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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.