**4. Field measurements and spectral analysis**

Dynamic responses were measured on an actual ballasted track of a main conventional railway line in Japan to identify the dominant natural vibration modes of the ballasted track. The track structure at the measurement site, consisting of continuous welded rail weighing 60 kg/m and type 3 PC sleepers, was designed based on the Japanese standard [25], which allows a running speed higher than 130 km/h. The measurement site was located on a solid embankment in a straight section. For spacing between the sleepers, 41–42 sleepers are positioned over a distance of 25 m. The author chose a straight section with satisfied track conditions, based on measurement data from an inspection car. The ballast layer at the measurement site is made of new andesite hard stones with clear-cut edges. The ballast layer is approx. 30 cm thick.

feature enables high-quality load measurement. Both terminals output a charge that is proportional to the impact load, but digitization of the charge output is extremely difficult. For that reason, the charge from the sensor is usually converted into a voltage by integrating the electric circuit attached to a sensor output terminal (charge amplifier). For that purpose, an impedance transformation circuit with extra-high impedance, ultra-low noise and differential input-type operational amplifiers (OP-amps) can be used for the instrumentation preamplifier. Moreover, this sensor has good reactivity. Because the output voltage can be as high as several tens of volts, the ratio of noise to the maximum measuring load is as low as 0.003%.

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**Figure 6** shows the acceleration amplitude spectrum and the displacement amplitude spectrum of the ballast gravel at 10 cm depth. The acceleration spectrum shows that components at frequencies higher than 100 Hz as well as the low-frequency components contribute greatly to the ballast response. These high-frequency vibration components are attributable to the sharp pulse-shaped impact loads induced by the dynamic mechanisms between the wheels and rails. When particularly addressing the ballast displacement, its amplitude is extremely small in the high-frequency domain. For instance, the displacement amplitude is only 1/1000 μm at a frequency of approx. 800 Hz, which is equivalent to the natural frequency of the ballasted track entailing the third mode of the vertical bending of the sleeper. Therefore, the vibration components in the high-frequency domain are not transmitted by rigid-body vibrations around the centre of gravity of the ballast gravel, but the dynamic loads are transmitted through the elastic undulation propagation because of the local and minute deformation behaviour and sliding behaviour at the tips of the edges of contact points between the ballast stones. However, the displacement amplitude in the low-frequency domain from several Hertz to 20 Hz is several thousand times higher than those in the high-frequency domain. Consequently, the loads in the low-frequency domain are transmitted mainly through rotational and translational rigid-body vibrations of the individual ballast gravel particles. This figure also depicts peak profiles of responses related to the natural vibration modes of the

The sensor can measure load characteristics at high frequencies.

**Figure 6.** Acceleration and displacement amplitude spectra of the ballast (measured).

**Figure 4** presents an overview of sensor positions. Details of the measurements are described in earlier reports of the literature [26, 27]. This article specifically examines the measured responses for a passenger train moving at approx. 120 km/h (sampling frequency is 10 kHz). The sleeper vibration acceleration and the ballast vibration acceleration were measured using piezoelectric triaxial acceleration sensors: 10 mV/G sensitivity, 500 G measurement range and 2–10,000 Hz frequency range within 5% deviation. The ratio of noise to the maximum measurable acceleration is approximately 0.002%. The acceleration sensor also offers an appropriate level of performance to enable measurement for the determination of load characteristics in a high-frequency domain. The following analyses were conducted by obtaining linear amplitude spectra by application of fast Fourier transformation of the time history response waveforms in response to vibration accelerations, with smoothing at a 20 Hz bandwidth.

**Figure 5** shows a special sensing sleeper designed to assess the dynamic load distribution on the sleeper bottom, for a wide frequency range from a low frequency of 0.01 Hz up to a high frequency of several tens of kilohertz. The sensing unit comprises a type 3 PC sleeper fitted with many ultra-thin-type impact load sensors. Attached to the sleeper's whole undersurface is a solid mass comprising 75 impact load sensors (25 pieces × 3 rows). Each impact load sensor has a main body and cover members. The main body including a piezoelectric film has solid cover plates on both surfaces. The cover plates (8 cm × 8 cm) transmit impact load to the main body in cases of impact loads of a running train, thereby preventing sensor breakage [12, 27]. Each sensor can measure a load up to a maximum of 10 kN. The sensor has thin metal plates attached to both sides of a thin piezo-film. The structure, which resembles that of a condenser, has no internal resistance. For that reason, no current is induced by noise sources, even in the electromagnetically high-tension environment that prevails during train operation. This

**Figure 4.** Measuring sensor positions.

**Figure 5.** Overview of sensing sleeper.

feature enables high-quality load measurement. Both terminals output a charge that is proportional to the impact load, but digitization of the charge output is extremely difficult. For that reason, the charge from the sensor is usually converted into a voltage by integrating the electric circuit attached to a sensor output terminal (charge amplifier). For that purpose, an impedance transformation circuit with extra-high impedance, ultra-low noise and differential input-type operational amplifiers (OP-amps) can be used for the instrumentation preamplifier. Moreover, this sensor has good reactivity. Because the output voltage can be as high as several tens of volts, the ratio of noise to the maximum measuring load is as low as 0.003%. The sensor can measure load characteristics at high frequencies.

distance of 25 m. The author chose a straight section with satisfied track conditions, based on measurement data from an inspection car. The ballast layer at the measurement site is made of new andesite hard stones with clear-cut edges. The ballast layer is approx. 30 cm thick.

**Figure 4** presents an overview of sensor positions. Details of the measurements are described in earlier reports of the literature [26, 27]. This article specifically examines the measured responses for a passenger train moving at approx. 120 km/h (sampling frequency is 10 kHz). The sleeper vibration acceleration and the ballast vibration acceleration were measured using piezoelectric triaxial acceleration sensors: 10 mV/G sensitivity, 500 G measurement range and 2–10,000 Hz frequency range within 5% deviation. The ratio of noise to the maximum measurable acceleration is approximately 0.002%. The acceleration sensor also offers an appropriate level of performance to enable measurement for the determination of load characteristics in a high-frequency domain. The following analyses were conducted by obtaining linear amplitude spectra by application of fast Fourier transformation of the time history response wave-

forms in response to vibration accelerations, with smoothing at a 20 Hz bandwidth.

**Figure 5.** Overview of sensing sleeper.

**Figure 4.** Measuring sensor positions.

108 New Trends in Structural Engineering

**Figure 5** shows a special sensing sleeper designed to assess the dynamic load distribution on the sleeper bottom, for a wide frequency range from a low frequency of 0.01 Hz up to a high frequency of several tens of kilohertz. The sensing unit comprises a type 3 PC sleeper fitted with many ultra-thin-type impact load sensors. Attached to the sleeper's whole undersurface is a solid mass comprising 75 impact load sensors (25 pieces × 3 rows). Each impact load sensor has a main body and cover members. The main body including a piezoelectric film has solid cover plates on both surfaces. The cover plates (8 cm × 8 cm) transmit impact load to the main body in cases of impact loads of a running train, thereby preventing sensor breakage [12, 27]. Each sensor can measure a load up to a maximum of 10 kN. The sensor has thin metal plates attached to both sides of a thin piezo-film. The structure, which resembles that of a condenser, has no internal resistance. For that reason, no current is induced by noise sources, even in the electromagnetically high-tension environment that prevails during train operation. This **Figure 6** shows the acceleration amplitude spectrum and the displacement amplitude spectrum of the ballast gravel at 10 cm depth. The acceleration spectrum shows that components at frequencies higher than 100 Hz as well as the low-frequency components contribute greatly to the ballast response. These high-frequency vibration components are attributable to the sharp pulse-shaped impact loads induced by the dynamic mechanisms between the wheels and rails.

When particularly addressing the ballast displacement, its amplitude is extremely small in the high-frequency domain. For instance, the displacement amplitude is only 1/1000 μm at a frequency of approx. 800 Hz, which is equivalent to the natural frequency of the ballasted track entailing the third mode of the vertical bending of the sleeper. Therefore, the vibration components in the high-frequency domain are not transmitted by rigid-body vibrations around the centre of gravity of the ballast gravel, but the dynamic loads are transmitted through the elastic undulation propagation because of the local and minute deformation behaviour and sliding behaviour at the tips of the edges of contact points between the ballast stones. However, the displacement amplitude in the low-frequency domain from several Hertz to 20 Hz is several thousand times higher than those in the high-frequency domain. Consequently, the loads in the low-frequency domain are transmitted mainly through rotational and translational rigid-body vibrations of the individual ballast gravel particles. This figure also depicts peak profiles of responses related to the natural vibration modes of the

**Figure 6.** Acceleration and displacement amplitude spectra of the ballast (measured).

**Figure 7.** Distribution of vertical loading at the bottom of the sensing sleeper and normalized displacement at the top of the sleeper (measured).

ballasted track explained in the preceding paragraph. These curves identify the rigid-body resonance mode of the ballast layer around 100 Hz and indicate another large peak profile at around 300 Hz. From the full-scale experiment presented in **Figure 3**, the rigid-body natural vibration mode of the ballasted track appears at 98 Hz.

**Figure 7** shows the relation between the two-dimensional distribution of the vertical loading on the bottom surface of the sleeper and the normalized vertical displacement of the sleeper in cases of two frequencies (110 and 310 Hz), which give the peak profiles of the response curves. In the figures, *θ* denotes the relative phase angles with reference to vertical motion at the centre of the sleeper. In the distribution maps, red denotes the positive load (compression). Blue shows the negative load (tension). Regarding the sleeper motion, the downward direction indicates the downward behaviour of the sleeper. The upward direction indicates the upward behaviour of the sleeper. Panels (a) and (b) show that the sleeper repeats a vertical periodic movement at these frequencies, entailing bending deformation of the sleeper at high frequencies, in synchronization with the phase angles.

> the sleepers and the acceleration responses of sleepers and ballast were recorded by sampling the data at 10 kHz or 20 kHz. This chapter presents a discussion of the measurement results

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**Figure 8.** Overview of impact loading test. (a) Drop-weight impact test device, (b) sensor positions.

**Figure 9(a)** shows the time history response of the centre sleeper's vertical displacement after impact loading. This average curve shows results obtained from about 4000 loading tests, excluding initial loading of the first 1000 iterations. The downward displacement in the chart shows the ballast layer compression. The upward displacement represents extension of the ballast layer. **Figure 9(b)** especially depicts data obtained at the moment immediately after loading. The average value of the impact load on the ballast through the left and right rails was 217 kN. The figure shows that because of the compression applied by an impact load, the ballast layer instantaneously deforms elastically. The compression produces maximum downward displacement of 0.178 mm in 0.71 ms. Subsequently, it returns to the preloading

of the displacement responses of the sleepers [9, 13].
