Introduction

The railway induced vibration is examined as a reason of damage in civil engineering objects (Beben 2014; Jones 2009). Such a vibration causes annoyance to people, therefore the reduction in the vibration level is an important task in designing railways (e.g.Dijckmans et al 2016; Li et al. 2016; Thompson et al. 2016). The railway induced vibration was analysed in various local conditions (Farghaly and Contoni 2018; Conolly et al. 2015, 2016). Verification of railway induced ground vibration forecast is performed by comparison of the predicted to the measured values of root mean square (RMS) acceleration or velocity level in one-third octave bands. The spectrum range applied during research varies depending on the research centre or author. The frequency range of 1 to 125 Hz and 1 to 100 Hz is applied by Lombaert et al. (2014) and by Jones (2009). The range of 2.5 to 100 Hz is applied by Li et al. (2016), and the range of 8 to 125 Hz by Kuo et al. (2016). Apparently low values of RMS vibration level are observed for frequency band centres between 1 and 8 Hz for relatively short passages of ca. 5 s (eg. Li et al. 2016; Lombaert et al. 2014; Jones 2009).

In recent years, an increase in the research area of vibration analysis was observed. Numerous case studies related to road traffic (eg. Beben et al. 2022) and rail traffic (Tao et al. 2022) analyse the impact of vibration on people in buildings. General approach to the problem of influence of rail and road vibration on typical residential buildings is presented by Erkal and Kocagoz (2020).

The vibration spectrum of seismic noise is strongly dependent on local geological conditions (e.g. Soler-Llorens et al. 2018). The dependence of surface noise vibration spectrum on surface stiffness was the topic of separate research (Dal-Moro 2015) where attenuation of horizontal components in frequency range below 80 Hz was observed after application of stiff pavement on the surface. The observation time interval influences RMS value, the ratio of observation time interval to excitation time is an important parameter (Kornowski 2003) influencing the RMS value.

Analysis of ground vibration induced by natural seismicity and mining is performed for civil engineering purposes and further analysed in terms of maximum ground acceleration and velocity (eg. Maleska et al. 2019; Strzalkowski 2019; Boron and Dulinska 2017), and compared with Fourier spectra (eg. Zembaty et al. 2017). However, Strzalkowski (2019) concentrates on horizontal components, while Boron & Dulinska (2017) and Zembaty et al., (2017) analyse both the horizontal and vertical components of ground vibration. In the literature, spectral analysis of mining induced seismicity is analysed in the frequency range up to 20 Hz (e.g. Zembaty et al. 2017).

The problem of vibration influence on civil engineering objects and people is of great importance to investigate the reduction in a vibration level as well as to increase the engineering objects resistance to such excitation (Beben and Wrzeciono 2017) and also to predict and prevent the vibration caused by anthropogenic factors (e.g. Jiang et al. 2018).

The present work addresses the problem of the comparison between the measured observables of the railway induced vibration and those caused by a hammer. The vibration level is compared to the background noise level. We compared our data analysis on measurements of the railway-induced and the hammer induced vibration with the literature data analysis of railway induced, mining-induced and natural seismic ground vibrations.

The literature investigation indicated lack of unified methodology to analyse vibration caused by both the railway transport and mining activity in spite of similar values of maximum ground acceleration and velocity observed. In our opinion, this lack results from various sampling frequencies of the vibration records applied to the analysis. The presented research concentrates on the possibility of novel comparison methodology of the railway induced vibration with the vibration induced by mining. Our contribution to the state-of-the-art is development of the strategies that might be used in automatization of vibration monitoring and analysis in aspect of influence on people in buildings.

Case study and methodology

The experimental setup involved the installation of a high sensitivity seismic accelerometer (PCB 393 type) measuring ground vertical acceleration, (e.g. see Kuo et al. 2016). The accelerometer was installed 8 m from the track. A sensor was fixed to the ground with the use of a fixing device. The measuring set, the vibration source and the sensor are presented in Fig. 1.

Fig. 1
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Sensor arrangement in test field for a railway excitation, b hammer excitation, c measurement set in site

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Vibration caused by a series of freight trains passages was measured and analysed (Fig. 1a). The freight trains passages, examined in this research were characterised by an axle load from 162 to 221 kN and train speed up to 70 km/h in the examined localization. In the next step, the vibration caused by series of hammer induced excitations in the same distance was measured and analysed. A hammer weighing 20 kg was dropped from a constant height of 0.3 m with the use of a trigger mechanism and a guide bar (Fig. 1b). The measurement set during the survey is presented in Fig. 1c. The wave excitation device applied in this research was described in the patent description (Duda 2019) and was designed with the reference to the solution described by Temple and Bennett (2007). From the series of freight train passages and hammer excitations, three records of each source were selected for further calculations. Figures 4, 5, 6, 7, present the results of vibration analysis in the form of the average value and dispersion with the use of line and shaded field respectively. The initial analysis involved timeline, running RMS and narrow band spectrum (Figs. 2 and 3). The main analysis involved basic parameters estimation: duration, maximum acceleration, maximum velocity, RMS acceleration and RMS velocity in one third octave bands spectrum. The duration was defined as the time when acceleration/velocity is bigger than 20% of the maximum value, according to Kowalska-Koczwara & Stypula (2017). RMS acceleration and RMS velocity were calculated in dB unit, with the reference level of 10–6 m/s2 and 10–9 m/s, respectively, according to Jones (2009). Vibration analyses were carried out for the acceleration records and calculated velocities. Velocities were calculated with the use of the inverse Fast Fourier Transform (FFT) method with a baseline correction.

Fig. 2
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Acceleration time histories of excitations (left column), running rms (middle column) and narrow band spectra (right column) of freight train passages (first three lines) and hammer percussion (fourth line)

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Fig. 3
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Velocity time histories of excitations (left column), running rms (middle column) and narrow band spectra (right column) of freight train passages (first three lines) and hammer percussion (fourth line)

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Initial analysis

Raw data were first analysed using basic tools which involved timeline analysis, running RMS and a narrow band spectrum. The running RMS calculation procedure with the use of time window of 1 s is described by Lombaert et al. (2014); however; the time window of 5 s was applied in the presented study. The application of 5 s time window is the consequence of a relatively long duration of freight train passages in comparison to fast passenger trains passages described by Lombaert et al. (2014).

Narrow band spectrum analysis allows for dominant frequencies recognition. The results for acceleration are presented in Fig. 2 and for velocities in Fig. 3. The timeline analysis allows for estimation of duration and maximum values. Additionally, the timeline analysis indicates homogenous (quasi-stationary character) vibration intensity during freight train passages of relatively long duration, during which the vibration is considered as stationary.

Analysis of background noise

Background noise was measured in various time intervals, the comparison was performed to examine the influence of time interval length on RMS acceleration and velocity in one-third octave bands. The examined time-interval lengths were 0.2 s, 1 s, 5 s, 10 s and 20 s.

The comparison results are presented in Fig. 4. A time interval length influences RMS acceleration and velocity level. RMS acceleration and velocity level are reduced in various frequency ranges depending on the time interval. RMS acceleration and velocity are reduced within the entire examined frequency range for 0.2 s time interval, in frequency range below ca. 16 Hz for 1 s time interval, in frequency range below 5 Hz for 5 s time interval and in frequency range below 2.5 Hz for 10 s time interval. For 20 s the time interval acceleration chart is almost flat, while the velocity chart is slightly decreasing at low frequencies, after a maximum at 1.6 Hz The selected parameters of background noise are presented in Table 1.

Fig. 4
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Comparison of background noise with the use of time windows of 20, 10, 5, 1 and 0.2 s, for a acceleration and b velocity

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Table 1 Selected parameters of background noise with application of various time window length
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Analysis of induced vibration

Vibration was induced by the series of trains holding cargo wagons and by a device for excitation of soil seismic waves. The selected parameters of vibrations are presented in Table 2. The maximum vertical acceleration value in the range of 51–54 cm/s2 for impulse excitation is higher than that obtained for the train passage in the range of 33–35 cm/s2. The maximum vertical velocity value obtained for a train passage in the range of 0.14–0.16 cm/s is higher than that obtained for impulse excitation in the range of 0.10–0.14 cm/s. Consequently, az max to vz max ratio is higher for the train induced vibration than that obtained for the hammer excitation.

Table 2 Selected vibration observables resulting from a series of cargo wagon passages and hammer excitations, 8 m away from a sensor
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The analysis of RMS acceleration caused by cargo wagons passages vs background noise demonstrates exceeding values of train passage vibration in comparison to the background vibration in frequency range above 5 Hz (Fig. 5a). The observation time length cut to 5 s caused decrement of RMS acceleration below 3 Hz both for the excitation and background vibration (Fig. 5b).

Fig. 5
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Ground vertical acceleration caused by freight train passages compared to background vibration in the same localization, recorded during a whole passage time and b time window of 5 s

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The acceleration caused by the impulse excitation exceeds the background vibration in the frequency range above 8 Hz (Fig. 6b) when measuring in 5 s time window observation. RMS value is strongly dependent on the time window in case of impulse excitation with the duration of ca. 0.2 s. Only the highest frequencies, above 16 Hz are observed in this case (Fig. 6a). The observed RMS caused by an impulse exceeds the background vibration in the mentioned frequency range.

Fig. 6
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Ground vertical acceleration caused by hammer excitation compared to background vibration in the same localization, recorded during a excitation duration and b time window of 5 s

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The analysis of RMS velocity caused by cargo wagons passages vs the background noise observed during the whole passage time, illustrates that the train passage vibration exceeds the background vibration in the frequency range above 4 Hz (Fig. 7a). The observation time cut to 5 s results in decreased RMS velocity below 3 Hz for both the excitation and background (Fig. 7b), while RMS values for frequencies above 3 Hz exceed the background vibration level for frequencies above 4 Hz, same as in 5 s observation time.

Fig. 7
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Ground vertical velocity caused by freight train passages compared to background vibration in the same localization, recorded during a whole passage time and b time window of 5 s

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The ground vertical velocity caused by an impulse excitation exceeds the background vibration in the frequency range above 3 Hz (Fig. 8b) when measuring in 5 s time window observation. The RMS value is strongly dependent on the time window in case of the impulse excitation with duration of ca. 0.2 s. Only the highest frequencies, above 10 Hz for excitation and above 16 Hz for background are observable in this case (Fig. 8a). The observed RMS caused by an impulse exceeds background vibration in the frequency range above 10 Hz.

Fig. 8
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Ground vertical velocity caused by hammer excitation compared to background vibration in the same localization, recorded during a excitation duration and b time window of 5 s

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The main observations concerning ground velocity are in accordance with the observations of ground acceleration. The difference is that the background velocity level measured in 20 s time window is slightly decreasing towards higher frequencies, while the ground acceleration level is almost equal for the whole observed frequency range.

Results comparison and discussion

The comparison of the selected vibration observables described in the present work with the observables described in the literature is presented in Tables 3 and 4. The freight train induced vibration observables are compared to these resulting from mining and natural seismicity (Table 3). The natural seismic event of 24.12.2014 in the central Italy was described in Boron and Dulinska (2017), whereas the mine tremor of 12.12.2015 in SW Poland was described in Zembaty et al. (2017). On the basis of such data, it was possible to state that the maximum vertical acceleration (peak ground acceleration – PGA in vertical direction) of the railway-induced vibration in 8 m distance: 32.8 – 34.7 cm/s2 is bigger but comparable to the maximum acceleration of a mine tremor in 1 km distance: 21 cm/s2, and to the maximum acceleration of a seismic event in 2 km distance: 24.7 cm/s2. The maximum vertical velocity (peak ground velocity– PGV in vertical direction) of the railway induced vibration in 8 m distance: 0.14 m/s, is smaller but comparable to the maximum vertical velocity of the mining induced vibration in 1 km distance: 0.50 cm/s and the maximum vertical velocity of a natural seismic event in 2 km distance: 0.61 cm/s. The railway induced vibration is characterised by a much bigger az max to vz max ratio(PGA/PGV) of 209–273 in comparison to the mining induced and seismic induced vibration with the az max to vz max ratio of 40 – 42.

Table 3 Comparison of selected observables of freight train vibration found in present work with observables due to mine tremor seismic event acquired from literature
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Table 4 Comparison of selected vibration observables found in present work with data acquired from literature
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The railway induced vibration observables mentioned in the present work are compared to the observables of the railway induced vibration analysed in Drygala et al. (2019) in Table 4. The maximum vertical acceleration 32.8–34.7 cm/s2 in 8 m distance measured for the sake of the present work is ca. two times smaller than 61–81 cm/s2 in 10 m distance in Drygala et al. (2019). The time of excitation is above 30 s in both cases. The comparison analysis of the freight train induced vibration observables presented in the literature indicates a significant decrement in the maximum acceleration value, depending on distance.

Current RMS acceleration and velocity in one-third octave bands are compared to the literature examples in Tables 5 and 6. Table 5 illustrates that the maximum RMS vertical acceleration of 90 dB (reference level 10–6 m/s.2) observed at the distance of 8 m from the track corresponds to 85 dB (the same reference level) described in the literature (Li et al. 2016) at the distance of 15 m from the track. In both studies, the maximum acceleration is observed in the frequency bands of 31.5 and 40 Hz, respectively. The main difference is the duration, correlated with the train length and speed values. Since freight trains are longer and they travel with lower speed than passenger trains, the duration of the exposition to vibration is much longer in case of freight trains: 31 – 36 s in comparison to the vibration caused by passenger trains: 2–5 s, according to Kuo et al., (2016).

Table 5 RMS vertical acceleration in 1/3 octave band spectrum. Current research data compared to literature
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Table 6 RMS vertical velocity in 1/3 octave band spectrum: Current research data compared to literature
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Table 6 demonstrates the maximum RMS vertical velocity of 105 dB (reference level 10–9 m/s) observed at the distance of 8 m and it corresponds to 110 and 100 dB at the distances of 6 and 12 m, respectively, described by Kuo et al. (2016) and to 115 and 90 dB at the distances of 2 and 12 m, respectively, described by Lombaert et al. (2014). In Kuo et al. (2016) and Lombaert et al., (2014) the original reference level was 10–8 m/s, and therefore the RMS value was recalculated to enable comparison. The maximum RMS velocity was observed within 40 – 50 Hz frequency bands in the literature and in the frequency band of 31.5 Hz in the present work. These frequencies are assumed to be comparable.

Analysing the vibration induced by other sources, especially natural seismic and mining would add a novel perspective to the proper methodology of analysis in order to compare the vibrations caused by these factors.

Further research shall concentrate on the analysis in the same spectrum and band width of both the railway induced and mining induced or triggered vibration in order to compare these effects. Unification of the frequency spectrum and band width requires a detailed analysis of the records acquired with the use of various sampling frequencies. Measurements are planned to be performed in the mining areas since the mining induced and triggered seismicity is assumed to be predictable in the apparently short time perspective.

Conclusions

It was discerned that time window influences RMS vibration level of background noise. Shortening of the time window from 20 to 1 s caused reduction in the vibration level for the frequencies below 16 Hz, while shortening of the time window to 0.2 s caused reduction in the vibration level in all the measured frequencies (1–80 Hz). The impulse induced RMS vibration level is dependent on the time window in the whole observed spectrum (1–80 Hz). The duration of the hammer induced vibration is 0.20–0.25 s. The RMS vibration level of the hammer induced excitation, measured in the time window equal to vibration duration (ca. 0.2 s), is strongly influenced by the shortening of time window. The RMS vibration level of the hammer induced excitation, measured in the time window of 5 s exceeds background noise in the frequencies above 4 Hz.

Time window influences RMS vibration level caused by freight train. The time window shortened from 20 to 5 s causes reduction in the vibration level for the frequencies below 5 Hz. This is related to relatively long duration of train passage (generally above 5 s) and thus, it induced vibration. The RMS vibration level caused by train passages, measured in the time window of 5 s as well as in 20 s exceeds background noise in the frequencies above 4 Hz.

Ground vibration caused by both freight train and hammer caused contravention of background noise in the frequencies above 4 Hz. The apparent vibration level in the frequencies below 5 Hz is reduced by shortening the time window from 20 to 5 s. Train passages analysed in the literature are generally of duration of ca. 5 s. Therefore, it is reasonable to analyse train induced vibration in the frequency range 5 – 100 Hz, while the frequencies between 1 and 5 Hz are of smaller certainty.

Seismic induced vibrations, mentioned in Tables 2 and 3 are of comparable maximum vertical acceleration and velocity. However, the ratio between amax to vmax for the mining induced and natural seismicity is smaller than that for the railway and mining one. The vibration duration resulting from natural seismicity and mining is ca 5 s. When comparing the spectral characteristics of natural seismicity, the mining induced and railway induced vibration similar sampling frequency and calculation methods should be used.

The obtained results indicate the possibility to implement RMS analysis in one-third octave band spectrum, in a specified frequency range when a unified time window is applied. The time window length and frequency range unification requires detailed research basing on a larger number of vibration records. On the base of the presented research material, the optimum time window is considered to be 5 s and the optimum frequency range is 5–100 Hz.