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Volume : 44

Part : 2

Proceedings of the Institute of Acoustics

 

 

The time-frequency characteristics analysis and prediction of ground vibration near a subway station

 

Bideng Liu1, Beijing Academy of Science and Technology, Beijing, P. R. China

Yubin Wu, Beijing Academy of Science and Technology, Beijing, P. R. China

Ruixiang Song, Beijing Academy of Science and Technology, Beijing, P. R. China

Lei He, Beijing Academy of Science and Technology, Beijing, P. R. China

Qiong Wu, Beijing Academy of Science and Technology, Beijing, P. R. China

 

ABSTRACT

 

This paper presents the time-frequency characteristics of ground vibrations near subway stations through field tests and analyses. More than 15 ground vibration measurement points are set up in the longitudinal and transverse directions of the track near a subway station. Overall, the ground vibration level (VLzmax) above the tunnel is approximately 73 dB on the border between the station and mainline, while it attenuates to 63 dB away from the tunnel by approximately 30 meters; the dominant frequency in the mainline area is approximately 63-80 Hz. The results in the longitudinal direction show that the ground vibration increases rapidly as the train drives away from the station because of the train speed growing, and VLzmax is less than 10 dB between the station and near the mainline areas, while the dominant frequency in the mainline area is higher than that in the station area. The attenuation rate of the ground vibration in the transverse direction for the mainline area is faster than that for the station area. The power distribution law y=A*x-α can describe the vibration attenuation characteristics, and its "peak and long tail effect" and "scale-free characteristics" can predict the vibration at any position by measuring two specified locations.

 

1. INTRODUCTION

 

The speed of transit-oriented development (TOD) in metropolitan areas in China is becoming increasingly faster and significant for the following reasons: (1) With the deepening of the urbanization process, the need for increasing efficiency for traffic and growing intolerance to congestion by the huge number of private cars in core cities is increasing; (2) With the promotion of the integrated construction of metropolitan areas, the construction land available for development in central cities is becoming increasingly scarce. City blocks developed according to the TOD concept have become popular, such as in Hong Kong, Tokyo, Copenhagen, Guangzhou, Chongqing, Dongguan and Shenzhen [1], because of more possibilities brought by efficient transportation and open urban spaces, such as vertical urban design.

 

There is little research on the assessment of environmental vibrations induced by subways near the station. However, vibration evaluation in the station area is of great significance to the application of TOD in metropolises in China. Researchers in England [2], Switzerland [3], Japan [4] and China [5] report that excessive environmental vibration is harmful to human beings. The vibration characteristics induced by railway operation in station areas are different from those in mainline areas because of the traveling speeds and accelerating or deceleration of trains, the type of tunnel structures, different wheel-rail systems, complex track line conditions and track bed systems.

 

In this research, the ground environment vibration near a subway station, while the tunnel is buried approximately 15 meters below the ground and the Type-5B-Train was operated in the tunnel, was measured through a high-precision vibration sensing network. The analysis results of the maximum Z vibration level (VLzmax) [6] and 1/3 Octave spectrum of multiple observation points show that the vibration increased rapidly with the train departures, and the vibration attenuated rapidly as the locations moved away from the tunnels. The power distribution law y=A*x-α can describe the ground vibration attenuation characteristics with the distance from the track, while the linear fitting equation y=B+C*x can predict the ground vibration level with the distance from the station.

 

2. METHODOLOGY

 

The methodology for this research was reported in this part, such as instrument specifications, the sensor arrangement in the field testing for environmental vibration measurement, and the performance assessment criteria.

 

2.1 Experimental setup and instrumentation

 

Ground vibration measurement locations were categorized as (1) perpendicular to the track direction, which was defined as transverse (x), and (2) parallel to the track direction, which was defined as longitudinal (y). Twelve train induced measurement sites with two profiles in the transverse (x) direction were selected to consider the different ground vibrations with different distances away from the track, which are in the mainline and station areas. Another 4 measurement sites in the longitudinal (y) direction were selected to consider the different ground vibrations with different distances away from the station. Figure 1 (a) shows the measurement sites setup in plan view, which contains a transverse direction profile in the station area (2-1, 2-2, 2-3, 2-4, 2-5, 2-6), in the mainline area (3-1, 3-2, 3-3, 3-4, 3-5, 3-6), and a longitudinal direction profile along the track (1-1, 1-2, 1-3, 1-4, 1-5, 1-6). The distance in the transverse direction of the mainline area and station area is approximately 90 meters. Sixteen accelerometers were positioned on the ground at same time, which glued on the brick or concrete or on the artificial steel platform, as shown in Figure 2. In the field test, a sensing system composed of several B&K 8344 accelerometers and 3 INV3062 DAQ, which has a 160 dB dynamic range, was used. Measurements were made at a sampling rate of 1024 Hz. Table 1 shows the specifications of the accelerometer used in the field tests.

 

 

Figure 1: Sketch map of the measurement locations (Plan view) and VLzmax at each location.

 

 

Figure 2: Accelerometers setup on the ground in different situations.

 

Table 1: Specifications for the B&K 8344 accelerometer

 

 

2.2 Performance assessment criteria

 

Two different indices, VLZmax and 1/3 Octave, were calculated for the performance assessment criteria to quantify the time-frequency characteristics of ground vibrations near subway stations.

 

VLZmax is the maximum value of the Z-weighted vibration level of the acceleration, VLZ, in the specified measurement duration time, t. VLZ is the vibration acceleration level, VAL, after correction by the human body vibration weighted factor in the Z direction, and the Z-weighted factor obtained from Code ISO 2631-1-1985 [8]. The calculation for VAL is shown in Equation (1):

 

 

where a and a0 denote the measured acceleration and the reference acceleration, respectively, which are often taken as 10-6 m/s2. The units of the VAL, VLZ and VLZmax are dB.

 

The 1/3 Octave was employed to analyze the frequency characteristics of the ground vibration, and the 1/3 Octave center frequency was used for the quantitative analysis. The unit of the 1/3 Octave center frequency is Hz.

 

3. RESULTS AND DISCUSSIONS

 

The field experiment results and the relationship between the vibration level and the distance in the mainline and station areas are illustrated in this section.

 

3.1 Relationship between the vibration and the distance from the track

 

The time-frequency characteristics of ground vibration for one typical travel-crossing case with different distances away from the track in the mainline and station areas were analyzed in this part. Figure 3 shows the ground acceleration time histories in two transverse profiles at different distances away from the track between 0 meters and 45 meters. The ground vibration duration was approximately 10 seconds. The amplitude of the ground acceleration in the mainline area was approximately 3 times that of the station area, which was approximately 4 cm/s2 and 13 cm/s2 at the top of the tunnel, respectively. Figure 1 (b) shows the maximum ground vibration VLZmax for one typical travel-crossing case, which contains a transverse direction profile in the station area (2-1, 2-2, 2-3, 2-4, 2-5, 2-6), in the mainline area (3-1, 3- 2, 3-3, 3-4, 3-5, 3-6), and a longitudinal direction profile along the track (1-1, 1-2, 1-3, 1-4, 1-5, 1-6). The VLZmax of the ground vibration are approximately 74.0, 70.5, 68.7, 72.6, 69.4 and 64.1 dB at distances of 0, 5, 10, 20, 30 and 45 meters away from the track, respectively, when the train crosses the mainline area; the VLZmax are approximately 62.9, 60.4, 60.3, 55.4, 55.9 and 56.9 dB at distances of 0, 5, 10, 20, 30, and 45 meters away from the track, respectively, when the train travels in the station area.

 

The researchers established the prediction equations between the ground vibration level and distance away from the track in the mainline and station areas. The authors employed the power distribution law y=A*x-α to describe the vibration attenuation characteristics, where y and x denote the vibration level (VLZmax) and the distance away from the track, respectively, and the coefficients A and ߙ are regression coefficients. The relationship between VLZmax and the distance in the mainline and station areas can be represented by Equations (2) and (3), respectively. Figure 4 exhibits the fitting curves of the prediction equation between the ground vibration level and the distance. The regression coefficients of the prediction equations are 74.5, 64.3, 0.0274, and 0.0382, which represent the ground vibration on the top of the tunnel and the gradient of the vibration attenuation factor in the mainline and station areas, respectively.

 

 

 

Figure 3: Ground acceleration time histories of one typical case for train crossing in the subway.

 

 

Figure 4: Fitting curves of the prediction equation between the ground vibration levels and distance (one train).

 

The researchers also calculated the VLZmax of 10 different train travel-crossing cases with 12 measurement sites in the transverse (x) direction in the mainline and station areas. Table 2 summarizes the VLZmax of 10 different cases with 12 different locations, where the trains traveled crossing the two profiles in the mainline and station areas. The VLZmax of the same location with different train crossings cases are similar. The maximum ground vibration VLZmax at the top of the tunnel in the mainline area and station area are 75.2 and 63.8 dB, respectively. The average VLZmax values of the ground vibration are approximately 73.8, 69.5, 67.5, 72.7, 64.3 and 60.8 dB at distances of 0, 5, 10, 20, 30 and 45 meters away from the track when the train crosses the mainline area. The average VLZmax are approximately 62.7, 61.3, 61.9, 56.9, 59.6 and 58.4 dB at distances of 0, 5, 10, 20, 30, and 45 meters from the track, respectively, when the train is traveling in the station area. The ground vibration above the tunnel is approximately 73 dB on the border between the station and mainline area, while it attenuates to 61 dB on average when the site is approximately 40 meters away from the track and 50 meters away from the station boundary. However, the vibration increased at locations 3-4 and 2-5, which are 20 to 30 meters away from the track.

 

Table 2: Ground vibration levels VLzmax (dB) with different distances away the track in the mainline area

 

 

3.2 Relationship between the vibration and the distance from the station

 

The researchers analyzed the time-frequency characteristics of ground vibration for one typical travel-crossing case with different distances away from the station, while the distance of measurement sites in the longitudinal direction profile was 30 meters away from the track. Figure 5(a) shows the acceleration time history for three typical cases 0, 20, and 90 meters away from the station. The farther distance away the station is, the higher the travel speed of the train and the higher the amplitude of acceleration. When the train traveled 90 meters away from the station, the ground acceleration amplitude was increased by 3 times.

 

Figure 1 (b) shows the maximum ground vibration VLZmax for one typical travel-crossing case in the longitudinal direction profile along the track (1-1, 1-2, 1-3, 1-4, 1-5, 1-6). The VLZmax of the ground vibration are approximately 55.9, 59.7, 64.8 and 69.4 dB at distances of 0, 20, 50 and 90 meters from the station, respectively. Figure 5(b) exhibits the spectrum characteristics for three typical cases of different distances away from the station. The dominant frequency of the ground vibration for the train crossing is approximately 60 Hz to 80 Hz. The results in the longitudinal direction show that the ground vibration increases rapidly as the train drives away from the station because of the train speed growing, and VLZmax is less than 10 dB between the station and near the mainline area, while the dominant frequency in the mainline area is higher than that in the station area.

 

The researchers established the prediction equations between the ground vibration level and distance from the station. The authors employed the Perform Linear Fitting equation y=B+C*x, where y and x denote the vibration level and the distance away from the station, respectively, and the coefficients B and C are regression coefficients. The relationship between the ground vibration level and distance away from the station can be represented by Equation (4), which can predict the ground vibration of the distance away from the station. Figure 6 exhibits the fitting curves of the prediction equation between the ground vibration level and the distance. The regression coefficients of the prediction function are 52 and 0.18, which represent the background ground vibration and the gradient of vibration growth, respectively. The prediction function employed by the power distribution law VLZmax,30m = 52+0.18*d, can describe the vibration attenuation characteristics, and its "peak and long tail effect" and "scale-free characteristics" can predict the vibration at any position by measuring two specified locations along the tunnel when the longitudinal profile is 30 meters away from the track.

 

 

 

Figure 5: Ground acceleration time-history and spectrum characteristics of typical train travel at different locations.

 

 

Figure 6: Fitting figures of the prediction equation between the ground vibration levels with different distances away from the station.

 

4. CONCLUSIONS

 

This research has presented a ground vibration test in the field near a subway station, which provided the relationship between the vibration level and frequency characteristics and the distance from the tunnel and the station. In the experimental test, researchers arranged 12 locations along with two profiles in the transverse (x) direction to consider the different ground vibrations with different distances away from the track and another 4 locations in the longitudinal (y) direction to consider the different ground vibrations with different distances away from the station. The authors collected more than 10 cases in each location. From the analyzed data collected in the field test, the maximum and average vibration levels, VLZmax, and the frequency characteristics in different locations were determined. The experimental results show the following:

  1. The ground vibration level VLZmax and the acceleration amplitude increase rapidly as the train drives away from the station because the train speed increases. The amplitude of ground acceleration in the mainline area (the train traveled at 90 meters away from the station) was approximately 3 times that of the station area, which was approximately 4 cm/s2 and 13 cm/s2 at the top of the tunnel, respectively, and VLZmax was less than 10 dB between the station and near the mainline area, which was approximately 75.2 and 63.8 dB at the top of the tunnel, respectively. The VLZmax of the ground vibration are approximately 55.9, 59.7, 64.8 and 69.4 dB at distances of 0, 20, 50 and 90 meters away from the station, respectively, where the longitudinal profile is 30 meters away from the tunnel. The ground vibration above the tunnel is approximately 73 dB on average on the border between the station and mainline area, while it attenuates to 61 dB on average when the site is approximately 40 meters away from the track and 50 meters away from the station boundary.

  2. The power distribution law VLZmax =A*d-α can describe the vibration attenuation characteristics between the vibration level and the distance away from the track. The regression coefficients A and ߙ of the prediction equations are 74.5, 64.3, 0.0274, and 0.0382, which represent the ground vibration on the top of the tunnel and the gradient of the vibration attenuation factor in the mainline and station areas, respectively. The linear fitting equation VLZmax=B+C*d can describe the vibration attenuation characteristics between the vibration level and the distance away from the station, where the longitudinal profile is 30 meters away from the tunnel. The regression coefficients B and C of the prediction function are 52 and 0.18, which represent the background ground vibration and the gradient of vibration growth, respectively.

  3. The dominant frequency of the ground vibration for the train crossing near the station is approximately 60 Hz to 80 Hz, and the dominant frequency in the mainline area is higher than that in the station area.

 

5. ACKNOWLEDGMENTS

 

This work is partly funded by the Beijing Natural Science Foundation of China (Grant No. 8202019) and the Beijing Financial Research Project (Grant No.11000022T000000468166 and 11000022T000000446408). The authors also acknowledge Mr. Ximing Zhang, Jianjun Guo, Qinglong Song, Wei Zhu, Jian Tan, and Xiaohui Liang for their help with the data collection in the field and Ms Chenyu Fan and Yujiao Tian for their coordination with field testing.

 

6. REFERENCES

 

  1. Statistics and analysis report of urban rail transit of China in 2020, China Association of Metros, (2021).

  2. Woodroof H and Griffin M. A survey of the effect of railway-induced building vibration on the community, ISVR Technical Report no. 160, University of Southampton, (1987).

  3. Müller R and Kostli K. Vibration and vibration induced noise emissions from railways: estimation of retrofit costs for Swiss railways, SBB report to Swiss federal office of transport, (2008).

  4. Yokoshima S. A study on factors constituting annoyance due to Shinkansen railway vibration, Journal of Architecture, Planning and Environmental Engineering, 526 (1999).

  5. Gu X. Analysis and research of the railway environmental vibration influence conditions and its control techniques, Railway Energy Saving & Environmental Protection & Occupational Safety and Health, 7(5), 223-228, (2017). [6] International Organization for Standardization. ISO 2631-1:1985: Evaluation of human exposure to whole-body vibration - Part 1: General requirements, (1985).

 

1 bidengliu@vip.163.com