Track bridge interaction on high speed railways selected and revised papers from the workshop on track bridge interaction on high speed railways, porto, portugal, 15–16 october, 2007 ( PDFDrive )

– Temperature variation maximum distance between based points – Deck end rotations – Braking & acceleration forces: maximum displacement under braking and accelerationforces ◦ This contr

TRACK-BRIDGE INTERACTION ON HIGH-SPEED RAILWAYS

Track-Bridge Interaction on

High-Speed Railways

Editors

Rui Calçada, Raimundo Delgado & António Campos e Matos

Department of Civil Engineering, Faculty of Engineering,

University of Porto, Portugal

José Maria Goicolea & Felipe Gabaldón

Computational Mechanics Group, Department of Mechanics and Structures, E.T.S Ingenieros de Caminos, Universidad Politécnica de Madrid, Spain

Published by: CRC Press/Balkema

P.O Box 447, 2300 AK Leiden, The Netherlands

e-mail: Pub.NL@taylorandfrancis.com

www.crcpress.com – www.taylorandfrancis.co.uk – www.balkema.nl

Library of Congress Cataloging-in-Publication Data

Track-bridge interaction on high-speed railways / edited by Rui Calcada [et al.].

p cm

Includes index

ISBN 978-0-415-45774-3 (hardcover) — ISBN 978-0-203-89539-9 (ebook)

1 High speed trains 2 Railroad bridges 3 Bridges—Live loads

5 Track-structure interaction and seismic design of the bearings system for some

F Millanes Mato & M Ortega Cornejo

6 Track structure interactions for the Taiwan High Speed Rail project 55

D Fitzwilliam

P Ramondenc, D Martin & P Schmitt

N Matsumoto & K Asanuma

9 Numerical methods for the analysis of longitudinal interaction between

M Cuadrado Sanguino & P González Requejo

P Ruge, D.R Widarda & C Birk

11 Structural analysis of high speed rail bridge substructures Application to

J.A Sobrino & J Murcia

M.P Petrangeli

J Hess

V

Subject index 213

The construction of high-speed railways comprises a set of demands, from safety aspects tonew types of equipment and construction solutions, involving the most recent and sophisticatedtechnologies

Among these, emphasis is given to the railway behaviour where the structural elements are ofgreat relevance One of the relevant aspects concerns the effects of the track-bridge interaction,which establishes restricted limits to the vibration and deformability of the structure in order tocontrol the acceleration, the stresses and the track deformations, so that the circulation safety issatisfied, while strongly conditioning the structural design solutions for bridges

The ability to address the multiple issues relevant to this process requires expertise and how, which have been recently developed in this field, with repercussions in terms of the Europeanregulations in this domain

know-The themes included in this book are mainly based on the papers presented at the workshop

“TRACK-BRIDGE INTERACTION ON HIGH-SPEED RAILWAYS” organised by the Faculdade

de Engenharia da Universidade do Porto (FEUP) and the Escuela Tecnica Superior de Ingenieros deCaminos Canales y Puertos de Madrid (ETSICCyP) This book is included in a set of three books:one with a more general thematic “BRIDGES FOR HIGH-SPEED RAILWAYS” and other with

a more focused thematic, such as the present book, “DYNAMICS OF HIGH-SPEED RAILWAYBRIDGES”

The editors would like to thank all those who contributed to this book, in particular our guished guest chapters’ authors who heightened, with their knowledge and expertise, to the presentinterest and quality of the book, the support of the sponsors for the events which originated thematerials for this book, and the institutional support of the Faculty of Engineering of the University

distin-of Porto and the RAVE – Rede Ferroviária de Alta Velocidade, S.A

We hope this book will be helpful not only to those professionals involved in the design, tion or maintenance of high speed railway systems, but also to researchers and students working inthis field

construc-VII

List of Authors

Antonio Martínez Cutillas, UPM and CFCsl – Spain

António Reis, IST and GRID – Portugal

Carolin Birk, TU Dresden – Germany

Daniel Dutoit, SYSTRA – France

Daniel Fitzwilliam, TY Lin – USA

Daniel Ribeiro, GRID – Portugal

Didier Martin, SNCF – France

Dina Rubiana Widarda, TU Dresden – Germany

Francisco Millanes Mato, UPM and IDEAM – Spain

Joep Tünnissen, JTüDEC – The Netherlands

José Maria Goicolea- Ruigómez, UPM – Spain

Josef Heß, BWG GmbH – Germany

Juan A Sobrino Almunia, Pedelta and UPC – Spain

Juan Murcia, UPC – Spain

Kiyoshi Asanuma, RTRI – Japan

Manuel Cuadrado Sanguino, Fundación Caminos de Hierro – Spain Mario Paolo Petrangeli, Università Roma “La Sapienza” – Italy Miguel Ortega Cornejo, IDEAM – Spain

Nobuyuki Matsumoto, RTRI – Japan

Nuno Lopes, GRID – Portugal

Patrice Schmitt, SNCF – France

Pedro González Requejo, Fundación Caminos de Hierro – Spain Peter Ruge, TU Dresden – Germany

Philippe Ramondenc, SNCF – France

Raimundo Delgado, FEUP – Portugal

Romeu Simões, FEUP – Portugal

Rui Calçada, FEUP – Portugal

Stuart Davis, Mott MacDonald – United Kingdom

IX

CHAPTER 1

New evolutions for high speed rail line bridge design criteria and corresponding design procedures

D Dutoit

Systra, Paris, France

ABSTRACT: The high speed rail lines bridges have always had specific design criteria theless, with the new development of the analysis of rail stresses due to rail structure interaction,some of the initial criteria used in France can be replaced by limitation of the rail stresses, asdescribed for instance in the Eurocode This can lead to significant savings, especially in highlyseismic zones

1.1 Typefont, typesize and spacing

Historically, the developement of the High Speed Lines in France has been done step by step Based

on actual measurements made of stress concentrations in the rail done on real sites, and based onthe experience of track stability and safety, rules were set-up to restrain specific features of thesupporting structures within empirial limits in order to provide for the track safety

Usually, and as described today in Eurocode, UIC and present SNCF standards, the structurescarrying the long welded rails for high speed trains have specific limitations due to 3 sets ofphenomena:

• Long Welded rail
Rail structure interaction

◦ Additional rail stresses brought by R.S.I

– Temperature variation maximum distance between based points

– Deck end rotations

– Braking & acceleration forces: maximum displacement under braking and accelerationforces

◦ This controls

– The location of expansion joint

– The girder stiffness

– The support stiffnesses (piers, foundations, bearings)

• High speed vehicle
Structure dynamic response

The high speed rail supports vehicles travelling at high speed This involves the analysis ofthe structures dynamic response to address the following items

◦ Control of vertical load (impact at resonance)

◦ Control of acceleration at deck level

– Track stability: acceleration at deck level

– Rail/wheel contact: acceleration at deck level

– Rolling stock stability: acceleration at deck level

– Passenger comfort: vertical acceleration in the cars

1

– Translated that into practical and simple High Speed Serviceability earthquake structuredesign criteria

◦ Consequence on High Speed Operation

Train switch off at certain level of earthquake

In order to address the concerns described above, specific design criteria had been developed byseveral national codes

These specific criteria involved:

• A limitation of maximum distance between bridge expansion joints when using a continuouswelded rail, in order to limit the additional stress in the rail due to the difference of displacementbetween the structure and the rail

• A maximum rotation at bridge ends in order to limit the additional stress in the rail due to bridgeend displacement and the corresponding force transmitted by the elasticity of the ballast or of therail supports in the case of slab track and to ensure the stability of the ballast This may controlthe deck rigidity

• A maximum displacement of the bridge when the maximum braking and acceleration force isapplied: this may control the foundation, pier and bearing design

In the new evolution, instead of controlling the additional stresses in the rail by the abovementioned limitations, a complete analysis of the additional stresses in the rail due to the bridgessupporting the track is limited to the followings

Ballasted track

• 72 N/mm2compression (Risk of track buckling in compression)

• 92 N/mm2tensionSlab track 92 N/mm2tension and compression

In addition, in case of the ballast track, other criteria shall be satisfied in order to ensure thestability of the ballast (relative displacement of the deck under braking and acceleration, maximum

relative displacement of the expansion joint between two bridges under live loads, ).

This calculation is done by computing, on a computer model describing a significant length ofthe line on each side of the considered structure:

• The foundations and the corresponding elasticities due to the soil – foundation interaction

• Pier flexibilities

• The bearings (fixed, sliding or its elasticity)

• The bridge superstructure

• The tracks, with the rail stiffnesses and the elasticities (horizontal) of the support between therail and the deck (ballast and ties, slab track, elastomeric pads underneath the rail)

• The rail expansion joints

New evolutions for high speed rail line bridge design criteria 3

• The environmental conditions (temperature variations, gradients, )

• The train characteristics

Based on the corresponding analysis, the piers and foundations can be optimized when compared

to the conventional HSR criteria (see example in part 4.1.)

In addition, it is also possible to identify critical points on the line where there are concentrations

of forces on the bearings and design the sub-structures in order to reduce this unfavourable effect(see example in 4.2.) This cannot be done by using the simplified approach (without the railinteraction analysis)

This new computerised method is therefore more economical and safer the simplified one

These new design procedures can induce a significant saving in the substructures (foundation,piers) These savings may be magnified in seismic areas Since the loads applied by a givenearthquake increase with the substructure rigidity, the additional elasticity of the substructure due

to the new HSR service load criteria will also induce a significant saving in the seismic analysis

of the structure

The following examples show that the simplified method (no track structure interaction modelled)used to avoid computerised calculation (track structure interaction modelled) is generally too con-servative and cannot identify the critical points on the line where very high bearing reactions canoccur

In the following examples, we compare the simplified method and the computerised method on

• Rail type UIC 60

• Succession of 30 m simply supported spans

4.1 Comparison between the simplified method and the computerised method – optimisation of the pier and foundation

(a) Simplified method:

In the case of a succession of simply supported spans, the braking and acceleration forces applied

on one span are fully transmitted to the bearings of the span

In the case of a 30 m simple span, the longitudinal braking and acceleration forces are:

The bearing reaction under temperature effect is calculated using the formula 8× L (L is thelength of the span) It can be estimated at 8 kN/m× 30 m = 240 kN

The maximum allowable relative displacement under braking and acceleration forces between

two decks is δ= 5 mm Therefore, the minimum stiffness of the pier and foundation is:

K= F

Each pier and foundation shall have a stiffness higher than 318000 kN/m

Figure 2 Stresses in the rails under Temperature, braking/acceleration and live loads.

The stresses in the rail is between−25 MPa and +30 MPa

New evolutions for high speed rail line bridge design criteria 5

The maximum relative displacement between two decks is below 2 mm

The maximum bearing reaction is 1019 kN This represents only 64% of the value given by thesimplified method (1590 kN)

It can also be noticed that the bearing reaction under temperature effect is almost zero compared

to 240 kN calculated by the simplified method

(c) Analysis of the results:

The table below shows the results of the computerised calculations

Table 1.

In addition, the bearing reaction under temperature, braking/acceleration and live loads is only56% of the value given by the simplified method

(d) Conclusion:

It is therefore possible to optimise the piers and foundation Additional calculations show that even

if the pier stiffness is reduced by more than 2, the safety of the track is still ensured

The bearing reactions calculated by the computerised method are also around half of the valuecalculated by the simplified method

4.2 Comparison between the simplified method and the computerised method – Identification

of the critical points on the line

Due to the link between adjacent girder created by the track, a force applied on one span istransmitted to the adjacent spans

Very stiff pier

The maximum bearing reaction is 2036 kN

Conclusion

The maximum bearing reaction is 2036 kN, which is 128% of the value calculated using the

simplified method (1590 kN – see 4.1.a).

Additional calculations shows that, in case of slab track, it is even more unfavourable The

maximum bearing reaction is then 155% of the value calculated using the simplified method.

The new computarised method allows therefore a better identification of the overstressed areas,and allows to make the required changes necessary to have a safer track

CHAPTER 2

Service limit states for railway bridges in new Design Codes

IAPF and Eurocodes

J.M Goicolea-Ruigómez

Escuela de Ingenieros de Caminos, Technical University of Madrid, Spain

ABSTRACT: The new and enhanced performance needs of bridges for high-speed railway lineshave prompted new requirements for design of structures These have been studied at national andinternational level within Europe (ERRI, UIC, Eurocode project teams) and have originated newengineering codes for actions and design requirements Between these we may cite the EurocodesEN1991-2 (2003) and EN1990-A1 (2005) and the new Spanish code IAPF (2007) An importantfeature in these codes is the consideration of service limit states These limit states are unique torailway bridges and are often the critical features conditioning the design Among these limits arethe maximum of displacements and stresses in the rail related to track-bridge interaction, and thelimit of accelerations at the track It must be stressed that some of these service limit states areindeed ultimate limit states related to safety of rail traffic, and hence of the utmost importance

In this work we shall review these limitations, the methods proposed for calculation, and theirrelevance for design

RAILWAY BRIDGES

New high speed railway lines are developing at a fast pace in some European countries In particular,

in Spain the plan for transport infrastructure (PEIT 2005–2020) devotes 78000 Millionato highspeed railways out of a total investment of 241000 Milliona

Railway bridges for the new high speed lines introduce a number of design requirements whichcause significant differences not only with road bridges but also with other railway bridges inconventional freight or passenger lines A first and obvious requirement arises directly from thehigher speed of traffic actions These not only produce a higher individual effect (measured through

the impact factor ), but more importantly for speeds above 200 km/h the risk of resonance appears.

As a result dynamic analyses must be carried out in general, and furthermore these considerationsmust be taken into account in the design of structural characteristics In particular, some structuraltypes such as short span isostatic bridges have been shown to originate high levels of vibrationexceeding the limits for comfort and safety

Furthermore the stricter requirements for the high speed lines (e.g maximum gradients, mum radii) and geometrical quality originate line layouts in which more and longer viaducts arenecessary This is particularly important in regions with rugged terrain like the Iberian Peninsula.For instance, the new lines in Spain include a number of viaducts longer than 1000 m, some evenreaching 3000 m

mini-The consideration of interaction between bridge and track introduces additional requirements to

be met by railway bridges These stem from limitations of stresses in the rail as well as maximumvalues of relative displacements in deck joints The magnitude of the track-bridge interaction

effects increases with the continuous length (expansion length L T) of the deck As a result, in short

7

level in EN1991-2 (2003).

In the remaining of this paper, in section 2 we shall firstly review some design considerations forhigh speed railway bridges, with special emphasis on those originating from dynamic behaviour.Following, in section 3 we shall review the methods and requirements for track-bridge interaction inthe codes, focusing on the new IAPF (2007) compared to EN1991-2 (2003) Here the serviceabilitylimit state checks regarding deformations of the deck will be discussed critically The paper finisheswith a summary of the main conclusions in section 4

Dynamic response of railway bridges is a major factor for design and maintenance, especially innew high speed railway lines The main concern is the risk of resonance from periodic action ofmoving train loads In cases when such risk is relevant (e.g for speeds above 200 km/h) a dynamicanalysis is mandatory

The new engineering codes [EN1991-2 (2003), EN1990-A1 (2005), IAPF (2007), FS (1997)]take into account these issues and define the conditions under which dynamic analysis must beperformed They provide guidelines for models, types of trains to be considered, and design criteria

or limits of acceptance [Goicolea, J.M (2004)]

Resonance for a train of periodically spaced loads may occur when these are applied sequentially

to the fundamental mode of vibration of a bridge and they all occur with the same phase, thus

accumulating the vibration energy from the action of each axle If the train speed is v, the spacing

of the loads D and the fundamental frequency f0, defining the excitation wavelength as λ = v/f0,the condition for critical resonant speeds may be expressed as [EN1991-2 (2003)]:

λ= D

Although the basic dynamic phenomena due to moving loads are known since long (e.g seethe book by Fryba, L (1972)) it has not been until recently that resonance phenomena in bridgesfrom high speed traffic have been well understood and practical methods of analysis developed[ERRI D214 (2002), Domínguez J (2001)] From a technical point of view a number of methodsfor dynamic analysis are available for engineering practice Briefly, the available methods are: a)dynamic analysis with time integration and moving loads; b) dynamic analysis with time integra-tion and bridge-vehicle interaction; and c) dynamic envelopes based on train signature methods.Rather than discussing these methods here, for which a complete description is given elsewhere[Domínguez, J (2001), Goicolea, J.M (2004)] we shall focus on the relevance of dynamic effectsfor structural designs

In railway bridge design often the most restrictive conditions in practice are the ServiceabilityLimit States (SLS) [EN1990-A1 (2005), Nasarre J (2004)] (maximum acceleration, rotations anddeflections, etc.) Accelerations must be independently obtained in the dynamic analysis In theexample shown in Figure 1, for a short span simply supported bridge, both maximum displacementsand accelerations are obtained independently and checked against their nominal (LM71) or limit

Service limit states for railway bridges in new Design Codes IAPF and Eurocodes 9

values respectively It is clearly seen that for a resonant train speed the deflection limits are above

the LM71 nominal values, resulting in an impact factor  greater than unity A more severe effect is

the accelerations which surpass by far the limits, thus invalidating this (purely theoretical) design.Further details may be seen in Goicolea, J.M (2004) These results have been obtained both withmoving loads and with bridge-vehicle interaction, showing that the gain of considering this latterand more advanced model, albeit significant in this case, still yields a non acceptable value

In order to consider the resonant velocities for dynamic calculations, these must be performedgenerally for all possible speeds The results may be presented as envelopes of resulting magnitudes

in these velocity sweeps Following we present a typical set of such calculations showing the factthat generally resonance may be much larger for short span bridges In this representative example,Figure 2 shows the normalised displacement response envelopes obtained for ICE2 train in avelocity sweep between 120 and 420 km/h at intervals of 5 km/h Calculations are performed forthree different bridges, from short to moderate lengths (20 m, 30 m and 40 m) The maximumresponse obtained for the short length bridge is many times larger that the other The physicalreason is that for bridges longer than coach length at any given time several axles or bogies will

be on the bridge with different phases, thus cancelling effects and impeding a clear resonance Wealso remark that for lower speeds in all three cases the response is approximately 2.5 times lowerthan that of the much heavier nominal train LM71 Resonance increases this response by a factor

of 5, thus surpassing by a factor of 2 the LM71 response

A significant reduction of vibration is obtained in short span bridges under resonance by usinginteraction models This may be explained considering that part of the energy from the vibration

is transmitted from the bridge to the vehicles However, only a modest reduction is obtained fornon-resonant speeds Further, in longer spans or in continuous deck bridges the advantage gained

by employing interaction models will generally be very small This is exemplified in Figure 2,showing results of sweeps of dynamic calculations for the three said bridges of different spans As

a consequence it is not generally considered necessary to perform dynamic analysis with interactionfor project or design purposes

The above results are not merely theoretical considerations It has been seen in practice thatthey reflect accurately the vibrations taking effect in real high speed railway bridges To showthis we comment some experimental results on an existing high speed bridge Figure 3 shows themeasured resonant response in the bridge over the river Tajo in the Madrid-Sevilla HS line Thebridge consists of a sequence of simply supported isostatic decks with spans of 38 m The dynamicamplification in this case is noticeable In spite of this, design responses keep within requiredlimits However, it is clear that the dynamic performance could be improved by a different structuraldesign

Another well-known issue is the fact that dynamic effects in indeterminate structures, especiallycontinuous deck beams, are generally much lower than isostatic structures [Domínguez, J (2001)].The vibration of simply supported beams is dominated clearly by the first mode, and moreoveronly the loads on the span under consideration excite the motion at a given instant This makesmuch more likely a resonant phenomenon, whenever condition (1) is met On the contrary, thevibration of continuous beams includes significant contributions of a number of modes, and loads

on other spans excite the motion of the span under consideration As a result, the algebraic sum ofthe effects tends to cancel to a large extent

We show a practical example of this effect in a student project for the Arroyo del Salado viaduct[Sanz, B (2005)] on the Córdoba-Málaga High Speed Line, with a total length of 900 m and 30spans of 30 m each The section is a prestressed concrete box deck, and the proposed solutionwas a continuous beam deck cast in-situ The comparison of this solution with a correspondingsimply supported multiple span viaduct is shown in Figure 4, where it may be seen the much betterperformance in terms of dynamic response of the continuous beam deck

Finally, we discuss the consideration of different high speed train types The existing trains inEurope are defined in EN1991-2 (2003), IAPF (2007), and may be classified into conventional (ICE,ETR-Y, VIRGIN), articulated (THALYS, AVE, EUROSTAR) and regular (TALGO) Variations ofthese trains which satisfy interoperability criteria have been shown to covered by the dynamic

Figure 1. Calculations for simply supported bridge from ERRI D214 (2002) catalogue (L = 15 m, f0 = 5 Hz,

(236.5 km/h, bottom) speeds, considering dynamic analysis with moving loads and with train-bridge tion Note that the response at the higher speed (360 km/h) is considerably smaller than for the critical speed

interac-of 236.5 km/h The graphs at left show displacements, comparing with the quasi-static response interac-of the real

(2005)].

Service limit states for railway bridges in new Design Codes IAPF and Eurocodes 11

(1996)], right graph analytical calculations [Domínguez, J (2001)] Horizontal scale is time (s), vertical scale displacements (mm).

accelerations in the deck The graph on the left corresponds to the proposed design as continuous beam, which

bridge with the same deck section; in this case the requirement for maximum accelerations is not fulfilled for high speeds.

effects of the High Speed Load Model (HSLM), a set of universal fictitious trains proposed byERRI D214 (2002) The use of this new load model is highly recommended for all new railway lines,and incorporated into codes EN1991-2 (2003) and IAPF (2007) More importantly, consideration ofHSLM model is mandatory for interoperable lines following the European Technical Specificationsfor Interoperability (TSI) in high speed lines [EC (2002)]

A useful way to compare the action of different trains and to evaluate the performance of HSLM

as an envelope is to employ the so-called dynamic train signature models These develop the

response as a combination of harmonic series, and establish an upper bound of this sum, avoiding adirect dynamic analysis by time integration Their basic description may be found in [ERRI D214.(2002)] They furnish an analytical evaluation of an upper bound for the dynamic response of a

given bridge The result is expressed as a function of the dynamic signature of the train G(λ) This

function depends only on the distribution of the train axle loads Each train has its own dynamicsignature, which is independent of the characteristics of the bridge The above expressions havebeen applied in Figure 5 to represent the envelope of all real existing HS trains in Europe, togetherwith the envelope of HSLM

Figure 5 Envelope of dynamic signatures for European HS trains, together with the envelope of signatures for High Speed Load Model HSLM-A, showing the adequacy of this load model for dynamic analysis.

3 TRACK-BRIDGE INTERACTION IN CODES IAPF (2007), EN1991-2 (2003)

3.1 Nature of phenomenon and effects to be evaluated

Track-bridge interaction originates from the fact that longitudinal forces in long welded rail aretransmitted both by the structure and the rail to the fixed points at piers or abutments Furthermore,

at joints in the deck there may be structural deformations which could modify the geometry of thetrack and thus endanger the safety of traffic

For short bridges this issue is not critical and in fact given certain conditions the calculation

of the nonlinear models described below may be avoided However, as has been said above, inhigh speed lines bridges and viaducts of substantial length are common and hence the issue oftrack-bridge interaction becomes a critical issue

The basic interpretation and methods agreed internationally are contained in the leaflet by UIC(1999), which summarises the results by ERRI subcommittee D213 Both the Spanish code IAPF(2007) and the Eurocode EN1991-2 (2003) follow generally the recommendations of the saidUIC leaflet They both contain a section describing specifically the objectives of this evaluation,the actions and models to consider and the design requirements In what follows we describe insummary the main principles, which are common between both codes and, wherever appropriate,underline and comment specifically the differences or additions

In both codes it is stated that consideration of track-bridge interaction is necessary in order toevaluate the following effects:

– Forces transmitted to piers and abutments from combined actions of structure and track;– Rail stresses due to variable actions, in particular thermal actions, braking and accelerationlongitudinal forces and vertical traffic loads;

– Relative movements and deformations at the ends of the deck due to the above variable actions

3.2 Models to employ in calculation

Several types of structures may be considered from the point of view of track-bridge interaction:a) single deck bridges, be this with one isostatic span or with a multiple span continuous beam,with a fixed bearing at one end; b) continuous beams with multiple spans with a fixed bearing at

Service limit states for railway bridges in new Design Codes IAPF and Eurocodes 13

shows a deck with one fixed point and two sliding supports, nonlinear “generalised springs” which model the longitudinal interaction between track and deck, and an optional rail expansion device at one end (figure translated from IAPF (2007)).

an intermediate point of the bridge; and c) multiple isostatic spans with fixed bearings ate the end

of each span

The general type of model to be considered is depicted schematically in Figure 6, for case a)above This model considers the track and the deck (both considered deformable elastically), thepiers, and the abutments which may also be flexible A key aspect in the model is the properconsideration of the interaction forces between rail and deck, in the figure represented through

generalised springs, which as we shall see below are of nonlinear nature Finally, in the

fig-ure a rail expansion device which would signify a longitudinal discontinuity for the rail is alsoshown

A characteristic value of these models is the so-called expansion length L T In the exampleshown it would be simply the length of the deck between the fixed support on one abutment and the

free-sliding joint on the other abutment The greater the value of L T the greater interaction effectswill be introduced at the free sliding joint

When expansion lengths are large the rail stresses may be reduced by the introduction of railexpansion devices In such case, the horizontal deck forces would be transferred integrally to thefixed bearing, alleviating the effects on the rail However, rail expansion devices are generallyundesirable from the point of view of track engineering and maintenance Expansion lengths ofthe order of 100 m may generally be accommodated without resorting to rail expansion devices.Expansion lengths of the order of 300 m to 400 m will very probably necessitate at least onerail expansion device Expansion lengths greater that this may necessitate at least two expansiondevices, say with a fixed point at the center, or other structural solutions

The above mentioned nonlinear generalised springs are defined with bilinear laws, of the typeshown in Figure 7 The first branch represents an elastic behaviour, whereas after a given dis-

placement u0the sliding limit is attained and the constant resistance k is developed The Eurocode EN1991-2 (2003) leaves the values of (u0, k) open, to be defined in national annex or other project specifications The code IAPF (2007) defines values for u0between 0.5 and 2.0 mm, and for k

between 20 and 60 kN/m, depending on the type of track, vertical load etc

The structural model described may be developed within a discretised computer model of thestructure with nonlinear material capabilities, such as finite element or other numerical programs.This program must have the capability to solve the resulting set of nonlinear algebraic equations,generally using an iterative procedure by Newton-type iterations until convergence is reached Anessential characteristic of nonlinear models is that superposition of actions is not valid; hence foreach calculation the complete set of actions must be applied in the correct sequence to the model

In particular for this case, for each scenario selected the thermal actions would be applied first andthen the vertical and longitudinal traffic actions

Figure 7. Force-displacement interaction law between track and deck The parameter u0defines the maximum

relative displacement at which sliding starts, with a plasticity or friction-type resistance defined as k Particular

from IAPF (2007)).

For short expansion lengths L T both codes allow simplified procedures for calculation In

par-ticular, for L T ≤ 40 m in EN1991-2 (2003) or L T≤ 60 m (steel) – 90 m (concrete) in IAPF (2007)

it may be considered that rail expansion devices are not needed, without a full justification by

the nonlinear models above described For somewhat longer expansion lengths, L T≤ 110 m, thecode IAPF (2007) refers to the simplified procedures defined in UIC (1999) based on charts forevaluating the interaction

Furthermore, the Eurocode EN1991-2 (2003) allows the simplification, for evaluating forces

in rails and bearings, of combining linearly the effects of the different actions As has been saidbefore, strictly speaking this linear combination is not valid; however for computation of forces

in general a conservative result will be obtained This is not generally the case for calculation ofdeformations, which may be underestimated using this simplification In the Spanish code IAPF(2007) this simplification is not considered

3.3 Design criteria

The maximum additional stresses in the rails from the variable actions (thermal and traffic loads)are limited to 72 MPa (compression) or 92 MPa (tension) It is understood that these stresses wouldapply on top of the existing stresses in the long welded rail, which amount to approx 105 MPa for

a maximum temperature increment T= 50◦C.

Regarding the deformation of the deck, it is required to limit the relative movements at the end ofthe deck in sliding joints (e.g between end of the deck and abutment) The following requirementsare defined, all related to the said relative movements:

– The horizontal movement from braking and acceleration forces must beδ B≤ 5 mm (calledδ 2inIAPF (2007)) Figure 8 shows a schematic representation of this movement

– The horizontal movement from vertical traffic loads must beδ H≤ 5 mm This movement inates mainly from bending, which produces horizontal movement at points eccentric from theneutral axis

orig-In IAPF (2007) this movement, which is calledδ 3, is more precisely defined to be computednot only from the bending caused by vertical traffic loads but also from eccentric horizontallongitudinal loads (i.e braking or acceleration acting on the rail surface), which also introducebending moments in the deck Figure 9 shows a schematic representation of this movement.– The vertical movement from bending and other effects must beδ V≤ 2 mm This limitation holdsfor lines with train speeds above 160 km/h which is the case for high speed

Service limit states for railway bridges in new Design Codes IAPF and Eurocodes 15

In the Spanish code IAPF (2007) again this limit (calledδ 4) is more precisely defined not asvertical but as normal to the rail within a vertical plane Figure 10 shows a schematic repre-sentation of this movement As may be seen there could be a noticeable difference between thenormal movement which actually alters the track geometry in a track with gradient, and thevertical movement which would be zero in this case For a long viaduct this difference may becritical

Furthermore to the above requirements, the following limit is defined in IAPF (2007), but not

in the Eurocode EN1991-2 (2003):

– The relative movement between rail and deck (or between rail and abutment platform) must be

δ 1≤ 4 mm under the actions for acceleration and braking This requirement may also be found

in UIC (1999)

The above design requirements both for stresses in the rail as well as for movements at the ends

of the deck represent Serviceability Limit States (SLS) for the structure However, in this case theimportance of these limit states is paramount, as they represent Ultimate Limit States (ULS) for therailway traffic It must be clearly understood by any structural engineer that these design criteria

Figure 10 Maximum relative normal displacement in vertical plane from variable actions ( δ 4 in IAPF (2007)

are often the critical requirements for railway bridges, contrary to the case for road bridges Thishas been clearly set out in the paper by Nasarre J (2004)

Considering the above, we summarise the following final remarks:

– In high speed railway lines it is common to be faced with bridges or viaducts of considerablelength, for which special consideration needs to be made at early stages of design to track-bridgeinteraction effects

– The reduction of dynamic effects is more favourable for continuous beams and for long spans;these factor again favour the consideration of long decks with potential problems for track-bridgeinteraction

– The proper consideration of track-bridge interaction requires a nonlinear structural model, whichrequires careful elaboration and checking on the part of adequately skilled structural engi-neers Simplifications to this model must be carefully justified and only employed when clearlyconservative

– Both the Eurocode EN1991-2 (2003) and the new Spanish code IAPF (2007) contain similarsets of recommendations for the models and design requirements These criteria originate fromthe report UIC (1999)

REFERENCES

Domínguez, J (2001) Dinámica de puentes de ferrocarril para alta velocidad: métodos de cálculo y estudio

de la resonancia Tesis Doctoral Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos

de Madrid (UPM), 2001 Publicada por la Asociación Nacional de Constructores Independientes (ANCI).

EC (2002) TSI-HS2002: Technical specification for Interoperability relating to the infrastructure subsystem

of the trans-European high-speed rail system Commission decision 2002/732/EC 20 may 2002, 2002.

Official journal of the European Communities OJ L 12/9/2002.

EN1991-2 (2003) European Committee for Standardization EN1991-2: EUROCODE 1 – Actions on structures, Part 2: Traffic loads on bridges European Union, 2003.

EN1990-A1 (2005) European Committee for Standardization {EN1990-A1}: EUROCODE 0 – Basis of Structural Design, Amendment A1: Annex {A2}, Application for bridges European Union, 2005.

ERRI D214 (2002) Utilisation de convois universels pour le dimensionnement dynamique de ponts-rails.

Synthèse des résultats du D214.2 (Rapport final) European Rail Research Institute (ERRI).

ERRI D214 RP9 (1998) European Railway Research Institute subcommitee D214 Design of Railway Bridges for Speed up to 350 km/h; Dynamic loading effects including resonance Final report, November 1998.

FS (1997) Ferrovie dello Stato; Sovraccarichi per il calcolo dei ponti ferroviari.

Service limit states for railway bridges in new Design Codes IAPF and Eurocodes 17

Fryba, L (1972) Vibration of solids and structures under moving loads Academia, Noordhoff, 1972 Goicolea, J.M (2004) Dynamic loads in new engineering codes for railway bridges in Europe and Spain.

Workshop on Bridges for High Speed Railways, Porto 3–4 June 2004, Faculty of Engineering, University

of Porto.

IAPF (2007) Instrucción de acciones a considerar en el proyecto de puentes de ferrocarril Ministerio de

Fomento de España, Dirección General de Ferrocarriles Oct 2007.

ave Madrid-Sevilla, ensayos dinámicos Technical report, Ministerio de Fomento de España, 1996 Nasarre, J (2004) Estados límite de servicio en relación con los puentes de ferrocarril In A Campos R Del- gado, R Calçada, editor, Bridges for High-Speed Railways, pages 237–250 Civil Engineering Dept., Faculty of Engineering of the University of Porto, 2004.

Sanz, B (2005) Proyecto de viaducto para el ferrocarril de alta velocidad sobre el arroyo del salado Master thesis, Escuela de Ingenieros de Caminos, UPM, 2005.

UIC (1999) Code UIC 774-3R Interaction voie/ouvrages d’art, Recommandations pour les calculs UIC, Union Internationale des Chemins de Fer, Feb1999.

UIC (2006) Leaflet UIC 776-1R: Charges a prendre en consideration dans le calcul des ponts-rails UIC, Union Internationale des Chemins de Fer, 2006 5 ed, Aug 2006.

CHAPTER 3

Track-bridge interaction problems in bridge design

A.M Cutillas

Technical University of Madrid & Carlos Fernández Casado S.L., Madrid, Spain

ABSTRACT: Track-bridge interaction problems have a main role in the design of bridges,especially at conception stage of long viaducts with high or short piers in high speed railwayslines

The presentation will focus on the main aspects of track bridge interaction aspects to be takeninto account in the design of these bridges:

• Bridge displacement limitations at track level

• Railway expansion joint needs

Some examples of recent bridges which have been designed in High speed railway lines in Spainwill be shown A special attention will be paid to the Viaduct over the Guadalete river It is a3221.70 m long viaduct in which the aforementioned problems were determinant in the conceptionand design of the bridge

Railway bridges, in general and high speed railway bridges in particular have to resist importanthorizontal loads.The horizontal loads are originated by the climate such as the wind The wind acts

on the whole structure surface exposed, the piers and the deck as well as on the live load itself.These loads produce bending moments of the deck’s vertical axis as well as twisting momentswhich are added to the combined pier-deck effects produced by the live load

The live loads produces two horizontal loads derived from the accelerations On the one hand,transverse radial accelerations in curved layouts, which bring about the centrifugal force On theother hand they bring about longitudinal accelerations produced by braking and traction forces.The stresses due to the centrifugal forces produce the same effects as those derived from thetransverse wind These forces can be very important for even though the radii are great so is thespeed (Fig 1)

19

such as the ground, its sizing depends on the vertical and horizontal loads transmitted by the railway,and the axial forces as a consequence of the deformations restrained by the temperature so thestrength reserve to failure is limited When the tracks are placed over a structure, the imposeddeformations produced by the uniform temperature variations and by the creep and shrinkagephenomena in the deck, produce relative displacements between the track and the deck that as aconsequence of friction forces with the ballast, produce horizontal loads over both the track andthe deck that may exhaust the resistant capacity of the rail This is the reason why the arrangement

Track-bridge interaction problems in bridge design 21

of the continuous rail is limited to concrete structures with a total expansion length not greaterthan 90 m

With the intention to optimise the design and viaducts construction conditions and track tion in continuous viaducts it will be necessary, whenever it is possible, to arrange an expansionjoint in one of the abutments In this way the phenomena of track-deck interaction disappear Oth-erwise, the viaducts would have to be sub-divided into smaller lengths with the resulting problems

exploita-of structural joints, duplication exploita-of the bearings and the placing exploita-of intermediate stiff and resistantelements in order to resist the horizontal loads in each structure

If all these factors are studied and properly balanced: the resistant problem for horizontal forcesand the track-deck interaction problems, different longitudinal configurations of the viaducts can

Figure 6 Bridge over Llobregat river in Martorell.

launched it is necessary to locate a segment casting yard on one of the abutments These yards musthave the capacity, among other things, to resist the horizontal forces during the launching as well

as the loads produced by the wind and temperatures under rest conditions These are, therefore,elements able to be adapted to become anchorage elements of the deck under service conditions.This is why most of the viaducts presented here, except the Viaduct 2 of the Sub-stretch VIII (Fig 1)and Martorell Viaduct (Fig 6), are anchored in the abutment corresponding to the segment castingyard The abutment-yard whole is the structure in charge of transmitting to the ground the horizontalforces produced by the braking and traction loads, the longitudinal wind and those produced byfriction forces of the elastomeric-teflon devices as a consequence of the deformations due to thetemperature, creep and shrinkage

The total horizontal forces, under service conditions, are much greater than those corresponding

to the situation during construction for the following reasons:

During construction, the reactions in the supports produced by the horizontal forces correspond

to the total permanent load and not self weight

The coefficient of friction of the teflon supports considered under service conditions amounts

to 5%, while during construction it amounts to 2.5% Actually, the value of 2% is hardly reached

if special greases are used to reduce this coefficient

Under service conditions we must take into account the braking and traction forces for viaductslonger than 300 m reach a maximum value of 700 T

In spite of the effectiveness of this structural disposition, we must bear in mind the fact thatthe viaduct length imposes certain limits: on the one hand, the availability of expansion devicesable to admit great movements At present, there are devices with the movement capacity of up

to 1200 mm, which establishes a length limit between 1200 and 1300 m for prestressed concreteviaducts On the other hand there is a limit, though higher than the previous one, which depends

on the capacity of the deck to admit the prestressing force that would counteract these horizontalforces

The concept of the Viaduct 2 of the sub-stretch VIII, mentioned before responds to the need toreduce the movements in the expansion joint and to place the fixed point by a delta shaped pier on

a small hill in the valley This disposition allows us to double the length of the viaducts by placingtwo small expansion joints in the rail

In Martorell Viaduct and intermediate V shaped pier was designed In order to resist the horizontalforces and to reduce the longitudinal movements in this section, the pier is founded over slurry-wallswith a big longitudinal stiffness (Fig 6) The deck has a total length of 202 m, the expansion length

is 101 m (greater than 90 m) In order to avoid the expansion joints at the abutments a completetrack-deck interaction analysis was performed The deck and rails were modelled connected with

Track-bridge interaction problems in bridge design 23

non linear springs corresponding to the mechanical behaviour of the ballast The main conclusions

of the analysis were:

The stress increment in the rail due temperature actions was 42 MPa (Fig 8)

The maximum stress increment in the rail, in compression, due to temperature and traction forces was 77.6 MPa

braking-The longitudinal displacement in the deck due to braking-traction forces was 4.27 mm and5.2 mm taking into account the foundation influence

The braking force transferred to de deck is 80% of the total force applied at the rail level

2.1 Structural concept General Description

The Viaduct over the Guadalete river is located in the railway line between Sevilla and Cádiz It has

a total length of 3221.70 m It is located in a circular alignment of 2200 m of radius The averageheight of the different piers is 10 m

The viaduct crosses twice the Guadalete River and the roads CA 2011 and CA 9023 A bridgewhich fulfils all the functional and structural requirements was designed from the beginning takeninto account the appearance suitable adapted to the landscape which is a very flat fertile valley.(Fig 9)

One of the most specific features of the bridge is the extremely length and the foundationconditions The soil has more than 25 m deep very soft layer These soil conditions are inadequatefor resisting horizontal forces due to braking and traction railway loads

Figure 9 Viaduct over the Guadalete river.

The length of the viaduct asks for a typological study taken into account track-deck action problems due to imposed deformations, horizontal loads and to the position of the railand deck expansion joints along the viaduct In this study different structural, constructional andenvironmental problems were considered (Fig 11)

inter-From the structural point of view, the strength to resist the horizontal forces due to braking andseismic loads should be compatible with the flexibility to reduce as much as possible the stressesdue to thermal and long term deformations It was decided to avoid any expansion joint on the rails

in order to improve as much as possible the exploitation of the railway A maximum length of 200 mbetween structural deck expansion joints was limited in order to avoid any overstressing on the railsdue to track-deck interaction problems In order to fulfill all the environmental requirements, thesupports over the river beds were reduced as much as possible A precast solution was designed toallow industrialized construction procedures suited to a very long viaduct (Fig 12)

The final solution adopted is a twin precast box girder 2.20 m deep and located below eachrailway axis, 2.15 m apart The total deck width is 13.0 m (Fig 10) This deck allows to span thelength of 30 m as a simply supported structure along most of the length of the bridge and to span

49 m with the help of two additional precast arches This concept allows with a very repetitivestructure to cross the longest spans due to the presence of Guadalete river beds and the road CA

Track-bridge interaction problems in bridge design 25

2011 With these criteria the viaduct is split in 7 stretches with the lengths and spans shown inTable 1 (Fig 13)

The use of continuous precast arches allows to balance the horizontal forces due to permanentloads on the intermediate supports creating a well suited and new structure (Fig 14)

2.2 Track deck interaction problems

During the design conception the main idea of a jointless rail bridge has been present in order

to reduce maintenance problems Two main aspects for track-deck interaction problems werestudied:

1 The structural scheme to resist the horizontal forces due to braking and traction railway loads

2 The maximum displacements due to thermal and long term deformations to avoid overstresses

on the rails produced by track-deck interaction problems

By these reasons the piers under simply supported girders are able to resist the horizontal loadsfrom each span and the expansion length of 30 m is far from producing any overstressing on the

7 420.00 14 30.00

rails For the greater spans the continuous precast arches are able to resist properly the horizontalloads with an expansion length to avoid any overstressing problems on the rails

Preliminary analysis to control track-deck interaction problems were performed: the expansionlengths limitation were fulfil so the maximum displacement due to braking loads should be limited

to 5 mm at deck level on the structural deck expansion joints These displacements were obtainedtaken into account the flexibility of the soil-foundation structure using the stiffness matrix of thewhole It was assumed that all the braking loads are transmitted to the continuous deck which can

be considered as an upper limit of the total load because of the continuity of the rails (Fig 15)

Track-bridge interaction problems in bridge design 27

A detailed model for the track interaction problems was made in order to confirm the mainassumptions done in the preliminary analysis The continuous precast arches were modelled withplane bar elements Four additional simply supported spans are added to avoid any perturbation

on the expansion joints results The rails were included in the model as an additional structure.The connection between the rail and the deck has been done with perfectly elastoplastic elementswhich represent the track-deck behaviour, as it has been mentioned above The maximum forcesand stiffnesses vary according the loaded or unloaded track situation (Fig 16)

The different load cases were done in two different models:

1 Built-in model, in which the arches are completed built in the foundation

2 Model with soil-structure interaction: in which the soil-foundation stiffness matrix has been

included

Three load cases have been considered on each model:

1 Case 1: Railway braking load at rail level

2 Case 2: Deck increment of temperature−20◦C.

3 Case 3: Deck increment of temperature+20◦C.

The summary of the main results is as follows:

1 For the braking loads the soil structure stiffness has a relevant importance in the totaldisplacements and on the overstressing in the rails (Figs 17–18)

2 For the thermal actions soil-structure interaction stiffness has no influence in the results.(Figs 19–20)

3 The increment of stresses due to the combination of thermal actions and braking forces are lowerthan the limits 72 MPa in compression and 92 MPa in tension

Figure 19 Thermal action +20 ◦C on the deck Axial forces on the rail with soil structure-interaction model.

REFERENCES

ENV 1991-3:1995 Eurocode 1 Basis of design and actions on structures Part 3 Traffic loads on bridges Manterola, J., Astiz, M.A., Martínez, A Puentes de ferrocarril de alta velocidad Revista de Obras Públicas

Manterola Armisén, J.; Martínez Cutillas, A Prestressed concrete railways bridges Workshop Bridges for high

speed railways Oporto (2004).

CHAPTER 4

Controlling track-structure interaction in seismic conditions

S.G Davis

Mott MacDonald, United Kingdom

ABSTRACT: In seismic regions, a major constraint affecting the design of high speed rail viaducts

is the track-structure interaction during the operation of the trains, and in particular when the trainmust remain safe at high speeds under the service design earthquake The paper describes studiesundertaken to establish design criteria and the analysis methods to be used for the design of highspeed rail viaducts These studies comprised non-linear analysis of the track and viaduct structuresystem under the actions of temperature variation, traction and braking, and multiple input non-linear time history analysis for the response under earthquake loading A series of parametric studieswere undertaken and the conclusions from this work used to form the basis of a design specification

Track-structure interaction is the transfer of the traction and braking longitudinal loads between thetrack and the viaduct deck through the ballast Ballast behaviour under these actions is non-linearand load and temperature dependent Typically, viaducts for high speed railways are a succession

of simply supported spans such that no rail movement joints are needed However it is essentialthat the viaduct is designed to limit the relative displacements between decks to 5mm so thatthe rails are not overstressed or the ballast destabilised under the traction and braking loads Thefundamental principles of the analysis method to calculate the relative displacements are given inthe Eurocode (UIC Code 774-3R), but use of these requires a finite element analysis modelling theelasto-plastic friction behaviour between the track and the bridge deck As part of Mott MacDonald’srole in the Taiwan High Speed Rail project, studies were carried out, aimed at providing simplifiedmethodology for use at the detailed design stage Existing in-house software was adapted to analysemodels comprising elastic deck and track members connected by non-linear ballast members asshown in Figure 1 The method and results were validated, and the process was automated to

Deck Member Track 1 Member

Track 2 Member

29