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A series of field vibration tests were carried out at an underground metro station underneath the high speed railway by installing accelerometers both on the side wall of the metro station and in the surrounding soil. Within the frequency domain of 0–200 Hz, the attenuation, transmission, and frequency response properties of vibration for both the underground structure and the surrounding soil were analyzed and compared. The attenuation index is found to be decreased with the increase of underground structure stiffness. The existence of damping and coupling effect of the surrounding soil, as well as the interference of axle spectrum from excitation sources, makes it very challenging to separate the frequency response characteristics of structures from soil at FFT (Fast Fourier Transform) spectrum. The combined NExT (Natural Excitation Technique) and HHT (Hilbert–Huang Transform) method are thus used to study the waveforms and propagation velocities of vibration waves in underground structure and surrounding soil. The wave types and their speeds are determined and used for evaluating the structural elastic modulus. Compared with the attenuation index or natural frequency, wave velocity is easier to be recognized, is sensitive to the change of the structural stiffness, and requires limited number of sensors in the field. Based on the properties of the vibration characteristics studied in this work, the wave velocity based method is recommended for the health monitoring of underground structures.

There has been great development of infrastructure constructions in China for the past three decades. The total length of the operating underground metro lines in China has been accumulating with an average speed of 270 km per year. As the serving time of these underground infrastructures gradually increases, the conditions of these systems may deteriorate rapidly due to the factors such as material aging, harsh environment, and dynamic loading. To ensure continuous safe operation of tunnels and other underground structures, the establishment of real-time health monitoring system for the evaluation of service performance is of great significance.

Health monitoring for the underground structures has been mainly relying on the static methods. For example, recent work by Bhalla et al. [

Since 1970s, vibration based health monitoring system has been widely used for the real-time monitoring of structural properties for infrastructures above the ground [

It has been well known that since the underground structures are strongly coupled with the surrounding soil, the constraining and damping effects as well as the dynamic behaviors of surrounding soil all cause major challenges for the recognition of vibration characteristics [

In this work, in order to investigate the vibration characteristics of underground structures and discuss the feasibility of using vibration based methods for the health monitoring of large underground structures, a series of field vibration tests were carried out at an underground metro station underneath the high speed railway. Within the frequency domain of 0–200 Hz, the attenuation, transmission, and frequency response properties of vibration for both the underground structure and the surrounding soil were analyzed and compared. Based on the properties of the vibration characteristics, some suggestions were given for the health monitoring of underground structures by using vibration based methods.

As shown in Figure

Floor plan of the test site showing the intersection of Shanghai-Hangzhou high speed railway on the ground surface and the underneath Shanghai no. 9 metro line.

Cross section view of the metro station with high speed railway on the ground surface; soil layers along the depth and the corresponding shear wave velocity are listed on the right.

In order to study the wave propagation in both the underground metro station and the surrounding soil and identify the difference of wave propagation characteristics in these two mediums, three measurement arrays were installed in the field, as shown in Figure

Parameters of accelerometer.

Item | Sensitivity (V/g) | Max acceleration (g) | Frequency range (Hz) | Resolution (g) |
---|---|---|---|---|

Value | 40 | 1.2 | 0.1–300 | 2 × 10^{−6} |

Design of measurement arrays.

The installation procedure of accelerometers W1 to W3 followed the standard of ISO 5348 [

Procedure for the installation of accelerometers in the soil.

Vibration attenuation index is one of the important parameters to determine the wave types and evaluate the attenuation characteristics [

In the half space medium, the vibration waves caused by pulse loads propagate outward as a combination of Rayleigh wave, compression wave, and shear wave. The propagation of elastic waves is also accompanied by the wave attenuation which includes two parts, one is the decay of the amplitude due to the increasing distance from the source and the other is due to the material damping and energy dissipation. The attenuation of vibration waves can be described by the following equation [

while

Table

Selection of attenuation index

Physical sources | Type of source | Wave type | Attenuation index |
---|---|---|---|

Line source [ | Line | Rayleigh | 0 |

Body | 0.5 | ||

Point source [ | Point | Rayleigh | 0.5 |

Body | 1.0 | ||

Short length and high speed train [ | Line | Body | 1.5 |

Long length and slow speed train [ | Line | Body | 1.0 |

Indicators which can be used to evaluate the vibration level include peak particle velocity (PPV), root mean square (RMS), continuous RMS, vibration magnitude, and vibration peak factor. In this work, the PPV value is used for the evaluation of attenuation characteristics. The detailed procedures are listed as follows.

One-third octave frequency bands of measurement points G1 to G4 before (a) and after (b) applying HHT.

The velocity time history of G1 by integrating acceleration.

According to the procedure described above, the maximum dB value of velocity was obtained at each of the measurement point. And the attenuation index along both the horizontal and vertical directions can be determined. The details can be seen in Section

The attenuation of vibration induced by a moving train is closely related to the speed of the train. Therefore, we proposed a method by which the speed of the train can be automatically determined by using the autocorrelation function.

When a train passes by with uniform speed, the wheel-rail force and its response function is a periodic function of the passing time of one carriage. Therefore the time history of autocorrelation function reaches the peak at the interval of the passing time of one carriage. Figure

The time history of autocorrelation function for the acceleration response of train vibration.

At the same time, eight peaks can be identified from Figure

Horizontal attenuation of vibration waves in the soil for two different train velocities and train lengths.

The results in Figure

Vertical attenuation of vibration waves in the soil for two different train velocities and train lengths.

Figure

Vertical attenuation of vibration waves in the underground structure for two different train velocities and train lengths.

In summary, the calculated attenuation index

Calculated attenuation index

Physical sources | Velocity (km/h)/number of carriages | Horizontal direction | Vertical direction |
---|---|---|---|

Soil surround the metro station | 180/16 | 1 | 1.5 |

300/16 | 1 | 1.5 | |

300/8 | 1 | 1.5 | |

| |||

Metro station | 180/16 | / | 0.8 |

300/(8, 16) | / | 0.5 |

By comparing Tables

The natural frequency and frequency response function spectrum (FRFs) based methods are common methods in structure health monitoring, but susceptible to temperature and the characteristics of vibration source [

Figure

The time history of the acceleration for the measurement points W2 on the wall of the metro station and G2 in the soil when a CRH380a train is passing by with uniform speed.

Figures

(a) FFT spectrum of measurement point W2, (b) FFT spectrum of measurement point G2, and (c) the axle spectrum of the moving train.

while

while

Substitute the following values into (

The results above show that the transient response generated by the moving train with uniform speed is dominated by the axle spectrum. Technically by the FFT method, it is difficult to recognize and extract the nature frequency for the vibration mode and the cut-off frequency for the propagation mode.

In order to avoid the interference from the axle spectrum, the characteristics of frequency spectrum for a stopping train was also analyzed. Figure

Time history of the acceleration for measurement points W2 on the wall of the metro station and G2 in the soil for a stopping train.

The power spectral density (PSD) of the two signals can be computed by applying the “pwelch” function in Matlab with the parameters of

(a) PSD frequency spectrum of signals for measurement point W2, (b) PSD frequency spectrum of signals for measurement point G2, and (c) the transfer function of these two signals.

while

Meanwhile, based on the “cpsd” and “pwelch” functions in Matlab, a transfer function can be defined in (

The transfer function stabilizes around 1 between 1 and 10 Hz which means that the vibration of metro station and surrounding soil are synchronous at low frequency. The vertical displacement history of the two measurement points W2 and G2 in Figure

Recorded vertical displacement history for measurement points W2 and G2.

The difference between the one-third octave band spectra of the transfer functions between the measurement points in the soil and on metro station wall is also provided in Figure

One-third octave band spectra of the transfer functions between the measurement points in the soil and on the metro station wall.

The above analysis of the frequency response for measurement points on the wall of the metro station and in the soil when the train was stopping shows that the frequency spectrum is dominated by the resonance frequency of the train and rail. Meanwhile, the structure and soil show good transmission properties at the low frequency range below 10 Hz; thus it is challenging to differentiate the performance change of the structure and soil based on the characteristics of frequency spectrum. In this respect, different from the applications for bridges and tall buildings, the structural health monitoring for the underground structures requires wider frequency band. Meanwhile, some resonance frequencies around 20 Hz and 50 Hz are found from the moderate amplification at the one-third octave band spectra of the transfer functions. However the accurate value need to be further investigated at the following section.

In order to accurately determine the resonance frequency and avoid the interference due to train operation, the ambient vibration test was conducted in the night with the benefit that the surrounding area of the test station is farmland and there is limited vibration disturbance. The characteristics of frequency spectrum of structural natural vibration and propagation mode were analyzed.

The sampling frequency for the natural excitation was 1000 Hz. Figure

Time history of the acceleration for measurement points W2 on the wall of the metro station and G2 in the soil with natural excitation in the night.

Figure

(a) Autocorrelation curve after the NExT processing and (b) its PSD frequency spectrum for measurement point W2 with natural excitation in the night.

Similarly, the same processing was done for the signal of G2. All the peaks identified in Figure

(a) Autocorrelation curve after the NExT processing and (b) its frequency spectrum for measurement point G2 with natural excitation in the night.

In summary, from the analysis of transfer function, it is found that the structure and soil show good transmission properties at the low frequency range below 10 Hz, but the difference of the vibration response considerably increases between 10 and 100 Hz. Meanwhile, some resonance frequencies can be found around 21 Hz, 49.5 Hz, 80.5 Hz, and 122.5 Hz. However, in contrast to the applications for bridges and tall buildings, the accurate recognition and extraction of the frequency response characteristics for the structure becomes more challenging and need wider frequency band because of the constraining and damping effects as well as the dynamic behaviors of surrounding soil, together with the interference of axle spectral and other characteristics of the train and rail system.

Waveforms and propagation velocities of vibration waves are important features which can be used to determine the wave types and back calculate the elastic modulus of the structures. Accordingly, the service performance of the structures can be evaluated by monitoring the changes of the wave velocities. In this section, the wave velocities between different measurement points were extracted by combining NExT and HHT. Vibration wave types and the propagation characteristic both in the structure of metro station and in the soil were then analyzed and compared.

Velocities of the vibration waves are often obtained either through measuring the travel time between measurement points in the time domain or by determining the wave phase shift based on methods such as SASW in the frequency domain [

(a) The time history of the acceleration for measurement points G1 to G4 after 5000 seconds continuous acquisition, (b) autocorrelation function after the NExT processing for G1, and (c) PSD frequency spectrum of signal in (b).

Autocorrelation function of G1 and cross-correlation functions between G1 and the other three points G2 to G4 in the soil and the determination of vertical wave velocity.

The wave velocities in the metro station side wall were also analyzed by using the combined NExT and HHT method and were compared with the ones in the soil. Figure

(a) Cross-correlation function between W1 and W3; (b) first intrinsic mode function (IMF1) based on HHT; (c) second intrinsic mode function (IMF2) based on HHT; (d) PSD frequency spectrum of the correlation function in (a) with the two peaks corresponding to the two intrinsic mode functions.

The same procedure was applied to get IMF1 and IMF2 of the autocorrelation function of W1 and other two points W2-W3 on the wall of the metro station, the results plotted in Figures

(a) IMF1 of the autocorrelation function of W1 and the cross-correlation functions between W1 and the other two points W2-W3 on the wall for the determination of vertical wave velocity and (b) the same plot for IMF2.

where ^{3}.

From the analysis above, it is found that, under the excitation of train induced vibration, the body wave types and their propagation speeds in the underground station can be obtained by combining NExT and HHT. Meanwhile, any structural performance deterioration will result in the body wave speed changes; this method thus can be used to monitor the service performance of underground structures.

To investigate the feasibility of using vibration characteristics for the health monitoring of underground structures, field vibration tests were carried out at the metro station underneath the high speed railway. The following conclusions are made based on the measured vibration characteristics of the underground structures and the surrounding soil.

The following suggestions are given for the health monitoring in underground structures by using vibration characteristics.

All data related to this study can be provided upon sending email request to

Xiongyao Xie was the PI of this research project, while Biao Zhou and Fengshou Zhang were the major group members to execute the project. Biao Zhou was responsible for making the testing plan and collecting the data. Fengshou Zhang together with Biao Zhou finished the data analysis and paper writing.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was initiated by Shanghai Shentong Metro Co., Ltd. Partial support was also received from the National Natural Science Foundation of China under Grants 51608379 and 51778476 and Shanghai Science and Technology Innovation Plan Funds under Grant 15DZ1203903. Those supports are greatly appreciated.