FATIGUE ASSESSMENT OF APPROACH VIADUCTS OF THE NEW …irf/Proceedings_IRF2016/data/papers/6273.pdf · span at the north side and near to the first bowstring arch of the main bridge

Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016

Editors J.F. Silva Gomes and S.A. Meguid

Publ. INEGI/FEUP (2016)

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PAPER REF: 6273

FATIGUE ASSESSMENT OF APPROACH VIADUCTS OF THE NEW

SADO RIVER RAILWAY CROSSING

G. Alencar1(*)

, R. Calçada1, J.G.S. Silva

2, A.M.P. Jesus

1

1Faculty of Engineering of University of Porto, FEUP, Porto, Portugal 2Structural Engineering Department (ESTR), State University of Rio de Janeiro (UERJ), Rio de Janeiro, Brazil (*)Email: [email protected]

ABSTRACT

Fatigue analysis of steel and composite bridges under real traffic is usually performed using

numerical models of the structures, due to the difficulty of in situ monitoring of all the

structural details. The common assumption is that if the numerical model reproduces well the

real behaviour of the structure at some reference points, extrapolation of the results to other

points is reasonable. This paper investigates the different aspects of the fatigue analysis of

approach viaducts of the new Sado River railway crossing, in Portugal.

Keywords: Fatigue analysis, structural dynamics, steel and composite railway bridges.

INTRODUCTION

The fatigue analysis of steel-concrete composite bridges under real traffic is a challenging

task. In situ monitoring of all the details of the structure is not economically (and even

technically) feasible and thus, numerical models are usually employed for that analysis. It can

be assumed that the extrapolation of numerical model results to any point are accurate if the

numerical model reproduces well the real behaviour of the structural system, namely in some

reference points. This paper investigates the fatigue performance of the approach viaducts of

the new Sado River railway crossing, in Portugal, shown in Figure 1, in the context of a

research project on the in situ monitoring of railway steel bridge details. These approach

viaducts have a twin girder steel-concrete composite solution, which is a common design for

railway bridges with spans up to 65 m.

a) Overview. b) Steelwork detail.

Fig. 1 - Approach viaducts of the new Sado River railway crossing (REFER, 2010).

Topic_C: Fracture and Fatigue

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To improve the knowledge on the fatigue prone details of the approach viaducts, in a

preliminary stage of this research project it is performed a numerical study using the Damage

Accumulation Method with nominal stresses obtained from a finite element model. The

Section 2 focuses on the bridge and its approach viaducts, while Section 3 performs a

description on the experimental work developed in a previous work with the aim of

characterize the real traffic (Albuquerque et al., 2012). Section 4 presents the numerical

model developed for the selected approach span. Finally, Section 5 presents some of the

results from the fatigue analysis which have been performed on the structure, according to the

EN 1993-1-9 (2005).

GENERAL DESIGN OF THE STEEL-CONCRETE COMPOSITE VIADUCTS

The new railway bridge over the Sado River, located in the Lisbon – Algarve connection, in

Portugal, has a total length of 2.7 km. The north and south approach viaducts account together

for 2225 m and the main bridge over the river has a total length of 480 m. This crossing is

part of a railway project to improve the connections to the south and to the sea port of Sines

on the Atlantic coast. It is prepared for passenger trains running at speeds up to 250 km/h, as

the Alfa Pendular tilting train, and for freight trains. Figure 2 presents a photo of the overall

crossing, showing the approach viaducts and the main bridge.

Fig. 2 - Overview of the new Sado River railway crossing (Mourão, 2010).

The bridge is intended to accommodate two ballasted rail tracks, requiring a typical deck

width of 13 m, nevertheless only the upstream track is in operation at the current time. The

entire north viaduct (1115 m) and the main bridge (480 m) follow a straight alignment, while

the south viaduct includes a straight alignment over 175 m, from the transition pier at the

main bridge, followed by a curved alignment 800 m long and finally a 165 m long straight

section.

Over the Sado River, the steel-concrete composite solution includes a bowstring arch bridge

with a continuous deck 480 m long and three spans of 160 m each. The drawback of this

option, according to the designers (Reis et al., 2010), is the need to increase the deck width to

insert the arch and to protect it from accidental loads due to train derailment. Thus, at the

approach viaducts it is necessary to widen the deck, from 13 m typical width to 15.7 m, in

order to insert the arch on bridge axis. The transition between different deck widths occurs in

Proceedings of the 5th International Conference on Integrity-Reliability-Failure

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only two spans of the approach viaducts, both in the north and the south. The superstructure

(steel girders and deck) of the others approach spans remains in a straight alignment.

To take into account track-structure interaction effects, the superstructure of approach

viaducts is divided into continuous bridge decks, as long as possible, separated by simply

supported “neutral” spans (GRID, 2006). Also, displacements due to temperature expansion

are minimized by adopting the “neutral” spans. This work focuses on the second “neutral”

span at the north side and near to the first bowstring arch of the main bridge (Figure 3), which

is a 45 m span consisting of a composite slab-girder deck.

Fig. 3 - Side view of the selected “neutral” approach span.

The twin plate girders of this approach span are 2600 mm deep, as shown in Figure 4, with a

top flange 700 mm wide and a thickness that varies from 40 mm at support to 90 mm at span

sections. The lower flange is 1000 mm wide and its thickness varies from 60 mm at support to

120 mm at span sections. The web thickness varies from 25 mm at support to 16 mm at span

sections. The reinforced concrete slab (concrete grade C40/50 and steel reinforcement with

500 N/mm2 yield stress) acting in composite action with the steel part, varies in thickness

across the width, with a maximum of 40 cm on the bridge axis and a minimum of 20 cm at the

limits.

The structure comprises cross diaphragms and horizontal bracing all in the form of steel

trusses, as shown in Figure 5. The vertical truss diaphragms are spaced 7500 mm apart and

are made of circular hollow sections of 193.7 and 139.7 mm dia., both sections with 8 mm

wall thickness. The diaphragms near support sections at the piers are made of CHS of 193.7

mm dia., with 12 mm wall thickness due to the increased shear and torsion effects at these

locations (GRID, 2006).

At the level of the lower flange, horizontal bracing made from ½ HEA 400 hot-rolled sections

are adopted, as illustrated in Figure 5, in order to provide an equivalent box section improving

the torsional deformability and torsional vibrations under eccentric railway traffic loads (Reis

et al., 2010; Rueda and Salcedo, 2012). The connections between the diaphragms and the

transverse stiffeners of the plate girders make use of grade 8.8 prestressed bolts (Reis et al.,

2010).

45 m

Lisbon Algarve

Sado River


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Fig. 4 - Typical wide cross section of the approach viaducts (units: centimetres).

The webs of the plate girders have transverse stiffeners made of ½ IPE hot-rolled sections.

Between each diaphragm there is a transverse stiffener, resulting in a spacing of 3750 mm. An

additional transverse stiffener is inserted at the web panel adjacent to the piers in order to

increase the ultimate web resistance under shear (Reis et al., 2010). The entire steelwork of

this “neutral” approach span has a total of 150 tonnes with required improved toughness

properties against brittle fracture (min. 27 J at –50 ºC) in S355 steel grade.

Fig. 5 - Horizontal bracing and steelwork plan view detail (units: centimetres).

1585

225 225 125 125

350 350

20

>257

225 225 100

100 167

60

100

200 25 50 25

260 1570

83

lower

flange

bracing

ch. 20mm

½ HEA400

½ IPE400 web

var. thick.

100

350

350

700

diaphragm

187.5 187.5 375

750

100


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According to the project authors (GRID, 2006; Reis et al., 2010), the design was developed

taking into consideration the Eurocodes for actions and for the design of steel and steel-

concrete composite bridges. Besides that, designers highlight that steel design at span sections

was mainly controlled by fatigue issues (Reis et al., 2010). Further information about the

bridge structure and its details can be found in Reis et al. (2010).

LONG-TERM MONITORING SYSTEM

In order to characterize the traffic, a long-term monitoring system was developed in a

previous work (Albuquerque et al., 2012; Albuquerque et al., 2013). Consequently, herein a

traffic characterization system is presented. A trigger system controls the amount of recorded

data. The acquisition system handles and stores the data, which is sent to FEUP, via a 3G

wireless connection, after a proper local treatment, as illustrated in Figure 6.

Fig. 6 - Long-term monitoring system (Albuquerque et al., 2012).

The traffic characterization system is performed both in qualitative and quantitative terms.

Qualitative information is provided by an IP Camera (Figure 7a) placed at one hanger of the

bridge (Figure 7b).

Quantitative information is provided by shear strain gages in the rails. These strain gages are

placed at 3 different sections of the rail (see Fig. 8). At each section, a full Wheatstone bridge

is installed. The principle of axle load measurement is based on proportionality between the

vertical load applied to the rail in the middle of two consecutive measurement sections and

the difference shear strain between them (Albuquerque et al., 2012).

The data is acquired and processed by the National Instruments cRIO-9024 and, then, stored

in a local disk and also sent, via a 3G connection, to a computer at FEUP. The long-term

monitoring system was applied, during a commissioning phase, in the load test, planned by

the Laboratório Nacional de Engenharia Civil (LNEC).


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a) IP camera b) IP camera location

c) Alfa Pendular train d) Intercity train e) Freight train

Fig. 7 - Typical traffic (Albuquerque et al., 2012).

a) Location scheme b) Installation b) Protection

Fig. 8 - Strain gages in the rails (Albuquerque et al., 2012).

Three different types of vehicles were used to load the bridge: a single power engine machine

(PEM), a short freight train (SFT) and a long freight train (LFT). In the case of the PEM, the

axle loads where known with high accuracy. Therefore, they were used on the calibration of

the traffic characterization system. For each position, the corresponding values of the strains

were measured for all the strain gages.

In a service phase, the traffic was monitored for a real traffic scenario. At this railway line,

traffic is composed mainly by fast passenger trains, such as Alfa Pendular (see Fig. 7c), with

speeds up to 220 km/h, and heavy freight trains, proceeding from or to the sea port of Sines.

A very good agreement between the experimental and the numerical results was generally

found (Albuquerque et al., 2012). Despite of the installed traffic monitoring system on the

bridge, in the current work it will used the Eurocode fatigue standard traffic in a preliminary

stage.

FINITE ELEMENT MODEL

Herein the finite element numerical model of the investigated “neutral” span of the approach

viaducts is presented. The global model of the structural system was developed within the

ANSYS (2013) software, using the ANSYS Parametric Design Language (APDL). In the

numerical model, the concrete deck, the girder steel plates and the transverse stiffeners were


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modelled by shell finite elements (SHELL181). The steel sections of the diaphragms, the

ballast retaining walls and the rails were modelled by beam elements (BEAM44) positioned at

the corresponding centres of gravity. The sleepers, rail pads and ballast layer were modelled

by solid elements (SOLID185).

Rigid link elements (MPC184) were introduced to connect the nodes of the slab to the bottom

of the ballast and to the girders top flange, in order to ensure the compatibility of

displacements and rotations between these nodes. After some sensitivity analysis, an average

mesh dimension of 0.5 m was adopted, with a fine mesh near to the transverse stiffeners,

resulting in a mesh with variable spacing along the deck.

Nodal mass elements (MASS21) were used to reproduce the self-weight of the inoperative

railway track and the non-structural components along the deck, such as the guardrails and the

sidewalk pavement. In order to equally distribute the mass values over an irregular mesh, an

APDL routine was created to compute the influence area of each node in the slab. Therefore,

the final finite element model resulted in a total of 23,592 nodes, 39,243 elements and

141,552 degrees of freedom. The isometric views, the cross section and the side view of the

numerical model with all mentioned elements are presented in Figure 9.

a) Isometric view b) Cross section at support

c) Side view

d) Railway track detail e) Detailed view

Fig. 9 - Overview of the finite element numerical model of the selected “neutral” approach span.


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A relevant number of vibration modes were reviewed, namely vertical bending and torsion of

the deck. Figure 10 presents the three main global vibration mode shapes of the approach

viaduct obtained by a modal analysis with ANSYS (2013).

a) f01 = 2,60 Hz b) f02 = 3,05 Hz c) f03 = 3,63 Hz

Fig. 10 - Main global vibration mode shapes from the numerical model.

It must be emphasized that, in the dynamic analysis performed in the subsequent sections, a

typical value of 0.5 % for the damping ratio was used for all vibration modes, as

recommended for steel-concrete composite bridges by EN 1991-2 (2003). In Table 1, the

information on the frequency and damping ratios of some vibration modes is summarized.

Table 1 - Frequencies and damping ratios of the numerical vibration modes.

Mode

number

Numerical Natural

Frequency (Hz)

Damping

(%) Description

1 2.60 0.5 Global vertical bending mode

2 3.05 0.5 Global torsion mode

3 3.63 0.5 Global torsion mode

5 5.47 0.5 Local bending mode of the concrete slab

33 14.28 0.5 Local bending mode of the concrete slab

35 14.74 0.5 Local vibration mode of the diaphragms

109 30.70 0.5 Local vibration mode of one web panel

PROPOSED METHODOLOGY FOR FATIGUE ANALYSIS

In railway bridges the existing stress amplitudes on structural details occurs owing to the

passage of trains, causing fatigue damage. In this paper, it was used a general procedure based

on the Damage Accumulation Method (DAM), as prescribed in EN 1993-1-9 (2005) for

fatigue analysis of structures subjected to variable-amplitude loading. According to

Nussbaumer et al. (2011) and Sousa et al. (2013) this methodology involves the following

analysis steps:

- definition of the traffic scenario (train types, frequent operating speeds and annual traffic volume);

- calculation of the stress history in critical structural details, including the effects of dynamic magnification of structural response;

- calculation of stress histograms, representing the number of cycles versus the

corresponding distribution of stress ranges, by using a cycle counting algorithm, e.g. the

rainflow algorithm (ASTM E1049 - 85, 2005; ESDEP, 1995);


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- adoption of suitable SN curves to describe the fatigue resistance of the detail; the curves proposed by the EN 1993-1-9 (2005) are employed; moreover, for a safe life assessment

with high consequences of failure, the standard recommends that the fatigue strength

reduction factor, γMf, should be taken as 1.35;

- computation of the fatigue damage, by using a linear damage accumulation model, as

proposed by Miner (1945), according to which the damage factor, D, is given by:

0.1... ∑13

3

2

2

1

1 ≤=+++==

k

i i

i

N

n

N

n

N

n

N

nD (1)

where ni is the number of applied load cycles for a given stress range and Ni denotes the

number of resisting load cycles for a given stress range. Fatigue failure is reached for D = 1.

In this numerical study, the main assumption of the referred methodology is to presume as

nominal stresses the stresses obtained from a finite element model at some specific points,

related to detail categories used to determine the corresponding SN curve.

It is important to highlight that for railway bridges dynamic analyses shall be carried out in

the case of high-speed traffic, i.e., when the Maximum Permitted Vehicle Speed exceeds 200

km/h (EN 1991-2, 2003). Proper models shall be also used for the distribution of the axle

forces through the rails, sleepers and ballast. Finally, the fatigue life estimation, in years, is

given by the inverse of the damage factor for 1 year of traffic.

Identification and Classification of Fatigue Prone Details

A crucial stage of the fatigue analysis is the identification and classification of structure’s

fatigue prone details. Herein, this classification is based on the available design and

construction information (GRID, 2006; REFER, 2010; Reis et al., 2011). Figure 11 presents a

3D modelling of the approach span steelwork, with the identification of the fatigue prone

details, and the corresponding classification according to a number which represents its

fatigue resistance for 2 million cycles (∆σC). The common direction of the nominal stress is

also indicated. Figure 12 shows a more detailed view of the fatigue details, with the

corresponding SN curve. Thus, the most relevant fatigue structural details are described

below:

- Category 80 (Figure 12a): Vertical stiffeners made of ½ IPE 400 hot-rolled sections

welded to the lower flange. The nominal stresses are obtained in the lower flange as the

maximum normal stress in the longitudinal direction;

- Category 71 (Figure 12b): Longitudinal butt web in the lower flanges with a cope hole in the web; The nominal stresses are obtained in the same manner as Category 80;

- Category 63 (Figure 12c): A tube-plate joint, with the tube notched and welded to plate. The end of the tube is cut in a normal angle and welded to thin plates used as covering.

The nominal stresses are obtained from the normal forces acting on the diaphragms;

- Category 56 (Figure 12d): Longitudinal plates welded to the web girder and bolted to the ½ HEA 400 hot-rolled sections used as horizontal bracing. The nominal stresses are

obtained in the web girder as the maximum normal stress in the longitudinal direction.


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Fig. 11 - Approach viaduct steelwork with the identification of fatigue prone details.

a) Fatigue structural detail category 80

b) Fatigue structural detail category 71

Fig. 12 - Fatigue structural details, SN curves and classification according to EN 1993-1-9 (2005).

10

100

1000

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

log ∆

σR(MPa)

log N

10

100

1000

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

log ∆

σR(MPa)

log N

80

∆∆∆∆σσσσ

71


80

71

γMf = 1.35

γMf = 1.00

∆σD

∆σL

∆σD

∆σL

80

56

71

63


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c) Fatigue structural detail category 63

d) Fatigue structural detail category 56

Fig. 12 - Fatigue structural details, SN curves and classification according to EN 1993-1-9, 2005 (continued)

Fatigue and Dynamic Analysis

In fatigue analyses, traffic effects are represented by means of 12 Fatigue Trains (FT1 to

FT12) as specified by the EN 1991-2 (2003). In this work, dynamic analyses were performed

for Fatigue Trains with speed higher than 200 km/h (FT3 and FT4). On the other hand, for the

remaining Fatigue Trains, static analyses were performed with a dynamic enhancement of

1+½(ϕ'+½ϕ''), which is sufficiently accurate for the purpose of calculating fatigue damage

caused by trains with speed up to 200 km/h, according to the Annex D of the referred

standard.

During this numerical study, among all the analysed details, the higher stress ranges were

obtained for the longitudinal plate detail, ∆σC = 56 MPa, welded to the girder below the

current active track in the second horizontal bracing connection, as illustrated in Figure 11

and Figure 12d. Therefore, one presents in Figure 13 the time history analyses for the

structural detail 56. In the curves below, each graph corresponds to one Standard Fatigue

Train crossing.

As indicated in Figure 13, the higher stress range is obtained for the Standard Fatigue Train 5.

Moreover, the structural detail 56, used in the connection of the horizontal bracing to the web

girder, also revealed to be the most critical to fatigue. The stress histograms for each train

crossing, representing the number of cycles versus the corresponding distribution of stress

ranges, are shown in Figure 14. The stress distribution showing the normal stresses in the

longitudinal direction at the structural detail 56 are also represented in Figure 15.

10

100

1000

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

log ∆

σR(MPa)

log N

10

100

1000

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

log ∆

σR(MPa)

log N


56

63


63

56

∆σD

∆σL

∆σD

∆σL


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Fig. 13 - Stress histories for the structural detail 56 due to the Standard Fatigue Trains.

0

15

30

45

60

0.0 1.0 2.0 3.0 4.0 5.0

σ(MPa)

Time (s)

Fatigue Train 1

0

15

30

45

60

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

σ(MPa)

Time (s)

Fatigue Train 2

-10

0

10

20

30

40

0.0 1.0 2.0 3.0 4.0 5.0 6.0

σ(MPa)

Time (s)

Fatigue Train 3

-10

0

10

20

30

40

0.0 1.0 2.0 3.0 4.0

σ(MPa)

Time (s)

Fatigue Train 4

0

15

30

45

60

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

σ(MPa)

Time (s)

Fatigue Train 5

0

15

30

45

60

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

σ(MPa)

Time (s)

Fatigue Train 6

0

15

30

45

60

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

σ(MPa)

Time (s)

Fatigue Train 6

0

15

30

45

60

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

σ(MPa)

Time (s)

Fatigue Train 6

0

15

30

45

60

0.0 1.0 2.0 3.0 4.0 5.0

σ(MPa)

Time (s)

Fatigue Train 9

0

15

30

45

60

0.0 1.0 2.0 3.0 4.0 5.0

σ(MPa)

Time (s)

Fatigue Train 10

0

15

30

45

60

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

σ(MPa)

Time (s)

Fatigue Train 11

0

15

30

45

60

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

σ(MPa)

Time (s)

Fatigue Train 12


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Fig. 14 - Rainflow cycles counting results.

-50 -37 -25 -13 0 11 24 49 (MPa)

a) Normal stress distribution b) Shell finite elements mesh

Fig. 15 - Normal stresses for Fatigue Train 5 in the structural detail 56.

1.5

8

21

0

4

8

12

1 2 3 31

Cycles (ni)

∆σR (MPa)

Fatigue Train 1

1.5

8

21

0

4

8

12

1 2 3 31

Cycles (ni)

∆σR (MPa)

Fatigue Train 1

31

2 2 3 3 1 1 1 0.50.50

10

20

30

40

1 5 6 7 8 9 10 11 15 19

Cycles (ni)

∆σR (MPa)

Fatigue Train 3

21.5

41 1.5 2 1.5 1 1 0.50.5

0

10

20

30

1 2 3 4 5 6 7 10 15 17

Cycles (ni)

∆σR (MPa)

Fatigue Train 4

22.513

10

20

40

60

1 2 49

Cycles (ni)

∆σR (MPa)

Fatigue Train 5

2.5121 1 1 1

0

4

8

12

1 3 10 15 16 18 37

Cycles (ni)

∆σR (MPa)

Fatigue Train 6

1 1

8

1

0

4

8

12

1 2 4 36

Cycles (ni)

∆σR (MPa)

Fatigue Train 7

33.5

10

20

40

60

1 34

Cycles (ni)

∆σR (MPa)

Fatigue Train 8

2.5 13

1

0

4

8

12

1 2 3 15

Cycles (ni)

∆σR (MPa)

Fatigue Train 9

8.5

1

0

4

8

12

1 18

Cycles (ni)

∆σR (MPa)

Fatigue Train 10

0.5 13

5

1

0

4

8

12

1 3 4 5 37

Cycles (ni)

∆σR (MPa)

Fatigue Train 11

0.5 13

5

1

0

4

8

12

1 3 4 5 37

Cycles (ni)

∆σR (MPa)

Fatigue Train 11



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Fatigue Damage

Three standard mixes of rail traffic are given as a basis for calculating the fatigue life

estimation of structures, depending on whether the structure carries “standard traffic” mix,

predominantly “heavy traffic” or “light traffic” (EN 1991-2, 2003). Each traffic scenario is

defined in terms of an annual traffic tonnage of 25x106 tonnes with variety and number of

Standard Fatigue Trains per day on each track. Thus, the damage values associated with an

isolated passage of each train were combined, in order to obtain the damages in a lifespan

period of 100 years for different traffic mixes (see Tables 2 to 4).

Table 2 - Fatigue damage for standard traffic mix scenario

Standard Traffic Mix

Train

type

Vehicle Speed

(km/h)

Number of

trains/day

Damage per

Crossing Annual Damage

1 200 12 2.0869E-07 9.1404E-04

2 160 12 4.8201E-08 2.1112E-04

3 250 5 9.2717E-09 1.6921E-05

4 250 5 5.3166E-09 9.7028E-06

5 80 7 8.2413E-07 2.1057E-03

6 100 12 3.6897E-07 1.6161E-03

7 120 8 3.2682E-07 9.5433E-04

8 100 6 2.7532E-07 6.0296E-04

Total: 6.4308E-03

Table 3 - Fatigue damage for heavy traffic mix scenario

Heavy traffic mix

Train

type

Vehicle Speed

(km/h)

Number of

trains/day

Damage per


5 80 6 8.2413E-07 1.8048E-03

6 100 13 3.6897E-07 1.7508E-03

11 120 16 3.5482E-07 2.0722E-03

12 100 16 3.2682E-07 1.9087E-03

Total: 7.5365E-03

Table 4 - Fatigue damage for light traffic mix scenario

Light traffic mix

Train

type

Vehicle Speed

(km/h)

Number of

trains/day

Damage per


1 200 10 2.0869E-07 7.6170E-04

2 160 5 4.8201E-08 8.7968E-05

5 80 2 8.2413E-07 6.0161E-04

9 120 190 0.0000E+00 0.0000E+00

Total: 1.4513E-03


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Considering the numerical results presented at Tables 2 to 4, it is possible to conclude that: i)

the Standard Fatigue Train which produces the greater damage is the FT5, a locomotive-

hauled freight train; ii) the traffic scenario with maximum total damage is the heavy traffic

mix; iii) the damage induced by FT3 and FT4 is negligible and by FT9 is null, since there are

few or none stress range cycles due to these trains higher than the design cut-off limit (∆σL =

17 MPa).

The log ∆σ-log N design curve of structural detail 56 is illustrated in Figure 16, with a double

inclination as specified by EN 1993-1-9 (2005), to take into account the effect of variable

amplitude-loading on the fatigue damage. As can be seen in the graph below, with the points

corresponding to each Fatigue Train for different traffic mixes, the number of cycles

associated with stress ranges higher than the cut-off limit is very low.

Fig. 16 - Stress spectrum against SN Curve for different traffic mixes.

Also, as shown in Figure 17, in all cases the annual damage obtained is much lower than unity

for the three traffic scenarios (heavy, standard and light). Therefore, the most conditioning

traffic scenario, which is the heavy traffic mix, leads to an annual fatigue damage of 0.0075,

and consequently to a structure fatigue life estimation of 133 years.

Fig. 17- Fatigue damage at the critical detail for different traffic scenarios.

10

100

1000

2.E+02 2.E+03 2.E+04 2.E+05 2.E+06 2.E+07 2.E+08

log ∆

σR(MPa)

log N

light traffic heavy traffic standard mix

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

Heavy traffic mix Standard Traffic Mix Light traffic mix

Annual Damage

Traffic Scenario

∆σL


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Impact of Global and Local Modes in Total Dynamic Response

Each mode of vibration of the selected “neutral” approach span has its own impact on total

dynamic response of the structure. In order to compute the contribution of higher frequency

modes to the stress response at the critical detail, with the crossing of the most conditioning

Fatigue Train, the total response was decomposed into some of its different components

through a dynamic mode superposition analysis, as shown in Figure 18a.

a) Stress history in structural detail 56 b) Fourier transform response of first mode

Fig. 18 - Contribution of different vibration modes to the total response.

The total dynamic response of Figure 18a reveals that, at the critical detail zone, only the first

three global vibration modes with frequencies up to 3.63 Hz are expressive to the total stress

range. The local vibration mode of diaphragms (Mode 35) yields to a low contribution of 2

MPa, while local vibration modes of the concrete slab and higher frequencies modes of the

steel web, such as Mode 109 are considered negligible to the total dynamic response of the

investigated structure.

In the component associated with the Mode 1, f01 = 2.60 Hz, it was observed a low resonance

effect, also confirmed by the Fourier Transform of the signal (Figure 12b). This is related to

an axle spacing between wagons of the FT5 equal to 4 m (Figure 19), in combination with a

speed of 80 km/h, considering the first integer submultiple (80/3.6/4/2 = 2.78 Hz).

It must be emphasized that the maximum stress obtained through a dynamic mode

superposition analysis (34 MPa) is different from that obtained through a static moving load

analysis with dynamic enhancement (49 MPa). Moreover, since the dynamic properties of the

Fatigue Train 5 are unknown, the train-track-bridge interaction and the track irregularities

were not considered in this dynamic analysis.

Fig. 19 - Arrangement of the Standard Fatigue Train 5 axle loads (EN 1991-2, 2003).

-5

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14

σ(MPa)

Time (s)

Mode 1 (2.60 Hz)

Mode 2 (3.05 Hz)

Mode 3 (3.63 Hz)

Mode 35 (14.74 Hz)

Mode 109 (30.7 Hz)

Total

0

0.5

1

1.5

2

2.5

3

2 2.5 3 3.5 4

Amplitude

Frequency (Hz)

6x225 kN 6x225 kN 6x225 kN 6x225 kN 6x225 kN

11x(6x225 kN)

2.1 4.4 2.1 1.8 5.7 1.8 1.8 1.8 1.8 1.8 1.8 1.85.7 5.7 5.7

2.0 2.1 2.1 2.0 1.8 2.01.8 2.01.8 1.8 1.8 1.8 2.0 1.8 1.8 2.0

16.8 16.9 16.9 16.9 16.9 11x16.92.0 2.0 2.0 2.0

f01 = 2,60 Hz


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CONCLUSIONS

The steel-concrete composite approach viaducts of new Sado River railway crossing are under

study concerning its fatigue behaviour. In this kind of analysis, the finite element model of the

structure is a very important tool. Nevertheless, it is important to assure that the developed

numerical model reproduces well the response of the real structure.

In the present work, a fatigue analysis on selected structural details of one “neutral” span of

the approach viaducts has been carried out. The main conclusions of this research work can be

summarized as follows:

- The railway traffic characterization made on previous works reveals to be very useful,

because it enables the extrapolation of the results to other points of the structure. Future

research into the fatigue behaviour of the railway viaducts over the River Sado will take

into account monitored real traffic;

- The detailed level of the structure finite element model allowed for fatigue analyses in

different points of the structure and for different traffic scenarios;

- The most critical detail was that on the longitudinal plate welded to the web girder below

the current active rail track. This plate is used in the connection of horizontal bracings of

the structural system, which are very important to improve the torsional deformability

and torsional vibrations under eccentric railway traffic loads. Therefore, it leads to

conclude that normal forces on horizontal bracings may introduce important normal

stresses on the web girder. For that detail, the worst loading case was the crossing of the

Standard Fatigue Train 5;

- According to the Damage Accumulation Method low damage levels were found.

Therefore, the assessment of the numerical results obtained through FE analyses revealed

that the fatigue design of the investigated “neutral” span is on the safe side;

- The global vibration modes, with lower frequencies, are the most determinant to the total

response of the investigated approach span at the critical detail;

- Local approaches to fatigue will in the future applied to the critical location detected in this paper. Also, multiaxiality of the stress histories will be investigated.

ACKNOWLEDGMENTS

Support from the National Council for Scientific and Technological Development, CNPq,

Brazil, through a research project related to evaluation of structural performance and dynamic

response monitoring of bridges is gratefully acknowledged. Support from the research team

on High-Speed Rail field of Faculty of Engineering of University of Porto is also gratefully

acknowledged.

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Documents

FATIGUE ASSESSMENT OF APPROACH VIADUCTS OF THE NEW …irf/Proceedings_IRF2016/data/papers/6273.pdf · span at the north side and near to the first bowstring arch of the main bridge