Presently, foundation pit support structures are generally regarded as the temporary structures and the impact of vibration loads is often overlooked. As opposed to static and seismic loads, the vibration loads of subway trains are a type of cyclic load with a relatively long duration of action and a definite cycle; it is of great importance for the design of foundation pit support structures to correctly evaluate the impact of subway train vibrations on deep foundation pit and support works. In this paper, a dynamic three-dimensional numerical model is built that considers the vibration load of subway trains on the basis of the static numerical model for deep foundation pit support structures and simplified train loads to study the impact of train vibrations on deep foundation pit and permanent support structures. Studies have shown that the dynamic response of surface displacement mainly occurs in the early period of dynamic load, the vibration load of subway trains has little impact on ground subsidence, the support pile structure is in an elastic state during dynamic response under the action of subway train vibrations, and the action of train vibration loads is inimical to the safety of foundation pit support structures and should be closely studied.
Presently, foundation pit support structures are generally regarded as temporary structures and the impact of vibration loads is often overlooked, which does not fit in with the actual stress situation of foundation pits. The existing static equilibrium of foundation pits is upset by the effect of ambient vibration and changes from a stable state to unstable state. Once instability is caused, it will definitely bring great damage to people’s lives and property. For example, road collapse suddenly occurred in the foundation pit construction site of Xianghu Station of Metro Line 1, Fengqing avenue, Xiaoshan district, Hangzhou, on November 15, 2008. One of the causes for this accident was that Fengqing avenue, where the foundation pit lies, had been used as a trunk road and the lateral displacement of the retaining diaphragm west of the foundation pit was increased by the loads of running vehicles. On March 19, 2009, slope failure occurred in the foundation pit of Jiahao plaza, Xining, and the vibration from construction was an inducing factor for the accident. In 2010, the planning and construction of rail transit was carried out in nearly 30 cities and regions of China, involving up to more than 110 lines. Subway construction entered a period of huge growth. In Chengdu, for example, ten subway lines were planned with a total length of 348.2 km. Line 1 and Line 2 were put into operation in October 2010 and September 2012, respectively. As an important part of urban underground space and rail transit, subway lines usually go through areas with dense population and buildings. The impact of the vibrations of running trains on the surrounding environment has attracted increasing attention from academic and engineer circles [
A foundation pit is usually in a complex environment. The impact of the vibration of road vehicles, neighboring subway trains, earthquakes, and construction blasting in the environment must be considered [
Thus, previous vibration studies focused on the dynamic response of shallow foundation pits and subway tunnels under ambient vibration conditions. However, there are no references on the impact of vibration on deep foundation pits and permanent support structures. Therefore, the study of the internal force and deformation of deep foundation pits and permanent support structures under train vibration loading in this paper is of great importance.
In this paper, the New Chengdu Museum deep foundation pit in China is taken as the object of study and the established numerical model [
This paper mainly studies the response laws of soil and support structure in a deep foundation pit under subway train vibration loading, so it is particularly important to determine the train vibration load. Vibration load is the periodic excitation vibration caused by the impact of running trains on the rails, wheel vibration, and irregularities of the rails caused by long-term operation as well as the eccentricity of the wheels. In this paper, spectral analysis is conducted on the basis of measured data from the site and then the vibration load of the train is derived; finally the value of the vibration load is calculated.
The expression of the oscillogram of actually measured rail acceleration (as shown in Figure
Measured rail vertical acceleration time history curve.
The acceleration oscillogram is divided into
The result of formula (
In formula (
So the Fourier coefficients are as follows:
The deterministic expression of the rail vibration oscillogram is
In the above formulae,
Before the simulation of train vibration load and when the train model is simplified, the following hypothesis needs to be made [ A running train produces much greater vertical excitation than horizontal excitation on the railway roadbed beneath the rail, so the horizontal excitation can be ignored. Regarding the impact on bounce between the wheel and rail and the sway and nodding of the train in motion, suppose the weight of the train can be evenly distributed on the wheels; we can take only one wheel system as the computation model. The simplified model of simulated interaction between the rail and wheel system is shown in Figure
Simplified model of wheel and rail.
In Figure
The dynamic balance equation of the wheel system is established as follows:
If the bounce effect between rail and wheel is ignored, the vertical acceleration
Equation (
According to vertical dynamic equilibrium conditions, the wheel-rail interaction force
Equation (
Assuming that
In this paper, the object of analysis is the deep foundation pit works of the New Chengdu Museum; east of the museum is the Tianfu Square Station of the Chengdu Metro. The train speed varies from 10 to 30 km when entering and leaving the station. According to a large amount of actual measurements of subway train vibrations made by domestic and foreign scholars, the ambient vibration induced by a running train increases with the increase of train speed. The train dynamic load diagram (Figure
Subway train vibration load diagram.
The deep foundation pit of the New Chengdu Museum is located west of Tianfu square, adjacent to Renmin middle road on the east and Xiyu street on the south, Xiaohe street on the west, and Sudu road on the north. The foundation pit is next to the Tianfu square transit hub of Chengdu metro. The foundation pit excavation line has a circumference of 410 m and an excavation depth of 25.4 m, with areas 26.6 m deep. A base isolation system has been adopted for the structure. The site elevation ±0.00 is equivalent to an absolute elevation of 504.50 m. The absolute elevation of the surrounding environment is about 502.50 m (−2.20 m); the pit bottom elevation is −25.40 m (−26.60 m in some areas).
The floor plan of the foundation pit is shown in Figure
Floor plan of deep foundation pit of Chengdu Museum.
The deep foundation pit works of the Chengdu Museum are taken as an example to establish a dynamic numerical model for deep foundation pits. First, the pit excavation static values calculations and then the dynamic calculations are conducted. Therefore, after excavation and support structure completion in static value calculation, the pit model can be used as a basic model for dynamic analysis, as shown in Figures
Numerical model after static calculation.
Support pile and top beam structure model.
Lining work and prestressed cable structure model.
In accordance with Geotechnical Investigation Report of the New Chengdu Museum, geotechnical material parameters of the deep foundation pit of new Chengdu Museum are listed in Table
Geomaterial parameters table.
Material | Stratum | Density |
Deformation modulus |
Poisson’s ratio |
Friction angle |
Cohesion |
Tensile strength |
Thickness (m) |
---|---|---|---|---|---|---|---|---|
1 | Miscellaneous fill | 1.75 | 30 | 0.35 | 9.0 | 0.01 | 0.00 | 1.4 |
2 | Slightly compact gravel | 2.10 | 50 | 0.28 | 38.0 | 0.00 | 0.00 | 3.5 |
3 | Moderately compact gravel | 2.15 | 60 | 0.25 | 43.0 | 0.00 | 0.00 | 4.5 |
4 | Compact gravel | 2.20 | 70 | 0.22 | 45.0 | 0.00 | 0.00 | 7.0 |
5 | Strong weathering | 2.25 | 200 | 0.28 | 30 | 0.08 | 0.01 | 9.0 |
6 | Moderately weathered mudstone | 2.30 | 500 | 0.30 | 35.0 | 0.30 | 0.10 | 50 |
In a numerical simulation of deep foundation pit excavation and support structure construction, the parameters for the support piles, top beam, and anchor cable of the support structure need to be set. In this paper, support structure parameters are provided according to the
Supporting pile body design parameters.
Location | Diameter (m) | Length (m) | Embedded depth (m) | Spacing (m) | Top beam section (m × m) | Clear distance between front and rear row piles (m) |
---|---|---|---|---|---|---|
North | 2.0 | 26.5 | 5.6 | 2.8 | 2.0 × 1.0 | 2.0 |
East | 1.2 | 26.5 | 5.1 | 2.0 | 1.2 × 0.8 | — |
South | 1.2 | 26.5 | 5.1 | 2.0 | 1.2 × 0.8 | — |
West | 1.2 | 26.5 | 5.1 | 2.0 | 1.2 × 0.8 | — |
Design parameters of anchor cables of northern support pile system.
Location | Anchor cable Location | Dip | Anchor cable length | Anchoring segment length | Anchoring location | Rod form |
---|---|---|---|---|---|---|
1st anchor cable | −10.0 m | 5°~10° | 25.0 m | 17.0 m | One pile with one anchor | 7 steel strands |
2nd anchor cable | −13.0 m | 5°~10° | 25.0 m | 17.0 m | One pile with one anchor | 7 steel strands |
Design parameters of anchor cables of eastern, southern, and western support pile systems.
Location | Anchor cable location | Dip | Anchor cable length | Anchoring segment length | Anchoring location | Rod form |
---|---|---|---|---|---|---|
1st anchor cable | −9.0 m | 10°~15° | 25.0 m | 17.0 m | One pile with one anchor | 7 steel strands |
2nd anchor cable | −12.0 m | 10°~15° | 25.0 m | 17.0 m | One pile with one anchor | 7 steel strands |
3rd anchor cable | −15.0 m | 10°~15° | 25.0 m | 17.0 m | One pile with one anchor | 7 steel strands |
4th anchor cable | −18.0 m | 10°~15° | 25.0 m | 17.0 m | One pile with one anchor | 7 steel strands |
In a dynamic analysis numerical model, the four monitoring points of DC3, DC5, DC7, and DC8 are established surrounding the deep foundation pit (refer to Figure
Time history diagram of surface displacement at the monitoring points surrounding the foundation pit. West monitoring site DC3 (black), south monitoring site DC5 (red), east monitoring site DC7 (purple), and north monitoring site DC8 (blue).
As can be seen from a comparative analysis of the four subsidence curves in Figure
Taking Nanjing Metro Line 2 as an example, Yang and Cao [
Figures
In the dynamic analysis, the soil body is usually regarded as continuous medium. In fact, soil body consists of the framework (soil particles) and the fluid inside the pore, once the cementing force between soil particles becomes smaller, the framework of soil body is more instable. The vibration load of subway trains is weaker than that of explosion or earthquake load, the energy loss is also smaller because of the relative motion between particles, the soil raises the compressive stress with a little tensile stress, and it keeps the elastic-viscous and is not destroyed.
Figure
Time history curve of pile bending moment at the monitoring points monitoring site DY1 (black), monitoring site DY2 (red), and monitoring site DY3 (blue).
Comparison between the three curves in Figure
Figure
Anchor cable axial force time history. Monitoring site DM1 (black), monitoring site DM2 (red), monitoring site DM3 (purple), and monitoring site DM4 (blue).
Sectional view of foundation support structure.
Comparison between the four curves in Figure
Spectral analysis was conducted on rail acceleration oscillograms and the train vibration loads were derived. Taking the deep foundation pit of the New Chengdu Museum as an example, a dynamic three-dimensional numerical model was built that considers the vibration load of subway trains, and the following conclusions were drawn through calculation and analysis: Foundation pit soil subsidence: In the sandy cobble stratum media of Chengdu Plain where the site lies, the dynamic response of surface displacement mainly occurs in the early period of dynamic load. Train vibration is damped fast. The energy of surface displacement decays due to the damping of stratum soil in the later period of dynamic loading (1 s–7 s). The vibration load of subway trains has little impact on ground subsidence (the maximum subsidence is only −2.26 mm), no more than Foundation pit Earth pressure: The vibration of subway trains has significant impact on the Earth pressure behind the pile, and the closer the origin of vibration, the more intense the dynamic response. Dynamic response of support piles: The support piles’ internal force dynamic response occurs between 0 s and 4 s. After the dynamic response of the support piles under the effect of train vibration loads, the residual internal forces are smaller than the calculated initial values of dynamics, respectively, 80 kN·m, 22 kN·m, and 30 kN·m. Therefore, it can be approximated that the vibration response of the support pile structure of the foundation pit occurs under the effect of train vibration and the dynamic response process is in an elastic state. Dynamic response of prestressed cables: The axial force response of the first and fourth row of anchor cables is weak and that of the third row is the most obvious, followed by that of the second. Subway train vibration changes the initial internal force distribution of prestressed cables and the force gathers inside the cables. Therefore, the action of train vibration loads is inimical to the safety of foundation pit support structures and should be closely studied. The supporting structure of piles and anchor cables has to be adopted due to the foundation pit depth up to 25.4 m; no negative influence of metro vibration on prestressed cable’s power has been discovered in foreign and domestic reference literature, from which the unique feature of this study is induced.
All the authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge the project supported by the National Natural Science Foundation of China (Grant no. 41302256) and SWPU Geotechnical Mechanics and Engineering Science & Technology Innovation (Cultivation) Youth Team (no. 2013XJZT006).