Metro property buildings developed rapidly in metropolitan cities over last several years in China. The subwayinduced vibration, which may influence the serviceability of the buildings and the comfortability of their occupants over or near the metro lines, has been paid more and more attention by professional and academic experts. Based on the vibration measurement data of a construction site over Shenzhen Metro line No. 1, this paper utilizes the reasonable and completed data processing method to handle and analyse the measured data. Through the analysis of the data, the subwayinduced vibration propagation trend of free field along the perpendicular direction to metro line was investigated. It is demonstrated that the subwayinduced vibration propagation along the perpendicular direction to metro line was damped out on free field as a whole. But there may exist “rebound phenomenon” at local zones. The responses on pile top and soil adjacent to pile in the vertical shaft along three directions were investigated, and their characteristics in time and frequency domains are compared. Comparison indicates that the subwayinduced vibration on pile top is stronger than soil site near the pile. The measurement results on free field reveal that the most obvious feature of this metro line with curved section is that the vibration along the perpendicular direction is stronger than the other directions. But the measurement results in the vertical shaft show that the vertical vibration mainly transferring through the pile and pile’s vibration in the vertical direction is dominant. Finally, the dynamic timehistory analysis of the building model under the measured acceleration was conducted. The analytical results show that the vibration response of two evaluation indicators increases with the decrease of damping ratio along all three directions. The vertical vibration is more dominant than other two directions at each floor of building. The vibration levels decrease with the increase of story number along vertical direction and firstly decrease and then increase with the increase of story number increasing along two lateral directions.
With the rapid development of urbanization and uninterrupted increase of population, rational plan and efficient utilization of urban land have become imperative. The estate exploitation of metro depots and vicinity adjacent to metro station, which is socalled development of metro property buildings, gradually becomes the focus of major property developers and would have a desirable prospect. The metro property buildings over or near the metro line, especially the buildings over the metro line, potentially have the problems for comfortability and serviceability which were induced by subway. The subwayinduced vibration propagates to structures above the tunnel through rails and via track beds, piles, and soil covered tunnels when metro vehicles pass. The subwayinduced vibration leads to the vibration and noise of the structure, which are undesirable environmental issues and can cause occupants’ discomfort and impair the commercial value of the residences when the vibration level exceeded the certain limits. For example, according to field test of vibration of metro depot of one city in China, the vibration level of residential buildings rightly over the metro depot reached 85 dB when subway passes at the speed of 15∼20 km per hour, where it caused the complaint from the occupants [
Environmental vibration induced by subway or other rail traffic is a type of vibration between the deterministic and random vibration. The determinacy is that marshalling and model of train are almost unchanged and the sleeper spacing is also determined. The randomness is that tread of wheel and track is distributed randomly, and underground geotechnical condition is complex, and the weight of the train is also changed. It is difficult to accurately determine the impact of the environment vibration induced by metro, meanwhile the analysis should be combined with field measurement.
Hassan [
Some field vibration measurements are carried out on different zones. For example, Chen et al. [
Also, many numerical studies had been done on the subwayinduced vibration. Zhou et al. [
This research mainly includes two parts. In the first part, firstly, the vibration measurements were carried out on a construction field over a curved segment of Shenzhen Metro line No. 1, and measurement points were set on free field and in the vertical shaft. Secondly, the measured acceleration was operated by reasonable data processing technology, including removal of background vibration which was emphasised, and then the dynamic timehistory responses of acceleration, velocity, and displacement at the measurement points in three directions were obtained. Fourier transform technology (FFT) was used to gain the vibration characteristics of timefrequency domain of measurement points. Finally, from the perspectives of time and frequency domain, the vibration prorogation trend of free field in three directions was analysed, and the subwayinduced vibration between pile top and soil site near the pile is compared. In the second part, the analysis was concentrated on the vibration analysis of the substructure. Based on the structure model of the building to be built over the vertical shaft and the measured accelerations of the pile as the excitation to the base, the influence of damping ratio on average vibration level of the evaluation points at each floor was studied. The distribution of the average vibration level along the highwise of the building was also reported.
Although there was already a lot of field measurements on the vibration induced by rail transit, it is well known that the complexity of the soil itself, the variability of the regional sites, and the randomness of the rail transit vibration will cause local differences of subwayinduced vibrations. Carrying out field vibration measurement is quite necessary in order to more reliably predict the vibration level of the proposed building.
The vibration measurement was executed, and the measuring points were arranged on the free field and in vertical shaft of a construction site over the curved segment of Shenzhen Metro line No. 1 where a building complex will be built. The vibration measurement includes two parts. The first part was executed on a free field that its elevation is ±0.00 m, and the specific measuring point diagram is shown in Figure
Measuring points of construction site.
Photo of measuring points in vertical shaft.
Soil parameters of different soil layers.
Soil layer no.  Soil type  Water content (%)  Thickness (m)  Depth (m)  Density (kg/m3)  Shear wave velocity (m/s) 

1  Filled Earth  40.6  1.20  1.20  1930  72 
2  Mucky clay  53.6  3.40  4.60  1720  92 
3  Clay  25.1  2.20  6.80  1940  84 
4  Sandy clay  32.2  10.30  17.10  1950  115 
When subway is been driving off on this curved section of metro line No.1, the speed is under 40 km per hour. For left line, the running direction of metro is from down to up, and it is exactly the opposite for right line as shown as Figure
Each of the measuring points was mounted three acceleration sensors labelled with X, Y, and Z that are the identifiers of directions which are parallel to metro line, perpendicular to metro line, and vertical to ground, respectively. The following chapters all obey this naming rule.
The instrumentation used the SVSA data acquisition and signal processing system in this measurement. This system that was initially developed independently by our research team in 2006 [
Lance LC0132 T piezoelectric accelerometers (with sensitivity 49.67 V/g; amplitude range: ±0.1 g; frequency range: 0.05–500 Hz; resolution ratio: 0.0000006 g; weight: 1200 g and using gravity to mount) are used. All accelerometers were calibrated before the field measurement. The dominant energy of targeted field is generally below 100 Hz, and focused sensitive frequencies of vibration serviceability evaluation are in range 1∼80 Hz. Based on sampling theory (Nyquist theory), the sample frequency is set as 200 Hz, which can satisfy with the requirements. The whole vibration test system, mainly consisted of accelerometers and the SVSA data acquisition instrument, is presented as Figure
SVSA vibration test system.
The data or signal, acquired by the vibration test system, needs to be preprocessed to gain the probable time domain information of relative indexes such as acceleration, velocity, and displacement. The frequency domain information of relative indexes is obtained with an appropriate timefrequency analysis method after preprocessing the data [
Data preprocessing is the foundation of assessing environmental vibrations correctly. The evaluation results will be inaccurate if the preprocessing steps are not appropriate or the impact of subjective human factors is introduced. According to the analysis needs of this research, the preprocessing step is displayed as Figure
Preprocessing step of measured data.
The Earth pulsates, as a phenomenon of inherent environmental vibration, is called background vibration which is dominant in low frequency. The vibration measured on field shows a tendency that components of low frequency is enhanced and high frequency is weakened as the distance between the measuring point and the vibration source (subway line) increases. Therefore, removal of background vibration from the vibration measured directly is necessary. In this section, A signifies the subwayinduced vibration, B signifies the background vibration, and A + B signifies the overall vibration consisting of subwayinduced vibration and background vibration. The following steps depict the process of removing the background vibration.
Firstly, for the acceleration timehistory
Secondly,
Thirdly, the difference between
Lastly, the discrete Fourier inverse transform is executed on
The corresponding MATLAB computer program is compiled based on the above theory. Vertical vibration of measuring point W4 that is farthest from the metro line is taken as an example, and the acceleration timehistory and Fourier amplitude spectrum of background vibration, overall vibration, and subwayinduced vibration are presented as Figure
Signal comparison of background vibration, overall vibration, and subwayinduced vibration. (a) Background vibration. (b) Overall vibration. (c) Subwayinduced vibration.
In Figure
Firstly, the data of field vibration measurement were collected by the SVSA vibration test system shown in Figure
More than one subwayinduced vibration data were collected when the field measurement was taken. The statistical results of peak value and rootmeansquare (rms) value for all timehistory signals of each measuring point were analysed.
In order to illustrate the vibration on the free field, the acceleration timehistories and corresponding PSD of measuring point W1 in Z direction as the typical example as Figure
The acceleration signals of measuring point W1 in Z direction. (a) Timehistory curves of acceleration. (b) PSD curves of acceleration.
The timehistory of measuring point W1 in three directions for metro 1.
The average value of 3 indexes induced by subways on free field. (a) Acceleration. (b) Velocity. (c) Displacement.
Mean values, standard deviations, and variation coefficients of peak and Rms values of accelerations induced by metros in three directions.
Index  Acceleration (cm/s^{2})  

Peak  Rms  
Measurement point  W1  W2  W3  W4  W1  W2  W3  W4  
Distance to metro line (m)  5  17  26  35  5  17  26  35  
X direction  Metro 1  2.749  0.981  0.605  0.771  0.471  0.183  0.107  0.143 
Metro 2  3.525  0.986  1.720  0.453  0.739  0.164  0.354  0.083  
Metro 3  3.413  0.771  0.978  0.421  0.650  0.146  0.187  0.084  
Mean values 









Standard deviations 









Variation coefficients 











Y direction  Metro 1  10.798  1.518  0.800  0.363  1.504  0.221  0.133  0.079 
Metro 2  7.366  1.150  1.237  0.746  1.323  0.223  0.249  0.142  
Metro 3  3.524  0.596  0.940  0.739  0.550  0.102  0.197  0.153  
Metro 4  12.754  1.420  0.557  0.395  1.744  0.230  0.132  0.072  
Mean values 









Standard deviations 









Variation coefficients 











Z direction  Metro 1  1.794  0.893  0.402  0.265  0.309  0.156  0.077  0.054 
Metro 2  1.610  1.140  0.463  0.538  0.226  0.160  0.097  0.100  
Metro 3  1.841  1.309  0.532  0.609  0.275  0.179  0.099  0.092  
Metro 4  1.457  0.996  0.448  0.508  0.226  0.160  0.100  0.106  
Metro 5  1.666  1.118  0.530  0.508  0.226  0.166  0.102  0.099  
Mean values 









Standard deviations 









Variation coefficients 








It can be found from Figure
Figure
Table
In order to investigate the propagation of vibration on free field from the view of frequency domain and energy, the average smoothed power spectral densities (PSDs) of 4 measuring points in three directions were calculated, and they were plotted in one figure as presented in Figure
The smoothed average acceleration PSDs of subwayinduced vibration on free field. (a) X direction. (b) Y direction. (c) Z direction.
It is observed that the subwayinduced vibration energy of point W1 in the frequency band which is greater than 10 Hz is dominant, but the vibration energy of point W4 is reversely dominant in the frequency band that is less than 10 Hz in three directions; the vibration energy of Y direction is obviously stronger than other directions, and this can also be explained by the different features with between curved and straight segment of metro line. It is also observed that the dominant frequency of measuring points W1, W2, W3, and W4 offset towards to left in X and Y direction as a whole, but there is local “rebound phenomenon,” such as the dominant frequency of measuring points W3 is on the right side of W2. The dominant frequencies of four measuring points are essentially constant in Z direction.
Statistical acceleration timehistory results of subwayinduced vibration of S1 and S2 points are shown in Figure
The average vibration acceleration of measuring points S1 and S2 induced by subway. (a) Peak values. (b) Rms values.
Figure
To investigate the vibration differences in the vertical shaft from the view of frequency and energy, the average smoothed power spectral densities (PSDs) of measuring points S1 and S2 in three directions were calculated and fitted, respectively. The smoothed average acceleration PSDs of measuring points S1 and S2 were plotted in one figure as shown in Figure
The smoothed average acceleration PSD of measured points S1 and S2 induced by subway. (a) X direction. (b) Y direction. (c) Z direction.
Figure
The building to be built is rightly over the zone of vertical shaft, and the longitudinal direction of building is parallel with direction of perpendicular to metro line (Y direction).
The building will be used as the serviced apartment that includes three stories underground and ten stories above the ground. The function of three stories underground will be as parking lots and supermarkets, and ten stories above the ground will become luxury apartments. The building plan of the typical story (6th story of the building) is shown as Figure
The plan view of the evaluation points at typical story (6^{th} story).
The structure of underground part is reinforced concrete shear wall, and the above part is reinforced concrete frame. The type of foundation of the building is the pile foundation. For the underground part, typical column is circular for which diameter is 1000 mm, typical beam is rectangle of which size is 800 mm
The structure model of the building was built by SAP2000. The mass in the model is considered as combination of 1.0
The SAP2000 model of the building.
In this research, since it is assumed that the presence of the building does not affect the vibration generation source [
The excitations to be inputted. (a) X direction. (b) Y direction. (c) Z direction.
The directions input to structure are in accord with the arrow direction in Figure
As is shown in Figure
The vibration level is the usual indicator when evaluating all kinds of vibrations. Here, two evaluation indicators are adopted, which are acceleration vibration level
According to International Standard for Human Response to Wholebody Vibration (ISO2631) [
The velocity level is an indicator that is mainly recommended by Federal Transit Administration (FTA) criteria [
The Rayleigh damping approach was followed in this research, and the damping matrix
The value of
As the most important parameter in the Rayleigh damping approach, the damping ratio
The average onethird octave spectra of the acceleration level of typical story (6^{th} story) for different damping ratio. (a) X direction. (b) Y direction. (c) Z direction.
The onethird octave and average spectra of the accelerations of each evaluation point at typical story (6^{th} story, damping ratio = 0.02). (a) X direction. (b) Y direction. (c) Z direction.
The average onethird octave spectrum of the acceleration level of typical story in three directions for different damping ratios is shown in Figure
Also, the average onethird octave spectra of the velocity level of typical story in three directions for different damping ratio are shown in Figure
The average onethird octave spectra of the velocity level of typical story (6^{th} story) for different damping ratio. (a) X direction. (b) Y direction. (c) Z direction.
In order to discern the distribution of acceleration indicators along the highwise, onethird octave spectra of accelerations of each evaluation point and their average spectra were gained and pictured as Figure
The distribution of maximum frequency acceleration level along the highwise (damping ratio = 0.02).
It is observed from the curves of “average values” in Figure
The comparison of the distribution of maximum frequency acceleration level
Also, in order to discern the distribution of velocity indicator along the highwise, onethird octave spectra of velocities of each evaluation point at the typical story and their average spectra were gained and pictured as Figure
The 1/3 octave frequency band velocity level of the typical story (6^{th} story, damping ratio = 0.02). (a) X direction. (b) Y direction. (c) Z direction.
The distribution of velocity level along the highwise (damping ratio = 0.02).
From Figures
This paper mainly includes two parts, the first part had presented the results of subwayinduced vibration measured on a construction site at the curved section of Shenzhen Metro line No. 1 in China. The other part, based on the results of the field measurement, had calculated the different vibration indicators and investigated the distribution of vibration level along the highwise of the building to be built over the site of vertical shaft. Especially, the influence of damping ratio on the vibration level has been studied. By the analysis to the results of field vibration measurement and the dynamic behaviour of the building model under the measured accelerations, the following main conclusions were gained.
In the time domain, the subwayinduced vibration propagation along direction of perpendicular subway line damped out on the free field as a whole, but there is “rebound phenomenon” at local zone. This is right for X and Z direction, but not for Y direction. In frequency domain, the vibration energy has different distribution at different frequency sections in three directions.
In vertical shaft, the subwayinduced vibration of pile top is stronger than the soil site near the pile from view of time domain, and this is right for all three directions. In frequency domain, the vibration energy of two measuring points has its own high and low at different frequency bands.
For this curved section of the metro line, the most obvious feature is that the vibration in Y direction is stronger than the other directions on the free field. But for the measuring point of pile top in vertical shaft, the vertical vibration level accords with the straight sections of the metro line and greater than the other directions.
The vibration responses of two evaluation indicators increase as the damping ratio in three directions reduces, and the vertical vibration spectral shapes are obviously different with the spectral shapes of two lateral directions.
For the acceleration level and velocity level, the vertical vibration is more dominant than another two directions at each story of the building, and the maximum frequency vibration levels decrease as the story number increases in vertical direction. But in the two lateral directions, it decreases first, then increases, and then decreases again as the number of stories increase in vertical direction.
The data used to support the findings of this study are available from the corresponding author or
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (no. 51578273).