Seismic responses of subway station with different distributions of soft soil in Tianjin

Abstract

In connection with the practical project of Kunming Road station of Tianjin subway Line 3, the paper established a two-dimensional finite element model with visco-elastic boundary by using ANSYS and analyzed seismic responses of subway station with different distribution of soft soil. The nonlinear dynamic properties of soft soils are modeled by the KINH. And obtain the response rules about displacement and internal force on subway station in the general field soil and five different distributions of soft soil. Provide reference for improving the seismic performance of subway stations in Tianjin soft soil.

Keywords

distribution of soft soil / soft soil in Tianjin / seismic response / ANSYS

Introduction

Earthquakes in history have proved that [1–3], the foundation in soft soil will increase the destructive degree under the action of earthquake. And Tianjin region belongs to soft soil foundation, the geological conditions are generally poor, and the soft soil layer is thick, there generally exist muddy clay, muddy silty clay, clayey silt which is easy to vibrate and liquefy, sandy silt and silty sand and so on among the shallow layer. It will increase the damage in earthquake.

The current research about seismic responses of underground structure such as subway station in soft soil site is still in the preliminary stage, Bai et al. [4] and Zheng et al. [5] have researched the seismic performance of subway tunnel in soft soil foundation, but researches about seismic performance of subway station structure in soft soil foundation is quite a few. Zhuang et al. [6] have comparatively studied the seismic response rules of subway station structure in different soft soil sites, but the related research results are not enough to guide the selection and seismic designation of engineering projects of the subway station structure in complex soft soil sites in Tianjin. It is necessary to analyze the dynamic responses and study design methods about the subway station structure in soft soil foundation in Tianjin area in connection with underground engineering structural characteristics and soil conditions.

Engineering situation and the determination of calculation model parameters

Dynamic constitutive model of the soil

Dynamic constitutive model of the soil adopts multilinear kinematic hardening model which is mainly based on the model of Besseling [7] (also known as sublayer model and overlay model [8]) to analyze the dynamic property of elastic-plastic material. This model can take a full consideration to nonlinear characteristic of soil material under earthquake load. It is widely used by elastic-plastic material which has characteristic of strain hardening and within the scope of cyclic loading .So it is taken for ideal constitutive model for studying dynamic responses under earthquake. Its principle assumes that the elastic-plastic material is composed of multiple sub surfaces, and each of them with different yield strength could produce the same strain. Each sub surface based on the principle of ideal elastic-plastic stress-strain relationship carries on the simple elaboration, but the combination of them can depict the complex properties of soil materials, and depict the stress-strain relationship curve through the elastic modulus E, Poisson's ratio ν and the breakpoint coordinate (ξ_k, σ_k) on the stress-strain relationship curve finally, just as seen in Fig. 1. Every breakpoint on poly-lines reflects the yield performance of one sub surface.

The engineering site conditions

According to the national standard of “Seismic ground motion parameter zonation map of China” (GB18306-2001) (10% probability of exceedance in 50 years), the basic seismic intensity of the site is VII, classification of design earthquake is Group 2, the ground motion peak acceleration is 0.15 g. The classifications of site soil for subway construction and construction site are ruled according to the national standard of “railway engineering seismic design specification” (GB50111-2006) which regulated that, based on the test result of geophysical shear wave velocity, the equivalent shear wave velocity within the scope of 25 m is 178 m/s, the site soil belongs to medium soft soil, the classification of site is Level III. According to the survey report of geotechnical engineering on Kunming Road station of Tianjin subway Line 3, the main design parameters of the foundation soil where the station structure located are shown in Table 1, a total of 7 soil layers. This paper assumed that the soft soil is muddy clay (soil layer No. 4), and the distributions of soft soil can be seen in Table 2.

The establishment of numerical model and mesh generation

The Kunming Road station of Tianjin subway Line 3 adopts the frame structure with three-layer and three-span under the ground. The main structural section sizes of the station are shown in Fig. 2.

The soil is simulated by PLANE42 unit with four nodes and the frame structure is simulated by BEAM3 unit with two nodes. The usage of different units with common nodes between the soil and structure realizes the interaction of structure-soil while meshing the grid; it is able to simulate the structural internal force changes and deformation caused by the soil displacement under earthquake action. The total thickness of soil is 81.308 m, and the frame structure uses C50 concrete whose model parameters listed as follows, elastic modulus E = 3.45e⁴ MPa, the density ρ = 2550 kg/m³ and Poisson's ratio ν = 0.20.

The boundary conditions

The bedrock surface adopts fixed constraint when modeling, both sides of the soil use visco-elastic boundary to simulate the earthquake energy dissipating toward the infinity [9], the visco-elastic boundary spring damper parameters k = 2.0e6 and the elastic damping coefficient c = 0.4. The calculation model and mesh generation are shown in Fig. 3. And the two parameters are calculated by formulas below.

(1)C_{\mathrm{s}}=\sqrt{{\displaystyle \frac{G}{\rho }}},

(2)C=\rho C_{\mathrm{s}},

(3)k=\mathrm{2}{r}_{\mathrm{b}},

where G is shear modulus, ρ is mass density, r_b is the distance between wave source and artificial boundary.

Seismic wave input

The Tianjin Ninghe horizontal seismic wave is inputted from the bedrock, whose sampling frequency is 0.01 s, duration is 19.19 s, and the peak acceleration is 104.18 cm/s².The acceleration time-history curve of the seismic wave in basic seismic intensity is shown in Fig. 4, and the adjustment coefficient of seismic wave intensity is 1.41.

Results of analysis

The horizontal displacement nephogram occurred at the time of maximum deformation of station structure in general field is shown in Fig. 5, we can know that, the maximum absolute displacement appeared in nodes of the bottom side walls and bottom plate at 7.67 s, and the displacement is 0.0725179 m with the direction for the negative direction of X axis, the absolute amplitudes of displacement present a trend of increasing in turn from the top to the bottom of the station structure. At this moment, the corresponding equivalent stress nephogram of the structure is shown in Fig. 6, the maximum stress occurred at the connected joints of the interior columns and bottom plate, the value of equivalent stress can be up to 982.044 kPa, and the equivalent stress of side walls and each floor is less than the corresponding value of each node of the interior columns. The equivalent stress of the structural floor, the interior columns and the middle of the side walls is generally less than that of the each node of the structure.

The influences on structural displacement exerted by the distribution of soft soil

Strong earthquake will lead to a large dynamic deformation of the soft soil, and the deformation will directly act on the side walls of subway station structure, so as to cause the local large deformation of the station structure. This paper analyzed the relative lateral displacements of side walls of the station structure in different soft soil sites, the relative lateral displacements along the height of side walls of subway station structure in different soft soil sites are shown in Fig. 7, the relative displacement time-history curve of the top plate of station structure is shown in Fig. 8. Table 3 lists the relative displacement amplitude and the occurrence time between the top and bottom plate of station structure.

As shown in Figs. 7, 8 and Table 3: 1) In soft sites of Nos. 1–3, the relative displacement amplitude at each key point of the side walls of station structure increases with the embedded depth of soft soil layer increased, and is bigger than that in the general field. And in soft site of No. 3, the horizontal relative displacement amplitude of each key part of the side walls reaches the maximum. From the overall structural seismic point of view, when the soft soil layer is distributed in the lateral foundation of the subway station structure, the lateral displacement response of the side walls of station structure is stronger, and is easier to cause the destruction of the station structure. 2) In soft sites of Nos. 4 and 5, with the embedded depth of soft soil distribution increased, the horizontal relative displacement amplitudes on key parts of the side walls of station structure are decreasing, and are less than the corresponding value in general field. It indicates that the swing amplitude from side to side of station structure gradually becomes weak. From the overall structural seismic point of view, when the soft soil layer is distributed at the bottom foundation of the subway station structure, the dynamic nonlinear large deformation occurred in soft soil layer will have effects on energy dissipation and vibration reduction, with the embedded depth increased, the dynamic displacement response of station structure is less intense, while the effects of seismic isolation and shock absorption of station structure are more obvious.

The effects on the structural internal force in the distribution of soft soil

This paper analyzed the dynamic internal force response on the key sections of structural interior columns, and the key section positions and numbers are shown in Fig. 2. Table 4 has given the peak internal forces on the key sections of interior columns in different distribution of soft soil, also provided the variation of the ratio (which is also called internal force response coefficient in this paper) of internal force response amplitude on the key sections of interior columns in different soft soil sites and general field with the distribution of soft soil, just as shown in Fig. 9.

Table 4, Fig. 9 and Fig. 10 showed that:

1) When the soft soil layer is located in the lateral foundation of subway station structure, the dynamic internal force responses in the upper interior columns are fewer than that in the lower interior columns. The moment response coefficient of interior columns in the No. 1 soft site is about 1.1–1.5, shear response coefficient is about 0.8–1.4; The moment response coefficient of interior columns in the No. 2 soft site is about 1.8–3.0, shear response coefficient is about 1.2–2.6; The moment response coefficient of interior columns in the No.3 soft site is about 1.4–3.7, shear response coefficient is about 1.3–2.5; the No. 2 soft site has more obvious effects on internal force response on the upper sections of interior columns in underground first story than the effects which are caused by No. 1 and No. 3 soft sites .And with the embedded depth of lateral soft soil layer increased, the dynamic internal force responses of bottom interior columns also become large gradually. We can initially identified, when the soft soil layer is located in the lateral position of intermediate floor of the subway station structure, it has the greatest impact on dynamic internal force response on the upper sections of interior columns in underground first story, while the soft soil layer is located at the bottom of the side walls, the corresponding dynamic internal force response reaches the maximum.

2) When the soft soil layer is located at the bottom of the subway station structure, due to its effect of shock absorption and seismic isolation, the internal force response of the station structure is weaker than that in the general field; especially the weakening effect on the internal force response of interior column is more obvious.

Conclusions

In this paper, numerical simulation is carried out by the seismic response of subway station structure in different distributions of soft soil in Tianjin soft site, and compared with it in general field; the influences of displacement and internal force response of subway station structure in different distributions of soft soil are summarized as follows:

1) The maximum absolute displacement of station structure in general field happened to the bottom nodes and bottom side walls, the absolute amplitudes of displacement present a trend of increasing in turn from the top to the bottom of the station structure. The equivalent stress of each key position in the interior columns is the maximum at this moment, especially the peak stress in the connection of interior columns and the bottom plate reaches the maximum, and is the most advanced into the stage of plastic failure under strong earthquake action, so the bottom interior columns are the seismic weak links for the whole station, and should be designed deliberately.

2) When the soft soil layer is located in the lateral foundation of subway station structure, along with the increasing of the embedded depth of soft soil layer, the absolute value of the amplitude of lateral relative horizontal displacement increases, and is larger than the amplitude of displacement response of station structure in general field. That is to say, from the overall structural seismic point of view, when the soft soil layer is located in the lateral foundation of subway station structure, the dynamic deformation of station structure reacted strongly, and is more likely to cause destruction of the station structure.

3) When the soft soil layer is located in the lateral foundation of subway station structure, it will produce significant amplifications on dynamic internal force responses of the key parts of subway station structure, and the different relative embedded depth of soft soil layer has different amplify effects on internal force in different parts of the subway station structure, the local internal force reaction coefficient can be up to as much as 3–4 times of the corresponding value in the general field .Therefore, the different distributions of soft soil in the lateral of subway station structure will result in serious local earthquake damage of the subway station structure.

References

[1] DowdingC H, RozenA. Damage to rock tunnels from earthquake shaking. Journal of the Geotechnical Engineering Division, ASCE (GT2), 1978: 175–191

[2] UenishiK, SakuraiS. Characteristic of the vertical seismic waves associated with the 1995 Hyogo-Nanbu (KOBE), Japan earthquake estimated from the failure of the Dakai underground station. Earthquake Engineering & Structural Dynamics, 2000, 29(6): 813–821

[3] IidaH, HirotoT, YoshidaN, IwafujiM. Damage to Dakai subway station. Soils and Foundations, 1996, 34: 283–300

[4] BaiY, ZhouJ. Tunnel seismic stability analysis of soft soil layer. Journal of Foshan University, 2001, 19(1): 39–44 (in Chinese)

[5] ZhengY L, LiuS G, TangL D, TongF. Study on seismic design of subway tunnel in soft soil. Underground Space, 2003, 23(2): 111–118(in Chinese)

[6] ZhuangH Y, WangX X, ChenX G. Earthquake responses of subway station with different depths of soft soil. Journal of Geotechnical Engineering, 2009, 31(8): 1258–1266(in Chinese)

[7] BesselingJ F. A theory of elastic, plastic, and creep deformations of an initially isotropic material showing anisotropic strain-hardening, creep recovery, and secondary creep. Journal of Applied Mechanics, 1958, 25: 529–536

[8] OwenR J, PrakashA, ZienkiewiczO C. Finite Element Analysis of Non-Linear Composite Materials by Use of Overlay Systems. Computers & Structures, 1974, 4(6): 1251–1267

[9] BaoP, ShengG L. Study on seismic performance of subway station. Journal of Henan University, 2009, 39(4): 428–431 (in Chinese)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg