Some Thoughts on Variation of Response according to Longitudinal

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 5 (2016) pp 3689-3695

© Research India Publications. http://www.ripublication.com

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Some Thoughts on Variation of Response according to Longitudinal Track-

Bridge Interaction Analysis Methods

K. M. Yun

Ph.D. Candidate, Department of Civil Engineering, Chungnam National University, Daejeon, South Korea.

B. H. Park

Ph.D. Candidate, Department of Civil Engineering, Chungnam National University, Daejeon, South Korea.

H. U. Bae

Post-doctoral Researcher, Department of Civil Engineering, Chungnam National University, Daejeon, South Korea.

N. H. Lim* Professor, Department of Civil Engineering,

Chungnam National University, Daejeon, South Korea.

Abstract

Additional axial stress of the rail and displacement are

induced by the influence of the track-bridge interaction when

the CWR(Continuous Welded Rail) track is constructed on the

bridge. That is the main cause of the restriction of length of

bridge deck and an increase in the construction cost. And the

track-bridge interaction analysis is performed in order to

examine the influence of the interaction. Two analysis

methods are proposed in UIC 774-3R according to whether

the loading history is considered or not. In this paper, the

fundamental study was carried out for inducing an economic

design of the railway bridge applying the proper analysis

methods. For this purpose, track-bridge interaction analysis

was performed on various types of bridges and the variation

of response according to each analysis method was analyzed

by comparing and analyzing the interaction analysis results.

Keywords: Track-bridge interaction, additional axial stress,

load sequence, finite element analysis, complete analysis

Introduction The axial stress distribution of the rail generated by the track-

bridge interaction in the case of the CWR(Continuous Welded

Rail) installed on a bridge is very complex compared to the

CWR on an embankment. This is because the track-bridge

interaction is brought about by the various factors applied to

the bridge, such as the temperature load, the acceleration and

braking loads and the vertical load of vehicles. In order to

prevent any problems which may be caused by a track-bridge

interaction, longitudinal track-bridge interaction examination

methods are proposed, these proposals are based on various

criteria as shown in UIC 774-3R[1], KR C-08080[2], and

Euro code EN1992-2[3].

EN 1992-2 and KR C-08080 propose a separate analysis

method which neglects completely the influence of the

loading history. Therefore this method may have some error

because of the behavior of the longitudinal resistance

connecting the rail and the a separate analysis the load

combination method that handles the respective influences

arising from the change in temperature on the bridge, the

acceleration and braking loads of a train, and the vertical load

of the train, as mutually independent loads simply combines

the analysis results for the respective loads. Such an analysis

method like this ignores the influence of loads on the

nonlinearity of the loading history. Therefore it includes an

error caused by the nonlinear behavior of the longitudinal

resisting force of ballast. Thus, in order to allow for any kind

of influence on this, it is necessary to consider a complete

analysis which takes into consideration the effect of the

loading history.

The European Rail Research Institute (ERRI)[4,5] in Europe

have developed a program for measuring the longitudinal and

lateral resisting forces of a ballast track and a CWR buckling

and track-bridge interaction analysis program (LOGIN). P.

Ruge and C. Birk[6] in Germany proposed a new technique

for analyzing the longitudinal track-bridge interaction under a

stage-by-stage loading. In addition, Yun[7], M.C.Sanguino[8]

analyzed the variation of response in the case of allowing for

the loading history during the longitudinal and vertical track-

bridge interaction of continuous welded rails on bridges.

However, sufficient research on the variation of response

according to the analysis methods has not yet been performed

on various types of actually designed bridges. In this paper,

the longitudinal track-bridge interaction analysis was

performed on various types of bridges using LUSAS 15.0[9],

which is a general-purpose finite element program. The

additional axial stresses and displacements were compared



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and analyzed according to two different analysis methods:

One is the separate analysis, which individually considers the

loads that generate the longitudinal track-bridge interaction,

and the second is a complete analysis, which considers the

history of the short and long-term loads.

Analysis Methods UIC 774-3R provides two analysis methods according to the

structural design of a bridge and its importance. It suggests

both the separate analysis method and the complete analysis

method in order to select one of the two analysis methods for

the purpose of performing analysis.

Separate analysis The separate analysis method considers the temperature load,

the acceleration/braking loads and the vertical load

independently without taking the load combination into

consideration. And the additional stress of the rail is

calculated as Eq.1

( )

( / ) ( )

R R temperature loadR acceleration braking bending

(1)

where, the value of 1 is used for α, β and γ respectively.

Figure 1: Longitudinal resistance of the connection between

the rail and deck

Complete analysis The complete analysis method considers the loading history

by allowing for the longitudinal resistance force of ballast that

changed due to the temperature load. The complete analysis is

performed through two of the following analysis stages:

① 1st stage-the stage intended to consider only the

temperature load which is thought to be a long-term

load before vehicle loading

② 2nd stage-the stage intended to carry out vehicle

loading whereby allowing for the longitudinal

resisting force of ballast changed from the 1st

analysis stage

Fig. 2 shows the changed longitudinal resistance curve

with/without the vehicle load in 2nd stage when the

longitudinal resistance exists in the elastic(a) and plastic(b)

regions, due to the temperature load (1st stage). Fig. 2 (a)

shows a case where the state of the longitudinal resistance

changed by the temperature load at the 1st stage is in the

elastic region. If resisting direction is the same direction in the

2nd stage as it did during the first stage in the region where

there is no vehicle loading, it can resist as much additional

resistance as ( Un elaF F ). If the resistance force acts in the

opposite direction in the same location at the 2nd stage, it can

resist up to ( Un elaF F ).In the zone where there is vehicle

loading imposed at the 2nd stage, the ballast can resist greater

loads because the frictional force increases due to the vehicle

loading. Thus, if the ballast resists at the 2nd stage in the same

direction as it did at the 1st, it can exert as much resistance as

( L ElaF F ).If the ballast resists in the opposite direction, it can

exert the resistance of ( L ElaF F ).

Fig.2 (b) shows a case where the state of the longitudinal

resistance changed by the temperature load at the 1st stage is

in the plastic region. If the resistance force acts in the same

direction as it did at the 1st stage in the region where there is

no vehicle loading at the 2nd stage, it cannot exert any

additional resistance. If the ballast resists in the opposite

direction in the same region at the 2nd stage, it can exert the

resistance of ( Un UnF F ).If the resistance force acts in the

same direction as it did at the 1st stage in the region where

there is any vehicle loading imposed at the 2nd stage, it can

exert as much resistance as ( L UnF F ).If the ballast resists in

the opposite direction in the same region, it can exert the

resistance of ( L UnF F ).

Figure 2: Changes in the longitudinal resistance considering

the loading history[7] (a) elastic state after 1st stage (b) plastic

state after 1st stage

Numerical Analysis Models Target bridges The target bridges are 20 bridges that are designed for a

ballasted single track. The summarized types of the selected

bridges are as shown in Table 1.

One representative bridge is described minutely this paper.

The representative bridge is composed of PSC, WPC and

BICON girders and total length is 450m(Br-18). Fig. 3 shows



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its longitudinal section and cross section view. And Table 2, 3

show the material properties of decks and piers respectively.

Table 1: Type of 20 actually designed bridges

Bridge Form of Span and length(m)

Br-1 29.95m(PSC-e)*16= 479.2m

Br-2 24.945m(PSC)+39.9m(WPC)*5= 224.445m

Br-3 39.9m(WPC)*8+34.94m(IPC)+39.9m(PRECOM)= 394.04m

Br-4 40.05m(WPC)*2+40m(WPC)*5+45m(IT)*2+10m(Rahmen)= 380.1m

Br-5 35.03m(PSC-e)+30m(PSC-e)+50.05m(SB composite girder)+14.9m(Rahmen)*4+55.1m(STB)+50.1m(SB composite

girder)*5+9.9m(Rahmen)*2+14.95m(Rahmen)+35.06(PSC-e)= 555.09m

Br-6 25.025m(PSC)*2+35m(PSC-e)*6= 260.05m

Br-7 35.08m(PSC-e)+35.05m(PSC-e)*12+30.05m(PSC-e)*2+35m(PSC-

e)*4+45m(PRECOM)*3+40m(WPC)*4+55m(STB)*2+15m(Rahmen)*2+35.03m(PSC-e)= 1125.81m

Br-8 25m(PSC)*2+55m(STB)*1+10m(Rahmen)*2= 125.0m

Br-9 29.95m(IPC)*3+34.94m(IPC)*10+39.9(PRECOM)= 479.15m

Br-10 24.95m(PSC)*4+49.9m(SCP)*2+34.94m(IPC)*21+31.44m(IPC)+79.8m(ARCH)*2+29.95m(IPC)*2+39.9m(PRECOM)*2= 1264.08m

Br-11 25.025m(PSC)*2+25.005m(PSC)*2+35m(PSC-e)*14= 596.06m

Br-12 30.055m(PSC)*2+30.03m(PSC)*3= 150.2m

Br-13 45m(PRECOM)*1+35m(PSC-e)*10+30.005m(PSC-e)+30.025m(PSC-e)*3+35.02(PSC-e)*2+35.03(PSC-e)+45m(PSC-e)*4= 740.1m

Br-14 34.99m(PRECOM)+35m(IPC)*5+35.03m(IPC)= 245.02m

Br-15 34.94m(IPC)*24+29.95m(IPC)+24.95m(PSC)= 893.46m

Br-16 25.025m(PSC)+35m(IT)*3+45m(PRECOM)= 175.025m

Br-17 25.025m(PSC)+35.05(PSC-e)*5+25(PSC)= 225.275m

Br-18 25.025(PSC)+40m(WPC)+35m(BICON)*11= 450.025m

Br-19 25.025m(PSC)*2+25m(PSC)*10= 300.05m

Br-20 24.95m(PSC)*5+34.94m(IPC)*2= 194.63m

Table.2. Material Properties of Decks

Member Cross-sectional area

[m2]

Young’s modulus

[N/m2]

Span Length

[m]

Moment of Inertia

[m4]

Depth

[m]

Distance from the center of the gravity to

the top [m]

PSC 4.743 3.0×107 25.025 4.253 2.642 0.835

WPC 6.457 3.12×107 40 5.718 2.622 0.974

BICON (S3~9) 5.307 3.0×107 35 5.221 2.597 0.968

BICON

(S10~13)

5.248 3.0×107 35 3.017 2.592 0.974

Table.3. Material Properties of Piers

Pier Cross-sectional area[m2] Young’s

modulus

[N/m2]

Height

[m]

Moment of Inertia

[m4]

Foundation stiffness

Longitudinal

[N/m]

Vertical

[N/m]

Rotational

[N/rad]

P1 6.158 2.75×107 6.7 3.017 7.03×109 9.93×109 5.51×1010

P2 6.158 2.75×107 6.7 3.017 7.25×109 5.02×109 3.00×1010

P3,P4,P5 6.158 2.75×107 7.7 3.017 4.08×109 2.69×109 1.77×1010

P6 6.158 2.75×107 9.2 3.017 1.71×109 2.96×109 1.78×1010

P7 6.158 2.75×107 9.2 3.017 8.72×109 2.54×109 1.84×1010

P8~P12 6.158 2.75×107 10.2 3.017 8.72×109 2.54×109 1.84×1010



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(a) Longitudinal Section of Br-18

(b) WPC(S1) (c) PSC BEAM(S2) (d) BICON(S3~S13)

Figure 3: Longitudinal Section Geometric Properties of the Model

Track-bridge interaction analysis modeling LUSAS Ver.15.0, a finite element analysis (FEA) program,

was used for the longitudinal track-bridge interaction analysis.

The rails and the bridge decks were modeled using

Timoshenko beam elements. The ballasts were modeled using

elasto-plastically behaving nonlinear joint elements (elasto-

plastic joints). Rigid beam elements expressing a distance

from the neutral axis of the bridge deck to the bridge pier

were added. Constraint equations were applied so that in the

event of any flexural displacement in the bridge deck, its

influence on the actual height of the upper structure of the

bridge could be taken into consideration.(Fig. 4)

(a) Schematic Diagram of Track-Deck-Pier

(b) Model of the Track-Deck-Bearing system

Figure 4. Analysis model

The longitudinal resistance curve of the ballast track was

taken into consideration as shown in Fig. 5. The temperature

load, the acceleration and braking loads, and the vertical load

of trains were considered in various positions to obtain the

most unfavorable results as shown in Table 4.

Figure 5. Longitudinal Resistance of Ballast in Model

Table 4: Temperature and vehicle load

Load Magnitude (applied length)

Variation of temperature +25℃,-25℃

Vehicle load Acceleration load 33KN/m/Track(33m)

Braking load 20KN/m/Track(400m)

Vertical load 80KN/m/Track(400m)



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Track-bridge interaction analysis results according to

analysis

Analysis from the responses of the representative bridges The responses obtained by the track-bridge interaction

analysis were compared. Comparisons were also made for the

additional axial stress of the rail, the relative displacements

between the rail and deck or embankment, the absolute

displacements of the deck, and the displacement of the upper

edge of the deck, these are limited by limit values in designing

them in the Korean design standards (KR C-08080).

Additional axial stress

The additional axial stress of the rail were compared in a case

where the maximum tensile stress has occurred in

consideration of the temperature load of-25℃ at the girder,

the acceleration or braking load, and the vertical load(the

same location with braking load) of vehicles(Fig. 6).

Figure 6: Additional axial stress curves of rail according to

analysis methods

The maximum tensile stress occurred at P12, and the

maximum additional axial stress of rail according to each

analysis method was found to have occurred at 46.07 MPa in

the complete analysis and as 58.83 MPa in the separate

analysis. The additional axial stress of rail which was shown

to have occurred in the complete analysis was 21.69% lower

in comparison to the separate analysis.

Displacement

Fig. 7 shows the displacement comparison which were made

for the relative displacements between the rail and deck(Fig.

7, (a)), the absolute displacements of the deck(Fig. 7, (b)) and

the displacement of the upper edge of the deck(Fig. 7, (c)).

(a) The relative displacement between the rail and the deck

(b) The absolute displacements of the deck

(c) The displacement of the upper edge of the deck

Figure 7: Displacement curves according to analysis methods

Cause Analysis Fig.8 shows the condition of the longitudinal resistance of

ballast under each load in the location where the maximum

tensile stress occurs in the separate analysis. It reaches the

plastic region on the longitudinal resistance under the

temperature load as shown in Fig. 8 (a). It is in the state of the

plastic region on the longitudinal resistance under the braking

load as shown in Fig. 8 (b) and in the state of the elastic

region under the vertical load as shown Fig. 8 (c). In the

separate analysis, the longitudinal resistance of ballast

changed under the temperature load (which is a long-term

load), is not taken into consideration during vehicle

loading(which is a short-term load).

Longitudinal Ballast Resistance of Temperature Load(T-25℃)

Longitudinal Ballast Resistance of Braking Load



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Longitudinal Ballast Resistance of Vertical Load

Figure 8: Longitudinal Ballast Resistance of Separate

Analysis (Br-18)

Fig. 9 shows the longitudinal resistance state(condition) of

ballast at the 2nd stages of the complete analysis at Pier 12.

The 1st analysis gives out the same results as those obtained

under the temperature load in the separate analysis (Fig. 8(a)).

In addition, the location where the maximum tensile stress has

occurred is the region where vehicle loading is imposed after

the resistance reaches the plastic region in the 1st analysis. It

behaves along the resistance curve as shown Fig. 9.

Figure 9: Longitudinal Ballast Resistance according to

Complete Analysis (Br-18)

As Fig. 9, if the direction of resistance in 1st stage analysis

and the direction in the 2nd stage analysis are the same, it can

exert additional resistance which is excluded from the

marginal resistance under vehicle loading. The longitudinal

resistance of the ballast in the 2nd analysis reaches the plastic

region under vehicle loading, thus being unable to resist the

load any longer and showing the state of only the relative

displacement between the rail and the bridge. In the separate

analysis which independently considers the three important

loads the temperature load, the starting/braking load and the

vertical load of vehicles. This generates the track-bridge

interaction, the longitudinal resistance of ballast is assumed

each load considered separately. However in regards to the

complete analysis, the longitudinal resistance of ballast

considers the full effect of the load history. Therefore, as the

size of the longitudinal resisting force of ballast (which resists

each load) is small in comparison with the separate analysis,

the amount of the additional axial stress which occurs on the

rail also becomes small and a large displacement occurs.

Responses of various types of bridge Additional axial stress of the rail:

The maximum additional tensile stress of rail was deducted

and the analysis results on 20 different bridges were also

analyzed. The maximum tensile stress of rail and the variation

ratios according to the analysis methods(complete and

separate analysis results) are as shown in Fig. 10.[10]

Figure 10: Maximum additional tensile stress of rail

There was a maximum decrease of 21.69% and a minimum

decrease of 2.85% discovered in the complete analysis in

comparison to the separate analysis. The additional tensile

stress of the rail was found to have decreased by an average of

11.09%.

Relative displacements between the rail and deck

The results that were obtained by the analysis methods were

then analyzed with respect to the longitudinal relative

displacement between the rail and deck under the acceleration

or braking load. The maximum relative displacements and the

variation ratios which occur according to the analysis methods

(complete and separate analysis results) are as shown in Fig.

11. [10]

Figure 11: Maximum relative displacement between the rail

and deck

There was a maximum increase of 46.59% and a minimum

increase of 19.17% discovered in the complete analysis in

comparison to the separate analysis, and the relative

displacement had been detected to have increased by an

average of 29.22%.



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Figure 12: Maximum absolute displacement of deck

There was a maximum decrease of 22.11% and a minimum

decrease of 6.16% discovered in the complete analysis,

compared to the separate analysis. The additional tensile stress

of the rail was found to have decreased by an average of

11.82%.

The displacement of the upper edge of the deck

The results obtained by the analysis methods were analyzed

with respect to the displacement of the upper edge of the deck

under the vertical load of trains. The maximum tensile stress

and the variation ratios which occur according to the analysis

methods are as shown in Fig. 13.

Figure 13: Maximum displacement of the upper edge

of the deck

There was a maximum increase of 19.75% exposed in the

complete analysis in comparison to the separate analysis.

There was also a slight difference in the longitudinal

displacement between the two analysis methods.

Conclusions The objective of this research was to analyze the effect on the

track-bridge interaction analysis methods. For this, track-

bridge interaction analysis was performed on 20 designed

bridges by applying two different analysis methods according

to consider a loading history or not.

If a track-bridge interaction analysis is performed on the same

bridge through a complete analysis method, the additional

axial stress of the rail can be decreased by up to 21.7% in

comparison to the separate analysis. Moreover, the relative

displacement between the rail and the deck, the absolute

displacement of the deck, the displacement of the upper edge

of the deck can be increased by up to 46.6%, 22.1% and

19.8% respectively. When using the existing separate analysis

method, an excessive design is induced in terms of the

additional axial stress of the rail. On the other hand, the

displacement is designed with safety in mind.

Acknowledgements This research was supported by a grant (15RTRP-B067919-

03) from Railroad Technology Research Program funded by

Ministry of Land, Infrastructure and Transport of Korean

government.

References

[1] UIC, Code 774-3R, Track/bridge Interaction

Recommendations for Calculations (2001).

[2] KR(Korea Rail Network Authority), Korea Railway

Design Guideline (2011).

[3] CEN, EN9: EN1991-2, Eurocode 1-Actions on

structures-part 2 Traffic loads on bridges (2003)

[4] ERRI D 202/RP 3, Theory of CWR track stability,

Utrecht (1995)

[5] ERRI D 202/RP 4, Stability of continuous welded

track, Utrecht (1999)

[6] P. Ruge, C. Birk, Longitudinal forces in continuously

welded rails on bridge decks due to nonlinear track-

bridge interaction, Computer & Structures, 85(4), pp.

458-475 (2007)

[7] K.-M. Yun, J.-Y. Choi, J.-O Lee, N.-H. Lim,

Modification of the conventional method for the

track-bridge interaction, Applied Mechanics and

Materials, Vols. 204-208, pp. 1988-1991 (2012)

[8] M.C.Sanguino, P.G.Requejo, Numerical methods for

the analysis of longitudinal interaction between track

and structure, Track-Bridge Interaction on High-

Speed Railways, CRC Pr I Llc, Porto, Portugal(2008)

[9] LUSAS Inc., LUSAS User’s manual, Surrey, KT1

1HN, UK(2006)

[10] K.-M. Yun, B.-H. Park, H.-U Bae, S.-H Choi, N.-H.

Lim, Study on Response according to Longitudinal

Track-Brdige Interaction Analysis Methods with

respect to Various Type of Bridge, Information,

International Information Institute(in press)

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Some Thoughts on Variation of Response according to Longitudinal