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Dynamic characteristics of railway concrete sleepers using impact excitation techniques and model analysis

Akira Aikawa *, Fumihiro Urakawa *, Kazuhisa Abe **, Akira Namura *

* Railway Technical Research Institute

2-8-38 Hikari-cho, Kokubunji, Tokyo, 185-8540, Japan

** Niigata University

8050 Igarashi 2-nocho, Nishi-ku, Niigata, 950-2181, Japan

SUMMARY A concrete sleeper transmits an impact load to ballast grains through multicontact loading conditions

within the boundary layer separating a sleeper and ballasts. The occurrence of plastic deformation in

the ballasted track is affected by characteristics of dynamic loads on sleeper bottoms. The sleeper,

which has several natural frequencies in frequency bands up to 1 kHz, vibrates sympathetically with

dynamic loads of a running train. Such vibration of concrete sleepers is an important factor giving rise

to track deterioration. As described in this paper, field measurements and experimental modal

analysis of dynamic characteristics of concrete sleepers were conducted based on an impact

excitation technique.

Key Words: Ballasted track, Load on sleeper bottom plane, Sleeper deformation

1. INTRODUCTION Dynamic load transmission to the ballast layer through the bottom plane of the sleeper causes track

settlement. To identify effective measures against track bed deterioration and to perform more

effective maintenance, it is important to understand the mechanisms underlying track deterioration by

identifying the characteristics of load transmission to the ballast layer. Measurements of the load

exerted on the bottom plane of sleepers are therefore necessary. The load on the sleeper bottom

results from vibrations of the track and sleeper caused by passing trains. A key assumption is that

track settlement is worsened not only because of resonance caused by the sleeper vibrating at a

frequency close to its natural frequency, but also because of the uneven distribution of that load on

the sleeper bottom, which can occur because of sleeper deformation. Moreover, past research [1] has

demonstrated that concrete sleepers have several normal modes in the frequency range below 1 kHz.

In this research, the normal mode for a 3PR-type mono-block concrete sleeper was determined

through experimental modal analyses to identify the relation with the characteristics of load

transmission to the ballast layer. Sleeper vibration, the vibration load on the ballast, and the ballast

layer response were measured dynamically on the existing track using an impulse hammer and during

the actual passage of trains. The measurement results were discussed through comparison with the

experimental and numerical results related to the sleeper's normal mode.

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2. MEASURING THE NORMAL MODE FOR A SINGLE SLEEPER One property of a structure with a defined set of conditions (shape, material and bearing conditions) is

that the structure vibrates at a given frequency (its natural frequency) when it is in a normal state: this

is called its normal mode. The number of normal modes agrees with the value of the structure's

degrees of freedom. Arbitrary structural deformation can be shown by overlapping linearly normal

modes.

After analyzing the vibration test data of the vibrational force and response, experimental modal

analysis was adopted to measure the set of normal modes for a sleeper. Experimental modal analysis

can identify individual modes by disassembly of the overlapped modes. Figure 1 portrays the

experimental setup of a sleeper in a free–free condition. To reproduce the free–free condition, the

sleeper was placed on a 600-mm-thick extremely soft urethane mat. When an excitation impulse was

applied to one end of sleeper edge, accelerance (acceleration/excitation force) at 22 points located

along the sleeper, as well as excitation load, were measured simultaneously. Experimental modal

analysis software ME’ scope VES (Vibrant Technology Inc.) was used to analyze the measurement

data obtained for 1.6 kHz or less.

Measurement points o f accelerance（22point，3 direct ion）

Excitation（3 direction）Urethane mat

Sleeper（3PR）

Fig. 1 Sleeper excitation test of experimental modal analysis.

Table 1 and Fig. 2 present the six normal modes identified in the frequency range below 1 kHz

through this process. The sleeper vibration on existing track will correspond to each of the mode

shapes with a response showing a peak at a value that is close to the natural frequencies. However,

in a similar experiment where the sleeper is placed on a ballast layer, Remennikov et al. [1] showed

that the natural frequency of the sleeper in the in situ condition increases by a maximum of about 40

Hz in comparison with the sleeper in the free–free condition. In addition to the ballast layer support,

the stiffness and mass of the rail and the rail fastening system were added.

Table 1 Measurement result of 3PR-sleeper’s natural modes

No. m ode shapenatural

frequency [Hz]

1 1st vertical bending 148

2 1st horizontal bending 241

3 2nd vertical bending 435

4 1st twisting 538

5 2nd horizontal bending 630

6 3rd vertical bending 825

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(1) First vertical bending (4) First twisting

(2) First horizontal bending (5) Second horizontal bending

(3) Second vertical bending (6) Third vertical bending

Fig. 2 Mode shapes of 3PR-sleeper.

3. DYNAMIC SLEEPER CHARACTERISTICS UNDER REAL TRACK CONDITIONS A vibration test was conducted using an impulse hammer under existing track conditions to examine

the relation among sleeper vibration, the excitation load acting on the ballast, and the ballast

response.

3.1 Experimental conditions

The vertical response was measured for the three following parameters: sleeper vibration acceleration,

load exerted on the sleeper bottom, and vibration acceleration of the ballast. Figure 3 shows the

measurement points. For measurements up to the vertical third bending mode, the sleeper vibration

acceleration was measured in eight places (see Fig. 3). The load exerted on the sleeper bottom was

measured using a specially developed sensing-sleeper [2]. The sensing-sleeper is a sleeper fitted

with 75 force impact force sensors (25 columns × 3 rows) designed to measure the load distribution

on its bottom plane. To compare the average load distribution by location along the bottom plane of

the sleeper, the sleeper was divided into five sections: SM1, SM2, SM3, SM4, and SM5 (each section

having 15 sensors) as portrayed in Fig. 4. Then a total measurement value was calculated for each

section. As presented in Fig. 4, in the test, the left rail head was excited with a force of about 20 kN in

the Z (vertical) direction and Y (horizontal) direction with five times in succession. The transfer

function (response/excitation force) was measured each time. The measurement value attributed to

each measurement point was assumed as the mean of five measurements.

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B 5B 4B 2B 1 B 3Y

Z

X10cm

Sensing sleeperS1 S3

S2 S4S 6 S 5

S8S7

Sleeper vibration acceleration(S1-S8)

Ballast vibration acceleration (B1-B5)

Left Right

(1) Overall

S1

S2

S3S4

S5

S6

S7

S8

570m m 570m m 410m m410m m (2) Sleeper vibration acceleration

Fig. 3 Measurement points.

vertical Z excitation horizontal Y

excitation

SM 1 SM 2 SM 3 SM 4 SM 5Y

Z

X

Left Right

Fig. 4 Impulse hammer test.

3.2 Experimental results for the transfer function

Figure 5(1) shows the transfer function for total load values for SM1–SM5 and for the entire sleeper

bottom plane for the Z direction; Fig. 6(1) shows that for the Y direction. The transfer functions for

sleeper vibration acceleration for vertical Z excitation and for horizontal excitation Y are shown in Figs.

5(2) and 6(2). The transfer functions ballast vibration acceleration for vertical Z and horizontal Y

excitation are presented respectively in Figs. 5(3) and 6(3). The transfer function for load on the

sleeper bottom is greatest in the range of frequencies between 100 and 200 Hz. It decreases as the

frequency increases above 200 Hz, up to 700 Hz, at which point it once again begins to increase. The

transfer functions for sleeper vibration acceleration increase with frequency up to about 200 Hz, after

which they level off.

Regarding comparison of the peak frequencies obtained for each measurement value, the load on

the sleeper bottom, sleeper vibration acceleration, and ballast vibration acceleration reach peak

values at around 180 Hz, 400 Hz, 600 Hz, and 860 Hz for excitation in both vertical Z and horizontal Y

directions. In the range of 80 Hz and 100 Hz, the load on the sleeper bottom reaches a peak under

vertical Z excitation and the transfer functions for sleeper and ballast vibration acceleration are small.

At around 300 Hz, when the load on the sleeper bottom reaches a peak, the sleeper and ballast

vibration acceleration (B1, B5) at each extremity of the sleeper also register small peaks.

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3.3 Comparison with normal sleeper mode

Transfer functions of the load on the sleeper bottom, sleeper vibration acceleration, and ballast

vibration acceleration registered several peaks at frequencies of less than 1 kHz; these peak

frequencies were almost identical. The results suggest that the normal mode of the sleeper is situated

in the region close to the frequency at which the transfer function shows a peak. To identify which

normal mode causes transfer function peaks, sleeper responses on existing track were compared with

the normal mode of the sleeper described previously in Chapter 2.

Figure 7(a)–7(f) present the transfer function distribution of load on the sleeper bottom and the

shape of its deformation under vertical Z excitation at the peak frequencies of load on the sleeper

bottom. The acceleration measurements of the measuring points S1–S8 of the sleeper were

integrated twice in the frequency domain. The sleeper deformation is calculated by converting

acceleration measurements S1–S8 into time-dependent displacement data of t = 0, t = T/4, and t =

T/2 (where T: Period). This figure clearly illustrates the vibration mode, t = 0 is adjusted to each

frequency. The distribution of the load on the sleeper bottom is presented with a color-coded load,

where the load is converted into a time-dependent series for each sensor, in the same way as

deformation measurements were converted above for each sensor. Moreover, because the load and

displacement values differ greatly at each frequency, figures are arranged according to the frequency

range.

0 100 200 300 400 500 600 700 800 900 10001E-4

1E-3

0.01

0.1

1

SM 1 SM 2 SM 3 SM 4 SM 5 Entire

Load on sleeper bottom plane [kN/kN

]

Frequency [Hz] 0 100 200 300 400 500 600 700 800 900 1000

1E-4

1E-3

0.01

0.1

1

S M 1 S M 2 S M 3 S M 4 S M 5 Entire

Load on sleeper bottom plane [kN/kN

]

Frequency [Hz] (1) Load on the sleeper bottom plane (1) Load on the sleeper bottom plane

0 100 200 300 400 500 600 700 800 900 10000.01

0.1

1

10

100

Sleeper vibration acceleration[m

/s2/kN

]

Frequency [Hz]

S1 S3

S6 S8

S 2 S 4 S 5 S 7

0 100 200 300 400 500 600 700 800 900 1000

0.01

0.1

1

10

100

S 1 S 3

S 6 S 8

S2 S4 S5 S7

Sleeper vibration acceleration[m

/s2/kN

]

Frequency [Hz] (2) Sleeper vibration acceleration (2) Sleeper vibration acceleration

0 100 200 300 400 500 600 700 800 900 10000.01

0.1

1

10

100

B 1 B 2 B 3 B 4 B 5

Ballast vibration acceleration [m/s

2/kN]

Frequency [Hz] 0 100 200 300 400 500 600 700 800 900 1000

0.01

0.1

1

10

100

B1 B2 B3 B4 B5

Ballast vibration acceleration[m

/s2/kN]

Frequency [Hz] (3) Ballast vibration acceleration (3) Ballast vibration acceleration

Fig. 5 Transfer functions for vertical Z excitation. Fig. 6 Transfer functions for horizontal Y excitation.

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Figures 8(1)–8(6) portray corresponding data for horizontal Y excitation. At 80 Hz, where the load

on the sleeper bottom reaches a peak under vertical Z excitation, the shape in Fig. 7(1) shows that

high-level vibration is only visible around the excitation point. Nevertheless, there is no normal mode

at which the sleeper undergoes deformation corresponding to that occurring around this frequency.

Moreover, the load only reaches a peak value for vertical Z excitation, which engenders the

assumption that this peak results from the vertical or rotational rigid body mode because of the ballast

layer rigid support.

Under horizontal Y excitation, the waveform representing the load on the sleeper bottom shows a

sharp peak at 180 Hz (Fig. 6(2)). By examining deformation of the sleeper at this frequency (Fig. 6(1)),

it can be concluded that this peak is caused by a first bending mode. The fact that this peak frequency

is higher than the natural frequency of a sleeper unit is probably attributable to the influence of the

support stiffness of the ballast. No normal mode or specific sleeper deformation appears to

correspond to the peak reached for 300 Hz. The assumption therefore is that the peak here results

from some other track material or element other than the sleeper, such as the rails.

At 435 Hz in the region of 400 Hz, the sleeper unit normal mode appears to be a second bending

mode. Deformation of the sleeper and the load exerted on the sleeper bottom are both larger close to

the regions around the left and right rails (deformation is shown in Figs. 7(5) and 8(5), and the load is

shown in Figs. 5(1) and 6(1)).

The normal mode for vertical vibration around 600 Hz is a single torsion mode (538 Hz). Under

horizontal Y vibration, a twisting vibration that shifts the phase at the front and back is apparent in the

sleeper deformation mode (Fig. 8(5)). Furthermore, second and third bending deformation is apparent

under vertical Z excitation. Therefore, the assumption is that these modes strongly influence the

response around 600 Hz. At 860 Hz, sleeper deformation under vertical Z excitation (Fig. 7(6)) and

the normal mode for this frequency range indicate clearly that the sleeper vibrates in a third bending

mode.

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4. MEASURING DYNAMIC RESPONSE UNDER TRAIN OPERATION 4.1 Frequency response measurement results

The dynamic response was measured during train operation. The train speed was 125 km/h.

The Fourier amplitude spectra for loads exerted on the sleeper bottom, sleeper vibration acceleration,

and ballast vibration acceleration are shown, respectively, in Figs. 9(1), 9(2), and 9(3). The values

were obtained by application of FFT to data collected during 6.55 s (65536 points) as the train passed,

and smoothed through a Parzen window of 20 Hz bandwidth. The load exerted on the sleeper bottom

decreases rapidly as the frequency rises above 0 Hz, then it dips at around 45 Hz; it then increases

again gradually up to 100 Hz. After reaching a peak at 100 Hz, the load decreases rapidly again to

（1）80Hz-1 10 -1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 -1 10-1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 - 1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 - 1 10- 1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 - 1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 - 1 10- 1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 - 1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 - 1 10- 1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 - 1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 - 1 10- 1 10 -1 10-1 10t = 0 t = T/4 t = T/2

（2）180Hz

（3）300Hz

（4）400Hz

（6）860Hz

-1 10 -1 10-1 10-1 10t = 0 t = T/4 t = T/2（5）600Hz

（1）80Hz

（2）180Hz

（3）300Hz

（4）400Hz

- 1 10 -1 10 -1 10t = 0 t = T/4 t = T/2- 1 10- 1 10 -1 10-1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 - 1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 - 1 10- 1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 - 1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 - 1 10- 1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 -1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 -1 10-1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 -1 10-1 10-1 10t = 0 t = T/4 t = T/2（5）600Hz

（6）860Hz

Loadlarge

small

0

vertical downward

Load on sleeper bottom Deformation shape

-1 10 -1 10-1 10-1 10t = 0 t = T/4 t = T/2

Fig. 7 Load on the sleeper bottom plane Fig. 8 Load on the sleeper bottom plane

and the shape of its deformation and the shape of its deformation under vertical Z excitation. under horizontal Y excitation.

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150 Hz. Then it peaks at 200 Hz, 280 Hz, 340 Hz, 430 Hz, 550 Hz, and 670 Hz, after which it begins

once again to decrease. The load reaches a minimum at around 700 Hz, increasing again thereafter,

and peaks again at around 900 Hz. The Fourier amplitudes of the sleeper and ballast vibration

acceleration reach their respective peaks at around the same time as the sleeper bottom plane

frequency reaches its peak (Figs. 9(2) and 9(3)).

0 100 200 300 400 500 600 700 800 900 10001E-4

1E-3

0.01

0.1

1 SM 1 SM 2 SM 3 SM 4 SM 5 Entire

Load on sleeper bottom plane [kN

・s]

Frequency [Hz] (1) Load on sleeper bottom plane

0 100 200 300 400 500 600 700 800 900 10000.01

0.1

1

10

Sleeper vibration acceleration [m

/s2 ・

s]

Frequency [Hz]

S 2 S 4 S 5 S 7

S 1 S 3

S 6 S 8

(2) Sleeper vibration acceleration

0 100 200 300 400 500 600 700 800 900 10000.01

0.1

1 B1 B2 B3 B4 B5

Ballast vibration acceleration [m/s2 ・

s]

Frequency [H z] (3) Ballast vibration acceleration

Fig. 9 Fourier amplitude spectrum under train operation.

4.2 Sleeper deformation and load distribution on the bottom plane of the sleeper

Figures 10(1)–10(8) show the load distribution on the sleeper bottom and sleeper deformation at the

point where the frequency shows a peak on the load on the sleeper bottom plane spectrum. The FFT

and smoothing processes described above were applied to data collected for the load on the sleeper

bottom and sleeper vibration acceleration in order values within the frequency limit. Subsequently,

the values were converted into time series by application of the Fourier amplitude to the vibration

amplitude and S5 phase difference to the phase to obtain t = 0, t = T/4, and t = T/2 (where T: Period),

which were then shown.

At 100 Hz, both ends of the sleeper undergo large vibration in phase, although the center vibrates

less, in similar fashion to vibration under the first bending mode (Fig. 10(1)). However, in the impulse

hammer tests under real track conditions, the first bending mode appears at 180 Hz. Therefore, in this

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case, the load peak seems to correspond to that of the rigid vertical body mode obtained in the region

of 80 Hz in the same test. At 200 Hz, both ends of the sleeper vibrate strongly with a 90° phase

difference (Fig. 10(2)). At 280 Hz, only the right side of the sleeper vibrates strongly (Fig. 10(3)). At

340 Hz, the form of vibration becomes very complex, with the previously only slightly vibrating center

part of the sleeper beginning to vibrate strongly, together with both extremities (Fig. 10(4)). At 430 Hz,

close to where vibration is strong under the rail, vertical second bending also appears. At 550 Hz and

670 Hz, vertical second and third bending appear. Moreover, within this frequency range, which is the

sleeper’s normal mode, the single torsion mode which occurs here is not apparent because of

deformation of the sleeper. At 900 Hz, third bending appears where the center and both ends of the

sleeper vibrate strongly in phase (Fig. 10(8)).

5. CONCLUSION The six normal modes of a 3PR-sleeper were identified for frequencies of 1 kHz or less using

experimental modal analysis to clarify the relation between the sleeper’s normal mode and load

transmission characteristics to the ballast layer. Impulse hammer test results showed that the

sleeper’s normal modes existed in the region where the load on the sleeper bottom plane and sleeper

vibration acceleration frequencies reach a peak. Test results also showed that deformation

corresponded to the specified normal modes. Furthermore, results showed that the load distribution

on the sleeper bottom became uneven, depending on the sleeper deformation. Moreover, despite

（1）100Hz

（2）200Hz

（3）280Hz

（4）340Hz

-1 10 -1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 -1 10-1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 -1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 -1 10-1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 -1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 -1 10-1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 -1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 -1 10-1 10 -1 10-1 10t = 0 t = T/4 t = T/2

（5）430Hz

（8）900Hz-1 10 - 1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 - 1 10- 1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 - 1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 - 1 10- 1 10 -1 10-1 10t = 0 t = T/4 t = T/2

-1 10 -1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 -1 10-1 10 -1 10-1 10t = 0 t = T/4 t = T/2（6）550Hz

（7）670Hz-1 10 -1 10 -1 10t = 0 t = T/4 t = T/2-1 10-1 10 -1 10-1 10 -1 10-1 10t = 0 t = T/4 t = T/2

Loadlarge

small

0

vertical downward

Load on sleeper bottom Deformation shape

Fig. 10 Sleeper deformation and under sleeper load distribution under train operation.

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being less obvious than in the impulse hammer tests, under actual track conditions with the passing of

a train, it was possible to identify vibration characteristics influenced by the sleeper’s normal mode

from various frequencies at which the load on the sleeper bottom plane reached a peak.

REFERENCES [1] Remennikov, A., Kaewunruen, S., “Investigation of vibration characteristics of prestressed

concrete sleepers in free–free and in-situ conditions,” Australian Structural Engineering Conference

2005 (ASEC 2005), Newcastle, Australia, 11–14 September, 2005.

[2] Aikawa, A., Urakawa, F., Kono, A., Namura, A., “Sensing sleeper for dynamic pressure

measurement on a sleeper bottom induced by running trains,” Railway Engineering 2009, CD-ROM,

University of Westminster, London, UK, 2009.