laboratory mock-up tests - railway research · mock-up b: two 8.8m slabs connected with a dowel...

The 9th World Congress on Railway Research, Lille, France, 22-26 May, 2011Challenge B: An environmentally friendly railway

Jang et al./Evaluation of static and dynamic performance of floating slab track 1/8

Evaluation of static and dynamic performance of floating slab track by real-scalelaboratory mock-up tests

1S. Y. Jang, 1S. H. Hwang, 1S. C. Yang, 2H. H. Cho and 1E. Kim1Korea Railroad Research Institute, Uiwang, South Korea2Korea Institute of Nuclear Safety, Daejeon, South Korea

Abstract

The floating slab track (FST) is one of strong alternatives to attenuate the vibration of structure andground induced by passing trains. However, the dynamic behavior of the FST is so complicated, and itshould be checked in advance to application through a detailed evaluation of performance. In thisstudy, to verify the design of recently developed FST using elastomeric bearings, the real-scale mock-up test tracks have been manufactured and tested to evaluate the static and dynamic performance.Prior to the test, the numerical modal analysis has been performed to investigate the modal properties.After that, two mock-up test tracks are fabricated; one is a continuous 18.87m long FST and the otheris a dowel-connected 2×8.8m long FST, and the static load test and the modal test under harmonicload have been performed. From the numerical analysis and test results, the static performance of theFST design has been verified and the dynamic modal properties such as vibration mode shapes andnatural frequencies have been investigated. Also the effect of the dowel joint on the static deflectionsand dynamic modal properties was also discussed.

Keywords: floating slab track(FST), elastomeric bearings, modal test, static and dynamic performance

Introduction

Recently, despite high demands of speed-up of conventional lines and increase of high-speed lines,strict criteria for the vibration and noise induced by trains are applied, and thus, it is of great concernin railway industry. The floating slab track (FST) is one of strong alternatives to attenuate the vibrationof structure and ground induced by passing trains. However, the dynamic behavior of the FST is socomplicated that a detailed analysis and thorough evaluation of dynamic performance are necessarybefore installing a new FST system on site.

In this study, therefore, to verify the design of recently developed FST using elastomeric bearings,the real-scale mock-up test specimens have been manufactured and tested to evaluate the static anddynamic performance including the natural frequencies and vibration mode shapes of the system.

System outlines

The recently developed floating slab track is a low tuned, high-performance system using highefficient anti-vibration elastomeric bearings, i.e., rubber mounts. The basic structure of this floatingslab track is similar to existing systems as shown in Fig. 1. However, a unique feature of this systemarises from the rubber mount which provides self-lifting and post-alignment using pre-installedhydraulic pressure cylinder, see Fig. 1 and 2.

Steel casing

Insert of rubbermount in this direction

Concrete slabRubbermount

H





Abstract



Introduction



System outlines


Steel casing



H





Abstract



Introduction



System outlines


Steel casing



H



Fig. 1. Basic structure of floating slab track

Fig. 2. Rubber mounts

(a) vertical (b) horizontal

Fig. 3. Static load-displacement relationship of rubber mounts

Due to its diagonal shape and multi-layered structure of rubber parts, the rubber mount shows analmost linear vertical load-displacement relationship in the range of service load as shown in Fig. 3.The static vertical spring constant can be lowered down to around 10kN/mm. The horizontal springconstant is around 80% of the vertical spring constant as shown in Fig. 3(b), and the damping ratio isobtained about 10%.

Modal analysis of test mock-up

Prior to the test, to determine the appropriate length of the test mock-up, 3D FE modal analyseshave been carried out, and natural frequencies and vibration mode shapes according to slab lengthwere examined. According to Hui et al.(2008; 2009), the bending mode of the floating slab has aconsiderable influence on the overall mobility of the system. Thus, it is important that the test mock-uphas bending modes to make sure it behaves like the actual track.

Inner steel plate

Outer steel plates

Rubber

Lock boltHydraulic pressurecylinder

Rubber

Oil valve

0 1 2 3 4 5 6 7 8

0

20

40

60

80

100

Load

[kN]

Displacement [mm]0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

5

10

15

20

Load

[kN]

Displacement [mm]

0

40

80

120

160

200

240

0 10 20 30 40

Natu

ral fr

equency

(H

z)

Slab length (m)

1st Bending Mode

2nd Bending Mode

Length of test mock-up



Fig. 4. Bending mode natural frequency according to slab length

Fig. 5. Mode shapes of vertical translation and bending modes

Table 1. Natural frequencies and vibration modes of the test mock-up (L=18.87m)

No. Natural frequency(Hz) Vibration mode1 6.69631 Lateral translation (y-axis)2 6.73858 Longitudinal translation (x-axis)3 7.16302 Rotation around z-axis (yawing)4 7.4403 Vertical translation (z-axis)5 7.93535 Rotation around y-axis (pitching)6 9.019 Rotation around x-axis (rolling)7 9.62659 1st Bending at x-axis8 15.9944 2nd Bending at x-axis9 21.8853 Warping

10 25.5048 Bending at y-axis

The natural frequencies according to slab lengths were plotted in Fig. 4, in which one can find theshorter the slab length, the greater the natural frequencies of the bending modes become. Hence, inorder that the test mock-up behaves in the bending mode like the actual track, the slab length shouldnot be less than around 18~20m. Considering the sleeper spacing, the length of the test mock-up wasdetermined as 18.87m for the control specimen. Summarized in Table 1 are the natural modes andfrequencies of the 18.87m long test mock-up with the cross-section shown in Fig. 6 supported byrubber mounts with 10kN/mm vertical static spring constant, equally spaced at 2.52m. Most rigid bodymodes are found in the range of 6.7 to 9Hz; e.g., the vertical rigid body translation mode occurs at7.44Hz. The actual bending modes occur at 9.63Hz for the 1st mode and 15.99Hz for the 2nd mode,respectively. Fig. 5 shows the mode shapes of the bending modes.

Experimental Program

To investigate the dynamic behavior of the floating slab, the following two types of test mock-upsshown in Fig. 6 have been installed in the laboratory test facility.

Mock-up A: a 18.87m slab without any joints (spacing of rubber isolators = 2.52m)Mock-up B: two 8.8m slabs connected with a dowel joint (spacing of rubber isolators = 2.52m)

The first mock-up (Mock-up A) is tested to verify the basic performance of the floating slab trackdesign, and the second mock-up (Mock-up B) is to investigate the structural behavior of the dowelexpansion joint section, compared with that of Mock-up A.

For each test mock-up, the static load test and the modal test by harmonic load at 5 to 20Hz havebeen carried out. Two dynamic actuators were used to simulate the axle load at mid-slab or 1/4 point.The static axle load of Korean high-speed train (KTX) is 170kN, and the maximum service load isdetermined to be 210kN considering the dynamic amplification factor of 1.27, which has been

xy

z1st bending mode (9.63Hz) 2nd bending mode (15.99Hz)

xy

z



estimated by a track-train interaction analysis using the model proposed by Yang (2009). Fig. 7 showsthe test set-up in the laboratory test facility of Korea Railroad Research Institute.

Fig. 6. Schematics of test mock-up

Fig. 7. Installation and test set-up (Mock-up A)

Results and Discussion

Result of static load test

Up to the static load of 490kN, vertical slab deflections and rail-slab relative deflections weremeasured through 7 loading-unloading steps with loading speed of 2kN/s, following DIN 45673-1(2000), as shown in Fig. 8. Fig. 8 demonstrates that the load-deflection curve is almost linear up to490kN maximum load. In Fig. 9, the maximum deflections of slab and rail at each step are plotted.This shows that the slab deflections at the dowel joint of Mock-up B are slightly higher than those atmid-slab of Mock-up A. It is probably because the bending stiffness of the dowel joint is relatively low.Fig. 10 shows the deflections along the slab length under 210kN. Fig. 10 also shows that the slabdeflection of Mock-up B with the dowel joint is higher, and the difference of deflections between two

Concrete Strains (4)

¼ point loading

Vertical displacements (20)- Rail-slab relative displ. (10)- Slab displ. (10)

Steel Strains (3)- Reinforcing steel(3)

Mock-up A

2.52m

Rail

Slab

Rubber mount

Rail fastener

Concrete Strains (8)

¼ point loading

Vertical displacements (20)- Rail-slab relative displ.(4x2)- Slab displ. (6x2)

Steel Strains (10)- Reinforcing steel (6)- Dowel bar (4)

Mock-up B

2.52m

Rail

Slab

Rubber mount

Rail fastener Dowel

8.8m 8.8m

18.87m

½ point loading

½ point loading

17.61m

0.615m

0.615m 1.26m

A

A’

750750

2, 800

C L TR

ACK

540

A-A’

8@350=2, 800

750750

540

2, 800

C L TR

ACK

A-A’

mailto:8@350



adjacent slab ends is around 0.3mm. This dislocation and increased vertical deflection may affect thedynamic stability of train. Thus, it is recommended this be checked through a detailed dynamicanalysis.

Fig. 8. Static load - deflection relationship(Mock-up A)

Fig. 9. Maximum static deflections at each loadstep

(a) Rail-slab relative deflection (b) Slab deflection

Fig. 10. Deflection curves under static load of 210kN

Strains of concrete and reinforcing steel at the loading point were also measured as shown in Fig.11. Concrete and rebar strains of Mock-up B are much smaller than those of Mock-up A. This isobviously due to that the dowel bar can transfer the shear force but not the moment, and thus itbehaves like hinge. The strain of rebar at tension part of Mock-up A is increased up to 220µε, but thestress is only 46MPa, much less than the yield strength (400MPa). In Mock-up B, the strain of steeldowel bar is also measured and shown in Fig. 12. The strains of steel dowel bar are increased up to270µε under 490kN maximum load; however, it is also much less than the yield strength.

(a) Concrete (b) Steel rebar



Fig. 11. Strain of concrete and steel rebar measured at loading point

Fig. 12. Strain of steel dowel bars of Mock-up B Fig. 13. Simplified models for FST

Result of modal test

To investigate the dynamic properties of the system, the modal test has been carried out. Theloading frequency is varied in the range of 5Hz to 20Hz. Fig. 14 and 15 demonstrate the mode shapesfor mid-slab loading and 1/4 point loading, respectively. The mode shape when excited at mid-slab isclose to 1st bending mode combined with the vertical translation mode; pure rigid body translationmode alone did not occur. Also, the mode shape when excited at 1/4 point shows the 2nd bendingmode. In general, the basic tuning frequency of the FST is assumed by Eq.(1), based on the verticalrigid body frequency based on the single D.O.F system as shown in Fig. 13(a) [Wagner, 2002].

M

kfn

2

1(1)

where k is the spring constant of bearing and M is the mass. However, from the test results, we cannotice that the dominant vibration modes are not the rigid body translation modes, but the bendingmodes. Thus the tuning frequency should be determined based on these bending mode frequencies.According to Blevins(1979), the bending mode frequencies for a beam supported by continuousWinkler springs can be obtained by

2

2

2

2

2

42

md

k

m

EI

Lf i

n (2)

where L is the length of the beam, m is the mass of the beam per unit length, EI is the flexuralrigidity of the beam, d is the spacing of springs, and i is a dimensionless parameter accounting forthe boundary conditions. For a free-free beam, i = 4.730, 7.853, 10.996 for i = 1, 2 and 3,respectively [Blevins, 1979]. Eq.(2) and the numerical modal analyses results show that, when theslab length is long enough, the bending mode frequencies decrease and converge to the vertical rigidbody translation mode frequency. However, if the slab length is short, the bending mode frequencybecomes much higher than the rigid body mode frequency. This result in the increased system tuningfrequency, which means that the dynamic stability and the target anti-vibration efficiency expectedbased on the single D.O.F model cannot be achieved.

Fig. 16 (a), (b) and (c) shows the point receptances of slab deflections measured at mid-slab, 1/4point and slab ends, respectively, when excited at mid-slab or 1/4 point. As shown in Fig. 16 (a) and(b), the 1st bending mode frequency of Mock-up A is found at around 9.4Hz when excited at mid-slabor 1/4 point, while that for Mock-up B is found in the range of 9.8 to 10.5Hz according to measuringand loading points; however, the difference is not so remarkable. The 2nd bending mode occurs ataround 17Hz for Mock-up A and 18.5Hz for Mock-up B as demonstrated in Fig.16 (b). The 2nd

M

F0 sin wt

k c

F0 sin wt

m EI

k

d

c

(a) Single D.O.F (b) Beam on elastic foundation



bending mode frequency of Mock-up B is also a little higher than that of Mock-up A. The differencebetween Mock-up A and B may be attributed to the load transfer efficiency at the dowel joint. However,the vibration modes of Mock-up B with the dowel joint are not different with those of the Mock-up A.

Fig. 14. Mode shapes for mid-slab loading Fig. 15. Mode shapes for 1/4 point loading

(a) Mid-slab (b) 1/4 pointFig. 16. Receptances for slab deflection at different positions

Fig. 17. Deflection response of a 4.7m short slab at frequency domain

According to the numerical modal analyses, the natural frequencies for the 1st bending mode is9.63Hz and that for 2nd bending mode is 15.99Hz as shown in Table 1. It is said that the measureddominant frequencies well agree with the calculated ones, but the vibration mode shapes are slightly



different – i.e., the combined modes with bending mode and the rigid body mode are found in the test.Then it can be inferred that the actual frequencies of the individual modes may be slightly differentwith the analysis results. Fig. 17 shows the slab deflection responses at frequency domain of a 4.7mshort slab cut and taken from the Mock-up A, supported by four rubber mounts at corners. Theresponses were measured from the free vibration after push and sudden release. This resultdemonstrates that the vertical rigid body translation mode frequency is close to 8Hz, which is a littlehigher than 7.44Hz obtained by the numerical modal analysis. This difference is attributed to theviscoelastic characteristics of the rubber mounts such as the preload effect and frequency-dependence [Maesa et al., 2006].

One of main concerns in the design of FST is to avoid the resonance. If the wheelset distance is 3m,the resonance can occur at the train speed of 100 to 110km/h for the 1st bending mode frequency of9.4 to 10.5Hz, and 180 to 200km/h for the 2nd bending mode frequency of 17 to 18.5Hz. Therefore,the FST should be carefully tuned considering the actual vibration modes and the speed profile of thesite.

Conclusions

In this study, to verify the new design of the FST, the real-scale mock-up tests have been carriedout, and the static and dynamic performance including the static deflection, natural frequencies andvibration mode shapes of the system were investigated. From this study, the following conclusionscan be drawn.

(1) From the static test, the static performance of the FST design has been verified. The differenceof the mid-slab deflection and increase of the deflection at the dowel joint are found, and this shouldbe carefully checked since it may affect the dynamic stability of train.

(2) The modal test results have shown that the dominant vibration modes are not the rigid bodytranslation modes, but the bending modes. Thus the tuning frequency should be determined based onthe bending mode frequencies, rather than the vertical rigid body translation mode frequency basedon single D.O.F system. According to the numerical modal analysis, when the slab length is not longenough, the system tuning frequency can be increased, resulting in the instability and low anti-vibration efficiency of the system.

(3) The natural frequencies and mode shapes found in the modal test reasonably agree with thecalculated ones. Nevertheless, the vibration mode shapes are slightly different – i.e., the combinedmodes with bending mode and the rigid body mode are found in the test. The actual frequencies ofthe individual modes are expected to be slightly different with the analysis results. This discrepancymay occur due to the viscoelastic characteristics of the rubber mounts.

(4) The natural frequencies of Mock-up B with the dowel joint are slightly higher than those of Mock-up A without the joint, which implies that the load transfer efficiency at the dowel joint may affect thenatural frequencies; however, the vibration modes are not affected.

Acknowledgement

This study was supported by a grant (code 07-Next-Generation High-speed Rail-A01) from RailroadTechnology Development Program (RTDP) funded by Ministry of Land, Transport and Maritime Affairsof Korean government.

References

Blevins, R. D.(1979) Formulas for Natural Frequency and Mode Shape, Robert E. Kieger PublishingCompany, New York.

DIN 45673-1 (2000) Elastische Elemente des Oberbaus von Schienenfahrwegen.Hui, C. K. and Ng, C. F.(2008) Coupling resonance of floating slab and supporting concrete box

structure, Applied Acoustics, Vol. 69, No.11, pp. 1044-1062.Hui, C. K. and Ng, C. F.(2009) The effects of floating slab bending resonances on the vibration

isolation of rail viaduct, Applied Acoustics, Vol. 70(6), pp. 830-844.Maesa, J., Sola, H., and Guillaumeb, P.(2006) Measurements of the dynamic railpad properties,

Journal of Sound and Vibration, Vol. 293(3-5), pp. 557-565.Wagner, H.G.(2002) Attenuation of transmission of vibrations and ground-borne noise by means of

steel spring supported low-tuned floating trackbed, 2002 World Metro Symposium, Taipeh.



Yang, S. C.(2009) Enhancement of the finite-element method for the analysis of vertical train–trackinteractions, Proc. IMechE Part F: Journal of Rail and Rapid Transit, Vol. 223(F6), pp. 609-620.

laboratory mock-up tests - railway research · mock-up b: two 8.8m slabs connected with a dowel...

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