SEISMIC DAMAGE ANALYSIS OF DOUBLE-DECK SUBWAY STATION
Guozheng XU，Zhixin YIN，Yanjia QIU，Hongru ZHANG
School of Civil Engineering，Beijing Jiaotong University，Beijing 100044
Abstract：In this paper，the failure process of a double-deck subway station under the action of strong earthquakes is analyzed.At first，the construction process is simulated by excavating the soil from the structure frames in order to obtain the initial static stress of the structure and the surrounding soil.Then the seismic response behaviors are calculated by non-linear dynamic time-history analysis method in which the soil and structure were modeled by linear-elastic and elasto-plastic model.The failure process was considered by increasing the peak acceleration of the seismic ground motion，until the ultimate internal force was reached in any structure member.To estimate the effect of ground motion characteristic，three seismic acceleration records（1990 Upland，1989 Loma Prieta and 1998San Juan Bautista）are used as the seismic excitation to compare the failure behaviors.The simulation result shows that when the acceleration of the earthquake reached 0.4 g，the plastic zone would appear in the joint between the middle plate and the side wall of the underground structure；The failure is always caused by the loss of bending bearing capacity while the member can still resist axial force.Furthermore，the 1998 San Juan Bautista record produces the minimum internal force among the three earthquake records with the same peak acceleration.
Keywords：subway station，seismic damage，failure process，non-linear analysis
Email：1564480490@qq.com
1 Introduction
In recent years，subway has been highly popularized with the high-speed development of economy and the increasingly serious traffic congestion[1].The failure of the Daikai Station in Japan（1995）caused by the earthquake has aroused wide attention in civil engineering field[2-3].Therefore，seismic design of underground structure is becoming an important direction of earthquake engineering.
Liu[4]studied the feasibility of Pushover analysis method in different structure’s burial depth，soil’s stiffness and structure’s stiffness.He also used Pushover analysis method to study how different factors（parallel tunnel distance，material properties，and lining thickness，etc.）influence the seismic response of metro shield tunnel.Based on lumped mass model of soil-structure dynamic interaction system，Chen[5]proposed a simplified method of soil-underground structure dynamic interaction system constructed with the consideration of the shear stiffness and damping characteristic of equivalent soil layers.Ren[6]employed the SBFEM（Scaled Boundary Finite Element Method）in the seismic response analysis of the underground structures under inhomogeneous medium.Jiang[7]used the coupling method of spline finite element method and semi-analytical infinite element to analyze the seismic response of underground tunnel structure.Chen[8]compared large-size shaking table test results and numerical simulation of a subway station structure based on ABAQUS.
In this paper，we studied the internal force of different parts of a double-deck subway station under earthquake excitation based on PLAXIS8.5and the failure process was obtained.Two main subjects were studied：where and when the plastic zone could be found first and different principles of failure under three types of seismic wave.
2 Analytical Model and Parameters
2.1 Modeling
To study the dynamic response and failure process of double-deck subway station under different earthquake excitation，elasto-plastic dynamic soil-structure numerical model is built up.
2.1.1 Model of structure
The model of the double-deck three-span structure derives from a subway station of the urban rail transit line in Hefei City，Anhui Provence.The standard cross section and the surrounding soil deposit are shown in Figure 1.
Figure 1 Model of structure
The structure has a total width of 21 m and a total height of 12.05 m，the structure member size is shown in Table 1.
Table 1 Size of structure（m）
The structure is modeled as plane plate element.In the plane strain numerical model，the stiffness of the structure is distributed in the column space of 6 m to obtain the equivalent parameters in unit thickness along the 3rd direction.The structure is simulated using 5nodes Euler beam element.
2.1.2 Model of soil
The soil is composed of six layers，and the thickness of soil layer is shown in Table 2.
Table 2 Thickness of soil（m）
The geometric model of soil is simulated with a method to form plane strain triangle element with 15 nodes in finite element calculation.
The soil’s total thickness is 55 m，modeling from the bottom y=0 to the top y=55.With the structure model’s total width of 21 m，the boundary value has a great influence on the calculation in seismic analysis.In this case，we take soil model into consideration whose width is five times the width of structure model on both sides from the left boundary x=-90 to the right boundary x=110，the total width of which is 200 m.
2.2 Material parameters
2.2.1 Parameters of soil
Mohr-Coulomb model is applied to soil，whose material parameters are shown in Table 3.
Table 3 Material parameters of soil
2.2.2 Parameters of structures
The structure is simulated by using the elasto-plastic model，whose material parameters are shown in Table 4.
Table 4 Parameters of concrete
2.3 Boundary condition and seismic input
Viscous boundary is applied to left and right sides of the model while the free boundary is applied to the top.Seismic waves are input from the bottom of the model，as is shown in Figure 2.Rayleigh damping[9]is adopted to account the energy dissipation.
Figure 2 Model of interaction between soil and structure
We need to zoom and integrate seismic acceleration according to the seismic intensity to get the displacement after scaling.Finally seismic effect will be input in the form of displacement.
We choose three representative earthquakes in American history，which are 1990 Upland，1989 Loma Prieta and 1998 San Juan Bautista.Their original peak accelerations are 0.24g，0.22g and 0.10g respectively.The specific acceleration time-histories curves are shown in the Figure 3.
Figure 3 Time history curves of different seismic waves
3 Result of Calculation and Analysis
3.1 Results under 1990 Upland seismic waves
We set different multipliers for 1990 Upland earthquake wave to obtain different accelerations.Then we get the bending moment and axial force of the different component of the model which are shown in Figure 4，Table 5 and Table 6.We found that axial forces are still not beyond the bearing capacity of structures even when the acceleration reached 0.8g.On the contrary，when the acceleration reached 0.4g，the bending moment is beyond the capacity of the structure.And the first parts of the model damaged are the joint between the side wall and middle plate.We also found that the plastic zones always appeared in both end of the components.
Figure 4 Bending moment and axial force of 1990 Upland
Table 5 Maximum axial force of different components of model
Table 6 Maximum bending moment of different components of model
3.2 Results under different characteristics of seismic waves
We change the types of earthquake to explore how the structure response to the different characteristics of seismic wave in the same acceleration by adjusting the multiplier.We found the similar conclusion as 1940.But the internal force results differ.Table 7 and Table 8show results of the bending moment and axial force in the structure under the three characteristics of seismic waves whose acceleration reaches 0.6g.Although seismic waves have the same maximum accelerations，but structure’s seismic response behaves obvious differences because of the different characteristic of frequency.
Table 7 Maximum axial force of different components of model
Table 8 Maximum bending moment of different components of model
4 Conclusions
（1）When the acceleration of the 1990 Upland seismic wave reaches 0.4g，the plastic zones appear in structure.With the increasing earthquake acceleration，we can find the main damage type is bending failure and almost no tension and compression failure.
（2）The damages always appear not at the column but at the ends of the beams firstly in our simulated seismic model.
（3）Although seismic waves have the same maximum accelerations，but structure’s seismic response exists obvious differences because of the different characteristic of frequency.The axial force and bending moment in structure caused by the 1998 San Juan Bautista seismic wave were significantly lower than 1990Upland and 1989 Loma Prieta seismic waves.
References
[1]Qian Q.H.，2000.Modern Technology of Underground Space Development and Utilization in City and its Developing Trend[J].Railway Construction Technology，5：1-6.
[2]Cao B.Z.，Luo Q.F.，Ma S.，et al.，2002.Seismic Response Analysis of Dakai Subway Station in Hyogoken-nanbu Earthquake[J].Earthquake Engineering and Engineering Vibration，22（4）：102-107.
[3]Okada T.，Hasegawa A.，Suganomata J.，et al.，2007.Imaging the Heterogeneous Source Area of the 2003 M6.4 Northern Miyagi Earthquake，NE Japan，by Double-difference Tomography[J].Tectonophysics，430（1-4）：67-81.
[4]Liu J.B.，Liu X.Q.，Li B.，2008.A Pushover Method for Seismic Response Analysis and Design of Underground Structures［J］.China Civil Engineering Journal，41（4）：87-94.
[5]Chen G.X.，Zuo X.，Du X.L.，2010.A Simplified Method of Seismic Response Analysis of Soil-underground Structure System[J].Rock and Soil Mechanics，31（s1）：1-8.
[6]Ren H.M.，Lin Q.，2005.Seismic Analysis of the Underground Structures Based on SBFEM[J].Journal of Anhui Construction Industry Institute，13（3）：28-31.
[7]Jiang X.L.，Song L.M.，1999.Seismic Response Analysis of Underground Tunnel in Soft Soil[J].Earthquake Engineering and Engineering Vibration，19（1）：65-69.
[8]Cheng G.X.，Zuo X.，Zhuang H.Y.，et al.，2008.A Comparison between Large-size Shaking Table Test Results and Numerical Simulation of a Subway Station Structure[J].Journal of Earthquake Engineering and Engineering Vibration，1：157-164.
[9]Spears R.E.，Jensen S.R.，2012.Approach for Selection of Rayleigh Damping Parameters Used for Time History Analysis[J].Journal of Pressure Vessel Technology，134（6）：67-75.
ICRE2016-International Conference on Railway Engineering