Received May 30, 2018, accepted June 21, 2018, date of publication June 26, 2018, date of current version July 30, 2018. Digital Object Identifier 10.1109/ACCESS.2018.2850359
Field Tests and Simulation of Ground and Building Vibrations Caused by Metros on an Elevated Bridge MING CAI1,2 , WEI WAN1,2 , AND HAIBO WANG
2,3
1 School
of Intelligent Systems Engineering, Sun Yat-sen University, Guangzhou 510275, China 2 Guangdong Provincial Key Laboratory of Intelligent Transportation System, School of Intelligent Systems Engineering, Sun Yat-sen University, Guangzhou 510275, China 3 School of Civil and Transportation Engineering, Hebei University of Technology, Tianjin 300401, China
Corresponding author: Haibo Wang (
[email protected]) This work was supported in part by the National Natural Science Foundation of China under Grant 11574407, and in part by the Science and Technology Planning Project of Guangzhou City, China, under Grant 201704020142.
ABSTRACT The vibration induced by metros is having a growing impact on people’s daily work and life. This paper proposes a propagation rule and an evaluation method for vibration based on experimental data on the ground and inside a 4-story building subjected to trains running on an elevated bridge in Guangzhou, China. This paper discusses the propagation characteristics of the vibration wave in different directions on the ground and inside the building. Then, a vibration level attenuation model of an elevated bridge section of Guangzhou was built using a linear regression method. Moreover, a finite-element model of a test building was built to study the influence of the building structure on the building vibration response. The results reveal that vertical vibrations are much larger than the horizontal vibrations on the ground and inside the building near the elevated bridge. This paper found a rebound acceleration area at a distance of 10–15 m away from the bridge. Inside the four-story building, the acceleration levels increased gradually with increasing floor level. Slab thickness had little effect on the vibration and the story height of the building along the elevated bridge should be limited to below 3.7 m. Moreover, proper column size can effectively reduce building vibrations. INDEX TERMS Vibration, metros, elevated bridge, experiment, attenuation model, finite element model.
I. INTRODUCTION
Economic globalization and world urbanization are developing rapidly. However, these developments raise a contradiction between the expansion on an urban scale and the reduction of land resources. The metro has become an effective way to alleviate traffic pressure, because of its large volume, high speed and low air pollution. By the end of 2016, 30 cities in China established rail transportation systems, which include more than 133 lines with a total length of 4152.8 km [1]. The vibration pollution due to rail transportation is becoming more and more serious. Exposure to vibration from environmental sources such as railway and metro is thought to result in adverse effects. Vibrations can do harm to the human body. This harmful physical factor endangers human health not only at work but also in everyday life [2]. The exposure to vibrations can affect the function of the nervous system and lead to physiological changes [3]. Moreover, long-term exposure to vibrations can result in hyperactivity of the sympathetic nervous system [4]. VOLUME 6, 2018
A detailed review of testing and analysis on railwayinduced vibration has been carried out [5]. To address groundborne and building vibrations, field experiments and surveys have been conducted in Mexico [6], Portugal [7], Japan [8], Spain [9], Athens [10] and China [11]. Moreover, many theoretical studies considering the connection between trains and bridge had been conducted [12]–[14]. There are different indicators for the vibration level around the world, such as the root-mean square value [15], the vibration velocity level [16] and the vibration acceleration level [17]. Considering a three-dimensional finite element model, a simulation of the acceleration level of different railway infrastructure elements was conducted [18]. However, the model only considered a rail track on the ground without considering an elevated bridge or underground tunnel. A study that included the Beijing Metro Line 5 performed a test for environmental vibration induced by trains on an elevated bridge [19]. In that study, building vibrations were not measured, which are significant to the construction of metros.
2169-3536 2018 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
38627
M. Cai et al.: Field Tests and Simulation of Ground and Building Vibrations Caused by Metros
Large vibrations, which are created by the frequently moving trains, can directly pass through columns and walls to the upper floors [20]. Greater vibrations in over-track buildings can be induced by these waves that have a high energy [21]. Moreover, in consideration of the current needs of reliable measurement data for the construction of metros and buildings near the bridge, it is significant to fully understand the characteristics of train-induced vibrations on the ground and in the near-bridge buildings and to develop effective methods to weaken the vibration levels. In this study, measurements were performed to determine the influence of metro-induced vibration on the ground and inside a 4-story building near an elevated bridge. Because there are so many similar structures along the subway, this study selects one of them to research. The results can be extended to other buildings in the area and will be useful for the planning and design of vibration mitigation methods on the ground and to minimize the vibration levels in near-bridge buildings.
TABLE 1. Soil parameters of different soil layers.
II. EXPERIMENTAL PROGRAM A. EXPERIMENTAL SITES
The measurements were performed in Guangzhou, a city in southern China. The elevated bridge is part of Guangzhou Metro Line 4 as shown in Fig. 1. Vibration measurements were performed under the elevated bridge at different distances away from the centerline of the bridge and inside a 4-story building.
FIGURE 2. Accelerometer setups. (a) Accelerometer set on the ground. (b) Vertical plan of the test building.
B. INSTRUMENTATION
FIGURE 1. Test field in Guangzhou.
The ground test line set in this experiment was perpendicular to the direction of metro operation. There were 6 test points. The test point under the bridge was set in the middle of the bridge piers. The soil parameters of different soil layers at experimental ground were shown in Table 1. The tested 4-story building was built in 2016, which had a concrete frame construction with walls that were made of concrete bricks. The detailed experimental setting is shown in Fig. 2. The experiments were conducted from March to April 2017 for a total of 6 times. The vibration data generated by 43 trains in three directions were collected. For all the recorded train passages on the bridge, the speeds ranged from 66 km/h to 76 km/h. The collected data were sorted according to different distances and floors. 38628
The instrumentation used in the measurement included NI9234 acquisition cards (Fig. 3a) with 4 channels and ULT2061 three-direction accelerometers (Fig. 3b) which were integral electronic piezoelectric acceleration sensors. The accelerometers with the sensitivity of 0.1 V/m/s2 were mounted at target locations with a measuring range
FIGURE 3. Instruments of the measurement. (a) NI 9234 acquisition cards. (b) Accelerometers. VOLUME 6, 2018
M. Cai et al.: Field Tests and Simulation of Ground and Building Vibrations Caused by Metros
of 50m/s2 and resolution of 2×10−4 m/s2 . The range of frequency measurement was 0.1-1000Hz. This equipment could simultaneously measure the acceleration of the vibration in three directions for 6 measuring points. All instruments were calibrated before the measurement.
Thus, a Fourier series, like (1), can be used to describe the time history data acquired at the scene.
III. VIBRATION ANALYSIS OF THE CHARACTERISTICS A. GROUND-BORNE VIBRATIONS
Since the time domain signals acquired on the ground are discrete signals with a limited length, a discrete Fourier transform can be used to process the data. The formula is given as (2) and (3).
This chapter includes the measured vibration data and shows the analysis of its time history and frequency domain to understand the characteristics and attenuation role of the ground-borne vibration. 1) TIME HISTORY ANALYSIS OF THE VIBRATIONS
Fig. 4 shows time history vibration examples of test points 0 m and 5 m. The red lines represent the far field results from the centerline of the bridge, and the black lines are the near field results.
f (x) = a0 +
∞ X
[an cos (nx) + bn sin (nx)]
(1)
n=1
X (ω) = X (t) =
N −1 X
x (t) e−j2π ωt/N
t=0 N −1 X
1 N
x (ω) ej2π ωt/N
(2)
(3)
ω=0
The Fast Fourier Transform algorithm [24] is adopted in this paper, because its computing results meet demand with shorter computing time. Assuming that there are N points, compared to the computational complexity 2N2 of DFT (Discrete Fourier Transform), the computational complexity of FFT is only (3N/2) log2 N [25]. For a further understanding of the characteristics of vibrations induced by trains, Fig. 5 shows the amplitude frequencies for 0 m and 5 m in three directions, which is averaged by measured data with 35 passing-by trains.
FIGURE 4. Ground-borne acceleration in three directions. (a) L direction. (b) T direction. (c) V direction.
It was observed that the metro vibration duration was approximately 6 s. The vertical acceleration was much larger than the horizontal acceleration at the measured ground location. The peak acceleration of the near field in the V direction was 0.125 m/s2 which is almost 2 times larger than in the other two directions. That is because the vibration generated by the metro is in the vertical direction. When the acceleration spread from 0 m to 5 m, the accelerations in all directions decreased, and the vertical acceleration had a maximum attenuation from 0.125 m/s2 to 0.046 m/s2 , which was a decrease of nearly 63%. Possibly, the vertical vibration was mainly made of Rayleigh waves whose attenuation was faster than P and S waves [22]. 2) FREQUENCY SPECTRUM ANALYSIS OF THE VIBRATIONS
Although the magnitude of the vibrations generated by the metro operation is random, it satisfies a Gaussian distribution with a mean value of 0 [23]. As a consequence, the time history curves can be regarded as the result of a superposition of many different frequencies of sinusoidal waves. VOLUME 6, 2018
FIGURE 5. Frequency Spectra of the ground-borne vibrations in three directions. (a) 0 m in L direction. (b) 0 m in T direction. (c) 0 m in V direction. (e) 5 m in L direction. (f) 5 m in T direction. (g) 5 m in V direction. 38629
M. Cai et al.: Field Tests and Simulation of Ground and Building Vibrations Caused by Metros
As shown in Fig. 5, the distribution of peak acceleration dispersed in different directions. The T direction at 0 m shows a peak at 88 Hz. The V direction at 0 m shows a peak at 55Hz. When the vibration wave spread from 0 m to 5 m, the attenuations of the dominant frequency bands like 50Hz and 75Hz were larger with average 75% declines. Luo et al. obtained similar results based on the car-line-bridge coupling dynamic model that components of higher frequency decay more quickly with the increase of vibration wave propagation distance [26]. In other directions, the location of the predominant frequencies remained almost unchanged.
As Fig. 6(b) shows, the changing tendency of the vibration level with various different distances away from the elevated bridge is approximately the same. The vibration level in the V direction of 1-1.6 Hz increases with the increase of distance from the bridge. For the 1.6-16 Hz frequency band, the vibration level is basically the same at different distances. There is a trough of a wave at 16 Hz, which suggests that the soil at the test site absorbs vibrations at frequencies of 16 Hz. 3) THE ATTENUATION OF PEAK ACCELERATION
To understand the attenuation role of ground-borne vibrations in different directions, Fig. 7 plots the attenuation of peak acceleration as a function of distance, which is the average of 35 sets of data. And peak acceleration in different directions and distances of one set is measured simultaneously.
FIGURE 6. Mean acceleration levels of ground-borne vibrations. (a) 0 m in three directions. (b) 0 m, 5 m, and 15m in the V direction.
Fig. 6 shows the mean acceleration levels calculated by using (4) and (5). s Z 1 T 2 a (t) d (t) (4) a= T 0 i a VAL = 20 log (5) a0
FIGURE 7. Peak accelerations as a function of distance from the Bridge. (a) L direction. (b) T direction. (c) V direction.
The research frequency is 1-80Hz, which is main frequencies of vibrations that influence humans in [27] and [28]. For the vibration level of the same measured point in different directions (Fig. 6a), for the 1-1.6 Hz band, the vibration level of the L direction was larger than in the other two directions. However, for the 1.6-10 Hz band, the vibration level of the T direction was the largest, and the V direction vibration level was higher than the other two directions for the 10-80 Hz band. Thus, the vibration has its dominant frequency band in different directions. The dominant frequency band is determined by the soil layer composition.
As shown in Fig. 7, the peak acceleration decreases with increasing distance away from the bridge. However, there is a vibration rebound acceleration area in all three directions 10-15 meters away from the elevated bridge. For example, at a distance of 5 meters, T direction acceleration decays rapidly. When the wave spreads to 15 meters, the vibration increases from 0.036 m/s2 to 0.039 m/s2 . Then, it decreases to the minimum at 30 meters away from the bridge. The rebound range at 15 meters is approximately 8.33%. The reason for the rebound range is that the acceleration in the 50-80 Hz band
38630
VOLUME 6, 2018
M. Cai et al.: Field Tests and Simulation of Ground and Building Vibrations Caused by Metros
increases at 15 meters (Fig. 6b). This increase is possibly affected by the soil layer composition and bridge height. B. FLOOR VIBRATIONS IN THE 4-STORY BUILDING
This chapter includes the measured vibration data in the building and describes the analysis of its time history and frequency domain to understand the characteristics and variation trend of the vibrations on different floors. The position selected for acceleration measurement on every floor was the same, which was mid of one slab in the living room. The vibrations of the building caused by 8 passing-by trains were collected. When a train passes by, the vibrations in different directions and floors would be measured simultaneously. 1) TIME HISTORY ANALYSIS OF THE VIBRATIONS
The authors set up the accelerometer at the same position on different floors. When the train passed, the accelerometers recorded the acceleration data for different floors in the building. Fig. 8 plots the time history samples for each floor in three directions.
FIGURE 9. Vertical accelerations at different frequencies in the building.
However, the vertical vibrations above 20Hz decreased on the middle floors with a 67% decline and increased significantly again on the top floor. The variation trend of vibration at different frequencies is different because along the direction of the vibration wave propagation, the concrete floor yields a damping effect; however, the dissipative degrees differ for elastic waves with different frequencies [31]. 3) VARIATION TREND OF THE VIBRATIONS FIGURE 8. Acceleration of the test building in three directions. (a) L direction. (b) T direction. (c) V direction.
Generally, the vertical vibration was higher than in the other directions, and the acceleration in the building exhibited the same features in [20] and [29]. The peak acceleration in the V direction of the 1st floor was 0.012 m/s2 which is almost 2 times larger than in the other two directions. As shown in Fig. 8, the acceleration in three directions increased gradually with the increase of floor. The increase in the V direction was the largest, which was from 0.012 m/s2 for the 1st floor to 0.033 m/s2 for the 4th floor, an increase of 175%.
The maximum and average velocity levels at different floors are summarized in Table 2. The vertical acceleration levels were an average of 6 dB greater than the horizontal levels, which demonstrates that metro-induced vibrations inside buildings primarily occurs in vertical directions. TABLE 2. Maximum and average acceleration levels at different floors.
2) FREQUENCY SPECTRAL ANALYSIS OF THE VIBRATIONS
For a further understanding of the characteristics of the vibrations induced by the trains, the frequencies of the vertical vibrations of every floor are shown in Fig. 9. In order to avoid the influence of other factors on the frequency domain analysis, several frequencies were chosen to analyze the propagation of vertical vibrations. The low frequency vibrations below 16Hz slightly increased with the rise of the floor. The average increase from 1st floor to 4th floor of vibrations under 20Hz is about 70%. The vibration in 2.5Hz was higher than other low frequency vibrations which was caused by natural vibration periods of whole building [30]. VOLUME 6, 2018
Fig. 10 plots the variation trend of the acceleration levels as a function of the floor. As shown, the level in the L direction and V direction increase with increasing height in the building, and the rate of rise is approximately 0.5 dB/m with a story height of 3 m. The vibration of the acceleration level in the T direction is different from that in other directions because the vibration energy reflects the furniture in the room. According to ISO2631-1 [27], the main frequencies 38631
M. Cai et al.: Field Tests and Simulation of Ground and Building Vibrations Caused by Metros
and x = log10 (R/10). Then, (6) can be changed into: y = a + bx
FIGURE 10. Vertical acceleration levels in the building.
of vibrations that influence humans is within 1-80 Hz. The data in Fig. 10 were filtered to 80Hz before verification of the serviceability limit. The vibration influence criteria of GB-10070 [17] gave a limit value of 70 dB for train-induced vibrations for institutional land uses with primarily daytime use and established vibration criteria with a limit of 67 dB for residences and buildings where people normally sleep. The measured vibration in the V direction of this building was already above the standard. This means that people living in this test building will be affected by the running metro on the elevated bridge. It suggests that careful study of other near-bridge building constructions is required and to possibly avoid building within 40 m of an elevated bridge. IV. VIBRATION PREDICTION
According to the measured data of ground-borne vibrations under the elevated bridge, the vertical acceleration level propagation formula can be fitted via a statistical regression method. There are many factors that affect the environmental vibrations of an elevated metro, such as the span of the bridge, soil properties, axle load and quality of the beams. In reality, it is difficult to consider all factors. Therefore, focusing on the main factors can achieve reasonable results. This regression method does not consider the train speed and other factors except for the distance from the bridge. According to previous research and experimental data, the acceleration level is basically linear with the logarithm of the distance away from the centerline of the bridge. This study applies the empirical calculation formula as (6) for the elevated bridge from the Japan National Railway Technology Research Institute [32]. VL = VL0 − (dVL/ log 2) × log
R R0
(6)
Based on the environment of the field, R0 is set to 10 m. The authors also set y = VL, a = VL0 , b = −dVL/log10 2, 38632
(7)
The linear regression analysis can be performed by the least square method, and values a and b, which give the regression result for satisfying the residual minimum, can be obtained. 35 groups of measured data are calculated. The authors obtained VL 0 = 85.83 dB and dVL = 3.12 dB. Since the original data was sample data and there was a deviation from the overall data, it was necessary to check the error of parameters a and b obtained via the linear regression analysis. The significance test was conducted with the t-test as (8)-(10). q (8) t = b SS xx Se ! 2 n n X 1 X SS xx = xi2 − xi (9) n i=1 i=1 r X 2 yi − yˆ i / (n − 2) (10) Se = For n = 198, the result obtained via the calculation was |t| = 424.3 > tα=0.001 = 3.340. This means that at 99.9% confidence, there is a linear relationship between x and y. Moreover, the regression correlation coefficient, R2 , calculated according to (11) was 0.6251. 2 n P (xi − x¯ ) (yi − y¯ ) i=1 (11) R2 = n n P P (yi − y¯ )2 (xi − x¯ )2 i=1
i=1
Thus, the authors can obtain the viaduct section of Guangzhou Metro Line 4, and the attenuation formula for the ground-borne vibrations is shown in (12). R (12) 10 To verify the exactness of this model, Table 3 shows a comparison between the measured values and the predicted values. Two groups of measured data were not used to calculate the VL0 and dVL values, which worked as a validation set in Table 3. The difference between the predictions and the field measurements is within the acceptable range, which is 3.24 dB on average. Fig. 11 plots the comparison between measured values and regression results. VL = 85.83 − (3.12/ log 2) × log
V. INFLUENCE OF BUILDING STRUCTURE ON VIBRATION RESPONSE A. ESTABLISHMENT OF THE STRUCTURAL SIMULATION MODEL
Many researchers developed finite element modeling to study vibration propagation rule like [33] and [34]. In this study, to determine the influence of the building structure on the building vibrations, finite element modeling was applied to VOLUME 6, 2018
M. Cai et al.: Field Tests and Simulation of Ground and Building Vibrations Caused by Metros
TABLE 3. Comparison between predicted and measured values.
FIGURE 12. Building structural simulation model (in mm). (a) Simulation model of the test building. (b) Structure plan view.
Where ct is set as 0.0466 and x is set as 0.9 for reinforced concrete structure. H is the height of test building.
FIGURE 11. Comparison between measured values and regression results.
the test building using SAP2000, an integrated software for structural analysis and design. This paper simulates the upper part of the building with its actual framework. The building model is shown in Fig. 12(a). And Fig. 12(b) plots the structure plan view of the test building. To achieve an accurate simulation of the structural vibrations, the model’s cross section and material are the same as for the actual structure. The story height of the test building is 3 m, the plane is rectangular, the slab thickness is 100 mm, the size of the column is 250 × 250mm and the concrete material is C30. The load cases are composed of linear static, modal and linear modal history, and the type of linear modal history is time history, which is the acceleration measured on the 1st floor. Area uniform loads to frames with static pattern and frame loads are gravity static pattern. Eigen model analysis was applied to the numerical model. The mean period for the modelled building was 0.453s, which was close to the reference period 0.436s calculated by using (13) from ASCE [35]. Ta = ct H x
VOLUME 6, 2018
(13)
B. COMPARISON OF THE NUMERICAL AND MEASURED RESULTS
To demonstrate the accuracy of the simulation model, the numerical and measured results were compared. The measured data is the same as in Fig. 8(c). Fig. 13 plots the comparison of the measured and numerical results for the 4th floor. TABLE 4. Difference between numerical and measured results.
As shown in Table 4, the difference between the rootmean square values of the numerical and the measured results is less than 2dB. The error for each measuring point is within the acceptable range. The time history of measured data and numerical result basically coincide. And there are coincidences of vertical vibrations in both low frequency and high frequency as Fig. 13(b). Thus, the numerical results are reliable.
38633
M. Cai et al.: Field Tests and Simulation of Ground and Building Vibrations Caused by Metros
FIGURE 14. Influence of Building Structures on Vertical Vibration. (a) Slab thickness. (b) Story height. (c) Column size. FIGURE 13. Comparison of the measured and numerical results for the 4th floor. (a) Time history comparison. (b) Frequency comparison.
C. INFLUENCE OF SLAB THICKNESS ON THE VIBRATION RESPONSE TO THE METRO
To understand the influence of slab thickness on the vibration response to the metro, five models were established. All of the structural factors are the same except for the slab thickness. The slab thicknesses are 100 mm, 110 mm, 120 mm, 130 mm and 140 mm. Fig. 14(a) plots the influence of slab thickness on the vibration response. The acceleration level decreases slightly when the slab thickness varies from 100 mm to 110 mm. During the change from 110 mm to 140 mm, the change curve slowly rises. In general, as the slab thickness increases, the acceleration level in the building exhibits no significant change which is within 1 dB. The change curve is basically horizontal, which means that the slab thickness has little effect on the vibrations. D. INFLUENCE OF STORY HEIGHT ON THE VIBRATION RESPONSE TO THE METRO
To determine the influence of story height on the vibration response to the metro, ten models are established. All of the structural factors are the same except for the story height. 38634
The story heights are 3-3.9 m and the step length is 0.1 m. Fig. 14(b) plots the influence of story height on the vibration response. The acceleration level has no significant change when the story height varies from 3 m to 3.5 m with a 1.72 dB/m growth rate on average. The minimum vibration level is 66.08 dB for the story height of 3.3 m. However, with a change from 3.7 m to 4 m, the growth rate of the vibration level was 3.9 dB/m. This indicates that the story height of the buildings along the elevated bridge should be limited to below 3.7m, which should not be too high. E. INFLUENCE OF COLUMN SIZE ON THE VIBRATION RESPONSE TO THE METRO
Analysis of column size is similar to the analysis of slab thickness and story height. Five models are established with different column sizes, which are 200 × 200 mm, 250 × 250 mm, 300 × 300 mm, 350 × 350mm and 400 × 400mm. Fig. 14(c) plots the influence of column size on the vibration response. With the increase of column size, the acceleration level decreases first and then increases. The acceleration level is smaller when the column sizes are 250 × 250 mm and VOLUME 6, 2018
M. Cai et al.: Field Tests and Simulation of Ground and Building Vibrations Caused by Metros
300×300 mm, which are consistent with the limits mentioned in the Chinese standard [36]. When column size is 400 × 400 mm, the acceleration level for the 1st floor is 68.65 dB, which is 2.4 dB higher than the acceleration level with a column size of 250×250 mm. This means that proper column size like 250 × 250 mm and 300 × 300 mm can effectively reduce building vibrations. VI. CONCLUSION
Field tests and simulations relative to the train-induced vibration on the ground and inside a 4-story building near an elevated bridge in Guangzhou, China have been presented. The goal of this study was to fully understand the propagation of train-induced vibrations near the elevated bridge and to provide a quantification of the vibration data for designers to develop safe and effective measures to weaken the acceleration levels in nearby buildings. Slab thickness, story height and column size were selected to study the influence of the building structure on the building vibration response to the metro. For ground vibrations, the control of the vibrations should mainly focus on the vertical direction near the elevated bridge. With increasing distance away from the elevated bridge, the trend of the acceleration do not decrease monotonically; however, a rebound acceleration area at a distance of 10-15 m away from the bridge is found. The rebound ratio is approximately 9%. The vibrations in different directions have different dominant frequency bands. This suggests that the vertical vibration is not always the largest for different frequency bands. When the frequency is less than 10 Hz, the dominant direction is the L or T direction, and when the frequency is greater than 10Hz, the dominant direction is the V direction. According to this result, relevant departments can formulate standards for vibrations in different directions. The predicted models for ground-borne vibrations caused by metros on the elevated bridge provide a first estimation based on existing models. This estimation can be used in the design and assessment of elevated rail transit systems. For the 4-story building vibrations, the acceleration levels increase gradually with increasing floor, and the frequencies of vibration transmitting to the test building are similar to the frequencies of the ground-borne vibration. The building model established in this paper conforms to the test building. The difference between the root-mean square values of the numerical and the measured results is within the acceptable range, which is 1.13 dB on average. A series of simulated models have been set to study the influence of slab thickness and story height on the vibration response. The results demonstrate that the slab thickness has little effect on the vibration because the acceleration level in the building has no significant change, which is within 1 dB. Additionally, the story height of buildings along the elevated bridge should be limited to below 3.7 m and proper column size like 250 × 250 mm can effectively reduce building vibrations. VOLUME 6, 2018
According to the limit value of 75 dB given by the FTA (2006), no higher than 3-story buildings should be built within 40 m of both sides of an elevated bridge. REFERENCES [1] China Association of Metro, Beijing, China. (Mar. 2017). Statistics and Analysis Report of Urban Rail Transit in 2016. [Online]. Available: http://wcm.cnautonews.com/pub/gdjt/hyxw/201703/t20170331_530367. htm [2] R. Nagy and K. Menyhardt, ‘‘Vibration aspects on local light rail transportation,’’ Appl. Mech. Mater., vol. 801, no. 3, pp. 249–253, 2015. [3] K. Jiao, Z. Y. Li, M. Chen, C. Wang, and S. Qi, ‘‘Effect of different vibration frequencies on heart rate variability and driving fatigue in healthy drivers,’’ Int. Arch. Occupat. Environ. Health, vol. 77, pp. 205–212, Apr. 2004. [4] N. Harada, ‘‘Autonomic nervous function of hand-arm vibration syndrome patients,’’ Nagoya J. Med. Sci., vol. 57, pp. 77–85, May 1994. [5] J. W. Li, ‘‘Review of testing and analysis on metro-induced vibration,’’ Appl. Mech. Mater., vols. 580–583, pp. 1088–1091, Jul. 2014. [6] D. Murià-Vila, A. R. Sánchez-Ramírez, C. H. Huerta-Carpizo, and G. Aguilar, ‘‘Field tests of elevated viaducts in Mexico City,’’ J. Struct. Eng., vol. 141, no. 1, pp. D4014001-1–D4014001-15, 2015. [7] A. Cunha, E. Caetano, F. Magalhães, and C. Moutinho, ‘‘Recent perspectives in dynamic testing and monitoring of bridges,’’ Struct. Control Health Monit., vol. 20, no. 6, pp. 853–877, 2013. [8] T. Fujikake, ‘‘A prediction method for the propagation of ground vibration from railway trains on level tracks with welded rails,’’ J. Sound Vib., vol. 128, no. 3, pp. 524–527, 1989. [9] P. Galvín and J. Domínguez, ‘‘Experimental and numerical analyses of vibrations induced by high-speed trains on the Córdoba–Málaga line,’’ Soil Dyn. Earthquake Eng., vol. 29, no. 4, pp. 641–657, 2009. [10] K. E. Vogiatzis, ‘‘Athens metro extension project to piraeus ground borne noise and vibration assessment and control,’’ Int. J. Mech., vol. 6, no. 2, pp. 130–139, 2012. [11] C. Zou, Y. Wang, P. Wang, and J. Guo, ‘‘Measurement of ground and nearby building vibration and noise induced by trains in a metro depot,’’ Sci. Total Environ., vol. 536, pp. 761–773, Dec. 2015. [12] W. J. Luo, X. Y. Lei, and S. L. Lian, ‘‘The analysis of vibration for ballastless track-bridge base on a hybrid FE-SEA method,’’ Appl. Mech. Mater., vols. 405–408, pp. 3213–3217, Sep. 2012. [13] T. Pinkaew, Y. Fujino, and B. K. Bhartia, ‘‘Control of traffic-induced vibrations of elevated urban highways,’’ Comput.-Aided Civil Infrastruct. Eng., vol. 11, no. 5, pp. 333–341, 2010. [14] J. Tong and C.-S. Cheng, ‘‘Environmental vibration induced by elevated railway traffic using thin-layer method,’’ J. Vib. Eng., vol. 20, no. 6, pp. 623–628, 2007. [15] Mechanical Vibration and Shock—Evaluation of Human Exposure to Whole-Body Vibration—Part 1: General Requirements, document ISO 2631-2, 2003. [16] C. Hanson, D. Towers, and L. Meister, ‘‘Transit noise and vibration impact assessment,’’ Federal Transit Admin., Washington, DC, USA, Tech. Rep. FTA-VA-90-1003-06, 2006. [17] Standard of Environmental Vibration in Urban Area, document GB 10070-1988, 1988. [18] J. I. Real, T. Asensio, L. Montalbán, C. Zamorano, and T. Real, ‘‘Railway traffic induced vibrations: Comparison of analytical and finite element models,’’ J. Vibroeng., vol. 15, pp. 1701–1710, Dec. 2013. [19] J.-G. Chen, H. Xia, and J.-B. Yao, ‘‘Test for environment vibration induced by trains on viaduct,’’ J. Vib. Shock, vol. 30, pp. 159–163, Feb. 2011. [20] H. J. Zhou, W. He, and W. Xie, ‘‘Research on vibration serviceability of over-track buildings,’’ ICTIS, Improving Multimodal Transp. Syst.-Inf., Saf., Integr., vol. 46, pp. 621–626, Jun. 2013. [21] C. Zou, Y. Wang, J. A. Moore, and M. Sanayei, ‘‘Train-induced field vibration measurements of ground and over-track buildings,’’ Sci. Total Environ., vol. 575, pp. 1339–1351, Jan. 2017. [22] Y. F. Zhang, Traffic Environmental Engineering. Beijing, China: China Communications Press, 2011. [23] W. Peter, ‘‘Fatigue assessment of non-stationary random vibrations by using decomposition in Gaussian portions,’’ Int. J. Mech. Sci., vol. 127, pp. 10–22, Jul. 2017. [24] M. Anderson, ‘‘A faster Fourier transform,’’ Technol. Rev., vol. 116, no. 3, pp. 43–43, 2012. 38635
M. Cai et al.: Field Tests and Simulation of Ground and Building Vibrations Caused by Metros
[25] K. M. Qiu and S. K. Zhao, ‘‘Performance comparison between DFT and FFT in actual application,’’ J. Northern Jiaotong Univ., vol. 24, no. 5, pp. 60–62, 2000. [26] W. Luo, P. Wang, L. Yan, H. Liu, and R. Chen, ‘‘Research on the laws of the environmental vibration induced by elevated rail transit,’’ Appl. Mech. Mater., vols. 405–408, pp. 1881–1886, Sep. 2013. [27] Mechanical Vibration and Shock—Evaluation of Human Exposure to Whole-Body Vibration—Part 1: General Requirements, document ISO 2631-1, 1997. [28] Standard of Limit and Measurement Method of Vibration in the Room of Residential Buildings, document GB/T 50355-2005, 2005. [29] M. Sanayei, P. Maurya, and J. A. Moore, ‘‘Measurement of building foundation and ground-borne vibrations due to surface trains and subways,’’ Eng. Struct., vol. 53, pp. 102–111, Aug. 2013. [30] P. F. Xu, C. Z. Xiao, and J. H. Li, ‘‘Study on relationship between natural vibration periods and heights of structures for high-rise buildings and its reference range,’’ China Civil Eng. J., vol. 47, no. 2, pp. 1–11, 2014. [31] K. Sun, W. Zhang, Y. Xu, L. Zhou, and F. Zhou, ‘‘Measurement and evaluation on vibration effects of underground space adjoining the subway station,’’ Chin. J. Underground Space Eng., vol. 12, no. 1, pp. 169–176, 2016. [32] Y. M. Chen and H. Takemiyu, Environmental Vibration Prediction, Monitoring and Evaluation. Beijing, China: China Communications Press, 2003, pp. 427–431. [33] F. Benedettini, M. Dilena, and A. Morassi, ‘‘Vibration analysis and structural identification of a curved multi-span viaduct,’’ Mech. Syst. Signal Process., vols. 54–55, pp. 84–107, Mar. 2015. [34] K. K. Reichl and D. J. Inman, ‘‘Finite element modeling of longitudinal metastructures for passive vibration suppression,’’ in Proc. AIAA/ASCE/AHS/ASC Struct., Struct. Dyn., Mater. Conf., 2016, p. 1. [35] Minimum Design Loads for Buildings and Other Structures, Amer. Soc. Civil Eng., Reston, VA, USA, 2005. [36] Code for Seismic Design of Buildings, document GB 50011-2010, 2010.
38636
MING CAI received the B.S. and Ph.D. degrees from Sun Yat-sen University, Guangzhou, China. He is currently a Professor with the Research Center of Intelligent Transportation Systems, School of Intelligent Systems Engineering, Sun Yat-sen University, where he is also the Presiding Work Associate Dean with the School of Intelligent Systems Engineering. He has authored over 30 papers in international journals. His current research interests include ITS, big data, and transportation environment. WEI WAN received the B.E. degrees from Sun Yat-sen University, Guangzhou, China, where he is currently pursuing the master’s degree with the School of Engineering. His current research interests include environment acoustics and vibration simulation.
HAIBO WANG received the B.E. and Ph.D. degrees from Sun Yat-sen University, Guangzhou, China. He is currently a Research Fellow with the Research Center of Intelligent Transportation Systems, School of Engineering, Sun Yat-sen University. He has authored over 10 papers in international journals. He has authored over 20 papers in international journals. His current research interests include transportation environment, ITS, and high-performance computing.
VOLUME 6, 2018