1. Introduction
Train-induced vibration is indeed a significant issue, especially for buildings adjacent to the subway. In Beijing, a metropolis with a rich history, the metro line will inevitably pass by certain structures having historical and cultural significance [
1]. Consequently, the safety of these structures and the comfort of their occupants are also impacted. For these buildings, the vibrations caused by subway operations are a negative factor that cannot be ignored; hence, the structures’ safety and the residents’ comfort are also affected.
Recently, many scholars have been concerned about the influence of tunnel construction on strata and adjacent buildings [
2,
3,
4]. Many studies focus on the specific type of building [
5,
6,
7,
8] or surface [
9,
10,
11,
12] subjected to the influence of the subway. Using field measurements and numerical simulations, several scholars have investigated the safety of ancient building structures under the impact of traffic-induced vibrations in great detail [
13,
14,
15,
16]. Ma et al. [
17] established a model of the impact of various types of vibrations on the ancient bell tower and used it to predict the potential impact of the new subway line on the aforementioned structure. Javad et al. [
18] classified the subway structural system, the surrounding soil media, and types of cultural and historical structures (CHS). They developed a safe distance prediction model (in the form of practicable graphs) that can be utilized to determine the required minimum metro distances from CHSs. Poovarodom et al. [
9] used in situ vibration measurements to determine the intensity of ground vibrations and the attenuation of vibration waves coming from traffic sources and proposed the attenuation curves derived from regression analysis for risk management of the heritage site. Ma et al. [
10] proposed a soil–tunnel periodic model with a track slab based on wave transform to simulate the propagation of train-induced vibrations and predict ground vibrations induced by subways, which can be used to predict the areas with the most severe vibration effects and design vibration mitigation measures. Nielsen et al. [
11] proposed a hybrid model for predicting ground vibration caused by discrete irregularity of wheels and tracks, showing the effects of wheel plane size and vehicle speed on the maximum wheel–rail vertical contact force and free-field ground vibration. However, there are few studies on the impact of subway-induced vibration on historical and cultural reserves. There are many structures with different shapes in the broad area of the historical and cultural district. In this regard, a comprehensive treatment strategy based on the degree of vibration influence of the building is required; however, there is currently a lack of research in this field.
There are also studies that focus on a specific type of vibration damping measure as the object [
19,
20,
21,
22,
23,
24,
25,
26,
27], some scholars have improved measures such as periodic pile row, metamaterials, and steel spring floating slab track, or adopted new methods to study the vibration reduction effect of these measures, and some scholars have used the life cycle analysis method [
28,
29] to compare and evaluate several vibration reduction technologies. Kaewunruen et al. [
23] were the first to use an effective infinite-boundary train–track–soil coupling model to study the effect of piles on the vibration response of high-speed railways with slab track and concludes that periodic pile rows can significantly reduce the dynamic response of the soil under train vibration, and with the increase in the depth of the pile into the soil, the smaller the dynamic response. Li et al. [
25] were the first to investigate the surface vibration mitigation using seismic metamaterial (SMM) barriers in high-speed railways by establishing a 3D coupled train–track–soil model and concluded that the SMM interferes with the propagation path of dynamic waves and attenuates the vibration acceleration in the SMM region. Zhao et al. [
27] proposed to use a nonlinear quasizero-stiffness (OZS) vibration isolator to improve the low-frequency vibration damping effect of steel spring floating slab track (FST). The nonlinear characteristics of the vibration isolator and its influence on the dynamic response of FST were analyzed by establishing a dynamic coupling model of QZS-FST, and the key parameters of the QZS vibration isolator were optimized. Kaewunruen et al. [
28] conducted a 50-year life cycle analysis of vibration damping methods such as geosynthetics, metamaterials, and foundation improvement, and concluded that geogrids in combination with foundation improvement techniques are economical and effective vibration damping methods. In summary, these studies often focus on a specific vibration reduction method [
30]. In practice, measures can be taken in three stages: vibration generation, vibration propagation, and vibration effects on the structure. For various engineering backgrounds, there are significant differences in the effectiveness of these measures [
20]. Hence, for cultural protection areas with buildings of different shapes, it is necessary to evaluate the effectiveness of various vibration reduction techniques by considering the engineering background in the area.
In response to this demand, the whole Fayuan Temple historic and cultural reserve is taken as the research object in this paper, large-scale in situ tests are conducted on the surface and buildings of the historic and cultural reserve. Based on the test results, the building’s impact is determined, the influence area is divided according to the impact degree, and the block is designated appropriately. The three vibration stages, namely, active vibration isolation of the vibration source, cutting the vibration propagation channel, and passive vibration isolation of the vibration-affected object, are chosen and used to study the impacts of vibration reduction. Finally, a comprehensive vibration reduction scheme based on regional division is proposed. The vibration zoning method proposed in this paper and the comprehensive vibration reduction scheme based on the vibration zoning can be applied to the vibration reduction and isolation of other similar historical and cultural reserves.
2. Problem Background
The Fayuan Temple historic and cultural reserve is located in the city center of Beijing, and its ground is divided into artificial accumulation layer and Quaternary sedimentary layer in the depth range of 21 m disclosed by ground investigation, which mainly consists of gravelly soil, miscellaneous fill, pulverized soil, and sandy soil.
The Fayuan Temple historic and cultural reserve is affected by vibrations from Metro Line 4. The center-to-center distance of the tracks is 15 m. The horseshoe tunnel, with maximum excavation dimensions of 5.9 m in width and 6.33 m in height, was constructed using the mining method. Metro Line 4‘s north–south route along Caishikou Street is depicted in
Figure 1. The distance from the downline’s outer edge to the ancient buildings in the reserve ranges from 16 to 25 m, and the distance from the tunnel to Nanbanjie Hutong varies between 78 and 95 m.
Since Metro Line 4’s inauguration in 2009, the reserve, spanning 13,526 m2 and encompassing 435 households, has experienced significant vibration impacts from the subway. The most severe damage is located east of Nanbanjie Hutong. Despite measures such as track polishing and lubrication, vibration reduction is limited and typically lasts only 1 to 2 months. The vibration’s effect on residents has not been fully mitigated.
In order to address this issue, a detailed vibration test was conducted within the reserve to identify vibration-sensitive areas, categorize the vibration-affected zones, and analyze the causes of excessive vibration. Based on this regional division, a comprehensive vibration reduction scheme was proposed, potentially applicable to similar blocks in the future, offering substantial social and economic benefits.
3. In Situ Measurement
In situ measurements included surface vibration tests and building vibration tests, as illustrated in
Figure 2. The test equipment employed a V001 magnetoelectric acceleration sensor, depicted in
Figure 2a. Its sensitivity is 0.298 V/(m/s
2), the measuring range is up to 20 m/s
2, the frequency range spans from 0.5 to 100 Hz, the resolution varies by gear, ranging from 1 × 10
−8 to 3 × 10
−6 m/s
2, and the operational temperature ranges from −10 to +50 °C. The equipment is equipped with the TDD-16D dynamic signal test and analysis system, which is suitable for high requirements such as modal testing and other testing occasions. The equipment is perfectly suited for low amplitude detection. The sensor was affixed to the measurement point surfaces using glue.
As per the “GB10071-88” Code for “Measurement Methods of Environmental Vibration in Urban Areas” [
31] and the “JGJT 170-2009” Code for “Urban Railway Traffic Building Vibration and Secondary Radiated Noise Limits and Measurement Methods Standard” [
32], the arrangement of surface measurement points is shown in
Figure 3. East–west surface vibration measuring lines were established along Nanheng West Street and Lianhua Hutong, with eight points on each line situated at 20, 40, 60, 80, 120, 160, 200, and 240 m from the subway. Conversely, north–south surface vibration measuring lines along Caishikou Street and Nanbanjie Hutong had points at 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, and 300 m from Nanheng West Street. Additionally, two extra points were positioned at each end of Tianjing Hutong, approximately 134 m from Nanheng West Street.
The main types of houses in the zone are single-story masonry structures. Six single-story masonry structures with high protection value were selected for vibration testing as follows: Liuyang Guild Hall, No. 2 Yard, Nanbanjie Hutong, No. 108 Yard, Lanman Hutong, No. 7 Yard, No. 9 Yard, Tianjing Hutong, and Shaoxing Guild Hall. The single-layer masonry structure is shown in
Figure 4.
As per the “GB50355-2018” Code for “Vibration Limits and Measurement Methods of Residential Buildings”, rooms under 20 m
2 require one measurement point, while rooms over 20 m
2 need three points [
33]. The points’ layout is presented in
Figure 5. The distance between the measuring point on the far right of the building and the center line of the train is shown in
Table 1.
5. Study on Vibration Reduction Measures
Currently, the common vibration isolation measures are divided into three categories as follows: active vibration isolation, cutting vibration propagation paths, and passive vibration isolation. Common active vibration isolation measures include grinding rail, installing damping fastener, laying steel spring floating plate rail and so on. The common measures to cut off the vibration propagation path are air ditch isolation, continuous wall isolation, periodic pile isolation, etc. [
36,
37,
38].
In order to reasonably formulate vibration control measures, reasonable control measures are selected in different regions based on the regional division in
Section 4, as shown in
Figure 11. This chapter mainly introduces three kinds of vibration reduction measures, namely, steel spring floating plate track vibration reduction, periodic pile row vibration reduction, and building anti-vibration reinforcement or renovation, and carries out numerical simulation calculations for the vibration reduction effect of steel spring floating plate track vibration reduction and periodic pile row vibration reduction for the severely exceeding vibration in Fayuan Temple historic and cultural reserve.
5.1. The Dynamic Coupling Model of Vehicle–Track–Tunnel–Stratification–Structure
5.1.1. Model Building
According to the relative position between Liuyang Guild Hall and Metro Line 4, a dynamic coupling model of vehicle–track–tunnel–stratification–structure was established. The first part of this model is the vehicle–rail coupling model, as shown in
Figure 12. This model comprises a train model, a track model, and a wheel–rail coupling relationship. The train model consists of a body, two bogies, and four wheelsets. The track interacts with the foundation through fasteners, which are considered discrete supported Euler beams [
39]. Hertz’s nonlinear contact theory simulated the elastic contact between the wheel and rail.
The second part, a tunnel–stratum–structure model, is depicted in
Figure 13. This model was created using the three-dimensional finite element software MIDAS-GTS 2019. Its dimensions are 150 × 100 × 50 m (length × width × height), with the minimum mesh size being 0.3 m. Rayleigh’s linear group method calculated the model damping. The viscoelastic boundary conditions were implemented using the ground surface spring element.
5.1.2. Materials Parameters
- 1.
Soil parameters
Based on an actual measured survey report, the modeled stratigraphy was divided into six layers according to soil conditions, as shown in
Table 6.
- 2.
Tunnel and ground building structure parameters
The material parameters for the tunnel and roadbed were sourced from the Beijing subway tunnel. The tunnel is made of No. C50 concrete, and the roadbed of No. C30 concrete. The parameters for the tunnel, track, and ground building are presented in
Table 7.
- 3.
Rayleigh damping parameters
The damping matrix in the model was calculated using Rayleigh’s linear combination method, assuming that the damping matrix of the system is a linear combination of the mass matrix [M] and stiffness matrix [K].
The expression for the sum of Rayleigh damping constants is as follows:
where [C] is 0.03,
are the vibration frequencies of the two modes of the system; ζ is the damping ratio of the system and the angular frequency of the two modes of the system, α is 0.2370 and β is 0.0038.
5.1.3. Materials Parameters
In order to avoid vibration reflection at the truncation boundary, a spring-damping absorption boundary was set. In MIDAS/GTS 2019, the spring stiffness coefficient adopts the foundation reaction coefficient, and the damping coefficient is determined by the following formula:
where
are unit area damping constants of compression wave and shear wave, respectively; A
i is the area represented by the boundary point i.
where
; G is the shear elastic modulus; ρ is the density of the material; E is the elastic modulus.
5.1.4. Validation of Numerical Models
In order to verify the accuracy of the numerical models and analysis method, the structural part of the tunnel–stratum–structure model is deleted to form the tunnel–soil model, and the ordinary track wheel-rail force shown in
Figure 14 is applied for calculation. The maximum Z vibration level curve of subway vibration transmission horizontally are extracted at different train operating speeds, as shown in
Figure 14, and compared with the measured Z vibration level data on the surface, as shown in
Table 8.
The maximum Z-levels of 20 m and 40 m from the metro obtained by numerical calculation are close to the measured results. Due to the uncontrollable speed of the subway in the measurement, there is a difference between the two results, the error range meets the calculation requirements, and the model can be used to carry out subsequent calculations.
5.2. Steel Spring Floating Slab Track
This railway structural system was first used in Germany in 1965. Due to its excellent vibration and noise reduction performance, it is frequently utilized in urban rail transit. This track type is currently used by numerous subway lines in Beijing, including the special sections of Lines 4, 5, 9, 10, and 13 of the Beijing Metro.
The wheel–rail force (fastener response force) of the steel spring floating slab track and regular ballast bed track at v = 40, 60, and 80 km/h was determined using MATLAB (version 9.10) and the above-mentioned vehicle–track coupling model. The outcomes are displayed in
Figure 15.
The vibration responses of the standard section and the extension section of the tunnel in this study were simulated under three different operating speeds. The standard section simulates the train intersection condition, and the train runs in opposite direction at constant speed in the left and right line tunnel. The extended section simulates the extended section condition of the right line, and the train travels at a constant speed in the tunnel of the left line. The calculation conditions are shown in
Table 9.
The wheel–rail force in the calculations was input into the tunnel–stratum–structure model, whereas the vibration response of the sensitive building was obtained when the steel spring floating slab track was used or not. The track state of the plate spring floating plate was then compared with the common track state. The maximum vertical vibration level represented the vibration response, and the results are shown in
Table 10.
It can be inferred from
Table 8 that the steel spring floating slab track has a significant damping effect. The maximum vertical vibration level at measuring points in sensitive buildings was reduced by 6.93 to 10.81 dB (reduction rate is 9.9% to 14.0%).
5.3. Periodic Pile Row
The common configuration of multi-row pile construction features equal spacing, which prevents the propagation of vibration waves within the band gap frequency range through such periodic structures. Thus, periodic pile rows can control and isolate vibrations of specific frequencies [
40,
41,
42]. The staggered pile row used in this study, with a 3 m core spacing and a 1 m pile diameter, comprises three rows, as shown in
Figure 16.
The row piles’ finite element model and the tunnel–stratum–structure model are based on the aforementioned parameters. The grid parameters, damping conditions, boundary conditions, and wheel–rail forces are consistent with the above description. The model is depicted in
Figure 17.
As
Table 11 indicates, 12 conditions were established to simulate the vibration response at various speeds, tunnel sections, and vibration-damping measures. Each condition simulates the encounter of two trains traveling at a constant speed.
The vibration response of a train passing under piling was calculated and compared with that under no measure. The maximum vertical vibration level represents the vibration response, with results shown in
Table 12.
Table 12 reveals that the periodic pile row significantly reduces vibrations affecting sensitive buildings in this area. The maximum vertical vibration level at measuring points in sensitive buildings decreased 6.11 to 9.98 dB (a reduction rate from 8.7% to 12.9%).
5.4. Anti-Vibration Reinforcement or Reconstruction of the Building
For the excessively vibrating area of Fayuan Temple historic and cultural reserve, targeted reinforcement or reconstruction measures can be formulated for the affected houses. These specific techniques include the following:
The primary steps involve demolishing the original structure, installing vibration isolation devices on the foundation, and reconstructing the superstructure. The vibration isolation component serves as the elastic link between the building and the foundation, reducing vibrations by controlling the transmission rate of the isolation system. Depending on the building’s form, isolation components may include steel spring isolators, rubber isolators, or isolation pads.
After demolishing the original building, a new building with an anti-vibration foundation was designed and constructed. Typical measures include pile foundations, raft foundations, and new basements. The ground floor’s vibration input was reduced due to the altered load transfer path, which lowered the building’s shaking intensities.
The indoor floating floor reduces vibration by utilizing isolation components and controlling the isolation system’s transmission rate. A concrete floor slab was laid over the structural floor slab, supported by vibration-isolation components. The floating floor’s thickness is generally from 50 to 100 mm, with a 30 to 50 mm gap between it and the structural floor. Steel spring vibration isolators are commonly used as the vibration isolation element, offering effective vibration isolation.
6. Vibration Reduction Scheme
Considering the effects, feasibility, and economy of these measures, their advantages and disadvantages are compared, as shown in
Table 13.
Taking into account the site conditions, construction difficulty, and project cost, the periodic pile row was preferable to internal subway reconstruction and building reinforcement or reconstruction, making it the priority vibration reduction scheme.
In order to ensure reasonable and economic vibration reduction and isolation and reduce the impact of vibration on the cultural protection area, necessary measures shall be taken to control the impact of vibration within the permissible range. According to in situ measurements and the study of various vibration reduction techniques, comprehensive multi-aspect solutions were proposed for buildings located in different affected areas.
Buildings in the severely excessive standard area (vertical vibration level ≥ 70 dB):
- ➀
If feasible, a periodic pile row should be the primary measure to reduce vibration in the Fayuan Temple historic and cultural reserve, with anti-vibration reinforcement or reconstruction of the building as supplementary measures. Periodic pile rows significantly reduce vibration transmission when used as the primary strategy, while targeted anti-vibration reinforcement or reconstruction can address specific local areas or cultural buildings with serious over-standard issues.
- ➁
If periodic pile rows cannot be constructed, residents should be relocated, and homes converted from residential to commercial use.
- ➂
If periodic pile driving is not feasible and residents cannot be relocated, the vibration isolation foundation, vibration resistance foundation, or indoor floating floor can be used to transform or reinforce the building.
Buildings in the generally excessive standard area (vertical vibration level ≥ 67 dB, <70 dB):
- ➀
If feasible, the use of a periodic pile for vibration isolation can meet human comfort requirements.
- ➁
If a periodic pile row cannot be completed, the building’s foundation or main body can be reorganized and reinforced to enhance its anti-vibration performance.
7. Conclusions
Most of the previous studies only focus on the surface or specific types of buildings, but lack research on the vibration law and vibration mitigation measures of the whole area of vibration. In order to study the extent of vibration impact in the Fayuan Temple historic and cultural reserve and to determine an appropriate vibration reduction scheme, comprehensive testing of the surface and buildings in this area was conducted. Based on the in situ test results, the reserve was categorized into three zones with varying levels of vibration, determined by the maximum vertical vibration level. For regions with excessive vibration, a dynamic coupling model encompassing vehicle, track, tunnel, stratum, and structure was developed. The effectiveness of the wire spring floating slab track and periodic pile row in mitigating vibration was validated. A comprehensive solution for these regions was formulated based on this research. The main conclusions of this paper are as follows:
- (1)
The in situ test indicated that the vibration levels of several buildings in the reserve exceeded the standard limits. Analysis of the typical time-history spectrum curve and the maximum vertical vibration level suggested that the subway was the primary source of excessive vibration in this area. The area experiencing excessive vibration was mainly situated between Caishikou Street and Nanbanjie Hutong, with approximately 40% of the areas exceeding the daylight control level of 70 dB and 60% surpassing the nighttime control standard of 67 dB. Based on the vibration test findings, the reserve was segmented into zones of extremely excessive vibration, typically excessive vibration, and non-excessive vibration.
- (2)
The control ideas of vibration impact from active vibration isolation at the source, interruption of the vibration propagation path, and passive vibration isolation of the affected object, and the numerical simulation is adopted to study the steel spring floating slab track and periodic pile, and the results show that the steel spring floating plate rail and the periodic pile row can significantly reduce the maximum Z vibration level of the sensitive building, and the reduction ranges are 6.93–10.81 dB and 6.11–9.98 dB, and the reduction rates are 9.9–14.0% and 8.7–12.9%, respectively.
- (3)
A comprehensive scheme for the Fayuan Temple historic and cultural reserve Temple is proposed by considering the vibration regional division, numerical simulation results, the importance of the buildings in the historic and cultural reserve, and the operability of the construction. Periodic pile row should be considered the primary control measure, and anti-vibration reinforcement or reconstruction of buildings should serve as a supplementary measure in the areas with severely excessive standards. For buildings in generally excessive standard areas, employing periodic pile vibration isolation can satisfy the needs of building protection and human comfort requirements.
- (4)
In the process of measurement in this study, the comprehensive schemes mentioned in this paper have not been taken in the protected area, so we cannot test the vibration reduction effect of the comprehensive vibration reduction scheme in this area. After the comprehensive vibration reduction scheme is adopted in this area, we will carry out in situ testing and compare it with this study.
It is also noted that this study proposes a comprehensive vibration reduction scheme based on the vibration area division in the context of the Fayuan Temple historic and cultural reserve. This idea can be used to formulate comprehensive vibration reduction schemes for other similar cultural reserves, and in the future, the method can be studied and improved in depth by taking into account the effect of the implementation of this comprehensive vibration reduction scheme in the Fayuan Temple historic and cultural reserve.