastless track for UIC 60kg rai l track radius higher than 150m.

Criteria Method to check fastener upl ift and compression is provided. In addition, tra ns verse relative movement a t bridge expansion joint is limited.

For ba llastless track, cri teria rel ated to rail s tress are provided. Methods to check fa s tener uplift and compression is a lso provided. Methods to calculate bal lastless tra ck precast slab s tability a nd defined a l lowable rail gap in case of broken rail are also defined.

RSDO Indian guidelines

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RSDO a re based on European standards and Korea n code for RSI ana lysis. As for Korean code, a llowable ra il stress for ba llast and ballastless track a re defined. Compare to Eurocode, allowable rail s tresses are provided for

It covers ballasted tra ck and ba l last track with track radi us higher than 300m.

RAIL STRUCTURE INTERACTION DESIGN GUIDELINES

Criteri a related to rail stress, rel ative displacement between ra il and top of deck a nd maximum vertical di s placement a t bridge ends a re provi ded.

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Codes/standards

Description

Range of application

Criteria

track ra dius as low as 300m. ACI 343.1R-12

AREMA 2012 Vol . 2

Thi s American document does not provi de details on RSI, but contains i nformation on temperature definition, ra dial force from RSI on bridge and calculation on rail gap i n case of broken ra il. AREMA does not include description or method related to rail structure i nteraction. A s i mplified method to calculate braking and acceleration pier reactions is provi ded, applicable only i n some s pecific cases. Japanese design standards do not provi de detailed ca lculation method, pa rameters a nd criteria for ca lculating ra il s tress a nd RSI a nalysis. It is not the focus of the standard.

Ja pa nese Design Standards

TB10621-2014

SNCF IN 04190 a nd 02915

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Metro, conventional train and high s peed train.

Criteri a regarding maximum broken rail gap is provided. Method to ca lculate braking a nd a cceleration l oads on pi er is provided. Criteri a regarding angular rotati on at bridge ends, para llel s hift of deck and rel ative vertical a nd hori zontal displacements a t bri dge ends are provi ded for bal last and ballastless tra ck. Ja pa nese Design Standards a re the most comprehensive s tandards for these criteria, whi ch are sometimes mi s sing i n other standards.

Deformations and di s placements cri teria rel a ted to servi ceability, s a fety and restorability are provi ded.

The Chi nese s tandard for High Speed Railway does not provi de detailed on RSI. Chi nese Standard

Ba l last and ballastless tra ck.

Ba l last and ballastless tra ck.

Criteri a related to:

Hi gh s peed tra in.

·

It i s based on cri teria rel a ted to pier stiffness, to l imit structure di s placement and rail s tress.

· · · ·

Long term deformation of bri dge Verti cal a nd Transverse bri dge deformation Rotation a t bridge’s ends Pi er s tiffness Pi er s ettlement

SNCF’s IN 04190 and 02915 provides general requirements regarding importance of rail s tructure interaction depending on the type of bridge (and if calculations a re necessary) and minimum distance between s ingularity on the line (such a s end of turnout and bri dge’s end with moveable bearings).

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7. FEEDBACKS FROM EXISTING PROJECTS 7.1 HYDERABAD METRO PROJECT (INDIA) Oliphenta ROB : 80m steel structure. This stretch includes simply supported box girder spans, cross over , 80m steel structure and station. The calculation has carried out by CWRBIA software using UIC Code 774-3. Difficulties : Stresses in rails due to Rail-Structureinteraction are exceeding permissible limits. Solution : we have proposed Low toe load fastener over length of ROB span. Result : with above solution stresses in rail are within permissible limits. Please add, a sketch of the bridge layout, graphics showing rail stresses before and after use of low toe load fastener, length of use of low toe load fastener and broken rail gap before and after use of low toe load fastener. Bharat Nagar ROB: Three Span continuous box girder ROB 39m+65m+39m span This stretch includes simply supported boxgirder spans, threespan continuous box girder and station. The calculation has carried out by CWRBIA software using UIC Code 774-3. Difficulties : Stresses in rails due to Rail-Structureinteraction are exceeding permissible limits. Solution : we have proposed two options here 1) Alternativebearing arrangement for ROB 2) Low toe load fastener over length of ROB span. Result: due to site constraint client adopted second option (Low toe load fastener). Please add, a sketch of the bridge layout, graphics showing rail stresses before and after use of low toe load fastener, length of use of low toe load fastener and broken rail gap before and after use of low toe load fastener. Boiguda ROB : Steel bridge 67m span. This stretch includes simply supported box girder spans and 67m steel bridge. The calculation has carried out by CWRBIA software using UIC Code 774-3. Difficulties : Stresses in rails due to Rail-Structureinteraction are exceeding permissible limits. Solution : we have proposed Low toe load fastener over length of ROB span. Result : with above solution stresses in rail are within permissible limits. Note: 80m steel truss is in sharp curvature with 128m Radius and having major issue of guided bearing orientation. We proposed that guided bearing should be oriented along the alignment to avoid additional stress in rail. Please add, a sketch of the bridge layout, graphics showing rail stresses before and after use of low toe load fastener, length of use of low toe load fastener and broken rail gap before and after use of low toe load fastener.

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7.2 VIADUCT ON VIENNE – SEA (FRANCE) 7.2.1 Introduction The Vienne viaduct located in the department of Indre-et-Loire in Nouâtre. It crosses the river of Vienne and it supports the two ways of the SEA high speed. The referencespeed on this structure is V = 350 km / h. The viaduct is located on the communes of Ports and Nouâtre (Indre-et-Loire, Chinon district, Sainte-Maure-de-Touraine canton).

7.2.2 Description of the bridge The VIENNE viaduct is a two-beam structurewith2traffic lanes. The structureis in a straight alignment and has a symmetrical cross-section (axis of the railway lines coinciding with the axis of the deck). The main features are as follows: · · ·

Platform profile in "roof" at 1% The tracks do not have any cant The deck consists of 6 spans: 56.50 - 62.50 - 60.50 - 58.50 - 56.50 - 50 = 344.5m

The track is continuous at the fixed point C6only. It is interrupted at the right of the C0 abutment. The track is equipped with a rail expansion device + ballast guard seal. The deck is a steel-concrete type "beam" with a constant height PRS with metallic diaphragm and bracing. The structure has 2 railways lines. The track is made up of profile rails E60E1 with a cross-section of 76.86 cm², fixed on monobloc concrete crossbeams of 2.42m length, placed at 1666 units per kilometer. The track is continuous on the structure. At the ends of the decks, the long welded rails pass through the joints without discontinuity. A third anti-derailment rail is placed on the structure. The minimum thickness of the ballast under the crosspiece is 450mm. Fig. 58

Cross section of the Viaduct

7.2.3 Track/bridge Interaction The track is continuous on the abutment C6and discontinuous on C0, the rails are welded to the ends of the structure and the abutment C6 serves as a fixed point for the resumption of the longitudinal

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forces. The expansion length of the deck is 344.50m> 90m. A complete Track/Bridge Interaction study is therefore necessary to check the stresses in the rails. Fig. 59

Static arrangement of the bearings

The viaduct is modeled in the ANSYS finiteelement code.The supports are consideredwithout friction and they are characterized by spring stiffness. The apron is modeled by a series of elements of the beam type. The two tracks are modeled by a sequenceof beam elements. The endsof the track in part platform are blocked horizontally. A full study interaction track/bridge study have two objectives: · ·

Check that the stresses in the rails and deformations of the deck remain below the limits imposed by the regulations. Quantify the impact of taking into account the Interaction track/bridge on the displacements obtained, in particular under braking-starting.

It is important to remember that the characteristics of the ballast must be taken into account depending on whether the ballast is frozen or not. Thus, for Interaction Track Structure calculations, two cases must be taken into account: ·

Ballast not frozen.

The resistance threshold K, by type of track is: ü Loaded track, k = 60 KN / m of track. ü Unloaded track, k = 20 KN / m of track. ·

Frozen ballast.

This hypothesis is not retained on the French national rail network, for the following reasons: ·

·

The high level of maintenance provided by the SNCF on the high speed linesof the RFN (high maintenance level of the track) maintains a clean ballast not having a particular sensitivity to frost. In the time of a prolonged cold period,particular operatingconditionsare applied, in particular, reduction of train speeds.

For the Interaction Track/Bridge calculation of this structure, vigilance should be provided on the following points: XXXXXXXX

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·

·

· · ·

The presence of the third rail must not be taken into account in the calculation. Its role is also neglected for the justification of the structure. Special arrangements for the safety rails are required on the fixed abutment side C6 so that the horizontal forces transmitted to the deck and the supports are not increased by these rails. The presence of railway loads on the embankment located behind the fixed abutment C6 increases the stiffness of the ballast and therefore of the forces applied to the rails on the structure. The calculation madewithout these charges isthereforeunsafe. Thisload case must be taken into account in order to evaluate the maximum loads in the rails generated by the brake-starting forces and by the vertical loads. The taking into account of the inertia cracked on support will increase the rotations, thus increase the stresses in the rails. In accordance with §6.5.4.3 of EN1991-2, the Interaction Rail/Structure study under vertical loads shall not consider dynamic amplification. The taking into account of the forces separately (thermal, braking / starting and bending) is difficult to apprehend from the point of view of concomitance of the forces.

At the end of the IRS calculation carried out, the conclusion is as follows: · · · · ·

The total additional constraints due to the interaction track/structure are satisfactory compared to the permissible values (72N/mm² in compression and 92 N/mm² in tension) The absolute horizontal displacement of the deck due to braking/acceleration is less than the permissible value of 5mm The relative horizontal displacement between the deck and the rail under braking / bending loads is less than the value of 4 mm The maximum horizontal displacement between the upper abutment edge of thedeck and the abutment due to vertical bending is less than 8mm The maximum vertical displacement of the upper edgeof the slab at the deck ends is less than the limit set at 2 mm

Please provide someresults(graphic) and more explanation on the impact of loading on abutment (rail stresses with and without). The purposeof this REX is to provide information on issue s and errors that can be made during rail structure interaction analysis, the text should focus on this. I have removed the second case (Charente), as it seems similar to the first.

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7.3 TRAMWAY LINE Tramway lines are more and more elevated in various parts of the world, as cities do not want to reduce car traffic flow. Fig. 60

Elevated tramway line

As the line is a tramway, train loads, braking forces and centrifugal forces are relatively small compared to typical railway line. In addition, the train length is short, which is favorable in terms of rail stress under braking/traction, as the rail stress does not build upon long distance along the train when braking/accelerating. This leads to very light and economical bridge structures, but less robust than railway line structure. Therefore, the risk related to rail structure interaction on the substructure are amplified and shall not be underestimated. In addition, tramway line alignment tends to be more complex than typical metro and railway ones as it adapts to the existing roads. Therefore, various problems may arise during construction if rail structure interaction analysis is not properly studied. Fig. 61

Excessive forces on substructure leading to cracking

The cause of excessive forces on substructure were: ·

Pier with fixed bearings on both sides located below a rail expansion joint: Forces due to variation of temperature in the rail are transferred to the bearings and leads to excessive

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·

forces on the bearings. The residual force on the pier remains low (see figure below), as the bridge/track system is symmetrical. Pier with fixed bearings on both sides located below a turnout: Deformation due to variation of temperature in the bridge are resisted by the track and forces are transferred to the bearings, leading to excessive forces on the bearings (see figure below). Fig. 62

Forces on bearings due to Rail Expansion Joint above pier with fixed bearings on both sides

Fig. 63

Forces on bearings due to pier with fixed bearings on both sides

In the first case, the rail expansion joint was set by the track specialty a long time after the civil works were designed (and built). In addition, as the residual force on the pier is small (but forceson bearings are high), the risks are difficult to spot. Prior coordination and studies shall be carried out before deciding setting Rail Expansion Joint on viaduct. In the second case, the excessive loads on substructure results from theuse of pierswith fixedbearings on both sides. The key element is the symmetry of the bridge/track system. It prevents pier displacements to adapt to track displacements and reduce the loads on substructure. Due to the symmetry, the pier does not move under rail structure interaction loads and can be considered infinitely stiff. Conclusion: ·

Rail Structure Interaction for light tramway line (or light metro) may be more critical than for railway line, as the design is less robust to cope with rail structure interaction loads.

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·

· · ·

Definition of the spanning, bearing arrangement, compatibility with track requirements and the analysis of the structural layout should be done at an early stage of the design and any change should be analyzed from a RSI point of view. Track and structure specialties coordination is key for a proper design process. Complex areas for tramway lines for RSI should be identified early in the design process, as existing software may not be able to model these areas. Symmetry of bridge/track system that prevents displacements of structure under temperature loads should be identified and impact investigated. In general, it is preferable to avoid such arrangement.

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7.4 METRO LINES 1, 2 AND 3 OF JAKARTA (INDONESIA) On Jakarta metro Line 1, 2 and 3, the civil works designer choses to use Lead Rubber Bearings for Single Track U beams in order to reduce earthquake loads on substructures. The LRB characteristics allows a shift in the eigen-period of the structure and increase energy dissipation during earthquake. The LRB has a nonlinear horizontal force-distortion relationship, as shown on the figure below. Fig. 64

LRB characteristics

Until the characteristics strength Qd is reached, the force-distortion relationship is linear, with a equivalent stiffness of 3712kN/m. At Qd, the distortion is around10mm. Above this threshold, thepost yielding stiffness Kr is very low and maximum distortion can reach 140mm under earthquake. This behavior is very favorable for earthquake design. Various type of LRB exists with different characteristics. In order to mitigate the forces on substructure under earthquake, it is necessary to select the lower possible characteristics strengthQd. Nevertheless, it ispreferablethat, under service fatigue loads,the force on the LRB remains below Qd in order to prevent early aging of the bearing. Rail Structure Interaction was used in order to define more precisely temperature and braking/acceleration loads on LRB and select LRBs with proper characteristics strength. In order to mitigate forceson LRB due to transverse loads (such as hunting,centrifugal forces and wind loads) and to prevent excessive forces on rails and fasteners, link beams, connecting track p linths on adjacent U beams, are designed to prevent excessive relative displacements between adjacent U beams (see figure below).

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Fig. 65

FEM model of Link Beam and rail at bridge expansion joint

It is necessary to consider these link beams for the seismicdesign of the bridge and LRB or to ensure that they act as fuse at low earthquake levels, so that relative transverse displacements between structure are not restraint in case of major earthquake. They serve two different purposes: ·

·

Distribute evenly the transverse loads on the four LRBs next to U beams’ expansion joints and therefore reduce the value of the characteristic strength Qd (and related earthquake loadson substructures). Prevent relative displacements betweenadjacent structuresand related excessive stresseson rails and fastening system in service, as required by standards and design practice.

It is particularly important to prevent relative transverse displacements in case of LRB because if, on one side of the bridge expansion joint, the LRBs reaches the yield threshold, then the relative transverses (and related stresses on track elements) increases dramatically under added loads due to the lower post yielding LRB’s stiffness Kr.

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7.5 DELHI AIRPORT LINE (INDIA) The Delhi Airport Line in India is a 7km metro line built using full precasted single track U beam. Fig. 66

Viaduct of Delhi Airport Line in construction

In order to improve pier cap slenderness, the pier cap are prefabricated with a “hidden top beam” which add strength to the pier cap but is not visible by the public, as shown below. Fig. 67

Pier cap “hidden top beam”

Therefore, at each pier, there are two expansion joints: · ·

Between the first Ubeam and the “hidden top beam” Between the “hidden top beam” and the second U beam

As the U beam are set on elastomeric bearings with low stiffness, but the track on the “hidden top beam” is directly fixed to the pier cap and piers, up to 80 % of transverse loads applied on the Ubeams are transferred to the pier by the rails and fasteners and the remaining 20% are transferred by the bearings. In order to prevent excessive stresses on the rails and fasteners, transverse shear keys were set in between the pier cap and U beams. Fig. 68

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Locations of transverse shear key between U beam and pier cap

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These transverse shear key are vertical elastomeric bearings, set after the U beams have been install on the pier cap. The detailed design is shown below. Fig. 69

Transverse shear key design

With this design, it is not possible to take advantage of the low stiffness of elastomeric bearings to reduce earthquake loads in transversedirection. This may significantly impact the pier and foundation design.

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8. IMPACTS OF CONSTRUCTION METHODS AND MAINTENANCE ON RAIL STRUCTURE INTERACTION Construction and maintenanceof existing track railway are not coveredby standards. These standards are written with standard railway structures in mind and, as these structures are robust, risks related to track construction and maintenance are relatively low. Nevertheless, it is necessary to check with the track specialty that track construction and maintenance methods do not lead to unacceptable loads on structures. As long as there is no continuity of the rails or as long as the rails are not restraint in the fastening systems, there is no load transfers between the rail and structure and therefore, no rail structure interaction. The key construction stage for the track is the rail destressing, when the rails are set at their neutral temperature. Before this stage, rails may be already welded to form long segment (several hundred meters), it is thereforenecessary to ensure that the rails are not fully restraint in the fastening system (most fasteners remain unclipped), so to mitigate transfer of loads on structures due to temperature variation in rails. The destressing process is normally carried out as follow: Fig. 70 L1 unclip

a nchor OTT

ITT

RP1

RP2

Destressing process

X

a nchor

L1 uncl i p RP2

RP1

ITT

OTT

OTT: outer tell tale ITT: inner tell tales RP: reference point X pulling point 1. Identify the positions and lengths of the anchors, lengths to be pulled, and pulling points. 2. Mark the outer and inner tell tales, any reference points and the pulling point. Unclip tell tales and reference points. 3. Cut the CWR at the pulling point. 4. Unclip the rail from the pulling point towards the inner tell tales. 5. Place unclipped rails on rollers and positions rollers as necessary. 6. Check any movement at the tell tales 7. Measure rail temperature 8. Calculate the extension of the rails 9. Mark the calculated extensions at the pulling point and at any reference points 10. Cut the rails again at the pulling point to allow for the calculated extension, a 5mm working gap and any movement at the inner tell tales.

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11. Fit tensors and applied tension to both rails until the required extension is achieved. 12. Check any further movement of the inner tell tales to ensure that the anchors have held 13. Fasten down 40m of rail on each side of the pulling point,outsidethe tensor. Cut the rail again if necessary to produce the correct welding gap and complete the welds at the pulling point, with the tensors in position. 14. Remove all rollers, replace all pads, insulators and clips. 15. Remove tensors, removewelding debris, Fig. 71

Welding machine and rail hydraulic tensors

Two main checking are necessary: · ·

Before welding, it is necessary to avoid long rail segment clipped to the fastening system, in order to avoid force transfer due to daily temperature variation in the rail. Rail pulling force varies according to temperatureand may reach 60t per rail. On viaduct, these forces are then transfer to the structure in the anchored area. It is necessary to check that the structures can sustain these loads. The anchored area length can be extended in order to distribute the forces over several spans.

Coordination with the track specialty and contractor is necessary to validate the track construction method and structure design. During maintenance, it is also necessary to check that the track maintenance methods do not impact the bridge structure. If a track is completely cut (both rails), it acts as a rail expansion joint and large force transfers may be expected to the structures and the remaining track (in case of double tracks on viaduct). Once again, it is necessary to check with the track specialty and maintenance may be permissible only during short duration at temperature near the rail neutral temperature. In case of bridge, track specialty and bridge specialty must coordinate to define clearly the bridge bearing replacement method. Fasteners may be unclippedon both side of the expansion joint in order to avoid excessivefastener uplift and rail stresses whenthe bridge structureis lifted to replacebearing. Alternatively, lifting simultaneously both structures on each side of the bridge expansion joint can be implemented to maintain track integrity during bearing replacement.

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9. PRESENTATION OF RAIL STRUCTURE INTERACTION SOFTWARES These sub-chapters are just short presentation of the softwareand their capabilities/requirements.

9.1 CWRBIA CWRBIA (Continuous Welded Rail Bridge Interaction Analysis) is a pre -post processor using the software ST1 (from SETRA) to perform the non-linear calculation. It is an Excel macro and requires the proper version of ST1 on the same computer to function. It is one of the first dedicated rail structure interaction program developed at SYSTRA. Its main advantage is the simplicity to model simplecases (succession of spans) and to obtain the results in an Excel format (data and graph). The learning curve is also very short. Nevertheless,as the software ST1 does not perform directly nonlinear calculations, iterative process is carried out and calculations are quite slow for large model. It has been widely used at SYSTRA in the past (as it was the only tool available), but is replaced today by software that can model and calculate quickly more complex track and bridge arrangement.

9.2 SOFISTIK E. Cogny -Please complete this part.

9.3 CWR-BUCKLE/INDY As part of the Federal Railroad Administration’s (FRA) track systems research program, the US DOT’S Volpe Center has developedsoftware to evaluate track lateral strength and stabilitylimitsfor improved safety and performance of CWR. They are called CWR-BUCKLE and CWR-INDY. CWR-INDY is a userfriendly version of CWR-BUCKLE with parameters for various types of track already entered in a database for easy selection. A risk based approach of track buckling safety is provided by the software CWR-SAFE. These software do not carried rail structure interaction analysis in case of bridge, but can be used to define the maximum allowablerail temperature on a project in order to avoid buckling risk (either with a deterministic approach or a risk base approach of track buckling safety). As for CWERRI software (see below), they were used to define the allowable temperature (track buckling) for various typical cases in the UIC 720. No information is provided on the availability of the software for purchase and use.

9.4 CWERRI CWERRI has been developed by the university of technology ofDelft for the design and analysis ofCWR track, commissioned by the European Railway Research Institute. It covers straight and curve track, typical and embedded rail system, track bridges interaction, buckling anal ysis of ballasted track. As for CWR-BUCKLE and CWR-INDY, It was used to define the allowable temperature (track buckling) for various typical cases in the UIC 720. No information is provided on the availability of the software for purchase and use.

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9.5 MIDAS Rail Track Analysis Model Wizard in MIDAS is provided to calculate additional stresses and displacements due to an interaction between decks and rails. It is based on UIC 774-3. Horizontal loadings due to temperature, braking/acceleration and vertical train loading are taken into account. Calculation for broken rail case can also be carried out, but effect of track curvature cannot be taken into account.

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10. CONCLUSION This technical guide presents the specifications related to rail structure interaction from codes and technical recommendations documentsused by Systra on its projects. Feedbacks from existing project are also provided. Improvement in computationcapabilities has allowed extensive useof finite element modelling (FEM) and refinement in the analysis, but to apprehend rail structure interaction analysis in the design of railway structure remains a challengetoday. The main difficulty is not the FEM calculation itself,but is the understanding of the phenomenon and is selecting appropriate standards and criteria. As the reader may have noticed during its reading, there is a wide variety of approach from standards and each standard may cover some cases and not others. In conclusion, there isn’t a unified theory regarding rail structure interaction. This report focuses on existing standards and in which cases they can be used. Standardsare presented in chapters 4 and 5. Chapter 6 provides a synthetic table of the criteria related to rail structure interaction. Cases not covered by standards require dedicated study to assess which criteria can safely be applied. Methodology to define criteria for these cases is out of the scope of this guide and will be the subject of further technical guides.

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11. APPENDIX 1: SIMPLIFIED METHOD TO CALCULATE RSI RADIAL FORCE IN CURVE As the rail are restrained transversally by the fastening system in the structure, rail stress increaseand decrease generate radial force on the bearings, piers and foundations. The resulting transverse displacement of the structuretendsin return to decreasethe rail stress until an equilibrium is reached. Fig. 72

Radial effects of rail compressive internal forces in curve

In addition, external transverse forces, such as centrifugal forces, hunting forces and wind load, tends to decrease the rail stress (and transverse forces due to these rail stress) when they act in the same direction as the effect of rail stress until, once again, an equilibrium is reached. The method below present a methodology to assess these forces on bearings and piers. For the temperature load, the transverse force per bearing (in MN) is calculated using the following formula: F1 = si,1 / (1 + E * Nr * A * L / (K1 * R^2)) * (Nr *A * L / R) / Nbearing With

si,1 : Average stress in the rail under temperature load (MN/m2) E : Rail elasticity modulus (MN/m2) Nr: Number of rail Nbearings : Number of bearings A: Rail section (one rail) (m2) L: Average span length on pier (m) K1: Pier + bearings stiffness according to temperature load case –long term (MN/m) R: Track radius (m)

For the braking and acceleration load, the transverse force per bearing (in MN) is calculated using the following formula: F2 = si,2 / (1 + E * Nr * A * L / (K2 * R^2)) * (Nr *A * L / R) / Nbearing With

si,2 : Average stress in the rail under braking/acceleration load (MN/m2) K2: Pier + bearings stiffness according to braking load case – short term (MN/m)

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Considering an externally applied force due to centrifugal forces, hunting forces and wind load of F ext, acting in the same direction as the transverse effect of rail stress, then the reduced externally force, per bearing, taken into account rail stress decrease, is: Fext,red = Fext / (1 + (E / (K2 * R)) * (A * Nr * L / R)) / Nbearing

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