# Vibration Characteristics of Underground Structure and Surrounding Soil Underneath High Speed Railway Based on Field Vibration Tests

Authors: Biao Zhou; Fengshou Zhang; Xiongyao Xie
Journal: Shock and Vibration
 (2018)

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## Abstract

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.


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## Body

## 1. Introduction

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. [1] and Bennett et al. [2] introduced the applications of environmental and static structural deformation monitoring system for the metro tunnels in London. Nevertheless, it was found that the structural damage in hidden places is difficult to be detected by using static methods. Meanwhile, static monitoring is only able to cover relatively small measurement area. Therefore, there is a great demand of developing vibration based health monitoring methods that have the potential of inspecting the overall underground structure as well as the surrounding soil.Since 1970s, vibration based health monitoring system has been widely used for the real-time monitoring of structural properties for infrastructures above the ground [5–8]. The vibration characteristics of structures, determined by either from the properties of wave propagation within the structures or from the vibration modes, are the key to apply the vibration based health monitoring methods. Wave propagation properties mainly depend on their attenuation properties and waveform characteristics [9–11]. Vibration modes and related methods are more commonly used, including natural frequency and frequency response function spectrum (FRFs) based methods [12–15], mode shape based methods [16], mode shape curvature/strain mode shape based methods [17, 18], model and related matrix based methods [19], and data driven methods [20]. Some signal processing techniques are proposed for the extraction of vibration characteristics [21]. In addition, there is some reported work which focused on the interaction between soil and structure in conjunction with the low-frequency seismic response [16]. However, the vibration characteristics of underground structures have not been well understood yet, which greatly limits the application of vibration based health monitoring methods in monitoring underground structures.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 [22, 23], especially when applying those vibration modes based methods. Similarly, the mode characteristics of hydraulic structures and tall buildings are greatly affected by the coupling with the surrounding water and the connected foundation, respectively, and are typically polluted with noises [24, 25]. Health monitoring of underground pipelines is therefore mostly based on wave propagation characteristics and related methods [26–28]. For tunnels, underground metro stations, and other large underground structures, the influence from the surrounding soil is more significant because of the large size and buried depth. Previous research on the vibration characteristics of underground structures mainly focused on the generating mechanism of vibration and the attenuation characteristics of vibration waves. For example, Heckl et al. [29], Yang and Hung [30], and Forrest and Hunt [31] presented the generating mechanisms of structure-borne vibrations caused by underground railway. Degrande et al. [32] reported the results of in situ vibration measurements at a site of London metro line and found that the vibration level and the frequency content is a function of train speed and the distance to the tunnel. The above research however was not able to systematically study the vibration characteristics of large underground structures and compare them with the vibration characteristics of the surrounding soil.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.


## 2. Engineering Background and Field Test Plan

### 2.1. Engineering Background

As shown in Figure1, the test site is located at the underground metro station of Shanghai no. 9 metro line. The metro line is nearly perpendicularly intersected by the operating Shanghai-Hangzhou high speed railway on the ground surface. The high speed railway operates with a train speed of either 180 km/h with train type CRH2a or 300 km/h with train type CRH380a. The metro station was under construction when the field vibration tests were carried out. Figure 2 shows the cross section view of the metro station with high speed railway on the ground surface. The details of the soil layers along the depth and the corresponding shear wave velocity are shown on the right side of the plot. The distance from the roof of the metro station to the high speed railway is about 4.55 m. The metro station was excavated mainly in the soft clay and silt clay layers. The results of SPT (Standard Penetration Test) [33] showed that the shear wave velocity in these soils is about 110 m/s and the compression wave velocity is about 687 m/s [34].Figure 1
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.Figure 2
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.


### 2.2. Design of Measurement Arrays

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 Figure3. The first array with three measurement points (W1 to W3) was vertically aligned on the side wall of the metro station. The second array with four measurement points (G1 to G4) was parallel to the first array but buried into the soil surrounding the metro station. The third array with three measurement points (G5 to G7) was at the same elevation of G1 but along the horizontal direction and parallel with the side wall of the metro station. The second and third arrays were used to test the vertical and horizontal wave propagation in the soil, respectively. The LC130 IC piezoelectric accelerometer was employed in the field test. The specific parameters of the accelerometer are listed in Table 1.Table 1
Parameters of accelerometer.
Item Sensitivity (V/g) Max acceleration (g) Frequency range (Hz) Resolution (g) Value 40 1.2 0.1–300 2 × 10−6Figure 3
Design of measurement arrays.


### 2.3. Installation Procedure of Accelerometers

The installation procedure of accelerometers W1 to W3 followed the standard of ISO 5348 [35]. Accelerometers G1 to G7 were located inside the soil which is behind the wall of the metro station and also underneath the high speed railway. The installation was through a drilling hole from the wall of the metro station. As shown in Figure 4, the installation procedure for accelerometers in the soil has the following steps.Figure 4
Procedure for the installation of accelerometers in the soil.( 1 ) Prefabricate soil column with accelerometers embedded: a soil column with diameter of 8 cm and length of 1 m was made from clay. Accelerometers along with some earth pressure sensors and water pressure sensors were embedded in the soil.( 2 ) Drill the hole for the installation of soil column: a hole with diameter of 8.9 cm and length of 3 m was drilled starting from the wall of the metro station. The drilling points were determined by a laser positioning system.( 3 ) Install the soil column: after the hole was drilled, the soil column placed in a PVC pipe was inserted into the drilling hole.( 4 ) Backfill and seal the drilling hole: after the soil column was placed in the drilling hole, the part of the hole in the soil was infilled with clay while the part of the hole on the wall was infilled with quick-setting cement first and then sealed with waterproof polyurethane.


## 2.1. Engineering Background

As shown in Figure1, the test site is located at the underground metro station of Shanghai no. 9 metro line. The metro line is nearly perpendicularly intersected by the operating Shanghai-Hangzhou high speed railway on the ground surface. The high speed railway operates with a train speed of either 180 km/h with train type CRH2a or 300 km/h with train type CRH380a. The metro station was under construction when the field vibration tests were carried out. Figure 2 shows the cross section view of the metro station with high speed railway on the ground surface. The details of the soil layers along the depth and the corresponding shear wave velocity are shown on the right side of the plot. The distance from the roof of the metro station to the high speed railway is about 4.55 m. The metro station was excavated mainly in the soft clay and silt clay layers. The results of SPT (Standard Penetration Test) [33] showed that the shear wave velocity in these soils is about 110 m/s and the compression wave velocity is about 687 m/s [34].Figure 1
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.Figure 2
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.


## 2.2. Design of Measurement Arrays

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 Figure3. The first array with three measurement points (W1 to W3) was vertically aligned on the side wall of the metro station. The second array with four measurement points (G1 to G4) was parallel to the first array but buried into the soil surrounding the metro station. The third array with three measurement points (G5 to G7) was at the same elevation of G1 but along the horizontal direction and parallel with the side wall of the metro station. The second and third arrays were used to test the vertical and horizontal wave propagation in the soil, respectively. The LC130 IC piezoelectric accelerometer was employed in the field test. The specific parameters of the accelerometer are listed in Table 1.Table 1
Parameters of accelerometer.
Item Sensitivity (V/g) Max acceleration (g) Frequency range (Hz) Resolution (g) Value 40 1.2 0.1–300 2 × 10−6Figure 3
Design of measurement arrays.


## 2.3. Installation Procedure of Accelerometers

The installation procedure of accelerometers W1 to W3 followed the standard of ISO 5348 [35]. Accelerometers G1 to G7 were located inside the soil which is behind the wall of the metro station and also underneath the high speed railway. The installation was through a drilling hole from the wall of the metro station. As shown in Figure 4, the installation procedure for accelerometers in the soil has the following steps.Figure 4
Procedure for the installation of accelerometers in the soil.( 1 ) Prefabricate soil column with accelerometers embedded: a soil column with diameter of 8 cm and length of 1 m was made from clay. Accelerometers along with some earth pressure sensors and water pressure sensors were embedded in the soil.( 2 ) Drill the hole for the installation of soil column: a hole with diameter of 8.9 cm and length of 3 m was drilled starting from the wall of the metro station. The drilling points were determined by a laser positioning system.( 3 ) Install the soil column: after the hole was drilled, the soil column placed in a PVC pipe was inserted into the drilling hole.( 4 ) Backfill and seal the drilling hole: after the soil column was placed in the drilling hole, the part of the hole in the soil was infilled with clay while the part of the hole on the wall was infilled with quick-setting cement first and then sealed with waterproof polyurethane.


## 3. Attenuation Characteristics of Vibration

Vibration attenuation index is one of the important parameters to determine the wave types and evaluate the attenuation characteristics [36]. In this section, based on the data gathered by accelerometers installed both on the side wall of the metro station and in the surrounding soil, we analyze the attenuation indices in both the horizontal and vertical directions and investigate the types of the vibration waves and the association between the attenuation characteristics and the train speed as well as the structural stiffness.


### 3.1. Vibration Attenuation Characteristics in the Half Space Medium

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 [37]:(1)v=v0·rr0-m·e-αr-r0whilev and v0 are the vibration magnitude at the measurement point and the vibration source, respectively; r0 is the measured distance from the vibration source to a reference point; r is the distance between the measurement point and the vibration source; α is the material damping ratio; m is the size related attenuation index. Equation (1) suggests that m is the slope of the vibration magnitude versus the measured distance, both in logarithmic scales.Table2 lists some specific values of m for different physical sources from the literature. It shows that the vibration wave propagation and attenuation depend on the types of vibration source and the wave types. The m value for the train with short length and high speed (m=1.5) is different from the train with long length and slow speed (m=1.0) [4].Table 2
Selection of attenuation indexm for different physical sources from the literature.
Physical sources Type of source Wave type Attenuation indexm Line source [3] Line Rayleigh 0 Body 0.5 Point source [3] Point Rayleigh 0.5 Body 1.0 Short length and high speed train [4] Line Body 1.5 Long length and slow speed train [4] Line Body 1.0


### 3.2. Evaluation of Vibration Level and Determination of Attenuation Index

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.(1  ) Denoising Based on HHT (Hilbert–Huang Transform).Based on the original frequency spectrum of acceleration from each measurement point, it can be seen that the frequency of the train vibration wave falls into the range of 2 Hz to 100 Hz. In order to ensure consistency on the frequency spectrum for all measurement points, HHT transform [38] was applied to filter out the signal with frequency greater than 100 Hz. HHT method was pioneered by Huang et al. [38] for nonlinear and nonstationary signal analysis. Figure 5 shows the one-third octave frequency bands of measurement points G1 to G4 before (a) and after (b) applying HHT. After the HHT processing, the frequency spectrum in the range of 0 to 100 Hz is highly consistent among all measurement points, and the difference between G1 and G3 in the 100 Hz to 300 Hz range is mostly suppressed.Figure 5
One-third octave frequency bands of measurement points G1 to G4 before (a) and after (b) applying HHT.
(a) (b)(2  ) Determine the Attenuation Index.As shown in Figure 6, the time history of the velocity is obtained by integrating acceleration. Take logarithm on both sides of (1) and reference value of 5e-8 m/s is used to convert the velocity on the left side to dB; (1) becomes(2)20×lgv/5e-8v0/5e-8dB=-20×mlgrr0-20×lge×αr-r0.Figure 6
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 Section3.4.


### 3.3. Automatic Determination of the Train Speed and Train Length Based on Autocorrelation Function

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. Figure7 shows the time history of autocorrelation function for the acceleration response of a CRH380a train. There are a total of nine peaks in the autocorrelation function with the time interval of 0.296 s which indicates that the passing time δt of each carriage is 0.296 s. Since the length of one carriage L is 25 m, the running speed of the train can be calculated as v = L/δt = 25/0.296 = 84.45 m/s = 304 km/h. The calculated train speed fit well with the designed operating speed 300 km/h.Figure 7
The time history of autocorrelation function for the acceleration response of train vibration.At the same time, eight peaks can be identified from Figure7, which indicates that there are a total of eight car carriages. Thus the train length can be further obtained based on the number of carriages with the given carriage length.


### 3.4. Vibration Attenuation Characteristics in the Metro Station and Surrounding Soil

(1  ) Characteristics of Horizontal Attenuation. Figure 8 plots the horizontal attenuation of vibration in the soil for the two different train velocities and car lengths. All curves show the pattern of two linear pieces. The slope of the curve between G1 to G5 is nearly zero (m=0) while the slope between G5 and G7 is close to 1 (m=1). The vibration magnitude for the case with velocity of 300 km/h and 16 carriages is 1 dB larger than the case with the same velocity but 8 carriages and 5 dB larger than the case with the same train length but velocity of 184 km/h.Figure 8
Horizontal attenuation of vibration waves in the soil for two different train velocities and train lengths.The results in Figure8 clearly indicate the difference of horizontal attenuation of vibration waves below the track and away from the track. The zero attenuation index below the track indicates that horizontal attenuation is limited. The attenuation index m away from the track is 1, consistent with the value of long length and slow speed train as shown in Table 2 and different from the value of short length and high speed train (m=1.5).(2  ) Characteristics of Vertical Attenuation. Similarly, the vertical attenuation of vibration waves in the surrounding soil for the two different train velocities is plotted in Figure 9. Different from the horizontal attenuation, the three curves in Figure 9 show only one slope. The attenuation index m is 1.5 for the all the cases listed. These two index values are consistent with the values for the case of short length and high speed train as shown in Table 2.Figure 9
Vertical attenuation of vibration waves in the soil for two different train velocities and train lengths.Figure10 plots the vertical attenuation of vibration waves in the underground structure for two different train velocities and train lengths. Although the vibration level in the structure is smaller than the one in the soil, similar attenuation characteristics are obtained. The attenuation index m is between 0.5 and 1 for all the three cases listed.Figure 10
Vertical attenuation of vibration waves in the underground structure for two different train velocities and train lengths.In summary, the calculated attenuation indexm for the propagation of vibration waves in the underground structure and surrounding soil is listed in Table 3.Table 3
Calculated attenuation indexm for the propagation of vibration waves in the underground structure and soil.
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) / 0.5By comparing Tables2 and 3, the results indicate that the body waves including shear wave and compression wave are the main vibration wave modes in both the underground structure and surrounding soil. However, the attenuation characteristics of body waves are affected by the stiffness of the underground structure and can be different from the one in the half space medium. The effect of structural stiffness is more profound in the horizontal direction and resulting in the decrease of the attenuation index m from 1.5 to 1. But the propagation of body waves in the vertical direction is less affected by the stiffness of the metro station, and the attenuation index is consistent with the one for the half space medium. Meanwhile, the influence of train length (i.e., carriage numbers) is also considered, and it is found that the increase of carriages from 8 to 16 will lead to the increase of vibration magnitude but has limited impact to the attenuation index m. Therefore, the attenuation index can be used to determine the types of the vibration wave but can hardly be used to precisely evaluate the performance of underground structures.


## 3.1. Vibration Attenuation Characteristics in the Half Space Medium

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 [37]:(1)v=v0·rr0-m·e-αr-r0whilev and v0 are the vibration magnitude at the measurement point and the vibration source, respectively; r0 is the measured distance from the vibration source to a reference point; r is the distance between the measurement point and the vibration source; α is the material damping ratio; m is the size related attenuation index. Equation (1) suggests that m is the slope of the vibration magnitude versus the measured distance, both in logarithmic scales.Table2 lists some specific values of m for different physical sources from the literature. It shows that the vibration wave propagation and attenuation depend on the types of vibration source and the wave types. The m value for the train with short length and high speed (m=1.5) is different from the train with long length and slow speed (m=1.0) [4].Table 2
Selection of attenuation indexm for different physical sources from the literature.
Physical sources Type of source Wave type Attenuation indexm Line source [3] Line Rayleigh 0 Body 0.5 Point source [3] Point Rayleigh 0.5 Body 1.0 Short length and high speed train [4] Line Body 1.5 Long length and slow speed train [4] Line Body 1.0


## 3.2. Evaluation of Vibration Level and Determination of Attenuation Index

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.(1  ) Denoising Based on HHT (Hilbert–Huang Transform).Based on the original frequency spectrum of acceleration from each measurement point, it can be seen that the frequency of the train vibration wave falls into the range of 2 Hz to 100 Hz. In order to ensure consistency on the frequency spectrum for all measurement points, HHT transform [38] was applied to filter out the signal with frequency greater than 100 Hz. HHT method was pioneered by Huang et al. [38] for nonlinear and nonstationary signal analysis. Figure 5 shows the one-third octave frequency bands of measurement points G1 to G4 before (a) and after (b) applying HHT. After the HHT processing, the frequency spectrum in the range of 0 to 100 Hz is highly consistent among all measurement points, and the difference between G1 and G3 in the 100 Hz to 300 Hz range is mostly suppressed.Figure 5
One-third octave frequency bands of measurement points G1 to G4 before (a) and after (b) applying HHT.
(a) (b)(2  ) Determine the Attenuation Index.As shown in Figure 6, the time history of the velocity is obtained by integrating acceleration. Take logarithm on both sides of (1) and reference value of 5e-8 m/s is used to convert the velocity on the left side to dB; (1) becomes(2)20×lgv/5e-8v0/5e-8dB=-20×mlgrr0-20×lge×αr-r0.Figure 6
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 Section3.4.


## 3.3. Automatic Determination of the Train Speed and Train Length Based on Autocorrelation Function

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. Figure7 shows the time history of autocorrelation function for the acceleration response of a CRH380a train. There are a total of nine peaks in the autocorrelation function with the time interval of 0.296 s which indicates that the passing time δt of each carriage is 0.296 s. Since the length of one carriage L is 25 m, the running speed of the train can be calculated as v = L/δt = 25/0.296 = 84.45 m/s = 304 km/h. The calculated train speed fit well with the designed operating speed 300 km/h.Figure 7
The time history of autocorrelation function for the acceleration response of train vibration.At the same time, eight peaks can be identified from Figure7, which indicates that there are a total of eight car carriages. Thus the train length can be further obtained based on the number of carriages with the given carriage length.


## 3.4. Vibration Attenuation Characteristics in the Metro Station and Surrounding Soil

(1  ) Characteristics of Horizontal Attenuation. Figure 8 plots the horizontal attenuation of vibration in the soil for the two different train velocities and car lengths. All curves show the pattern of two linear pieces. The slope of the curve between G1 to G5 is nearly zero (m=0) while the slope between G5 and G7 is close to 1 (m=1). The vibration magnitude for the case with velocity of 300 km/h and 16 carriages is 1 dB larger than the case with the same velocity but 8 carriages and 5 dB larger than the case with the same train length but velocity of 184 km/h.Figure 8
Horizontal attenuation of vibration waves in the soil for two different train velocities and train lengths.The results in Figure8 clearly indicate the difference of horizontal attenuation of vibration waves below the track and away from the track. The zero attenuation index below the track indicates that horizontal attenuation is limited. The attenuation index m away from the track is 1, consistent with the value of long length and slow speed train as shown in Table 2 and different from the value of short length and high speed train (m=1.5).(2  ) Characteristics of Vertical Attenuation. Similarly, the vertical attenuation of vibration waves in the surrounding soil for the two different train velocities is plotted in Figure 9. Different from the horizontal attenuation, the three curves in Figure 9 show only one slope. The attenuation index m is 1.5 for the all the cases listed. These two index values are consistent with the values for the case of short length and high speed train as shown in Table 2.Figure 9
Vertical attenuation of vibration waves in the soil for two different train velocities and train lengths.Figure10 plots the vertical attenuation of vibration waves in the underground structure for two different train velocities and train lengths. Although the vibration level in the structure is smaller than the one in the soil, similar attenuation characteristics are obtained. The attenuation index m is between 0.5 and 1 for all the three cases listed.Figure 10
Vertical attenuation of vibration waves in the underground structure for two different train velocities and train lengths.In summary, the calculated attenuation indexm for the propagation of vibration waves in the underground structure and surrounding soil is listed in Table 3.Table 3
Calculated attenuation indexm for the propagation of vibration waves in the underground structure and soil.
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) / 0.5By comparing Tables2 and 3, the results indicate that the body waves including shear wave and compression wave are the main vibration wave modes in both the underground structure and surrounding soil. However, the attenuation characteristics of body waves are affected by the stiffness of the underground structure and can be different from the one in the half space medium. The effect of structural stiffness is more profound in the horizontal direction and resulting in the decrease of the attenuation index m from 1.5 to 1. But the propagation of body waves in the vertical direction is less affected by the stiffness of the metro station, and the attenuation index is consistent with the one for the half space medium. Meanwhile, the influence of train length (i.e., carriage numbers) is also considered, and it is found that the increase of carriages from 8 to 16 will lead to the increase of vibration magnitude but has limited impact to the attenuation index m. Therefore, the attenuation index can be used to determine the types of the vibration wave but can hardly be used to precisely evaluate the performance of underground structures.


## 4. Characteristics of Frequency Response Spectrum and Interference from the Vibration Source

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 [12–15]. In order to analyze the frequency response of the underground structure and the surrounding soil and explore the interference from the vibration source, three different cases corresponding for the effects of a moving train with uniform speed, a stopping train, and ambient vibration, were investigated.


### 4.1. Characteristics of Frequency Spectrum for a Moving Train with Uniform Speed

Figure11 shows 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 of 300 km/h. Although the two measurement points were at the same depth, the acceleration response for the measurement point in the soil is much larger than the one on the wall of the metro station.Figure 11
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.Figures12(a) and 12(b) show the FFT (Fast Fourier Transform) spectrum of measurement points W2 and G2, respectively, in contrast with the axle spectrum of the moving train in Figure 12(c). Axle spectrum is generated by the periodic train wheel load of a moving train with uniform speed. It can be expressed by the equation below:(3)ut=∑i=1nut-TiFigure 12
(a) FFT spectrum of measurement point W2, (b) FFT spectrum of measurement point G2, and (c) the axle spectrum of the moving train.
(a) (b) (c)whileTi is the time lag of the train wheel and i is the number of the train wheels. Equation (3) can be further expressed as follows:(4)U~f=U0f∑i=1nei2πfTi=U0fXfwhileU0f is the uniaxial displacement response amplitude and Xf characterizes the spatial distribution function of the wheels.Substitute the following values into (4): train speed 304 km/h based on the calculation in Section 2, length of single carriage 25 m, wheelbase 2.5 m, and length between bogie pivot centers 18 m. The axle spectrum then can be obtained as shown in Figure 12(c). It can be found that the peaks on the FFT spectrum of W2 and G2 agree well with those peaks on the axle spectrum which makes it hard to identify and differentiate the natural frequency spectrums for the train, rail, and the underground structures.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.


### 4.2. Characteristics of Frequency Spectrum for a Stopping Train

In order to avoid the interference from the axle spectrum, the characteristics of frequency spectrum for a stopping train was also analyzed. Figure13 shows the 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.Figure 13
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 ofpwelchx,hanning512,256,N,1000, as shown in Figures 14(a) and 14(b). It can be seen that the response frequency for a stopping train mainly falls into the range of 20 Hz to 200 Hz and has wider distribution than the case when the train is moving with uniform speed. (5)Hf=PxyPxx=cpsdx,y,hanning512,256,N,1000pwelchx,hanning512,256,N,1000Figure 14
(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.
(a) (b) (c)whilex and y are time history of the acceleration for W2 and G2, respectively.Meanwhile, based on the “cpsd” and “pwelch” functions in Matlab, a transfer function can be defined in (6) to illustrate the vibration transmission properties between the soil and the structure. Figure 14(c) shows the curve of the transfer function. The value of the transfer function is nearly 1 within the range of 1 Hz to 10 Hz which indicates that the structure and soil have good transmission properties. Subsequently, the value of the transfer function gradually decreases from 1 which reveals the gradual enlargement of the difference of the vibration response between these two measurement points.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 Figure15 further proves that the vertical displacements of these two points have the same magnitude level.Figure 15
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 Figure16. Similar with PSD frequency spectrum, the value of the transfer function stabilizes around 1 between 1 and 10 Hz. It is also found that the transfer function is considerably reduced between 10 and 100 Hz. And some moderate amplifications are found in the low-frequency range around 20 Hz and 50 Hz, which is probably related to the resonance frequency of the structure and surrounding soil.Figure 16
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.


### 4.3. Characteristics of Frequency Spectrum from Ambient Vibration Analysis

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. Figure17 shows the time history of the acceleration for measurement points W2 on the wall of the metro station and G2 in the soil with a total length of 4 hours. The data was further processed by NExT (Natural Excitation Technique) method [39]. NExT utilizes the auto or cross-correlation function of acceleration for measurement points under the condition of white noise excitation.Figure 17
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.Figure18(a) shows the autocorrelation function after the NExT processing for measurement point W2 and Figure 18(b) shows the corresponding PSD frequency spectrum from Figure 18(b); some peaks can be found at 21 Hz, 49.5 Hz, 80.5 Hz, and 122.5 Hz. It can be concluded that various types of vibration wave modes are excited with natural excitation. But all the peaks in the PSD frequency spectrum are relatively flat due to the effect of soil damping.Figure 18
(a) Autocorrelation curve after the NExT processing and (b) its PSD frequency spectrum for measurement point W2 with natural excitation in the night.
(a) (b)Similarly, the same processing was done for the signal of G2. All the peaks identified in Figure18(b) also appeared in Figure 19(b), which suggests that soil and structure have some shared vibration modes. In addition, Figure 19(b) shows some peaks at the frequencies of 61 Hz, 101.5 Hz, and 142 Hz, which implies that some of the vibration modes only exist in the soil but not in the underground structure.Figure 19
(a) Autocorrelation curve after the NExT processing and (b) its frequency spectrum for measurement point G2 with natural excitation in the night.
(a) (b)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.


## 4.1. Characteristics of Frequency Spectrum for a Moving Train with Uniform Speed

Figure11 shows 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 of 300 km/h. Although the two measurement points were at the same depth, the acceleration response for the measurement point in the soil is much larger than the one on the wall of the metro station.Figure 11
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.Figures12(a) and 12(b) show the FFT (Fast Fourier Transform) spectrum of measurement points W2 and G2, respectively, in contrast with the axle spectrum of the moving train in Figure 12(c). Axle spectrum is generated by the periodic train wheel load of a moving train with uniform speed. It can be expressed by the equation below:(3)ut=∑i=1nut-TiFigure 12
(a) FFT spectrum of measurement point W2, (b) FFT spectrum of measurement point G2, and (c) the axle spectrum of the moving train.
(a) (b) (c)whileTi is the time lag of the train wheel and i is the number of the train wheels. Equation (3) can be further expressed as follows:(4)U~f=U0f∑i=1nei2πfTi=U0fXfwhileU0f is the uniaxial displacement response amplitude and Xf characterizes the spatial distribution function of the wheels.Substitute the following values into (4): train speed 304 km/h based on the calculation in Section 2, length of single carriage 25 m, wheelbase 2.5 m, and length between bogie pivot centers 18 m. The axle spectrum then can be obtained as shown in Figure 12(c). It can be found that the peaks on the FFT spectrum of W2 and G2 agree well with those peaks on the axle spectrum which makes it hard to identify and differentiate the natural frequency spectrums for the train, rail, and the underground structures.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.


## 4.2. Characteristics of Frequency Spectrum for a Stopping Train

In order to avoid the interference from the axle spectrum, the characteristics of frequency spectrum for a stopping train was also analyzed. Figure13 shows the 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.Figure 13
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 ofpwelchx,hanning512,256,N,1000, as shown in Figures 14(a) and 14(b). It can be seen that the response frequency for a stopping train mainly falls into the range of 20 Hz to 200 Hz and has wider distribution than the case when the train is moving with uniform speed. (5)Hf=PxyPxx=cpsdx,y,hanning512,256,N,1000pwelchx,hanning512,256,N,1000Figure 14
(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.
(a) (b) (c)whilex and y are time history of the acceleration for W2 and G2, respectively.Meanwhile, based on the “cpsd” and “pwelch” functions in Matlab, a transfer function can be defined in (6) to illustrate the vibration transmission properties between the soil and the structure. Figure 14(c) shows the curve of the transfer function. The value of the transfer function is nearly 1 within the range of 1 Hz to 10 Hz which indicates that the structure and soil have good transmission properties. Subsequently, the value of the transfer function gradually decreases from 1 which reveals the gradual enlargement of the difference of the vibration response between these two measurement points.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 Figure15 further proves that the vertical displacements of these two points have the same magnitude level.Figure 15
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 Figure16. Similar with PSD frequency spectrum, the value of the transfer function stabilizes around 1 between 1 and 10 Hz. It is also found that the transfer function is considerably reduced between 10 and 100 Hz. And some moderate amplifications are found in the low-frequency range around 20 Hz and 50 Hz, which is probably related to the resonance frequency of the structure and surrounding soil.Figure 16
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.


## 4.3. Characteristics of Frequency Spectrum from Ambient Vibration Analysis

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. Figure17 shows the time history of the acceleration for measurement points W2 on the wall of the metro station and G2 in the soil with a total length of 4 hours. The data was further processed by NExT (Natural Excitation Technique) method [39]. NExT utilizes the auto or cross-correlation function of acceleration for measurement points under the condition of white noise excitation.Figure 17
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.Figure18(a) shows the autocorrelation function after the NExT processing for measurement point W2 and Figure 18(b) shows the corresponding PSD frequency spectrum from Figure 18(b); some peaks can be found at 21 Hz, 49.5 Hz, 80.5 Hz, and 122.5 Hz. It can be concluded that various types of vibration wave modes are excited with natural excitation. But all the peaks in the PSD frequency spectrum are relatively flat due to the effect of soil damping.Figure 18
(a) Autocorrelation curve after the NExT processing and (b) its PSD frequency spectrum for measurement point W2 with natural excitation in the night.
(a) (b)Similarly, the same processing was done for the signal of G2. All the peaks identified in Figure18(b) also appeared in Figure 19(b), which suggests that soil and structure have some shared vibration modes. In addition, Figure 19(b) shows some peaks at the frequencies of 61 Hz, 101.5 Hz, and 142 Hz, which implies that some of the vibration modes only exist in the soil but not in the underground structure.Figure 19
(a) Autocorrelation curve after the NExT processing and (b) its frequency spectrum for measurement point G2 with natural excitation in the night.
(a) (b)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.


## 5. Waveforms and Propagation Velocities of Vibration Waves

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.


### 5.1. Waveforms and Propagation Velocities Determination by Combining NExT and HHT Method

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 [40]. Obtaining the wave phase shift in the frequency domain requires that the acceleration sensors have stable performance and wide frequency range. As a result, achieving both economic and sustainable health monitoring system meets great challenges. Therefore, in this work we utilized the combined NExT and HHT method to extract different vibration waves from the signal and calculate the corresponding wave velocities. NExT is used to obtain the free oscillation signal from the random response; then the needed propagation modes are decomposed with HHT method. Because the accelerometers are only arranged at the vertical direction, an illustrated example of processing the wave velocity at measurement points G1 to G4 is given in the section below.


### 5.2. Propagation Velocities of Vibration Waves in Soil

(1  ) Propagation Velocities of Vibration Waves in the Vertical Direction.Figure 20(a) shows the time history of the acceleration for measurement points G1 to G4 after 5000-second continuous acquisition. The signal included the passing by of the train, the stopping of the train, and also the natural excitation. The signal was further processed with NExT with the superposition length of 128 data points. Figure 20(b) plots the autocorrelation function after the NExT processing for G1 which indicates a periodic wave with attenuation in the time domain. The PSD frequency spectrum in Figure 20(c) shows that the autocorrelation function is a free oscillation signal with the main frequency of 37 Hz which is derived from the resonance of train wheel and rail. Autocorrelation function of G1 and cross-correlation functions between G1 and the other three points G2 to G4 was calculated with NExT and plotted in Figure 21. The three correlation functions as well as the autocorrelation function of G1 are stacked in the y axis based on the propagation distance from G1. By identifying the event points from the four curves in Figure 21, a straight line can be drawn while the slope of the line indicates the wave velocity of 684 m/s.Figure 20
(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).
(a) (b) (c)Figure 21
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.(2  ) Types of Vibration Waves in the Soil. Based on the results above, the vertical wave velocity in the soil (684 m/s) is very close to the measured in situ compression wave velocity of soft clay. It can be inferred that compression wave is the dominant wave type in the vertical direction.


### 5.3. Propagation Velocities of Vibration Waves in the Underground Structure

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. Figure22(a) plots the cross-correlation function between W1 and W3. The PSD frequency spectrum of the cross-correlation function in Figure 22(d) shows two peaks. After applying the decomposition based on HHT, two intrinsic mode functions (IMF1 and IMF2) corresponding to the two peaks can be obtained, as shown in Figures 22(b) and 22(c), respectively. The dominating frequency of IMF2 is consistent with the one for the soil (see Figure 20(c)).Figure 22
(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 Figures23(a) and 23(b), respectively. By identifying the event points, two wave velocities can be determined as 2352 m/s and 3636 m/s. These two velocities are consistent with the shear wave velocity cs and the compression wave velocity cp of concrete, which can be determined by (6) as 2328 m/s and 3800 m/s, respectively.(6)cp=λ+2μρ,cs=μρ,λ=νE1+ν1-2ν,μ=E21+ν,Figure 23
(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.
(a) (b)whereE is the elastic modulus of concrete and equal to 3.25e10 Pa; ν is Poission’s ratio and equal to 0.2; the density ρ is taken as 2500 kg/m3.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.


## 5.1. Waveforms and Propagation Velocities Determination by Combining NExT and HHT Method

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 [40]. Obtaining the wave phase shift in the frequency domain requires that the acceleration sensors have stable performance and wide frequency range. As a result, achieving both economic and sustainable health monitoring system meets great challenges. Therefore, in this work we utilized the combined NExT and HHT method to extract different vibration waves from the signal and calculate the corresponding wave velocities. NExT is used to obtain the free oscillation signal from the random response; then the needed propagation modes are decomposed with HHT method. Because the accelerometers are only arranged at the vertical direction, an illustrated example of processing the wave velocity at measurement points G1 to G4 is given in the section below.


## 5.2. Propagation Velocities of Vibration Waves in Soil

(1  ) Propagation Velocities of Vibration Waves in the Vertical Direction.Figure 20(a) shows the time history of the acceleration for measurement points G1 to G4 after 5000-second continuous acquisition. The signal included the passing by of the train, the stopping of the train, and also the natural excitation. The signal was further processed with NExT with the superposition length of 128 data points. Figure 20(b) plots the autocorrelation function after the NExT processing for G1 which indicates a periodic wave with attenuation in the time domain. The PSD frequency spectrum in Figure 20(c) shows that the autocorrelation function is a free oscillation signal with the main frequency of 37 Hz which is derived from the resonance of train wheel and rail. Autocorrelation function of G1 and cross-correlation functions between G1 and the other three points G2 to G4 was calculated with NExT and plotted in Figure 21. The three correlation functions as well as the autocorrelation function of G1 are stacked in the y axis based on the propagation distance from G1. By identifying the event points from the four curves in Figure 21, a straight line can be drawn while the slope of the line indicates the wave velocity of 684 m/s.Figure 20
(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).
(a) (b) (c)Figure 21
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.(2  ) Types of Vibration Waves in the Soil. Based on the results above, the vertical wave velocity in the soil (684 m/s) is very close to the measured in situ compression wave velocity of soft clay. It can be inferred that compression wave is the dominant wave type in the vertical direction.


## 5.3. Propagation Velocities of Vibration Waves in the Underground Structure

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. Figure22(a) plots the cross-correlation function between W1 and W3. The PSD frequency spectrum of the cross-correlation function in Figure 22(d) shows two peaks. After applying the decomposition based on HHT, two intrinsic mode functions (IMF1 and IMF2) corresponding to the two peaks can be obtained, as shown in Figures 22(b) and 22(c), respectively. The dominating frequency of IMF2 is consistent with the one for the soil (see Figure 20(c)).Figure 22
(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 Figures23(a) and 23(b), respectively. By identifying the event points, two wave velocities can be determined as 2352 m/s and 3636 m/s. These two velocities are consistent with the shear wave velocity cs and the compression wave velocity cp of concrete, which can be determined by (6) as 2328 m/s and 3800 m/s, respectively.(6)cp=λ+2μρ,cs=μρ,λ=νE1+ν1-2ν,μ=E21+ν,Figure 23
(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.
(a) (b)whereE is the elastic modulus of concrete and equal to 3.25e10 Pa; ν is Poission’s ratio and equal to 0.2; the density ρ is taken as 2500 kg/m3.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.


## 6. Conclusions and Discussions

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.( 1 ) The attenuation characteristics of the vibration waves for the propagation in the underground structure and soil are subject to the stiffness of the underground structure. The attenuation index m decreases as the effect of the structural stiffness increases.( 2 ) The results from the ambient test showed that the underground metro station and surrounding soil shared many resonance frequencies. And, together with the constraining and damping effects from the soil, the recognition and extraction of the frequency response characteristics for the structure only are very challenging.( 3 ) The train induced vibration is the common exciting source in the underground space. The metro station structure and soil show good transmission properties at the low frequency range below 10 Hz based on the transfer function and displacement analysis. And the interference of axis spectral and other characteristics of the train and rail system will make the recognition and extraction of frequency response characteristics difficult for the underground structures. However, the waveform and propagation velocities of vibration waves in underground structure and surrounding soil can be obtained by using the combined NExT and HHT method, and the vibration wave types in the structure and in the surrounding soil can also be determined and separated.The following suggestions are given for the health monitoring in underground structures by using vibration characteristics.( 1 ) Because of the coupling between the underground structures and the surrounding soil, the recognition of the structure mode characteristics and the differentiation from the mode characteristics of soil becomes difficult. Therefore, the mode based method is more suitable for cases of large excavation monitoring, which will result in great change to the modes characteristics. The results also suggest that a wider frequency band is required for the underground structures monitoring than bridges or tall buildings and measurement points should be installed in both the structures and the soil.( 2 ) Attenuation index, natural frequency, and vibration wave velocity can all be used to evaluate the stiffness change for the underground structures. 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.



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*Source: 3526952-2018-05-23.xml*