application limits for continuously welded rails on...

Jef Pauwels

temporary bridge decksApplication limits for continuously welded rails on

Academic year 2014-2015Faculty of Engineering and ArchitectureChairman: Prof. dr. ir. Peter TrochDepartment of Civil Engineering

Master of Science in Civil EngineeringMaster's dissertation submitted in order to obtain the academic degree of

Counsellor: Ir. Ken SchotteSupervisors: Prof. Jan Mys, Prof. dr. ir. Hans De Backer

i

PREFACE

During the first of two master years of my education for Civil Engineer: Construction, a course of choice

had to be followed. I chose to follow the course ‘Railroads’ taught by Prof. Jan Mys, and thanks to this

course my interests in railroads increased. Additionally, during my education of Civil Engineering

Technology at Kaho Sint-Lieven Ghent, I had the privilege to be allowed to follow an internship at Victor

Buyck Steel Construction. During this internship my interest in bridge structures was triggered and

therefore I started to look for a dissertation topic in this field. When I subsequently stumbled on the

title “Application limits for continuously welded rails on temporary bridge decks”, combining two

subjects which had my interest in one dissertation, it was a logic choice to apply for this topic.

ACKNOWLEDGEMENTS

Throughout my studies and my Master’s dissertation in particular, I acquired more appreciation for

several people. All of these people helped me in one way or another and I therefore would like to

mention them.

First of all I would like to thank prof. dr. ir. Hans De Backer and prof. ir. Jan Mys for giving me the

opportunity to work on this subject. It was a pleasure working with them and I am grateful for the

feedback, ideas and help they both offered me.

Furthermore, I extensively want to thank ir. Ken Schotte. Whenever I had questions or encountered a

complication regarding the implementation of the model into the Samcef Software, he was available

and ready to help me.

Finally, I would also like to thank ir. Ben Ferdinande, ir Didier van de Velde and ir. Alex Lefevre of

INFRABEL. They have put a lot of time and work in assisting me during various meetings. Moreover

they enriched me with their insights and ideas to complement my thesis. I really enjoyed assisting in

the research they are performing on the application of temporary bridge decks.

ii

PERMISSION FOR USAGE

The author gives permission to make this master dissertation available for consultation and to copy

parts of this master dissertation for personal use. In the case of any other use, the limitations of the

copyright have to be respected, in particular with regard to the obligation to state expressly the source

when quoting results from this master dissertation.

22th of May Jef Pauwels

iii

ABSTRACT

This study investigates the possibility of omitting rail expansion devices from the track configuration

when CWR is continued over temporary bridge decks. This is done by analysing the arising track/bridge

interaction phenomena. In a first parametric analysis the additional rail stresses due to moving train

loads and temperature variations are assessed using a computer model based on stipulations provided

in the UIC code 774-3R. Subsequently the model is expanded to a more complex model which is able

to simulate the buckling behaviour of the rail track. Using this model a second parametric study is

performed in which the model is only loaded with thermal loads. In this way the parameters which are

predominant in determining the critical buckling temperature of the rails are determined and an

assessment is made on the magnitude of the margin of safety with respect to thermal buckling.

It is found that depending on the magnitude of two main factors, the lateral ballast resistance and the

amplitude of the initial misalignment a large reduction of the track stability might arise. Therefore a

minimal characteristic lateral ballast resistance of 4 kN is recommended along with a maximal

allowable misalignment amplitude of 7 mm for the case of thermal track buckling.

In order to be able to make a good founded conclusion on the allowance of train passage over a

temporary bridge deck without expansion devices it will be necessary to perform further research by

expanding the 3D model assembled in this dissertation in order to be able to correctly take into account

the influence of both the moving train loads and thermal loads.

Author

Jef Pauwels

Academic year

2014 - 2015

Supervisors

Prof. dr. ir. Hans De Backer

Prof. ir. Jan Mys

Counsellor

Ir. Ken Schotte

Title

Application limits for continuously welded rails on temporary

bridge decks

Department, faculty and chairman

Department of Civil Engineering

Chairman: Prof. dr. ir. Peter Troch

Faculty of Engineering and Architecture, University of Ghent

Keywords:

Track-bridge interaction, temporary bridge decks, application limits, parametric study

iv

Application limits for continuously welded rails on

temporary bridge decks

Jef Pauwels

Supervisors: Prof. dr. ir. Hans De Backer, Prof. Jan Mys

Counsellor: Ir. Ken Schotte

Abstract This study investigates the possibility of omitting

rail expansion devices from the track configuration when CWR is

continued over temporary bridge decks. This is done by analysing

the arising track/bridge interaction phenomena. In a first

parametric analysis the additional rail stresses due to moving

train loads and temperature variations are assessed using a

computer model based on stipulations provided in the UIC code

774-3R [1]. Subsequently the model is expanded to a more

complex model which is able to simulate the buckling behaviour

of the rail track. Using this model a second parametric study is

performed in which the model is only loaded with thermal loads.

In this way the parameters which are predominant in

determining the critical buckling temperature of the rails are

determined and an assessment can is made on the magnitude of

the margin of safety with respect to thermal buckling.

It is found that depending on the magnitude of two main

factors, the lateral ballast resistance and the amplitude of the

initial misalignment a large reduction of the track stability might

arise. Therefore a minimal characteristic lateral ballast resistance

of 4 kN is recommended along with a maximal allowable

misalignment amplitude of 7 mm for the case of thermal track

buckling.

In order to be able to make a good founded conclusion on the

allowance of train passage over a temporary bridge deck without

expansion devices it will be necessary to perform further research

by expanding the 3D model assembled in this dissertation in

order to be able to correctly take into account the influence of

both the moving train loads and thermal loads.

Keywords Track/bridge interaction, temporary bridge decks,

applications limits, parametric study

I. INTRODUCTION

In situations where maintenance works on the track bed

cannot be done while assuring stability of the tracks temporary

bridge decks are used. An example of such a configuration is

given in Figure 1. In such situations, the ballast layers are

entirely replaced by temporary bridge decks. For safety

reasons and in the absence of clear application criteria, the

continuous welded rails are systematically interrupted before

and after these temporary constructions. However, this method

causes high costs since the need to install expansion joints also

requires permanent maintenance works.

The aim of this dissertation is to study this problem in depth

and to determine in which circumstances the use of continuous

welded rails without expansion joints could be allowed when

using such temporary bridges. Although these temporary

bridge decks are in many ways different from actual bridges,

J. Pauwels is a student at the, Ghent University (UGent), Gent, Belgium.

E-mail: [email protected] .

they also show a lot of interesting similarities which can be

used for the evaluation of the interaction between temporary

bridge decks and tracks.

In order to determine all the conditions that are strictly

necessary for the use of continuously welded rails and what

condition are advantageous but not necessary, a parametric

study will be performed using the infinite elements program

Samcef Field. Based on the results of this analysis, eventually

specific proposals will be developed to allow the use of

continuously welded rails in specific circumstances

determined by clear criteria.

Figure 1: Example of a twin girder temporary bridge deck [2]

II. TRACK/BRIDGE INTERACTION

If continuous welded rails are continued over bridges the

track and bridge are interlinked to each other, regardless of

whether the track is directly fastened or laid on a ballasted

bed. This interlinking affects the behaviour of one on the

other, which can be termed as the interaction between the

bridge and the track. Movement of either one of them will

result in forces on the other.

During the past decennia a lot of research has been

performed on the subject of interaction. The ERRI (the

European Rail Research Institute) Committee D 213 carried

out an extensive study to analyse and asses these interactive

forces. The results of these studies were subsequently

summarized in the form of a report which is named UIC code

774-3R[1]. This report contains the actions to be considered,

the configuration of test models and the design requirements

needed in order to prevent damage due to these interaction

effects. This leaflet has been accepted as the general guideline

for all interaction analyses and will therefore also play an

important role in this dissertation.

The forces causing the interaction between track and bridge

are those that cause relative- displacements between track and

v

the bridge Three different loading cases should be regarded

according to the UIC code 774-3R [1] for each direction of the

moving train. These are:

- Vertical forces of 80 kN/m situated on left

respectively right embankment and bridge fully

loaded.

- Braking forces of 20 kN/m situated on left

respectively right embankment and bridge fully

loaded

- Influence of temperature variation in bridge due

to respectively a temperature increase of +35°C and a

temperature decrease of -35°C

Due to these forces, additional rail stresses arise in the track

and these might, in some cases, become too large resulting in

track buckling for the case of large compressive forces or rail

breaks for the case of large tensile forces. It should therefore

be verified whether these additional rail stresses remain within

acceptable limits, which are imposed by the UIC code 774-3R.

In order to do so a computer model will be assembled by

which these additional rail stresses can be computed.

III. ASSESSMENT OF ADDITIONAL RAIL STRESSES IN FIRST

PARAMETRIC STUDY ON 2D MODEL

Using the model configuration shown in Figure 2 a first

parametric analysis is performed in which multiple parameters

of both the temporary bridge deck and surroundings are

analysed. Their influence on the arising stresses in the rails

due the different interaction loading cases are investigated. At

the same time it is also verified whether the arising rail

stresses and rail/bridge displacements comply with the

limitations given in the UIC leaflet 774-3R.

A. General composition

The track is represented by one single Wire-type element to

which a flexible beam behaviour is assigned which

corresponds to two UIC 60 rails. The position of the track

coincides with the upper face of the bridge deck. The bridge

deck is modelled horizontal flexible beam-type elements

which have the same properties (bending stiffness, material

properties,…) as the actual bridge. These elements are located

at the centre of gravity of the bridge and are depicted in Figure

2 as (5). Additionally vertical rigid beam-type elements which

have an infinite stiffness connect the horizontal elements to the

bearings or to the track. These and are depicted in Figure 2 as

(6) respectively (4).The connection between track and

embankment/bridge deck is modelled using bilinear

longitudinal spring elements. In case of a temporary bridge

deck usually neoprene bearings are used for which one bearing

is fixed and the other one is movable.

In order to ensure the model yields the correct interaction

behavior first the assembly was validated by checking multiple

test-cases provided in the UIC code 774-3R[1]. Subsequently,

the validated model was then adjusted and expanded to the

case of a temporary bridge deck.

B. Model properties

Table 1 shows the model properties and reference values of

the parameters investigated in this study. Each parameter is

varied in a practical range while the other parameters are kept

constant. Only the properties of the track were not altered. The

properties of the temporary bridge deck used are those

corresponding to a temporary bridge deck used by

INFRABEL for a span of 12 metres. [2]

Figure 2: Schematic overview of the temporary bridge deck model in Samcef Field

Table 1: Properties of 2D model Table 2 : Characteristic long. ballast resistance [kN/m]

Table 3: Characteristic long. fastener resistance [kN/m]

vi

Figure 3: Sensitivity of rail stresses with respect to bridge span

length

Figure 4: Sensitivity of rail stresses with respect to bearing stiffness

C. Results

In Figure 3 to Figure 7 the results of the parametric analysis

are shown. It was found that the span length and bridge

bending stiffness are the most determining parameters with

respect to the arising additional rail stresses. It will thus be

compulsory to impose certain application limits to these

parameters for the allowance of continuing CWR track over a

temporary bridge deck. The other parameters examined also

had an influence on the arising stresses but this influence was

less decisive.

The standard configuration used in this parametric analysis

corresponds to the case of a temporary bridge deck with a

span length of 20 metres. The bending stiffness of the

temporary bridge deck is chosen equal to the stiffness of an

actual temporary bridge deck used by INFRABEL for a span

length of 12 metres. The characteristics for the longitudinal

track resistance and the loads applied to the model are both

based on the values imposed by the UIC code 774-3R.

Therefore, if this configuration complies with the limitations

given by the UIC code 774-3R (maximum additional

compressive rail stress 72 N/mm² and maximum additional

tensile rail stress is 92 N/mm²) , one can assume that for this

span length and temporary bridge deck configuration it is

allowed to continue CWR track over the bridge structure

without providing an expansion device.

When considering the graphs shown above, it is found that,

not only for the standard configuration but also for all other

test-cases examined (except for the one with a span length of

30 metres), the limitations imposed by the UIC code 774-3R

are met. As a result one can state that for these configurations

it is allowed to omit the expansion device from the structural

configuration of the track.

Furthermore, it could even be concluded that, if the

temporary bridge decks used by INFRABEL are applied

Figure 5: Sensitivity of rail stresses with respect to ballast quality

Figure 6: Sensitivity of rail stresses with respect to fastener long.

resistance on temporary bridge deck

Figure 7: Sensitivity of rail stresses with respect to bending stiffness

of temporary bridge deck

corresponding to their practical applied span range, there is

still a large safety margin with respect to the additional rail

stresses and displacements.

IV. PARAMETRIC STUDY ON 3D TEMPORARY BRIDGE DECK

MODEL

In the previous section use has been made of a 2D model in

which only the influence of the longitudinal and vertical

displacements of track and bridge were taken into account. In

these models the lateral component has been neglected. This

simplification was acceptable as long as the arising additional

rail stresses and relative and absolute displacements due to the

interaction effect remained within certain limits provided by

the UIC Code 774-3R. If this was the case then one could state

that the design provided sufficient safety against track

buckling and rail break.

However, in an attempt to find the more exact boundaries

concerning track buckling due to interaction the model

assembled in section III will now be further expanded to a 3D

model. This 3D model will take into account the lateral

deflections of the rail and the elastoplastic behaviour of the

rail. In this way it will become possible to simulate the actual

buckling behaviour of the track.

vii

A. Modifications with respect to 2D model

The following modifications with respect to the 2D model

were made: The track is modelled using two separate

elastoplastic beam elements representing each one UIC 60

rail. Every 0.5 metres the lateral distance between a pair of

opposing mesh nodes of the rail elements is fixed in order to

simulate the presence of a sleeper. The centre line of the

bridge deck is now situated in between both rails at equal

distances, additional lateral beams are required to provide the

connection between rails and bridge deck. In order to model

the lateral ballast resistance bilinear spring elements are

applied to both rails each 0.5 metres. An overview of this new

configuration is given in Figure 8.

B. Loads

Since the Samcef model assembled in this dissertation does

not allow to perform a complete analysis (applying the

temperature loads first on an unloaded track and afterwards

adding the moving train loads) it does not seem too suitable to

perform a sensitivity analysis with respect to the buckling of a

rail track loaded by both the moving train loads and the

temperature loads. As a result it is opted to only check the

buckling behaviour for an unloaded track charged with

temperature loads (rail expansion and bridge expansion).

It is opted to make a distinction between the temperature

increase of the bridge deck and the one of the rail track. For

the temperature increase of the bridge deck an upper limit of

35°C is chosen, in accordance with the UIC code 774-3R.The

temperature of the bridge deck can never exceed this limit. In

this way it is possible to investigate the critical temperature

increase of the rail for which buckling occurs. This allowable

temperature increase of the rail can then be regarded as a

measure in order to express the level of safety against thermal

track buckling.

C. Model properties

All test cases are assembled starting from the same standard

case. Subsequently, in an attempt to investigate the influence

of each parameter, all parameters are kept constant except for

the one being investigated. In this way it is possible to check

the influence of the regarded parameter on the arising critical

buckling temperature. The properties of the standard case are

provided in Table 4. As found in Table 4 a lateral

misalignment with a wavelength of 4 meters and an amplitude

of 3 millimetres is standardly incorporated in each model. This

is done in order to destabilize the model. If no lateral

misalignment would be applied to the configuration the model

would not yield any solutions due to the perfect straightness of

the beams used. There are however two exceptions with

respect to the standard properties used. For the tests in which

the position of the amplitude is analysed a misalignment

amplitude of 17mm is used. For the tests in which the

wavelength of the misalignment is analysed both an amplitude

of 17mm is used and the position of the maximal deflection is

situated 6 metres away from the temporary bridge deck.

Table 4: Properties of 3D model

D. Results

Based on previous studies and the results obtained in the

parametric analysis using the 2D model it was opted to

examine the influence of the following parameters: span

length, longitudinal resistance of fasteners on temporary

bridge deck, longitudinal ballast resistance, lateral ballast

resistance, wavelength of initial misalignment, amplitude of

initial misalignment and position of initial misalignment. The

results are given in Figure 9 to Figure 15.

Figure 9: Sensitivity of critical temperature increase with respect to

the position of the misalignment

Figure 8: Overview of configuration of 3D model

viii


the amplitude of the misalignment


the span length


the longitudinal ballast resistance

Based on the results it is found that the lateral ballast

resistance and amplitude of the initial wavelength are the most

determining factors with respect to the buckling resistance of

the track. Therefore in order to ensure a sufficient margin of

safety is present with respect to track buckling it will be

compulsory to impose limits to these parameters. Additionally

it is found that the magnitude of the wavelength of the

misalignment, the position of the misalignment, the span

length and the longitudinal resistance of the fasteners on the

temporary bridge deck can influence the critical temperature

increase in a significant way. The influence of the longitudinal

ballast resistance was rather negligible.


the wavelength of the misalignment


the lateral ballast resistance


the longitudinal fastener resistance on the temporary bridge deck

V. FORMULATION OF APPLICATION LIMITS BASED ON 3D

MODEL

Based on the findings of the parametric study shown in the

previous section, the following recommendations are given in

order to ensure a safe application of CWR track over a

temporary bridge deck without having to install an expansion

device. It should be emphasized that these recommendations

are only valid for the case of thermal loading of the bridge and

track. No moving train loads were applied to the model and

therefore additional research will have to be performed in

order to check the application limits for these loading cases.

(1) In order to limit the detrimental influence of lateral

misalignments on the track stability it will be compulsory to

measure the maximal arising lateral misalignment amplitude

ix

during the execution of the maintenance works. As can be

derived from Figure 10 the major decrease of the critical rail

buckling temperature arises in the interval of 3 to 12

millimetres for the track misalignment amplitude. Therefore it

might be advisable to monitor the lateral misalignments during

the maintenance works and try to restrict the arising

misalignment amplitudes to a maximum of approximately 7

millimetres.

(2) Due to the incorporation of the temporary bridge deck in

the track configuration and the presence of heavy machinery

on the construction site locally a reduced compaction and thus

reduced lateral ballast resistance might arise. As proven in the

parametric study this can be very detrimental with respect to

the stability of the track and therefore limitations should be

imposed with respect to the minimum required lateral ballast

resistance. Based on in situ measurements performed by the

Technical University of Munich and the track measurement

department of DB a mean value of 6 kN was found for the

characteristic resistance of timber sleepers in a consolidated

condition[3].For this condition very high safety margins are

found with respect to the critical temperature increase.

Therefore a slightly lower lateral ballast resistance of 4 kN can

still be allowed. Additionally it is also advised in order to

make sure that a sufficient high lateral ballast resistance is

preserved that the track is compacted after implementation of

the temporary bridge deck.

(3) As found in the parametric study the most critical position

of a track defect is situated in the immediate surroundings of

the movable support. Still, the deviation between the different

critical temperature increases up to a position of 20 metres

away from the movable support remains rather small. From

this one could conclude that the part of the track beyond the

movable support, with a length of a factor 1 or 1.5 times the

bridge span length, should be monitored more strictly for the

presence of misalignments.

(4) When analysing the influence of the longitudinal resistance

of the fasteners on the temporary bridge deck it can be seen in

Figure 15 that a reduced clamping force results in a higher

buckling resistance of the track. Therefore the usage of such

fasteners might be advantageous with respect to the track

stability. However the influence of this parameter is not that

decisive in determining the critical temperature increase of the

rails.

(5) For the wavelength of the initial misalignment it was found

that the most critical wavelength is dependent on the

magnitude of the lateral ballast resistance. For lateral ballast

resistances equal to 4 or 6 kN the most critical wavelengths for

the initial misalignment were found in the range of 8 to 12

metres. For smaller initial misalignment wavelengths slightly

higher critical temperature increases were found. However the

relative deviation is not that high. For misalignment

wavelengths longer than 12 metres no tests were performed.

Further research for these misalignment wavelengths might be

advisable.

VI. GENERAL CONCLUSION

If one would rely on the model assembled according to the

UIC code 774-3R in section III one could conclude that it is

allowed to continue CWR track over a temporary bridge deck

without providing expansion devices in front and after the

temporary bridge. However if one considers the results

obtained in the parametric analysis using the 3D model, in

which the track is loaded with temperature loads only, it is

found that the conclusion is not that straightforward. It is

acquired that depending on the magnitude of two main factors,

the lateral ballast resistance and the amplitude of the initial

misalignment (which are not incorporated in the 2D model of

section III), a large reduction of the track stability might arise.

It is found that, for a situation in which very bad track

conditions are present, this reduction may even lead to a

critical buckling temperature increase of only 29°C, being

smaller than the imposed temperature increase (35°C for a

bridge deck and 50°C for the track) by the UIC code 774-3R.

Therefore it is compulsory to impose strict limits to the

magnitude of these parameters in order to ensure an adequate

track stability with respect to thermal buckling. A minimal

characteristic lateral ballast resistance of 4 kN is

recommended along with a maximal allowable misalignment

amplitude of 7 mm.

It should be noted that these limitations are only valid with

respect to the stability of the track loaded with temperature

loads only. It is not possible to make a conclusion on the fact

whether it is allowed to allow train passage over the temporary

bridge decks since no vertical and braking loads due to a

moving train have been incorporated in the models of section

IV. In order to be able to make a good founded conclusion on

the allowance of train passage over a temporary bridge deck

without expansion devices it will be necessary to perform

further research by expanding the 3D model of section IV.

ACKNOWLEDGEMENTS

The author would like to thank prof. dr. ir. Hans De Backer

and prof. ir. Jan Mys for giving me the opportunity to work on

this subject. It was a pleasure working with them and I am

grateful for the feedback, ideas and help they both offered me.

Furthermore, I extensively want to thank ir. Ken Schotte.

Whenever I had questions or encountered a complication

regarding the implementation of the model into the Samcef

Software, he was available and ready to help me.

Finally, I would also like to thank ir. Ben Ferdinande, ir

Didier van de Velde and ir. Alex Lefevre of INFRABEL.

They have put a lot of time and work in assisting me during

various meetings. Moreover they enriched me with their

insights and ideas to complement my thesis. I really enjoyed

assisting in the research they are performing on the application

of temporary bridge decks

REFERENCES

[1] Union Internationale de Chemins Fer, “UIC Code 774-3 :

Track/bridge interaction,” 2001.

[2] A. (INFRABEL) Lefevre, “Bundel 34.6: Spoorversterkingen,

voorlopige brugdekken en stalen boogbekisting,” 2015.

[3] M. Zacher, “Calculation of the critical temperature for track

buckling in a switch P3550 – XAM 1 / 46 on the line Liège -

Brussels Document : Date : 10-P-4926 - ICE3 MS Belgien

Fahrzeug / Fahrbahn-Wechselwirkung Völckerstraße 5 80939

München,” 2011.

x

TABLE OF CONTENTS

Preface………………………………………………………………………………………………………………………………………………..i

Acknowledgements……………………………………………………………………………………………………………………………..i

Permission for usage….……………………………………………………………………………………………………………………….ii

Abstract………………………………………………………………………………………………………………………………………….….iii

Extended Abstract………………………….......................................................................................................iv

Table of Contents ..................................................................................................................................... x

List of abbreviations and symbols ......................................................................................................... xiv

Introduction ....................................................................................................................... I-1

Literature study ............................................................................................................ II-2

1 Introduction .............................................................................................................................. II-2

2 Concept of continuous welded rail on an embankment .......................................................... II-2

3 Track-bridge interaction ........................................................................................................... II-3

4 ZLR Fastenings .......................................................................................................................... II-5

5 Track Stability ........................................................................................................................... II-7

5.1 Introduction ...................................................................................................................... II-7

5.2 Buckling theory ................................................................................................................. II-9

5.3 Safety Concept ................................................................................................................ II-11

5.4 Buckling parameters for cwr on an embankment .......................................................... II-13

6 Temporary bridge decks ......................................................................................................... II-17

6.1 Introduction .................................................................................................................... II-17

6.2 Temporary bridge deck configuration ............................................................................ II-18

Design and validation of preliminary 2D model ........................................................ III-20

1 Introduction ........................................................................................................................... III-20

2 Assembly of classical bridge model ....................................................................................... III-20

2.1 Modeler ......................................................................................................................... III-20

2.2 Analysis Data ................................................................................................................. III-21

xi

2.3 Mesh .............................................................................................................................. III-24

2.4 Solver Settings ............................................................................................................... III-24

3 loading cases ......................................................................................................................... III-25

4 Validation of the model ......................................................................................................... III-28

4.1 Data ............................................................................................................................... III-28

4.2 Loads .............................................................................................................................. III-29

4.3 Results ........................................................................................................................... III-30

4.4 Overview results ............................................................................................................ III-33

5 Conclusion ............................................................................................................................. III-34

Design of 2D temporary bridge deck model and execution of a first parametric study

IV-35

1 Introduction ........................................................................................................................... IV-35

2 Assembly of temporary bridge deck model .......................................................................... IV-35

2.1 Modeler ......................................................................................................................... IV-35

2.2 Analysis Data ................................................................................................................. IV-36

2.3 Loads .............................................................................................................................. IV-40

2.4 Mesh .............................................................................................................................. IV-40

2.5 Solver Settings ............................................................................................................... IV-41

3 Parametric study ................................................................................................................... IV-41

3.1 Imposed limitations for track-bridge interaction effects .............................................. IV-41

3.2 Data ............................................................................................................................... IV-42

3.3 Results ........................................................................................................................... IV-43

4 General conclusions .............................................................................................................. IV-53

Design and validation of 3D model for the case of a temporary bridge deck ............ V-56

1 introduction ............................................................................................................................ V-56

2 Assembly of 3D temporary bridge model .............................................................................. V-56

2.1 Modeler .......................................................................................................................... V-56

2.2 Analysis Data .................................................................................................................. V-57

xii

2.3 Mesh ............................................................................................................................... V-61

2.4 Solver Settings ................................................................................................................ V-62

3 Validation of the model .......................................................................................................... V-62

3.1 Data ................................................................................................................................ V-62

3.2 Loads ............................................................................................................................... V-63

3.3 Results ............................................................................................................................ V-63

Parametric study on 3D temporary bridge deck model ............................................ VI-68

1 Introduction ........................................................................................................................... VI-68

2 Clarifications regarding the procedure of the parametric study .......................................... VI-68

2.1 Analysis type .................................................................................................................. VI-68

2.2 Loads .............................................................................................................................. VI-68

2.3 Definition of critical temperature increase ................................................................... VI-69

2.4 Obtained results ............................................................................................................ VI-70

2.5 Standard case ................................................................................................................ VI-71

3 Parameters to be examined .................................................................................................. VI-72

3.1 Presence of lateral misalignment in rail configuration ................................................. VI-73

3.2 Lateral ballast resistance ............................................................................................... VI-76

3.3 Torsional resistance fasteners ....................................................................................... VI-76

3.4 Bending stiffness temporary bridge deck ...................................................................... VI-76

3.5 Stiffness of fixed bearing ............................................................................................... VI-76

3.6 Longitudinal track resistance embankments ................................................................ VI-77

3.7 Longitudinal track resistance fasteners on temporary bridge deck .............................. VI-77

3.8 Span length .................................................................................................................... VI-77

4 Results ................................................................................................................................... VI-78

4.1 Presence of lateral misalignment in rail configuration ................................................. VI-78

4.2 Longitudinal ballast resistance embankments .............................................................. VI-80

4.3 Longitudinal track resistance fasteners on temporary bridge deck .............................. VI-81


xiii

4.5 Span length .................................................................................................................... VI-82

5 Discussion of results .............................................................................................................. VI-83

5.1 Position of lateral misalignment.................................................................................... VI-83

5.2 Amplitude of lateral misalignment ................................................................................ VI-84

5.3 Wavelength of lateral misalignment ............................................................................. VI-84

5.4 Longitudinal ballast resistance embankments .............................................................. VI-85

5.5 Longitudinal resistance fasteners on temporary bridge deck ....................................... VI-86


5.7 Span length .................................................................................................................... VI-87

6 Quantification of safety margin............................................................................................. VI-88

7 Important remarks regarding the obtained results .............................................................. VI-89

General conclusions and formulation of application limits...................................... VII-90

1 Conclusions and application limits based on 2D interaction model assembled in Chapter IV VII-

90

1.1 conclusions ................................................................................................................... VII-90

1.2 Formulation of application limits ................................................................................. VII-91

2 Conclusions and application limits based on 3D model simulating thermal buckling ......... VII-93

2.1 conclusions ................................................................................................................... VII-93

2.2 Formulation of application limits ................................................................................. VII-94

3 General conclusion ............................................................................................................... VII-96

Further research suggestions .............................................................................. VIII-97

References ............................................................................................................................................. 98

List of figures ......................................................................................................................................... 99

List of tables ........................................................................................................................................ 102

Annexes………………………………………………………………………………………………………………………………………….104

xiv

LIST OF ABBREVIATIONS AND SYMBOLS

Roman upper case letters

CWR Continuous Welded Rail

E Modulus of elasticity; Young’s modulus

ZLR Zero Longitudinal Restraint

Tall The allowable temperature increase of the rail above the rail neutral temperature in

order to ensure adequate rail buckling safety

Tmax Temperature increase above rail stress-free temperature for which the track will

buckle without any addition of external energy

Tmin Minimal temperature increase above rail stress-free temperature for which track

buckling can still occur if sufficient external energy is supplied

Ksupport Longitudinal resistance of fixed support

Usupport Elastic-plastic boundary of longitudinal support spring

S Area of cross section of bridge deck

Vi Distance of neutral axis bridge deck to position of bridge bearing

Wi Distance of neutral axis bridge deck to upper face deck

Roman lower case letters

α Coefficient of thermal expansion

kn Longitudinal stiffness of neoprene bearing pad

k Characteristic longitudinal track resistance

u0 Elastic-plastic boundary for longitudinal track resistance

Chapter I Introduction

Application limits for continuously welded rail on temporary bridge decks I-1

INTRODUCTION

These days most modern railways use continuously welded rails (CWR) for their track configuration.

Continuously welded rails are composed of multiple smaller rails which are welded together forming

one continuous rail which may extend over several kilometres. The use of this technique offers a lot

of advantages, such as an enhanced riding quality, better maintainability of the track and reduced

costs of maintenance resulting in a high economic benefit. But at the same time it also poses new

challenges to the railway engineers.

In situations where maintenance works on the track bed cannot be done while assuring stability of

the tracks temporary bridge decks are used. In such situations, the ballast layers are removed and

entirely replaced by temporary bridge decks. For safety reasons and in the absence of clear

application criteria, the continuous welded rails are systematically interrupted before and after these

temporary constructions. This causes high costs because the need to install expansion joints also

necessitates permanent maintenance works.

The aim of this dissertation is to study this problem in depth and to determine in which

circumstances the use of continuous welded rails without expansion joints could be allowed when

using such temporary bridges. During the past few decennia a lot of research has been done on the

subject of track-bridge interaction. The UIC Leaflet 774-3R and Euro-code 1991-2:2003 include the

basic methodology for analysis of track-bridge interaction and describe the actions to be considered

and the limit values to be complied with as regard to both the stresses and the displacements of rails.

Although these temporary bridge decks are in many ways different from actual bridges, they also

show a lot of interesting similarities which can be used for the evaluation of the interaction between

temporary bridge decks and tracks.

In order to determine all the conditions that are strictly necessary for the use of continuously welded

rails and what condition are advantageous but not necessary, a parametric study is performed using

the infinite elements program Samcef Field. Based on the results of this analysis, eventually specific

proposals are developed to allow the use of continuously welded rails in specific circumstances

determined by clear criteria.

Chapter II Literature study

Application limits for continuously welded rail on temporary bridge decks II-2

LITERATURE STUDY

1 INTRODUCTION

During this chapter existing papers and guidelines are condensed to an extensive introduction

regarding the analysis of continuing continuous welded rails over temporary bridge decks. First of all,

a short introduction on the general behaviour of continuous welded rail track situated on

embankments and on bridges is given. Secondly, the applicability of ZLR fastenings for temporary

bridge decks is examined in order to reduce the track-bridge interaction phenomena. Subsequently

the general stability of a train track is discussed, with the emphasis on the track buckling behaviour.

The different influencing factors are regarded and a first assessment is made on which factors will

prove to be important for the parametric analysis performed further in this dissertation. Finally, also

a short description on the use and composition of temporary bridge decks is given.

2 CONCEPT OF CONTINUOUS WELDED RAIL ON AN EMBANKMENT

In recent years continuous welded rails (CWR) have become an essential part of the modern railway

track structures due to their higher maintainability, safety and better riding quality compared to the

former fish plated track. Because of these advantages trains can travel at higher speeds and with less

friction. Therefore, this type of track is especially used for high-speed trains.

For the general case of a continuous welded rail on an embankment, the displacement of the rails is

prevented through the track fastening elements. These fasteners exert a clamping force onto the rail

in a way that all the longitudinal movement of the rail is transmitted to the sleepers, since the

resistance to rail/sleeper sliding is greater than the resistance to sleeper/ballast sliding. A typical

configuration of a ballasted track on an embankment is depicted in Fig. II-1. If consequently, a

thermal or traffic force is exerted onto the rail, longitudinal forces will arise in the tracks as a result of

the prohibited movement of the rails.

Fig. II-1: Typical cross section of ballasted track [1]



Due to these longitudinal forces, continuous welded rail track can typically be split up into three

different zones: a central zone, in which no displacements of the rails occur as a result of the

ballast/sleeper resistance, and two “breather” zones at each end of the central zone where

displacements augment when approaching the expansion devices resulting in decreasing normal

forces. This thermal behaviour is shown in Fig. II-2. [2]

Fig. II-2: Behaviour of CWR under the effects of temperature changes [2]

The magnitude of this arising normal forces ‘P’ equals:

𝑃 = 𝐴𝐸𝛼∆𝑇𝑅

In which:

α = the coefficient of thermal expansion (12.10-6 /°C)

ΔTR = the change in rail temperature relative to the rail neutral temperature

E = Young’s modulus of steel (210 000 N/mm²)

A = Combined cross-section of two rails

P = Normal force in the rail track

3 TRACK-BRIDGE INTERACTION

If now continuous welded rails are continued over bridges the track and bridge are interlinked to

each other, regardless of whether the track is directly fastened or laid on a ballasted bed. This

interlinking affects the behaviour of one on the other, which can be termed as the interaction

between the bridge and the track. Movement of either one of them will result in forces on the other.

As a result interaction between track and bridge is manifested in the following way [2]:

- Forces applied to a CWR track induce additional forces into the track and/or into the bearings

supporting the deck and movements of the track and of the deck.



- Any movement of the deck induces a movement of the track and an additional force in the

track and, indirectly, in the bridge bearings.

Fig. II-3: Example of a curve showing rail stresses due to a temperature variation in the bridge

deck [2]

During the past decennia a lot of research has been performed on the subject of interaction. The

ERRI (the European Rail Research Institute) Committee D 213 carried out an extensive study to

analyse and asses these interactive forces. The results of these studies were subsequently

summarized in the form of a report which was given the name ‘UIC code 774-3R’ [2]. This report

contains the actions to be considered, the configuration of test models and the design requirements

needed in order to prevent damage due to these interaction effects. This leaflet has been accepted

as the general guideline for all interaction analyses and will therefore also play an important role in

this dissertation.

The forces causing the interaction between track and bridge are those that cause relative-

displacements between track and the bridge. These are [2]:

1. The thermal expansion of the deck only, in the case of CWR, or the thermal expansion of the

deck and of the rail, whenever a rail expansion device is present

2. Horizontal braking and acceleration forces

3. Rotation of the deck on its supports as a result of the deck bending under vertical traffic

loads

4. Deformation of the concrete structure due to creep and shrinkage

5. Longitudinal displacement of the supports under the influence of the thermal gradient

6. Deformation of the structure due to the vertical temperature gradient

In most cases, the first three effects are the most important in bridge design. More information

concerning these first three effects is given in §3 Chapter III.

The additional forces, which arise in the track due to the interaction between track and bridge might,

in some cases, become too large resulting in track buckling for the case of large compressive forces

or rail breaks for the case of large tensile forces.



In order to solve this problem rail expansion devices might be used. However, this is not a very

attractive solution since these devices generate high impact loads and may accelerate bridge

degradation. Also, they are expensive to install and require a lot of maintenance. Therefore, during

this dissertation, it is tried to find an alternative in which expansion devices are not used.

An alternative to these rail expansion devices in CWR for example, is to allow the rail to be

unanchored in longitudinal direction over a certain length. For this, zero longitudinal restraint (ZLR)

fastenings could be used [3]. This alternative is briefly discussed in §4.

Another alternative, and the one which is examined in this dissertation, is to simply eliminate the

expansion device from the track configuration and continue the CWR track over the bridge without

making any alterations to the track design. This solution will however result in larger rail stresses and

it will therefore be compulsory to verify whether the arising stresses remain within acceptable limits.

This verification is performed in Chapter IV.

4 ZLR FASTENINGS

In order to prevent the need for rail expansion devices in CWR track when continuing CWR over

bridges zero longitudinal restraint (ZLR) fasteners might be useful.[3] These zero longitudinal

restraint fasteners do not prevent any longitudinal displacement of the rails and therefore no

(longitudinal) forces will be transferred to the bridge.

This type of fastening consists of a special steel baseplate which is fastened to the sleeper by means

of a Pandrol railclip, as depicted in Fig. II-5. Typically, a small opening is present which permits the

rails to move longitudinally with temperature changes, while holding the rail vertically in place. When

large lateral forces are present, the baseplate provides lateral restraint and prevents turning-over of

the rail. The rail pad under the rail is made of a low friction material such as Teflon and provides

almost no longitudinal restraint against movement of the rails with respect to the sleepers when

train loading is absent.[3]



Fig. II-4: Pandrol® ZLR System Fig. II-5: Principle sketch Pandrol® ZLR System [3]

However, a first disadvantage of this technique is that, if a rail fracture would occur, the gap at

fracture could enlarge as a result of the absence of longitudinal anchoring and movement of trains

passing over it, resulting eventually in a possible derailment. Also, when train loading is present, the

longitudinal restraint will increase, reducing the favourable effect of these fastenings.

Despite these disadvantages, this method has already been successfully applied several times.

Examples can be found at the ‘Olifants River Bridge’ in South Africa, the high-speed line Brussels-Lille

[3], the Mission Valley West light rail extension in San Diego[4], etc…

Also ‘The Manual of Instructions on Long Welded Rails’[5], which contains instructions for the

installation of Long Welded Rails and Continuous Welded Rails on Indian Railways, has incorporated a

section with regard to the application of ZLR fastenings on bridges. This manual states that bridges of

which the overall length does not exceed 30 metres can be provided with rail-free fastenings if the

following requirements are fulfilled:

1) The approach track up to 50 metres on both sides shall be well anchored by providing any

one of the following:

a. ST sleepers with elastic fastenings

b. PRC sleepers with elastic rail clips with fair ‘T’ or similar type creep anchors.

2) The ballast section of the approach track up to 50 metres shall be heaped up to the foot of

the rail on the shoulders and kept in well compacted and consolidated condition during the

months of extreme summer and winter.

Conclusion

Based on the information given above one could assume that the application of ZLR fastenings on

temporary bridge decks could form a valid solution in order to solve the problem of track-bridge



interaction when continuing CWR over a temporary bridge deck. Still, further research will be

required in order to verify their applicability, but this is not further examined during this dissertation.

5 TRACK STABILITY

5.1 INTRODUCTION

In order to obtain a better insight in the stability of continuous welded track on a temporary bridge

deck first the stability of a track on an embankment is analysed. Many different factors play a role in

this phenomenon. One tries to obtain a complete overview of the different influencing factors as a

first step towards determining the most important factors for the parametric study which is executed

further in this dissertation.

5.1.1 TRACK BUCKLING

A first instability phenomenon which might arise in a rail track is the formation of a large lateral

misalignment. This phenomenon is called track buckling and can have disastrous consequences such

as derailments. The amplitudes of the buckling deflections can range up to 1 metre and the length of

the deformed track can measure up to 25 metres long. The origin of this instability problem can be

the result of three different factors, these are large compressive forces in the rail, weakened track

conditions and vehicle induced loads.

Fig. II-6: Examples of track buckling in CWR

The compressive forces are the result of the constrained movement of the rail by the sleepers,

fasteners and ballast, in case the rail is loaded with a temperature above its ‘stress-free

temperature’. Also, compressive forces might occur as a result of braking and accelerating of a

moving train. This ‘stress-free’ temperature which is mentioned, is the temperature in the rail at

which the rail experiences zero longitudinal force. In Belgium, values for the stress-free temperature



are situated in the range of 20 to 30 °C. When the temperature in the rail increases above this

temperature, the rail experiences a compression force. When the temperature in the rail drops

below this ‘stress-free temperature’ tensile forces are developed. In order to prevent buckling of the

track it is essential to maintain a stable and high stress-free temperature.

Another major factor which influences the track buckling behaviour are weakened track conditions.

Examples of these weakened conditions are reduced longitudinal and lateral track resistance, lateral

alignment defects and lowered rail neutral temperature. These are factors which will prove to be

very important in delineating the required circumstances in which continuous welded rails are

allowed on temporary bridge decks. They will be discussed more thoroughly in §5.4.

A third and final critical issue on the subject of continuous welded track stability is the influence of

vehicle loads. Track buckling usually starts from an initial small alignment error. However, due to

train passage over this section this alignment error might aggravate and trigger buckling of the track.

This aggravation of the misalignment is caused by lateral wheel forces which arise in curved track or

in tangent track due to line or surface deviations. The type of track instability which is caused by

thermal and vehicle loads is called dynamic buckling. However, in the early theories of buckling, only

thermal loads were taken into account and vehicle loads were not accounted for. These theories are

designated as static theories.

5.1.2 RAIL BREAKS

The previous instability problem occurred due to an increase of the rail temperature above the

‘stress-free temperature’. When adversely the temperature is decreased below the ‘stress-free

temperature’ tensile forces will arise in the rail. When these forces become too large, rail cracks and

eventually rail breaks might occur at locations where internal defects are present or at weak welds.

This phenomenon is denoted with the term ‘rail pull apart’. Initial small cracks do not form any large

problems to the rails. The problems start when the cracks start to grow in size under the influence of

cyclic loading due to vehicle and thermal loads. This increase of the crack gap might eventually result

into disastrous derailments. In order to counter the increase of the crack sizes good anchoring of the

rails is essential. In most cases the initial gap size is rather small and the breaks are detected by the

use of a standard signalling system. Therefore rail breaks are considered to be less dangerous from a

safety point of view than track buckling. Hence the stress-free temperature of rails is often chosen

higher so lower compressive forces in the rails are obtained to the cost of higher tensile forces in

winter conditions.



5.2 BUCKLING THEORY

5.2.1 BUCKLING MECHANISM

As discussed above, track buckling can be initiated by a small initial misalignment 0. Subsequently

due to thermal compressive forces this misalignment may increase up to a lateral displacement wB,

which represents the boundary for a stable equilibrium. This maximum lateral displacement is

obtained at a temperature increase ΔTBmax above the tracks neutral temperature. At higher

temperatures the compressive forces will become too large and the track will become unstable,

resulting into buckling of the track. As a result a new equilibrium position is obtained corresponding

to a lateral displacement wC. This mechanism is depicted in Fig. II-7. From a thermal point of view the

track’s behaviour is shown in the buckling response curves in Fig. II-8.

Fig. II-7: Pre- and postbuckled track configurations [6]

Fig. II-8: Buckling response curves [6]

Fig. II-8 shows the behaviour of a track subjected to thermal forces only, as described above. In this

case buckling will occur at a temperature increase ΔTBmax above the neutral temperature. However,

buckling can also occur at a temperature increase ΔT smaller than ΔTBmax. This can take place if

sufficient extra energy is supplied, for example by means of vehicle induced forces. In this

mechanism, the track will jump from a stable pre-buckling equilibrium (1) to a stable post-buckling

equilibrium (3) through an unstable configuration (2) as shown in Fig. II-8. The lowest temperature

increase ΔT for which this alternative mechanism might occur is designated with the term ΔTBmin.

During this dissertation the influence of different track and bridge parameters on the upper buckling

temperature ΔTBmax will be investigated. The influence on the lower buckling temperature ΔTBmin will



not be investigated since it is not possible to calculate this value using the model assembled in this

dissertation.

5.2.2 STATIC VERSUS DYNAMIC BUCKLING MODEL

As mentioned before a distinction is made between static buckling and dynamic buckling. In the

static buckling theory vehicle induced forces are not taken into account. Therefore, their influence on

the lateral stability of the tracks is not regarded. As a result, computational models based on the

static theory cannot be used in order to explain buckling occurring in conjunction with train

movements.

Fig. II-9: Definition of uplift waves [6]

Dynamic buckling models on the other hand, do take into account vehicle induced forces and their

influences on the lateral stability of the track. As a train moves along a track, it exerts vertical forces

onto the track at the position of its axles. Due to these axle loads the lateral resistance of the track

increases at these positions. However, in between the axles an uplift wave is generated, depicted in

Fig. II-9 as ‘central wave’, which results in a decrease of the lateral stability of the track. Also in front

and behind a moving train two smaller uplift waves are generated; the latter is denoted with the

term ‘recession wave’ and the former with ‘precession wave’. Usually, the central wave results in the

largest decrease of lateral stability and therefore track buckling under the train is a frequent

occurring phenomenon. So, in order to obtain a model which reflects the actual behaviour of a track

subjected to train passage in a realistic way, account has to be taken of this dynamic uplift wave.

However, in order to take into account these dynamic effects due to vertical traffic loads a quite

complex model should be assembled. Therefore during this dissertation, it is opted to make use of a

more simplified static buckling model.



5.2.3 TANGENT VERSUS CURVED TRACK

A distinction should be made between tangent and curved track since they have a different buckling

behaviour. For curved track, the post-buckling shape I, which reflects a symmetric half sine wave, is

obtained most often. This is due to the fact that the energy required to bend the track inwards, as in

shape III, is too high.

Tangent track, the type of track which is discussed in this dissertation, buckles out in a rather

explosive way, to the left or the right side. The direction of the lateral displacement depends on the

track characteristics such as lateral resistance of the track at the right and left side, or on the

direction of the initial misalignment. The post-buckling shape which is obtained most often here is

the symmetric shape III, given in Fig. II-10. However, an asymmetric shape II given by a complete sine

wave can also occur.

Fig. II-10: Possible buckling shapes [6]

5.3 SAFETY CONCEPT

The safety concept with regard to buckling defined in the UIC code 720 [7] is based on the parameter

Tall, which represents the allowable temperature increase above the stress-free temperature of the

rail. Tall can also be considered as the required buckling strength of the track. It forms a buffer against

all sorts of phenomena which increase the rails temperature such as air temperature, sunlight, eddy

current brakes and interaction with other structures such as bridges.

The allowable value for the temperature Tall is determined by the components ΔTb,max and ΔTb,min (Fig.

II-11), which were already discussed in §5.2.1. As mentioned, ΔTb,max is the temperature increase

above its stress-free temperature, for which the track will buckle without any addition of external

energy. ΔTb,min on the other hand, is the minimal increase of the rail temperature for which buckling



can still occur if sufficient external energy is supplied. Below this value buckling of the track is not

possible. This behaviour is shown below in Fig. II-11, for temperature increases larger than ΔTb,min the

required external energy in order to initiate track buckling decreases significantly. So therefore, in

order to obtain a safe criteria, Tall cannot be much larger than ΔTb,min.

Fig. II-11: Energy required to buckle [6]

The UIC code 720 [7] defines two types of safety levels, both based on Tb,minl:

- Level 1 Safety: Tall = Tb,min

- Level 2 Safety: Tall = Tb,min + ΔT

Fig. II-12: Safety criteria definition in terms of ‘allowable temperature increase’ [7]

However, as mentioned before it will not be possible during this dissertation to calculate the value of

Tb,min. Therefore it will not be possible to define an allowable temperature Tall for the temporary

bridge deck configurations calculated in this dissertation. As a result the defined critical buckling

temperatures in this dissertation do not guarantee a safe buckling behaviour of the rail track. It



should always be kept in mind that, when adding extra energy to the rail, track buckling can still

occur for a rail temperature below Tb,max but still above Tb,min.

5.4 BUCKLING PARAMETERS FOR CWR ON AN EMBANKMENT

This section tries to provide an overview of all factors which might play a role in the buckling

behaviour for the general case of continuous welded rails on an embankment. Afterwards, when the

different parametric studies are performed, a selection will be made joining the most determining

parameters for the case of CWR over a temporary bridge deck. Below an overview of the discussed

parameters is given:

- Longitudinal track resistance

- Lateral track resistance

- Track defect (Lateral misalignment)

- Span length

- Support stiffness

- Bending behaviour of the bridge

- Torsional resistance of the rail fastenings

- Cross sectional area of the rail

- Curvature

- Rail stress-free temperature

5.4.1 LONGITUDINAL TRACK RESISTANCE

The longitudinal track resistance ‘k’ is the resistance of the track to longitudinal movement, per unit

of length, provided by ties and ballast. The longitudinal resistance varies with the longitudinal

displacement of the rail relative to its support. At first the resistance increases linearly until a certain

limit, beyond this limit the resistance remains rather constant. This behaviour is simplified to a

bilinear behaviour in the UIC code 774-3R as depicted in Fig. II-13 below.



Fig. II-13: Resistance ‘k’ of the track per unit length as a function of the longitudinal displacements of the rail

The magnitude of the longitudinal resistance ‘k’ depends on different factors such as loaded or

unloaded situation, degree of maintenance, ballasted or unballasted track,… An overview of the

different values proposed by the UIC Code 774-3R is given below:

Ballasted track

- Displacement u0 between elastic and plastic zones:

o U0 = 0.5mm for the resistance of the rail to sliding relative to the

sleeper

o U0 = 2 mm for the resistance of the sleeper in the ballast

- Resistance k in the plastic zone

o K = 12 kN/m resistance of sleeper in ballast (unloaded track), moderate

maintenance

o K = 20 kN/m resistance of sleeper in ballast (unloaded track), good

maintenance

o K = 60 kN/m resistance of loaded track or track with frozen ballast

Unballasted track

- Displacement u0 between elastic and plastic zones:

o U0 = 0.5mm

- Resistance k in plastic zone

o K = 40 kN/m Unloaded track

o K = 60 kN/m Loaded track



Previous studies by for example D. Choi et al. (2010) [8] and Samavedam et al. (1993) [9] have shown

that the influence of the longitudinal track resistance on the upper buckling temperature Tmax is

practically negligible, whereas the lower buckling temperature shows a slight increase with

increasing longitudinal stiffness.

5.4.2 LATERAL TRACK RESISTANCE

One of the most important contributors to the buckling resistance of the track is the lateral track

resistance. This lateral track resistance, in case of ballasted track, is provided by the ballast and is the

result of friction between the ballast and the rail-sleepers. The lateral resistance depends to a large

extend on the degree of compaction of the ballast, being greatest when the ballast is fully compacted

and least when it is freshly tamped. Depending on the state of the ballast, consolidated or freshly

tamped, a different characteristic behaviour is also found for the lateral ballast resistance. In case of

consolidated track, a drop in resistance arises after the peak value is reached. After this drop a

relative constant resistance is found. For freshly tamped ballast on the other hand, the lateral ballast

resistance remains rather constant after reaching the peak value. This behaviour is shown in Fig. II-14

below.

Fig. II-14: Typical lateral resistance characteristic [6]

In case of unballasted track, for example for the case of a track continuing over a temporary bridge

deck, the lateral resistance is much higher than for the case of ballasted track. This is due to the fact

that the fastenings are rigidly connected to the bridge deck which has a very large lateral stiffness. As

a result, buckling is not likely to occur over the length of the temporary bridge deck.

Apart from the degree of compaction, the lateral resistance is also dependant on the type and

spacing of the sleepers used. It speaks for itself that, when the spacing is increased, the degree of

lateral restraint decreases and thus the track is more likely to buckle. But also the type of sleepers

used (concrete, steel, wooden) influences the lateral resistance. Dependant on the shape, mass,

surface area of the sleepers end,… different lateral resistance characteristics are found.



5.4.3 LATERAL MISALIGNMENT

Another very important factor which influences the buckling behaviour of a continuous welded track

is the presence of lateral misalignments in the track geometry. These lateral misalignments tend to

increase under loading conditions and can ultimately lead to track buckling. Parametric studies by

among others Samavedam et al. (1993) and C. Esveld (1997) [10] have shown that both the

amplitude and wavelength of these anomalies strongly influence the buckling resistance of the CWR

track. As mentioned in §5.2.3 the shape of the buckled track is strongly influenced by the shape of

the initial misalignment. The different possible types of misalignment shapes are depicted in Fig.

II-10.

5.4.4 SPAN LENGTH

Given the fact that an increase in span length results in an increase in rail stresses, the span length of

the bridge will surely influence the buckling behaviour of the continuous welded rail on top of it.

Different bridge deck lengths will have to be checked when performing the parametric analysis.

5.4.5 SUPPORT STIFFNESS

The stiffness of the supports on which the bridge is constructed also has an influence on the stresses

arising in the rail track and thus influences the buckling behaviour of the rails. This overall stiffness

which is described, is dependent on contributions of different structural arrangements. A first

example of such a contribution is the type of bearings which is used. For example, when elastomeric

bearings are used, a certain degree of resistance to longitudinal movement of the bridge is provided

by these bearings and this will affect the stresses arising in the rail. However when movable bearings

are used generally no contribution to the stiffness is taken into account. Another contributor to the

overall stiffness of the bridge supports is the stiffness of the support itself, for example the stiffness

of a bridge pier and its foundation.

5.4.6 BENDING BEHAVIOUR OF THE BRIDGE DECK

When loads are exerted onto the bridge deck, the bridge will deform and bend about its lateral axis.

As a result, the bridge deck will in turn exert forces onto the rails which are situated on top of it. The

interaction effects are predominantly influenced by the bending stiffness of the bridge deck, but also

by the position of the neutral axis with respect to the position of the rails and bearings.



5.4.7 TORSIONAL RESISTANCE OF THE RAIL FASTENINGS

The rail fasteners also provide, apart from longitudinal and lateral support, some restraint against

rotation about the vertical axis. It has been proven in several studies by for example D. Choi et al.

(2010) or Samavedam et al. (1993) that the lower buckling temperature significantly increases when

increasing the torsional resistance. The upper buckling temperature however, which is more relevant

to our models, does not change significantly.

5.4.8 CROSS SECTIONAL AREA OF THE RAIL

Various parametric studies by for example D. Choi et al. (2010) or Samavedam et al. (1993) have

proven that an increase in rail size results in a decrease of the critical buckling temperature of the rail

track. This due to the fact that an increase in rail size also results in an increase of the thermal force

which counteracts the positive effect of an increased bending stiffness of the rail.

5.4.9 CURVATURE

It has been proven (D. Choi et al., 2010) that curved tracks are more prone to buckle than

corresponding straight tracks. Especially for high curved tracks the critical buckling temperature is

drastically reduced compared to low curved tracks.

5.4.10 RAIL NEUTRAL TEMPERATURE

During the parametric study performed in Chapter VI it should be verified for which deviation of the

rail neutral temperature the track starts to buckle. Dependant on the degree of safety subsequently

an appropriate rail neutral temperature can be defined. If the rail neutral temperature is too low, rail

buckling in hot summers becomes an actual threat. On the other hand, when this temperature is too

high, then the danger of rail breaks in cold winters increases.

6 TEMPORARY BRIDGE DECKS

6.1 INTRODUCTION

In order to be able to perform maintenance works on the track bed (for example when constructing a

tunnel underneath the train tracks) without having to stop train passage, INFRABEL uses a certain

technique in which they entirely replace the existing track bed by a temporary bridge deck. This

technique is used for spans ranging up to a maximum of about 25 metres. In the following part a

short introduction to how these temporary bridge decks are configured and how they are adopted

into the track configuration is provided. However for further details reference is made to the report



of INFRABEL regarding temporary bridge decks [11]. With respect to the different available

temporary bridge decks built by INFRABEL, an overview is given in Annex C.

6.2 TEMPORARY BRIDGE DECK CONFIGURATION

There are three different temporary bridge deck configurations which are used by INFRABEL: a twin

girder, a tube girder and an assembled girder configuration. The first two types are applied most and

will be discussed in depth. The assembled girder configuration is less commonly applied and will

therefore not be discussed.

6.2.1 TYPE 1: TWIN GIRDER CONFIGURATION

In the twin girder configuration the temporary bridge deck is composed of two separate decks, each

consisting of two metal girders. Depending on the magnitude of the span different magnitudes of

metal girders might be used. These metal girders are usually also reinforced by using additional

stiffening plates welded onto both flanges. Both girders are interconnected by transversal stiffeners.

On these transversal stiffeners the bearing plates are situated to which the train tracks are

connected. These separate bridge decks are in turn connected to each other by the means of metal

cross girders and bolts. An overview of this arrangement is given in Fig. II-15.

Fig. II-15: Example of a twin girder temporary bridge deck [11]

The temporary bridge deck is usually placed on neoprene or wooden bearings which in turn are

situated on a concrete beam. When the wooden bearings are used the displacement in lateral

direction are stopped by using metal profiles and in longitudinal direction they are stopped by using

wooden thrust pieces. At the ends of the temporary bridge deck the ballast layer is fixed using

wooden beams or a concrete wall.[11]



6.2.2 TYPE 2: TUBE GIRDER CONFIGURATION

In the tube girder configuration the temporary bridge deck is composed of one massive tube girder

provisioned of multiple bearing plates to which the train tracks can be connected. This massive tube

girder is reinforced using additional steel plates which are welded onto the upper flange of the girder

and also additional transversal stiffening plates are placed each metre. Similar to the twin girder

configuration the tube girder temporary bridge deck is also placed on neoprene bearings which are

situated on a concrete beam. The ballast is again fixed using a concrete wall in order to prevent

deconsolidation.

Fig. II-16: Example of a tube girder temporary bridge deck [11]

Chapter III Design and validation of preliminary 2D model

Application limits for continuously welded rail on temporary bridge decks III-20

DESIGN AND VALIDATION OF PRELIMINARY 2D

MODEL

1 INTRODUCTION

In this chapter it is tried to build a computer model for the case of a track passing over a classic

bridge deck first. For this situation the UIC provides test-cases in the UIC code 774-3R by which a

track-bridge interaction model can be validated. In this way one can ensure that the obtained results

using the computer model are correct. Subsequently, the validated model will be adjusted and

expanded to the case of a temporary bridge deck.

2 ASSEMBLY OF CLASSICAL BRIDGE MODEL

As mentioned above, it is opted to start by creating a model for the general case of a track running

over a classical bridge. This is done using the software Samcef Field. The assembly of the model is

based upon the descriptions given in the UIC leaflet 774-3R. A schematic overview of the model is

given in Fig. III-1 and will be discussed more thoroughly in the following sections.

In order to create and calculate a model in Samcef Field each time the same 4 steps have to be

followed. First the geometry of the model is entered in the “Modeler” tab, next the behaviour,

material, constraints and loads are applied to the different model elements in the “Analysis Data”

tab. Subsequently a mesh has to be created in the “Mesh” tab and finally the solver settings have to

be entered in the “Solver” tab after which the calculations can be launched. These different design

steps will be partially adopted as intermediate section titles in order to maintain a clear overview of

the design of the models created in this dissertation.

2.1 MODELER

In general the model can be subdivided into two main parts: a track situated on a bridge deck and a

track situated on an embankment on both sides of the bridge. The length of the track situated on the

embankments amounts 100 meters, which is the minimum allowable length according to the UIC

code 774-3R to be modelled. The length of the track on the bridge deck is variable depending on

which bridge span is considered.



All elements entered in this model, for modelling both the bridge and track structure, are made up

using ‘Wire’-type elements. These are line-elements to which a certain behaviour (beam, volume,…),

material,… can be appointed in the ‘Analysis Data’-tab.

Fig. III-1: Schematic overview of the finite elements model in Samcef Field

2.2 ANALYSIS DATA

As mentioned above, in the ‘Analysis Data’-tab it is possible to apply a certain behaviour, material,

constraints and loadings to the ‘Wire-type’ elements. Which settings are used to reproduce the

actual behaviour of the track-bridge interaction is discussed below.

2.2.1 TRACK

2.2.1.1. BEHAVIOUR

In Belgium the majority of the rail tracks are constructed using UIC 60 rails. As a results all models will

be designed assuming this rail type is present. The properties of a single UIC 60 rail are given in Table

III-1.

Cross-sectional area 76.70 cm²

Moment of inertia about lateral axis 3038.3 cm4

Table III-1: Properties of single UIC60 rail

For the ease of modelling however the track is represented by one single Wire-type element to which

a flexible beam behaviour is assigned which corresponds to two UIC 60 rails. This is done by making

use of an ‘undefined cross-section’ for which the following properties are entered:

Cross-sectional area 153.4 cm²

Moment of inertia about lateral axis 6076.6 cm4

Table III-2: Properties of beam corresponding to two UIC 60 rail



Note: The position of the track coincides with the upper face of the bridge deck. This is not the actual

position of the track but this simplification is allowed according to the UIC 774-3R leaflet.

2.2.1.2. MATERIAL

The track is made of steel and thus has an E-modulus of 210.109 N/m² and is given an elastic material

behaviour, as imposed by the UIC Code 774-3R.

2.2.1.3. CONSTRAINTS

In order to discuss the constraints applied to the track, a distinction should be made between the

track situated on the embankments and the track situated on the bridge deck. The part of track

situated on the bridge has 6 degrees of freedom. For the part of the track situated on the

embankments the displacements in vertical direction are prohibited. All other displacements and

rotations are free.

2.2.2 BRIDGE DECK

2.2.2.1. BEHAVIOUR

The bridge deck is modelled using two types of elements:

1) Horizontal flexible beam-type elements which have the same properties (bending stiffness,

material properties,…) as the actual bridge. These elements are located at the centre of

gravity of the bridge and are depicted in Fig. III-1 as (5).

2) Vertical rigid beam-type elements which have an infinite stiffness. These elements connect

the horizontal elements to the bearings or to the track and are depicted in Fig. III-1 as (6)

respectively (4).

2.2.2.2. MATERIAL

It is assumed the bridge deck is entirely made of steel and thus has an E-modulus of 210.109 N/m².

Similar to the track, the bridge deck is also given an elastic material behaviour, as imposed by the UIC

Code 774-3R.


All elements have six degrees of freedom. Except for the modelling of the bearings no constraints are

applied to the beams representing the bridge structure.

2.2.3 CONNECTION BETWEEN TRACK AND BALLAST

For the test-cases in the UIC leaflet it is assumed that the bridges have a ballasted deck. As a result

the longitudinal track resistance for the part of the track on the bridge deck is identical to the



resistance on the embankments. However, when advancing to a temporary bridge deck in a further

stage this will no longer be the case and thus will have to be adjusted.

As discussed in Chapter II §5.4.1 the connection between track and ballast should follow a bilinear

behaviour characterized by a threshold displacement u0 and a maximum longitudinal resistance ‘k’.

This resistance depends on whether the track is loaded or unloaded and the corresponding values

are repeated below:

- K = 20 kN per unit length of track, for unloaded track with good maintenance level

- K = 60 kN per unit length of track, for loaded track

- u0 = 2 mm

In order for the spring to provide resistance in both longitudinal directions this bilinear behaviour

should be defined point-symmetrical with respect to the origin of the coordinate system, as shown in

Fig. III-2 below.

Fig. III-2: Entry of bilinear behaviour for longitudinal springs in Samcef Field

Unidirectional ground bushings

For the connection between track and embankment unidirectional (in the longitudinal rail direction)

‘ground-bushings’ are used. These ground bushings are applied to the track every metre and are

given the characteristic spring behaviour as described above. The position of these ground bushings

is shown in Fig. III-1, in which they are designated as (2).

Bidirectional bushings

For the part of the track running over the bridge bidirectional (longitudinal and vertical direction)

bushings are used. For the longitudinal direction the same bilinear behaviour is applied as for the

unidirectional ground bushings on the embankments. However, now an additional stiffness is

entered for the vertical direction in order to allow the bushings to transfer the vertical forces from



the rail to the bridge. For the vertical stiffness of the bushings a value of 1015 N/mm is entered in

order to simulate a quasi-rigid vertical connection of the track with the bridge deck.

2.2.4 DECK BEARINGS

Two types of deck bearings are considered in these test-cases:

- A fixed bearing at the left side of the bridge. This bearing is situated at its actual position and

is connected using a rigid beam to the centre of gravity of the beam. The bearings are

modelled by restricting vertical displacements and by adding a bilinear spring in horizontal

direction. The threshold displacement Usupport and longitudinal resistance ‘Ksupport’ of the fixed

bearing are different for each model and will be defined in §4 - Validation of the model.

- A sliding bearing at the right side of the bridge. This bearing is modelled by again restricting

vertical displacement but now allowing horizontal displacement. In these test-cases friction is

not taken into account.

The actual position of the bearings is clarified in Fig. III-1.

2.3 MESH

The UIC Code 774-3R imposes a maximum limit for the spacing of the mesh nodes of 2 meters. In

order to ensure an adequate dense mesh a spacing of 5 centimetres is used for all models

throughout this dissertation.

2.4 SOLVER SETTINGS

In order to be able to increase the load over a certain interval of time an implicit nonlinear

calculation has to be performed. Also use is made of a static computation in which the inertia and

velocity dependent phenomena are not taken into account.



3 LOADING CASES

In order to validate the interaction model different loading cases have to be considered in which

interaction between track and bridge might occur. The cases which result into interaction effects are

those in which relative displacements between track and deck arise, these actions were already

summed up in Chapter II §3. In the test-cases only the three most important interaction loads are

regarded: braking forces, vertical forces and temperature loading. More specifications concerning

their way of application and magnitude, as described in UIC leaflet 774-3R, are given below.

However first a decision will have to be made concerning the type of analysis. How will the different

loading cases be combined? According to the UIC leaflet 774-3R two different methods can be used

in order to evaluate the stresses and displacements resulting from the different loading cases.

Depending on the degree of accuracy which has to be obtained and the capabilities of the computer

program a choice has to be made between:

1) A simplified separate analysis for the different loading cases

2) A complete analysis of the joint effects of the different loads being applied simultaneously

It should be noted that for the loading cases (braking and vertical loading) simulating the presence of

a moving train as many analyses should be performed as there are different positions of the moving

train on the bridge. However, in most cases it is sufficient to only check the case in which the bridge

deck is fully loaded since this often gives the most critical values. Due to the limitations of the model

assembled in this dissertation, no intermediate positions of the train on the bridge structure are

investigated. Only the case for which the train is situated over the full length of the bridge span is

looked into.

Additionally, in order to find the maximal stresses arising in the rail, both directions of travel should

be examined: thus both for a train moving from the fixed support to the movable support and the

other way around.

3.1.1 SIMPLIFIED SEPARATE ANALYSIS

In this type of analysis the loads are applied separately and the obtained results are simply added to

each other. In other words, a linear combination is made using the results of the separate analyses.

This will obviously lead to an overestimation of the actual stresses given the fact that the model itself

has a nonlinear character due to the bilinear connection between rail and track.

When simplified separate analyses are carried out, the temperature effects should be assessed

assuming non-loaded track conditions. However, for the vertical and braking loading cases, the



stiffness of the track-connection springs should be adjusted in accordance with the fact whether the

track is loaded or not.

3.1.1.1. VERTICAL LOADS (CASE 1/4)

When a train passes over a bridge, the bridge will experience a vertical loading due to the weight of

the train. This vertical loading will result into bending of the bridge deck and thus also into bending of

the upper face of the bridge to which the rails are connected. As a result this bending will in turn

cause additional stresses in the rail track. The magnitude of the vertical forces which are applied are

conform the standards described in the UIC 774-3R leaflet. They suggest this vertical train loading

can be modelled using a line load of 80 kN/m over a length of maximum 300 metres. As mentioned,

both train moving directions should be evaluated. The case for which the vertical loads move from

fixed to movable support is designated as case 1. The case for which the vertical loads move in the

opposite direction is designated as case 4.

Fig. III-3: Representation of loading cases regarded for train moving direction 1

3.1.1.2. BRAKING OR ACCELERATION FORCES (CASE 2/5)

As a result of braking or accelerating of a train, horizontal forces will be exerted onto the track. These

horizontal forces will result into relative displacements of the rail with respect to the bridge deck and

will thus result into interaction effects. In case of acceleration of a train a line load of 33 kN/m per

track should be applied over a maximal distance of 30 meters. In case of braking a line load of 20

kN/m per track should be applied over a maximal distance of 300m.

In the test cases it is assumed the train has a length of 100 meters and applies braking forces of 20

kN/m over its entire length. Again, both train running directions are examined. Case 2 corresponds to

a train running from fixed to movable support and case 4 corresponds to the opposite direction. Also,

when performing a simplified separate analysis the deck was assumed to be rigid in order to evaluate

the effects of braking alone and to prevent interaction by bending of the deck.

3.1.1.3. TEMPERATURE LOADING (CASE 3/6)

Depending on the presence of an expansion device in the track configuration, a different

temperature loading should be applied. For the case of a normal continuous welded rail, expansion

of the rail will not result in any differential movement of the rail with respect to the bridge and



therefore should not be checked. Therefore it is sufficient to only check the interaction effects due to

a temperature variation of the bridge deck.

However, for the case in which an expansion device is present in the track configuration, there will

be differential displacements between track and bridge structure in case of a temperature variation

in the track. As a result in this case interaction effects should be checked for both a temperature

increase of the bridge deck and a temperature increase of the track. In this dissertation however no

expansion devices are incorporated in the model and therefore only the interaction due to a

temperature variation of the bridge deck will be regarded.

According to the UIC leaflet 774-3R the temperature of the bridge does not deviate from the

reference temperature (temperature of the deck at which the rail was fixed) by more than ± 35°C.

For the rail track this deviation is limited at ± 50°C. However for the validation of the model

performed in §4 only positive temperature deviations are regarded.

When applying a temperature loading onto the track the stiffness of the springs should correspond

to an unloaded situation. As a result for this loading situation case 3 and 6 are identical.

3.1.2 COMPLETE ANALYSIS

When a complete analysis is performed, first the temperature loads are applied and then the moving

train loads (horizontal and vertical loads) are added. In this way more realistic results are found.

Again the longitudinal stiffness of the rail-ballast connection should vary depending on whether the

rail is loaded or not.



4 VALIDATION OF THE MODEL

The UIC leaflet 774-3R provides multiple test-cases in order to be able to validate an interaction

computer model. All test-cases treat the interaction of a moving train passing over a single span

bridge. Despite the diversity of different test-cases, it is sufficient for a computer model to produce

acceptable results for the fundamental cases E1-3 and E4-6 in order to be validated.

The limitations for results, in order to be accepted, is such that the error on the single effects

obtained, in the simplified analysis as well as on the overall effect, is less than 10% with respect to

the corresponding type of analysis (sum of effects or global effect). Larger tolerances, up to 20%, can

be accepted if the error is on the safe side.

In order to validate our model 4 cases are checked: the fundamental cases E1-3 and E4-6 and two

additional cases A1-3 and A4-6.

4.1 DATA

For each test case the properties of the bridge structure, such as bending stiffness, span length,

composition of the cross-section,… are altered. Below, a table is given providing all information

regarding the properties of the bridge structure for the different test-cases to be examined, in which:

- Ksupoort = Longitudinal resistance of fixed support

- Usupport = Elastic-plastic boundary of longitudinal support spring

- I = Moment of inertia for bending about transversal axis

- H = Height of bridge deck

- S = Area of cross-section of bridge deck

- Vi = Distance of neutral axis bridge deck to position of bridge bearing

Case

No.

Span

(m)

Usupport

(mm)

Direct. Ksupport

(kN/m²)

I (m4) H (m) S (m²) Vi (m)

A 1-3 30 1 1 300000 0.165 3.00 0.57 2.64

A 4-6 30 1 2 300000 0.165 3.00 0.57 2.64

E 1-3 60 1 1 600000 2.590 6.00 0.74 4.79

E 4-6 60 1 2 600000 2.590 6.00 0.74 4.79

Table III-3: Data with respect to test-cases considered



For the entire length of the track, both on the embankment and on the bridge structure, ballasted

track is assumed with the following characteristic resistance per unit track length:

- k = 20 kN/m for unloaded track

- k = 60 kN/m for loaded track

4.2 LOADS

The loads which are applied are the ones discussed in §3.1.1. Below a small summary is given. In total

4 different types of analyses are carried out:

Case 1 and 4 : vertical forces of 80 kN/m situated on left respectively right embankment and

bridge fully loaded

Case 2 and 5: deck assumed rigid, braking forces of 20 kN/m situated on left respectively

right embankment and bridge fully loaded

Case 3 and 6: influence of temperature variation in bridge (+35°C) or rail (+50°C)

Complete analysis: the three effects are evaluated simultaneously, applying the temperature

variation first and then the moving train loads.

All loads are applied in the same manner over a time interval of 10 seconds. Initially at t = 0 s already

a small load is present on the structure in order to prevent the calculation from diverging.

Subsequently the load is increased linearly reaching its maximum design value at 10 seconds. An

example of such a load progress is shown in Fig. III-4.

Fig. III-4: Progress of braking load over period of 10s



4.3 RESULTS

In the figures below the different normal stress progresses found with Samcef Field for the multiple

loading cases discussed in §3.1.1 are given. From these figures the maximum arising rail stresses can

be derived and these are summarized in the tables of §4.4.

Note: With regard to the sign of the stresses shown in the figures below and throughout this

dissertation, Samcef Field follows the following convention: negative stresses indicate compressive

forces are present in the track while positive stresses correspond to tensile stresses.

4.3.1 CASE E1: VERTICAL FORCES – DIR 1

Fig. III-5: Rail normal stress data due to vertical forces for train moving direction 1

4.3.2 CASE E2: BRAKING FORCES (DECK ASSUMED RIGID) – DIR 1

Fig. III-6: Rail normal stress data due to braking forces for train moving direction 1



4.3.3 CASE E4: VERTICAL FORCES – DIR 2

Fig. III-7: Rail normal stress data due to vertical forces for train moving direction 2

4.3.4 CASE E5: BRAKING FORCES (DECK ASSUMED RIGID) – DIR 2

Fig. III-8: Rail normal stress data due to braking forces for train moving direction 2

4.3.5 CASE E3/6: TEMPERATURE LOADING

4.3.5.1. EXPANSION BRIDGE

Fig. III-9: Rail normal stress data due to bridge deck expansion (+35°C)



4.3.5.2. EXPANSION RAIL

Fig. III-10: Rail normal stress data due to rail expansion (+50°C)

4.3.6 COMPLETE ANALYSIS: ALL LOADS APPLIED

Fig. III-11: Rail normal stress data due moving train loads and bridge deck expansion (35°C) for

train moving direction 2



4.4 OVERVIEW RESULTS

In the tables below the maximal arising compressive rail stresses for the different loading cases are

summarized. Subsequently it is possible to compare these rail stresses with the stresses specified by

the UIC code 774-3R. In this way one can subsequently derive whether the assembled model

provides acceptable results regarding the interaction analysis.

Separate simplified analysis Complete analysis

T rail T deck Braking End rot Sum

E1-3 UIC [MPa] -126 -30.7 -16.4 -17.0 -64.07 -56.4

Model [MPa] -126 -31.5 -19.3 -17.6 -68.4 -84.4

Error [%] 0 2.6 18 4 6.8 49.6

Table III-4: Additional rail stresses for test-case E1-3



E4-6 UIC [MPa] -126 -30.7 -15.9 -28.2 -74.84 -36.06

Model [MPa] -126 -31.5 -14.5 -25.7 -71.7 -71.4

Error [%] 0 3 -9 -9 -4 98

Table III-5: Additional rail stresses for test-case E4-6

The calculations for test cases A1 to A6 are carried out analogously to case E. The results are given

below.



A1-3 UIC [MPa] -126 -13.22 -12.7 -14.98 -40.96 -38.89

Model [MPa] -126 -12.6 -11.5 -15.4 -38.1 -48

Error [%] 0 -5 -10 3 -7 23

Table III-6: Additional rail stresses for test-case A1-3





A4-6 UIC [MPa] -126 -13.22 -12.7 -24.75 -50.67 -23.9

Model [MPa] -126 -12.6 -13.3 -22.0 -47.9 -52

Error [%] 0 -5 5 -10 -5.5 117

Table III-7: Additional rail stresses for test-case A4-6

5 CONCLUSION

As stated before, the limitations for results in order to be accepted is such that the error on the

single effects obtained in the simplified analysis as well as on the overall effect should be less than

10% with respect to the corresponding type of analysis (sum of effects or global effect). Larger

tolerances, up to 20%, can be accepted if the error is on the safe side. It is clear that the results of the

separate simplified analysis found for both the determining case E and the additionally investigated

case A comply with these limitations and therefore one can conclude that this type of model can be

reckoned as validated.

However, for the complete analysis larger deviations are obtained which are no longer acceptable.

This is due to the fact that the model, assembled in this dissertation, does not allow to take into

account the load dependant behaviour of the track resistance. In order to obtain acceptable results,

the temperature loads should be applied assuming an unloaded track situation. Afterwards the

moving train loads should be applied taking into account an increased stiffness for the longitudinal

track resistance. Due to this restriction of the Samcef model it is not allowed to calculate the

interaction stresses using the complete analysis. Therefore for the remaining part of this dissertation

it is opted to make use of the simplified separate analysis.

Chapter IV Design of 2D temporary bridge deck model and execution of a first parametric study

Application limits for continuously welded rail on temporary bridge decks IV-35

DESIGN OF 2D TEMPORARY BRIDGE DECK

MODEL AND EXECUTION OF A FIRST PARAMETRIC STUDY

1 INTRODUCTION

In this chapter the model assembled in Chapter III (see Fig. IV-1) is further adjusted to the case of a

temporary bridge deck. Subsequently a parametric study is performed in order to be able to make a

first selection regarding the parameters to be analysed in the parametric study of Chapter VI. Also, it

is possible to verify, for these several cases, whether the arising additional rail stresses, absolute and

relative displacements resulting from the interaction between track and temporary bridge deck are

conform the limitations given in the UIC code 774-3R. In this way a first conclusion regarding the use

of continuous welded rails on temporary bridge decks might be defined.

Fig. IV-1: Schematic overview of the finite elements model in Samcef Field

2 ASSEMBLY OF TEMPORARY BRIDGE DECK MODEL

2.1 MODELER

It is again opted to model the embankments over a length of 100 meters, which is the minimum

allowable length according to the UIC code 774-3R. For the temporary bridge deck a length of 20

meters is chosen.

The model is built up in the same way as described in Chapter III. The composing elements of this

model are depicted in Fig. IV-1.



2.2 ANALYSIS DATA

2.2.1 TRACK

The track is represented in the same way as described in Chapter III §2.2.1. No additional

modifications are made.

2.2.2 TEMPORARY BRIDGE DECK

2.2.2.1. BEHAVIOUR

The bridge deck is modelled in the same way as described in Chapter III §2.2.2 using vertical rigid

beam elements and a horizontal flexible beam element at the centre line which has the same

properties as the temporary bridge deck.

As discussed in Chapter II §6 there are two main configurations for a temporary bridge deck which

are applied in most cases: a tube girder configuration (Fig. IV-2) and a twin girder configuration (Fig.

IV-3). Both temporary bridge deck configurations have their own specific characteristics and

therefore need a separate model. In order to make a valid comparison between both types it is opted

to model two actual built temporary bridge decks by INFRABEL used for an equal span. According to

table C-1 of Annex C INFRABEL has only built one actual tube girder temporary bridge deck for a span

length of 12 metres. Therefore this configuration will be compared to a twin girder configuration for

an equal span length.

Tube girder

In order to determine the required properties (surface area, moment of inertia about lateral axis,

position of neutral axis) of the tube girder for the SAMCEF analysis use has been made of the cross-

section editor of SCIA Engineer.

Fig. IV-2: Cross-section of tube girder temporary bridge deck by INFRABEL for a span length of 12

metres [11]



The DWG-drawing depicted in Fig. IV-2 is imported into the cross-section editor of SCIA Engineer and

in this way the required properties of the tube girder are found. It is important to mention that in

practice there are also transverse stiffeners situated every metre throughout the entire length of the

temporary bridge deck. As a result the obtained vertical stiffness of the tube girder using the cross-

section editor will be slightly smaller than in reality and thus the interaction effects will be

overestimated. The properties found using the cross-section editor are listed below:

Tube girder

S [m²] 0.169

Iy [m4] 0.011

Vi [m] 0.317

Wi [m] 0.237

Table IV-1: Properties of Tube girder temporary bridge deck by INFRABEL for span of 12 metres

Apart from the cross-section area and bending stiffness about the lateral axis also the relative

positioning of the centre of gravity of the temporary bridge deck with respect to the bearing pads

and to the centre of gravity of the rails play a role in the interaction effects. The latter amounts

237 mm and the former 317 mm. These distances are designated in Fig. IV-2.

Twin girder

According to table C-1 of Annex C for a span of 12,5 metres INFRABEL has built an actual twin girder

configuration which is assembled using four HEB 500 profiles. In order to determine the properties of

this configuration the DWG-drawing, as depicted in Fig. IV-3, was imported into SCIA Engineer. Again

some simplifications are made compared to the actual cross-section. In practice the rails are

supported each 600 millimetres by transverse stiffeners and also the coupled girders are

interconnected to each other every 1.2 meters by the means of transverse girders. These structural

elements are not taken into account when calculating the properties of the cross-section and

therefore the vertical stiffness in the model will be smaller than the actual stiffness of temporary

bridge deck and the interaction effects are slightly overestimated.

Fig. IV-3: Cross-section of twin girder temporary bridge deck by INFRABEL for span of 12 metres

[11]



The properties found for the twin girder configuration are the following:

Twin girder

S [m²] 0.185

Iy [m4] 0.011

Vi [m] 0.290

Wi [m] 0.240

Table IV-2: Properties of twin girder temporary bridge deck by INFRABEL for a span length of 12 metres [11]

Again, the relative positioning of the centre of gravity of the temporary bridge deck with respect to

the bearing pads and to the centre of gravity of the rails was determined. The latter amounts

240 mm and the former 290 mm. These distances are also depicted in Fig. IV-3.

Comparing of tube girder to twin girder

An overview of the determining characteristics of the two temporary bridge deck types is given in

Table IV-3. As one can see the characteristics of both temporary bridge decks are almost identical.

Therefore no significant difference in interaction behaviour will occur and it should be sufficient to

check only one of both temporary bridge deck types.

Tube girder Twin girder

S [m²] 0.169 0.185

Iy [m4] 0.011 0.011

Vi [m] 0.317 0.290

Wi [m] 0.237 0.240

Table IV-3: Comparison of properties of both temporary bridge deck types

Note: It should be noted that only one tube girder configuration has been built in practice by

INFRABEL. Therefore it is not possible to check the difference in behaviour between a tube girder and

twin girder configuration for other span lengths.

2.2.2.2. MATERIAL


Similar to the track, the bridge deck is also given an elastic material behaviour, as imposed by the UIC

Code 774-3R [2].



2.2.3 CONNECTION BETWEEN TRACK AND EMBANKMENTS

For the part of the track situated on the embankments ballasted track is assumed. As a result the

longitudinal ballast resistance is modelled in the same way as described in Chapter III §2.2.3.

2.2.4 CONNECTION BETWEEN TRACK AND TEMPORARY BRIDGE DECK

For the part of the track situated on the temporary bridge deck the track is directly fastened to the

bridge and no ballast is present. Therefore a different characteristic behaviour for the longitudinal

resistance is applied in the model. The behaviour is characterised by the following values suggested

by the UIC code 774-3R:

- k = 40 kN per unit length of track, for unloaded track

- k = 60 kN per unit length of track, for loaded track

- u0 = 0.5 mm

In order to model this longitudinal restraint again bidirectional bushings are used as described in

Chapter III §2.2.3 and depicted in Fig. IV-1 as (2).

2.2.5 DECK BEARINGS

In case of a temporary bridge deck usually neoprene bearings are used for which one bearing is fixed

and the other one is movable:

- The fixed bearing is situated at the left side of the bridge. This bearing is situated at its actual

position and is connected using a rigid beam to the centre of gravity of the beam. The

bearing is modelled by restricting vertical displacements and by adding a linear spring in

horizontal direction. The stiffness of the spring has been estimated as the stiffness of the

compressed neoprene interfacing deck and abutment and assuming an abutment with

infinite stiffness[12]:

𝑘𝑛 =𝐸𝑛𝐴𝑛

𝑒𝑛≈ 6,000,000 𝑘𝑁/𝑚

In which:

o kn = stiffness of neoprene anchoring

o En = Young’s modulus of neoprene = 420 MPa

o An = total cross-section of neoprene = 2 x 0.50 x 0.30 = 0.30 m²

o en = net thickness of neoprene = 0.021 m



- The sliding bearing is situated at the right side of the bridge. This bearing is modelled by

again restricting vertical displacements but now allowing horizontal displacement. As a

simplification it is assumed no friction is present.

2.3 LOADS

As mentioned in Chapter III §5 the model does not allow to perform a complete analysis in which the

temperature loads are applied first on the unloaded track and then the moving train loads. Therefore

it is opted to use the simplified separate analysis and make a linear combination of the results.

However since the model itself has non-linear characteristics this method will lead to an

overestimation of the interaction effects. So if one can show that the results obtained using the

simplified separate analysis comply with the limitations given by the UIC code 774-3R then one can

assume that the interaction effects will not result in any unsafe situations.

Again three different loading cases will be regarded for each direction of the moving train: vertical

loading, horizontal loading and temperature loading. These loading cases are identical to the ones

described in Chapter III §3. Below a small summary is given. In total 3 different types of analyses are

carried out:

Case 1 and 4 : Vertical forces of 80 kN/m situated on left respectively right embankment and

bridge fully loaded

Case 2 and 5: Deck assumed rigid, braking forces of 20 kN/m situated on left respectively

right embankment and bridge fully loaded

Case 3 and 6: Influence of temperature variation in bridge due to a temperature increase of

+35°C and a temperature decrease of -35°C

Again it should be noted that for both loading cases (braking and vertical loading) as many analyses

should be performed as there are different positions of the moving train on the bridge. However in

most cases it is sufficient to only check the case in which the train is positioned on one of both

embankments and on the entire length of the bridge deck since this often gives the most critical

values. Due to the limitations of the model no intermediate positions of the train on the bridge

structure will be investigated.

2.4 MESH


order to ensure an adequate dense mesh a spacing of 5 centimetres is used for all models.



2.5 SOLVER SETTINGS

In order to be able to increase the load over a certain interval of time it is opted to make use of an

implicit nonlinear calculation. Also use has been made of a static computation in which the inertia

and velocity dependent phenomena are not taken into account.

3 PARAMETRIC STUDY

In the following section a parametric analysis will be performed in which multiple parameters of both

the temporary bridge deck and surroundings will be analysed. Their influence on the arising rail

stresses due to interaction will be investigated. As mentioned the UIC code 774-3R also provides

multiple criteria for the track-bridge interaction effects in order to prevent damage to track and

bridge. At the same time it will also be verified for these multiple test cases whether the arising rail

stresses and rail/bridge displacements comply with these limitations given in the UIC leaflet.

3.1 IMPOSED LIMITATIONS FOR TRACK-BRIDGE INTERACTION EFFECTS

First of all the permissible additional stresses due to the track-bridge interaction in continuous

welded rails on bridges are to be limited. For a UIC 60 rail the following limitations are given:

The maximum permissible additional compressive rail stress is 72 N/mm²

The maximum permissible additional tensile rail stress is 92 N/mm²

Also, limitations are given for the displacement of the deck and track in order to prevent excessive

deconsolidation of the ballast. The displacement limits also play a role in limiting indirectly the

additional longitudinal stress in the rails. These limits are:

The maximum permissible displacement between rail and deck or embankment under

braking and/or acceleration forces is 4 mm

The maximum permissible absolute horizontal displacement of the deck for the same

braking/acceleration forces is ± 5 mm if the rails run across one or both ends of the

bridge/embankment transition

Finally, the end rotation of a bridge deck due to traffic loads is an important factor to determine

satisfactory track-bridge interaction behaviour. Under vertical loads, the displacements of the upper

edge of the deck end must be limited in order to maintain ballast stability. However, since in the case

of a temporary bridge deck no ballasted deck is present, this criteria should not be checked.



3.2 DATA

As mentioned, a parametric analysis will be performed in which varying parameters are altered. An

overview of the parameters to be examined is given below:

- Span length

- Stiffness of fixed bearing

- Deck bending stiffness

- Longitudinal ballast resistance on embankments

- Longitudinal fastener resistance on temporary bridge deck

All models are created starting from the same standard configuration. In turn each parameter is

altered in a practical range while the other parameters are kept constant. The properties of the

standard configuration are given below in Table IV-4:

Span length 20 metres

Longitudinal ballast resistance on

embankments

Characteristic resistance (unloaded): 20 kN/m

Characteristic resistance (loaded): 60 kN/m

Elastic limit: 2 mm

Longitudinal fastener resistance on

temporary bridge deck



Elastic limit: 0.5 mm

Stiffness fixed bearing 6,000,000 kN/m

Temporary bridge deck (Tube girder) S = 0.169 m²

Iy =0.011 m4

Vi = 0.317 m

Wi = 0.237 m

Table IV-4: Properties of the standard configuration used for the parametric study

For each case to be examined both the maximum arising compressive stress and tensile stress will be

regarded. Also both moving train directions have to be regarded which are designated in the

following way:

o Direction 1 = moving from fixed to movable support

o Direction 2 = moving from movable to fixed support



3.3 RESULTS

In each section the results of the sensitivity analysis for the regarded parameter on the maximum

compressive and tensile rails stresses and the absolute and relative rail displacements are given.

However first, in order to provide some clarifications on how these results given in these sections are

obtained, the standard case for which the settings are given in Table IV-4 is discussed in depth. The

results of the other cases are obtained analogously and the different intermediate results regarding

the rail stresses for each separate loading case as shown in §3.3.1 are given in Annex A.

3.3.1 RESULTS FOR STANDARD CASE (CASE B)

3.3.1.1. NORMAL RAIL STRESS DEVELOPMENT

In the figures below the different normal rail stress progresses for the multiple loading cases

discussed in §2.3 of this chapter are given. Subsequently the enveloping normal stress progress for

both the compressive and tensile rail stresses can be obtained by adding these different progresses

to each other. It can then be verified whether the restrictions regarding the maximum compressive

and tensile rail stresses are met.

Note 1: With regard to the sign of the stresses shown in the figures below, Samcef Field follows the

following convention. Negative stresses indicate compressive forces are present in the track while

positive stresses correspond to tensile stresses.

Note 2: In order to calculate the enveloping normal rail stress progress for both tensile and

compressive rail stresses one should take into account the combined appearance of the horizontal

and vertical moving train loads and the fact that the maximum rail stresses can also arise due to the

temperature variation of the bridge deck alone.

Case B1: Vertical forces – DIR 1

Fig. IV-4: Rail normal stress data due to vertical forces for train moving direction 1



Case B2: Braking forces (deck assumed rigid) – DIR 1

Fig. IV-5: Rail normal stress data due to braking forces for train moving direction 1

Case B4: Vertical forces – DIR 2

Fig. IV-6: Rail normal stress data due to vertical forces for train moving direction 2

Case B5: Braking forces (deck assumed rigid) – DIR 2

Fig. IV-7: Rail normal stress data due to braking forces for train moving direction 2



Case B3: Expansion bridge deck (+35°C)

Fig. IV-8: Rail normal stress data due to deck expansion (+35°C)

Case B6: Contraction bridge deck (-35°C)

Fig. IV-9: Rail normal stress data due to deck contraction (-35°C)

As mentioned in §3.1 the additional rail stresses due to interaction should comply with the following

limitations:

The maximum permissible additional compressive rail stress is 72 N/mm²

The maximum permissible additional tensile rail stress is 92 N/mm²

In Fig. IV-10 & Fig. IV-11 the envelope of the maximum arising additional tensile and compressive rail

stresses due to interaction effects are depicted. These maxima are either the result of a combined

loading of both the moving train loads (horizontal and vertical loading) and the expansion of the

bridge deck, or of the moving train loads or the temperature variation alone.



Fig. IV-10: Envelope of additional stresses in rail on bridge for train moving direction 1

Fig. IV-11: Envelope of additional stresses in rail on bridge for train moving direction 2

Conclusion

When these graphs are regarded, it is clear that all additional rail stresses remain within the given

boundaries of §3.1. As a result, the first demand with respect to an acceptable interaction behaviour

is met.

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

0 5 10 15 20

Ad

dit

ion

al r

ail s

tres

ses

[MP

a]

Position on bridge deck [m]

Enveloping compressive stresses Enveloping tensile stresses

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

0 5 10 15 20

Ad

dit

ion

al r

ail s

tres

ses

[MP

a]

Position on bridge deck[m]

Enveloping compressive stresses Enveloping tensile stresses



3.3.1.2. LONGITUDINAL RAIL/DECK DISPLACEMENTS

As mentioned in §3.1 also limitations are given for the displacement of the deck and track:

The maximum permissible relative longitudinal displacement between rail and deck or

embankment under braking forces is 4mm

Below the relative longitudinal displacement of the rail with respect to the bridge deck is given for

both train movement directions. It is clear that for both cases the relative longitudinal displacements

remain within the boundaries given by the UIC.

Fig. IV-12: Progress of relative displacement of rail with respect to bridge deck – dir 1

Fig. IV-13: Progress of relative displacement of rail with respect to bridge deck – dir 2

The maximum permissible absolute horizontal displacement of the deck for the same

braking/acceleration forces is ± 5 mm if the rails run across one or both ends of the

bridge/embankment transition

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15 20

Rel

ativ

e d

isp

lace

men

t ra

il/d

eck

[mm

]


-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 5 10 15 20

Rel

ativ

e d

isp

lace

men

t ra

il/d

eck

[mm

]




The absolute horizontal displacement of the deck when loaded with braking forces amounts

0.457 mm and is therefore acceptable.

3.3.1.3. GENERAL CONCLUSION

It is clear that the additional rail stresses, absolute and relative rail displacements found for this test

case comply with the limitations given by the UIC code 774-3R. Therefore one can assume that the

interaction effects remain within acceptable limits for this configuration.

3.3.2 SPAN LENGTH

The first influencing factor which is regarded is the span length of the temporary bridge deck. Three

different span lengths are regarded: 10m, 20m and 30m. The results are obtained analogously to

§3.3.1. The Cases 1-3 denote the results for the moving train loads going from the fixed support

towards the movable support while the cases 4-6 denote the inverse direction.

Additional rail stresses

[MPa]

Long. relative

displacements

Long. displacement

deck

Case Compression Tension [mm] [mm]

A1-3 / 10m 22.9 16.7 0.57 0.03

B1-3 / 20m 52.6 67.0 0.61 0.06

C1-3 / 30m 53.9 125.3 0.63 0.09

A4-6 / 10m 18.1 14.3 -0.57 -0.03

B4-6 / 20m 49.7 48.5 -0.61 -0.06

C4-6 / 30m 60.0 93.6 -0.63 -0.09

Table IV-5: Results of parametric study with regard to changing span length

Fig. IV-14: Sensitivity of rail stresses with respect to bridge span length

0

20

40

60

80

100

120

140

10 15 20 25 30

Ab

solu

te r

ail s

tre

ss [

MP

a]

Bridge span length [m]

Compression - dir 1

Tension - dir 1

Compression - dir 2

Tension - dir 2



3.3.3 LONGITUDINAL BALLAST RESISTANCE EMBANKMENTS

As mentioned in Chapter II, depending on the degree of maintenance and compaction of the ballast,

a different longitudinal ballast resistance may occur. In the following section therefore the influence

of the longitudinal resistance of the ballast on the rail stresses is investigated. Since no ballast is

present on the temporary bridge deck only the longitudinal resistance of the part of the track

situated on the embankments is altered. The following situations are investigated:

Moderate maintenance:

o Unloaded situation: characteristic resistance = 10 kN/m

o Loaded situation: characteristic resistance = 50 kN/m

Good maintenance:



Excellent maintenance:




[MPa]

Long. relative

displacements

Long. displacement

deck


D1-3 / Moderate 45.4 65.3 0.66 0.06

B1-3 / Good 52.6 67 0.61 0.06

E1-3 / Excellent 57.8 73.7 0.58 0.05

D4-6 / Moderate 48.5 42.5 -0.66 -0.06

B4-6 / Good 49.7 48.5 -0.61 -0.06

E4-6 / Excellent 51.9 55.8 -0.58 -0.05

Table IV-6: Results of parametric study with regard to long. ballast resistance on embankments



Fig. IV-15: Sensitivity of rail stresses with respect to long. ballast resistance on embankments

3.3.4 STIFFNESS OF THE FIXED BEARING

Another factor which is looked into is the stiffness of the fixed bearing. The effect of multiplying and

dividing the stiffness of the standard case with a factor of 10 is evaluated.

Additional rail stresses [MPa]

Long. Relative

displacements

Long. Displacement

deck


F1-3 / 6.105 kN/m 48.8 63.2 0.51 0.45

B1-3 / 6.106 kN/m 52.6 67 0.61 0.06

G1-3 / 6.107 kN/m 53 67.4 0.63 0.005

F4-6 / 6.105 kN/m 39.8 36.9 -0.51 -0.45

B4-6 / 6.106 kN/m 49.7 48.5 -0.61 -0.06

G4-6 / 6.107 kN/m 54.8 50.4 -0.63 -0.005

Table IV-7: Results of parametric study with regard to stiffness of fixed bearing

Fig. IV-16: Sensitivity of rail stresses with respect to bearing stiffness

Moderate Good Excellent40

45

50

55

60

65

70

75A

bso

lute

rai

l str

ess

[M

Pa]

Ballast quality

Compression - dir 1

Tension - dir 1

Compression - dir 2

Tension - dir 2

35

40

45

50

55

60

65

70

6 60 600

Ab

solu

te r

ail s

tre

ss [

MP

a]

Bearing stiffness [105 kN/m]

Compression - dir 1

Tension - dir 1

Compression - dir 2

Tension - dir 2



3.3.5 DECK BENDING STIFFNESS

As indicated in the UIC code 774-3R the bending stiffness of the bridge deck is also a determining

factor with regard to the magnitude of the interaction effects. As a results its influence should

certainly be investigated.

Additional rail stresses [MPa]

Long. Relative

displacement

Long deck

displacement


H1-3 / 0,005 m4 53.5 81.7 0.61 0.06

B1-3 / 0,01 m4 52.6 67 0.61 0.06

I1-3 / 0,02 m4 48.1 50 0.61 0.06

H4-6 / 0,005 m4 53.8 51.1 -0.61 -0.06

B4-6 / 0,01 m4 49.7 48.5 -0.61 -0.06

I4-6 / 0,02 m4 44.6 34 -0.61 -0.06

Table IV-8: Results of parametric study with regard to deck bending stiffness

Fig. IV-17: Sensitivity of rail stresses with respect to bridge bending stiffness

3.3.6 LONGITUDINAL FASTENER RESISTANCE ON TEMPORARY BRIDGE DECK

In this section the influence of a reduced/enhanced clamping action of the fasteners situated on the

temporary bridge deck are investigated. The following situations are regarded:

Moderate clamping force:



30

40

50

60

70

80

0.005 0.01 0.015 0.02

Ab

solu

te r

ail s

tre

ss [

MP

a]

Bridge bending stiffness [m4]

Compression - dir 1

Tension - dir 1

Compression - dir 2

Tension - dir 2



Good clamping force:



Excellent clamping force:




[MPa]

Long. relative

displacements

Long. displacement

deck


J1-3 / Moderate 47.8 62.2 0.69 0.05

B1-3 / Good 52.6 67 0.61 0.06

K1-3 / Excellent 56.7 71.7 0.61 0.06

J4-6 / Moderate 42.6 42.9 -0.69 -0.05

B4-6 / Good 49.7 48.5 -0.61 -0.06

K4-6 / Excellent 56.6 52.9 -0.61 0.06

Table IV-9: Sensitivity of rail stresses with regard to long. fastener resistance on bridge deck

Fig. IV-18: Sensitivity of rail stresses with regard to fastener longitudinal resistance on bridge deck

Moderate Good Excellent

40

45

50

55

60

65

70

75

Ab

solu

te r

ail s

tre

ss [

MP

a]

Quality of clamping force

Compression - dir 1

Tension - dir 1

Compression - dir 2

Tension - dir 2



4 GENERAL CONCLUSIONS

Standard case

The standard configuration (Case B) corresponds to the case of a temporary bridge deck with a span

length of 20 metres. The bending stiffness of the temporary bridge deck is chosen equal to the

stiffness of an actual temporary bridge deck used by INFRABEL for a span length of 12 metres. The

characteristics for the longitudinal track resistance and the magnitude of the loads applied are based

on the values imposed by the UIC code 774-3R. Therefore, if this configuration complies with the

limitations given by the UIC code 774-3R, one can assume that for this span length and temporary

bridge deck configuration it is allowed to continue CWR track over the bridge structure without

providing an expansion device.

When considering the results it is clear that the model complies with the limitations given by the UIC

code 774-3R for both the additional rail stresses and the longitudinal displacements. As a result one

can state that for this configuration it is allowed to omit the expansion device from the structural

configuration of the track given the fact that the interaction effects remain within acceptable limits.

As mentioned the bending stiffness of the temporary bridge deck used in this standard case (case B)

corresponds to a temporary bridge configuration used by INFRABEL for a span length of 12 metres.

From this one can derive that INFRABEL still has an adequate safety margin with respect to the

bending stiffness of the temporary bridge deck. If one regards the results of case A (span length

equal to 10 metres), which corresponds more to the actual applied span range (12 metres) by

INFRABEL for the temporary bridge deck used, one can see that the obtained additional rail stresses

are very limited. This again, is a confirmation of the fact that there is still sufficient safety margin with

respect to the bending stiffness of the temporary bridge decks used. Additionally one should also

bear in mind that a simplified separate analysis is performed in which the interaction stresses are

overestimated. As a result the actual safety margin will be even higher.

Span length

When Fig. IV-14 is regarded, it is clear that the span length has a major influence on the obtained

maximal rail stresses. If the individual rail stress progresses are considered for test cases A (span

length of 10 metres) and C (span length of 30 metres), shown in Fig. A-1 to Fig. A-12 of Annex A, then

one can derive that this influence is predominantly originating from the vertical loading case and

bridge expansion.



For the tension stresses a clear approximate linear relationship is found between span length and

maximal arising tensile rail stress for both train moving directions. When the compressive rail

stresses are regarded a similar increase of the rail stresses is found, going from 10 to 20 metres of

span. However for the branch going from 20 to 30 metres a much smaller increase of compressive

rail stresses is found. This is due to the fact that for the case of a span length of 30 metres a different

load combination becomes determining. For both a span length of 10 and 20 metres the maximal

compressive rail stresses were found for the combination in which both the train moving loads and

the bridge deck expansion were applied to the model. However for the case of a span length of 30

metres the maximal arising rail stresses are found for the case in which the expansion of the bridge

deck was applied alone. An explanation for this change of determining load combination can be

found when comparing the normal rail stress evolution for the vertical loading situation of both case

B (Fig. IV-4) and case C (Fig. A-7 of Annex A). At the side of the bridge at which the maximal

compressive rail stress is found a tensile contribution is found for the vertical loading case for a span

of 30 metres. This tensile contribution is larger than the compressive contribution due to the

horizontal braking force of the moving train (shown in Fig A-8 of Annex A) and therefore a smaller

maximal compressive rail stress is found for the loading combination which contains all loads

compared to the loading combination which only contains the temperature variation of the deck.

When considering Table IV-5 it can be seen that the span length influences the arising rail stresses

even in such a way that for the case of a span length of 30 metres the limitations given by the UIC are

no longer met. However it should be noted that for this case (Case C) the same temporary bridge

deck is used as INFRABEL uses for a span length of 12 metres. In reality for a span length of 30 metres

a much stiffer bridge deck will be used and therefore the arising rail stresses will be lower compared

to the ones calculated in this section. This influence of the bridge bending stiffness is demonstrated

in §3.3.5 of this chapter.

Still, an increased bending stiffness of the bridge deck will not influence the arising additional rail

stresses due to bridge deck expansion in a significant manner, as proven in §3.3.5. Therefore the

increase of the additional rail stresses for an increased span length due to bridge deck expansion

might result in considerable problems. As can be seen in Fig. A-11 of Annex A for a span length of 30

metres the additional compressive rail stress at movable support due to bridge deck expansion

amounts 50 MPa. Given the fact that the upper limit for the compressive rail stresses imposed by the

UIC code 774-3R equals 72 MPa one can thus understand that this behaviour will limit the application

range of the temporary bridge decks.



Longitudinal ballast resistance embankments

As can be derived from Fig. IV-15 the longitudinal resistance of the ballast on the embankments has a

moderate influence on the arising rail stresses. For an increasing longitudinal ballast resistance

slightly increasing rail stresses are found. This increase follows an approximate linear relationship.

Stiffness of the fixed bearing

On Fig. IV-16 it can be seen that when the stiffness of the fixed bearing is increased with a power of

10, the rail stresses do not change too much. However if the bearing stiffness is decreased with a

power of 10, then a much larger stress variation is encountered. This stress variation is especially

found for train moving direction 2. For train moving direction 1 this sensitivity is much less

pronounced. Since the largest rail stresses are found for train moving direction 1 this factor will thus

have no large influence on the track stability.

Deck bending stiffness

When considering Fig. IV-17 one notices a large sensitivity of the maximal tensile forces with regard

to the bridge deck bending stiffness. If one considers the normal stress developments in the rails of

the individual loading cases for test cases H (bending stiffness equal to 0.005 m4) and I (bending

stiffness equal to 0.02 m4) depicted in Fig. A-37 to A-48 of Annex A, it can be seen that this sensitivity

only originates from the loading cases containing the vertical forces of the moving train. The stresses

due to the horizontal and thermal loads remain practically unchanged. The influence of the bridge

bending stiffness on the maximal compressive forces is much less pronounced. Therefore this factor

will not have a large influence on the track buckling stability.

Longitudinal fastener resistance on temporary bridge deck

Similar to the influence of the longitudinal resistance of the ballast again a linear relationship is found

for the influence of the longitudinal fastener resistance situated on the temporary bridge deck. For

an increasing longitudinal resistance increasing rail stresses are found. When the different loading

cases are regarded it is found that mainly the rail stresses due to bridge deck expansion and vertical

loading are affected.

Chapter V Design and validation of 3D model for the case of a temporary bridge deck

Application limits for continuously welded rail on temporary bridge decks V-56

DESIGN AND VALIDATION OF 3D MODEL FOR

THE CASE OF A TEMPORARY BRIDGE DECK

1 INTRODUCTION

In the previous chapters use has been made of a 2D model in which only the influence of the

longitudinal and vertical displacements of track and bridge was taken into account. In these models

the lateral component has been neglected.

This simplification was acceptable as long as the arising additional rail stresses and relative and

absolute displacements due to the interaction effect remained within certain limits provided by the

UIC Code 774-3R. If this was the case then one could state that the design provided sufficient safety

against track buckling and rail break.

In an attempt to find the more exact boundaries concerning track buckling due to interaction the

model assembled in Chapter III and IV will now be expanded to a 3D model. This 3D model will take

into account the lateral deflections of the rail and the elastoplastic behaviour of the rail. In this way it

will become possible to simulate the actual buckling behaviour of the track.

However before performing a sensitivity analysis regarding the buckling behaviour of the track it

should first be checked whether the modified model assembled in this chapter still provides the

correct rail stresses.

2 ASSEMBLY OF 3D TEMPORARY BRIDGE MODEL

2.1 MODELER

A first major adjustment made, is the deduplication of the train track. In this new configuration each

rail is represented individually using again ‘wire-type’ elements. As a result of this deduplication the

model of the bridge deck also needed some adjustments. The centre line of the bridge deck is now

situated in between both rails at equal distances. The relative position in vertical direction remains

the same. Given the fact that the rails are now no longer situated immediately above the centre line

of the bridge deck, additional lateral beams are required to provide the connection between rails and

bridge deck. An overview of the configuration is given in Fig. V-1 .



With respect to the dimensions of the modelled track parts no changes are made. Again, the

embankments are modelled over a length of 100 metres at both sides of the bridge. The span length

of the bridge is dependent on the type of case regarded.

Fig. V-1: Overview of configuration of the model

2.2 ANALYSIS DATA

Due to this new configuration of the model, with the implementation of the lateral rigid beams, it

should first be checked whether the model still yields the correct normal rail stresses. This check is

done assuming the same settings (elastic rail behaviour, static computation,…) as for the 2D

temporary bridge deck model described in Chapter IV and is performed in §3 of this chapter. After

performing this validation, the model is further adjusted in order to be able to simulate the buckling

behaviour of the rails, which is covered in Chapter VI.

Since the settings for both the model used for the validation of the new configuration (§3) and the

simulation of the rail buckling behaviour (Chapter VI) do not differ too much both will be described in

this section. Whenever necessary a clear distinction will be made between both models.

2.2.1 TRACK

2.2.1.1. BEHAVIOUR

Given the fact it is not possible to apply an elastoplastic behaviour to an ‘undefined cross-section’ in

Samcef Field it is necessary to deduplicate the rails from one beam element to two single beam

elements. These beam elements are entered as I-profiles due to the afore mentioned problem of the

application of the elastoplastic behaviour.

In order to make sure the I-profiles behave in the same way as an UIC 60 rail the I-profiles are

dimensioned in such a way that their relevant characteristics are approximately equal to those of an

UIC 60 rail. The dimensions used and the characteristics obtained are depicted below:



Fig. V-2: Relevant dimensions for design of rail

Table V-1: Comparison of actual UIC 60 properties to approximated rail in Samcef Field

Table V-2: Dimensions used for I-profile in order to approximate UIC 60 rail

2.2.1.2. MATERIAL

Validation of the model (Chapter V §3)

For the validation of the model in §3 still an elastic behaviour should be applied to the rails in order

to rule out any lateral displacements and to be able to compare the model of Chapter IV to the one

described in this chapter.

Simulation of buckling behaviour (Chapter VI)

In order to be able to simulate the buckling behaviour of the track it is necessary to adjust the

material behaviour of the rails from an elastic behaviour, used in the previous models, to an

elastoplastic behaviour. It is still assumed the rails are made of steel with an E-modulus of 210.109

N/m², however in this case a yield stress is also entered. This yield stress amounts about 900 N/mm²

for a typical UIC 60 rail.


Regarding the degrees of freedom of the track structure no modifications are made with respect to

the models of Chapter III and IV.

Since in this new configuration both rails are modelled separately, attention has to be paid to their

relative behaviour. In practice both rails do not move with respect to each other in transversal

direction due to the connection of the rails to the sleepers. In order to simulate this behaviour use

has been made of the assembly type ‘connection between mesh nodes’. This assembly type allows

one to prevent any differential movement in a direction of choice for two selected mesh nodes.

UIC 60 Samcef rail Deviation

Iy 3038,3 m4 3117 m4 2,6 %

Iz 512,3 m4 515,9 m4 0,7 %

A 7670 m2 7671 m2 0,01 %

H [mm] 176 B1 [mm] 135

TW [mm] 20 B2 [mm] 63

R1 [mm] 10.75 TF1 [mm] 21

R2 [mm] 10.75 TF2 [mm] 35



Assuming a sleeper spacing of 500 mm this assembly was applied to an opposing couple of mesh

nodes every 500 mm.

2.2.2 BRIDGE DECK

2.2.2.1. BEHAVIOUR

In this new configuration the bridge deck is modelled using three types of elements:

1) Vertical rigid beam-type elements which have an infinite stiffness. These elements connect

the rails to the lateral rigid beams and connect the bearings to the deck centre line. They are

depicted in Fig. V-1 as (1) respectively (2).

2) Lateral rigid beam-type elements which have and infinite stiffness. These elements connect

the vertical rigid beams to the deck centre line and are depicted in Fig. V-1 as (3).

3) Horizontal flexible beam-type elements which have the same properties (bending stiffness,

longitudinal stiffness , …) as the temporary bridge deck. These elements are located at the

centre of gravity of the bridge and are depicted in Fig. V-1 as (4).

The basic model for the sensitivity analysis will be based on a twin girder configuration for a bridge

span of 20 meters. According to Table C-1 of Annex C INFRABEL has built an actual twin girder

configuration for a span of 21,7 metres which is assembled using 4 HEM650 profiles reinforced with

additional steel plates connected to the flanges. In order to determine the properties of this

configuration the DWG-drawing of the cross-section was imported into SCIA Engineer. This cross-

section has the following characteristics:

Twin girder

S [m²] 0.239

Iy [m4] 0.0225

vi [m] 0.424

wi [m] 0.317

Table V-3 : Properties of twin girder temporary bridge deck built by INFRABEL for a span of 21.7m

2.2.2.2. MATERIAL


Similar to the track the bridge deck is also given an elastic material behaviour as imposed by the UIC

Code 774-3R.


As a manner of simplification it is assumed the temporary bridge deck cannot move in lateral

direction. Therefore the displacements in lateral direction of the bridge-elements are restricted.



2.2.3 CONNECTION BETWEEN TRACK AND EMBANKMENTS

2.2.3.1. LONGITUDINAL TRACK RESISTANCE

The longitudinal track resistance is modelled in the same way is described in Chapter III and Chapter

IV.

2.2.3.2. LATERAL TRACK RESISTANCE (ONLY VALID FOR CHAPTER VI MODEL)

As mentioned, the model of Chapter VI should also take into account the influence of the lateral

displacement component. Therefore it is necessary to implement the lateral track resistance of the

ballast on the sleepers into the model. In order to do so the ground bushings used to model the

longitudinal track resistance are now given an additional lateral spring stiffness following the bilinear

behaviour as described in the section below. These bushings are applied to the track each 0.5 metres

in order to simulate a corresponding sleeper spacing.

Depending on the degree of compaction (consolidated or freshly tamped track), the lateral resistance

can follow a different characteristic behaviour (as described in Chapter II §5.4.2). Since for situations

in which a temporary bridge deck is applied the compaction of the ballast might be affected. It is

chosen to assume a freshly tamped track characteristic behaviour. This behaviour can be

approximated by a bilinear behaviour characterized by a limit resistance Fl. In order for the spring to

provide resistance in both lateral directions this bilinear behaviour should be defined point-

symmetrical with respect to the origin of the coordinate system, as shown in Fig. V-3 below. Based

on in situ measurements performed by the Technical University of Munich and the track

measurement department of DB a mean value1 of 6000 kN is assumed for this limit resistance at a

displacement of 2mm [13]. Since there are two lateral springs applied to the track to represent the

support of each sleeper, this limit resistance Fl should be halved when entering the bilinear

behaviour of the springs.

1 The mean value is derived from 251 measurements on timber sleepers in a consolidated condition [13]



Fig. V-3 : Entry of bilinear behaviour for lateral springs in Samcef Field [6]

2.2.4 CONNECTION BETWEEN TRACK AND TEMPORARY BRIDGE DECK

2.2.4.1. LONGITUDINAL TRACK RESISTANCE

The connection between track and temporary bridge deck is modelled in the same way as described

in Chapter IV §2.2.4, no additional modifications are made.

2.2.4.2. LATERAL TRACK RESISTANCE (ONLY FOR CHAPTER VI MODEL)

The temporary bridge deck configuration is of the non-ballasted track type. As a result, the lateral

track resistance is only dependant on the lateral resistance of the fastenings and is therefore much

larger than the lateral resistance of the ballasted track. It is assumed the lateral stiffness of the rail

fastenings amounts at about 500 kN/mm [13]. In order to incorporate this lateral resistance into the

model similar as for the track on the embankment this lateral stiffness is entered using the bushings

used to model the longitudinal resistance.

2.2.5 DECK BEARINGS

The deck bearings are modelled in the same way as described in Chapter IV §2.2.5, with the

exception that now also the displacement in lateral direction is prohibited.

2.3 MESH


order to ensure an adequate dense mesh a spacing of 5 centimetres is used for all models.



2.4 SOLVER SETTINGS

Validation of the model

In order to be able to increase the load over a certain interval of time, it is opted to make use of an

implicit non-linear calculation. Also use has been made of a static computation in which the inertia

and velocity dependent phenomena are not taken into account.

Simulation of buckling behaviour

For the simulation of the rail buckling behaviour still use is made of an implicit non-linear calculation.

However, for this case, a switch is made from a static computation to a dynamic computation in

which the inertia and velocity dependent phenomena are also taken into account.

3 VALIDATION OF THE MODEL

As mentioned, it should be checked whether the new 2-rail-configuration for the 3D temporary

bridge deck model yields the same results with respect to arising rail stresses as for the 2D temporary

bridge deck configuration assembled in Chapter IV. In order to do so one configuration representing

a temporary bridge deck spanning a length of 20 metres is calculated. The relevant data, analysed

loading cases and results are given below.

3.1 DATA

In Table V-4 a small overview of all relevant data is given:


Longitudinal ballast resistance on

embankments



Elastic limit: 2mm

Longitudinal fastener resistance on




Elastic limit: 0.5 mm


Temporary bridge deck (Tube girder) S = 0.239 m²

Iy =0.023 m4

vi = 0.424 m

wi = 0.317 m

Table V-4: Properties of the model regarded



3.2 LOADS

The same 4 loading cases are regarded as in the previous chapters. These are listed below. However,

now only train moving direction 1 is considered. The other train moving direction is disregarded.

Case 1: Vertical forces of 80 kN/m situated on left embankment and bridge fully loaded

Case 2: Deck assumed rigid. Braking forces of 20 kN/m situated on left embankment and

bridge fully loaded

Case 3: influence of temperature variation in bridge (+35°C) and rail (+50°C)

3.3 RESULTS

Below the progress of the normal stresses/forces in the track and rail are given for respectively the

2D model assembled according to Chapter IV and the 2-rail-configuration described in this chapter.

3.3.1 CASE 1: VERTICAL FORCES – DIR 1

3.3.1.1. 2D MODEL

Fig. V-4: Rail normal stress data for 2D model due to vertical forces for train moving direction 1

Maximal tensile stress : 27.8 MPa

Maximal compressive stress : 13.9 MPa



3.3.1.2. 2-RAIL-CONFIGURATION

Fig. V-5: Rail normal force data for 2-rail-configuration model due to vertical forces for train

moving direction 1

Maximal tensile force : 210.3 kN

o Maximal tensile stress : 210.3 kN / 7670 mm² = 27.4 MPa

Maximal compressive force : 103.6 kN

o Maximal compressive stress : 103.6 kN / 7670 mm² = 13.5 MPa

3.3.2 CASE 2: BRAKING FORCES; BRIDGE FULLY LOADED – DIR 1

3.3.2.1. 2D MODEL

Fig. V-6: Rail normal stress data for 2D-model due to horizontal forces for train moving direction 1






Fig. V-7: Rail normal force data for 2-rail-configuration model due to horizontal forces for train

moving direction 1



Maximal compressive force : 44.6 kN

o Maximal compressive stress : 44.6 kN / 7670 mm² = 5.81 MPa

3.3.3 CASE 3: EXPANSION BRIDGE DECK

3.3.3.1. 2D MODEL

Fig. V-8: Rail normal stress data for 2D model due to deck expansion (+35°C)






Fig. V-9: Rail normal force data for 2-rail-configuration model due to deck expansion (35°C)



Maximal compressive force : 159 kN

o Maximal tensile stress : 159 kN / 7670 mm² = 20.7 MPa

3.3.4 CASE 4: EXPANSION RAIL

3.3.4.1. 2D MODEL

Fig. V-10: Rail normal stress data for 2D-model due to rail expansion (50°C)

Rail compressive stress : 126 MPa




Fig. V-11: Rail normal stress data for 2-rail-configuration model due to rail expansion (50°C)

Rail compressive stress : 126 MPa

3.3.5 RESULT OVERVIEW

Braking loads Vertical loads Deck expansion Rail expansion

Compr. Tension Compr. Tension Compr. Tension Compression

2D model

[MPa] 6.2 1.4 13.9 27.8 25.8 23.0 126

2-rail-config.

[MPa] 5.81 1.55 13.5 27.4 24.6 20.7 126

Deviation [%] -6.3 10.7 -2.9 -1.4 -4.7 -10.0 0

Table V-5: Overview of results with regard to arising rail stresses for both configuration types

3.3.6 CONCLUSION

As can be derived from Table V-5 the adjustments made to the model assembled in Chapter IV and

described in this chapter only result in small changes of the obtained rail stresses. All deviations

remain within acceptable limits. There are no deviations larger than 10% with respect to values

obtained using the model assembled according to Chapter IV. Therefore one can assume that the

model described in this chapter can be applied successfully in Chapter VI in order to simulate the

buckling behaviour of the CWR track.

Chapter VI Parametric study on 3D temporary bridge deck model

Application limits for continuously welded rail on temporary bridge decks VI-68

PARAMETRIC STUDY ON 3D TEMPORARY

BRIDGE DECK MODEL

1 INTRODUCTION

In the following chapter a parametric study is performed on the model described in the previous

chapter. The goal of this study is to determine the parameters of the model which are predominant

in determining the critical buckling temperature of the rails. After this parametric study it will then be

possible to determine all conditions that are strictly necessary for the use of continuously welded

rails without expansion devices and what conditions are advantageous but not necessary.

2 CLARIFICATIONS REGARDING THE PROCEDURE OF THE PARAMETRIC

STUDY

2.1 ANALYSIS TYPE

As mentioned in Chapter III the Samcef model does not allow to perform a complete analysis

(applying the temperature loads first on an unloaded track and afterwards adding the moving train

loads). It was found that, when applying all loads at once (braking, vertical and temperature loads),

deviations of 50% to 100% arised with respect to the expected rail stresses given by the UIC for the

model assembled in Chapter III. Therefore it does not seem too suitable, using this model, to

perform a sensitivity analysis with respect to the buckling of a rail track loaded by both the moving

train loads and the temperature loads. As a result it is opted to only check the buckling behaviour for

an unloaded track charged with temperature loads only (rail expansion and bridge expansion).

2.2 LOADS

It is opted to make a distinction between the temperature increase of the bridge deck and the

temperature increase of the rail track. For the temperature increase of the bridge deck an upper limit

of 35°C is chosen, in accordance with the UIC code 774-3R. The temperature of the bridge deck can

never exceed this limit. In this way it is possible to investigate the degree of safety on the allowable

temperature increase of the rail up to buckling.

Fig. VI-1 and Fig. VI-2 show the way in which the temperature loading for both the temporary bridge

deck and the rail are applied. Up to 35°C this temperature increase is identical: Initially, at t = 0 s, a



small temperature load (0.1°C) is present on both the rail and the bridge deck in order to prevent the

calculation from diverging. This situation corresponds to the case in which the rail’s temperature is

(approximately) equal to its neutral temperature, since there are no stresses present in the track.

Subsequently the temperature of both the bridge and rail is increased linearly with a speed of 10°C/s

to a temperature of 20°C. When reaching this value the temperature is then kept constant for a short

period of 1s allowing the structure to stabilize and after this short period the temperature is

increased further with the same rate to 35°C. After reaching this temperature the temperature of the

temporary bridge deck is kept constant for the remainder of the test and only the temperature of the

rail is increased further at the same rate of 10°C/s.

Fig. VI-1: Temp increase of bridge deck Fig. VI-2: Temp increase of rails

2.3 DEFINITION OF CRITICAL TEMPERATURE INCREASE

At a certain temperature the compressive forces in the rails will become too large and buckling will

occur. However initially this buckling temperature is unknown. Therefore a large temperature

increase is applied to the rail (for example 120°C at t = 13 s as shown in Fig. VI-2) such that buckling

will surely occur. Afterwards the displacements of the different mesh nodes as a function of time can

be plotted and from this plot the time and thus also the critical temperature increase at which

buckling initiates can be derived. An example of such a plot for the mesh node at the top of the

misalignment is given in Fig. VI-3.

As can be seen, the development of the lateral deflection takes place over a certain temperature

interval. It is thus quite difficult to quantify a specific buckling temperature. In order to do so, a

simplified definition is used. Since it is found in multiple test cases that the interval in which the

lateral deflections grow is relatively small (approximately 3°C) and the position of the maximum



deflection due to buckling does not differ too much from the initial position with the maximal

misalignment amplitude it is opted to define the critical buckling temperature as the temperature

corresponding to the peak value in the lateral displacement – temperature plot.

In Fig. VI-3 given below the progress of the lateral displacement as a function of time (and thus also

temperature) is given for the mesh node with the initial maximal misalignment amlitude. The

boundary for which the critical buckling temperature will be defined is designated with the red line.

Fig. VI-3: Progress of lateral displacement as a function of time for mesh node at top of the

misalignment

Inevitably there will be a certain margin of error on the obtained critical temperature increase but

still the obtained values will provide a good insight on the sensitivity of the buckling temperature

with respect to the different parameters examined. Additionally one will also gain a good

understanding on the order of magnitude of the arising critical temperature increases.

Note: The temperature increase at which buckling initiates is not equal to the rail’s physical

temperature at that moment. If one would want to calculate the physical temperature at which

buckling initiates the obtained critical temperature increase should be added to the rail’s neutral

temperature.

2.4 OBTAINED RESULTS

It is possible to retrieve the deformed track geometry of the buckled track. In this way it is possible to

obtain information regarding the shape and wavelength of the buckle. An example of such a buckled

track geometry obtained using the Samcef Field model is shown in Fig. VI-4.



Fig. VI-4: Track geometry after buckling

Furthermore it is also possible to consider the normal forces in the buckled track as shown in Fig.

VI-5. As can be seen the rail force severely drops in the buckled zone. This is due to the large lateral

displacement contributing to the rail extension that releases some of the compressive load. Also due

to this lateral displacement the rails in the adjoining zone will be pulled inwards to the buckled zone

also resulting in an altered normal force distribution in these zones.

Fig. VI-5: Rail force distribution after buckling

2.5 STANDARD CASE

All test cases, except for those investigating the influence of the misalignments, will be assembled

starting from the same standard case. Subsequently, in an attempt to investigate the influence of

each parameter, all parameters will be kept constant except for the one being investigated. In this

way it will be possible to check the influence of the regarded parameter on the arising critical

buckling temperature. The properties of the standard case are provided in Table VI-1.




Longitudinal track resistance Characteristic resistance (unloaded): 20 kN/m


Elastic limit: 2mm

Lateral track resistance Characteristic resistance: 6000 N

Elastic limit: 2mm

Lateral misalignment Amplitude : 3mm

Wavelength: 4m

Position: Max deflection situated 3m right of



Temporary bridge deck S = 0.239 m²

Iy = 0.0225 m4

vi = 0.424 m

wi = 0.317 m

Table VI-1: Properties of standard case forming basis for parametric study

Note: As depicted in Table VI-1 a lateral misalignment with a wavelength of 4 meters and an

amplitude of 3 millimetres is standardly incorporated in each model. This is done in order to

destabilize the model. If no lateral misalignment would be applied to the configuration the model

would not yield any solutions due to the perfect straightness of the beams used. The magnitude of

the amplitude of 3 millimetres is chosen according to the target values for construction imposed by

INFRABEL, shown in Table D-1 of Annex D.

3 PARAMETERS TO BE EXAMINED

In order to determine the parameters which should be examined in this parametric study each

possible parameter is discussed based on the information provided in the literature study of Chapter

II §5 and on the results of the preliminary parametric study of Chapter IV. The different parameters

which are discussed are listed below:

- Presence of lateral misalignment in rail configuration

o Position of lateral misalignment

o Amplitude of lateral misalignment

o Wavelength of lateral misalignment



- Lateral track resistance

- Torsional resistance fasteners

- Span length

- Bending stiffness temporary bridge deck

- Longitudinal stiffness of fixed bearing

- Longitudinal track resistance embankments

- Longitudinal track resistance fasteners on temporary bridge deck

3.1 PRESENCE OF LATERAL MISALIGNMENT IN RAIL CONFIGURATION

It has been proven in several studies that the presence of a lateral misalignment in the track

configuration severely influences the critical track buckling temperature. Therefore the influence of

this parameter should absolutely be checked in the parametric analysis. As mentioned in Chapter II

§5 and depicted in Fig. VI-6 multiple types of initial misalignment shapes might occur. For this

dissertation it is opted to assume the misalignments have a shape corresponding to the anti-

symmetric mode shape. The other misalignment shapes are not regarded in this dissertation.

However, it should be mentioned that they could have an influence on the critical buckling

temperature. In a future further elaboration of this dissertation it might be interesting to examine

this influence.

Fig. VI-6: Possible buckling shapes

As mentioned the models examining the influence of the presence of a lateral misalignment on the

critical buckling temperature use a slightly different configuration with respect to the standard

configuration described in Table VI-1. All properties given in this table also apply for the models

examined in this section except for the properties describing the small misalignment. In order to



better examine the influence of the presence of a misalignment in the track configuration slightly

different properties with respect to the misalignment will be applied. In the following sections it will

be mentioned clearly which properties do apply for the misalignments.

3.1.1 POSITION OF LATERAL MISALIGNMENT

Due to the presence of the temporary bridge deck locally larger compressive forces will arise in the

track, situated at the side of the movable bridge bearing, when expansion of the bridge deck takes

place. This behaviour is depicted in Fig. VI-7 where the normal rail stress evolution due to a

temperature increase of 35°C for the temporary bridge deck and 50°C for the rails is depicted.

Fig. VI-7: Normal stress evolution for deck expansion (35°C) and rail expansion (50°C)

As a result the most critical position for a track misalignment to occur will also be situated at that

part of the track. At which exact location (variable for each different considered case) the track is

most sensitive to the presence of a track misalignment is mainly dependent on two factors. First of

all the magnitude of the stabilizing effect of the stiff fasteners situated on the temporary bridge deck.

And secondly the magnitude of the destabilizing additional compressive stresses resulting from the

interaction due to the bridge deck expansion.

In order to now check this critical position different positions for the misalignment are applied in the

Samcef model. The properties of the models checked are discussed below:

Wavelength : 4 metres

Amplitude : 17 millimetres

o This magnitude is chosen corresponding to the ‘DAN’-value of the amplitude for

which INFRABEL suggests actions are required. (as shown in Table D-1 of Annex D)

Position: the position of the misalignments is characterized by the distance of the point with

the maximal initial amplitude closest to the movable support of the temporary bridge deck.



In order to clarify this position an example is given in Fig. VI-8. The following distances will be

checked: 3m, 7m, 11m, 15m, 19m, 25m, 50m

The resulting properties of the models are depicted in Table VI-1 (the properties regarding

the misalignment given in this table should be neglected)

Fig. VI-8: definition of position of misalignment

3.1.2 AMPLITUDE OF LATERAL MISALIGNMENT

Multiple studies by for example Samavedam (1993) have shown that the magnitude of the

misalignment present in the track has an important impact on the critical buckling temperature.

Therefore the magnitude of this parameter will also be investigated in the parametric study. The

properties of the models checked are listed below:

Wavelength : 4 metres

Position: point with maximal amplitude closest to the temporary bridge deck situated at a

distance of 3 metres to the movable support

Amplitude: The following magnitudes will be checked: 3mm, 7mm, 12mm, 17mm

The resulting properties are depicted in Table VI-1 (the properties regarding the

misalignment given in this table should be neglected).

3.1.3 WAVELENGTH OF LATERAL MISALIGNMENT

Samavedam (1993) and others also proved that apart from the amplitude of the misalignment also

the wavelength (equal to a distance of 2 times L for shape II in Fig. VI-6) plays an important role in

determining the critical buckling temperature of the track. The properties of the models used to

verify this influence are given below:

Position: point with maximal amplitude closest to the temporary bridge deck situated at a

distance of 6 metres to the movable support

Amplitude : 17 millimetres

Wavelength: the following magnitudes are regarded: 4 m, 6 m, 8 m, 12 m



The resulting properties are depicted in Table VI-1 (the properties regarding the

misalignment given in this table should be neglected).

3.2 LATERAL BALLAST RESISTANCE

Multiple studies by for example Choi (2010) and Samavedam et al. (1993) have shown that the

magnitude of the lateral track resistance severely influences the critical track buckling temperature.

Therefore the influence of this track parameter will be examined in the parametric analysis. As

mentioned in Table VI-1, for the standard case a bilinear behaviour is assumed characterized by a

maximum resistance value of 6 kN combined with an elastic limit of 2 mm2. In the parametric study

this maximum characteristic resistance will be varied over the following values:

2000 N, 4000 N, 6000 N, 8000 N, 10000 N

3.3 TORSIONAL RESISTANCE FASTENERS

As proven in multiple studies by for example Samavedam et al. (1993) the torsional resistance of the

fasteners has a negligible influence on the critical buckling temperature of the track. It is thus safe to

assume the fasteners do not exert any resisting moment to the track. The influence of this parameter

will not be regarded in the parametric analysis.

3.4 BENDING STIFFNESS TEMPORARY BRIDGE DECK

As mentioned for the parametric study performed in this chapter only thermal expansion of both the

rail and bridge deck are regarded. Therefore, in order to make a decision on which parameters

should be examined one can base itself on the results obtained in Chapter IV for loading case 3. As

concluded in Chapter IV the additional rail stresses due to bridge deck expansion remain unchanged

for varying bridge deck bending stiffnesses. Therefore this factor will not have a significant influence

on the arising critical buckling temperature of the rail and can thus be disregarded.

3.5 STIFFNESS OF FIXED BEARING

As can be seen in Fig. A-29 and Fig. A-35 of annex A and concluded in Chapter IV the influence of the

stiffness of the fixed bearing on the arising compressive rail stress at the movable bearing is rather

small. Therefore it is opted to not examine the influence of this parameter in the parametric study.

2 Value corresponding to timber sleepers with a length of 2.6 metres[13]



3.6 LONGITUDINAL TRACK RESISTANCE EMBANKMENTS

When comparing Fig. A-17 and Fig. A-23 of Annex A a change of the compressive rail stress at the

movable support can be distinguished. In order to check the influence of this variation on the critical

rail buckling temperature the characteristic longitudinal resistance will by varied. The following

characteristic resistance values will be evaluated:

10 kN/m, 20 kN/m, 30 kN/m, 40 kN/m

3.7 LONGITUDINAL TRACK RESISTANCE FASTENERS ON TEMPORARY BRIDGE DECK

Looking at the arising compressive rail stress at the movable support for both Fig. A-53 and Fig. A-59

of Annex A, a variation of the compressive rail stress at the movable support is found. Therefore it is

opted to evaluate the influence of this factor on the critical rail buckling temperature. In order to do

so the following characteristic resistance values are checked:

30 kN/m, 40 kN/m, 50 kN/m, 60 kN/m

3.8 SPAN LENGTH

In Chapter IV it is proven that the span length can have a significant influence on the arising

additional rail stresses for the different interaction loading cases. Especially the rail stresses resulting

from the vertical loading case and deck expansion showed a severe increase in rail stresses.

Therefore it is advised to also check the influence of the span length on the critical rail buckling

temperature. The following span lengths will be checked:

10 m, 20 m, 30 m



4 RESULTS

In the following section an overview is given of the results obtained in the parametric study. The

critical temperature increases of the rail for which buckling occurs are calculated as described in §2.3.

The graphs used in order to determine these values are given in Annex B. With respect to the

description of the different parameters and models examined, reference is made to the previous

section.

Note: The calculated critical temperature increases depicted in the graphs below are not equal to the

buckling temperature of the rails. These temperature increases are a relative increase with respect to

the neutral rail temperature of the rails. If one wants to calculate the actual buckling temperature of

the rails these obtained critical temperature increases should thus be added to the neutral

temperature of the rail. In Belgium typical values for the rail neutral temperature are situated in the

range of 20 to 30°C.

4.1 PRESENCE OF LATERAL MISALIGNMENT IN RAIL CONFIGURATION

4.1.1 POSITION OF LATERAL MISALIGNMENT

The position of the misalignments investigated is characterized by the distance of the point with the

maximal amplitude closest to the movable support of the temporary bridge deck. The following

distances are checked: 3m, , 7m, , 11m, 15m, 19m, 25m, 50m

Position misalignment

3 m 7 m 11 m 15 m 19 m 25 m 50 m

Temp increase [C°] 59.4 58.9 60.2 62.2 65 67.8 78.7

Deviation [%] / -0.84 1.35 4.71 9.43 14.14 32.49

Table VI-2: Critical temperature increase with regard to position of lateral misalignment



Fig. VI-9: Representation of influence of position misalignment on critical temperature increase

4.1.2 AMPLITUDE OF LATERAL MISALIGNMENT

The following magnitudes of the lateral misalignment are checked: 3mm, 7mm, 12mm, 17mm

Amplitude misalignment

3 mm 7 mm 12 mm 17 mm

Temp increase [C°] 109 80.2 65.9 59.4

Deviation [%] 83.5 35.0 10.9 /

Table VI-3: Critical temperature increase with regard to amplitude of lateral misalignment

Fig. VI-10: Representation of influence of amplitude of misalignment on critical temperature increase

50

55

60

65

70

75

80

85

0 10 20 30 40 50

Cri

tica

l tem

per

atu

re in

crea

se [

°C]

Distance point of maximal amplitude to movable support [m]

40

50

60

70

80

90

100

110

120

0 5 10 15 20

Cri

tica

l tem

per

atu

re in

crea

se [

°C]

Amplitude of lateral misalignment [mm]



4.1.3 WAVELENGTH OF LATERAL MISALIGNMENT

The following magnitudes for the lateral misalignment wavelength are regarded:

4 m, 6 m, 8 m, 12 m

Wavelength misalignment

4 m 6 m 8 m 12 m

Temp increase [C°] 59.8 51.2 47.6 48.7

Deviation [%] / -14.38 -20.4 -18.6

Table VI-4: Critical temperature increase with regard to wavelength of lateral misalignment

Fig. VI-11: Representation of influence of wavelength of misalignment on critical temperature

increase

4.2 LONGITUDINAL BALLAST RESISTANCE EMBANKMENTS

As mentioned, the progress of the critical buckling temperature is investigated for the following

values of the characteristic resistance assessed at a displacement of 2mm:

10 kN/m, 20 kN/m, 30 kN/m, 40 kN/m

Longitudinal ballast resistance on embankments

10 kN/m 20 kN/m 30 kN/m 40 kN/m

Temp increase [C°] 109.4 109.3 109.2 109.2

Deviation [%] 0.09 / -0.09 -0.09

Table VI-5: Critical temperature increase with regard to longitudinal ballast resistance on embankments

40

45

50

55

60

65

4 5 6 7 8 9 10 11 12

Cri

tica

l tem

per

atu

re in

crea

se [

°C]

Wavelength misalignment [m]



Fig. VI-12: Representation of influence of longitudinal ballast resistance of track situation on

embankment on the critical temperature increase

4.3 LONGITUDINAL TRACK RESISTANCE FASTENERS ON TEMPORARY BRIDGE DECK

The progress of the critical buckling temperature is investigated for the following values of the

characteristic resistance assessed at a displacement of 0.5 mm:

30 kN/m, 40 kN/m, 50 kN/m, 60 kN/m

Longitudinal fastener resistance temporary bridge deck

30 kN/m 40 kN/m 50 kN/m 60 kN/m

Temp increase [C°] 111.2 109.3 107.9 106.4

Deviation [%] 1.74 / -1.28 -2.65

Table VI-6: Critical temperature increase with regard to longitudinal fastener resistance on temporary bridge deck

Fig. VI-13: Representation of influence of longitudinal resistance of fasteners on temporary bridge

deck on the critical temperature increase

109.15

109.2

109.25

109.3

109.35

109.4

109.45

10 15 20 25 30 35 40

Cri

tica

l te

mp

erat

ure

incr

ease

[°C

]

Longitudinal ballast resistance [kN/m]

106

107

108

109

110

111

112

113

20 25 30 35 40 45 50 55 60

Cri

tica

l te

mp

erat

ure

tem

per

atu

re

[°C

]

Longitudinal fastener resistance [kN/m]




As mentioned, the progress of the critical buckling temperature is investigated for the following

values of the characteristic resistance assessed at a displacement of 2mm:

2000 N, 4000 N, 6000 N, 8000 N, 10000 N

Lateral ballast resistance

2000 N 4000 N 6000 N 8000 N 10000 N

Temp increase [C°] 67.9 92 109.3 125.2 136.5

Deviation [%] -37.9 -15.8 / 14.6 24.9

Table VI-7: Critical temperature increase with regard to lateral ballast resistance

Fig. VI-14: Representation of influence of lateral ballast resistance on critical temperature increase

4.5 SPAN LENGTH

The progress of the critical buckling temperature is investigated for the following span lengths:

10 m, 20 m, 30 m

Span length

10 m 20 m 30 m

Temp increase [C°] 112.4 109.3 105.9

Deviation [%] 2.84 0.00 -3.11

Table VI-8: Critical temperature increase with regard to span length

40

60

80

100

120

140

160

1000 3000 5000 7000 9000 11000

Cri

tica

l tem

per

atu

re in

crea

se [

°C]

Characteristic lateral ballast resistance [N]



Fig. VI-15: Representation of influence of span length on critical temperature increase

5 DISCUSSION OF RESULTS

5.1 POSITION OF LATERAL MISALIGNMENT

It is found that the most critical position for a track defect is situated in the immediate surroundings

of the movable support. For a track misalignment position moving away from the temporary bridge

deck the obtained allowable temperature increase augments and eventually will become constant.

This increased sensitivity at the movable support is off course the result of the local increased

compressive rail stresses due to the expansion of the temporary bridge deck, as shown in Fig. VI-16.

Fig. VI-16: Normal stress evolution for deck expansion (35°C) and rail expansion (50°C)

Still, the deviation between the different critical temperature increases remains rather small. For a

misalignment situated up to 25 metres away from the movable support the relative increase, with

respect to the critical temperature increase found for a misalignment situated 3 metres away from

the movable support, amounts only approximately 14%. For a misalignment position situated 50

105

106

107

108

109

110

111

112

113

10 15 20 25 30Cri

tica

l te

mp

erat

ure

tem

per

atu

re [

°C]

Span length [m]



metres away from the movable support this relative deviation has grown to 32%. From this one could

conclude that the part of the track beyond the movable support, with a length of a factor 1 or 1.5

times the bridge span length, should be monitored more strictly for the presence of misalignments.

5.2 AMPLITUDE OF LATERAL MISALIGNMENT

When considering Fig. VI-10 it is clear that the amplitude of the lateral misalignment will be one of

the determining factors with respect to the critical buckling temperature of the track. For decreasing

amplitude magnitudes, an exponential relationship is found with respect to the critical rail

temperature increase. In order to preserve sufficient safety margin against track buckling it will thus

be compulsory to limit the arising lateral misalignment amplitudes in the track. Since an inverse

exponential relationship is found for increasing misalignment amplitudes and the critical

temperature increase it will be very important to limit the arising misalignment amplitudes in an

early stage, since in this range the maximal decrease of the buckling temperature is found.

5.3 WAVELENGTH OF LATERAL MISALIGNMENT

When considering Fig. VI-11 it can be derived that the wavelength of the track misalignment also has

a considerable influence on the obtained critical buckling temperature of the track. It appears that

the buckling behaviour of the track is most critical for a misalignment wavelength situated in the

range of 8 to 12 metres. For wavelengths smaller than 8 metres the required temperature increase of

the track for buckling grows. For wavelengths longer than 12 metres no tests have been performed.

Further research might be needed.

In order to find an explanation for this phenomenon the geometry of the buckled track is regarded.

This is done for the different cases examined in §3.1.3. An example of such a deformed track is given

in Fig. VI-17 for the case of an initial wavelength of 4 metres and in Fig. VI-18 for an initial wavelength

of 8 metres. As can be derived from both figures the obtained final wavelength of the buckled track

measures respectively 8 and 12 metres. In the same way, for an initial misalignment wavelength of 6

metres, a buckled track wavelength of 11 metres was found.

It appears thus that, dependant on the magnitude of the initial misalignment, postbuckled track

wavelengths of 9 to 12 metres are found. Due to the tendency of the track to buckle with a

wavelength situated in this range, the track will thus be more prone to buckle for initial misalignment

wavelengths situated in the same range. This might explain the obtained minimum in Fig. VI-11 for an

initial misalignment wavelength situated in the range of 8 to 12 metres.



Fig. VI-17: Geometry of buckled track for an initial misalignment length of 4 metres

Fig. VI-18: Geometry of buckled track for an initial misalignment length of 8 metres

It should however be noted that the wavelength for which the track is most prone to buckle is

dependent on the magnitude of the lateral resistance, as shown in § 5.6. It appears that for

increasing lateral resistances the obtained wavelength of the buckled track decreases. Therefore it is

difficult to define a general wavelength of the initial misalignment for which the track is most prone

to buckle. As shown in §5.6 for a lateral resistance of 4 kN the obtained wavelength of the buckled

track amounts approximately 13 metres. However for a lateral resistance of 6 kN this wavelength has

decreased to 11 metres.

5.4 LONGITUDINAL BALLAST RESISTANCE EMBANKMENTS

When considering Fig. VI-12 it can be derived that the magnitude of the longitudinal track resistance,

for the part of the track situated on the embankments, does not influence the rail buckling

temperature in a considerable way. Its influence is negligible.



5.5 LONGITUDINAL RESISTANCE FASTENERS ON TEMPORARY BRIDGE DECK

It is found that an increased characteristic longitudinal resistance of the fasteners situated on the

temporary bridge deck results in a slight decrease of the critical buckling temperature. The influence

is more pronounced than for the longitudinal resistance of the track on the embankments, but still

remains quite small. These results also show that, if one would apply ZLR fastenings along the entire

bridge length, the critical buckling temperature would increase. Still, this increase would be rather

limited and therefore the benefits of the application of ZLR fastenings might not outweigh the

increased risk for rail breaks.


As expected the lateral ballast resistance also plays a major role in the buckling behaviour of the

track. First of all it is found that for increasing characteristic ballast resistances the critical buckling

temperature also severely increases. The rate at which the critical buckling temperature rises

however slightly decreases for growing resistances. Furthermore, when analysing the buckled state

of the track, a second influence of the lateral ballast resistance on the buckling behaviour of the track

is found. It appears that for decreasing lateral ballast resistances the obtained wavelength of the

buckled track increases. This effect can clearly be seen when analysing both Fig. VI-19 and Fig. VI-20 .

Fig. VI-19: Buckled track for characteristic lateral ballast resistance of 4kN



Fig. VI-20: Post-buckled track for characteristic lateral ballast resistance of 6 kN

For a characteristic ballast resistance of 6 kN and an initial wavelength of the track misalignment of 6

metres a post-buckling wavelength of approximately 11 metres is found. For, the case of a

characteristic ballast resistance of 4 kN this post-buckling wavelength amounts approximately 13

metres. A reasonable explanation for this behaviour could be that depending on the magnitude of

the lateral restraint a different representative buckling length of the track is valid: the larger the

lateral ballast resistance the smaller the relevant track buckling length.

As a result the increased critical buckling temperature is the result of both an increased restraint

against the lateral deformation of the track and a smaller representative track buckling length

resulting in a higher required normal force for buckling.

5.7 SPAN LENGTH

As shown in Fig. VI-14 the increase of the span length results in a decrease of the critical temperature

increase. This influence however, is not that determining as would be expected based on the results

obtained in Chapter IV. An explanation for this can be found in the fact that the applied amplitude of

the track misalignment in the standard case is rather small (3mm). Therefore the required

temperature increase of the track (≈ 110°C) in order to initiate buckling is very high compared to the

temperature increase of the bridge deck (35°C). Thus also the share of the normal forces present in

the track due to bridge deck expansion is very small compared to the normal forces originating from

the rail expansion. However if the misalignment amplitude would increase then the required rail

temperature will decrease and thus the relative share of the normal forces due to bridge deck

expansion will increase and will become more determining. This explanation is also valid for the

influence of the longitudinal resistance of the fasteners situated on the temporary bridge deck.



6 QUANTIFICATION OF SAFETY MARGIN

In order to get an idea on the margin of safety against buckling for the case of very bad track

conditions, the critical temperature increase is calculated for a model with the following properties:

- Misalignment wavelength = 8 metres

- Misalignment amplitude = 17 millimetres

- Misalignment position = point with maximal amplitude closest to the temporary bridge deck

situated at a distance of 6 metres to the movable support

- Lateral ballast resistance = 2 kN/m

- Resulting properties are equal to those mentioned in Table VI-1

As can be witnessed in Fig. VI-21 the obtained critical temperature increase amounts approximately

29°C. This is even smaller than the imposed allowable temperature increase by the UIC of 35°C for

the bridge and 50 °C for the rails. It is thus clear that if a lowered lateral ballast resistance might

occur in combination with a large lateral misalignment the safety margin is severely reduced. Even in

such a way that the safety limits do not meet the demands imposed by the UIC code 774-3R

anymore.

Fig. VI-21: Lateral displacement/temperature plot for critical test case

0

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30 35

Late

ral d

isp

lace

men

ts [

mm

]

Temperature increase above rail neutral temperature [°C]



7 IMPORTANT REMARKS REGARDING THE OBTAINED RESULTS

Some important additional remarks should be made regarding the results obtained in the parametric

study. First of all it should be noted that the obtained critical temperature increases are equal to the

component ΔTb,max which was defined in the literature study of Chapter II. This component equals the

temperature increase above the rail’s stress-free temperature, for which the track will buckle

without any addition of external energy. However as discussed, the track may also buckle for a

temperature increase lower than ΔTb,max if sufficient external energy is supplied. The safety levels

defined by the UIC code 720 [7] are all based on this lower temperature increase ΔTb,min. Therefore it

should always be kept in mind that, when adding extra energy to the rail, track buckling can still

occur for a rail temperature under Tb,max but still above Tb,min.

Additionally, it was also mentioned that there is a certain margin of error on the defined critical

temperature increases. The interval in which the lateral displacements grow has a magnitude of

approximately 5°C. In this dissertation the critical temperature was taken equal to the temperature

corresponding to the peak value of the lateral displacement/temperature plot shown in Fig. VI-3.

However the critical temperature increase at which the maximal arising lateral displacement in the

track exceeds the limit value imposed by INFRABEL for which immediate action is required (22

millimetres) will be slightly smaller. In the parametric study therefore a slight overestimation of the

safety margin is obtained.

Chapter VII General conclusions and formulation of application limits

Application limits for continuously welded rail on temporary bridge decks VII-90

GENERAL CONCLUSIONS AND FORMULATION

OF APPLICATION LIMITS

1 CONCLUSIONS AND APPLICATION LIMITS BASED ON 2D INTERACTION

MODEL ASSEMBLED IN CHAPTER IV

1.1 CONCLUSIONS

In Chapter IV multiple test cases have been examined in the parametric analysis with respect to their

interaction effects. For this parametric analysis a 2D temporary bridge deck model was assembled

based on the prescriptions of the UIC code 774-3R. This model only takes into account the stresses

arising in the rails due longitudinal and vertical (for the part of the track situated on the temporary

bridge deck) displacements of the rails. The lateral component is disregarded in these models. In

order to be able to verify whether CWR can be continued over the temporary bridge deck without

providing expansion devices all interaction loads imposed by the UIC code 774-3R were applied to

the structure. These loads consisted of braking and vertical loads due to a moving train and

temperature variations in the bridge (±35°C) and track (+50°C) expansion.

The following parameters have been examined: span length, longitudinal ballast resistance,

longitudinal resistance of fasteners situated on the temporary bridge deck, bending stiffness of the

temporary bridge deck, and stiffness of the fixed bearing. It was found that the span length and

bridge bending stiffness are the most determining parameters with respect to the arising additional

rail stresses. It will thus be compulsory to impose certain application limits to these parameters for

the allowance of continuing CWR track over a temporary bridge deck. The other parameters

examined also had an influence on the arising stresses but this influence was less decisive.

The standard configuration used in this parametric analysis corresponds to the case of a temporary

bridge deck with a span length of 20 metres. The bending stiffness of the temporary bridge deck is

chosen equal to the stiffness of an actual temporary bridge deck used by INFRABEL for a span length

of 12 metres. The characteristics for the longitudinal track resistance and the loads imposed to the

model are based on the values imposed by the UIC code 774-3R. Therefore, if this configuration

complies with the limitations given by the UIC code 774-3R, one can assume that for this span length

and temporary bridge deck configuration it is allowed to continue CWR track over the bridge

structure without providing an expansion device.



It is found that, not only for this configuration but also for all other test-cases examined (except for

the one with a span length of 30 metres), the limitations imposed by the UIC code 774-3R are met. As

a result one can state that for these configurations it is allowed to omit the expansion device from

the structural configuration of the track.

Furthermore, it could even be concluded that, if the temporary bridge decks used by INFRABEL are

applied corresponding to their practical applied span range, there is still a large safety margin with

respect to the additional rail stresses and displacements.

1.2 FORMULATION OF APPLICATION LIMITS

Based on the parametric study performed in Chapter IV the following recommendations are given in

order to ensure a safe application of CWR track over a temporary bridge deck without having to

install an expansion device:

One of the most determining factors in reducing the interaction stresses is the choice of an

appropriate bending stiffness for the temporary bridge deck with respect to the span to be

covered. As found in the parametric analysis of Chapter IV the increase of the interaction

stresses for an increasing span length is predominantly originating from the vertical and

thermal loading cases. If thus a temporary bridge deck with a sufficient bending stiffness is

chosen then, as proven in §3.3.5 of Chapter IV, the arising additional rail stresses for the

vertical loading case can be severely reduced.

Still, an increased bending stiffness of the bridge deck will not influence the arising additional

rail stresses due to bridge deck expansion in a significant manner, as proven in §3.3.5 of

Chapter IV. Therefore the increase of the additional rail stresses for an increased span length

due to bridge deck expansion might result in considerable problems. As can be seen in Fig. A-

11 of Annex A, for a span length of 30 metres the additional compressive rail stress at the

movable support due to bridge deck expansion amounts 50 MPa. Given the fact that the

upper limit for the compressive rail stresses imposed by the UIC code 774-3R equals 72 MPa

one can thus understand that this behaviour will limit the application range of the temporary

bridge decks. If a sufficient bending stiff temporary bridge deck is chosen the additional rail

stresses due to the vertical loading case can be limited and in this way the imposed limit of

72 MPa might still be obtained for a span length of 30 metres. However for larger spans this

will not be possible anymore.



As mentioned in the literature study of Chapter II, the implementation of zero longitudinal

rail fastenings would result in much smaller interaction forces since no longitudinal rail forces

would be transferred to the lower bridge structure. This beneficial behaviour is

demonstrated in the parametric study performed in Chapter IV. Nevertheless one should still

take into account the risk of rail breaks and therefore at any time a small longitudinal

resistance should be present on the bridge. Therefore, with respect to the rail fasteners

situated onto the bridge, a reduced clamping force would be beneficial but is not

compulsory. Conversely, an increased clamping force with respect to the one assumed in the

UIC code (40 kN/m in unloaded state and 60 kN/m in loaded state) has a negative influence

on the arising rail stresses but this increase remains rather small and will therefore not be

determining.

Similar to the longitudinal fastener resistance on the temporary bridge deck, limited

decreases of rail stresses are found for decreasing characteristic ballast resistance values. As

a result a reduced longitudinal ballast resistance is beneficial but not determining with

regard to the arising interaction stresses.

Finally it was also found that by choosing a sufficient flexible fixed bearing the arising rail

stresses can be reduced. This stress decrease is predominantly present for train moving

direction 2. For train moving direction 1 however this sensitivity is less pronounced. Since the

largest rail stresses are found for train moving direction 1 this factor will thus have no

significant influence on the overall track stability but it can prove to be helpful in order to

reduce the rail stresses for train moving direction 2.



2 CONCLUSIONS AND APPLICATION LIMITS BASED ON 3D MODEL

SIMULATING THERMAL BUCKLING

2.1 CONCLUSIONS

In Chapter VI a parametric analysis was performed in order to find the parameters which are decisive

in determining the track stability on and in the surroundings of the temporary bridge deck. In order

to do so the 2D model assembled in Chapter IV was expanded to a 3D model which is able to take

into account the elastoplastic behaviour and lateral displacements of the rails. In this way it was

possible to simulate the actual buckling behaviour of the rails. Since it was not possible to perform a

complete analysis using the model assembled in this dissertation it was opted to only apply

temperature loads to the models. First of all a temperature load of 35°C was applied to the

temporary bridge deck. Subsequently the temperature of the rails was increased until buckling

occurred. In this way it was possible to define a critical temperature increase of the track with

respect to thermal track buckling.

Multiple parameters have been examined, these are: position of the initial misalignment, amplitude

of the initial misalignment, wavelength of the initial misalignment, lateral ballast resistance,

longitudinal ballast resistance, longitudinal resistance of fasteners on the temporary bridge deck and

span length. The lateral ballast resistance and amplitude of the initial wavelength proved to be the

most determining factors with respect to the buckling resistance of the track. Therefore in order to

ensure a sufficient margin of safety is present with respect to track buckling it will be compulsory to

impose limits to these parameters. Additionally it was found that the magnitude of the wavelength of

the misalignment, the position of the misalignment, the span length and the longitudinal resistance

of the fasteners on the temporary bridge deck can influence the critical temperature increase in a

significant way. The influence of the longitudinal ballast resistance was rather negligible.

Based on these findings it was also tried to quantify the margin of safety with respect to track

buckling for a more critical case in which both a reduced lateral track resistance of 2 kN was assumed

and a large lateral misalignment amplitude of 17 millimetres situated 6 metres from the movable

support. For this case only an allowable temperature increase of 29°C for both the bridge deck and

rails was found. It is thus clear that if a lowered lateral ballast resistance might occur in combination

with a large lateral misalignment the safety margin is severely reduced. Even in such a way that the

safety limits do not meet the demands imposed by the UIC code 774-3R anymore (temperature

increase of 35°C for the bridge deck and 50°C for the track).



Additionally it should also be mentioned that there is a certain margin of error on the defined critical

temperature increases obtained in the parametric study. The interval in which the lateral

displacements grow has a magnitude of approximately 5°C. In this dissertation the critical

temperature was taken equal to the temperature corresponding to the peak value of the lateral

displacement/temperature plot shown in Fig. VI-3. However the critical temperature increase at

which the maximal arising lateral displacement in the track exceeds the limit value imposed by

INFRABEL for which immediate action is required (22 millimetres) will be slightly smaller. Also the

obtained critical temperature increases correspond to the temperature increase ΔTb,max for which the

track will buckle without any addition of external energy. However as discussed, the track may also

buckle for a temperature increase lower than ΔTb,max if sufficient external energy is supplied.

Therefore the margin of safety of for example 29°C defined in the paragraph above will be even

smaller.

2.2 FORMULATION OF APPLICATION LIMITS

Based on the findings of the parametric study performed in Chapter VI in the following section

recommendations are given in order to ensure a safe application of CWR track over a temporary

bridge deck without having to install an expansion device. It should be emphasized that these

recommendations are only valid for the case of thermal loading of the bridge and track. No moving

train loads were applied to the model and therefore additional research will have to be performed in

order to check the application limits for these loading cases.

In order to limit the detrimental influence of lateral misalignments on the track stability it

will be compulsory to measure the maximal arising lateral misalignment amplitude during

the execution of the maintenance works. INFRABEL has the following policy on the maximum

misalignment amplitude which is allowed to be present for a limited track speed of 40 km/h:

- Values for which an intervention is necessary ‘DAN’: 17mm

- Values for which immediate intervention is necessary: 22mm

These values were defined for the situation of a traditional track on an embankment.

However, for the case of a track situated immediately next to a temporary bridge deck the

increased compressive rail stresses will result in an increased buckling risk and therefore it

might be advisable to change these limits. As can be derived from Fig. VI-10 the major

decrease of the critical rail buckling temperature arises in the interval of 3 to 12 millimetres

for the track misalignment amplitude. Therefore it might be advisable to monitor the lateral



misalignments during the maintenance works and try to restrict the arising misalignment

amplitudes to a maximum of approximately 7 millimetres.

Due to the incorporation of the temporary bridge deck in the track configuration and the

presence of heavy machinery on the construction site locally a reduced compaction and thus

reduced lateral ballast resistance might arise. As proven in the parametric study this can be

very detrimental with respect to the stability of the track and therefore limitations should be

imposed with respect to the minimum required lateral ballast resistance. Based on in situ

measurements performed by the Technical University of Munich and the track measurement

department of DB a mean value of 6 kN was found for the characteristic resistance of timber

sleepers in a consolidated condition [13]. For this condition very high safety margins are

found with respect to the critical temperature increase. Therefore a slightly lower lateral

ballast resistance of 4 kN can still be allowed. Additionally it is also advised in order to make

sure that a sufficient high lateral ballast resistance is preserved that the track is compacted

after implementation of the temporary bridge deck.

As found in the parametric study the most critical position of a track defect is situated in the

immediate surroundings of the movable support. Still, the deviation of the different critical

temperature increases obtained remains rather small. For a misalignment situated up to 25

metres away from the movable support the relative increase, with respect to the critical

temperature increase found for a misalignment situated 3 metres away from the movable

support, amounts only approximately 14%. For a misalignment position situated 50 metres

away from the movable support this relative deviation has grown to 32%. From this one

could conclude that the part of the track beyond the movable support, with a length of a

factor 1 or 1.5 times the bridge span length, should be monitored more strictly for the

presence of misalignments.

For the wavelength of the initial misalignment it was found that the most critical wavelength

is dependent on the magnitude of the lateral ballast resistance. For lateral ballast resistances

equal to 4 or 6 kN the most critical wavelength of the initial misalignment was found in the

range of 8 to 12 metres. However no tests were performed for misalignment lengths longer

than 12 metres so no conclusion can be made for this situation. Further research for these

misalignment wavelengths might advisable.

With respect to the influence of the longitudinal resistance of the fasteners on the

temporary bridge deck the same conclusion can be made as found in Chapter IV. A reduced

clamping force would be beneficial but is not compulsory. Conversely, an increased clamping



force with respect to the one assumed in the UIC code (40 kN/m in unloaded state) has a

negative influence on the critical temperature increase but this influence remains rather

small and will therefore not be determining.

Finally, It should be noted that it is not possible to make a conclusion on the fact whether it is

allowed to allow train passage over the temporary bridge decks since no vertical and braking loads

due to a moving train have been incorporated in the model. However it is found that when the

expansion device is omitted from the track configuration the additional rail stresses due to thermal

expansion of both the temporary bridge deck and rails can be kept within acceptable limits as long as

certain demands with respect to the track quality are met.

3 GENERAL CONCLUSION

If one would rely on the model assembled according to the UIC code 774-3R of Chapter IV one could

conclude that it is allowed to continue CWR track over a temporary bridge deck without providing

expansion devices in front and after the temporary bridge. However if one considers the results

obtained in the parametric analysis of Chapter VI, in which the track is loaded with temperature

loads only, it is found that the conclusion is not that straightforward. It is found that depending on

the magnitude of two main factors, the lateral ballast resistance and the amplitude of the initial

misalignment (which are not incorporated in the 2D model of Chapter IV), a large reduction of the

track stability might arise. It is found that, for a situation in which very bad track conditions are

present, this reduction may even lead to a critical buckling temperature increase of only 29°C, being

smaller than the imposed temperature increase (35°C for a bridge deck and 50°C for the track) by the

UIC code 774-3R. Therefore it is compulsory to impose strict limits to the magnitude of these

parameters in order to ensure an adequate track stability with respect to thermal buckling. A

minimal characteristic lateral ballast resistance of 4 kN is recommended along with a maximal

allowable misalignment amplitude of 7 mm.

It should be noted that these limitations are only valid with respect to the stability of the track

loaded with temperature loads only. It is not possible to make a conclusion on the fact whether it is

allowed to allow train passage over the temporary bridge decks since no vertical and braking loads

due to a moving train have been incorporated in the model of Chapter VI. In order to be able to make

a good founded conclusion on the allowance of train passage over a temporary bridge deck without

expansion devices it will be necessary to perform further research by expanding the 3D model of

Chapter VI.

Chapter VIII Further research suggestions

Application limits for continuously welded rail on temporary bridge decks VIII-97

FURTHER RESEARCH SUGGESTIONS

During this dissertation a first step towards modelling the correct interaction behaviour of a CWR

track which is continued over a temporary bridge deck is provided. However in order to do so

multiple simplifications were made. In order to be able to approach the exact interaction behaviour

more accurately the following suggestions are made for further research:

First of all the model should be expanded in such a way that it becomes possible to execute a

complete analysis in which temperature loads should be applied first assuming an unloaded

track situation. Afterwards the moving train loads should be applied taking into account an

increased stiffness for the longitudinal track resistance.

Additionally the model can be further expanded to a dynamic buckling model which does

take into account the vehicle induced forces (dynamic uplift wave) and their influences on

the lateral stability of the track as discussed in Chapter II §5.2.2.

Application limits for continuously welded rail on temporary bridge decks 98

REFERENCES

[1] C. Esveld, Modern railway track. MRT-Productions, 2001.

[2] Union Internationale de Chemins Fer, “UIC Code 774-3 : Track/bridge interaction,” 2001.

[3] C. Esveld, “Avoidance of expansion joints in high speed tracks on bridges.pdf,” Rail Eng. Int. Ed., no. 3, pp. 7–9, 1995.

[4] K. R. Chaudhary and A. N. Sinha, “A study of various methods adopted by world railways to continue LWR over bridges.”

[5] IRICEN, Manual of Instructions on Long Welded Rails, no. 2. Indian Railways Institute of Civil Engineering, 2005.

[6] A. Kish and G. Samavedam, “Track Buckling Prevention : Theory , Safety Concepts , and Applications,” 2013.

[7] Union Internationale de Chemins Fer, “UIC Code 720,” 2005.

[8] D. Choi and H. Na, “Parametric Study of Thermal Stability on Continuous Welded Rail,” IJR Int. J. Railw., vol. 3, no. 4, pp. 126–133, 2010.

[9] G. Samavedam, A. Kish, and J. Schoengart, “Parametric Analysis and Safety Concepts of CWR Track Buckling,” 1993.

[10] C. Esveld, “Improved knowledge of CWR track,” 1992.

[11] A. (INFRABEL) Lefevre, “Bundel 34.6: Spoorversterkingen, voorlopige brugdekken en stalen boogbekisting,” 2015.

[12] M. C. Sanguino and P. G. Requejo, “Chapter 9: Numerical methods for the analysis of longitudinal interaction between track and structure,” in Track bridge interaction on high speed railways, 2009, pp. 95–108.

[13] M. Zacher, “Calculation of the critical temperature for track buckling in a switch P3550 – XAM 1 / 46 on the line Liège - Brussels Document : Date : 10-P-4926 - ICE3 MS Belgien Fahrzeug / Fahrbahn-Wechselwirkung Völckerstraße 5 80939 München,” 2011.


LIST OF FIGURES

Fig. II-1: Typical cross section of ballasted track [1] ............................................................................. II-2

Fig. II-2: Behaviour of CWR under the effects of temperature changes [2] ......................................... II-3

Fig. II-3: Example of a curve showing rail stresses due to a temperature variation in the bridge deck

[2] ......................................................................................................................................................... II-4

Fig. II-4: Pandrol® ZLR System .............................................................................................................. II-6

Fig. II-5: Principle sketch Pandrol® ZLR System [3] ............................................................................... II-6

Fig. II-6: Examples of track buckling in CWR......................................................................................... II-7

Fig. II-7: Pre- and postbuckled track configurations [6] ....................................................................... II-9

Fig. II-8: Buckling response curves [6] .................................................................................................. II-9

Fig. II-9: Definition of uplift waves [6] ................................................................................................ II-10

Fig. II-10: Possible buckling shapes [6] ............................................................................................... II-11

Fig. II-11: Energy required to buckle [6] ............................................................................................. II-12

Fig. II-12: Safety criteria definition in terms of ‘allowable temperature increase’ [7] ....................... II-12

Fig. II-13: Resistance ‘k’ of the track per unit length as a function of the longitudinal displacements of

the rail ................................................................................................................................................ II-14

Fig. II-14: Typical lateral resistance characteristic [6] ........................................................................ II-15

Fig. II-15: Example of a twin girder temporary bridge deck [11] ....................................................... II-18

Fig. II-16: Example of a tube girder temporary bridge deck [11] ....................................................... II-19

Fig. III-1: Schematic overview of the finite elements model in Samcef Field ................................... III-21

Fig. III-2: Entry of bilinear behaviour for longitudinal springs in Samcef Field.................................. III-23

Fig. III-3: Representation of loading cases regarded for train moving direction 1 ............................ III-26

Fig. III-4: Progress of braking load over period of 10s ....................................................................... III-29

Fig. III-5: Rail normal stress data due to vertical forces for train moving direction 1 ....................... III-30

Fig. III-6: Rail normal stress data due to braking forces for train moving direction 1 ....................... III-30

Fig. III-7: Rail normal stress data due to vertical forces for train moving direction 2 ....................... III-31

Fig. III-8: Rail normal stress data due to braking forces for train moving direction 2 ....................... III-31

Fig. III-9: Rail normal stress data due to bridge deck expansion (+35°C) .......................................... III-31

Fig. III-10: Rail normal stress data due to rail expansion (+50°C) ...................................................... III-32

Fig. III-11: Rail normal stress data due moving train loads and bridge deck expansion (35°C) for train

moving direction 2 ............................................................................................................................. III-32

Fig. IV-1: Schematic overview of the finite elements model in Samcef Field ................................... IV-35


Fig. IV-2: Cross-section of tube girder temporary bridge deck by INFRABEL for a span length of 12

metres [11] ........................................................................................................................................ IV-36

Fig. IV-3: Cross-section of twin girder temporary bridge deck by INFRABEL for span of 12 metres [11]

........................................................................................................................................................... IV-37

Fig. IV-4: Rail normal stress data due to vertical forces for train moving direction 1 ....................... IV-43

Fig. IV-5: Rail normal stress data due to braking forces for train moving direction 1 ...................... IV-44

Fig. IV-6: Rail normal stress data due to vertical forces for train moving direction 2 ....................... IV-44

Fig. IV-7: Rail normal stress data due to braking forces for train moving direction 2 ...................... IV-44

Fig. IV-8: Rail normal stress data due to deck expansion (+35°C) ..................................................... IV-45

Fig. IV-9: Rail normal stress data due to deck contraction (-35°C).................................................... IV-45

Fig. IV-10: Envelope of additional stresses in rail on bridge for train moving direction 1 ................ IV-46

Fig. IV-11: Envelope of additional stresses in rail on bridge for train moving direction 2 ................ IV-46

Fig. IV-12: Progress of relative displacement of rail with respect to bridge deck – dir 1 ................. IV-47

Fig. IV-13: Progress of relative displacement of rail with respect to bridge deck – dir 2 ................. IV-47

Fig. IV-14: Sensitivity of rail stresses with respect to bridge span length ......................................... IV-48

Fig. IV-15: Sensitivity of rail stresses with respect to long. ballast resistance on embankments ..... IV-50

Fig. IV-16: Sensitivity of rail stresses with respect to bearing stiffness ............................................ IV-50

Fig. IV-17: Sensitivity of rail stresses with respect to bridge bending stiffness ................................ IV-51

Fig. IV-18: Sensitivity of rail stresses with regard to fastener longitudinal resistance on bridge deck . IV-

52

Fig. V-1: Overview of configuration of the model .............................................................................. V-57

Fig. V-2: Relevant dimensions for design of rail ................................................................................. V-58

Fig. V-3 : Entry of bilinear behaviour for lateral springs in Samcef Field [6] ...................................... V-61

Fig. V-4: Rail normal stress data for 2D model due to vertical forces for train moving direction 1 .. V-63

Fig. V-5: Rail normal force data for 2-rail-configuration model due to vertical forces for train moving

direction 1 .......................................................................................................................................... V-64

Fig. V-6: Rail normal stress data for 2D-model due to horizontal forces for train moving direction 1 .. V-

64

Fig. V-7: Rail normal force data for 2-rail-configuration model due to horizontal forces for train

moving direction 1 .............................................................................................................................. V-65

Fig. V-8: Rail normal stress data for 2D model due to deck expansion (+35°C) ................................. V-65

Fig. V-9: Rail normal force data for 2-rail-configuration model due to deck expansion (35°C) ......... V-66

Fig. V-10: Rail normal stress data for 2D-model due to rail expansion (50°C) ................................... V-66


Fig. V-11: Rail normal stress data for 2-rail-configuration model due to rail expansion (50°C) ........ V-67

Fig. VI-1: Temp increase of bridge deck ............................................................................................ VI-69

Fig. VI-2: Temp increase of rails ........................................................................................................ VI-69

Fig. VI-3: Progress of lateral displacement as a function of time for mesh node at top of the

misalignment ..................................................................................................................................... VI-70

Fig. VI-4: Track geometry after buckling ........................................................................................... VI-71

Fig. VI-5: Rail force distribution after buckling .................................................................................. VI-71

Fig. VI-6: Possible buckling shapes .................................................................................................... VI-73

Fig. VI-7: Normal stress evolution for deck expansion (35°C) and rail expansion (50°C) .................. VI-74

Fig. VI-8: definition of position of misalignment ............................................................................... VI-75

Fig. VI-9: Representation of influence of position misalignment on critical temperature increase . VI-79

Fig. VI-10: Representation of influence of amplitude of misalignment on critical temperature increase

........................................................................................................................................................... VI-79

Fig. VI-11: Representation of influence of wavelength of misalignment on critical temperature

increase ............................................................................................................................................. VI-80

Fig. VI-12: Representation of influence of longitudinal ballast resistance of track situation on

embankment on the critical temperature increase .......................................................................... VI-81

Fig. VI-13: Representation of influence of longitudinal resistance of fasteners on temporary bridge

deck on the critical temperature increase ........................................................................................ VI-81

Fig. VI-14: Representation of influence of lateral ballast resistance on critical temperature increase VI-

82

Fig. VI-15: Representation of influence of span length on critical temperature increase ................ VI-83

Fig. VI-16: Normal stress evolution for deck expansion (35°C) and rail expansion (50°C) ................ VI-83

Fig. VI-17: Geometry of buckled track for an initial misalignment length of 4 metres ..................... VI-85

Fig. VI-18: Geometry of buckled track for an initial misalignment length of 8 metres ..................... VI-85

Fig. VI-19: Buckled track for characteristic lateral ballast resistance of 4kN ................................... VI-86

Fig. VI-20: Post-buckled track for characteristic lateral ballast resistance of 6 kN ........................... VI-87

Fig. VI-21: Lateral displacement/temperature plot for critical test case .......................................... VI-88


LIST OF TABLES

Table III-1: Properties of single UIC60 rail ......................................................................................... III-21

Table III-2: Properties of beam corresponding to two UIC 60 rail .................................................... III-21

Table III-3: Data with respect to test-cases considered .................................................................... III-28

Table III-4: Additional rail stresses for test-case E1-3 ....................................................................... III-33

Table III-5: Additional rail stresses for test-case E4-6 ....................................................................... III-33

Table III-6: Additional rail stresses for test-case A1-3 ....................................................................... III-33

Table III-7: Additional rail stresses for test-case A4-6 ....................................................................... III-34

Table IV-1: Properties of Tube girder temporary bridge deck by INFRABEL for span of 12 metres . IV-37

Table IV-2: Properties of twin girder temporary bridge deck by INFRABEL for a span length of 12

metres [11] ........................................................................................................................................ IV-38

Table IV-3: Comparison of properties of both temporary bridge deck types ................................... IV-38

Table IV-4: Properties of the standard configuration used for the parametric study ...................... IV-42

Table IV-5: Results of parametric study with regard to changing span length ................................. IV-48

Table IV-6: Results of parametric study with regard to long. ballast resistance on embankments . IV-49

Table IV-7: Results of parametric study with regard to stiffness of fixed bearing ............................ IV-50

Table IV-8: Results of parametric study with regard to deck bending stiffness ............................... IV-51

Table IV-9: Sensitivity of rail stresses with regard to long. fastener resistance on bridge deck ....... IV-52

Table V-1: Comparison of actual UIC 60 properties to approximated rail in Samcef Field ................ V-58

Table V-2: Dimensions used for I-profile in order to approximate UIC 60 rail ................................... V-58

Table V-3 : Properties of twin girder temporary bridge deck built by INFRABEL for a span of 21.7m .. V-

59

Table V-4: Properties of the model regarded..................................................................................... V-62

Table V-5: Overview of results with regard to arising rail stresses for both configuration types...... V-67

Table VI-1: Properties of standard case forming basis for parametric study .................................... VI-72

Table VI-2: Critical temperature increase with regard to position of lateral misalignment ............. VI-78

Table VI-3: Critical temperature increase with regard to amplitude of lateral misalignment .......... VI-79

Table VI-4: Critical temperature increase with regard to wavelength of lateral misalignment ....... VI-80

Table VI-5: Critical temperature increase with regard to longitudinal ballast resistance on

embankments .................................................................................................................................... VI-80

Table VI-6: Critical temperature increase with regard to longitudinal fastener resistance on

temporary bridge deck ...................................................................................................................... VI-81


Table VI-7: Critical temperature increase with regard to lateral ballast resistance ......................... VI-82

Table VI-8: Critical temperature increase with regard to span length .............................................. VI-82

Application limits for continuously welded rail on temporary bridge decks A-104

Annex A. RESULTS CHAPTER IV

1 CASE A – SPAN LENGTH – 10 METRES

Fig. A-1: Case A1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-2: Case A2 - Normal rail stress progress – Braking forces dir 1

Fig. A-3: Case A4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-4: Case A5 - Normal rail stress progress – Braking forces dir 2

Fig. A-5: Case A3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-6: Case A3/6 - Normal rail stress progress – Bridge contraction (-35°C)


2 CASE C – SPAN LENGTH – 30 METRES

Fig. A-7: Case C1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-8: Case C2 - Normal rail stress progress – Braking forces dir 1

Fig. A-9: Case C4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-10: Case C5 - Normal rail stress progress – Braking forces dir 2

Fig. A-11 Case C3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-12: Case C3/6 - Normal rail stress progress – Bridge contraction (-35°C)


3 CASE D – BALLAST QUALITY – MODERATE

Fig. A-13: Case D1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-14: Case D2 - Normal rail stress progress – Braking forces dir 1

Fig. A-15: Case D4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-16: Case D5 - Normal rail stress progress – Braking forces dir 2

Fig. A-17 Case D3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-18: Case D3/6 - Normal rail stress progress – Bridge contraction (-35°C)


4 CASE E – BALLAST QUALITY – EXCELLENT

Fig. A-19: Case E1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-20: Case E2 - Normal rail stress progress – Braking forces dir 1

Fig. A-21: Case E4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-22: Case E5 - Normal rail stress progress – Braking forces dir 2

Fig. A-23: Case E3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-24: Case E3/6 - Normal rail stress progress – Bridge contraction (-35°C)


5 CASE F – BRIDGE BEARING STIFFNESS – 6.105 KN/M

Fig. A-25: Case F1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-26: Case F2 - Normal rail stress progress – Braking forces dir 1

Fig. A-27: Case F4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-28: Case F5 - Normal rail stress progress – Braking forces dir 2

Fig. A-29: Case F3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-30: Case F3/6 - Normal rail stress progress – Bridge contraction (-35°C)


6 CASE G – BRIDGE BEARING STIFFNESS – 6.107 KN/M

Fig. A-31: Case G1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-32: Case G2 - Normal rail stress progress – Braking forces dir 1

Fig. A-33: Case G4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-34: Case G5 - Normal rail stress progress – Braking forces dir 2

Fig. A-35: Case G3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-36: Case G3/6 - Normal rail stress progress – Bridge contraction (-35°C)


7 CASE H – BRIDGE BENDING STIFFNESS – 0.005 M4

Fig. A-37: Case H1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-38: Case H2 - Normal rail stress progress – Braking forces dir 1

Fig. A-39: Case H4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-40: Case H5 - Normal rail stress progress – Braking forces dir 2

Fig. A-41: Case H3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-42: Case H3/6 - Normal rail stress progress – Bridge contraction (-35°C)


8 CASE I – BRIDGE BENDING STIFFNESS – 0.02 M4

Fig. A-43: Case I1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-44: Case I2 - Normal rail stress progress – Braking forces dir 1

Fig. A-45: Case I4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-46: Case I5 - Normal rail stress progress – Braking forces dir 2

Fig. A-47: Case I3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-48: Case I3/6 - Normal rail stress progress – Bridge contraction (-35°C)


9 CASE J – LONG RESISTANCE FASTENER – MODERATE CLAMPING

Fig. A-49: Case J1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-50: Case J2 - Normal rail stress progress – Braking forces dir 1

Fig. A-51: Case J4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-52: Case J5 - Normal rail stress progress – Braking forces dir 2

Fig. A-53: Case J3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-54: Case J3/6 - Normal rail stress progress – Bridge contraction (-35°C)


10 CASE K – LONG RESISTANCE FASTENER – EXCELLENT CLAMPING

Fig. A-55: Case K1 - Normal rail stress progress – Vertical forces dir 1

Fig. A-56: Case K2 - Normal rail stress progress – Braking forces dir 1

Fig. A-57: Case K4 - Normal rail stress progress – Vertical forces dir 2


Fig. A-58: Case K5 - Normal rail stress progress – Braking forces dir 2

Fig. A-59: Case K3/6 - Normal rail stress progress – Bridge expansion (+35°C)

Fig. A-60: Case K3/6 - Normal rail stress progress – Bridge contraction (-35°C)

Application limits for continuously welded rail on temporary bridge decks B-124

Annex B. RESULTS CHAPTER VI

1 INFLUENCE OF MISALIGNMENT AMPLITUDE

Fig. B-1: Lateral displacement/temperature plot for misalignment amplitude of 3mm



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2 INFLUENCE OF WAVELENGTH MISALIGNMENT

Fig. B-5: Lateral displacement/temperature plot for misalignment wavelength of 4 metres


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Table B-1: Lateral displacement/temperature plot for misalignment wavelength of 12 metres

3 INFLUENCE OF POSITION OF MISALIGNMENT

Fig. B-8: Lateral displacement/temperature plot for misalignment position for which the maximum amplitude is situated 3 metres away from the movable support

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Fig. B-12: Lateral displacement/temperature plot for misalignment position for which the maximum

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4 INFLUENCE OF LATERAL BALLAST RESISTANCE

Fig. B-15: Lateral displacement/temperature plot for lateral ballast resistance of 2 kN



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5 INFLUENCE OF LONGITUDINAL BALLAST RESISTANCE ON EMBANKMENTS

Fig. B-20: Lateral displacement/temperature plot for longitudinal ballast resistance of 10 kN

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6 INFLUENCE OF LONGITUDINAL RESISTANCE OF FASTENERS ON

TEMPORARY BRIDGE DECK

Fig. B-23: Lateral displacement/temperature plot for longitudinal fastener resistance on temporary bridge deck of 30 kN

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Fig. B-24: Lateral displacement/temperature plot for longitudinal fastener resistance on temporary

bridge deck of 50 kN

Fig. B-25: Lateral displacement/temperature plot for longitudinal fastener resistance on temporary bridge deck of 60 kN

7 SPAN LENGTH

Fig. B-26: Lateral displacement/temperature plot for span length of 10 metres

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Fig. B-27: Lateral displacement/temperature plot for span length of 30 metres

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Application limits for continuously welded rail on temporary bridge decks C-134

Annex C. Table C-1: Overview of available temporary bridge decks used by INFRABEL

Application limits for continuously welded rail on temporary bridge decks D-135

Annex D. Table D-1: Extract of leaflet 13 I-I/2013 by INFRABEL containing the adjustments of the misalignment tolerances

application limits for continuously welded rails on...

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