HIGH-SPEED RAILWAY BRIDGES

Foreword xv

About the Authors xvii

Acknowledgements xix

1 Introduction to High-Speed Railway Bridges 1
José Romo

1.1 Book’s Content 1

1.2 What is Special About a High-Speed Rail Bridge? 2

1.2.1 Dynamic Amplification and Resonance 2

1.2.2 Rail Traffic Security 3

1.2.3 Passenger’s Comfort 3

1.2.4 Track–Structure Interaction 4

1.3 General Ideas on High-Speed Railway Bridges 4

1.4 Evolution and Trends in High-Speed Bridge Design 6

1.4.1 First High-Speed Bridges 6

1.4.1.1 First-Generation German Bridges 6

1.4.1.2 First-Generation French Bridges 8

1.4.1.3 First-Generation Spanish Bridges 8

1.4.2 Recent High-Speed Bridges 9

1.4.2.1 Recent French Bridges 9

1.4.2.2 Second-Generation German Bridges 9

1.4.2.3 Recent Spanish HSRB 10

1.4.2.4 Bridges for High-Speed Railway Lines in China 10

1.4.2.5 British High-Speed Bridges 12

1.4.2.6 High-Speed Railway Bridges in the USA 12

1.4.3 Conclusions 12

1.4.3.1 Viaducts 13

1.4.3.2 Long-Span Bridges 13

1.5 The Landscape and the Design of High-Speed Railway Bridges 13

1.5.1 The Traveller’s Experience 13

1.5.2 The Bridge in the Landscape 15

1.5.2.1 Long Viaducts with Low Vertical Level 16

1.5.2.2 Long Viaducts with Medium or High Level 16

1.6 Railway Bridges as Landmarks or Icons of a Line 22

1.7 Railway Bridge’s Legacy 23

1.8 Building for the 21st Century 24

1.9 Conclusions 24

References 25

2 Track for High-Speed Bridges 29
Manuel Cuadrado

2.1 Introduction 29

2.2 Specific Criteria for Railway Bridges 29

2.2.1 General Criteria 29

2.2.2 Specific Criteria for High-Speed Bridges 31

2.3 Description of the Track Superstructure 31

2.3.1 Track Components: Definitions, Functions, and Qualities 32

2.3.1.1 Ballast 32

2.3.1.2 Sleepers 32

2.3.1.3 Fasteners 33

2.3.1.4 Rails 33

2.3.1.5 Switches and Crossings 34

2.3.2 Most Important Conceptual Improvements 35

2.3.2.1 Continuous Welded Rail (CWR) 35

2.3.2.2 Track–Infrastructure Interaction: Better Understanding 36

2.3.3 Evolution of the Different Components 36

2.3.3.1 Ballast 36

2.3.3.2 Sleepers 37

2.3.3.3 Fastenings 39

2.3.3.4 Rails 40

2.3.4 Track Options Currently Available for High Speed 41

2.3.4.1 Optimised Ballasted Track 41

2.3.4.2 New Ballastless Track 43

2.4 SLS Related to the Track 44

2.4.1 Dynamic Interaction: Track–Vehicle 44

2.4.2 Track Geometry Quality 46

2.4.3 SLS Verifications Regarding Deformations and Vibrations 48

2.4.3.1 Criteria for Traffic Safety 48

2.4.3.2 Comfort Criteria 55

References 57

3 Conceptual Design of High-Speed Railway Bridges 61
José Romo

3.1 Introduction 61

3.2 Structural and Functional Specific Requirements for High-Speed Railway Bridges 62

3.2.1 Introduction 62

3.2.2 Control of Vertical Acceleration 62

3.2.3 Rotation at Expansion Joints 62

3.2.4 Horizontal Braking and Traction Forces and Relative Movements Between Deck and Infrastructure 62

3.2.5 Track-Bridge Deck Interaction 63

3.2.6 Expansion Joints 63

3.3 Longitudinal Design Strategies 64

3.3.1 General Concepts 64

3.3.2 Ballasted Track 65

3.3.3 Ballastless Track 66

3.3.4 Actions to be Considered at the Fixed Point 66

3.4 Design Situation of High-Speed Railway Bridges 66

3.4.1 Short Crossing at Low Level 67

3.4.2 Long Structures 67

3.4.2.1 Low Profile 68

3.4.3 High-Level Viaducts 71

3.4.4 Long Span Structures 72

3.5 Structural Types 72

3.5.1 Straight Deck Solutions 72

3.5.1.1 Simply Supported Deck 72

3.5.1.2 Continuous Slab Concrete Decks 73

3.5.1.3 Precast Beam Decks 74

3.5.1.4 Concrete Box Hollow Sections 78

3.5.1.5 Steel Beam Decks 80

3.5.1.6 Steel Semi-through Decks 81

3.5.2 Truss Bridges 82

3.5.3 Arch Bridges 83

3.5.3.1 Upper Deck Bridges 83

3.5.3.2 Tied Arch Bridges 85

3.5.4 Cable-Supported Bridges 85

3.5.4.1 Extradosed Bridges 85

3.5.4.2 Cable-Stayed Bridges 86

3.5.4.3 Suspension Bridges 88

3.5.4.4 Hybrid Bridges 89

3.6 Structural Elements – Substructure 89

3.6.1 Abutments 90

3.6.1.1 Abutments with Expansion Joint in Structure Only 90

3.6.1.2 Abutments with Expansion Joint in Structure and Track 90

3.6.1.3 Fixed Abutments 91

3.6.2 Piers 95

3.6.3 Bearings 95

3.6.3.1 General Bearing Layout 96

3.7 Seismic Design 99

3.7.1 Seismic Design Strategies 99

3.7.2 Seismic Behaviour and Deck Articulation 99

3.7.3 Longitudinal Behaviour 100

3.7.3.1 Simply Supported Spans 100

3.7.3.2 Continuous Deck 100

3.7.4 Transversal Behaviour 101

3.7.4.1 Introduction 101

3.7.4.2 Fixed Transversal Support 101

3.7.4.3 Transversal Damping Systems 102

3.7.4.4 Damping Devices Plus Bearings 104

3.8 Worked Example 106

3.8.1 Introduction: Aim and Data 106

3.8.1.1 Topography 106

3.8.1.2 Plan and Elevation 106

3.8.1.3 Railway Platform Section – Project Speed 106

3.8.1.4 Water Flood Level 107

3.8.1.5 Preliminary Geotechnical Data 107

3.8.2 Methodology 107

3.8.3 Critical Analysis of Existing Information 107

3.8.4 Determination of the Length of the Viaduct, Selection of the Fixed Point 108

3.8.5 Span Distribution 109

3.8.6 Deck Pre-dimensioning 109

3.8.7 Pre-design of the Infrastructure 112

3.8.7.1 Fixed Point 112

3.8.7.2 Bearings 112

3.8.7.3 Abutments 112

3.8.7.4 Piers 113

References 115

4 Design Basis 117
José Romo

4.1 Introduction 117

4.2 Design Situations 117

4.3 Rail Traffic Actions and Other Actions Specific of Railway Bridges 118

4.3.1 Permanent Loads 118

4.3.1.1 Self-Weight 118

4.3.1.2 Dead Loads 118

4.3.1.3 Partial Ballast Removal 119

4.3.2 Variable Loads 119

4.3.2.1 Vertical Live Loads 119

4.3.2.2 Traction and Braking Forces 121

4.3.2.3 Centrifugal Forces 122

4.3.2.4 Nosing Forces 123

4.3.2.5 Aerodynamic Actions from Passing Trains 123

4.3.2.6 Thermal Actions 123

4.3.2.7 Bearing Friction 124

4.3.3 Dynamics Effects 124

4.3.3.1 Introduction 124

4.3.3.2 Consideration of Dynamic Effects 125

4.3.4 Railway Vehicle Derailment 125

4.3.4.1 Railway Vehicle Impacts 125

4.4 Application of Traffic Loads on Railway Bridges 126

4.4.1 General 126

4.4.1.1 Load Situations for Structural Design 127

4.4.1.2 Load Situations for Limit State and Associated Acceptance Criteria 127

4.4.2 Groups of Loads 127

4.4.2.1 Characteristic Values of Multicomponent Action 127

4.5 Traffic Loads for Fatigue 128

4.6 Verifications Regarding Deformation and Vibrations for Railway Bridges 128

4.7 Worked Example 129

4.7.1 Introduction 129

4.7.1.1 Calculation of Reactions at Bearings: Pre-dimensioning 130

4.7.1.2 Calculation of Forces and Preliminary Design of the Fixed Abutment 130

4.7.2 Actions 130

4.7.2.1 Vertical Loads 130

4.7.2.2 Horizontal Forces 131

4.7.2.3 Wind Speed 132

4.7.3 Calculation of Reactions at Bearings: Pre-dimensioning 133

4.7.3.1 Vertical Forces 133

4.7.3.2 Centrifugal Forces 134

4.7.3.3 Wind at Unloaded State 135

4.7.3.4 Wind with Live Load 135

4.7.3.5 Reactions in Pier Heads 135

4.7.3.6 Transversal Wind Bearings Reactions 136

4.7.3.7 Loads per Bearings 136

4.7.4 Fixed Abutment Loads 137

4.7.4.1 Introduction 137

4.7.4.2 Loads Transmitted by the Deck 137

4.7.4.3 Forces Acting on the Abutment 138

References 140

5 Dynamic Behaviour of High-Speed Railway Bridges 143
Alejandro Pérez-Caldentey

5.1 Introduction 143

5.1.1 Resonance 143

5.1.2 Envelope Dynamic Factor 144

5.1.3 Dynamic Factor for Real Trains Obtained by Means of Analytical Formulations 145

5.1.4 Dynamic Factor Obtained by Dynamic Analysis 147

5.2 Methods for Dynamic Calculations and Structural Response 153

5.2.1 Modal Superposition 153

5.2.1.1 Matrix Formulation for Finite Element Analysis 153

5.2.1.2 Formulation Based on Assumed Eigenforms 155

5.2.2 Response to the Isolated Load 158

5.2.3 Response to the Train Loads 162

5.2.4 Effect of Damping 164

5.2.5 Dynamic Interaction Between Vehicle and Structure 165

5.3 Interoperability 167

5.3.1 Introduction 167

5.3.2 Universal Dynamic Train A 167

5.3.3 Universal Dynamic Train B 167

5.4 Application Examples 168

5.4.1 Case Without Dynamic Analysis 168

5.4.2 Case with Dynamic Analysis 169

References 183

6 Longitudinal Track–Structure Interaction 185
Manuel Cuadrado and Alejandro Pérez-Caldentey

6.1 Introduction 185

6.2 Problem Statement 185

6.3 Model for Analysis 188

6.3.1 General Considerations 188

6.3.1.1 Rails 189

6.3.1.2 Deck 189

6.3.1.3 Interaction Between Rails and Track Base 189

6.3.1.4 Bearings 189

6.3.1.5 Columns 190

6.3.1.6 Foundations 190

6.4 Actions 191

6.4.1 Temperature Variations 191

6.4.1.1 Case Without Track Joint 191

6.4.1.2 Case with Track Joint 191

6.4.2 Traction and Braking Forces 191

6.4.3 Vertical Loads 192

6.4.4 Creep and Shrinkage 192

6.4.5 Combination of Actions 193

6.5 Verifications 194

6.5.1 Verifications in Terms of Stresses 194

6.5.2 Verifications in Terms of Displacements 195

6.5.3 Criteria for Placing a Track Joint 196

6.6 Rail Expansion Joints 197

6.6.1 Design of REJs – Calculation of the Maximum Displacement 197

6.6.2 Regulation 201

6.6.3 Installation 201

6.7 Longitudinal Schemes 203

6.7.1 Continous Deck with a Single Fixed Point Located at One of the Abutments 203

6.7.1.1 General 203

6.7.1.2 Examples 204

6.7.2 Continous Deck with the Fixed Point Located on One of the Central Piers 211

6.7.2.1 General 211

6.7.3 Simply Supported Spans Without Longitudinal Continuity, with a Fixed Point on Each Span 211

6.7.3.1 General 211

6.7.3.2 Example 212

6.7.4 Fixed Points at the Two Abutments and a Structural Joint in the Middle 212

6.7.4.1 General 212

6.7.4.2 Example 214

6.7.5 Deck Divided into Several Continuous Stretches, Each One Including Several Spans and One Fixed Point 216

6.7.5.1 General 216

6.7.5.2 Example 217

6.7.6 Especial Situations 218

6.7.6.1 Seismic Design 218

6.7.6.2 Exceptional Geometries 226

6.7.6.3 Example of Exceptional Geometry 226

6.8 Example of Track–Structure Interaction 229

6.8.1 Verification of Stresses in the Rails 229

6.8.2 Verification of Horizontal Displacement at Abutment 2 Due to Braking and Traction Forces 231

6.8.3 Verification of Horizontal Displacement at Abutment 2 Due to Vertical Train Loads 232

6.8.4 Verification of Vertical Displacement at Abutment 2 Due to Vertical Train Loads and Temperature Variations 234

References 235

7 Conceptual Design for Maintenance 239
José Romo

7.1 Introduction 239

7.2 Accesses 240

7.2.1 Decks 240

7.2.2 Piers 240

7.2.3 Abutments 241

7.3 Bearings 242

7.4 Expansion Joints 243

7.5 Drainage 246

7.6 Conclusions 248

References 248

Appendix A Basic Concepts of Dynamics 249
Alejandro Pérez-Caldentey

A. 1 Dynamics of Single Degree-of-Freedom Systems 249

A.. 1 Dynamic Response to Moving Loads (Dynamic Load Factor) 249

A.1. 2 Basics of Resonance 257

A.1. 3 Solution of the Equation of Motion of a SDOF Damped System Subjected to a Triangular Load 258

A..3. 1 Auxiliary Expressions – Integrals I 1 , I 2 , and Their Derivatives 259

A.1.3. 2 Solution for the damped SDOF System Subjected to a Triangular Load 261

Reference 262

Appendix B Singular Bridges for High-Speed Railway Lines 263
José Romo

B. 1 Germany 263

B.. 1 Gemünden Bridge 264

B 1 Data Summary 264

B.1.1. 2 Description 264

Further Reading 264

B.1. 2 Veitshöchheim Bridge 266

B..2. 1 Data Summary 266

B.1.. 2 Description 266

Further Reading 266

B.1. 3 Pfieffetal Bridge 268

B..3. 1 Data Summary 268

B.1.3. 2 Description 268

Further Reading 268

B.1. 4 Nantenbach Bridge 270

B..4. 1 Data Summary 270

B.1.4. 2 Description 270

Further Reading 270

B.1. 5 Unstruttal Bridge 272

B..5. 1 Data Summary 272

B.1.5. 2 Description 272

Further Reading 272

B.1. 6 Gänsebachtal Viaduct 274

B..6. 1 Data Summary 274

B.1.6. 2 Description 274

Further Reading 274

B.1. 7 Hämerten Bridge 276

B..7. 1 Data Summary 276

B.1.7. 2 Description 276

Further Reading 276

B.1. 8 Filstal Bridge 278

B..8. 1 Data Summary 278

B.1.8. 2 Description 278

Further Reading 278

B. 2 France 281

B.2. 1 Garde-Adhémar Viaduct 282

B.2.. 1 Data Summary 282

B..1. 2 Description 282

Further Reading 282

B.. 2 Avignon Viaducts 284

B.2.2. 1 Data Summary 284

B 2 Description 284

Further Reading 284

B.2. 3 Mornas Viaduct 286

B.2.3. 1 Data Summary 286

B..3. 2 Description 286

Further Reading 286

B.2. 4 Savoureuse Viaduct 288

B.2.4. 1 Data Summary 288

B..4. 2 Description 288

Further Reading 288

B. 3 Spain 291

B.3. 1 Osera Bridge 292

B.3.. 1 Data Summary 292

B.3.1. 2 Description 292

Further Reading 292

B.3. 2 Llinars Del Vallès Viaduct 294

B.3.2. 1 Data Summary 294

B.3.. 2 Description 294

Further Reading 294

B.. 3 Salto Del Carnero Railway Bridge, Saragossa 296

B.3.3. 1 Data Summary 296

B.3.3. 2 Description 296

Further Reading 296

B.3. 4 Viaduct Over AP7 Riudellots de la Selva 298

B.3.4. 1 Data Summary 298

B.3.4. 2 Description 298

Further Reading 298

B.3. 5 Contreras Bridge 300

B.3.5. 1 Data Summary 300

B.3.5. 2 Description 300

Further Reading 300

B.3. 6 Viaduct Over River Ulla 302

B.3.6. 1 Data Summary 302

B.3.6. 2 Description 302

Further Reading 302

B.3. 7 Almonte Bridge 304

B.3.7. 1 Data Summary 304

B.3.7. 2 Description 304

Further Reading 304

B.3. 8 Alcántara Bridge 306

B.3.8. 1 Data Summary 306

B.3.8. 2 Description 306

Further Reading 306

B. 4 Japan 309

B.4. 1 Yashiro Bridge 310

B.4.. 1 Data Summary 310

B.4.1. 2 Description 310

Further Reading 310

B.4. 2 Kumagawa Bridge 312

B.4.2. 1 Data Summary 312

B.4.. 2 Description 312

B.4. 3 Sannai-Maruyama Bridge 314

B.4.3. 1 Data Summary 314

B.4.3. 2 Description 314

Further Reading 314

B. 5 China 317

B.5. 1 Tianxingzhou Yangtze River Bridge 318

B.5.. 1 Data Summary 318

B.5.1. 2 Description 318

Further Reading 318

B.5. 2 Nanjing Dashengguan Yangtze River Bridge 320

B.5.2. 1 Data Summary 320

B.5.. 2 Description 320

Further Reading 320

B.5. 3 Tongling Yangtze River Bridge 322

B.5.3. 1 Data Summary 322

B.5.3. 2 Description 322

Further Reading 322

B.5. 4 Beipanjiang Bridge 324

B.5.4. 1 Data Summary 324

B.5.4. 2 Description 324

Further Reading 324

B.. 5 Yachihe Bridge 326

B.5.5. 1 Data Summary 326

B.5.5. 2 Description 326

Further Reading 326

B.5. 6 Wufengshan Yangtze River Bridge 328

B.5.6. 1 Data Summary 328

B.5.6. 2 Description 328

Further Reading 328

Index 331

The need for large-scale bridges is constantly growing worldwide, as the expansion of transport infrastructures with rail roads and high-speed lines is an important current task in many regions.
This book develops all aspects referring to the structural conceptional design and analysis that are taken into account when planning a bridge or viaduct for a high-speed rail line. That includes the characteristics of the railway traffic such as speeds, actions, limit states, etc., and a detailed analysis of the superstructure of the track with its various components and singular elements.
One of the special features of the book is that it not only highlights the bridge typologies and structural components related to the bridge design but also takes into account the issues of the track construction. The design basis, the requirements from different situations, and solutions are given.
Special attention is paid to the interactions between the structure and the track and to the dynamic nature of railway actions, studying the dynamic response of the structure and its influence on the behaviour of the track and its components as well as on safety, traffic flow quality, and maintenance needs. The particulars of the design of high-speed rail bridges located in seismic areas are included as well.
Numerous examples in all chapters serve the book's character as a useful guide to HSR bridge design, and to prevent typical problems and errors.
An appendix with selected HSR bridges built worldwide completes the work.
With this work the authors provide first-hand experience gained from many years of planning of completed bridges for high-speed rail lines.