End-Shield Bridges for High- Speed Railway1086102/FULLTEXT02.pdf · HESHAM ELGAZZAR Licentiate...

End-Shield Bridges for High-Speed Railway

Full scale dynamic testing and numerical simulations

HESHAM ELGAZZAR

Licentiate Thesis Stockholm, Sweden 2017

TRITA-BKN. Bulletin 148, 2017

ISSN 1103-4270

ISRN KTH/BKN/B--148--SE

KTH School of ABE

SE-100 44 Stockholm

SWEDEN

Akademisk avhandling som med tillstånd av Kungliga Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie licentiatexamen i bro- och stålbyggnad fredagen den 5 maj 2017 klockan 13:00 i rum B24, Kungliga Tekniska högskolan, Brinellvägen 23, Stockholm.

© Hesham Elgazzar, March 2017

i

Abstract

The increasing need for High-Speed Railway (HSR) to improve the infrastructure of the transport network and reduce the travelling time requires increasing research within this field. Bridges are main components of any railway network, including HSR networks, and the optimization of their design for this purpose would contribute to a faster and more cost effective development of the HSR network. The initial investment, and even the running and maintenance costs, of the bridges can be decreased by reaching a better and deeper understanding of the their dynamic behaviour under HSR operation. This can be achieved by developing more reliable analysis techniques that can predict the dynamic response of the bridges with high accuracy.

This licentiate thesis aims to study the dynamic behaviour of end-shield railway bridges under the operation of high-speed trains. 2D beam analysis is used to study the effect of the distribution of the train’s axle load. Relatively accurate 3D FE-models are developed to study the effect of Soil-Structure Interaction (SSI) and predict the dynamic response of the bridges. A range of modelling alternatives are studied to develop the most accurate model. The project includes a full scale test of a simply supported Bridge with end-shields using load-controlled forced excitation. The results from the test is used to update and verify the theoretical models.

A manual model updating process of the material properties of the 3D FE-model is performed using the frequency response functions (FRF) from the field measurements. A Simple 2D model is also developed, where a spring/dashpot system is implemented to simplify the Soil-Structure interaction, and updated to try to reproduce the field measured responses.

The conclusions driven from the project emphasize the importance of including the effects of Soil-Structure Interaction in the dynamic analysis of end-shield bridges for an enhanced prediction of their dynamic behaviour regarding natural frequencies, mode shapes, damping, amplitudes of vibration of the bridge.

The conclusions also show that the modelling of the surrounding soil and the careful assumption of the soil material parameters have significant effect on the dynamic response of the bridge. Even the boundary conditions, bedrock level and the ballast on the railway track have considerable effects on the response. The results of the full-scale testing along with the FE model show that the bridge’s concrete section behaves as uncracked section under the studied dynamic loading.

Keywords: high-speed railway, end-shield bridges, structural dynamics, soil structure interaction, full scale bridge testing, controlled forced excitation, hydraulic bridge exciter, frequency response function.

iii

Sammanfattning

Det ökande behovet av höghastighetsjärnväg för att förbättra infrastrukturen till transportnätet och minska restiden kräver ökad forskning inom detta område. Broar är centrala delar av järnvägsnätet, särskilt för höghastighetsbanor och med optimal utformning kommer detta bidra till snabbare och mer kostnadseffektiv utveckling av höghastighetsbanorna. Såväl investeringskostnader som drift- och underhållskostnader kan minskas genom ökad förståelse kring broars dynamiska verkningssätt. Detta möjliggörs genom att utveckla analysmetoder som med större tillförlitlighet beskriver den dynamiska responsen.

Föreliggande licentiatuppsats syftar till att studera det dynamiska verkningssättet hos ändskärmsbroar på höghastighetbanor för järnväg. 2D balkanalys används för att undersöka inverkan av lastfördelning från tåglast. Relativt noggranna 3D FE-modeller har upprättats för att undersöka inverkan av jord-strukturinteraktion och för att beskriva brons dynamiska respons. Ett antal modelleringsalternativ har studerats för att komma fram till den mest noggranna modellen. Fullskaletester med last-kontrollerad excitering har utförts på en fritt upplagd ändskämsbro. De experimentella resultaten används för att uppdatera och verifiera de teoretiska modellerna.

En 3D FE-modell av bron har använts för manuell modelluppdatering av materialegenskaper, baserat på experimentella frekvenssvarsfunktioner. Även en 2D FE-modell av bron har upprättats, där jord-strukturinteraktion förenklat beskrivs med fjäder/dämparelement för att återge uppmätt respons.

Som slutsats från detta arbete betonas vikten av att beakta inverkan av jord-strukturinteraktion i dynamiska analyser av ändskärmsbroar, för att möjliggöra tillförlitliga uppskattningar av egenfrekvenser, modformer, dämpning och vibrationsnivåer hos bron.

Det visas även att modellering av omgivande jordfyllning och jordprofil samt val av dessa parametrar har stor betydelse för den dynamiska responsen. Även randvillkor, avstånd till fast grund samt ballasten på bron har betydande inverkan. Resultaten från fullskaletesterna tillsammans med modellerna visar att betongen i bron troligen fungerar som osprucken vid dessa lastnivåer.

Nyckelord: Höghastighetståg; ändskärmsbroar, strukturdynamik; jord-strukturinteraktion; full-skale test; last-kontrollerad excitering; frekvenssvarsfunktion.

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Acknowledgement

The research work presented in this licentiate thesis was carried out at the division of Structural Engineering and Bridges, department of Civil and Architectural Engineering, at the Royal Institute of Technology KTH. It has been appreciatively financed by KTH railway group.

I would like to thank my supervisor Professor Jean-Marc Battini for the careful, detailed supervision as well as his thorough guidance throughout the whole licentiate project. I would also like to thank my co-supervisor Dr. Mahir Ülker-Kaustell for his supervision and helpful advices during the project.

I would like to express my gratitude for Dr. Andreas Andersson for his voluntary engagement to the project. He has always provided unconditional advice and help in different stages of the project. He was also a great road trip companion during the field measurements.

My gratitude extends to my colleagues at Reinertsen Sverige and ÅF, especially Dr. Henrik Gabrielsson, Martin Henriksson and Örjan Bryggö for their sincere encouragement and overwhelming help at all times.

I would like to thank all the members of my reference group for the insightful discussions and advices. I frankly treasure the sincere engagement and time devotion of Dr. Rainer Massarsch and Dr. Anders Beijer to the project. They helped me to easily understand the deep field of soil dynamics at which they humbly excel.

I thank the Swedish road administration (Trafikverket) for the opportunity to perform the field measurements. I would also like to express my appreciation to our lab technicians Stefan Trillkott and Claes Kullberg for their assistance and unconditional sharing of their long years of practical experience during the field measurements.

I express my appreciation for the division of Bridges and Structural Engineering and Professor Raid Karoumi for giving me the opportunity to work on such an interesting project and the space to develop my professional and academic skills in a very helpful environment. My appreciation is endless for having such amazing work colleagues in this division and in the whole department. I’m very thankful for all the interesting discussions, insights, help,

encouragement and spirit lifting attitude of each and every one of them. This will not be easy to replace.

I never had the chance to properly thank Professor Håkan Sundquist and Professor Anders Wörman for their tremendous assistance during my previous studies at KTH. Their voluntary assistance and support were the first, and greatest, reason I believed that KTH and Sweden is a great place to study and develop my career.

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I would like to thank my amazing friends, in Stockholm, Egypt and the ones scattered around the globe, for their continuous support, encouragement and great company, I can never wish for better friends especially at the times of need.

I’m very grateful for all the hours long dinners, sharing apartments, road trips and jazz concerts with Yalin along with Camille and Ahmed, the long distance phone calls with Omar discussing life goals and ways of achieving them. I appreciate deeply all the days and nights spent discussing and experiencing life and science with my bohemian housemates Carlos, Gabriel, Jennine and Haixia.

Thanks to Amer, Ricardo, Rita, Andreas, Yasmine and Thaer for enriching my life with your sincere support, compassion and sharing so many long night discussions about life, work and research. Thanks to Lamis, Lita, Francisco, Elias for all the after work burgers, drinks and movies cheering me up after long working days. I’m very lucky to enjoy the spontaneous, long conversations with my dear friend Nora inspiring me with her free soul.

I owe a lot of inspiration to Yasmine, Radwa, Luli, Thaer, Sameh, Sandy, Mahmoud, Karim and the rest of my Egyptian friends living in Stockholm as we dreamed, debated and struggled through the years of the Egyptian revolution together.

I owe all my achievements to my family who believes in me more than myself. I feel confident, secured and extremely empowered because of their support. I will always be in debt for my parents Mohamed and Mona, my brother Hossam, my sister Noha, Ranya, Mohamed and Adam.

I have no words to describe how lucky I feel to have a loving, endlessly supporting, understanding, funny, truthful, and extremely passionate about everything I choose to do like my best half and travelling partner Angela. This would have been impossible without her by my side.

Stockholm, March 2017

HHeesshhaamm EEllggaazzzzaarr

vii

لوال إختالف الرأي يا محترم

لوال الزلطین ما الوقود إنضرم

لیف سوا مخالیف ولوال فرعین

كان بینا حبل الود كیف إتبرم؟

عجبي!!

جاھین صالح

If it wasn’t for the difference in opinions my dear Sir

If it weren’t for two clashing flint stones, there wouldn’t be fire

And if it weren’t for two fiber strands rolling against each other

How could we have ever crafted our friendship tie?

Salah Jahin

ix

Nomenclature

Abbreviations

HSR High-Speed Railway

TGV Train à Grande Vitesse (High-Speed train in France)

TEN-R Trans-European high-speed rail network.

CEN European committee for standardisation

ERRI European Rail Research Institute

FE Finite element

FRF Frequency response function

DFT Discrete Fourier Transform.

FFT Fast Fourier Transform algorithm

Geo Geotechnical

SSI Soil structure interaction

SSI (signal processing context) Stochastic subspace identification

FDD Frequency decomposition domain

MAC Modal assurance criterion

CG Centre of gravity

N.B. Nota Bene (note well in Latin)

Lower case Latin letters

a acceleration

f frequency

x

Upper case Latin letters

Kv vertical stiffness of the spring

Kr Rotational stiffness of the spring

Cv vertical damping of the dashpot.

Cr Rotational damping of the dashpot

E Elasticity modulus

Ec Elasticity modulus of concrete

Eb Elasticity modulus of ballast

Es1 Elasticity modulus of soil layer 1

Es2 Elasticity modulus of soil layer 2

Lower case Greek letters

ζ Damping ratio

γ unit weight

υ Poisson’s ratio

Others

CEN European committee for Standardization

ERRI European Rail Research Institute

Trafikverket The Swedish Transport Administration

Banverket The Swedish Railway Administration.

Vägverket The Swedish Road administration.

BaTMan The Swedish Transport Administration Bridge and Tunnel management software.

BIS The Swedish Transport administration course information system

ARTeMIS Ambient Response Testing and Modal Identification Software

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Contents

Abstract ................................................................................................................................. i

Sammanfattning.................................................................................................................. iii

Acknowledgement ................................................................................................................ v

Nomenclature ...................................................................................................................... ix

Abbreviations ............................................................................................................... ix

Lower case Latin letters ............................................................................................... ix

Upper case Latin letters ................................................................................................. x

Lower case Greek letters ............................................................................................... x

Others ............................................................................................................................ x

1 Introduction ......................................................................................................... 13

1.1 Background ...................................................................................................... 13

1.2 Aim and scope of work .................................................................................... 15

1.3 Limitations ....................................................................................................... 15

2 Preliminary studies .............................................................................................. 17

2.1 Theoretical background .................................................................................... 17

2.1.1 Dynamic soil properties ........................................................................ 17

2.1.2 Soil Structure Interaction (SSI) for Bridges .......................................... 20

2.2 Bothnia-line project .......................................................................................... 23

2.2.1 Stage 1 ................................................................................................... 24

2.2.2 Stage 2 ................................................................................................... 26

2.3 Dynamic behaviour of end-shield bridges ....................................................... 30

3 Full scale testing ................................................................................................... 33

3.1 Case study: Aspan Bridge ................................................................................ 33

3.2 Bridge Exciter .................................................................................................. 37

3.3 Experiment setup .............................................................................................. 38

3.4 Signal processing .............................................................................................. 42

4 FE- analysis and model updating ....................................................................... 47

4.1 Methodology and modelling aspects ................................................................ 47

xii

4.2 Reference model ............................................................................................... 47

4.3 Solid and Shell elements .................................................................................. 51

4.4 Silent boundaries .............................................................................................. 53

4.5 Ballast continuity .............................................................................................. 55

5 Results ................................................................................................................... 57

5.1 3D model and sensitivity analysis .................................................................... 57

5.1.1 Best fit 3D model .................................................................................. 57

5.1.2 Sensitivity analysis results .................................................................... 62

5.2 2D beam model ................................................................................................ 66

6 Conclusions and future research ........................................................................ 69

6.1 Conclusions ...................................................................................................... 69

6.2 Future research ................................................................................................. 70

Bibliography ....................................................................................................................... 73

Appendix A: Results from full scale testing .................................................................... 77

Appendix B: Results from FE-modelling ........................................................................ 83

Chapter 1 Introduction

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1 Introduction

1.1 Background

One of the cornerstones of any successful socio-economic development plan is the establishment and the expansion of a reliable and efficient transportation network adopting faster and more economic ways of transporting people as well as goods. This proves more challenging for less developed countries due to their limited financial resources that could be allocated for the, very expensive, infrastructure development projects even with the anticipated, and most importantly needed, positive effects on their development.

High speed railway (HSR) is being increasingly considered as an essential component of the transportation network. Many countries have included HSR in their network with the leadership of Japan as early as 1964 operating the bullet train, Tōkaidō Shinkansen, between Tokyo and Shin-Osaka at 285 km/h. In Europe, France took the lead regarding the HSR development with the first TGV running from Paris to Lyon at the speed of 260 km/h in 1981 (UIC International union of Railways 2016a).

In Sweden, the construction of the first HSR project is planned to start in 2017. The project will be built to connect Stockholm to Göteborg and Malmö and then through Denmark to the rest of Europe with a double track HSR operating at 320 km/h (Trafikverket 2016a). Upon the completion of this project, Sweden will be able to join the Trans-European high-speed rail network (TEN-R) as planned (Figure 1).

The financially exhausting initial investment of building new HSR network promotes the less expensive alternative of re-assessing the already built railway infrastructure (Figure 2) to allow the operation of high-Speed trains, e.g. Bothnia-Line project in Northeast Sweden which will be described in more details in the coming chapters.

These initial investments, and even the running and maintenance costs, of bridges for HSR can be decreased by reaching a better and deeper understanding of the dynamic behavior of these bridges. This will allow for developing more reliable analysis techniques that can predict more accurately the behaviour of these bridges. This will lead to designing and building more efficient bridges, regarding their performance and investment costs. Reducing the cost of building HSR makes the goal of expanding the efficient transportation network within hands even for societies with limited budgets and resources, thus contributing to the development and economic flourishment of societies.

1.1 Background

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Figure 1 The Trans-European high-speed railway network (UIC International union of Railways 2016b)

Figure 2 The Swedish Railway network (Trafikverket 2016b)

A lot of research has been conducted in the field of Earthquake Engineering which is concerned with the study of high amplitude vibration waves, originated within the earth crust, and their travelling through the soil along with the effect on the structures e.g. buildings and

Chapter 1 Introduction

15

infrastructure. This is almost the vice-versa of what we are interested in, in the bridge dynamics field of research. We are mainly concerned with the vibrations of the structures resulting from the external excitation sources, e.g. passing trains, and the interaction between these structures and the surroundings e.g. soil and other structures nearby. This field has not been explored as intensively as Earthquake Engineering, according to the author’s knowledge.

The main design problem is that the dynamic behaviour of bridges is usually underestimated by the numerical models used in the design process, resulting in building bridges that perform much better than anticipated. This has been reported for some full scale testing results (James et al. 2005)

There appears to be a shortage, according to the author’s knowledge, in the published research regarding full scale dynamic testing of end-shield Bridges, especially using controlled forced excitation loads. Studies concerned with the dynamic behaviour of end-Shield bridges and the effect of soil structure interaction (SSI) on their responses is not fully explored as well. This can be of high importance considering the large anticipated effect on the big areas of interface between the soil and the end-shields of this type of bridges.

Developing more reliable numerical models that can predict accurately the dynamic response of bridges is under investigation by an increasing number of research groups from many different aspects at the moment. It is of a crucial importance for high speed railway projects due to the expected economic gain from the optimization of their design regarding dynamic behaviour calculations.

1.2 Aim and scope of work

This licentiate project studies the possibility of building more cost-effective bridges for HSR network by developing a deeper understanding of the dynamic behaviour of the end-shield bridges under the operation of high-speed trains.

This will be achieved by developing more reliable numerical models to simulate the dynamic behaviour of the bridges with end-shields. Full scale testing of a case study bridge will be performed, using load-controlled forced excitation, in order to use the results in verifying and calibrating the numerical models.

The SSI effects on the dynamic behaviour of the bridge, especially at the end frames of the bridge, is to be studied through comparing different modelling alternatives. The effects of different material parameters and modelling aspects on the response of the bridge will be analyzed using detailed 3D FE-models as well as simple 2D beam models.

1.3 Limitations

This thesis concerns only bridges with end-shields.

Only a single case study is included which means that conclusions cannot be derived as a general conclusion for all the bridges of the same type but only for this specific case study. This does not mean that the knowledge about this bridge type will not benefit from this single

1.3 Limitations

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case study, but this will rather serve as a starting point or a reference for future discussion and research.

No soil measurements are included in the full scale dynamic testing of the bridge.

Chapter 2 Preliminary studies

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2 Preliminary studies

2.1 Theoretical background

2.1.1 Dynamic soil properties

The assumption of a linear elastic behaviour of a soil in the numerical modelling requires mainly the definition of the elasticity modulus (E), the damping ratio (ζ), Poisson’s ratio (υ) and the unit weight of the material (γ). The unit mass of the soil and Poisson’s ratio can safely be assumed as independent constant material characteristics and can be determined easily by lab tests. On the contrary, the elasticity modulus and the damping of the soil varies largely based on the rate of loading and the strain levels induced in the material. E and ζ cannot be measured directly for the soil but instead can be calculated based on other soil parameters, e.g. Shear modulus, void ratio and strain levels and drainage conditions of the soil.

The accurate assumption of these soil parameters for numerical dynamic analysis of any kind is not a simple task, since the soil behaviour under dynamic loading is very different from that under static loading. In the case of static loading, the soil may develop some plastic behaviour, while when subjected to dynamic loading, the soil behaves in an almost totally elastic way (Hardin 1970).The shear modulus and the damping ratio generated from the soil are among the most important parameters to define the soil behaviour under dynamic loading (Rollins et al. 1998). Both parameters are strain dependant and many tests have been conducted to establish a trustworthy empirical relationship between them. Most of these studies were performed for sand and gravelly soils and curves were fitted to the results of the tests as reported by (Seed & Idriss 1970; Seed et al. 1986) and for gravelly sand by (Rollins et al. 1998)

The main factors affecting the soil moduli and damping as studied and mentioned by (Seed & Idriss 1970; Hardin & Drnevich 1970; Clayton 2011) are as follows

· The strain amplitude of the soil

· The effective mean principal stress

· The void ratio of the soil

For the standard dynamic analysis, the soil is assumed to experience small strain levels, less than 10-4. For this case, a semi-empirical relationship was proposed by (Hardin 1970) for calculating the shear modulus at small strain levels of the soil as follows:


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5.0'02max )(

3.0

625a

k POCRe

G s+

=

Where Gmax is the maximum shear modulus of the soil material, e is the void ratio which is the ratio of void to the total volume of the soil material. OCR is the over consolidation ratio which is the ratio of the pre-consolidation stress to the initial vertical effective stress (equals to unity for normally consolidated soils), k is the empirical constant which depends on the plasticity index (PI), σ´

0 is the effective earth pressure of the soil at chosen depth and Pa is the reference stress (98.1 kPa)

e depends on the size of the material grains and the compaction of the soil. Tests on reconstructed soil specimens have shown that it has great effect on the soil stiffness (Clayton 2011). σ´

0 depends on the depth of the soil, the unit mass of the soil material, the ground water level and the coefficient of lateral earth pressure of the soil (passive or active earth pressure)

The following equation was suggested by (Hardin 1970) to calculate the value of k

0045.0006.0 += PIk

PI is the measure of the plasticity of the soil. It is the difference between the water content limit at which the soil is considered liquefied (liquid limit LL) and the water content limit at which the soil is considered plastic (plastic limit PL)

PLLLPI -=

After obtaining the shear modulus of the soil (Gmax), E can be calculated assuming an isotropic and elastic material

)1(*2 u+=

EG

E is the elasticity modulus of the soil, υ is the Poisson’s ratio of the soil material.

υ depends on the material type. It is usually assumed 0.4 - 0.5 for static loading problems with large strains but according to (Massarsch 2004), it can be assumed 0.15 - 0.3 for small strain levels, preferably at the lower limit for coarse grain materials.

Based on this equation, the variation of Gmax can be shown, for a coefficient of lateral earth pressure of 0.3 and an assumed Poisson’s ratio at small strains of 0.15, to vary with the depth as shown in Figure 3 for different void ratios. Subsequently Emax can be also plotted, for the same condition, to vary with depth as shown in Figure 4


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Figure 3 Gmax variation with depth of soil for different void ratios (Massarsch 2004)

Figure 4 Emax variation with depth of soil for different void ratios (Massarsch 2004)

The dissipation of the energy content of the induced vibrations in in the soil medium can be defined as the damping in the soil. According to (Ülker-kaustell 2009), there are two main factors that contribute to the damping of the soil:

· The damping of the soil material

· The radiation damping


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The damping of the soil material is a characteristic for the material which depends on the material particles, their shape and their physical composition itself. The radiation or geometric damping is simply explained by (Gazetas & Dobry 1984) for the vibrations generated by a foundation. They explain that stress waves are originated at the contact surface between the vibrating foundation and the surrounding soil. These waves will travel away from the contact surface into the soil transmitting the vibration energy from the foundation to the soil and eventually dissipating through the infinite soil. The process is similar to the absorption of energy by viscous dampers and thus it was called radiation damping. The energy loss is directly proportional to the strain levels of the soil as it will generate more friction between the soil particles. Based on that, the soil layers closer to the surface are more likely to generate more damping due to less constraint to their movement.

The damping values generated from the surrounding soil under an induced excitation can vary greatly depending on the frequency of excitation, geometry of the soil and the excited modes of vibration. This can be interpreted from previous full scale dynamic tests results that calculated the associated modal damping of the excited bridge natural frequencies. In some cases, the damping associated with the second mode of the bridge was more than three times larger than that associated with the first mode (James et al. 2005). The difference in the associated modal damping is partly accredited to the difference in the generated damping from the surrounding soil among other factors e.g. damping in ballast, friction of bearings, and energy dissipation in concrete cracks.

2.1.2 Soil Structure Interaction (SSI) for Bridges

The early history and the evolution of the soil-structure interaction problem and the attempted ways of analysing and simulating the problem is assembled in a state of the art article by (Kausel 2010). It mentions that the earliest attempts were concerned only with the foundation interaction with the soil and the propagation of the vibration waves through the soil. One of the earliest attempts to consider this interaction taking into consideration the dissipation of energy from the wave propagation in the soil was performed as early as 1935 in Japan (Sezawa & Kanai 1935a, 1935b, 1935c).

The interaction between a bridge and the surrounding soil can be considered through different approaches. The contact surface, where the vibration waves are transmitted from the bridge to the soil, can be considered to simulate the interaction condition between the bridge and the soil. This can possibly represent a full coupling interaction, in which no vibration energy is lost at the contact surface through the transmission of waves. The other alternative is a partial coupling interaction, for which some energy is lost through the transmission of waves to the soil due to e.g. friction between the two surfaces due to sliding against each other. At low strain levels, which are usually associated with dynamic loading, it is reasonable to assume full interaction between the Bridge and the surrounding soil.

The induced vibration waves propagate through the soil in the form of surface and body waves (Figure 5). These two types of waves are defined by (Clayton 2011) as follows:

· Surface waves are the waves the propagates along the interfaces between materials with different densities and/or stiffness, or along the ground surface, e.g. Rayleigh waves


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· Body waves are those which travel through the body of a solid, unaffected by its surface, with a velocity and ray path controlled only by the density and stiffness, and their variation.

The body waves are separated into two types: Primary (P-), compressional waves and Secondary (S-), shear waves depending on the distortion of the material particles along their direction of travel (Figure 6). While Rayleigh surface waves are the result of the interaction of compressional and shear waves at the ground surface

In the soil structure interaction context, It is widely accepted that Rayleigh surface waves account for higher energy transmission than S- and P- body waves (Wolf & Song 2002). Since the shear waves are only dependant on the density of the soil and its shear stiffness, their travel velocities, changing for each material (Figure 7), can be used to determine the shear modulus of the soil (G) independent of the ground saturation level, which can be used to calculate young’s modulus of the soil (see 2.1.1).

Figure 5 The waves transmitted through the soil due to train induced vibrations (Hall 2002)


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Figure 6 Distortion of the soil particles along (a) Compressional wave. (b) Vertically polarised shear wave. (c) Horizontally polarised shear wave. (Clayton 2011)

Figure 7 Shear wave velocity ranges for different materials, In Swedish (Möller et al. 2000)

These waves propagate through the soil with decreasing amplitude due to damping effects of the soil (Galvin & Dominguez 2007). This effect on soil motion due to high speed Railway (HSR) has been experimentally observed through various publications (Degrande 2000; Degrande & Schillemans 2001; Auersch 2005; Madshus & Kaynia 2000). In an infinitely continuous soil, these waves are assumed to continue propagating until they diminish. The numerical modelling limits will not allow for the modelling of an infinite soil, but instead a


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finite soil volume with end boundary conditions can be used in the dynamic analysis calculations.

The volume of the soil and the type of boundary conditions to be used must be studied carefully to allow for the damping of all the waves and prevent the reflection of residual waves back into the Soil-Bridge system which may lead to misleading dynamic analysis results. Multiple techniques can be used to implement these artificial, absorbing, silent boundaries after an appropriate distance from the structure to simulate the propagation of waves through the infinite soil like infinite elements, or non-reflecting boundaries or absorbing layers e.g. perfectly matched layers PML (Kotronis et al. 2013).

The usage of viscous, frequency independent dashpots to absorb the energy from the propagating waves at the end boundaries of the soil was developed by (Lysmer & Kuhlemeyer 1969). The effectiveness of the developed silent boundary for absorbing the energy of the different types of waves were discussed and tested against other, already existing, viscous boundaries by (Cohen & Jennings 1983)

Some commercial finite element analysis softwares have formulated and implemented finite solid continuum elements to simulate the damping effect of the infinite soil on the propagating waves and it is available for usage in their elements library, e.g. infinite elements in Abaqus (Dassault Systemes Simulia Corp. 2014)

2.2 Bothnia-line project

The bothnia line is a single railway which links Kramfors and Umeå cities in the North-eastern parts of Sweden (Figure 8). The allowed speed on the line is 250 km/h for passenger trains and 120 km/h for freight trains. The project was finished in August 2010 with a total of 87 railway bridges according to The Swedish Transport administration bridge and tunnel management system, BaTMan (Trafikverket 2013).

The Bothnia-line was already under construction when a significant change in the dynamic checks of newly built bridges was issued in the Swedish standards BV-Bro, utgåva 7 (Banverket 2004). The new version stated that for the newly built bridges with planned speeds higher than 200 km/h, the dynamic calculations and checks should be performed considering a speed interval from 100 km/h up to 20% higher than the maximum speed. It stated also that the dynamic checks should be performed in order to guarantee the safe functioning of the structure at higher speeds.

The new version of the design standards, coming in action on October 2004, was only considered in the design of 14 bridges, according to The Swedish road administration course information system BIS (Trafikverket 2013). The rest of the 87 bridges were already designed according to the earlier versions, BV-Bro, utgåva 4 – 6 (Banverket 1997; Banverket 1999; Banverket 2002). Some of these bridges were checked later on, in accordance with the latest standards version, (Karoumi & Wiberg 2006) showing that 6 bridges, out of 10, failed to satisfy the dynamic requirements.

A project to check the dynamic requirements of the railway bridges on the Bothnia-line for future high-speed trains was commissioned to the division of Structural Engineering and Bridges in KTH. Only 76 bridges were deemed relevant to this study after excluding other


24

types of structures e.g. culverts. In the first stage of the project, calculation methods were developed to check the vertical accelerations of the bridges along the railway line. The bridges that fail to satisfy the requirements in the first stage were further investigated in the second and third stage of the project.

Figure 8 Bridges along Bothnia-line project (Johansson et al. 2013)

2.2.1 Stage 1

Simple 2D analytical models were previously developed by (Johansson et al. 2013) based on Euler-Bernoulli beam theory and mode superposition, the theoretical background and the development of the model is explained in details in the referred article. The 2D beam model was developed for simply supported and continuous spans, but through some additional assumptions the response of portal frame and end-shield bridges could also be described. The addition of vertical and rotational springs, with stiffness kv and kr respectively, and distributing the mass of the end shield and wing walls, m2, on 0.1 m distance at the end of the beam assumed to represent the effects of the end frames of the slab frame and end-shield bridges. The model ended at the end-shields centreline at both ends. The model was compared to relative 3D FE-models and good agreement of the vertical accelerations was shown (Johansson et al. 2012).

The model was used to calculate the mode shapes and the natural frequencies of each bridge with an upper frequency limit maxf (Hz)

),5.1,30max( 31max fff =

The vertical accelerations of the bridge under HSLM-A train load models were calculated, in accordance with EN 1991-2 (CEN 2003), within the speed range of 100 km/hr to 300 km/hr. The maximum vertical acceleration of the bridge deck should not exceed 3.5 m/s2 for ballasted tracks (CEN 2002).


25

The results from the first stage of the Bothnia-line project were put together in a report on April 2013 (Johansson et al. 2013). The report includes an appendix with each of the 76 bridges information, mass, section properties, and the results of, among others, max acceleration (amax), corresponding velocity (vcr), the first three natural frequencies and their mode shapes and a plot of the envelope of amax from all HSLM train load models through the full speed range of the analysis. The report also includes a table summarizing the results for all the bridges including the maximum allowed speed of the train, which corresponds to the maximum vertical acceleration limit. A sample of the report results for Aspan Bridge, as one of the highest acceleration levels of the end-shield bridges, is shown in Figure 9 and Figure 10.

The report concludes that 41 out of the 76 analysed bridges do not fulfil the dynamic requirements, including 12 out of 16 end-shield bridges. It also includes suggestions for the continuation of the dynamic investigation of these bridges in the later stages 2 and 3 of the project through advanced analysis and field measurements of some of the bridges under passing trains and controlled excitation.

Figure 9 First three modes and their natural frequencies of Aspan Bridge

Figure 10 Aspan Bridge amax envelope of all HSLM train load models


26

2.2.2 Stage 2

This stage of the project explored the conservative assumption of applying the axle load of the trains as a concentrated load on the beam model of the bridge deck. In reality the train’s

axle load acts upon the track rails and the load is vertically distributed through the depth of the ballast until it affects the deck of the bridge with lower load intensity (ERRI 1999)

The effects of the load distribution from the track through ballast for bridges with spans less than 10 m and comparison of the results from proposed distribution models and the Eurocode model is discussed in (Axelsson et al. 2014). In the work presented in this thesis, the axle load is distributed according to three models:

· Three point loads with half of the original axle load in the middle and quarter of the load on each of the adjacent sleepers according to Eurocode (CEN 2003). This load model was called EC

· Assuming 45 degrees as the load distribution angle in the ballast, replacing each of these three point loads with 5 equally distributed point loads over double the depth of the ballast under the sleepers. This load model was called ECdist.

· Considering the stress distribution under a point load, the axle load is replaced with a number of point loads with decreasing intensities forming a triangular distributed load along 3 m length, almost double the depth the ballast according to (Axelsson et al. 2014). This load model was called triangular.

Figure 11 The three distributed load models


27

This work presented here started by using the same 2D model from stage 1 and performing dynamic analysis after replacing the concentrated axle load with the different distributed axle load models. Since this project is limited to bridges with end-shields, the responses of only the end-shield bridges were calculated for the speed range of 100 - 300 km/hr and the maximum vertical accelerations were plotted due to the distributed axle load models of HSLM-A train load models. The triangular load model was tried with 11 and 21 point loads and the 11 loads model was adopted due to the similarity of the results.

The results were compared to each other to choose the most effective distribution model and they were also compared to the results from the previous stage to show the effect of load distribution. The triangular 11 loads model and the ECdist gave the most favourable effects and they are shown in comparison to the previous results (Table 1). Plots of all calculated amax

for Aspan Bridge under a single point load, triangular 11 loads and ECdist load for all trains are shown in Figure 12 - Figure 14 respectively showing very slight decrease in values of maximum acceleration levels.

The results show slightly lower vertical accelerations for the triangular 11 loads distribution model over the ECdist load model. The load distribution technique in general doesn’t show a significant effect on the levels of vertical acceleration compared to

Stage 1. Nevertheless, 4 end shield bridges seem to satisfy the vertical acceleration requirements after applying the method decreasing the non-satisfactory bridges to 50% of the total 16 Bridges as can be seen in (Table 1).

Figure 12 amax of Aspan Bridge under single axle point load


28

Figure 13 a max of Aspan Bridge under triangular 11 loads model

Figure 14 a max of Aspan Bridge under ECdist loads model


29

Table 1 Comparison of results for triangular 11 loads, ECdist and single concentrated axle loads

Bridge name

Span length

(m)

m (kg/m)

EI (GNm2)

Triangular 11 loads ECdist Single load

f1 (Hz)

amax

(m/s2)

vcr

(km/h)

v3,5

(km/h)

amax

(m/s2)

Vcr

(km/h)

v3,5

(km/h)

amax.old

(m/s2)

Aspan (1,7)+24+(1,7) 27720 36.7 3,1 15 300 198 15,2 300 143 15,6

Brustjärnsbäcken (1,5)+30+(1,5) 22800 90.7 3,5 6,1 298 277 6,2 295 277 6,5

Bubäcken (1,5)+17+(1,5) 33500 87.7 8,5 2,6 278 >300 2,8 278 >300 3,3

Degernäsbäcken (1,5)+20,5+(1,5) 35618 156.7 7,7 3,1 278 >300 3,2 278 >300 3,7

Hinnsjövägen (1,7)+16+20+16+(1,7) 25500 35.7 5,8 2,9 283 >300 3 286 >300 3,8

Husån (1,5)+21+35+26+(1,5) 19680 105.6 4,1 2,8 298 >300 2,9 298 >300 3

Leduån (1,75)+23+23+(1,75) 32200 32.6 3 6,7 289 189 6,7 288 188 7,1

Leån (1,5)+18+18+(1,5) 20400 20.4 4,7 4,8 234 226 4,9 234 225 5,1

Nordmaling (1,5)+11+14+11+(1,5) 21200 7.3 5,9 4,4 300 244 4,6 300 242 6

Norrmjöleån (2,3)+29+(2,3) 38200 143.6 3,5 4,4 300 296 4,5 300 287 4,7

Sidensjövägen (1,5)+13+17+13+(1,5) 19600 6.3 4 21,1 300 218 21,4 300 194 22

Stridbäcken (1,7)+19,5+22+(1,7) 26340 25.9 3,5 8,4 300 219 8,4 300 218 8,6

Styrnäs (1,5)+13+17+13+(1,5) 24400 44.9 9,5 1,4 297 >300 1,8 198 >300 3,2

Sörmjöleån (1,45)+15,3+21,4+15,3+(1,45) 20200 22.4 4,9 3,3 298 >300 3,6 298 296 4,6

Åhedaån (1,8)+21,2+35+21,2+(1,8) 20400 85 3,8 2,5 277 >300 2,5 277 >300 3,2

Ängerån (1,5)+21+(1,5) 35063 155.7 7,4 3,3 294 >300 3,4 293 >300 3,7

2.3 Dynamic behaviour of end-shield bridges

30


Aspan Bridge was chosen for further studies of the dynamic behaviour under HSR operation. The choice of the bridge was mainly based on the highest acceleration levels, amax, according to the preliminary studies (Table 1). The simple structure of Aspan bridge with only one span and shallow abutments’ foundations meant fewer factors affecting the dynamic behaviour of the bridge and thus simpler to analyse its responses compared to the other possible choice, e.g. Sidnesjövägen bridge with 3 spans and piled abutments’ foundations.

The further studies were directed towards the end-frame of the bridge, end-shields and wing walls, to predict their effect on the bridge response. The analysis in this stage served as preliminary guidelines for the more detailed FE modelling and analysis of the Bridge which is presented in Chapter 4.

The geometry and the structural system of the analytical 2D model were altered to explore the resulting effects. The end-shields along with the wing walls were removed (Figure 15) to check if the acceleration levels will decrease. The results in Figure 16 show a slight shift in all the resonance peaks decreasing amax by a small value (14 m/s2 instead of 15 m/s2).

Figure 15 2D beam structural system after removing end shields, wing walls

Figure 16 Response of Aspan Bridge after removing end shields and wing walls


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This results can be interpreted as a sign of the domination of the main span amplitude of vibrations on the overall dynamic behaviour of the bridge. It shows as well that the effect of the end shields, the way they are represented in this model, is only secondary as by removing them, the response of the bridge will only improve as little as described above.

Another effect that was studied at this stage was changing the structural system of the 2D beam model by adding stiff springs at the end-shields (Figure 17). This decreased the acceleration levels remarkably depending on the stiffness of the springs added. This is a simplified assumption of the soil support that might generate from the soil-structure interaction at the end-shields. This also emphasized the importance of studying the role of the soil at the end-shield and how that could affect the response of the bridge.

Figure 17 2D beam structural system after adding the springs and dashpots

Figure 18 Response of Aspan Bridge when modelling spring at the end of the wing walls with kv = 10 GN/m spring stiffness

The values of the spring stiffness (kv) at the ends of the beam model was assumed as 10 GN/m, after investigating with a range of values, to demonstrate the effect of the structural system change on the response of the bridge. The addition of the stiff springs at the end shields location changes the structural system from a simply supported beam with two cantilevers to a continuous beam with a long span in the middle and two short spans, 1.4 m each, at the ends. This new system introduces larger restrains to the amplitudes of vibration of the main span in the case of the chosen spring stiffness as shown in Figure 18.


32

The effect on the response varies with the choice of spring stiffness but the results from the analysis shows the plausible effect of the SSI at the end shields and wing walls on the overall dynamic behaviour of the bridge. This motivated the modelling of the soil surrounding the bridge in the more detailed FE models that will follow in Chapter 4.

Chapter 3 Full scale testing

33

3 Full scale testing

A great advantage of choosing an already built bridge as a case study is the possibility of performing full scale test to validate and update the numerical models used for calculations. The time response of the bridge due to train passage is typically recorded at several locations along the bridge to be able to describe the response of the whole bridge. The uncertainty of the exciting load from the passing train proves to be problematic when analysing the responses as the exciting loads cannot be calculated in an accurate way.

When the bridge is excited by train passage, due to the above mentioned uncertainties of the train loads, most of the signal analysis tend to consider only the free vibration of the bridge after the train passage (Liu et al. 2009). This leads, in most cases, to only exciting the lowest frequency modes of the bridge.

An alternative to excite the bridge is using an impact load with a known magnitude, e.g. dropping weight (James et al. 2005), leading to only exciting the lowest frequency modes of the bridge as well. This is mainly due to the low energy content transmitted by the impact load to excite the bridge modes.

In this project, a hydraulic bridge exciter (Figure 26) was used for the bridge excitement under the full scale testing of the bridge. The bridge exciter was designed and assembled at the lab of the division of Structural Engineering and Bridges at The Royal Institute of Technology (KTH). It was designed to keep control of the exciting load amplitude while sweeping through a range of load frequencies. The signal from the bridge is recorded simultaneously with the frequency and the amplitude of the exciting force.

The hydraulic bridge exciter was designed to excite the bottom of the bridge deck and thus eliminating the need to stop traffic on the bridge for the preparation and installation of the measuring equipment. This introduced a big flexibility in the planning of the measurements which could continue throughout the whole day if needed.

The main goal of performing the full scale test is to use the results for numerical model updating. Through calibration and verification of the numerical model, we can produce better numerical responses for design purposes. The full scale testing is performed aiming for a better understanding of the end shield bridge’s dynamic behaviour and the effects of soil structure interaction as defined in the main objectives of this project.

3.1 Case study: Aspan Bridge

Aspan Bridge was chosen as a case study for performing the full scale testing. The choice took into account that the bridge had one of the highest vertical acceleration from previous


34

calculations (2.2). The simplicity of the single span simply supported bridge highlighted the effect of the end shields and wing walls on the dynamic behaviour of the bridge. The significant decrease in the vertical accelerations when adding springs at the end-shields (shown in 2.3) emphasized the importance of the soil-structure interaction at the end shields of Aspan Bridge. The above mentioned factors made Aspan bridge a perfect candidate for the full scale test and further numerical modelling.

Aspan Bridge has a 24 m single span, simply supported on a hinge at one side and a roller at the other (axes 1 and 2 respectively in Figure 20). The 1.35 m depth bridge deck continues for 1 m after the supports and then the 1 m thick end shields with the 0.5 m thick, 5.6 m long wing walls form horizontal end frames for the bridge superstructure (Figure 19 and Figure 20). Regular 250×800 cm2 edge beams extend along the bridge body and the wing walls to support the guard rails and complete the bridge superstructure section (Figure 21).

Figure 19 Aspan bridge superstructure plan.

Figure 20 Aspan bridge superstructure elevation

The bridge substructure consists of two 6.4×5×1 m3 abutments supported on a 7.4×6×1 m3 isolated shallow foundations. Each wall has two support locations on its top edge which are connected to the bridge deck. These supports are designed to prevent translation in different directions while allowing rotation to behave as a hinge and a roller as mentioned before. The shallow foundations are resting on ca. 1.5 – 2 m of soil above the assumed bedrock level approximately (Figure 23). The bedrock has a varying level which is further studied and explored in the numerical modelling in stage (4).


35

Figure 21 Aspan bridge section and the edge beam sections

The water stream passing under the bridge has the same bottom level as the bedrock. The lined sides of the stream then elevate with a 1:2 slope allowing for a 2 m wide passage on one side of the stream (Figure 23). The level of the passage is the level above which the soil bank of the railway track starts. The top of the soil bank is as wide as the bridge itself and the sides has 2 slopes, starting from the top with a steeper slope of 1:1.5 until almost half the height and then continuing with a slope of 1:2 until the level of the passage which is the same level as the normal traffic road (Figure 22 - Figure 24). The man-made soil bank and the rest of the filling material used in the construction are mainly crushed stones (sprängsten and krossmaterial in Swedish) as indicated in the drawings and the geotechnical report (Botniabanan AB 2004).

The ballast of the single track railway is considered to have the same material as the soil bank. The ballast section extends along the whole track and above the bridge where it has at least 60 cm depth under sleepers (Figure 24).

Figure 22 Aspan Bridge plan


36

Figure 23 Aspan Bridge elevation

Figure 24 Aspan Bridge side view

Figure 25 Aspan Bridge full view


37

3.2 Bridge Exciter

The hydraulic bridge exciter used in the full scale field testing consisted of different parts that were assembled together on site (Figure 26). The main part consisted of an assembled truss column, which is made out of parts with different lengths to accommodate the different clearance heights of different bridges. The truss was mounted on top of the hydraulic load cylinder which was used to generate the input load through a prescribed piston displacement. A load cell was installed at the top of the truss, in contact to the bridge deck, to measure the input load at the point of application. when the bridge exciter main body was erected (Figure 27), an oil pump and a power generator were connected to it in order to start the excitation (Andersson et al. 2015).

The aimed frequency range of the bridge exciter was 0 - 50 Hz but it could be increased to a higher range if needed. The hydraulic load cylinder can generate up to 50 kN sinusoidal harmonic input load. The consistency of the input load amplitude was maintained through a connected MTS FlexTest SE controller (MTS systems 2011). The exciting load was recorded using the load cell at the end of the truss column to check the amplitude and frequency of the actual load transmitted to the bridge deck.

A full scale pilot test for the bridge exciter was performed on a three span railway bridge in the South-West of Stockholm in 2015 (Andersson et al. 2015) in which the bridge exciter was shown to produce a constant exciting load amplitude throughout the whole frequency range tested, even at resonance frequency. Based on this, the frequency response functions could be calculated from the recorded time signals at all the accelerometers. This was of great benefit for the numerical model updating of the tested bridge yielding good matching between the test results and the 3D FE model.

Figure 26 The bridge exciter’s truss and load cylinder (Andersson et al. 2015)

3.3 Experiment setup

38

Figure 27 The bridge exciter erected under Aspan Bridge (Lab. technician Stefan Trillkott in the picture)


A 3D FE-model of Aspan Bridge was developed using Abaqus to predict the frequencies and mode shapes prior to the full scale test. A variety of modelling alternatives were compared to achieve an adequate reference model for the planning and preparation of the full scale testing, which discussed in details in chapter 4

16 single axis accelerometers in total were used in the full scale testing of Aspan Bridge (Figure 28 - Figure 30). 12 accelerometers were positioned vertically along the edge beams based on the anticipated mode shapes of the Bridge. The arrangement of these accelerometers was changed between two different setups (A, B), having five fixed accelerometers (3, 9, 13, 14, 15) for reference. This aimed at producing more accurate mode forms description of the bridge by combining the vertical acceleration results from both setups. Two accelerometers


39

were installed at each bridge abutment, one was installed vertically and the other was positioned horizontally (Figure 29).

The accelerometers used on the edge beams and the abutments are Colibrys SiFlex

SF1500S accelerometers. According to the datasheet provided by the manufacturer, the error anticipated cannot be more than 1% (within +/- 1 g acceleration range) (Colibrys 2013)

Figure 28 Setup A plan

Figure 29 Setup A side view with the bridge exciter’s location

Figure 30 Setup B plan


40

Figure 31 Vertical and horizontal accelerometers installed at the roller support wall

Figure 32 Vertical accelerometer installed on the top of the edge beam

Due to the site limitations, the exciter could only be erected on the two and a half meters wide unpaved passage next to the abutment passing under the bridge. The exciter was erected two meters from the abutment and only half a meter from the edge of the bridge body in the transverse direction. The location of the exciter was studied beforehand by running some FE measurement simulations to make sure that the this was the best location available to excite the maximum number of bridge modes of vibration with the available exciting load amplitudes.

The unpaved ground under the bridge was levelled and prepared for the bridge exciter installation with the help of heavy machinery. The truss column of the bridge exciter was assembled and erected in place with the rest of the bridge exciter parts. It was then connected to the oil pump and the control system. The accelerometers were installed on the edge beams (Figure 32) according to the designated setup, on the abutments (Figure 31).

With the help of the timetable of the passing trains, the measurements of the response of the bridge was planned to take part at the times without passing trains on the bridge. This


41

aimed at producing clear FRFs with no disturbance, the train passages were then recorded separately.

The measurements aimed at measuring the response of the bridge in the frequency range between 0 and 50 Hz with different Exciting load amplitudes. Due to frequent train passages on the bridge, the whole range measurements were divided into short frequency sweeps. Each frequency sweep adopted a predefined frequency range, scanning from the starting frequency with a predefined frequency resolution up till the final frequency. These short sweeps overlapped with each other’s in order to form a continuous full frequency range response with no gaps inbetween when assembled together. Some of these frequency sweeps were repeated with higher amplitude of the exciting load. The same frequency sweeps were performed for both accelerometers’ setups A and B to be able to combine results from both setups in the

signal processing stage.

The measurements started with one quick frequency sweep for the whole range to detect the position of the resonance peaks in the response. This was compared with the expected ones from the pre-calculations and the rest of the sweeps were adapted accordingly. Shorter sweeps with slower frequency resolutions followed which covered the whole range of frequency as well.

5 kN harmonic excitation load was applied during the measurements and it was increased, for some sweeps, to 10 and even 20 kN to check the existence of non-linearity in the response due to exciting load. A pre-stressing force of 5 kN was always applied before the start of excitation to make sure the exciter and the bridge deck are in contact during the whole measurement. The full scale test field work continued for 2 successive days with some in-situ analysis of recorded signals and refinement of measurement procedures. A sample of the frequency scans are presented in Table 2, while the full logbooks from the measurements, including all performed frequency sweeps, train passages, are shown in Appendix A.

The table includes the name of the frequency sweep, the accelerometers setup used, the exciting load amplitude (Famp), the minimum and maximum load frequencies (fmin and fmax

consecutively), the frequency resolution used for the sweep (df) and the time take to perform the frequency sweep (t).

Table 2 Sample of the frequency sweeps of the full scale test

Name setup: Famp (kN) fmin (Hz) fmax (Hz) df (Hz/s) t (min)

A1 A 20 1 23 0,05 7,3

A1x, B1 A, B 5 1 50 0,05 16,3

A3x, B3 A, B 5 3 12 0,02 7,5

A4x, B4 A, B 5 3 12 0,01 15,0

A5, B5 A, B 10 3 12 0,02 7,5

A9, B9 A, B 5 10 27 0,02 14,2

3.4 Signal processing

42

Figure 33 Bridge exciter connected to the oil pump, control system and the power generator


The controlled excitation recorded signals were checked and trimmed to include only the signal from the sensors under the period of excitation. On the other hand, the signals recorded under train passage were checked and trimmed to only include the free vibration stage of the bridge, after the train has completely left the bridge. The adjustments and checks of the recorded signals were performed using MATLAB version R2013b (The Mathworks inc. 2013) and the processed results were saved as files for further analysis and processing.

These checks considered the recorded time domain signals of the load and the sensors along with their calculated Frequency response functions (FRFs) for both accelerometers setups A and B. The FRFs of the time domain signals were calculated using Fast Fourier Transform (FFT) algorithm available in MATLAB. The FRFs of all the accelerometers were checked for disturbances for all the recorded frequency scans and the disturbed ones were excluded from the saved files.

The signal processing was performed by analysing these signal files using ARTeMIS extractor Pro software (Structural Vibration Solutions A/S 2005). The software is widely used in the operational modal analysis (OMA) field where the structures are usually subjected to stochastic or ambient exciting loads (Brincker & Ventura 2015), e.g. wind loads and other uncontrolled excitation loads. The software is expected to show good results in the analysis of structures under controlled excitation as well based on previous experience.

Some of the benefits of using ARTeMIS, includes the possibility of combining the recorded signals from the two setups of accelerometers for a refined results of the modal analysis. Also the mode shapes, natural frequencies and associated damping extraction can be performed using different techniques, e.g. Frequency Decomposition Domain (FDD), Stochastic Subspace Identification (SSI), and compared together using the Modal Assurance Criterion (MAC) matrix for a better overview of the modal analysis.

The geometry of the bridge is represented, in ARTeMIS, by surfaces and beams on the same level as the bridge deck (Figure 34). The geometry is drawn initially by nodes which are then connected together to form the shown geometry. The accelerometers are assigned to their


43

corresponding nodes and the five reference accelerometers are shown in blue in both setups. Since there are no nodes at the location of the abutments’ accelerometers, (a13, a14, a15, a16), they were assigned to the nodes at the edges instead. The accelerometers of the abutments were assigned to one edge only while the same vertical and horizontal accelerations were defined for the two opposite nodes assuming constant accelerations along the cross section of the abutment.

The recorded data in the files of the same frequency sweeps from both setups are processed together in ARTeMIS initially as a preparation step for the following modal estimation process. All the modal estimation techniques available in ARTeMIS were tried and since some of them gave very close results, only two techniques were chosen for the modal estimation process namely Enhanced frequency domain decomposition (EFDD) and Unweighted Principal Component Stochastic Subspace Identification SSI-UPC.

Figure 34 Accelerometers Setups, A and B respectively, as shown in ARTeMIS

EFDD is a modal estimation method that performs in the frequency domain. It is based on the singular value decomposition of the spectral density matrix resulting from combining measurements of different sensors. While the SSI-UPC technique performs in time domain and is based on estimation of state space models. It uses the standard least-squares fitting techniques to estimate the modal parameters in an unbiased way avoiding systematic estimation errors (Brincker & Ventura 2015; Structural Vibration Solutions A/S 2016).

When using EFDD technique, the peaks are picked from the plots of the normalized Singular values of the spectral density matrices of all the accelerometers included in the data processing, the plots representing the average of both setups (Figure 35). Based on some estimation controls, to assume the portion of the peak to be included in the calculations (Figure 36), the natural frequency, the mode shape and the associated damping are estimated.


44

Figure 35 EFDD peak picking process

Figure 36 EFDD portions of the peaks assumed for estimating the natural frequency and their associated damping

For UPC-SSI technique, the modes are chosen from the plots of the stabilized modes of each setup separetely (Figure 37). The chosen modes are then coupled together (Figure 38) and the final estimation of the natural freqeuncies, mode shapes and associated damping of each peak is the average of both setups

Figure 37 UPC-SSI stabilization of modes figure for mode picking of each setup


45

Number

Frequency [Hz]

0 5 10 15 20 25

1

2

UPC [Data Driven]

Figure 38 UPC-SSI coupling of the chosen modes from both setups

Comparing the results from both techniques, UPC-SSI technique was able to separately extract the, closely located, second bending and the first torsional from the second resonance peak as shown in Figure 39 - Figure 41. This was not the case with EFDD technique which showed a combination of both second bending and first torsional for both modes as shown in Appendix A. This favoured the UPC-SSI technique for the modal extraction of Aspan Bridge and the results for some of the performed frequency sweeps are shown in Table 3.

The table contains the frequency sweeps included in the modal estimation, the range of the frequency of the sweep (fs), the frequncy resolution of each sweep (df), the exciting load amplitude (Pamp), estimated natural frequency of each mode (f) and the associated damping of

each mode (ξ).

The variation of the frequency resolution for various frequency sweeps did not result in any significant change to the estimated natural frequencies or the associated damping of the vibration modes. On the other hand, the exciting load amplitude variation from 5 to 20 kN produced slight change in the 2nd and 3rd estimated natural frequencies which indicates some non-linearity in the response of the bridge in connection to the exciting load amplitude.

Figure 39 UPC-SSI 1st bridge mode


46

Figure 40 UPC-SSI 2nd bridge mode

Figure 41 UPC-SSI 3rd bridge mode

Table 3 Results from signal processing using UPC-SSI technique

Frequency

sweeps

A1x, B1 A3x, B3 A4x, B4 A5, B5 A9, B9 A1

fs (Hz) 1 - 50 3 - 12 3 - 12 3 - 12 10 - 27 1 - 23

df (Hz/s) 0,05 0,02 0,01 0,02 0,02 0,05 Pamp (kN) 5 5 5 10 5 20

Parameter f

(Hz)

ζ

(%)

f

(Hz)

ζ

(%)

f

(Hz)

ζ

(%)

f

(Hz)

ζ

(%)

f

(Hz)

ζ

(%)

f

(Hz)

ζ

(%)

Mode

No.

1st 6,7 1,7 6,6 1,3 6,6 1,1 6,6 1,7 6,5 3,4

2nd 17,9 2,6 17,9 2,7 17 1,6

3rd 18,8 3,5 18,6 4,2 18 1,5

Chapter 4 FE- analysis and model updating

47

4 FE- analysis and model updating

4.1 Methodology and modelling aspects

The finite element analysis of the selected bridge was performed using Abaqus Finite element modelling program. The aim of the FE-modelling was to produce a numerical model that is an acceptable representation of the real bridge and yields the same dynamic behaviour under working conditions.

The modelling was divided into a pre-measurements and a post-measurements stage. The pre-measurements stage was aimed at producing a reference FE-3D model to be used in the prediction of the bridge response as accurate and time efficient as possible. The post measurements stage included the calibration and validation of the 3D-FE model to reproduce the field measurements in the best possible way. The later stage involved mainly the optimization of the material parameters of the model.

The FE 3D reference model that is used in the model updating and the sensitivity analysis is presented and some of the choices made for different aspects of the model are motivated through comparisons with other alternatives.

The motivation of different modelling choices was performed at different stages of the model development process, throughout which the assumption of material dynamic behaviour and simplifications of the geometry were different. This resulted in the observed difference of frequency response function (FRF) shape and peaks for each comparison.

4.2 Reference model

The geometry of the reference model, resulting from the pre-measurements stage, which was adopted for the prediction of bridge responses and dynamic behaviour, is shown in Figure 42.

The super structure of the bridge consists of the bridge deck, the end shields, the wing walls and the edge beams. The substructure of the bridge consists of the two abutments and their attached isolated foundations. The bridge body is fully modelled while the ballast was only modelled above the bridge deck, only the distance between the end shields (Figure 43).

The soil surrounding the bridge was originally modelled as one layer with constant soil parameters but at a more advanced stage of the project, it was divided into 2 soil layers to match the variation of the soil parameters with the depth in a better way according to Figure 3 and Figure 4. Soil layer 1 extends from the top surface of the soil down to the bottom of the

4.2 Reference model

48

end shields. Soil layer 2 continues from the bottom level of the end shields down to the level of the varying bed rock. The soil extended for 40 meters on both sides of the longitudinal direction of the bridge, almost as long as the bridge’s length giving the model a total length of ca. 120 meters. Transversally, the soil was modelled until the end of the bank slopes, which were simplified into one slope on each side, ending with a vertical edge for the rest of the depth down to the bed rock level. The bed rock is modelled as a varying bed rock level with some steep variation at some areas (Figure 44) as interpreted from the geotechnical report.

The boundary conditions of the whole model were applied separately to the soil ends in the longitudinal and the transverse directions along with the bottom of the soil. While the bottom of the soil, representing the bed rock level was constrained from movement in all direction, both longitudinal and transversal ends of the soil were only constrained from movement perpendicular to their surfaces.

The bridge body and the abutments are modelled using linear thick shell elements, S4 and S3 (Figure 46) with a converged mesh size of 0.4 m. 3D quadratic solid elements are used for the soil, C3D10 and C3D20R, using a converged single biased mesh size of 2 m to 0.8 m for the areas in contact with the bridge. For the ballast, 3D linear solid elements are chosen, C3D4, with a converged mesh size of 0.4 m as for the bridge deck. The convergence of each mesh size was based on the frequency and acceleration in the FRF results at a2 and a3 sensors locations at an early stage of modelling (Figure 45).

Figure 42 The geometry of the reference FE-model

Figure 43 The ballast section only above the bridge deck


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Figure 44 The bed rock level and the two soil layers as divided in the FE model

Figure 45 Convergence analysis of S4 and S3 shell element size of the bridge deck and abutments

The bridge superstructure was modelled as separate shell plates for each concrete part (Figure 46). They were connected together using a full coupling master/slave connection. These connections act as rigid connections maintaining the continuity of the bridge body through the flow of the internal stresses between all connected elements.

The bridge deck is simply supported on two abutments (Figure 48) at four different locations, two support locations for each wall. The connections between the bridge deck and the abutment are chosen to simulate a hinge support at one wall and a roller at the other one. The connection is simulated through linking a 1 m edge length of the abutment and a surface area of 1×1 m2 of the bridge deck to a separate reference point each (Figure 47). The coupling of the 2 coinciding reference points defines the connection at this location through defining each of the six rotational and translational stiffness values of the wire element connecting them.

The abutments and foundations are fully coupled with the surrounding soil using a full coupling master/slave connection applied to the surfaces in direct contact between the parts. The same connection is applied for the bridge body areas that are in contact with the soil assuming the full interaction between the soil and the super/substructure areas in contact.

4.2 Reference model

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Figure 46 Aspan Bridge super and substructure shell model

Figure 47 The shell model connection between the bridge deck and the foundation wall

Figure 48 The simply supported bridge span


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4.3 Solid and Shell elements

Modelling the superstructure and the substructure of the bridge using shell elements (Figure 46) was assumed to simulate the dynamic behaviour of the bridge in a sufficiently accurate way for the purposes of the calculation. This choice was compared to the more geometrically accurate bridge model using solid elements taking into consideration the increase in the calculation time and the accuracy gained in the results. The comparison was performed through modelling only the superstructure and the substructure of the bridge and comparing their results.

The shell elements bridge model used in the comparison is exactly the same one used in the reference model (Figure 46). The solid elements bridge model used quadratic 3D solid elements, C3D10 and C3D20R, for modelling the superstructure and the substructure of the bridge with a converged mesh size of 0.4 m for all parts of the model. The bridge deck is simply supported on the two abutments, the same way as the reference model, except that the four connections are linking 1×1 m2 surface areas from the bottom surface of the bridge deck and the top surface of the abutment (Figure 50), rather than a surface and an edge in the shell elements case (Figure 47).

The boundary conditions of both models are applied to the bottom surface of the foundation to represent the bedrock by constraining the movement of the surface in all directions. The end shields and the wing walls are constrained from movement in the direction perpendicular to their surfaces as a simplification of the soil effect surrounding them.

Figure 49 Aspan Bridge super and substructure solid model

4.3 Solid and Shell elements

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Figure 50 The solid model connection between the bridge deck and the abutment

During this comparison of modelling aspects stage, cracked concrete sections were assumed as a material model having E-modulus of 21 GPa for superstructure and 20.4 GPa for substructure for the relative concrete classes C35/45 and C30/40. 2500 kg/m3 concrete unit weight and 1% structural damping were used for both models. E-modulus was changed later on for the reference model but for comparison means, it was only of importance that both models have the same material properties.

The Steady state dynamic response of the models were calculated between 0 – 25 Hz under a unit concentrated exciting load, using direct method, and the FRFs of a quarter span point on the edge beam are compared to show the difference between both models (Figure 51).

Figure 51 FRFs of solid and shell bridge model for a unit concentrated exciting load

The results show very good agreement for the first resonance peak, considering frequency and amplitude of acceleration, which corresponds to the first bending mode form of the


53

bridge. For the second and the third resonance peaks, corresponding to the first torsional and second bending mode forms, the shell elements model shows a slightly different response. It has a shifted second peak with higher frequency and amplitude and similar frequency with higher amplitude for the third resonance peak. The differences can be a result of the stiffer connections between bridge deck, end shields, wing walls and edge beams of the shell model compared to the solid model. The sensitivity of the second resonance peak to changes of the torsional stiffness, introduced by modelling the edge beams as shell elements instead of solid elements, can be a reason for the observed differences between the peaks.

The small differences between the solid and shell elements bridge models (Figure 51) are mostly for the second and third resonance peaks which change significantly in the reference model due to the influence of the surrounding soil on their shape and values. The decrease in the Steady state dynamic response calculation time, using 8 processors, 2 GB RAM computer, from 10 hours to 20 minutes, due to decreasing the number of nodes to ca. 10 %, supported the decision of using the shell elements bridge model for an economically efficient and sufficiently accurate reference model.

4.4 Silent boundaries

In reality, the vibration waves generated from the excitation of the bridge travel through the infinite soil surrounding the bridge from all sides until totally damped. If the length of soil modelled, before applying boundary conditions to the ends, is not long enough to damp the vibration waves, the waves will reflect back into the model and superimpose with the travelling waves causing response disturbance and unrealistic noise in the obtained results.

The length of the surrounding soil, necessary for the damping of the travelling vibration waves, within the frequency range of interest, was tested against modelling a silent boundary using 3D continuum one way linear infinite elements, CIN3D8, available in Abaqus element library. These elements are defined over semi-infinite domains with suitable decay functions to simulate the decay of the vibration waves through an infinite medium based on the work of Lysmer & Kuhlemeyer 1969 and Zienkiewicz et al. 1983. This was achieved through comparing the results from a model with the same soil size as in the reference model to the model including the infinite elements.

The infinite elements model was developed after extending the soil surrounding the bridge in the transverse direction so as to have the same length as the soil in the longitudinal direction of the bridge, thus forming a square shape of the model. The infinite elements were then added for the same length of the surrounding soil from all sides of the model (Figure 52). The bottom of the soil was constrained from movement in all direction to represent the bedrock effect.

At this stage of comparing modelling alternatives, the ballast was included only as an additional mass in the concrete bridge deck section for simplification. Cracked concrete section material properties were used for the bridge having E-modulus of 21 GPa for superstructure and 20.4 GPa for substructure. The bedrock level under the bridge was simplified to a constant level along the whole model.

4.4 Silent boundaries

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Figure 52 The model with infinite elements added to the extended soil areound the bridge

Figure 53 FRFs of infinite elements and reference soil size models

The same element types and mesh sizes of the reference model were applied to the infinite elements model. In addition to that, quadratic 3D solid elements, C3D20R were assigned to the added transversal extensions of the soil. They were modelled with an increased mesh size of 4 m to match the same mesh size assigned to the infinite elements attached, CIN3D8.

A direct steady state dynamic analysis between 0 - 25 Hz with a unit load as a concentrated exciting force was adopted for the comparison of the results. The exciting force was applied at a quarter span point on the bridge deck side edge to excite as many resonance peaks as possible and the FRF of the same point is shown for comparison (Figure 53).

The comparison of the FRFs of the 2 models shows the slight difference in the frequency of the resonance peaks which can be a result of the mass of the extra soil added in the infinite elements model. The reference soil size model FRF includes a bit more noise, than the infinite elements FRF, which is probably caused by the reflected vibration waves from the soil sides’

boundaries back into the system. The difference between both FRFs can be neglected


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compared to the almost doubled number of nodes and the complexity of modelling the silent boundaries.

4.5 Ballast continuity

The contribution of the ballast to the dynamic behaviour of the model was tested through comparing different alternatives for modelling the ballast along the railway track. Three of those alternatives are presented and discussed in this thesis. The basic model for all three alternatives is the reference model with the only different assumption of a constant bedrock level along the whole model (Figure 54).

The comparison was performed during the post-measurement stage where the concrete sections were assumed to be uncracked with E-modulus of 35 GPa for bridge superstructure and 34 GPa for the substructure.

The first alternative is including the ballast material only as an extra added mass embedded in the bridge concrete deck material definition. This, fast and simplified alternative, is done by only increasing the unit mass of the reinforced concrete material assigned to the bridge deck to 3010 kg/m3, instead of 2400 kg/m3, keeping all other properties of the uncracked concrete section.

The second, and most reality alike, alternative is modelling the ballast as a separate section along the whole length of the railway track (Figure 54), above the bridge deck and the soil. The ballast is connected through a full coupling master/slave tie connection keeping the ballast connected at all times to the underlying material. The third alternative for modelling the ballast is an adaptation of the second alternative by shortening the length of the modelled ballast to be only above the bridge deck, which is later used in the reference model (Figure 43).

The same element types and mesh sizes of the reference model were used in all three models in this comparison. The same element and mesh size of the ballast above the bridge deck was used when extending the ballast section for the full length of the model.

Figure 54 The ballast section modelled along the full length of the model

4.5 Ballast continuity

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Figure 55 FRFs of ballast modelling alternatives

A direct steady state dynamic analysis between 0 - 25 Hz with an exciting concentrated load of 5 kN was calculated for all three alternatives. The exciting force was applied at a quarter span point on the bridge deck side edge to excite as many resonance peaks as possible and the calculated FRF of the same point is shown for comparison (Figure 55).

As can be observed from the FRF comparison, the embedded ballast mass model is underestimating the frequency of the third resonance peak, corresponding to the first torsional mode, while having slightly higher amplitude as well. This can be due to the importance of the contribution of the ballast section to the torsional stiffness of the model. On the other hand, this contribution seems to be mainly from the ballast above the bridge deck as both the full length and only above the deck ballast models have an identical FRF along the studied range of frequencies.

According to these results, the continuity of the modelled ballast after the bridge deck is deemed of neglected importance in this case study. The ballast section, in the reference model, is only modelled above the bridge deck decreasing the number of nodes in the model and yielding an accurate representation of the ballast for the frequency range of interest in this study.

Chapter 5 Results

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5 Results

5.1 3D model and sensitivity analysis

5.1.1 Best fit 3D model

The process of finding the material parameters combination that makes the FRFs of the reference model fit with the field measured ones was performed in two stages. The first stage was to find multiple material combinations that fit well with the first resonance peak of the field measured response, which corresponds to the first bending mode of the bridge. The second stage was to pick some of the material combinations that fits well with the first resonance peak and at the same time have good agreements with the second and the third resonance peaks and alter the material parameters to achieve best possible match with the higher peaks, keeping the very good match with the first peak. This process considered peak frequencies, amplitudes and shape of all 15 FRFs in comparison.

Values of the material parameters were varied based on previous research, reports and/or theoretical initial calculations. Following a preliminary sensitivity analysis of the material parameters, Poisson’s ratio was chosen to be constant due to its negligible effect on the FRFs. Also the unit weight of the materials was chosen to be constant due to the relatively low uncertainty of their values compared to the other parameters and the negligible effect of their variation within small range of 5-10 %. Only E-modulus and damping ratio (ζ) were chosen to be varied to achieve the best fit material parameters combination according to the min. and max. values presented in Table 4.

Table 4 The min/max variation of parameters and the updated values from the model updating process of the reference model

Parameter E (MPa) ζ (%)

Value Min. Max. Updated Min. Max. Updated

Concrete 30000 40000 35000 0.5 1.5 1

Ballast 50 250 50 1 5 3

Soil 1 100 500 130 1 5 3

Soil 2 200 1000 800 1 5 1

The responses of the best fit FE-model are extracted at 15 locations, along the edge beams and at abutment walls, corresponding to the 15 field measured responses from accelerometers


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of Setup ‘A’ (Figure 56). The FE-model and measured responses are plotted together at all 15 locations to compare the behaviour of the different parts of the bridge. The material parameters of the reference model that best matches the field measured bridge responses are presented in Table 5

Table 5 The constant material parameters of the reference model

Parameter γ (kg/m3) υ

Concrete 2400 0.2

Ballast 1800 0.15

Soil 1 1800 0.15

Soil 2 1800 0.15

Figure 56 Setup ‘A’ Accelerometers location from field measurements where the results

are extracted in 3D FE-model as well

The results from the FE-model are compared with the continuous full frequency range sweep A1x in Figure 56. The results are almost identical for the first resonance peak, considering resonance frequency, amplitude of acceleration and associated damping. The frequencies of the second and third resonance peaks show very good agreement. The amplitude of acceleration of the second peak shows very good agreement as well but bigger difference exists for the acceleration of third resonance peak.

Chapter 5 Results

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Figure 57 The reference 3D FE-model responses compared to the field measured A1x sweep

N.B. The plotted 3D model responses were calculated with high resolution for the frequency intervals of 6-7 Hz and 17-21 Hz where the resonance peaks existed


60

The three resonance peaks in the frequency response function of the field measurements, as well as the FE-model, correspond to the first bending, the second bending combined with first torsional mode and the first torsional combined with second bending modes of the bridge respectively. By checking the real and imaginary parts of the deformation at the resonance peaks, it can be shown that the first peak corresponds to a pure first bending resonance (Figure 58). On the other hand, the second and the third resonance peaks are very close to each other making it very hard to define any of them as a pure second bending or first torsional resonance peak. The rapid change of the real part of the deformation around the resonance peaks is shown with more details in Appendix B.

When comparing the real and imaginary parts of the responses of the second or third peak, one can see that they change their deformation forms rapidly around each peak. While the imaginary parts of the deformation can be defined as pure second bending and first torsional resonance peaks respectively, the real parts, at the same frequency values, represent a combination of both forms. Since the real part of the deformation at these resonance peaks has values as small as 10% of the magnitude of the imaginary part, it is reasonable to assume that the mode forms associated with the resonance peaks can be mainly defined according to the imaginary parts, as second bending and first torsional modes respectively.

It is also worth mentioning that the real parts of the deformation have their peak values at lower and/or higher values than the mentioned ones for the second and the third resonance peaks. This mainly contributes to the slight changes in the frequency of the peaks at some points along the bridge (Appendix B). The fact that not all the points on the bridge has its peak values at the same frequency contributes to the combination of the 2 mode forms at the second and third peaks as well.

Figure 58 Deformation at the first resonance peak (imaginary and real part respectively)

Chapter 5 Results

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Figure 59 Deformation at the second resonance peak (imaginary and real part respectively)

Figure 60 Deformation at the third resonance peak (imaginary and real part respectively)

N.B. the figure has a reversed x-axis compared to Figure 58 and Figure 59 for better visualization of the torsional mode form


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5.1.2 Sensitivity analysis results

A preliminary sensitivity analysis was performed prior to manual model updating to determine the influence of each material parameter on the resulting response of the bridge. Based on this, some of the material parameters were excluded from the model updating process and the rest of them were included with different variation range for each parameter.

The post calculations sensitivity analysis considered only the E-modulus of the two soil layers in the FE-model. The effect of the variation of the material parameters was monitored for all 15 sensors along the edge beams, wing walls and at the abutments. The variation of the soil E-modulus considered a big range of values to represent a good picture of the influence of the parameter. Each E-modulus was varied separately while keeping the other values constant, at the reference model value. E-moduli were varied gradually from a min. to a max. value with a constant step according to Table 6.

The frequency of the first resonance peak was determined from the FRF of sensor a3 for each of the E-modulus values. The damping associated with the resonance peak was calculated for the same sensor using a matlab script based on the half-power bandwidth method for calculating the damping ratio. The variation of the associated damping is not affected by the structural material damping assigned to each material, which remained fixed for the whole range of E-modulus variation.

Table 6 The variation of the E-modulus of the both soil layers showing min/max values and the step of variation in-between

Parameter Min. Max. Step

Es1 (MPa) 30 300 30

Es2 (MPa) 200 1500 100

A tighter variation step, 10 MPa, of the E-modulus of Soil layer 1 (Es1) was considered between 120 and 150 MPa due to the high proximity of the response curves to the field measured ones. This resulted in setting the reference value of Es1 to 130 MPa which showed the best agreement of the selected values with the field measured response curves.

The acceleration results shown in the sensitivity analysis plots are chosen to give a good representation of the whole bridge super- and substructure. The values are taken from accelerometers locations according to setup A (Figure 56). Accelerometers 2 and 3 are plotted along the span of the bridge, accelerometer 6 for the wing wall end plot and accelerometer 13 for the abutment vertical acceleration plot. The variation of the first resonant frequency and the associated damping are presented to show the effect of E-modulus variation. The updated values of Es1 and Es2 are denoted by a vertical dashed red line and the field measured values are represented by a red circle on all plots.

E s1 Sensitivity

The results of the variation of Es1 value shows that it has different effects on different parts of the bridge regarding the amplitudes of acceleration of the first resonance peak as shown in Figure 61.

Chapter 5 Results

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The initial steep decrease of the damping associated with the first resonance peak, up to ca. 90 MPa (Figure 62), has a significant effect on the amplitudes of acceleration at the bridge span and at the abutment (Figure 61) causing them to increase accordingly, the effect is more significant for higher amplitudes close to the mid-span of the bridge. The amplitudes are stabilized afterwards at the same values following the almost constant damping ratio of the first resonance peak.

Increasing the value of Es1 up to 90 MPa leads to a steep increase in the first resonance frequency as can be seen in Figure 62 due to the increase in the total stiffness of the model. The rate of the increase of the curve of the first resonance frequency gradually becomes less steep until it is levelled off approaching 300 MPa. This initial steep increase in frequency might be due to the big change in the movement constraint the wing walls and end shields of the bridge which in-turn affects the movement of the whole bridge.

Figure 61 Variation of E-modulus of soil 1 plotted against accelerations at the first resonance peak of sensors along span, wing wall end and abutment of the bridge with the field measured values indicated by a red circle. Two sensors are plotted along the span for different amplitudes of acceleration, showing a3 with higher amplitudes due to being closer to the mid-span of the bridge


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Figure 62 Variation of E-modulus of soil 1 plotted against frequency of the first resonance peak of the bridge and the damping associated with the peak. The field measured values are indicated by a red circle

E s2 Sensitivity

The role of soil layer 2, as can be interpreted from plotting the variation of Es2 against the amplitudes of acceleration, frequency of the first resonance peak and damping, is to act as a support layer for the rest of the Soil-Bridge system above.

This effect is clearly demonstrated by the amplitudes of acceleration of the abutment of the bridge (Figure 63). The initial increase in Es2 from 200 MPa, increased the movement constraint of the abutments causing the steep decline in the accelerations that can be seen in Figure 63. Furthermore, the curve grows softer and nearly stabilizes after ca. 800 MPa suggesting that the abutments are allowed almost no movements at all.

The effect of increasing Es2 has very negligible effect on the amplitudes of acceleration along the bridge span and at the wing wall end (Figure 63). This can probably by explained by the negligible effect of the variation of Es2 on the damping of the first resonance peak which is visible in Figure 64, hence not affecting the amplitudes of acceleration of the bridge body directly.

The effect of the variation of Es2 is almost diminished after 800 MPa which is a value, interpreted as, high enough to restrain the movement of the foundation and the bottom of the end shields to an almost zero movement, a state which continues to exist as Es2 increases even more.

Chapter 5 Results

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Figure 63 Variation of E-modulus of soil 2 plotted against accelerations of points along span, wing wall end and abutment of the bridge with the field measured values indicated by a red circle. Two sensors are plotted along the span for different amplitudes of acceleration, showing a3 with higher amplitudes due to being closer to the mid-span of the bridge

Figure 64 Variation of E-modulus of soil 2 plotted against frequency of the first resonance peak of the bridge and the damping associated with the peak. The field measured values are indicated by a red circle

5.2 2D beam model

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5.2 2D beam model

A 2D beam model of the single track railway bridge was developed using Abaqus to determine the material properties that can yield a dynamic behaviour as close as possible to the real bridge with such a simple model. The 2D beam model results will be compared to that of the 3D model and the field measured responses for comparison and model updating purposes. The accelerations result points are chosen to represent the same cross sections at which the accelerometers of the 3D Fe-model and field measured ones exist.

The bridge model is simply supported on a hinge and a roller support and the beam is extended for 1.7 m after each support to end at the outer surface of the end shields. A vertical spring/dashpot system is implemented at both ends of the beam to simplify the effect of the soil on the end shields, in terms of stiffness and damping (Figure 65).

The dimensions of the section of the 2D beam are reverse calculated to have a similar longitudinal moment of inertia as the 3D bridge deck. The unit mass of the section is calculated to include the mass of the concrete bridge deck and the ballast of the track as well. The masses of the wing walls and the end shields were lumped onto a 0.1 m distance from both ends of the beam as a simplification of the model. An Euler-Bernoulli linear beam element, B23, was used with a converged mesh size of 1 m.

The concrete section properties acquired from the 3D model updating process is assigned to the 2D concrete beam section with varying the masses of different areas to accommodate the ballast mass and the additional lumped mass of the wing walls and end shields.

The Direct steady state dynamic analysis was calculated between 0 and 25 Hz with a unit concentrated load as an exciting force at 2.55 m from the hinged support, the same cross sectional location of the exciting force in 3D model and full scale testing. The FRFs of four sensors on an edge beam along the bridge span from the full scale test and the 3D model, 2, 3, 4 and 5, were chosen to compare to the FRFs of the corresponding locations on the 2D beam model (Figure 66)

The values of the spring stiffness, Kv, and the dashpot coefficient, Cv, at the two ends of the beam were altered to find the combination that best matches the 3D model and field measured responses. This was controlled through the comparison of the three different FRFs at the four mentioned points. The model with the best fit FRFs was found to have Kv = 6.7 GN/m and Cv = 1.6 N/m/s obtained from the manual variation of the parameters to find the best match for the first resonance peak. The compared responses (Figure 66) showed that the 2D beam model matches perfectly with the 3D model and the field measured responses for the first resonance peak.

The measured bridge response showed that the second and the third resonance peaks were a combination of the second bending and the first torsional modes and cannot be represented using the simple 2D beam model at hand due to the absence of torsional loading. Nevertheless, with only vertical spring/dashpot system to compensate for the soil effect, the second resonance peak, which has lower contribution from the torsional mode, is comparable with ca. 10 % increase in frequency and significant increase in amplitude.

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Figure 65 2D beam model of the bridge with springs and dashpots at the ends. The locations of the calculated FRFs are shown as well

Figure 66 The best fit 2D beam model FRFs plotted against the reference 3D FE-model responses along with the field measured ones

Chapter 6 Conclusions and future research

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6 Conclusions and future research

6.1 Conclusions

The work presented in this thesis included the full scale dynamic testing of Aspan Bridge and the analysis of the responses from the controlled forced excitation of the bridge. The development of the 3D-FE model of the Bridge went through many stages. The first, pre-measurements, stage aimed to optimize and verify the most adequate model to simulate the full scale test results. This stage included comparing different modelling alternatives to reach a reference model for the Bridge.

The later, post-measurements, stage was the calibration and validation of the reference model using the full scale testing responses. The material parameters used in the model were preliminary assumed based on calculations and/or previous research, they were then updated through the model updating process to find the best match with the full scale test responses. Sensitivity analysis was performed for some soil parameters and the dynamic behaviour variation was studied. A 2D beam model was developed, using the updated material parameters from the 3D model, to compare it with the real dynamic response of the bridge. As a result, some conclusions have been reached and are summarized below:

· The material properties of the bridge’s concrete section can be assumed as

uncracked concrete under dynamic loading.

· The effect of the surrounding soil on the dynamic behaviour of the bridge can’t be

ignored especially for Bridges with large interaction surface like end-shield bridges. SSI for the end-shield bridges has a very significant effect on the response of the bridge regarding frequencies, amplitude of vibrations and the damping of the resonance peaks. The effects of the soil surrounding the end-shields differs from the effect of the soil under the foundations.

· The updated E-modulus for soil layers, of the 3D reference model, vary from the theoretically calculated ones, lower for layer 1 (130 MPa instead of ca. 230 MPa) and much higher for layer 2 (800 MPa instead of ca. 360 MPa). These differences might be a result of the uncertainty of the soil/bedrock profile and/or some of the modelling choices such as:

o The assumption of the constant material properties for each of the soil layers not taking into consideration the variation of these parameters along the depth of soil layer, especially closer to the soil surface as shown in Figure 3 and Figure 4

6.2 Future research

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o The choice of the interface between the 2 soil layers at the same level of the bottom of the end shields. Based on this choice, the very high E-modulus of layer 2 that restricts the vibration of the abutments’ foundations will have the same effect on the bottom of the end-shields and wing walls. This enforced a lower E-modulus for layer 1 allowing larger vibrations along the end-shields and wing walls to counteract the effect of the extra restriction on the response of the bridge.

o The ignored variation of the bedrock level in the bridge transverse direction, which can vary very rapidly as seen in the longitudinal direction, might increase significantly the average assumed value of E-modulus for layer 2.

· The 3D model of the Soil-Bridge system indicated that:

o Modelling of the ballast above the bridge deck as a separate element improved the accuracy of the responses, whereas the continuity of the ballast along the soil bank could be ignored.

o The soil length in the longitudinal direction of the bridge had significant effect on the accuracy of the response and the amount of reflected waves from the end boundaries into the model. It was enough to include soil with the same length of the bridge in both directions to fully damp the propagating waves from the bridge induced vibration. The soil in the transverse direction had lower significance requiring only to be modelled until the end of the slopes of the soil bank to give the same effect.

o The horizontal end boundary conditions of the modelled soil proved to have rather insignificant role for the response of Aspan Bridge with regards to the used model. This might be due to the full dissipation/low content of energy of the propagating waves before reaching the end boundaries.

o The bed rock level should be carefully assumed according to geotechnical reports in order to simulate the Soil-Bridge system more accurately. It should be treated as natural end boundaries for the soil as it affects the amount of reflected waves back into the system as well.

· The simple 2D beam model was only successful in matching the first peak of the bridge response but proved harder for the other peaks due to the lack of torsional effects simulation. It was distinctly affected by the variation of the stiffness of the end springs and the beam material damping. The end dashpot coefficient variation did not have the same effects.

6.2 Future research

· Studying other cases of end-shield bridges to be able to identify other aspects of their dynamic behaviour. This can include studying the effects of multiple spans, deeper soil layers under the bridge, piled foundations effects. A good case study can be Sidensjövägen Bridge which is an end shield bridge with three spans and one piled foundation.

Chapter 6 Conclusions and future research

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· Further study of the SSI effects on the end-shields and the wing walls separately. The connection between the soil and the end-shields can be defined in a different way from that between the soil and the wing walls to simulate more accurate behaviour under loading. The effect of the relative movement at the interfaces at higher amplitudes of vibration on the dynamic behaviour of the bridge can be interesting to study as well.

· More detailed modelling of the soil to simulate the rapid change of properties with the depth especially close to the surface as shown in Figure 4. The soil layer closer to the ground surface can be divided into more layers with different soil properties for more accurate responses of the system. Development of more efficient models for representing the changes in the soil E and ζ with the depth should also be

considered for implementation in FE-models.

· Considering the changes of the dynamic behaviour with the temperature variation: this can be studied by changing the stiffness of both the ballast and soil layers between summer and winter along with the associated damping, taking into consideration the effect of being frozen in winter. The effect of the cold temperature can be considered through studying the effect of the shrinkage of the soil in winter by decreasing the contact surface between the soil and both the end-shields and the wing walls, especially for shallow soil depths.

· Studying the train passage effects on the FE-models and comparing them with field measurements. HSLM train load models can be simulated on 3D FE-models of Soil-Bridge systems to study the responses of the bridges and their dynamic behaviour.

Bibliography

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Bibliography

Andersson, A. et al., 2015. Pilot testing of a hydraulic bridge exciter. MATEC Web of

Conferences, 24, p.2001.

Auersch, L., 2005. The excitation of ground vibration by rail traffic: Theory of vehicle-track-soil interaction and measurements of high-speed lines. Journal of Sound and Vibration, 284, pp.103–132.

Axelsson, E. et al., 2014. Effect of axle load spreading and support stiffness on the dynamic response of short span railway bridges. Structural Engineering International: Journal of

the International Association for Bridge and Structural Engineering (IABSE), 24(4), pp.457–465.

Banverket, 1997. BV Bro, Utgåva 4. Banverkets ändringar och tillägg till vägverkets BRO 94,

Banverket, 1999. BV Bro, Utgåva 5. Banverkets ändringar och tillägg till vägverkets BRO 94,

Banverket, 2002. BV Bro, Utgåva 6. Banverkets ändringar och tillägg till vägverkets Bro

2002,

Banverket, 2004. BV Bro, Utgåva 7. Banverkets ändringar och tillägg till vägverkets Bro

2004,

Botniabanan AB, 2004. Botniabanan, Saluböle - Rundvik, Järnvägsbro över Aspan vid AVA,

km 53+250, Beskrivning Geoteknik, handling 11.3.,

Brincker, R. & Ventura, C., 2015. Introduction to Operational Modal Analysis,

CEN, 2002. EN 1990 Eurocode - Basis of structural design,

CEN, 2003. Eurocode 1 : Actions on structures – Part 2 : Traffic loads on bridges. SS-EN

1991-2,

Clayton, C.R.I., 2011. Stiffness at small strains Research and practice. Geotechnique, 61(1), pp.5–37.

Cohen, M. & Jennings, P.C., 1983. Silent boundary methods for transient Analysis. In Computational methods for transient analysis. pp. 301–360.

Colibrys, 2013. SF1500S.A accelerometer datasheet.

Dassault Systemes Simulia Corp., 2014. Abaqus 6.14-1, Abaqus Analysis User’s Guide,

section 28.3 Infinite elements.

Bibliography

74

Degrande, G., 2000. Free vibration measurements during the passage of a Thalys high speed

train, Internal report BMW-2000-06,

Degrande, G. & Schillemans, L., 2001. Free Field Vibrations During the Passage of a Thalys High-Speed Train At Variable Speed. Journal of Sound and Vibration, 247(1), pp.131–

144.

ERRI, 1999. RAIL BRIDGES FOR SPEEDS > 200 KM / H Final report,

Galvin, P. & Dominguez, J., 2007. High-speed train-induced ground motion and interaction with structures. Journal of Sound and Vibration, 307(3–5), pp.755–777.

Gazetas, G. & Dobry, R., 1984. Simple Radiation Damping Model for Piles and Footings. Journal of Engineering Mechanics, 110(1), pp.937–956.

Hall, L., 2002. Simulations and analyses of train-induced ground vibrations. KTH.

Hardin, B.O., 1970. The Nature of Stess-Strain Behavior for Soils. In ASCE.

Hardin, B.O. & Drnevich, V.P., 1970. Shear modulus and damping in soils: I- Measurement

and Parameter effects, II- Design equations,

James, G. et al., 2005. Measuring the Dynamic Properties of Bridges on the Bothnia Line,

Johansson, C., Andersson, A., et al., 2013. Järnvägsbroar på botniabanan, Dynamiska

kontroller för framtida höghastighetståg - Steg 1,

Johansson, C. et al., 2012. Probabilistic Dynamic Analysis of Existing Railway Bridges for High-Speed Traffic. Engineering Structure.

Johansson, C., Pacoste, C. & Karoumi, R., 2013. Closed-form solution for the mode superposition analysis of the vibratoin in multi-span beam caused by concentrated moving loads. Computers and Structures, 119.

Karoumi, R. & Wiberg, J., 2006. Kontroll av dynamiska effekter av passerande tåg på

Botniabanan broar - Sammanfattning,

Kausel, E., 2010. Early history of soil-structure interaction. Soil Dynamics and Earthquake

Engineering, 30(9), pp.822–832. Available at: http://dx.doi.org/10.1016/j.soildyn.2009.11.001.

Kotronis, P., Tamagnini, C. & Grange, S., 2013. Soil-Structure Interaction. Alert Doctoral School.

Liu, K. et al., 2009. Experimental and numerical analysis of a composite bridge for high-speed trains. Journal of Sound and Vibration, 320(1–2), pp.201–220. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0022460X08006329 [Accessed September 18, 2014].

Lysmer, J. & Kuhlemeyer, R.L., 1969. Finite Dynamic Model for Infinite Media. Journal of

Engineering Mechanics, (Div. ASCE), pp.859–877.

Bibliography

75

Madshus, C. & Kaynia, A.M., 2000. High-speed railway lines on soft ground: dnamics behaviour of criticalttrain speed. the journal of sound and vibration, 231, pp.689–701.

Massarsch, K.R., 2004. Deformation properties of fine-grained soils from seismic tests. Proceedings. Available at: http://geotechref.coppernorthern.com/library/Massarsch_2004-DeformationPropertiesSeismic.pdf [Accessed November 25, 2014].

Möller, B. et al., 2000. Information 17, Geodynamik i praktiken,

MTS systems, 2011. https://www.mts.com/ucm/groups/public/documents/library/dev_002696.pdf.

Rollins, K.M. et al., 1998. Shear Modulus and Damping Relationsidps for Gravels. Journal of

Geotechnical and Geoenvironmental Engineering, 124(5), pp.396–405.

Seed, H.B. et al., 1986. Moduli and damping factors for dynamic analyses of cohesionless soils. Journal of Geotechnical Engineering, 112(11), pp.1016–1032.

Seed, H.B. & Idriss, I.M., 1970. Soil moduli and damping factors for dynamic response analysis. Journal of Terramechanics, 8(3), p.109. Available at: papers3://publication/uuid/421C1337-8F56-4D82-9224-21A8F4465EFD%5Cnhttp://linkinghub.elsevier.com/retrieve/pii/0022489872901103.

Sezawa, K. & Kanai, K., 1935a. Decay in the seismic vibration of a simple or tall structure by dissipation of their energy into the ground. In bulletin of the earthquake research

institute, Japan, 13. pp. 681–696.

Sezawa, K. & Kanai, K., 1935b. Energy dissipation in seismic vibration of a framed structure. In bulletin of the earthquake research institute, Japan, 13. pp. 68–714.

Sezawa, K. & Kanai, K., 1935c. Energy dissipation in seismic vibration of actual buildings. In bulletin of the earthquake research institute, Japan, 13. pp. 925–941.

Structural Vibration Solutions A/S, 2005. ARTeMIS Extractor Pro, Release 3.5.

Structural Vibration Solutions A/S, 2016. http://www.svibs.com/products/ARTeMIS_Modal.aspx.

The Mathworks inc., 2013. MATLAB R2013b.

Trafikverket, 2016a. http://www.trafikverket.se/nara-dig/Sodermanland/projekt-i-sodermanlands-lan/Ostlanken/Om-projektet-Ostlanken-/.

Trafikverket, 2016b. http://www.trafikverket.se/resa-och-trafik/jarnvag/Sveriges-jarnvagsnat/.

Trafikverket, 2013. www.trafikverket.se/tjanster/system-och-verktyg/forvaltning-och-underhall/BIS---Baninformation/.

UIC International union of Railways, 2016a. http://www.uic.org/High-Speed-History.

UIC International union of Railways, 2016b. http://www.uic.org/highspeed.

Bibliography

76

Ülker-kaustell, M., 2009. Some aspects of the dynamic soil-structure interaction of a portal

frame railway bridge. Available at: http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:Some+aspects+of+the+dynamic+soil-structure+interaction+of+a+portal+frame+railway+bridge#0 [Accessed October 27, 2014].

Wolf, J.P. & Song, C., 2002. Some cornerstones of dynamic soil – structure interaction. Engineering Structures, 24, pp.13–28. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0141029601000827.

Zienkiewicz, O.C., Emson, C. & Bettess, P., 1983. A novel boundary infinite element. International Journal for numerical methods in Engineering, 19(3), pp.393–404.

77

Appendix A: Results from full scale

testing

Appendix A: Results from full scale testing

78

EFDD mode shapes:

Figure 67 EFDD first bending mode f = 6.59 Hz, ξ = 1.48 %

Figure 68 EFDD Second bending/First torsional mode f = 18.1 Hz, ξ = 1.86 %

Figure 69 EFDD First torsional/ Second bending mode f = 18.73 Hz, ξ = 2.2 %

79

Table 7 The full frequency sweeps performed in the full scale test for both setups and train passages

filnamn: setup: Famp (kN) fmin (Hz) fmax (Hz) df (Hz/s) t (min)

Asp_A1 A 20 1 23 0,05 7,3

Asp_A1x A, B 5 1 50 0,05 16,3

Asp_A3x A, B 5 3 12 0,02 7,5

Asp_A4 A, B 5 3 12 0,01 15,0

Asp_A5 A, B 10 3 12 0,02 7,5

Asp_A9 A, B 5 10 27 0,02 14,2

Asp_A11 A 5 25 37 0,01 20,0

Asp_A12 A,B 5 25 37 0,02 10,0

Asp_A16 A, B 5 35 50 0,02 12,5

Asp_B17 B 10 25 37 0,02 10,0

Asp_B18 B 10 10 27 0,02 14,2

80

Table 8 Setup A measurements log

Dag kl. filnamn: setup: Fpre (kN) Famp (kN) fmin (Hz) fmax (Hz) df (Hz/s) t (min) Notering

28-sep Asp_A1 A 25 20 1 50 0,05 16,3

28-sep 14:50 - 15:01 Asp_A1x A 10 5 1 50 0,05 16,3

28-sep 15:19 - 15:22 Asp_A2 A 10 5 3 12 0,05 3,0

28-sep 15:26 - 15:33 Asp_A3 A 10 5 3 12 0,02 7,5

29-sep 10:03 - 10:10 Asp_A3x A 10 5 3 12 0,02 7,5 mätat tåg passage norrut kl. 10:18

28-sep 15:35 - 15:51 Asp_A4 A 10 5 3 12 0,01 15,0 oväntad tåg pass kl. 15:43 norrut

28-sep 15:53 - 15:59 Asp_A4x A 10 5 5 9 0,01 6,7 för att kompensera tåg passage

29-sep 12:06 - 12:14 Asp_A5 A 15 10 3 12 0,02 7,5

29-sep 10:26 - 10:55 Asp_A8 A 10 5 10 27 0,01 28,3

28-sep 16:26- 16:41 Asp_A9 A 10 5 10 26,95 0,02 14,1 mätat tåg passage norrut kl. 16:41

29-sep 10:57 - 11:18 Asp_A11 A 10 5 25 37 0,01 20,0 mätat tåg passage norrut kl. 11:39

28-sep 16:46 - 16:57 Asp_A12 A 10 5 25 37 0,02 10,0

29-sep 11:44 - 11.57 Asp_A16 A 10 5 35 50 0,02 12,5 mätat tåg passage söderut kl. 11:59

28-sep 16:15 Asp_AT1 A tåg passage söderut

81

Table 9 Setup B measurements log

Dag kl. filnamn: setup: Fpre (kN) Famp (kN) fmin (Hz) fmax (Hz) df (Hz/s) t (min) Notering

29-sep 12:33 - 12:50 Asp_B1 B 10 5 1 50 0,05 16,3

29-sep 12:55 - 13:03 Asp_B3 B 10 5 3 12 0,02 7,5 mätat tåg passage söderut kl. 13:20

29-sep 13:25 - 13:44 Asp_B4 B 10 5 3 12 0,01 15,0

29-sep 13:43 - 13:51 Asp_B5 B 15 10 3 12 0,02 7,5

29-sep 13:54 - 14:09 Asp_B9 B 10 5 10 27 0,02 14,2

29-sep 14:10 - 14:20 Asp_B12 B 10 5 25 37 0,02 10,0 oväntad tåg passage RC4loq kl. 14:15

29-sep 14:22 - 14:32 Asp_B12x B 10 5 25 37 0,02 10,0 omkörning eftersom tåg passage

29-sep 14:47:_ Asp_B16 B 10 5 35 50 0,02 12,5 mätat tåg passage norrut kl. 14:57

29-sep 14:59 - 15:12 Asp_B16x B 10 5 35 50 0,02 12,5

29-sep 14:33 - 14:44 Asp_B17 B 15 10 25 37 0,02 10,0

29-sep 15:14 - 15:28 Asp_B18 B 15 10 10 27 0,02 14,2 mätat tåg passage kl. 15:43

83

Appendix B: Results from FE-

modelling

Appendix B: Results from FE-modelling

84

Figure 70 Imaginary part of the deformation at the second resonance peak (18 Hz) corresponding to a second bending mode form

Figure 71 Real parts of the deformation around the second resonance peak showing higher values and a considerable change of form at different values (17.8, 18 and 18.2 Hz respectively). Maximum deformations are almost 70% higher at a slightly higher frequency than that determined by the imaginary part of the response with a change in its location as well

85

Figure 72 Imaginary part of the deformation at the third resonance peak (19 Hz) corresponding to a first torsional mode form

Figure 73 Real part of the deformation around the third resonance peak showing higher values and a considerable change of form at different values (18.8, 19 and 19.2 Hz respectively). Maximum deformations are almost doubled at slightly lower and higher frequencies than that determined by the imaginary part of the response with a change in its location as well

87

List of Bulletins from the Department of Structural Engineering, The Royal Institute of Technology, Stockholm

TRITA-BKN. Bulletin Pacoste, C., On the Application of Catastrophe Theory to Stability Analyses of Elastic Structures. Doctoral Thesis, 1993. Bulletin 1. Stenmark, A-K., Dämpning av 13 m lång stålbalk - "Ullevibalken". Utprovning av dämpmassor och fastsättning av motbalk samt experimentell bestämning av modformer och förlustfaktorer. Vibration tests of full-scale steel girder to determine optimum passive control. Licentiatavhandling, 1993. Bulletin 2. Silfwerbrand, J., Renovering av asfaltgolv med cementbundna plastmodifierade avjämningsmassor. 1993. Bulletin 3. Norlin, B., Two-Layered Composite Beams with Nonlinear Connectors and Geometry - Tests and Theory. Doctoral Thesis, 1993. Bulletin 4. Habtezion, T., On the Behaviour of Equilibrium Near Critical States. Licentiate Thesis, 1993. Bulletin 5. Krus, J., Hållfasthet hos frostnedbruten betong. Licentiatavhandling, 1993. Bulletin 6.

Wiberg, U., Material Characterization and Defect Detection by Quantitative Ultrasonics. Doctoral Thesis, 1993. Bulletin 7. Lidström, T., Finite Element Modelling Supported by Object Oriented Methods. Licentiate Thesis, 1993. Bulletin 8. Hallgren, M., Flexural and Shear Capacity of Reinforced High Strength Concrete Beams without Stirrups. Licentiate Thesis, 1994. Bulletin 9. Krus, J., Betongbalkars lastkapacitet efter miljöbelastning. 1994. Bulletin 10. Sandahl, P., Analysis Sensitivity for Wind-related Fatigue in Lattice Structures. Licentiate Thesis, 1994. Bulletin 11. Sanne, L., Information Transfer Analysis and Modelling of the Structural Steel Construction Process. Licentiate Thesis, 1994. Bulletin 12. Zhitao, H., Influence of Web Buckling on Fatigue Life of Thin-Walled Columns. Doctoral Thesis, 1994. Bulletin 13. Kjörling, M., Dynamic response of railway track components. Measurements during train passage and dynamic laboratory loading. Licentiate Thesis, 1995. Bulletin 14. Yang, L., On Analysis Methods for Reinforced Concrete Structures. Doctoral Thesis, 1995. Bulletin 15. Petersson, Ö., Svensk metod för dimensionering av betongvägar. Licentiatavhandling, 1996. Bulletin 16. Lidström, T., Computational Methods for Finite Element Instability Analyses. Doctoral Thesis, 1996. Bulletin 17.

88

Krus, J., Environment- and Function-induced Degradation of Concrete Structures. Doctoral Thesis, 1996. Bulletin 18. Editor, Silfwerbrand, J., Structural Loadings in the 21st Century. Sven Sahlin Workshop, June 1996. Proceedings. Bulletin 19. Ansell, A., Frequency Dependent Matrices for Dynamic Analysis of Frame Type Structures. Licentiate Thesis, 1996. Bulletin 20.

Troive, S., Optimering av åtgärder för ökad livslängd hos infrastrukturkonstruktioner. Licentiatavhandling, 1996. Bulletin 21. Karoumi, R., Dynamic Response of Cable-Stayed Bridges Subjected to Moving Vehicles. Licentiate Thesis, 1996. Bulletin 22. Hallgren, M., Punching Shear Capacity of Reinforced High Strength Concrete Slabs. Doctoral Thesis, 1996. Bulletin 23. Hellgren, M., Strength of Bolt-Channel and Screw-Groove Joints in Aluminium Extrusions. Licentiate Thesis, 1996. Bulletin 24. Yagi, T., Wind-induced Instabilities of Structures. Doctoral Thesis, 1997. Bulletin 25. Eriksson, A., and Sandberg, G., (editors), Engineering Structures and Extreme Events - proceedings from a symposium, May 1997. Bulletin 26. Paulsson, J., Effects of Repairs on the Remaining Life of Concrete Bridge Decks. Licentiate Thesis, 1997. Bulletin 27. Olsson, A., Object-oriented finite element algorithms. Licentiate Thesis, 1997. Bulletin 28. Yunhua, L., On Shear Locking in Finite Elements. Licentiate Thesis, 1997. Bulletin 29. Ekman, M., Sprickor i betongkonstruktioner och dess inverkan på beständigheten. Licentiate Thesis, 1997. Bulletin 30. Karawajczyk, E., Finite Element Approach to the Mechanics of Track-Deck Systems. Licentiate Thesis, 1997. Bulletin 31. Fransson, H., Rotation Capacity of Reinforced High Strength Concrete Beams. Licentiate Thesis, 1997. Bulletin 32. Edlund, S., Arbitrary Thin-Walled Cross Sections. Theory and Computer Implementation. Licentiate Thesis, 1997. Bulletin 33. Forsell, K., Dynamic analyses of static instability phenomena. Licentiate Thesis, 1997. Bulletin 34. Ikäheimonen, J., Construction Loads on Shores and Stability of Horizontal Formworks. Doctoral Thesis, 1997. Bulletin 35. Racutanu, G., Konstbyggnaders reella livslängd. Licentiatavhandling, 1997. Bulletin 36. Appelqvist, I., Sammanbyggnad. Datastrukturer och utveckling av ett IT-stöd för byggprocessen. Licentiatavhandling, 1997. Bulletin 37.

89

Alavizadeh-Farhang, A., Plain and Steel Fibre Reinforced Concrete Beams Subjected to Combined Mechanical and Thermal Loading. Licentiate Thesis, 1998. Bulletin 38. Eriksson, A. and Pacoste, C., (editors), Proceedings of the NSCM-11: Nordic Seminar on Computational Mechanics, October 1998. Bulletin 39. Luo, Y., On some Finite Element Formulations in Structural Mechanics. Doctoral Thesis, 1998. Bulletin 40. Troive, S., Structural LCC Design of Concrete Bridges. Doctoral Thesis, 1998. Bulletin 41. Tärno, I., Effects of Contour Ellipticity upon Structural Behaviour of Hyparform Suspended Roofs. Licentiate Thesis, 1998. Bulletin 42. Hassanzadeh, G., Betongplattor på pelare. Förstärkningsmetoder och dimensioneringsmetoder för plattor med icke vidhäftande spännarmering. Licentiatavhandling, 1998. Bulletin 43. Karoumi, R., Response of Cable-Stayed and Suspension Bridges to Moving Vehicles. Analysis methods and practical modeling techniques. Doctoral Thesis, 1998. Bulletin 44. Johnson, R., Progression of the Dynamic Properties of Large Suspension Bridges during Construction - A Case Study of the Höga Kusten Bridge. Licentiate Thesis, 1999. Bulletin 45. Tibert, G., Numerical Analyses of Cable Roof Structures. Licentiate Thesis, 1999. Bulletin 46. Ahlenius, E., Explosionslaster och infrastrukturkonstruktioner - Risker, värderingar och kostnader. Licentiatavhandling, 1999. Bulletin 47. Battini, J-M., Plastic instability of plane frames using a co-rotational approach. Licentiate Thesis, 1999. Bulletin 48. Ay, L., Using Steel Fiber Reinforced High Performance Concrete in the Industrialization of Bridge Structures. Licentiate Thesis, 1999. Bulletin 49. Paulsson-Tralla, J., Service Life of Repaired Concrete Bridge Decks. Doctoral Thesis, 1999. Bulletin 50. Billberg, P., Some rheology aspects on fine mortar part of concrete. Licentiate Thesis, 1999. Bulletin 51. Ansell, A., Dynamically Loaded Rock Reinforcement. Doctoral Thesis, 1999. Bulletin 52. Forsell, K., Instability analyses of structures under dynamic loads. Doctoral Thesis, 2000. Bulletin 53. Edlund, S., Buckling of T-Section Beam-Columns in Aluminium with or without Transverse Welds. Doctoral Thesis, 2000. Bulletin 54. Löfsjögård, M., Functional Properties of Concrete Roads − General Interrelationships and Studies on Pavement

Brightness and Sawcutting Times for Joints. Licentiate Thesis, 2000. Bulletin 55.

90

Nilsson, U., Load bearing capacity of steel fibree reinforced shotcrete linings. Licentiate Thesis, 2000. Bulletin 56. Silfwerbrand, J. and Hassanzadeh, G., (editors), International Workshop on Punching Shear Capacity of RC Slabs − Proceedings. Dedicated to Professor Sven Kinnunen. Stockholm June 7-9, 2000. Bulletin 57. Wiberg, A., Strengthening and repair of structural concrete with advanced, cementitious composites. Licentiate Thesis, 2000. Bulletin 58. Racutanu, G., The Real Service Life of Swedish Road Bridges - A case study. Doctoral Thesis, 2000. Bulletin 59. Alavizadeh-Farhang, A., Concrete Structures Subjected to Combined Mechanical and Thermal Loading. Doctoral Thesis, 2000. Bulletin 60. Wäppling, M., Behaviour of Concrete Block Pavements - Field Tests and Surveys. Licentiate Thesis, 2000. Bulletin 61. Getachew, A., Trafiklaster på broar. Analys av insamlade och Monte Carlo genererade fordonsdata. Licentiatavhandling, 2000. Bulletin 62. James, G., Raising Allowable Axle Loads on Railway Bridges using Simulation and Field Data. Licentiate Thesis, 2001. Bulletin 63. Karawajczyk, E., Finite Elements Simulations of Integral Bridge Behaviour. Doctoral Thesis, 2001. Bulletin 64. Thöyrä, T., Strength of Slotted Steel Studs. Licentiate Thesis, 2001. Bulletin 65. Tranvik, P., Dynamic Behaviour under Wind Loading of a 90 m Steel Chimney. Licentiate Thesis, 2001. Bulletin 66. Ullman, R., Buckling of Aluminium Girders with Corrugated Webs. Licentiate Thesis, 2002. Bulletin 67. Getachew, A., Traffic Load Effects on Bridges. Statistical Analysis of Collected and Monte Carlo Simulated Vehicle Data. Doctoral Thesis, 2003. Bulletin 68. Quilligan, M., Bridge Weigh-in-Motion. Development of a 2-D Multi-Vehicle Algorithm. Licentiate Thesis, 2003. Bulletin 69. James, G., Analysis of Traffic Load Effects on Railway Bridges. Doctoral Thesis 2003. Bulletin 70. Nilsson, U., Structural behaviour of fibre reinforced sprayed concrete anchored in rock. Doctoral Thesis 2003. Bulletin 71. Wiberg, A., Strengthening of Concrete Beams Using Cementitious Carbon Fibre Composites. Doctoral Thesis 2003. Bulletin 72. Löfsjögård, M., Functional Properties of Concrete Roads – Development of an Optimisation Model and Studies on Road Lighting Design and Joint Performance. Doctoral Thesis 2003. Bulletin 73. Bayoglu-Flener, E., Soil-Structure Interaction for Integral Bridges and Culverts. Licentiate Thesis 2004. Bulletin 74.

91

Lutfi, A., Steel Fibrous Cement Based Composites. Part one: Material and mechanical properties. Part two: Behaviour in the anchorage zones of prestressed bridges. Doctoral Thesis 2004. Bulletin 75. Johansson, U., Fatigue Tests and Analysis of Reinforced Concrete Bridge Deck Models. Licentiate Thesis 2004. Bulletin 76. Roth, T., Langzeitverhalten von Spannstählen in Betonkonstruktionen. Licentitate Thesis 2004. Bulletin 77. Hedebratt, J., Integrerad projektering och produktion av industrigolv – Metoder för att förbättra kvaliteten. Licentiatavhandling, 2004. Bulletin 78. Österberg, E., Revealing of age-related deterioration of prestressed reinforced concrete containments in nuclear power plants – Requirements and NDT methods. Licentiate Thesis 2004. Bulletin 79. Broms, C.E., Concrete flat slabs and footings New design method for punching and detailing for ductility. Doctoral Thesis 2005. Bulletin 80. Wiberg, J., Bridge Monitoring to Allow for Reliable Dynamic FE Modelling - A Case Study of the New Årsta Railway Bridge. Licentiate Thesis 2006. Bulletin 81. Mattsson, H-Å., Funktionsentreprenad Brounderhåll – En pilotstudie i Uppsala län. Licentiate Thesis 2006. Bulletin 82. Masanja, D. P, Foam concrete as a structural material. Doctoral Thesis 2006. Bulletin 83. Johansson, A., Impregnation of Concrete Structures – Transportation and Fixation of Moisture in Water Repellent Treated Concrete. Licentiate Thesis 2006. Bulletin 84. Billberg, P., Form Pressure Generated by Self-Compacting Concrete – Influence of Thixotropy and Structural Behaviour at Rest. Doctoral Thesis 2006. Bulletin 85. Enckell, M., Structural Health Monitoring using Modern Sensor Technology – Long-term Monitoring of the New Årsta Railway Bridge. Licentiate Thesis 2006. Bulletin 86. Söderqvist, J., Design of Concrete Pavements – Design Criteria for Plain and Lean Concrete. Licentiate Thesis 2006. Bulletin 87. Malm, R., Shear cracks in concrete structures subjected to in-plane stresses. Licentiate Thesis 2006. Bulletin 88. Skoglund, P., Chloride Transport and Reinforcement Corrosion in the Vicinity of the Transition Zone between Substrate and Repair Concrete. Licentiate Thesis 2006. Bulletin 89. Liljencrantz, A., Monitoring railway traffic loads using Bridge Weight-in-Motion. Licentiate Thesis 2007. Bulletin 90. Stenbeck, T., Promoting Innovation in Transportation Infrastructure Maintenance – Incentives, Contracting and Performance-Based Specifications. Doctoral Thesis 2007. Bulletin 91

92

Magnusson, J., Structural Concrete Elements Subjected to Air Blast Loading. Licentiate Thesis 2007. Bulletin 92. Pettersson, L., G., Full Scale Tests and Structural Evaluation of Soil Steel Flexible Culverts with low Height of Cover. Doctoral Thesis 2007. Bulletin 93 Westerberg, B., Time-dependent effects in the analysis and design of slender concrete compression members. Doctoral Thesis 2008. Bulletin 94 Mattsson, H-Å, Integrated Bridge Maintenance. Evaluation of a pilot project and future perspectives. Doctoral Thesis 2008. Bulletin 95 Andersson, A., Utmattningsanalys av järnvägsbroar. En fallstudie av stålbroarna mellan Stockholm Central och Söder Mälarstrand, baserat på teoretiska analyser och töjningsmätningar. Licentiate Thesis 2009. Bulletin 96 Malm, R., Predicting shear type crack initiation and growth in concrete with non-linear finite element method. Doctoral Thesis 2009. Bulletin 97 Bayoglu Flener, E., Static and dynamic behavior of soil-steel composite bridges obtained by field testing. Doctoral Thesis 2009. Bulletin 98 Gram, A., Numerical Modelling of Self-Compacting Concrete Flow Licentiate Thesis 2009. Bulletin 99 Wiberg, J., Railway bridge response to passing trains. Measurements and FE model updating. Doctoral Thesis 2009. Bulletin 100 Athuman M.K. Ngoma, Characterisation and Consolidation of Historical Lime Mortars in Cultural Heritage Buildings and Associated Structures in East Africa. Doctoral Thesis 2009. Bulletin 101 Ülker-Kaustell, M., Some aspects of the dynamic soil-structure interaction of a portal frame railway bridge. Licentiate Thesis 2009. Bulletin 102 Vogt, C., Ultrafine particles in concrete Doctoral Thesis 2010. Bulletin 103 Selander, A., Hydrophobic Impregnation of Concrete Structures Doctoral Thesis 2010. Bulletin 104 Ilina, E., Understanding the application of knowledge management to safety critical facilities Doctoral Thesis 2010. Bulletin 105 Leander, J., Improving a bridge fatigue life prediction by monitoring Licentiate Thesis 2010. Bulletin 106 Andersson, A., Capacity assessment of arch bridges with backfill – Case of the old Årsta railway bridge Doctoral Thesis 2011. Bulletin 107 Enckell, M., Lessons Learned in Structural Health Monitoring of Bridges Using Advanced Sensor Technology Doctoral Thesis 2011. Bulletin 108 Hansson, H., Warhead penetration in concrete protective structures Licentiate Thesis 2011. Bulletin 109 Gonzalez Silva, I., Study and Application of Modern Bridge Monitoring Techniques Licentiate Thesis 2011. Bulletin 110

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Safi, M., LCC Applications for Bridges and Integration with BMS Licentiate Thesis 2012. Bulletin 111 Guangli, D., Towards sustainable construction, life cycle assessment of railway bridges Licentiate Thesis 2012. Bulletin 112 Hedebratt, J., Industrial Fibre Concrete Slabs – Experiences and Tests on Pile-Supported Slab Doctoral Thesis 2012. Bulletin 113 Ahmed, L., Models for analysis of shotcrete on rock exposed to blasting Licentiate Thesis 2012. Bulletin 114 Le, T., N., Corotational formulation for nonlinear dynamic analysis of flexible beam structures Licentiate Thesis 2012. Bulletin 115 Johansson, C., Simplified dynamic analysis of railway bridges under high-speed trains Licentiate Thesis 2013. Bulletin 116 Jansson, R., Fire Spalling of Concrete – Theoretical and Experimental Studies Doctoral Thesis 2013. Bulletin 117 Leander, J., Refining the fatigue assessment procedure of existing steel bridges Doctoral Thesis 2013. Bulletin 118 Le, T., N., Nonlinear dynamics of flexible structures using corotational beam elements Doctoral Thesis 2013. Bulletin 119 Ülker-Kaustell, M., Essential modelling details in dynamic FE-analyses of railway bridges Doctoral Thesis 2013. Bulletin 120 Safi, M., Life-Cycle Costing. Applications and Implementations in Bridge Investment and Management Doctoral Thesis 2013. Bulletin 121 Arvidsson, T., Train-Bridge Interaction: Literature Review and Parameter Screening Licentiate Thesis 2014. Bulletin 122 Rydell, C., Seismic high-frequency content loads on structures and components within nuclear facilities Licentiate Thesis 2014. Bulletin 123 Bryne, L. E., Time dependent material properties of shotcrete for hard rock tunnelling Doctoral Thesis 2014. Bulletin 124 Wennström, J., Life Cycle Costing in Road Planning and Management: A Case Study on Collisionfree Roads Licentiate Thesis 2014. Bulletin 125 Gonzalez Silva, I., Application of monitoring to dynamic characterization and damage detection in bridges Doctoral Thesis 2014. Bulletin 126 Sangiorgio, F., Safety Format for Non-linear Analysis of RC Structures Subjected to Multiple Failure Modes Doctoral Thesis 2015. Bulletin 127 Gram, A., Modelling of Cementitious Suspensial Flow – Influence of Viscosity and Aggregate Properties Doctoral Thesis 2015. Bulletin 128 Du, G., Life Cycle Assessment of bridges, model development and Case Studies Doctoral Thesis 2015. Bulletin 129 Zhu, J., Towards a Viscoelastic Model for Phase Separation in Polymer Modified Bitumen Licentiate Thesis 2015. Bulletin 130

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Chen, F., The Future of Smart Road Infrastructure. A Case Study for the eRoad. Licentiate Thesis 2015. Bulletin 131 Ahmed, L., Models for analysis of young cast and sprayed concrete subjected to impact-type loads Doctoral Thesis 2015. Bulletin 132 Albrektsson, J., Durability of Fire Exposed Concrete – Experimental Studies Focusing on Stiffness & Transport Properties Licentiate Thesis 2015. Bulletin 133 Wallin, J., Systematic planning and execution of finite element model updating Licentiate Thesis 2015. Bulletin 134 Wadi, A.,Flexible Culverts in Sloping Terrain Licentiate Thesis 2015. Bulletin 135 McCarthy, R., Self-Compacting Concrete for Improved Construction Technology Licentiate Thesis 2015. Bulletin 136 Veganzones Munõs,J.J., Bridge Edge Beams: LCCA and Structural Analysis for the Evaluation of New Concepts Licentiate Thesis 2016. Bulletin 137 Abbasiverki, R., Analysis of underground concrete pipelines subjected to seismic high-frequency loads Licentiate Thesis 2016. Bulletin 138 Gasch, T., Concrete as a multi-physical material with applications to hydro power facilities Licentiate Thesis 2016. Bulletin 139 Ali, M., M., Use of Macro Basalt Fibre Concrete for Marine Applications Licentiate Thesis 2016. Bulletin 140 Döse, M., Ionizing Radiation in Concrete and Concrete Buildings – Empirical Assessment Licentiate Thesis 2016. Bulletin 141 Khan, A., Fundamental investigation to improve the quality of cold mix asphalt Licentiate Thesis 2016. Bulletin 142 Zhu, J., Storage Stability and Phase Separation Behaviour of Polymer-Modified Bitumen Doctoral Thesis 2016. Bulletin 143 Chen, F., Sustainable Implementation of Electrified Roads Doctoral Thesis 2016. Bulletin 144 Svedholm, C., Efficient modelling techniques for vibration analyses of railway bridges Doctoral Thesis 2017. Bulletin 145 Solat Yavari, M., Slab Frame Bridges, Structural Optimization Considering Investment Cost and Environmental Impacts Licentiate Thesis 2017. Bulletin 146 Tell, S., Vibration mitigation of high-speed railway bridges, Application of fluid viscous dampers Licentiate Thesis 2017. Bulletin 147 The department also publishes other series. For full information see our homepage http://www.byv.kth.se

End-Shield Bridges for High- Speed Railway1086102/FULLTEXT02.pdf · HESHAM ELGAZZAR Licentiate...

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