TRACK-BRIDGE INTERACTION ON HIGH-SPEED RAILWAYS Track-Bridge Interaction on High-Speed Railways Editors Rui Calỗada, Raimundo Delgado & Antúnio 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 CRC Press/Balkema is an imprint of the Taylor & Francis Group, an informa business © 2009 Taylor & Francis Group, London, UK Typeset by Charon Tec Ltd (A Macmillan Company), Chennai, India Printed and bound in Great Britain by Antony Rowe (A CPI-group Company), Chippenham, Wiltshire All rights reserved No part of this publication or the information contained herein may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, by photocopying, recording or otherwise, without written prior permission from the publishers Although all care is taken to ensure integrity and the quality of this publication and the information herein, no responsibility is assumed by the publishers nor the author for any damage to the property or persons as a result of operation or use of this publication and/or the information contained herein 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) High speed trains Railroad bridges Bridges—Live loads I Calcada, Rui TF1460.T73 2008 625.1 4—dc22 ISBN: 978-0-415-45774-3 (hbk) ISBN: 978-0-203-89539-9 (ebook) 2008003167 Table of Contents Preface VII List of Authors IX New evolutions for high speed rail line bridge design criteria and corresponding design procedures D Dutoit Service limit states for railway bridges in new Design Codes IAPF and Eurocodes J.M Goicolea-Ruigómez Track-bridge interaction problems in bridge design A.M Cutillas 19 29 Controlling track-structure interaction in seismic conditions S.G Davis Track-structure interaction and seismic design of the bearings system for some viaducts of Ankara-Istanbul HSRL project F Millanes Mato & M Ortega Cornejo 37 Track structure interactions for the Taiwan High Speed Rail project D Fitzwilliam 55 Track-bridge interaction – the SNCF experience P Ramondenc, D Martin & P Schmitt 63 Some experiences on track-bridge interaction in Japan N Matsumoto & K Asanuma 77 Numerical methods for the analysis of longitudinal interaction between track and structure M Cuadrado Sanguino & P González Requejo 10 Longitudinal track-bridge interaction for load-sequences P Ruge, D.R Widarda & C Birk 11 Structural analysis of high speed rail bridge substructures Application to three Spanish case studies J.A Sobrino & J Murcia 95 109 129 12 The Italian experience: two case studies M.P Petrangeli 139 13 149 Rail expansion joints – the underestimated track work material? J Hess V VI Table of Contents 14 Dynamic aspects of the high-speed railway bridge across the Hollandsch Diep J.T.F.M Tünnissen 15 Track-structure interaction in long railway bridges A.J Reis, N.T Lopes & D Ribeiro 165 185 16 Track-bridge interaction in railway lines: Application to the study of the bridge over the River Moros R Simừes, R Calỗada & R Delgado 201 Author index 211 Subject index 213 Preface The construction of high-speed railways comprises a set of demands, from safety aspects to new types of equipment and construction solutions, involving the most recent and sophisticated technologies Among these, emphasis is given to the railway behaviour where the structural elements are of great 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 to control the acceleration, the stresses and the track deformations, so that the circulation safety is satisfied, while strongly conditioning the structural design solutions for bridges The ability to address the multiple issues relevant to this process requires expertise and knowhow, which have been recently developed in this field, with repercussions in terms of the European regulations in this domain 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 Porto (FEUP) and the Escuela Tecnica Superior de Ingenieros de Caminos 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 RAILWAY BRIDGES” The editors would like to thank all those who contributed to this book, in particular our distinguished guest chapters’ authors who heightened, with their knowledge and expertise, to the present interest and quality of the book, the support of the sponsors for the events which originated the materials for this book, and the institutional support of the Faculty of Engineering of the University 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, construction or maintenance of high speed railway systems, but also to researchers and students working in this field 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 H, 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 Calỗada, FEUP Portugal Stuart Davis, Mott MacDonald United Kingdom IX Track-bridge interaction in railway lines 203 The longitudinal behaviour of the track-deck connection can be modelled as a spring which behaviour is translated by a load/displacement relation similar to that illustrated in Figure 3, that is, a bi-linear relation consisting of an initial elastic section up to a relative displacement u0 and a section corresponding to the plastification of the connection for a load of value k, given in kN/m per metre of track length For the case of a ballasted track, u0 is equal to mm and k takes the values of 20 or 60 kN/m per metre of track development, whether the track is unloaded or loaded, respectively Hence, the effects of the track-deck interaction have to be derived by means of a non-linear analysis of the system In accordance with EN1991-2, the total effects may be determined by linear superposition of the effects obtained for each of the loads acting individually The total normal stress in the rails, or the total longitudinal reaction in the supports, can then be obtained by means of the expression: (1) FL = (ψ0i · FLi ) where FLi is the effect of load i and 0i is the combination coefficient relative to load i, which values are defined in EN 1990-A2 [8] For the calculation of the normal stress in the rails, the combination coefficients should be considered equal to 1.0 2.4 Track safety check In terms of the checks regarding track safety, EN1991-2 specifies relative limit states to the normal stress in the rails and the displacements of the structure In what concerns the rails, the stability analyses carried out for UIC60 rails, manufactured with a steel of strength equal to or higher than 900 N/mm2 , with a curvature radius equal to or higher than rail axis Longitudinal non-linear spring Longitudinal non-linear spring Und efo rma ble bar de Un Neutral axis of deck Z ble ma for Z r ba Fixed support X (a) Longitudinal model view Y (b) Section in deck support Longitudinal shear force in track per unit length, k [kN/m/m of track] Figure Location in height of the elements corresponding to the rails, the deck and the supports (adapted from [6]) Figure Resistence of rail in sleeper (Loaded track) Resistence of sleeper in ballast (Unloaded track) u0 Relative displacement between rail and top of supporting deck, u [mm] Load-displacement relation of the track-deck connection (adapted from [6]) 204 Track-Bridge Interaction on High-Speed Railways 1500 m, fixed to concrete sleeper with a spacing of 0.65 m or less, over a consolidated ballast layer with a minimum thickness of 0.30 m, have demonstrated that the normal stress in these elements, for the combined action of diverse loads, should not exceed the following values: a) 72 N/mm2 , in compression; b) 92 N/mm2 , in tension In terms of the structure displacements, the following limits should not be exceeded: i) due to starting and braking, the relative longitudinal displacement between the end of the deck and the abutment, or the relative longitudinal displacement between two consecutive spans of the deck, δB, should not go above mm, for the case of a continuous welded rail (CWR) without dilation devices or with one dilation device in one of the ends of the deck, and 30 mm, for the case of a deck with dilation joints in the rails at both ends and a continuous ballast layer over those ends; ii) due to vertical loads, the longitudinal displacement of the upper surface of the deck in its end, δH, should not exceed mm when the composite behaviour of the track and the structure is taken into account, and 10 mm when that composite behaviour is ignored; iii) furthermore, the vertical displacement of the upper surface of the deck in relation to the adjacent structural element (abutment or span of the deck), δV, should not exceed mm, for maximum speeds on site of 160 km/h, and mm, for maximum speeds greater than 160 km/h APPLICATION TO THE STUDY OF THE BRIDGE OVER RIO MOROS 3.1 Description The bridge over the river Moros, designed to operate in the Segóvia – Valladolid high-speed railway line, is composed by a continuous deck with total length of 476.0 m, consisting of seven intermediate spans of 56.0 m and two end spans of 42.0 m (Fig 4) Longitudinally, the deck has a fixed support (AF) located over the abutment E1, while the remaining supports are mobile (AM) The track exhibits one dilation device (AD) at the end of the deck adjacent to abutment E2 The deck, of pre-stressed reinforced concrete, presents a box type of cross-section and its geometry is represented in Figure 5, serving as support to two railway tracks (V1 e V2) The track is composed of UIC60 rails placed over concrete sleepers, spaced between them by 0.60 m, positioned on top of a ballast layer with a minimum thickness of 0.35 m under the sleepers The outline at the bridge site presents a longitudinal gradient of 0.21%, with a plan radius of 11 444 m 3.2 Modelling In Figure is illustrated the finite element model developed for the analysis of the track-deck interaction The deck has been discreetized by means of beam elements with the following characteristics: elasticity modulus E = 35 GPa; section A = 11.19 m2 ; moment of inertia I = 28.82 m4 and thermal dilation linear coefficient αC = 1.0 × 10−5 /◦ C Each of the tracks was modelled by means of beam elements placed in the alignment of the respective axles An extension of the track has been modelled corresponding to the length of the z[m] REJ 890 880 870 860 850 Track 892m FR FR FR FR FR REJ - Rail expansion joint Figure FR FR Moros River 862m FR -Free support FF- Fixed support Longitudinal view of the bridge over river Moros FR FR FF x[m] Track-bridge interaction in railway lines 205 0.30 0.30 deck and 300.0 m to the side of the abutment E1 in order to simulate the track over the adjacent embankment (Fig 6a)) The characteristics of these elements correspond to two UIC 60 rails, that is: elasticity modulus E = 210 GPa; section A = 0.0153 m2 ; moment of inertia I = 6.11 × 10−5 m4 ; thermal linear dilation coefficient α = 1.2 × 10−5 /◦ C The connection between the elements of the track and of the deck, and between the elements of the deck and the supports was simulated by means by rigid bars (Fig 6b)) The elements that model the track-deck connection, with non-linear behaviour translated by the relation presented in Figure 3, were placed at a height corresponding to the base of the sleepers As previously mentioned, the deck is supported by the E1 abutment by means of a fixed support The stiffness of the elastic support corresponding to the abutment/foundation group was determined based on a model using volume finite elements (Fig 7) where the elasticity moduli for the foundation soil and the abutment were considered to be Es = 190 MPa and Ec = 25 GPa, respectively, from which k = 660 × 103 kN/m was obtained In order to assess the influence of the group stiffness, other situations were also analysed corresponding to stiffness values equal to 330 × 103 kN/m (0.5 k), 3300 × 103 kN/m (5 k) and infinite stiffness, that is, deck fixed to the support The influence of the track length in the embankment zone beyond the E1 abutment was also analysed for the k = 660 × 103 kN/m scenario, and lengths of 100 and 200 m were considered, besides the 300 m N.A Figure Cross section of the deck z [ m] 1.76 1.76 3.00 2.75 N.A 0.73 3.00 1.64 N.A 2.75 1.64 4.50 5.23 3.00 0.10 3.00 0.73 a) E1 b) c) d) Figure Structural model of the track-deck system: (a) front view; (b) cross section of the support; (c) cross section of the span and (d) detail of the model at the zone of the fixed support 206 Track-Bridge Interaction on High-Speed Railways Figure Finite element model of the abutment-foundation system 3.3 Analysis and results In the analysis of the track-bridge interaction were considered the longitudinal loads due to starting (A) and braking (F) of the compositions, the vertical loads corresponding to the LM71 load model and the load corresponding to an uniform temperature variation ( TU) in the deck of ±35◦ C and in the track of ±50◦ C Loads resulting from retraction, creep and differential temperature variations were not considered in the present study For the determination of the effects induced by the LM71 load model, diverse loading configurations were considered in order to obtain the most unfavourable values for each parameter In what the longitudinal loads are concerned, the most adverse scenario was considered as corresponding to the consideration of braking in track V1 (→) and of traction in track V2 (→) In Figure are presented the results relative to the normal stress on the rails of track V2, which provided the most adverse results, for the different loads and for the different stiffness values considered for the abutment/foundation system In Table are presented, in turn, the maximum values of the support reactions and the relative longitudinal (δl ) and vertical (δv ) displacements between the ends of the deck and the respective abutment Combined observation of Figure and Table 1, enables to conclude that: i) the stiffness of the abutment/foundation group has great influence in the values of the normal stress on the rails and of the support reactions; ii) for the LM71 load model, the maximum tensions on the rails occur over the fixed support E1; iii) for an uniform temperature variation loading, the compressions on the rails at the abutment E1 vary according to the stiffness of the abutment/foundation group; iv) for a loading considering the LM71 load model and an uniform temperature variation, the increase of the stiffness of the abutment/foundation group results in an increase of the normal stresses in the rails and of the support reactions; v) for starting and braking loading, the maximum stresses (compression or tension according to the sign of these forces) occur over the fixed support E1; Track-bridge interaction in railway lines 207 Track T2 Additional rail stresses [MPa] 20 -20 -40 -51,74 -60 -80 -66,28 -76,64 -86,33 Fixed support k=3300x10³ kN/m k=660x10³ kN/m k=330x10³ kN/m -100 -120 -90,83 -126.11 -140 a) 100 200 300 400 500 600 x [m] Track T2 20 Fixed support k=3300x10³ kN/m k=660x10³ kN/m k=330x10³ kN/m Additional rail stresses [MPa] 15 10 15,30 14,28 11,54 9,27 -5 -10 -15 -20 b) 100 200 300 400 500 600 x [m] Track T2 20 Additional rail stresses [MPa] 10 -10 -16,27 -20 -30 -29,89 -40 -50 Fixed support k=3300x10³ kN/m k=660x10³ kN/m k=330x10³ kN/m -60 -70 -57,23 -77,07 -80 c) 100 200 300 x [m] 400 500 600 Figure Normal stress in the rails of track V2 as a function of the stiffness of the abutment/foundation group for the loads: (a) of an uniform temperature variation; (b) of the LM71 load model and (c) of starting and braking 208 Track-Bridge Interaction on High-Speed Railways Table Support reactions and longitudinal and vertical displacements of the deck for various loads as a function of the stiffness of the abutment/foundation group Displacement [mm] Stiffness of the abutment/foundation group [kN/m] E2 Loads Support reaction [kN] δl δv Fixed support, K=∞ TU LM71 F(V1)/A(V2) 2713 −471 −6529 −168,47 −0,73 3,04 0,21 K = 3300 × 103 TU LM71 F(V1)/A(V2) 2614 −439 −6106 −169,50 0,59 5,00 0,21 K = 660 × 103 TU LM71 F(V1)/A(V2) 2316 −355 −5251 −172,10 −0,22 10,79 0,21 K = 330 × 103 TU LM71 F(V1)/A(V2) 2038 −285 −4640 −174,54 0,10 16,80 0,21 Track T2 20 Additional rail stresses [MPa] -20 -40 -51,74 -60 -80 -91,77 300,0m -100 200,0m -120 -123,29 100,0m -126.11 -140 100 200 300 400 500 600 700 x [m] Figure Normal stress in the rails due to a loading of uniform temperature variation in the track and deck, for track lengths in the embankment zone of 100, 200 and 300 m vi) for this loading scheme, the normal stresses in the rails increase with the decrease of the stiffness of the abutment/foundation group; vii) the relative longitudinal displacements in the moving bearing E2 due to traction and braking loads are strongly influenced by the stiffness of the abutment/foundation group, taken values of 3.04 mm, for k = ∞, and of 16.80 mm, for k = 330 × 103 kN/m; viii) the maximum values of the longitudinal support reactions have occurred for the case corresponding to infinite stiffness of the abutment/foundation group In Figure are presented the normal stress results relative to track V2, for an uniform temperature variation loading, for track lengths in the embankment zone beyond abutment E1 equal to 100, 200 and 300 m By looking at the figure it is possible to conclude that, in this case, the minimum length to consider is of about 200 m, from which results an error of approximately 2.2%, taking as reference the compression stress obtained from length 300 m Track-bridge interaction in railway lines Fixed support (K → ∞), Track T2 K=3 300×10 kN/m, Track T2 240 ∆TU=+15ºC; BT ( → ) 120 ) Additional rail stresses [MPa] ∆TU=-15ºC; LM71; BT ( 160 → 200 126,03 117,06 51,30 80 61,10 40 -40 -54,78 -80 -52,62 -108,72 -120 -126,04 -160 200 ∆TU=-15ºC; LM71; BT ( 160 ∆TU=+15ºC; BT ( → ) 120 ) 126,08 125,56 51,89 80 47,34 40 -40 -50,40 -80 -52,60 -113,53 -120 -126,08 -160 -200 -200 -240 -240 100 200 300 400 500 600 700 100 200 300 400 500 600 700 x [m] x [m] K=660×103 kN/m, Track T2 K=660×103 kN/m, Track T2 240 ∆TU=-15ºC; LM71; BT ( 160 ∆TU=+15ºC; BT ( → ) 120 ) Additional rail stresses [MPa] → → 200 126,11 141,21 51,89 80 47,00 40 -40 -50,20 -80 -52,60 -120 -132,53 -126,11 -160 -200 200 ∆TU=-15ºC; LM71; BT ( 160 ∆TU=+15ºC; BT ( → ) 120 → 240 Additional rail stresses [MPa] → Additional rail stresses [MPa] 240 209 ) 126,11 141,21 51,89 80 47,00 40 -40 -50,20 -80 -52,60 -120 -132,53 -126,11 -160 -200 -240 -240 100 200 300 400 500 600 700 100 200 300 400 500 600 700 x [m] x [m] Figure 10 Maximum and minimum normal stresses in the rails of the V2 track, for the different values of the stiffness of the abutment/foundation group Table Track safety check in terms of deck displacements Stiffness of the abutment/foundation group [kN/m] δB [mm] ∞ 3300 × 103 660 × 103 330 × 103 3.04 5.00 10.79 16.80 5.0 mm δH [mm] δV [mm] 2.18 2.19 2.21 2.23 0.24 0.24 0.24 0.24 8.0 mm 2.0 mm 3.4 Track safety check For the track safety check, the combined action of the loads corresponding to an uniform temperature variation (±50◦ C in the track and ±35◦ C in the deck), of traction and braking loads and of the LM71 load model were considered The combined effects were obtained by means of linear superposition of the effects associated to each isolated load, according to expression (1) In Figure 10 are presented the tension and compression envelopes of the rails in track V2 for the different values of the stiffness of the abutment/foundation groups The observation of the figure also enables to conclude that the tension (92 + 126 = 218 MPa) and compression (−72−126 = −198 MPa) limits are not exceeded in any of the analysed situations In Table are presented the maximum values of the relative longitudinal displacement between the end of the deck and the abutment for the braking and starting loads (δB ), of the relative longitudinal displacement of the upper surface of the deck for the LM71 load model (δH ), and of the the relative longitudinal displacement of the upper surface of the deck in relation to the abutment (δV ) 210 Track-Bridge Interaction on High-Speed Railways From the inspection of the above table it is possible to conclude that it is only for those cases where the abutment/foundation group is stiffer (k = ∞ e k = 3300 × 103 kN/m) that the displacement δB is inferior to the limit established in EN1991-2 The remaining displacements, δH e δV , stay within the limits for all analysed cases CONCLUSIONS In the present paper, the effects resulting from the track-structure interaction have been assessed for the case of the bridge over the river Moros, a continuous deck bridge with a box type of cross section designed for the high-speed railway line between Segóvia and Valladolid In terms of connections, the deck features a fixed support at one of the ends and moving supports in the other abutment and columns The track contains a dilation device, next to the abutment with moveable bearings Analyses were carried out for different values of track length in the embankment zone and of the stiffness of the abutment/foundation group The obtained results enable to conclude that it will be necessary to model a minimum length of 200 m beyond the embankment zone, and that the results in terms of normal stresses in the rails, of longitudinal support reactions and deck displacements are highly inflenced by the stiffness of the abutment/foundation group In terms of track safety, it has only been possible to control the relative longitudinal displacement between the end of the deck and the abutment, calculated for the starting and braking loads, for the highest values of the stiffness of the abutment/foundation group, that is, k = ∞ and k = 3300 × 103 kN/m All other limits have been respected from all the cases considered for the stiffness of the abutment/foundation group ACKNOWLEDGEMENTS The authors wish to acknowledge RAVE for the support provided and to Prof José Maria Goicolea of ETSICCyP in Madrid for the design elements of the bridge over river Moros and for all information on this issue kindly made available REFERENCES [1] UIC Code 774-3-R, “Track/bridge interaction – Recommendations for calculations”, 2nd edition, Union Internationale des Chemins de Fer, UIC, 2001 [2] Parra, F., “Proyecto de una puente de alta velocidad”, E.T.S Ingenieros de Caminos, Canales y Puertos, Universidad Politộcnica de Madrid, 2005 [3] Simừes, R., Interacỗóo via-estrutura em pontes ferroviárias em linhas de alta velocidade”, Tese de Mestrado, FEUP, Porto, Portugal, 2006 (to be submitted) [4] EN1991-2, Actions on structures – Part 2: General actions – Traffic Loads on Bridges, European Committee for standardization, CEN, 2003 [5] EN1991-1-5, Actions on structures – Part 1-5: General actions – Thermal actions, European Committee for standardization, CEN (2003) [6] EN1990-A2, Basis of Structural Design – Annex A2: Application for bridges (normative), Final PT Draft, European Committee for standardization, CEN (2005) Author index Asanuma, K 77 Birk, C 109 Calỗada, R 201 Cuadrado Sanguino, M 95 Cutillas, A.M 19 Davis, S.G 29 Dutoit, D Delgado, R 201 Fitzwilliam, D 55 Goicolea-Ruigómez, J.M González Requejo, P 95 Hess, J 149 Ramondenc, P 63 Reis, A.J 185 Ribeiro, D 185 Ruge, P 109 Lopes, N.T 185 Martin, D 63 Matsumoto, N 77 Millanes Mato, F 37 Murcia, J 129 Schmitt, P 63 Simões, R 201 Sobrino, J.A 129 Tünnissen, J.T.F.M 165 Ortega Cornejo, M 37 Petrangeli, M.P 139 211 Widarda, D.R 109 Subject index Acceleration Car body 169 Filtered 181 Peak ground 31 Structural 169, 174, 176, 181 Analysis Dynamic 11, 118, 142, 168, 169–172, 174, 180 Elastic 41, 68 Life safety Linear 42, 68 Multimodal 43, 44, 45 Non-linear 32, 33, 130, 141 Plastic 42, 44 Response Spectrum 33, 41, 61 Risk Sequential 122 Single modal 43 Spectral 43, 44 Time history 33, 58, 60 Creep 98 Ballast Behaviour 29, 33, 63 Stability 2, 63 Stiffness 30, 119 Bearing Elasticity 44, 90 Elastomeric 48, 50 Fixed 12–13, 45, 73, 146 Lateral 38, 48, 49, 50 Neoprene 48, 52 Pot 48, 50, 51, 132 Sliding 43, 48, 104, 110 System 37, 43, 47, 51 Behaviour Elastic 13, 116 Factor 42 Friction 29, 168 Long term 65 Plastic 127 Braking 3, 4, 19, 20, 23, 27, 28, 66, 105, 199, 202 Bridge Cable stayed 141–146 Suspension 84, 162 Earthquake Moderate 55, 58, 60 Motion 77, 86, 87, 91, 92 Non-collapse 31 Service 2, 31–33 Severe 77, 86 Ultimate 31, 41 Eurocode EN 1991-2 12, 14, 139 Excitation Multi support 33 Single support 33 Comfort 91, 92, 169, 170, 172 Contact Force 69, 86 Model 87 Wheel/rail 87 Damping 60, 119 Ratio 172, 180, 181 Deck End rotation Displacement Longitudinal 38, 44–46, 193, 204 Relative 4, 5, 15, 29, 33, 34, 95, 97, 98, 100, 102 Vertical 88, 107, 194 Derailment 91, 162, 180 Design Criteria 14–16, 39–46, 129–141, 169–170 Life 31 Dynamic Analysis 168, 169–172, 174–179, 180–182 Behaviour 8, 165, 169, 171, 184 Response 1, 8, 169, 171 Signature 11, 12 Fatigue Damage 85 Crack 46 Fixed Point 39, 41 Foundation 3, 5, 42, 44, 132, 166, 206 Friction Coefficient 22, 132, 135, 152, 153 High-speed Line 7, 8, 124, 129, 156 Load Model 11, 12 Operation Train 1, 9, 170 Interaction Rail-structure 55–61 213 214 Subject index Soil-foundation 26, 27, 42 Track-bridge 189–196 Track-structure 29–35, 37–53, 55–60, 82–83, 185–199 Vehicle-bridge 8, Vehicle-structure 86, 88, 93 Interoperability 9, 129 Joint Expansion 2, 19, 20, 21, 22, 24, 38, 57, 58, 73, 79, 80, 85, 149 Movement 29, 31 Limit state Service 7–16 Ultimate 15, 41 Load Braking 22, 26, 27, 28, 29, 30, 31, 103, 196 Dead 31, 60, 130, 176, 181, 182 Dynamic 32, 55, 56, 59–60, 168 History 110, 114 Live 4, 5, 6, 19, 176 Longitudinal 14, 29, 53, 111, 206 Model 71 144, 176, 196 Model SW0 69 Model SW2 69, 144 Sequence 31, 109–127 Static 32, 114–117, 118, 168, 182 Traction 22, 30, 103, 196 Vertical 1, 31, 32, 33, 65, 67, 204 Maintenance Fair 97 Poor 100, 188 Movement Relative 12, 14, 31, 149 Noise Structure borne 82–83 Period Return 31 Rail Buckling 31, 34, 65 Compression 64, 124, 125, 209 Continuous welded 2, 193, 201 Expansion device 13, 14, 98, 102, 145–146 Expansion joint 21, 24, 38, 58, 149–163 Fastening 80, 155, 156, 158, 178, 179, Fixed stock 150, 151 Fracture 34, 78 Long welded 1, 12, 63–67 Movable switch 150, 151 Roughness 169, 173, 174, 178, 184 Stress 1, 2–6, 13, 34, 35, 70, 71, 102, 126, 127, 203, 208 Tension 124, 206, 209 Railway 7–16, 37, 86, 121, 124, 130, 140, 141, 165–184, 186 Resonance 8, Response Spectrum 33, 34, 41, 43, 55, 61 Riding Comfort 84, 90, 91, 162 Rolling Stock Rotation Angular 84, 85, 89, 91, 92, 93 Safety 1, 2, 5, 12, 31, 34, 35, 42, 43, 77, 84–85, 86–90, 91, 92, 93, 162, 188, 196, 199, 201, 202, 203–204, 209–210 Seismic Analysis 3, 33, 37, 41, 44–47, 143 Buffer 31 Condition 29–35, 90, 91, 92, 93 Criteria 39–47 Damper 188, 189 Excitation 31, 44, 45 Ground motion 31 Isolation 89, 90 Lock-up device 57, 58 Shear key 31 Shrinkage 20, 95, 98, 99, 104, 105, 131, 132, 133, 152, 201 Stress 2, 3, 102, 106 Compression 14, 23, 27, 34, 105, 122, 125, 178 198 Concentration 1, 189 Tension 14, 27, 34, 60, 122, 145, 155, 178, 193 Support Fixed 78, 134, 135, 136, 204, 205 Movable 78, 123 Stiffness 134, 137, 181 Temperature Dependent 29 Equivalent 98, 105, 131 Gradient 98, 191 Uniform 20, 114, 206, 207, 208 Variation 20, 31, 66, 69, 99, 149, 201, 202, 206, 208, 209 Test Shaking table 87, 89, 90 Track Ballasted 2, 68, 70, 97, 125, 130, 185, 203 Damage 85 Double 85, 124–125, 186, 187, 188, 190 Floating 81–82, 82–83 Geometry 2, 15 Ladder 81, 82, 83 Loaded 58, 124, 110, 111, 125, 194, 196 Non-ballasted 80–82, 92 Subject index Resilience 149, 162 Safety 1, 188, 199 203–204, 209–210 Slab 2, 6, 80, 81, 153, 155, 158, 159, 161, 163, 169, 170, 173, 184 Stability 1, 63 Straight 193 Unloaded 58, 97, 110, 111, 194, 196 Traction 19, 20, 22, 23, 25, 29, 30, 98, 99, 100, 102, 103, 104, 105, 106, 130, 144, 191, 193, 196, 197, 198, 208, 209 Traffic 2, 7, 8, 12, 14, 15, 43, 99, 100, 103, 105, 130, 134, 135, 150, 191, 193 215 Train 1, 8, 9, 11, 12, 30, 31, 32, 33, 55, 56, 57, 58, 59, 60, 66, 67, 83, 84–85, 86, 87, 88, 90, 92, 98, 99, 100, 109, 120, 125, 165, 166, 169, 170–171, 174, 176, 178, 182, 184 Transition Area 156–158 Slab 160, 161, 163, 168, 179–182, 183, 184 UIC Code 774-3R 29 Vehicle 1, 9, 84, 85, 86, 87, 93 ... kN/m (2 ) Track- Bridge Interaction on High- Speed Railways (b) Computerised method (including rail structure interaction) : 25 spans are modelled The pier stiffness is the one calculated using the. .. joints The magnitude of the track- bridge interaction effects increases with the continuous length (expansion length LT ) of the deck As a result, in short Track- Bridge Interaction on High- Speed Railways. .. model the longitudinal interaction between track and deck, and an optional rail expansion device at one end (figure translated from IAPF (2 00 7) ) an intermediate point of the bridge; and c) multiple