Finite element simulation of a pre-stressed concrete girder bridge: influences of construction stages and ground settlements on Gruvbron in Kiruna

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2009:151 CIV

M A S T E R ' S T H E S I S

Finite Element Simulation of a Pre-stressed Concrete Girder Bridge

Influences of Construction Stages and Ground Settlements on Gruvbron in Kiruna

Antoni Galí Isus

Luleå University of Technology

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Division of Structural Engineering

Department of Civil, Mining and Environmental Engineering Luleå University of Technology

MASTER'S THESIS

Finite Element Simulation of a Pre-stressed Concrete Girder Bridge

Influences of Construction Stages and Ground Settlements on Gruvbron in Kiruna

Antoni Gali Isus

Luleå 2009

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FE-Simulation of a Pre-stressed Concrete Girder Bridge – Influences of Construction Stages and Ground Settlements on Gruvbron in Kiruna Antoni Gali Isus

Master's Thesis 2009:151 ISSN 1402-1617

1^st Edition

Department of Civil, Mining and Environmental Engineering Luleå University of Technology

SE-971 87 LULEÅ, SWEDEN Telephone: + 46 (0)920 491 363

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Preface

This thesis completes six years of my studies. It has been a long way until I can write these words. The first five years I spent in Escola Tècnica Superior d’Enginyers Industrials de Barcelona (ETSEIB) in Universitat Politècnica de Catalunya (UPC) and the last one in Luleå University of Technology. This last year has definitely been the most exciting during my studies full of experiences to keep in my mind for all my life.

This thesis would not see the daylight without people who were helping me as my advisor Ola Enochsson. He always had time to discuss and help me with my questions. Lennart Elfgren gave me the possibility to write this thesis and graduate as an engineer and gave me the interest in bridges and the knowledge necessary to not be lost during the work.

I also want to thank my teachers in Barcelona, all of them, who gave me knowledge enough to become an engineer, specially my teachers in structures Joan Bisbal and Frederic Marimon, who passed on to me their interest in design of structures in concrete and steel respectively.

Luleå in January 2009 Antoni Gali Isus

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FE-Simulation of a Pre-stressed Concrete Girder Bridge

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Abstract

Due to mining operations, cracks are formed in the bedrock under the city of Kiruna in the northern part of Sweden. Therefore, the city, and the railway through it, is planned to be moved. A bridge – the Mine Bridge (Gruvbron) - overpasses the railway some distance south of the Kiruna railway station and connects the city centre to the mine. The bridge was built in 1960 and has five spans of pre-stressed concrete girders carrying a concrete slab. Cracking has been observed in the bottom part of the girder of the first span.

Finite element methods (FEM) have been developed during the last decades to be a reliable tool to solve structural problems. Such a tool, ATENA 3D, has been used to simulate and analyze the bridge in Kiruna. ATENA 3D is specially designed for computer simulation of concrete and reinforced concrete structural behaviour.

In this master thesis, results from analytical and numerical studies are compared with data from field experiments to validate the model and to perform other analysis to investigate the bridge behaviour during the construction stages and for expected future ground settlements.

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Sammanfattning (in Swedish)

Finit elementmodellering av en förspänd betongbro – Inverkan av byggskeden och sättningar på Gruvbron i Kiruna

På grund av gruvbrytning rör sig grunden under staden Kiruna i norra Sverige.

Planer finns därför på att flytta staden och dess järnväg. En bro – Gruvbron – förbinder järnvägen med gruvområdet och sättningar har observerats i dess närhet. Bron, som byggdes 1960, har fem spann och består av förspända betongbalkar som bär en pågjuten farbana i slakarmerad betong.

Beräkningsmetoder med finita element (FEM) har utvecklats under de senare decennierna för analys av strukturproblem. Ett sådant beräkningsprogram – ATENA 3D – har använts för att analysera Gruvbron.

I detta examensarbete jämförs resultat från analytiska och numeriska studier med uppmätta värden för att kalibrera en FE-modell som sedan används för att undersöka brons beteende under byggfasen samt vid förväntade framtida sättningar.

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Table of contents

1 INTRODUCTION

1.1 Background and problem definition

The town of Kiruna in Sweden is cracking apart. Like an earthquake in slow motion the ground near Kiruna cracks and sinks in an ever widening circle which is beginning to tear the city apart. A huge Iron ore mine to the west of the town has caused the earth to subside around the mine at an ever expanding rate, and like an earthquake, the earth displaces in an ever widening circle creating cracks and subsidence and destroying buildings. This slow motion is shown in Fig. 1.1.

Figure 1.1 Slow ground motion downwards of the ground in Kiruna due to miming at increasing depths, Lewisma Tectonic Notebook (2006).

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The railway line in Kiruna is planed to be moved before year 2012 due the expected cracking in the underlying rock. Within the dangerous area, along the entrance road (Gruvvägen) to the mining area and the head office for the mining company, LKAB, a bridge, Gruvbron (the Mine Bridge) is situated that overpasses the railway area some distance south of the Kiruna railway station, see encircled in Fig. 1.2. The bridge that was built in 1960 is a pre-stressed concrete girder bridge with five spans, see Fig. 1.3.

Figure 1.2 Part of Kiruna city and the mining area of the Kirunavaara-mine with

“Gruvbron” (the Mine Bridge) encircled. The bridge overpasses the railway and the Europe Road E10 and connects the city centre to the mining area.

The bridge needs, if possible, to be in use until year 2012, or preferably longer.

Until then increasing movements of the rock are expected close to the bridge initially at its west side (support 1) and further eastwards towards support number 6, see Fig. 1.3.

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Introduction

Figure 1.3 Elevation and plan of the bridge according to the construction drawing.

A Swedish consulting company, Sweco, has assessed the bridge. The assessment showed that the bridge has enough load-carrying capacity, but also that the length of the reinforcement in the bottom of the longitudinal girders close to the interior columns probably is a little bit too short. The function of the reinforcement is to resist the tensile forces in the bottom girders induced by the pre-stressing force in top of the girders. The company has inspected the bridge once a year from 2005. During the first inspection, cracks were discovered in the bottom of the main girders close to support number 2 and 5.

A certain worry has been expressed by the consultants that the expected ground movements can cause the cracks to propagate upward to the top of the girders;

therefore, the whole girder may have a reduced shear capacity. This resulted in a reduction of the allowed load-carrying capacity for the bridge from BK1 (axle/bogie/total = 12/18/60 ton) to BK3 (less than 10/16/51.4 ton = BK 2).

The whole infrastructure of Kiruna is affected by the settlement caused by the

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line “Malmbanan” (The Iron Ore line) and the European Road E10 in northern Sweden, needs to be assessed and monitored due to an increasing risk of settlements of the ground. The structure is shown in Fig. 1.4.

Figure 1.4 Bottom view of “Gruvbron”, a pre-stressed concrete girder bridge in Kiruna. The bridge passes over the railway line “Malmbanan” (the Iron Ore Line) and the European Road E10. Photo Ola Enochsson (2008).

1.2 Aim and scope

This thesis is a part of a project at Luleå University of Technology concerning analysis of the bridge in Kiruna. The scope of the research is to follow and check the actual level of stresses and deformations in the bridge using a refined FE-model and to study it for different scenarios of ground movements.

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Introduction

The next steps of the project, when the optimum model is found, is to apply different kind of load cases, to compare them with experimental data and to do simulations of the settlements to investigate the behaviour of the structure.

This work contains the following parts:

• Get knowledge of the ATENA software and how to apply it on the current structure.

• Compare the model with experimental data.

• Study the behaviour of the bridge for different loads cases and to finish with a performance a simulation of a slow motion of the ground, until the crashing of the concrete or the reinforcement steel enter the plastic area with large deformations.

• Analyze the influence of the reinforcement in the bottom part in the longitudinal girder close to the columns.

• Discuss the results and identify possible damages to the bridge. Also to give suggestions for future experimental work and to learn about possible problems for pre-stressed concrete girder bridge using FEM.

A specific objective of the analytical evaluation includes the development of a finite element model that can represent global bridge behaviour and predict strains, stresses and displacements in the structure. Dynamic, fatigue, and thermal analysis, although important, is not included in this study.

1.3 Method

The work is divided into the following parts, see also Fig. 1.5.

• Literature study. The aim is to get the knowledge about the program ATENA and methods to update finite element models.

• Finite element analysis. Create a model possible to perform load cases.

Update it and compare results with experimental data.

• Apply different load cases and study the results.

• Analyse the results and discuss them and draw conclusions.

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Figure 1.5 Flow diagram for thesis work.

1.4 Limitations and Outline

As said before, dynamic loads and thermal effects (which need a thorough and accurate treatment) are out of the objectives of the work. The experiments in the field are performed with dynamic loads; we may expect some divergence between the model and the analytical results.

In order to be able to perform many calculations and analysis the model has been reduced, in all ways possible, therefore some error is expected.

Thus, the expected results are not specific values of strains or stresses but rather the general behaviour of the bridge with examples of typical stresses and strains.

Outline

• Part 1: The introduction contains a short background and problem definition, the aim and scope of the thesis and also an outline and the method used.

• Part 2: Is an overview of the finite elements method using ATENA. How the program works, and how the parameters of the bridge are introduced in it.

• Part 3: Describe the load cases and show the process in the calculations that have been done and how they are introduced in ATENA. The field

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Finite Element Analysis

2 FINITE ELEMENT ANALYSIS

2.1 Introduction

Since the finite element method was introduced in the 1960s, it has been one of the most powerful methods to solve engineering problems. It was introduced to solve problems in aeronautic engineering, and soon was developed and implemented for all kinds of engineering. Nowadays, when computers are faster, new methods and programs have been developed for all kinds of engineering and their application to solve structural problems and in civil engineering in general.

It is difficult, however, to identify errors and discrepancies in the model, and to verify the accuracy of the computer codes. Results from finite element analysis need to be compared with those from experimental analysis. This may be achieved only if the analysis can account realistically for the material and geometric properties of the various components of a structure and the interaction among them (Chowdhury, 1995).

Reinforced concrete, one of the most important composite materials in construction, has not a definitive method for analysis. Finite element method work very well for many structural materials like steel, where material properties are easy defined. When the properties, as in the concrete, are not easy to define and discrete cracking occurs, this limits the feasibility of the finite element method.

Until recently, only linear methods were used to analyze reinforced concrete.

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2.2 ATENA program

The tool used to perform the model, and therefore the analysis, is the program ATENA version 3.3.2 released in August 2007. The ATENA program, which is determined for nonlinear finite element analysis of structures, offers tools specially designed for computer simulation of concrete and reinforced concrete structural behaviour. The program has three main functions:

• Pre-processing: Input of geometry objects, loading and boundary conditions, meshing and solution parameters.

• Analysis: Real time monitoring of results during calculations.

• Post-processing: Access to a wide range of graphical and numerical results.

Because of the complexity in the geometry of the bridge, many models have been done from models closer to the reality than other ones, with simplifications in the mesh, in the geometry and also with the reinforcement.

These simplifications have been done because the price in both memory and CPU.

Two solver types of equation solution are available and can be defined for nonlinearity, standard and sparse-iterative. The standard has been chosen for the analysis.

2.3 First model

This first model was the most close to the reality. More than five thousand discrete bars were defined as reinforcement. The model had 46 macro elements and more than 120.000 mesh elements. Because the part of the bridge that required to be monitored is close to the second support, the model that has been designed, just for the two first spans. Due the big size and the complexity of the model it could not run.

2.3.1 Materials

Five kinds of materials have been defined in this model; Figure 2.1 shows the materials, their names and their actual usage.

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Figure 2.1 Defined materials.

Two kind of concrete have been defined, K30 and K40. It is highly recommended in the user manual, for concrete, to use “fracture-plastic material 3C Nonlinear Cementitous”. The fracture-plastic model combines constitutive properties for tensile (fracturing) and compressive (plastic) behaviour. The fracture model is based on the classical orthotropic smeared crack formulation and the crack band model. It employs the Rankine failure criterion, exponential softening, and it can be used as a rotated or a fixed crack model. The hardening/softening plasticity model is based on the Menétrey-William or the Drucker-Prager failure surface.

Figure 2.2 Parameters generated for material 3C Nonlinear Cementitous (ATENA manual).

The cube strength must be entered. A set of generated parameters appears based on codes and recommendations, see Figure 2.2. The introduced concrete properties are: Young’s Modulus, E, Poisson’s Ratio, μ, tensile strength, ft and compressive strength, fc. The two kinds of concrete’s properties are shown in Table 2.1.

Table 2.1 Material properties for concrete.

Type Young Modulus, E [MPa]

Poisson’s Ratio,

μ ^[-] Tensile strength, fct [MPa]

Compressive strength, fcc [MPa]

K30 30.00 0.2 1.60 21.5

K40 31.14 0.2 1.95 28.5

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The concrete K40 has been used for beams, cross-beams and the concrete deck.

K30 is used only for columns.

It is possible to change the parameters for different load steps as function of time. Because we do not have data of the changes in the materials this function is not useful in this case.

Three kinds of materials have been defined for the reinforcement. The reinforcement is defined in the program for the yield point and for the Elastic Modulus but it is not possible to do a perfect definition of the material if one do not have the strains for each stress in the plastic curve. Figure 2.3 shows the definition of the reinforcement in the model.

Figure 2.3 Dialog box for definition of reinforcement.

The pre-stressing reinforcement is defined in the same way as the discrete reinforcing bars. The properties of those elements are shown in Table 2.2.

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Table 2.2 Material properties for steel bars.

Type Young Modulus, E [GPa]

Yield point, fsy [MPa]

Coefficient of thermal expansion, α^[1/K]

Ks40 210 400 1.2×10^-5

Ks60 210 600 1.2×10^-5

Bracing cable 200 1450 1.2×10^-5

2.3.2 Geometry

The geometry of solid objects is defined by macro elements, which are generated for extrusion of a previous surface definition or as a beam element.

As we can see the possibilities to generate complex geometries are restrained.

All macro elements generated are standard type for this first model. The cross- section is shown in Figure 2.4. When the surface of the cross-section was generated, the macro element is only an extrusion of it.

After the generation of the girder and the concrete deck it is time to create the cross-section beams and columns. They have been modelled as beam elements.

The geometry is shown, both a cross-section and a longitudinal section, in Figure 2.4 and Figure 2.5.

0,41 m

2,34 m 5 m

0,55 m 2,34 m 5 m

1,888 m

14,68 m

1,608 m

5% 0,3 m

0,3 m

0,22 m

0,22 m 0,3 m

Figure 2.4 Cross section of the bridge in model 1.

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1,608 m

19,3 m

9,15 m

5,65 m

9,15 m 0,79 m

20,5 m

6,46 m

6,833 m 6,833 m

6,833 m

0,3 m 0,6 m

Figure 2.5 Longitudinal section of the bridge in model 1.

After the geometry of the concrete has been generated it is time to introduce the reinforcement. It can be introduced as smeared reinforcement or as discrete bars. In this first model all 5417 bars, some with many segments, have been introduced as discrete bars, see Fig. 2.6.

Figure 2.6 Complete reinforcement in model 1.

2.3.3 FE mesh generation

When all geometry is defined, it is time to create the mesh, see Fig. 2.7.

ATENA has an automatic mesh generator. In our case, when the model also includes bar elements, the mesh generation is performed in two phases. First, a mesh of solid 3D elements is produced within the pre-processor. In the pre- processor the bars are still maintained as geometrical objects without mesh.

When the control is passed to analysis the bar finite elements are generated as embedded elements within the existing mesh of 3D solid elements.

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Figure 2.7 FE-mesh generation.

ATENA has three basic element types: tetrahedron, brick and pyramid. Global element size can be entered. Afterwards relative size for joints, lines, surfaces or macro elements can be more refined.

2.4 Second model

This second model, which all the calculations were performed with, is the most simple of the models that has been made. In it I have introduced many of the reinforcement bars as smeared, just only the most important reinforcement bars are still discrete bars. The cross-section is a distant approximation of the reality, and I have applied symmetries in it. All these simplifications that have been introduced sometimes do not give expected results. Therefore, results have to be looked at carefully and with prudence.

In Fig. 2.8 is shown, in red, the limits of the model used for the calculations with planes of symmetry in the middle of the spans and in the middle of the concrete deck.

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Figure 2.8 Part of the bridge that has been modelled with Atena.

2.4.1 Geometry

The model that has been used for the calculations has some simplifications in the concrete deck. The complex geometry in the deck implied that tetrahedron elements had to be used in ATENA instead of brick elements, which lead to a large model. To solve this problem, the cross-section of the deck has been reduced to an easy shape, see Fig. 2.9. Brick elements have been used to mesh the structure. Variable thickness in the deck has not been used due to the fact that shell macro elements with reinforcing layers must have constant thickness (in ATENA version 3).

Due the very small thickness of the deck compared to the other two elements, shell elements have been used to model it. In ATENA shell are modelled with

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Due to layers through the thickness, the number of integration points is high.

The two types of macro elements are compared in Table 2.3.

Table 2.3 Comparison between plates with two different element types.

Type Number of

elements

Number of nodal points

Number of integration points

Shell, 10 layers 1 20 126

Bricks, 5 in

thickness 3 125 4 056 25 000

2 m

0,55 m 5,65 m

1,7 m 0,22 m

5,205 m

Figure 2.9 Cross section of the bridge in model 1.

It is obvious that smaller number of integration points in the shell leads to a reduction of computation time in several orders of magnitude. 5 layers for the shell have been used.

2.4.2 Reinforcement

Most of the 5000 discrete bars of the first model have been reduced to embedded reinforcement. Only 500 discrete bars remain in the model. The smeared reinforcement is defined in ATENA with the following parameters:

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• Amount of reinforcement defined by reinforcing ratio, 100 ^s

c

A

ρ= A , where As is cross section area of smeared reinforcement and Ac is cross section area of concrete. Units of ρ are in percent.

• Direction of smeared reinforcement defined by components of a unit vector.

Figure 2.10 Smeared reinforcement definition for the beam element.

Reinforcing layers for shell elements are defined also with the angle between the local axis and the bar reinforcement orientation. The distance between the top and the bottom face of the shell is required too. See Fig. 2.11 and Fig. 2.12.

Figure 2.11 Layer of reinforcement in shell elements.

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Figure 2.12 Reinforcement definition for shell elements.

Discrete reinforcement has to be introduced manually. Only important bars, which we should study the behaviour of, and bars that can not be introduced as smeared have been modelled as discrete bars, see Fig. 2.13.

Figure 2.13 Discrete reinforcement bars and pre-stressing strands along the beam in the second model.

2.4.3 Pre-stressed reinforcement

Pre-stressed reinforcement is applied in ATENA only as a load in the reinforcement. The pre-stressing force is applied in one of the ends. The position of the starting point has no affect on the distribution of stresses in reinforcement. It means that stress losses along the pre-stressing reinforcement are not included in the program and have to be calculated manually.

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1,83 m 1,83 m 1,83 m 1,83 m 1,83 m

0,541 m 1,016m 1,463 m

2,05 m 2,05 m 2,05 m 2,05 m 2,05 m

0,22 m 1,657 m 1,392 m 0,854 m 0,396 m

0,07 m 0,195 m

Figure 2.14 Geometry of pre-stressed reinforcement.

Until the third span the pre-stressed used is BBRV 4 folders of 32ф6.

Properties of pre-stressed tendons are described in Fig. 2.15.

yk

folder uk

2 2

folder s

1450 70 mm

1700

900 mm 3848 mm

200 GPa f

f

A A

E

= Φ =

= =

=

Figure 2.15 Material properties for standard tendons, BBRV.

2.4.4 Boundary conditions

Since only a quarter of the structure is considered in the analysis, the symmetry boundary conditions are applied, see Fig. 2.16.

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For three-dimensional solid elements, symmetry boundary conditions are obtained by fixing the displacement in the horizontal direction on entire planes lying on symmetry axes. The columns allow rotation around the x and y-axes due the reinforcement topology but it has been impossible to model the correct union between the ground and the column with solid elements.

2.4.5 Mesh

Due the simplifications in the model, the mesh element used is brick. Many kinds of meshes have been tested to justify the validity of the results and to determine the number of elements. The model used to determine the number of elements is the model for the first load case, see in chapter 3.2.2, self weight.

As we can see in Fig. 2.16, the results are highly dependent on the mesh in the compression area. It can be explained by the fact that next to the support the compression stresses are increased very much in a small area, see Fig. 2.17.

The smaller the element size is, the more accurate are the results. An intermediate mesh of 2000 elements has been used for the calculations.

Figure 2.17 Stresses as function of the number of elements.

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Figure 2.18 Stress distribution in x-direction for the first load case.

2.5 Updating FEM model

With the final model it has been important to improve it in two important ways, with the mesh and with the pre-stressing -two important parameters that have a big influence on the results.

2.5.1 Mesh properties

Due to the importance of the mesh in the results, all possible tools have been studied to update the model, and the ambition was to obtain accurate results for all load steps. For example, for the first load case, where minimum stresses in x direction are found close to the column, and maximum stresses are found in the middle of the span, different size for lines has been tried. The number of elements does not increase much, and the results are improved.

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Meshes used for each load step is such that give an accurate results. Therefore, the first step for every calculation was to do a rude mesh and with primary results, for each load case, improve the mesh in the most important place of the structure. In Appendix A the meshes are listed for all calculations.

2.5.2 Losses of pre-stressing

When a tendon is tensioned, the force produced is not constant along the length of the tendon due to friction between the tendon and the duct, see Collins and Mitchell (1991).

The total friction loss ∂P over the length ∂x is thus, see also Fig. 2.20 P μ αP KP x

∂ = ∂ + ∂

The change in tendon force between point A and point B can be found as follows

0 0

A B

P x

P

P K x

P μ α

∂ = + ∂

∫ ∫ ∫

Solving this equation gives

( ^Kx)

B A

P =P e⁻^μα⁺

where PA Tendon force at location A.

PB Tendon force at location B.

K Wobble friction coefficient per meter of tendon.

α Total intended cumulative angle change between A and B in radians.

μ^Frictioncoefficient.

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Figure 2.20 Losses in curved tendons with N = P dα. From Collins and Mitchell (1991).

If a reasonably long tendon is stressed from only one end, there may be a considerable loss in force along the member length. If we guess that the tendon was stressed in only one end, and stressed for the length of the longer span, without overstressing technique, the variation in tendon force caused by friction should be big, see Fig. 2.21-23.

During the tensioning of the tendon, both the jack and the corresponding tendon elongation are recorded. The elongation readings are compared to the calculated elongation and must agree within specified tolerances (± 5 % is usually acceptable). Smaller than expected elongations may indicate that the tendon is jammed in the duct and hence only a portion of the tendon length is being stressed or it may indicate a higher than normal friction losses.

Figure 2.21 Tendon profile consisting of parabolic segments.

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Figure 2.23 Force variation when a tendon is stressed in stages from both ends.

From Collins and Mitchell (1991).

The elongation of the tendon can be calculated as follows:

av ps p

P L

Δ = A E 2.1

where Δ Expected tendon elongation.

Pav Average force in tendon determined from calculated force variation along the tendon.

L Length of the tendon.

Aps Cross sectional area of the tendon.

Ep Young’s modulus of the tendon.

The length affected by anchorage set can be calculated in the following manner:

set set

ps p

0.5 PL A E

Δ = Δ 2.2

Assuming a constant frictional loss per unit length, p, we obtain 2 set

P pL Δ =

where p is the friction expressed as a change in force per unit length calculated from a tendon force variation diagram. Substituting for ΔP in Equation 2.2 gives

Δ A E

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The five span continues bridge girder with a total area of tendon of 904 mm² with fyk = 1450 MPa. For this application the tendon properties are: Aps = 904 mm², Ep = 210 GPa, μ = 0.25, K = 0.003/m and Δset = 6 mm.

The average force in the tendon can be approximated as

( ) ( ) ( ) ( )

av

8.15 931 813 813 724 724 662 9.25 662 591 1

2 19.45

P + + + + + + +

= ⋅

av 738 kN P =

The length of the tendon affected by anchorage set is found to be

set ps p set

6 904 210000

8.7 m 15

L A E

p

Δ ⋅ ⋅

= = =

Assuming a constant frictional loss per unit length, see Fig. 2.24-25, obtains 2 set 2 15 8700 261 kN

P pL

Δ = = ⋅ ⋅ =

hence after anchoring, the force at the end of the tendon is 999 261 738 kN− =

The calculation above assumes a linear force variation between the ends of each parabolic segment. From Equation 2.1, the expected elongation is

( )

³

av

3 ps p

738 19.45 10

75.61 mm 210 10

P L A E

⋅ ⋅

Δ = = =

⋅

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Figure 2.25 Losses of the tension in the pre-stressed tendons until the middle of the second span.

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Load cases

3 LOAD CASES

3.1 Experimental study

The field experiments, which have been used for comparison with the analytical results, are a part of the project LTU are carrying out at the Kiruna bridge. These experiments include vibration tests to determine the eigen frequencies, mode shapes and damping ratios. By comparing the measured modal parameters with a numerical model of the same structure in an undamaged condition, damage detection, localization, and quantification is possible.

The experiments include also deflections under truck loads. The speed of the trucks was low enough to consider them as static loads.

In Fig. 3.1 we can see a sketch of the bridge with the direction and type of the truck. In the first load case, truck number two, circulated from the left right of the road from east to west. The second load case includes the first truck circulating from west to east.

GL1 indicates the position where displacements have been studied. The lines in red are the limits for the model in ATENA that has been modelled. ‘A’ marks the positions of the accelerometers, ‘L’ the longitudinal displacements and ‘R’

marks the positions of accelerometers that served as references.

Truck characteristics are shown in Fig. 3.2 and Table 3.1.

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a) Truck 2 driving west in south lane towards LKAB (truck no 052, gross weight 24.04 tons).

N

R 6

R 5 A 2 A 3

L 1 L 2 A 4

GL 2 Truck 2

b) Truck 1 driving east in south lane towards Kiruna (truck no 056, gross weight 23.32 tons).

GL 1

R 6

R 5 A 2 A 3

L 1 L 2 A 4

GL 2 GL 1

Truck 1

Figure 3.1 Two load cases from the test that have been compared with the analytical study.

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Load cases

Table 3.1 Characteristics of the applied load.

Vehicle Dim. A [m]

Dim. B [m]

Dim. C [m]

Dim. D [m]

Dim. E [m]

Total weight [kN]

Truck 1 2.25 2.0 2.55 1.32 5.52 229

Truck 2 2.25 2.0 2.55 1.32 5.52 236

3.2 Analytical study 3.2.1 Introduction

The strategy for the load cases has been divided in four parts:

1. Monitoring the model. Before a study of the structural behaviour under truck load and applying deformations to simulate a motion of the ground, the construction phase is analysed. First, the structure’s behaviour without the pre-stressed reinforcement is studied. Afterwards the bars of the reinforcement are introduced. The next step is to apply the load in the reinforcement and the surface load to simulate the pre- stressed and the pavement respectively, and to do this, many steps have been performed and to see the changes of the stresses along the beam.

2. Perform the truck load. The truck load, of the experimental study, has been modelled in this part.

3. Slow motion of the ground. In this load case, prescribed deformations have been applied. The aim of this load case is to compare the prescribed deformation to a real motion of the ground.

4. This last one has to answer how reinforcement can change cracking in the bottom part of the girder. Two kinds of reinforcement typology will be compared to the existing one.

3.2.2 First load cases Self weight

The first load step of the loading consists of applying the self weight of the concrete deck and beams. ATENA automatically applies it as a body force. The first load step (load case 1) is shown in Fig. 3.3.

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Figure 3.3 Model for the first load case without pre-stressed reinforcement. The monitoring points are indicated.

For this application monitoring points along the beam have been defined.

Monitoring points serve to monitor results of calculations during analysis and post-process.

There are two kind of monitoring points: in nodes where external forces, reactions and displacements can be monitored and in integration points where stresses, strains, crack attributes and more can be monitored.

For this application we monitored the stresses in the lower part of the beam and displacements where maximum deformations are expected, see Fig. 3.2.

Pre-stressed reinforcement

As we could see in Chapter 2 the pre-stressing is introduced by an applied force in the end of the reinforcement. Losses along the pre-stressed strands have been calculated. In this part many loads have been applied in the reinforcement to see how affects this to the behaviour of the structure.

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Load cases

Figure 3.4 Position of the applied load in the reinforcement to make it similar to the pre-stressing.

Three analyses for this part have been performed. The average of the force in the tendon, see Section 2.5.2, is around 730 kN. Due to the variations along the length of the strands, calculations have been performed for 600, 700 and 800 kN. The pre-stressed load has been divided in ten steps to monitor the results during the calculations.

The expected influence for this load case is shown in Fig. 3.4. In the picture we can see how a beam, with an applied load, where we had tensile stresses in the lower part of the beam, will become compressed or in equilibrium.

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Figure 3.5 Influence of the pre-stressing in a beam under stress.

Surface load

In previous analysis the self weigh did not include the weight of the pavement.

In this part the pavement load is included. The pavement load is applied as a surface load with a value of 4 kN/m², and uniformly distributed on the deck.

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Load cases

The surface load of 4 kN/m² has been increasing progressively. For the next steps only 4 kN/m² will remain as a surface load in the concrete deck. The other loads will be added to these first ones.

For this analysis the load of 700 kN has been taken for all the calculations and until the end of the calculations.

3.2.3 Multi axle truck load

This part is based on truck loads used in the earlier field test; the researchers assumed that the total truck weight was 229 kN for the first truck. The total load was distributed such that the truck’s front axle carried 25 % of the gross weight and the two rear axles carried the remaining 75 % of the weight. The appropriate dimensions and location of each tire patch and the total weight applied are illustrated in Fig. 3.1 and Table 3.1. The actual location of the load in the bridge was applied in the middle region between span 1 and 2, as shown as follows, see Fig. 3.7.

Figure 3.7 Tire patches and direction of the truck for each load case.

As we could see in the field test, the truck went in both directions, from the experiments. And we have data of both. Then, both experiments have been modelled and performed to compare with experimental data.

To apply the force of the wheels it has been necessary to define a surface to assimilate the footprints of the tires. The properties of these thin shells are not interesting for the analysis but it is important that the stiffness of them have to be higher not to meddle with the results.

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3.2.4 Prescribed deformation

In this part I have tried to model a slow motion of the ground has. A prescribed deformation in the surfaces of the middle of the span has been introduced. Two load cases were applied to the model; see Fig. 3.8, in the first one in the direction of the prescribed deformations in the end’s surface of the model and acting in opposite direction, to simulate an increasing settlement of the ground.

Figure 3.8 Different orientations of the prescribed deformations.

In the second one same direction for the prescribed deformation has been applied, to simulate the higher settlement of the ground next to the support.

The analysis has been performed, as in the others cases, with many load steps of 1 mm deformation. The aim of this analysis is to see the behaviour of the structure under a settlement of the ground until the steel reaches its yield stress or the concrete reaches its compressive strength.

3.2.5 Modified reinforcement

The SWECO assessment indicated that the length of the reinforcement in the bottom of the longitudinal girders is a little bit too short. The function of the reinforcement is to resist the tensile forces in the bottom girders induced by the

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Results and discussion

4 RESULTS AND DISCUSSION

4.1 Introduction

Damage can be successfully detected by comparing the modal parameters of the original undamaged structure to those of a damaged structure (Teughels and De Roeck 2004). But it has been difficult to validate the model. There is no data of the experimental tests which are in a form that can be compared to the results with those from the analytical and numerical study.

Only some useful data of deflections has been obtained. The deflection data of this experiment due a truck load (dynamic load but considered static) will be compared with a simulation with ATENA, using static load.

4.2 Experimental study

Fig 4.1 shows the deflection, in the field, of GL1 when the trucks load passes through it.

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As we can see, for both load cases, the deflection in GL1 is similar and never bigger than 0.2 mm. Around 0.15 for the first load case and around 0.18 for the second load case.

4.3 Analytical study 4.3.1 Construction phase Self weight

The analysis for self weight has been divided into ten steps of the same added load. In Fig. 4.3 we can see the progress of the calculation for each added load.

The maximum displacement of the concrete deck increase until the concrete can not absorb more tensile strength. The beams are not ready to work without pre-stressed; therefore cracks begin to grow up in the middle of the beam of the longer span.

The maximum displacement is found in the deck with a value of 3.3 mm.

But the cracks are growing up not for the place of maximum stress, see Fig.

4.4. Are increasing close to it and could be explained for the mesh size near the symmetry’s surface where boundary conditions have been applied.

The stress in the reinforcement and the maximum deflection is rapidly increasing when cracks appear.

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Figure 4.2 Stress evolution in the x-direction in the lower part of the beam. Until the 90 % of applied self weight there is linear behaviour between load and displacement. After the 90 %, the cracks are growing up and the maximum tensile stress decrease.

Figure 4.3 Stress in x direction, 90 % of the self weight in the left and 100 % of the self weight in the right. Both figures are with displacements

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Pre-stressed reinforcement

Three different kinds of calculations have been done. As we said in chapter 3, the reinforcement have been introduced and loaded with three different values, one calculation for each value. The loads are 600, 700 and 800 kN. For each calculation the load has been divided in 10 load steps to see the behaviour of the structure.

As we can see for 600 kN load, where we had tensile stress it becomes compressive stress and vice versa, see Fig 4.3. The cracks disappear when compressive stresses appear, more or less after the 90 % of the applied load in the pre-stressed. Fig 4.4 and Fig 4.5 shows stress and displacements for the last load step, with all applied load.

Figure 4.4 Stress evolution in x direction, in the middle of the span and in the support. The pre-stressing acts such the compressive stress become tensile and tensile becomes compressive. With 600 kN no cracks appear as the tensile stress is lower than 1.9 MPa.

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Figure 4.5 Stress distribution with 100 % of applied load in the pre-stressed reinforcement (600 kN). In red the tensile stressed, now close to the support. The units are in MPa.

Figure 4.6 Deformed shape magnified 500 times for pre-stressing of 600 kN.

There are positive displacements in z direction for the left part in the support. The units are in meters.

The behaviour for the second load case, with 700 kN, is the same than for 600 kN. But cracks are growing up for this second case.

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Figure 4.7 Relationship between displacement in the concrete deck and applied load in %. With 700 kN of applied load there are positive

displacements in the concrete deck. Both load cases show the same behaviour.

Figure 4.8 Stress comparison between the two load cases. As we can see the stresses near the support rise until we reach the tensile stress of the concrete. It makes sense to think that higher loads in the pre-stressed reinforcement lead to cracks near the support.

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Figure 4.9 Stresses in x direction for 700 kN load case. The main change between both load cases is found near the support where cracks are growing up for second load case.

With the 800 kN load case the same thing occurs as for 700 kN. Next to the support cracks appear but they appear earlier than for 700 kN load.

Compressive stresses increase compared to the other two load cases and the crack width is higher than for the 700 kN load case, therefore the stresses in the reinforcement also increase.

Figure 4.10 Comparison of cracks widths with the applied loads in the

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In the figure above we can see how cracks are growing with the applied load with 700 and 800 kN pre-stressing load respectively. With 800 kN applied load, the cracks begin to grow at the 80 %, and with 700 kN, they begin around 70 %, therefore, cracks begin to grow up when in the reinforcement there is an applied load bigger than 560 kN.

In the figure below the reinforcement behaviour is shown for 800 kN load in the reinforcement.

Figure 4.11 Reinforcement behaviour. The pre-stressing cause the cracks near the support to grow, therefore, the reinforcement stresses rise up to 50 MPa.

Stress evolution in 3D

It has been interesting to see the stress evolution that occurs in the structure during the calculations, and how the stresses are moving along the beam. The behaviour is the same for all load cases.

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Figure 4.12 The tensile stresses that we had with the self weight, in the middle of the span, are moving next to the support when the pre-stressing load is increased. In the first step of added load we still have tensile stresses in the middle of the beam, in the second step all are found close to the support and in the third step, the tensile stresses rise above 1.91 MPa and cracking occurs.

Surface load

With the pre-stressed reinforcement already in the structure it has been interesting to see the structure behaviour when surface load is applied on it.

The tensile stresses decrease close to the support, therefore, the cracks also decrease and begin to close, as we can see in Fig. 4.12, when surface load is increased.

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Figure 4.13 Stress evolution in x direction with increasing loads.

However, with higher applied loads, cracks in the concrete deck begin to grow while cracks in the beam close. The cracks in the surface are placed next to the beam, see Fig. 4.13, and can be explained by the poor definition of the concrete deck. The concrete thickness in the model is only 22 cm which differs considerably from the real value of 30 cm.

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In Fig. 4.15 the deflection is shown in the concrete deck during all added load steps. In the first step only the self weight is added, the deflection for this step is around - 2.7 mm along the z-axis. Between the second and twelfth step the pre-stressed load is added, then with the pre-stressing the deflection increases in the positive z-direction until + 0.6 mm (Δ3.3 mm pre-stressed deflection effect), which is then decreasing again when the surface load is added.

Figure 4.15 Deflection in the concrete deck during the calculations. In the first load step, the self weight is added. Between the first and the eleventh step the effect of the pre-stressed load is entered. Figure (2) shows the deflections with all pre-stressing. Between step numbers twelve and thirty-one surface load is added. Figure (3) shows the deflections for 4kN/m², otherwise when all pavement load is introduced.

4.3.2 Multi axle truck load

The aim of this analysis is to compare the deflections of the analysis with those from the experimental test. The current methodology of design the load is based on using static axle and wheel loads of the design vehicle. However,

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bridges with a high speed data acquisition system. They found that bridge deflections under dynamic loads were higher than those under static loads.

Therefore, actual forces applied to the bridge by a moving vehicle were greater than those assumed in a simple static analysis. The magnitudes of these forces are influences by factors such as vehicle characteristics, vehicle speed, road conditions, and bridge entrance conditions.

For an accurate analysis, the DAF (dynamic amplification factor) of the bridge is required. However due the few test data it is not possible to compare data from analysis with data from tests.

In the first load case the truck circulate in the direction shown in Fig. 4.16.

Figure 4.16 GL1 deflection during first analysis.

Results of deflections are shown in Fig. 4.16. The truck load causes a deflection of 0.7 mm in location GL1 of the concrete deck for the first pre- stressed reinforcement (650 kN load) and 0.9mm for the second (740 kN load).

Behaviours are similar for both load cases.

In the second load case, where the truck circulates in the other direction, displacements increase if it is compared with the first load case.

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Figure 4.17 GL1 deflection during second analysis.

4.3.3 Prescribed deformation

Prescribed deformation has been applied until crashing of the concrete or yielding of the steel.

First load case

In the first load case, with progressive deformation along the model, the tensile stresses, which were placed next to the column, become compression stresses and cracks close while in the right part of the beam the cracks grow caused by increasing tensile stresses.

Fig. 4.18 shows the stress evolution in the x direction. With 3 mm deformation for each side, tensile stresses are mostly in the right part of the beam. With 9 mm, the cracks are growing and with 24 mm the compressive stresses rise up to the compressive strength, in the right part of the beam there are cracks are along the entire beam.

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Figure 4.18 Stress evolution in x direction. Deformed shapes magnified 100 times.

The influence of the prescribed deformation is shown in the next figures for the reinforcement, the crack width and the compressive stress, see Fig. 4.19 - 21.

Figure 4.19 Compressive stresses in the concrete in the beam as function of the

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Figure 4.20 Reinforcement stresses as function of prescribed deformation. The tensile stresses in the reinforcement decrease in the first part of the analysis close to the support, between 0 and 3 mm deformation due the cracks close, and it increases afterwards when cracks grow up, first next to the support and after in the red part. Compressive stresses in the reinforcement rise, proportional with the deformation. The steel is still far from yielding with 25 mm deformation.

Figure 4.21 Cracks width in the beam as function of the prescribed deformation.

The first part of the curve refers to the area next to the support. After that the cracks grow in the end (middle of the span) and along the lower part of the beam.

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Second load case

In the second load case the deformations have been applied in the same direction in both sides of the structure to drive the column into the ground.

With this analysis, all possible cases have been studied.

In the beginning of the simulation, between 1 and 5 mm deformation, only the beam has been affected. The cracks in this case become bigger next to the support. When prescribed deformation is added in the analysis, it is the column which is affected directly for the load. After 7 mm displacement, the cracks grow up also in the column as shown in Fig. 4.23.

Figure 4.22 Compressive stresses in the beam as function of the applied

deformation. After 7 mm of added deformation, the stresses increase slowly due to the fact that the column begins to absorb stresses.

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Figure 4.23 Both, tensile and compressive stresses in the reinforcement have the same behaviour. Stresses increase rapidly in the beginning until cracks in the column appear. Tensile stresses are found where cracks are found, near the support. And compressive stresses, in blue in the picture, appear in the middle of the beam.

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Figure 4.24 Crack width as function of the displacement in the beam and in the column. Cracks are present in the beam from the beginning and grow slowly. However, cracks in the column grow after a deformation of 7 mm and increase faster. Due the low accuracy of the concrete deck model, cracks in it have been not considered.

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Figure 4.25 Displacements in the z-direction with deformations of 1, 5, 9 and 15 mm. With 1 mm deformation there is negative deformations next to the support. With 5 mm there is no more negative deformation. Due the cracks, with 9 mm deformation, displacements in the column begin to rise. This is also the case for a deformation of 15 mm.

4.3.4 Modified reinforcement

The results show that the limited length of the reinforcement does not cause the cracking in the concrete. For both lengths of reinforcements, cracking occurs in the same way, and the maximum values of cracks width are almost the same, see Fig. 4.26.

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Figure 4.26 Crack width depending on the length of the reinforcement in the bottom part of the longitudinal girder.

If the area of the reinforcement is changed instead of the length, the reduction in the crack width is considerable. With the new reinforcement, cracks widths are smaller but additional cracks appear also in the girder.

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Figure 4.27 Crack width with the improved reinforcement. Additional cracks occur also but the width decrease for the other.

Figure 4.28 Comparative crack width for existing reinforcement and for new reinforcement in bottom part of the longitudinal girder.

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4.4 Comparison

4.4.1 Truck load analysis

As said in section 3.3.4 is it difficult to compare the analysis with static loads with those with dynamic loads. Data from experimental analysis were taken from displacements in the concrete deck, where the model has less accuracy, see Fig. 4.29.

Due to this, the difference between the results can be explained. In the analysis both load cases results give a deflection of around 0.6 mm caused by the truck load. Results from the experimental analysis say that the deflections caused by the truck load in both load cases always are smaller than 0.2 mm. It is obvious that the real bridge is stiffer than the model.

Many parameters, as material and load in the reinforcement, have been modified to improve the model to be more close to the experimental results.

However, all efforts to get close to the measured values have been in vain.

Figure 4.29 Differences between cross-sections. Error is a combination of many factors.

4.4.2 Ground movement analysis

Both ground movements analyses have given the same behaviour when failure occurs: concrete crashing in the short span for 25 mm displacement.

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Figure 4.30 Comparison between compressive stresses.

Figure 4.31 Comparison between maximum crack widths. In both load cases, a small slow motion of the ground, causes the cracks to close in the neighbourhood of the column. But when the motion is increased, the cracks begin to grow (faster for first load case than the second).

Table 4.1 Crack widths (mm) for different deformations.

Load case Deformation 10 mm

Deformation 20 mm

0.20 0.44 0.36 0.53

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Figure 4.32 Stresses in the reinforcement as function of prescribed displacements.

The stresses increase when the prescribed deformation is applied. For the second load case the stresses increase faster in the beginning of the deformation.