Abstract
Underground-train-induced building vibration is a noteworthy new environmental problem. Aiming at the train-induced environmental vibration problem in practical engineering, a three-dimensional train–track–tunnel–soil–building coupled dynamic model is established in which the nonlinear wheel–rail interaction, tunnel–soil interaction, layered soil, and soil–building interaction are considered in detail. A test is conducted to validate its effectiveness, and the influences of running trains on tunnel wall, soil, and building are investigated in depth. The vibration-control effect of steel-spring floating-slab track (FST) and rubber-pad FST combined with structural gap on buildings is studied. Results show that the dynamic model and the simulation method employed are effective in predicting environmental vibration. The amplitude of tested tunnel acceleration is within 0.088–0.151 m/s2, and the predominant frequency is within 31.5–100 Hz. The maximum vibration level (VL) of tunnel wall in the 1/3 octave domain is 61–80 dB. Running trains indeed excite soil vibration; near the ground surface this is amplified. The predominant frequency of soil vibration is 50–80 Hz; vibrations above 100 Hz are largely absorbed by soil. When waves travel across an interface, refraction and reflection effects make the vibrations more complex. For tall building systems, the vertical total VL (VLzmax) is concentrated within 48.1–64.3 dB for vertical distribution, and the vibration energy is mainly concentrated at 63 Hz. In this project, the vibration-isolation effect of steel-spring FST is significant, and vibration above 16 Hz is effectively isolated, VL being reduced by 14.6 dB at most.
Underground systems have been widely designed and constructed worldwide ( 1 ). With the ramifying development of underground systems, environmental vibration induced by running trains has become a serious social problem, which has an obvious effect on normal working and human health ( 2 – 4 ). When the metro operates under the ground, wheel–rail dynamic interaction is aroused by track random irregularities, which directly excite vibration. Because of the mechanical connection between track and tunnel, the vibration is transmitted to the tunnel wall, which then results in soil vibration. Finally, the wave travels in the soil to aboveground buildings through the coupling between soil and building ( 5 , 6 ). The frequencies of train-induced building vibrations are usually lower than 80 Hz. However, in the international standards ISO2631-1 and ISO2631-2, it is pointed out that the vibration of 0.5 to 80 Hz is clearly perceived by the human body and causes annoyance. In addition, Huang et al. and Kim et al. tested the influence of vibrations under 100 Hz on the bodily comfort of volunteers in a sitting position; they found that the areas of discomfort changed with the change of frequency, and the amplitude did not change this phenomenon ( 7 , 8 ). Some scholars have constructed the functional relationship between annoyance to people and building-structure vibration ( 9 – 12 ). The research and evaluations show that train-induced environmental vibration has adverse effects on some people. Again, train-induced vibration of soil and buildings has a great influence on the human physiological system ( 13 ), making this kind of environmental problem non-negligible. Therefore the vibration of soil and tall buildings caused by underground trains needs to be investigated in depth.
The influence of underground trains on soil and building vibrations has been widely studied in recent years. The existing works can be classified into the following three aspects according to the method employed:
(a) Adopting an analytical or semi-analytical method. Balendra et al. ( 14 ) established a two-dimensional (2D) model of a rigid tunnel in viscoelastic half-space based on substructure method to study building vibration. Adopting the coordinate transformation method, Guan and Moore ( 15 ) investigated the tunnel vibration caused by a running train in viscoelastic soil. Krylov ( 16 ) established an analytical dynamic model of the tunnel–soil system, and then studied the system vibrations based on the Green function. Forrest and Hunt ( 17 ) adopted the pipe-in-pipe (PiP) model to solve three-dimensional (3D) tunnel–soil vibration. The analytical or semi-analytical method is also adopted by Hussein and Hunt ( 18 ), Kuo et al. ( 19 ), Haak ( 20 ), and so on.
(b) Adopting a numerical method. Finite element method (FEM), boundary element method (BEM), and infinite element method (IEM) are widely adopted in studies of train-induced building vibration. Chua et al. ( 21 ) established a 2D FEM of a train-tunnel–soil–building system to solve this vibration issue. Gardien and Stuit ( 22 ) built a 3D FEM of the whole system to study the wave propagation in soil. Hwang and Lysmer ( 23 ) proposed a 2.5D FEM to solve soil vibration. Adopting a 2D FEM–BEM method, Jones et al. ( 24 ) researched the ground-surface vibration caused by a running train. Sheng et al. ( 25 ) proposed a 2.5D FEM–BEM method to reduce the degrees of freedom of the model. This calculation method is also adopted by Mohammadi and Karabalis ( 26 ), Galvín et al. ( 27 ), Romero et al. ( 28 ), Gupta et al. ( 29 ), and so on, and plenty of beneficial conclusions have been reached.
(c) Adopting an empirical method. Kurzweil ( 30 ), Madshus et al. ( 31 ), Hood et al. ( 32 ), and Kourousis et al. ( 33 ) employed this method to study the train-induced vibration issue.
The theory and calculation processes of approach (a) are rigorous, and the computational efficiency is high; however, it is hard to consider layer properties, the ground surface, and noncircular tunnel sections. The accuracy of approach (c) depends on the effectiveness of the test method and the obtained data. Therefore approach (b) has been the most common method in recent years, and it is the one employed in this work.
Aiming at the train-induced environmental vibration problem in practical engineering, a prediction model is established in the next section. In the third to fifth sections, the propagation law of vibration in tunnel, soil, and building is thoroughly analyzed, and the vibration amplitude and predominant frequency of vibration in medium or structure are presented; isolation schemes are proposed in detail in the sixth section. Finally, some interesting conclusions are reached. The results of this study provide reliable data support for environmental vibration-control engineering. Engineering designers will be able to propose more targeted and effective vibration-isolation schemes based on the vibration characteristics of different materials and structures.
Integrated Dynamic Model of Train–Track–Tunnel–Soil–Building Coupled System
The integrated dynamic model of a train–track–tunnel–soil–building coupled system and the engineering problem being addressed are introduced in detail.
Vibration-Prediction Methodology and Model
The proposed vibration-prediction model consists of two parts: (a) the train–track dynamic interaction model (TTDIM), and (b) the track–tunnel–soil–building coupled model (TTSBM). The TTDIM is adopted to calculate the fastener force, which is then applied to the TTSBM to solve the train-induced building vibration issue, as seen in Figure 1. The TTDIM is adopted primarily to obtain all the fastener forces, which are then applied at corresponding locations in TTSBM to solve the tunnel–soil–building vibration issue.
Vibration-prediction methodology.
First, based on multi-body dynamics theory and beam vibration theory, the train submodel and track submodel are established. Second, based on nonlinear Hertz theory, the wheelset and the track are coupled. Then, based on finite element theory, models for tunnel, soil, and building are established. Finally, the fastener force is transmitted to the tunnel through the track structure and foundation, which causes vibration of structurally coupled soil and buildings. This methodology is completely performed in the time domain, and the connections between the two dynamic models are all the fastener forces in the range of the calculated length.
To ensure uniformity of calculating platform, the TTDIM is established and programmed adopting secondary development technology in ANSYS software using APDL (ANSYS Parametric Design Language). An explicit integration method, which can increase the computational speed, is adopted and programmed into ANSYS to solve the TTDIM. The TTSBM is also established in ANSYS, and this is solved by an implicit integration method to improve the computational efficiency ( 34 ).
The descriptions of the two submodels are presented below.
TTDIM
The TTDIM contains two submodels, namely the train submodel and the track submodel, which are connected by wheel–rail dynamic interaction (Figure 2).
The train–track dynamic interaction model.
The dynamic model of a metro train is established based on multi-body dynamics. The train is considered to be placed equidistantly at a certain interval for multiple vehicles. Each vehicle is simplified as a rigid body structure, including one car body, two frames, and four wheelsets. Each vehicle submodel includes 10 degrees of freedom. Elastic suspension elements are used to connect each rigid body. The rail is modeled by Euler beam, and the fastener is simulated as a linear elastic spring-damping element, the spring force depending on the difference between the displacement of the rail and the displacement of the ballast. Hertz nonlinear contact theory is adopted to describe the wheel–rail interaction. The detailed modeling process can be seen in the author’s published works ( 35 , 36 )
The above vibration equations of TTDIM are constructed in ANSYS by APDL, whose detailed implementation can be seen in the author’s published works ( 37 , 38 ).
TTSBM
FEM is adopted to establish TTSBM on the computational platform of ANSYS. According to the structural characteristics of different parts of the system, some key modeling principles are proposed:
1) A 3D solid element is used to simulate soil, tunnel, and monolithic track bed. The 3D shell element is used to simulate building floors and a 3D beam element is used to simulate buildings’ structural columns.
2) The soil is composed of soil layers with different properties, and the soil is layered in the model. Each part of the model is modeled by common nodes, and the bottom of the high-rise building and the surface of the soil are coupled by establishing rigid constraints.
3) According to the existing literature ( 39 ), to ensure calculation accuracy, the element size is not more than one-sixth of the minimum wavelength of the shear wave. The shear wave velocity of the soil is about 200 m/s, and the predominant frequency of the soil vibration is lower than 100 Hz; therefore, the minimum size of the element is set to 0.3 m.
4) To improve the reliability of the calculation results and weaken the rebound effect of the vibration wave transmitted to the edge of the soil, an artificial boundary is set on the side of the soil ( 40 ). Symmetrical constraints are imposed on both sides of the soil as boundary conditions.
5) The fastener force calculated by TTDIM is applied to the monolithic track bed in the form of moving load, and a loading point is placed at an interval of 0.6 m along the tunnel direction.
6) The implicit integration method called Newmark method is used as the solution method to calculate the model. The detailed solution method is given in the author’s published literature ( 34 ).
The relevant modeling methods are relatively mature, and the other detailed modeling details can be seen in the author’s published works ( 5 , 41 ).
Key Parameters Adopted in Calculation
A new underground line is planned in Chengdu city, China, next to a tall residential building (Figure 3). The shortest lateral distance from building to tunnel is 32.4 m, and the shortest vertical distance is only 21 m. Therefore the dynamic effect of underground trains on the tall building needs to be evaluated and it needs to be considered whether vibration absorbing measures should be taken.
Spatial location of the planned underground line and the building: (a) realistic drawing and (b) sectional drawing.
The parameters of the running train are given in Table 1. The track system part includes monolithic roadbed track, CN60 rail, and DZIII-3 fastener. Short-wave irregularity and Grade 6 of the American irregularity spectrum are considered. The characteristics of the fastener force calculated according to the TTDIM model are shown in Figure 4. The amplitude of the fastener force is about 33 kN, and the main frequency is concentrated in the low-frequency region of 1–10 Hz. The diameter of the cross section of the tunnel is 6 m, and the thickness of the lining is 350 mm. The property parameters of the soil are listed in Table 2; in the numerical model, the soil model is layered and given the corresponding properties.
Key Dynamic Parameters of Train
The characteristics of fastener force: (a) in time domain and (b) in frequency domain.
Geological Parameters of the Soil
The overall model is shown in Figure 5. The model contains 5,212,353 elements and 5,338,612 nodes. The integration time step of TTSBM is set to 0.002 s.
Track–tunnel–soil–building model .
Characteristics of Vibration Propagation in Tunnel
Before analyzing the vibration characteristics in the tunnel, a vibration source-strength test was carried out to verify the TTSBM model. To obtain the source strength of the metro train, a field test was carried out on an underground line in Chengdu, Southwest China. Table 3 gives the acquisition index and the sensor characteristics in the test. The sensor placement site is shown in Figure 6.
Acquired Index and Sensors Property
Installation of sensors on track–tunnel system: (a) sensors on track, (b) sensor on tunnel, and (c) rail status.
A total of 10 trains with a speed of about 74 km/h were tested. The measured acceleration and vibration level (VL) of the tunnel wall are given in Figure 7. The following results can be stated:
a) the peak acceleration of the tunnel wall is in the range of 0.088–0.151 m/s2;
b) the root mean square (RMS) of acceleration changes in the range of 0.0232–0.0275 m/s2;
c) the vertical total VL (VLzmax) is in the range of 70.3–71 dB;
d) the maximum VL in a 1/3 octave (under frequency division) is 65 dB, which appears at 63 Hz;
e) the predominant frequency of tunnel vibration is concentrated in 31.5–100 Hz, and especially in 40–80Hz.
Tested vibration of tunnel wall: (a) acceleration of tunnel wall, (b) maximum acceleration of tunnel wall, (c) VLzmax of tunnel wall, and (d) 1/3 octave of tunnel.
The comparison results for VL are as shown in Figure 8. The results of both are almost the same, including the dominant frequency band and amplitude; the reliability of the modified prediction model is proved.
Comparison between measured results and calculated results.
Further, another five locations on the cross section of tunnel, namely P1–P5, are chosen to investigate in depth the train-induced wave propagation in the tunnel (as seen in Figure 9). The location P1 is at the edge of the monolithic track bed, P2 is in the section-change area of the tunnel, P3 is at the broadest point of the tunnel, P4 is right above location P2, and P5 is the topmost location in the tunnel cross section. The vibration response of different positions in the tunnel is compared and analyzed: the vibration at P1 is the largest because this point belongs to the track, which is much closer to the wheel–rail dynamic interaction; the vibration at P2 is the largest among the tunnel vibrations; vibrations are greatly weakened in the area between P2 and P4; the calculated wave shape and peak value of tunnel acceleration are similar to the measured results in the above section.
Tunnel vibrations at different locations caused by running train.
The tunnel vibrations at different locations are investigated in the frequency domain, as seen in Figure 10. Maximum VLs under frequency division at different locations appear at 63 Hz, which is the same as the tested data in the above section. The maximum VL in 1/3 octave is 80 dB at P1, and is 76, 69, 62, and 61 dB at P2, P3, P4, and P5, respectively, which is also similar to the tested source strength. Therefore, the effectiveness of the established dynamic model can be validated. In addition, in the process of upward propagation along the tunnel wall, the vibration attenuation of 63–200 Hz is more significant, which indicates that the vibration energy in this frequency band is effectively absorbed and released by the tunnel structure.
VLs in 1/3 octave of tunnel accelerations at different locations: (a) P1, (b) P2, (c) P3, (d) P4, and (e) P5.
The VLzmax values of the tunnel at different locations are shown in Figure 11. It can be seen that the VLzmax of the tunnel wall is concentrated in the range of 63.3–82.4 dB and the area between P2 and P4 position is greatly weakened, while the level changes only slightly from P4 to the topmost location in the tunnel. It can be seen that the vibration energy below P4 is effectively absorbed by the tunnel structure and released into the soil during propagation. From position P4 to position P5, the vibration mainly propagates along the tunnel structure, the vibration energy released into the soil is less, and the attenuation is not significant.
VLzmax of tunnel vibrations at different location.
The above conclusions clearly reflect the propagation characteristics of the vibration source strength in the tunnel. The vibration caused in the tunnel is mainly concentrated in the low frequencies within 63 Hz, and most of the energy is concentrated in the lower part of the tunnel, which is directly caused by the wheel–rail interaction of the train. Most of the energy is released into the soil through the tunnel structure in the lower part of the tunnel. Therefore, energy-absorbing materials or structures can be considered in the track or tunnel to dissipate more vibration energy in the tunnel.
Characteristics of Vibration Propagation in Soil
Soil covers tunnels and supports buildings; therefore, the characteristics of vibration propagation in soil need to be focused on, which is the basic and important issue in this research.
Before the study of soil vibration characteristics, ground vibration tests are carried out to verify the validity of the soil model. The test site is located on the ground next to the building, as shown in Figure 12. High-performance acceleration sensors are used to collect vibration signals, and four measuring points at 20 m, 40 m, 60 m, and 80 m from the center line of the tunnel are selected on the ground.
Field test on earth surface.
It can be seen from Figure 13 that the peak frequency of vibration at each measuring point on the soil surface is in the range of 63–100 Hz. With distance from the center line of the tunnel, the vibration energy is significantly absorbed. In addition, the vibration at 20 m distance from the tunnel is compared (Figure 14), and it is found that the overall attenuation trend and peak frequency of the VL of the test results and the calculated results are almost the same, which can ensure the effectiveness of the soil model
1/3 octave frequency of ground.
The comparison between test results and calculation results.
Further, to analyze the transmission characteristics of vibration in different directions at different times, two cross sections (Figure 15) are chosen to present the results, as shown in Figure 16. For vertical acceleration and lateral acceleration, the presented cross section of the soil is located at the middle position of the dynamic model (cross section I). For longitudinal acceleration, the displayed cross section is located at the middle position of the tunnel (cross section II).
Cross sections chosen for illustration.
Wave propagations in soil space.
As can be seen from the results, vertical acceleration distribution in soil changes obviously. At 1 s, the train is moving into the tunnel, so the vertical vibrations of track and tunnel are aroused, while vibration in soil is relatively small. At 2 s, the vibrations of track and tunnel are greatly increased as more vehicles are applying in the model. Then at 3 s, the train moves to the selected cross section I, and the soil and nearby tunnel are greatly excited. The vibration waves propagating in different directions have offset or superposition effects when propagating in the soil, so the distribution of vibration in the soil is more complicated, and the wave propagates far in the soil, indicating that the train-induced vibration can travel a very long distance in soil and affect a large area. At 4 s, the train is passing through the selected cross section, and the wave propagation is clearly shown in the contour. At 5 s and 6 s, the running train has passed the relevant section, and the soil vibrations have been transmitted to the basement of the building. The vibrations reflect at the ground surface and then travel downward. At the same time, for wave propagation in the lateral direction, besides the sharp vibration of soil and nearby tunnel, the soil vibration for the nearby basement is also very obvious. The wave reflection that appears at the interface between concrete basement and soil is a result of the big difference between the two materials. Moreover, as seen from the vibration propagation in the longitudinal direction, the vibrations in this particular cross section are more complicated as a result of many running wheels. The vibrations caused by different wheels are superposed, and the reflected waves are also superposed with train-induced vibrations, leading to the chaotic acceleration distribution in soil. As a whole, soil vibrations are spatially complicated, and are greatly affected by reflection of boundary, vibration superposition caused by multiple wheels, material property, and so on.
Vibration Distribution in Vertical Direction
Further, to quantitatively investigate the wave propagations in vertical and lateral directions, 12 locations are chosen on cross section I, as seen in Figure 17. Points V1–V6 are located from ground surface to tunnel wall in the vertical direction. Points L1–L6 are from the tunnel wall to the left in the lateral direction.
Locations on cross section I.
Vertical vibrations at V1–V6 are shown in Figure 18. As can be seen from the results, vibration at V1 is the largest. From V1 to V5, the vibrations decrease because of the damping effect of soil. However, when the wave travels to V6, the vibration is amplified because the upper soil layer is soft. To more clearly outline the vibration attenuation seen in Figure 18, the vibration amplitude decreases first and then increases when the wave travels to the ground surface. Vibration decreases sharply from V3 to V4, indicating that this soil layer absorbs more vibrations.
Vertical acceleration at locations V1–V6.
For vertical vibrations in soil, the vibration of V1 can be regarded as the vibration source of vibrations of V2–V6 because V1 is next to the tunnel wall. Therefore, cross-correlation analysis is conducted to investigate the relationship between the vertical vibrations (Figure 19). The longer the distance between V1 and the concerned point, the larger the time delay, and the smaller the relevant cross-correlation. However, the cross-correlation between V1 and V6 is larger than that between V1 and V5 because of the vibration amplification effect in the upper soil layer. As the distance increases, the time delay increases nonlinearly.
Cross-correlations between vibration at V1 and vibrations at other locations.
On this basis, the vertical vibrations of soil in the 1/3 octave domain are given in Figure 20. The energy of vibration is concentrated in the low-frequency band of below 80 Hz, and especially in the range of 40–80 Hz. Vibrations above 100 Hz are largely absorbed by the soil. Further the calculated VLzmax is given in Figure 21. It can be seen that VLzmax decreases first and then increases with the distance between tunnel and the concerned point, with increases being a result of the layered soil.
Accelerations in 1/3 octave domain at different locations in the vertical direction.
VLzmax of soil vibrations at different locations in vertical direction.
Vibration Distribution in Lateral Direction
Further, the accelerations of points L1–L6 are investigated in Figure 22. Vibration distribution in the lateral direction presents more clear regularity. In the lateral direction, the longer the distance between L1 point and concerned point, the smaller the vibration at the concerned point is. Moreover exponential attenuation appears in the wave travel in the lateral direction, indicating that vibration greatly decreases as the travel distance increases.
Accelerations of Points L1–L6 in lateral direction: (a) in time domain and (b) amplitudes of calculated accelerations.
The cross-correlations of vibrations at L1–L6 are shown in Figure 23, from which it can be seen that the correlation decreases sharply as the distance between L1 and the concerned point increases.
Cross-correlations of vibrations at L1–L6.
Further VL and VLzmax of the above results are displayed in Figure 24. Maximum VLs appear at 63 Hz. Vibrations above 100 Hz are largely absorbed by soil. VLzmax almost decreases linearly as the distance increases. The vibration distribution in the lateral direction presents more regularity than that in the vertical direction because of the layered soil.
VL and VLzmax of the vibrations of L1–L6: (a) VL in 1/3 octave domain and (b) VLzmax at different locations.
Vibration Distribution at the Interface of Different Soil Layers
The interface between highly weathered argillaceous sandstone and moderately weathered argillaceous sandstone is chosen as the research area. Vibrations of the single layer element above (EA) the interface and the single layer element below (EB) the interface are emphasized in this part.
The results of a total of 15 points are thoroughly studied, as seen in Figure 25. A1–A5 are the top nodes of the EA layer, I1–I5 are the nodes on the interface, while B1–B5 are the bottom nodes of the EB layer.
Chosen points on and around the interface.
Figure 26 shows the vibrations at the interface. It can be seen that accelerations of Bi (i = 1–5) are largest while those of Ai (i = 1–5) are smallest, indicating that vibrations are absorbed when the wave travels.
Vibrations at interface area: (a) B1/I1/A1 and (b) B3/I3/A3.
Further joint time–frequency analysis is conducted to obtain the performance in the time–frequency domain, as seen in Figure 27. The predominant frequency of vibrations at the interface area is in the range of 60–75 Hz. Vibrations of Bi (i = 1–5) are obviously larger at 60–75 Hz than those of Ai (i = 1–5), while differences are also shown at a higher frequency band of 85–100 Hz. Moreover, vibrations at i1 (i = B, I, A) are different from those at i3 (i = B, I, A) because of the change of distance.
Vibrations (m/s2) at interface area in time–frequency domain: (a) B1/I1/A1 and (b) B3/I3/A3.
Figure 28 gives the comparison between the vibrations of the EA layer and the EB layer, from which it can be seen that the vibration of EB is larger than that of EA on the whole. However, in some situations, the vibration of the EA layer is larger and the appearance of peak value shifts when the wave travels through the interface area, indicating that reflection and refraction of the interface area indeed affect the vibration performance.
Vibrations at EA and EB layers.
The above conclusions reflect that the vibration has a certain randomness when propagating in the soil. Although the energy of the vibration decreases steadily with the increase of distance from the vibration source, when the vibration propagates along the vertical direction and between different soil layers, its performance changes because of the different properties of the soil layer and the reflection and refraction of the wave.
Influence of Underground Trains on Tall Buildings
The vibration source strength and soil vibration are studied above, based on which the influence of an underground train on a building is investigated in depth in this section.
Evaluation Criterion of Vibrations
In China, the limit of VLzmax is written in the code “Standard of vibration in urban area environment (GB 10070-88)”, and the limit of VLmax with frequency division is written in the code “Standard for limit and measuring method of building vibration and secondary noise caused by urban rail transit (JGJ/T 170-2009).”
In the research presented here, the concerned building belongs to a residential area; therefore, the relevant VLzmax is 70/67 dB (daytime/nighttime) and VLmax with frequency division is 65/62 dB (daytime/nighttime).
Moreover, the vibrometer weight factor is also suggested in the code “Standard for limit and measuring method of building vibration and secondary noise caused by urban rail transit (JGJ/T 170-2009)”, and this is given in Figure 29.
Vibrometer weight factor.
Vibration Transmission in Buildings
When an underground train is running through in the tunnel, the upper building vibrates. Figure 30 gives the building vibration at different times. As can be seen, the vibration shape of the building changes with time. The building vibrates obviously in the lateral direction. The whole building presents lateral vibration while local floors of the building mainly present vertical vibrations.
Building vibration at different times.
Further, the vibration transmission in the building in the vertical direction is investigated, as seen in Figure 31. As seen from the figure, for the aboveground building, vibration decreases with the increase of height. However, because the two basement floors are all surrounded by soil and the soil vibrations of the nearby ground surface are amplified to some degree, this results in almost the same vibration response for the soil and the basement floors −1F and −2F.
Building vertical vibrations at different floors.
The amplitudes of the above vibrations are illustrated in Figure 32. The vibration amplitudes of floors −1F and −2F appear simultaneously while those of the aboveground building shift to some extent. Vibration attenuation between floors −1F and 1F is the largest.
Parallel illustration of building vertical vibrations.
The building vibrations in the frequency domain are further displayed in Figure 33. The maximum VL appears at floor −2F, reaching 56.6 dB. The vibration of 63 Hz contributes the most energy in the building vibration.
Building vibration in frequency domain.
The VLzmax of the building is given in Figure 34. The VLzmax of −2F is the largest, which is 61.8 dB. The value is smaller than the limit value, also indicating that the influence of the running train on the building concerned is within acceptable limits.
VLzmax of the building vibrations.
The above results are obtained when the train runs through at 75 km/h. Further, to investigate the influence of running speed on VLzmax of buildings, Figure 35 displays the change of VLzmax with the increase of speed. VLzmax increases with the increase of speed. When the running speed changes from 60 km/h to 100 km/h, the change of VLzmax reaches 4.5 dB.
Influence of running speed on VLzmax of buildings.
The above conclusions show that the building vibration usually attenuates with the increase of the floor number, and the vibration is usually greater at the position closer to the vibration source, but in some specific cases ( 42 ), there is also an effect of superposition and amplification of vibration in the floor. And the running speed makes the wheelset–rail force change obviously, which is one of the important factors affecting the amplitude of building vibration.
Vibration Control of Building
According to the results of the previous section, the VL of the building is close to the limit, and the vibration of the building increases with the increase of the train speed. Therefore, it is necessary to adopt a vibration-control scheme to reduce the vibration to a lower level.
For this project, two schemes of steel-spring floating-slab track (SSFST) and rubber-pad floating-slab track (RPFST) combined with structural gap are adopted, as shown in Figure 36, and the key structural parameters of floating-slab track (FST) are shown in Table 4. In addition, the width of the structural gap is about 10 mm. The SOLID45 element is used to simulate the slab, and the COMBIN14 element with equidistant scattered arrangement is used to simulate the support stiffness under the slab.
Vibration-isolation measures schematic diagram: (a) SSFST and RPFST and (b) structural gap.
Key Parameters of FSTs
Note: FST = floating-slab track; SSFST = steel-spring floating-slab track; RPFST = rubber-pad floating-slab track.
After vibration-isolation measures are adopted, the vibration response of the building is shown in Figure 37. In the time domain, the acceleration amplitude is significantly reduced, with the vibration-isolation effect of SSFST being better than that of RPFST combined with the structural gap. In the frequency domain, SSFST has a better control effect on the vibration above 16 Hz, and VL is reduced by 14.6 dB at most, The RPFST scheme combined with structural gap has a better control effect on vibration above 4 Hz, and the VL is reduced by 9.7 dB at most. In general, when the two schemes are adopted, the building vibration level is significantly reduced, but the effect of setting SSFST is better, the maximum VL being lower than the limit of 14 dB.
Vibration response of building: (a) acceleration and (b) VL in 1/3 octave domain.
Conclusions
Aiming to address the train-induced environmental vibration problem in practical engineering, a 3D train–track–tunnel–soil–building coupled dynamic model has been established in this work, the propagation law of vibration in tunnel, soil, and building thoroughly analyzed, and the vibration amplitude and predominant frequency of vibration in medium or structure presented. Subsequently, vibration-control schemes have been proposed. The following conclusions of interest have been reached:
(1) Based on field test data, the peak acceleration of the tunnel wall is concentrated in the range 0.088–0.151 m/s2; the dominant frequency of tunnel vibration is concentrated in the range 31.5–100 Hz; and the VLzmax of the tunnel wall is concentrated in the range 70.3–71 dB. For tunnel vibration, vibration at the P2 location is the largest among the tunnel vibrations; vibrations are greatly weakened in the area between P2 and P4.
(2) For soil vibration: a running train indeed excites soil vibration, and the soil vibration at the nearby ground surface is even amplified; vibration decreases sharply from point V3 to V4; the predominant frequency of soil vibration is 50–80 Hz; vibrations above 100 Hz are largely absorbed by soil; when a wave travels across an interface, the refraction and reflection effects make the vibrations more complex; the VLzmax changes in the range of 58.9–63.1 dB in vertical distribution, which is 42.2–70.1 dB in the lateral distribution.
(3) For building vibration: the whole building presents lateral vibration while local floors of the building mainly present vertical vibrations; the vibration levels of floors −1F and −2F in the basement are similar; the maximum vibration energy of the floor is concentrated at 63 Hz.
(4) The vibration-isolation effect of SSFST is better than that of RPFST combined with the structural gap; SSFST has a better control effect on the vibration above 16 Hz, and VL is reduced by 14.6 dB at most.
Footnotes
Author Contributions
The authors confirm contribution to the paper as follows: study conception and design: Zhaowei Chen. Author, Song Peng. Author; data collection: Hong Xu. Author; analysis and interpretation of results: Qiang Yin. Author, Zhihui Chen. Author. Hong Xu. Author; draft manuscript preparation: Zhaowei Chen. Author. Song Peng. Author. All authors reviewed the results and approved the final version of the manuscript.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (Grant Number: 52008067), the Natural Science Foundation of Chongqing (Grant Number: CSTB2022NSCQ- MSX1193), the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant Number: KJZD-M202300701), and the open project of State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure (Grant Number: HJGZ2022103).