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The 12 International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6 October, 2008 Goa, India

th

Comparative Analysis on Earthquake Response of Subway Tunnels between Numerical Simulation and Shaking Table Test

CHEN Guo-xing ZUO Xi, ZHUANG Hai-yang

Institute of Geotechnical Engineering, Nanjing University of Technology, Nanjing, China

DU Xiu-li

College of Architecture and Civil Engineering, Beijing University of Technology, Beijing, China Keywords: subway tunnels; numerical simulation; shaking table test ABSTRACT: Based on the shaking table test result of the dynamic interaction between soil and subway tunnel in liquefiable soil, a 2-D nonlinear dynamic interaction finite element model is established to simulate the system of soil-tunnel with the platform of ABAQUS. In the finite element model, dynamic viscoplastic model with memorial nested yield surface is used to simulate the dynamic characteristic of soil, while the plastic-damage model is used to simulate the dynamic characteristic of concrete. Corresponding to the test conditions, all the instances are simulated. Compared with the test record, it is proved that both the finite element model and the shaking table test are correct, their results are well identical with each other's and the rules are coincident as well.

1 Introduction

With the development of the economy and the urban population, the urban traffic becomes the bottle-neck to hinder the development. Though the road area is limited, and people begin to establish underground traffic to release the tension. The underground structures, being confined by the surrounding rock or soil, are usually assumed to have good anti-seismic ability. However, according to earthquake disaster in recent years, the underground structures are not always safe. Therefore, it is necessary to study on seismic behavior of underground structure. So far, many researchers have learnt about the seismic response of underground structures. Liu Jingbo(2005) analyzed the seismic response of shield tunnels with complex response method, and also analyzed the influence of the factors such as the distance between the twins tunnels, the elastic modulus, thickness of the lining etc. Hongbin Huo(2003) compared the destruction of Dakai subway station and the finite element numerical simulation results, taking ABAQUS as simulation platform and considering the interaction between vertical and horizontal seismic. The feasibility of the finite element analysis about underground structure and soils is well proved. Yang Linde(2003) designed the model box and conducted shaking table model test on subway station. Then, the numerical simulation of model test is performed based on the Lagrangian difference algorithm. Due to lack of measured data and test record, numerical simulation without comparative object becomes the chief treatment method for seismic response of soil-underground structure system. In order to verify the reasonableness of calculation model and the reliability of test results, the comparison research between numerical simulation results and model test records is very necessary. In this paper, the numerical simulation of subway tunnels is well conducted with the platform of ABAQUS software to analyse the dynamic interaction between soil and subway tunnels. And then, the numerical simulation results are compared with the test results.

2 Brief introduction about large-size shaking table model test of liquefiable soil-subway tunnels

The test is conducted on the large-size shaking table(6m×6m,80t) in China Construction Science Research Institute. In the test, Nanjing fine sand is used as model soil with some clay on the top and the bottom of the model box. The thickness of clay, sand and clay layers in model ground is respectively 0.24m, 1.2m and 0.16m

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from top to bottom in the model box, and the width of model ground is 4.1m. The thickness of overlaying soil above subway station structure is 0.08m. In order to decrease the effect of rigid boundary to structural dynamic response, two polystyrene foam boards are placed beside two sidewalls of model box respectively. As preparation work of the test, the physical characteristics of model soil and micro-concrete are obtained by laboratory experiment. The schematic section of subway tunnels and arrangement of accelerometers is showed as Figure.1. The acceleration response of model soil and the strain response of model structure with different conditions under Kobe wave, El-Centro wave and Nanjing artificial wave are all recorded. The basic laws of seismic response of tunnel in liquefiable soils are recognized. The test records also provide some data for perfecting the analysis methods of seismic response of subway tunnels.

Fig.1 Schematic section of subway tunnels and site model, arrangement of accelerometers (unit: mm)

3 Analysis method of seismic response of liquefiable soil-subway tunnels

Based on implicit integration method, the soil-subway tunnels system is simulated as a plane strain problem. The calculation region is the scope of model box. The shaking table test is used to be simulated the seismic response of subway tunnels under horizontal ground motion, so there is free in horizontal direction and a constrained in vertical direction at the bottom and lateral boundaries in the model. The grids become bigger gradually from near station structure to the boundary, the meshes of soil-subway tunnels system in 2-D finite element analysis are showed as Figure.2. The model soil and subway tunnels are simulated by 4-node plane strain elements. In order to accelerate the calculation speed, reduced integral elements are used to simulate model soils, and complete integral elements are used to simulated model structure. The contact pairs are used to simulate dynamic transfer property between soil and tunnels. Dynamic visco-plastic memorial nested yield surface model is used to simulate the dynamic characteristics of soil. In the constitutive model, the inverted loading surface, the failure surface and the initial loading surface which was tangent with the inside of inverted loading surface were memorized at the end of any increment, and dynamic behavior of yield surface was defined by these surfaces. The soil density is measured by laboratory experiment. The average velocity of shear wave of model soil is measured by SUMIT shallow seismograph. The physical and mechanical parameters of model soils are listed in Table.1. The subway tunnels are of micro-concrete. Plasticdamage model is used to simulate dynamic characteristics of subway tunnels concrete. In the constitutive model, the two damage variables are used to describe stiffness attenuation law during the processes of tension failure and compressive failure of concrete, and many hardening variables are also used to modify the yield function. According to similarity law, the model parameters are determinate, and they are listed in Table.2. Crushable foam model is used to simulate the characteristics of foam board. The parameters are as follows: the 3 elastic modulus is 4.13MPa, the poisson ratio is 0.07 and the density is 15kg/m . Rigid material is used to simulate the model test box, whose elastic modulus of material is 200Gpa and the poisson ratio is 0.3.

Fig.2 Meshes of soil- subway station structure system in two dimensional finite element analysis

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Table.1 Physical and mechanical parameters of model soils

Soil layer Clay Slit fine sand Slit fine sand Slit fine sand Slit fine sand Slit fine sand Clay Thickness (m) 0.16 0.24 0.24 0.24 0.24 0.24 0.24 Density 3 (g/cm ) 1.75 1.80 1.80 1.80 1.80 1.80 1.85 Velocity of shear wave (m/s) 40 40 50 60 80 100 120 Poisson's ratio 0.49 0.49 0.49 0.49 0.49 0.49 0.49 Friction angle (°) 15 20 20 20 20 20 17

4 Comparative analysis between numerical simulation results and shaking table test records 4.1 Acceleration response

Table.2 Dynamic Plastic-damage model parameters of microconcrete for subway tunnels The test records and numerical simulation results of accelerometers A1, A9 and A12 Model parameters Parameter values are compared under S-K2, S-N2 and S-E2 Elastic modulus E (MPa) 0.85×104 test condition, and the acceleration timehistory and Fourier spectra are shown as 0.18 Poisson's ratio Figure.3, Figure.4 and Figure.5. The 3 2500 Density (kg/m ) second letter K, E, N denote the action of Kobe wave, El-Centro wave, Nanjing 32.4 Expansion angle (°) artificial wave respectively, the number 1, 2, 3 denote the load levels. It is shown from Initial yield compressive stress c0(MPa) 3.91 the figures that waveform change of Ultimate compressive stress cu (MPa) 5.69 acceleration time-history from the test Initial yield tensile stress t0(MPa) 0.68 records is in accordance with the numerical simulation results', so is the characteristic 0 t of Fourier spectrum obtained from 1 0 acceleration time-history. The result shows that the numerical simulation method can dc 0 well simulate the seismic response of 0.1 subway station structure in liquefiable soil. The variation law for positive peak acceleration and negative peak acceleration is showed as Figure.6. The peak acceleration of test records for accelerometers A1 and A12 under different load conditions is listed in Table.3 and Table.4. In general, the numerical simulation results are in accordance with the test records under Kobe wave and Nanjing artificial wave, and the similarity of numerical simulation results and the test records is a little weaker under El-Centro wave.

0. 6 Accel er at i ong

Accel er at i ong 0. 6 Accel er at i ong 0. 4 0. 2 0 - 0. 2 - 0. 4 - 0. 6 0

A9 N er i cal si m at i on um ul A9 Test r ecor ds

0. 6 0. 4 0. 2 0 - 0. 2 - 0. 4 - 0. 6 - 0. 8 0

A12 N er i cal si m at i on um ul A12 Test r ecor ds

0. 4 0. 2 0 - 0. 2 - 0. 4 - 0. 6 0 1 Timesec

A1 N er i cal si m at i on um ul A1 Test r ecor ds

A1 N er i cal si m at i on um ul A1 Test r ecor ds

2

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Four i er spect r um / s m

Four i er spect r um / s m

0. 2 0. 15 0. 1 0. 05 0 0

0. 2 0. 15 0. 1 0. 05 0 0

A9 N er i cal si m at i on um ul A9 Test r ecor ds

Four i er spect r um / s m

0. 25

0. 25

1 2 Ti m esec

3

0. 18 0. 15 0. 12 0. 09 0. 06 0. 03 0 0

1 2 Ti m esec

3

A12 N er i cal si m at i on um ul A12 Test r ecor ds

Fig.3 Time-history and Fourier spectra of acceleration with different depth in model site in S-K2 condition

20 40 z Fr equencyH

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20 40 Fr equencyH z

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20 40 Fr equencyH z

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0. 4 0. 3 0. 2 0. 1 0 - 0. 1 - 0. 2 - 0. 3 - 0. 4 - 0. 5

0. 3 Accel er at i ong

0. 6 Accel er at i ong 0. 4 0. 2 0 - 0. 2 - 0. 4 - 0. 6 - 0. 8

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A12 N er i cal si m at i on um ul A12 Test r ecor ds

Accel er at i ong

0. 2 0. 1 0

- 0. 1 - 0. 2 - 0. 3 - 0. 4 0 1 Ti m esec

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1 Ti m esec

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Four i er spect r um / s m

Four i er spect r um / s m

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0. 25 0. 2

A1 Num i cal si m at i on er ul A1 Test r ecor ds

A9 N er i cal si m at i on um ul A9 Test r ecor ds

0. 25 0. 2 0. 15 0. 1 0. 05 0 0

A12 N er i cal si m at i on um ul A12 Test r ecor ds

0. 15 0. 1

0. 15 0. 1

0. 05 0 0 20 40 Fr equencyH z 60

0. 05 0 0 20 40 Fr equencyH z 60

Fig.4 Time-history and Fourier spectra of acceleration with different depth in model site in S-N2 condition

0. 6 Accel er at i ong 0. 4 0. 2 0

0. 5 0. 4 0. 3 0. 2 0. 1 0 - 0. 1 - 0. 2 - 0. 3 - 0. 4 - 0. 5 1 0. 8 0. 6 0. 4 0. 2 0 - 0. 2 - 0. 4 - 0. 6 - 0. 8 Accel er at i ong Accel er at i ong

20 40 Fr equencyH z

60

- 0. 2 - 0. 4 - 0. 6 0 1 Ti m esec

A1 N er i cal si m at i on um ul A1 Test r ecor ds

A1 N er i cal si m at i on um ul A1 Test r ecor ds

A9 N er i cal si m at i on um ul A9 Test r ecor ds

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3 Four i er spect r um / s m 0. 4 0. 3 0. 2 0. 1 0

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Four i er spect r um / s m

0. 5 0. 4 0. 3 0. 2 0. 1 0 0

A9 N er i cal si m at i on um ul A9 Test r ecor ds

0. 5 0. 4 0. 3 0. 2 0. 1 0 0

A12 N er i cal si m at i on um ul A12 Test r ecor ds

Fig.5 Time-history and Fourier spectra of acceleration with different depth in model site in S-E2 condition

Peak accel er at i ong -1 - 0. 5 0 0. 4 Soi l dept hm 0. 8 1. 2 1. 6

N er i cal um si m at i on ul Test r ecor ds

20 40 Fr equencyH z

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0

20 40 Fr equencyH z

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20 40 Fr equencyH z

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Peak accel er at i ong

1

0

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-1

- 0. 5 0 0. 4 0. 8 1. 2 1 6

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0. 5

1

N er i cal um si m at i on ul Test r ecor ds

Peak accel er at i ong -1 - 0. 5 0 0. 4 0. 8 1. 2 1. 6 Soi l dept hm 0 0. 5 1

N er i cal um si m at i on ul Test r ecor ds

(a) Condition S-K2

(b) Condition S-N2

Soi l dept hm

(c) Condition S-E2

Fig.6 Peak acceleration at different test points

Table.3 Peak acceleration of test point A1 on ground surface Peak acceleration simulation 0.529 0.407 0.484 test 0.471 0.314 0.521 Relative error 12.3 29.6 7.1 Table.4 Peak acceleration of test point A12 under tunnel Peak acceleration simulation 0.610 0.559 0.842 test 0.525 0.322 0.554 Relative error 16.2 73.6 52.0

Condition

Condition

S-K2 S-N2 S-E2

S-K2 S-N2 S-E2

The test records and numerical simulation results of accelerometers A1, A9 and A12 are compared under test condition S-K1, S-K2 and S-K3, and the acceleration time-history and Fourier spectra are showed as Figure.7

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and Figure.8. The variation law for positive peak acceleration and negative peak acceleration is showed as Figure.9. The peak acceleration of test records for accelerometers A1 and A12 under test conditions S-K1, S-K2 and S-K3 is listed in Table.5 and Table.6. The results show that the difference between the numerical simulation results and shaking table test records is increasing with the peak acceleration increasing of inputting seismic waves. The simulation result under test condition S-K1 is best, and the simulation result under test condition S-K2 is worse than that under test condition S-K1. But under the test condition S-K3, the difference between simulation results and test records is great. This is because that the subway tunnels are floating, and the interface between soil and structure is separating under test condition S-K3. In the model, the contact pairs are used to simulated dynamic transfer property of soil and station, and there is some difference between simulation and test. So, how to simulate the interface exactly needs further research.

0. 4 0. 3 0. 2 0. 1 0 - 0. 1 - 0. 2 - 0. 3 - 0. 4 - 0. 5

0. 3 Accel er at i ong 0. 1 0 - 0. 1 - 0. 2 - 0. 3 - 0. 4 0

A9 N er i cal si m at i on um ul A9 Test r ecor ds

0. 3 Accel er at i ong 0. 2 0. 1 0 - 0. 1 - 0. 2 - 0. 3 - 0. 4 0

A12 N er i cal si m at i on um ul A12 Test r ecor ds

Accel er at i on g

0. 2

A1 N er i cal si m at i on um ul A1 Test r ecor ds

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1 Ti m esec

2

A1 Num i cal si m at i on er ul A1 Test r ecor ds

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A9 N er i cal si m at i on um ul A9 Test r ecor ds

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1 2 Ti m esec

A12 Num i cal si m at i on er ul A12 Test r ecor ds

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Four i er spect r um / s m

0. 12 0. 1 0. 08 0. 06 0. 04 0. 02 0 0

0. 1

0. 08 0. 06 0. 04 0. 02 0 0 20 40 Fr equencyH z 60

Four i er spect r um / s m

Four i er spect r um / s m

0. 14

0. 12

0. 1

0. 08 0. 06 0. 04 0. 02 0 0

Fig.7 Time-history and Fourier spectra of acceleration with different depth in model site in S-K1 condition

0. 8 0. 6 0. 4 0. 2 0 - 0. 2 - 0. 4 - 0. 6 - 0. 8

20 40 Fr equencyH z

60

20 40 Fr equencyH z

60

0. 8 Accel er at i ong 0. 6 0. 4 0. 2 0

A9 N er i cal si m at i on um ul A9 Test r ecor ds

- 0. 2 - 0. 4 - 0. 6 0 1 Ti m esec

A1 N er i cal si m at i on um ul A1 Test r ecor ds

0

Four i er spect r um / s m

Four i er spect r um / s m

Four i er spect r um / s m

0. 03

1 2 Ti m esec

A1 N er i cal si m at i on um ul A1 Test r ecor ds

3

0. 8 0. 6 0. 4 0. 2 0 - 0. 2 - 0. 4 - 0. 6 - 0. 8 -1

Accel er at i ong

Accel er at i ong

A12 N er i cal si m at i on um ul A12 Test r ecor ds

2

A9 N er i cal si m at i on um ul A9 Test r ecor ds

3

0

1 Ti m esec

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A12 N er i cal si m at i on um ul A12 Test r ecor ds

3

0. 03

0. 03

0. 025 0. 02 0. 01

0. 025 0. 02 0. 01

0. 025 0. 02 0. 01

0. 015 0. 005 0 0 20 40 Fr equencyH z 60

0. 015 0. 005 0 0 20 40 Fr equencyH z 60

0. 015 0. 005 0 0 20 40 Fr equencyH z 60

Fig.8 Time-history and Fourier spectra of acceleration with different depth in model site in S-K3 condition

Peak accel er at i ong -1 - 0. 5 0 0. 4 0. 8 1. 2 1 6 Soi l dept hm

N er i cal um si m at i on ul Test r ecor ds

Peak accel er at i ong

0

0. 5

1

-1

- 0. 5 0 0. 4 0. 8 1. 2 1. 6

0

0. 5

1

N er i cal um si m at i on ul Test r ecor ds

Peak accel er at i ong -1 - 0. 5 0 0. 4

N er i cal um si m at i on ul Test r ecor ds

0

0. 5

1

Soi l dept hm

1. 2 1. 6

(a) Condition S-K1

(b) Condition S-K2

(c) Condition S-K3

Fig.9 Peak acceleration of different test points when Kobe wave input

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Soi l dept hm

0. 8

Table.5 Peak acceleration of test point A1 on ground surface

Condition S- K1 S- K2 S- K3 Peak acceleration simulation 0.325 0.529 0.650 test 0.423 0.471 0.502 Relative error 23.2 12.3 29.5

Table.6 Peak acceleration of test point A12 under tunnel

Condition S- K1 S- K2 S- K3 Peak acceleration simulation 0.299 0.660 0.890 test 0.281 0.525 0.653 Relative error 6.4 25.7 36.3

4.2 Strain response

The arrangement plan of sensors at section is shown as Figure.10. The strain gauges S3 and S8 are placed on the position of 45°. Because of buoyancy, the tunnel is rotated by 12°. Therefore, the position of strain gauges S4 and S9 is close to the 45° positon. So, the strain gauges S1 and S11 are placed on the top and bottom respectively, and S6 is on the horizontal side of tunnel. The strain response of S1, S4, S6, S9 and S11 are analysed comparatively. The strain amplitudes at different positions of tunnel under different wave are listed in Table.7, Table.8 and Table.9. It can be found that the numerical simulation results of strain gauges S4, S9 and S11 are higher than test records (The amplitudes of strain gauges S6 are approximately the same under test condition S-K1, S-K2 and S-K3.). The numerical simulation results are lower than the test records on the position S1 under test condition S-K1, S-K2, S-K3 and SE1, S-E2, S-E3. The numerical simulation results are higher than the test records under test condition S-N1, SN2 and S-N3. It can also be found that there is some difference between numerical simulation results and test records. The reason is related with epoxy coatings of strain gauges area, and the characteristics of ground motion had also some effect on the station structure. Though there is some difference between numerical simulation results and test records, their seismic response general law is basically the same. The strain amplitudes of strain gauges S4 and S9 are obvious higher than that of the others. The strain amplitudes of strain gauge S11(on the bottom of tunnel) is obvious higher than that of strain gauge S1(on the top of tunnel). The strain amplitudes at the central angle 45° positon is maximum. It is in accordance with the numerical simulation results.

S20 S1 S2 S19 S3 S18 S17 S4 S16 S5 P1- 1 A1- 1 S15 S6 S14 S7 S8 S13 S9 S10 S11 S12

Fig.10 Arrangement plan of sensors at section of tunnel Table7. Strain amplitude at different positions of tunnel under Kobe wave(unit: )

Strain gauge S1 S4 S6 S9 S11 S-K1 Simulation 0.36 4.57 1.51 4.43 2.46 Test 0.92 3.06 1.69 2.79 2.26 S-K2 Simulation 0.52 8.66 2.80 8.10 4.41 Test 1.40 4.08 2.82 3.20 3.35 S-K3 Simulation 1.01 11.14 3.61 10.71 6.02 Test 1.72 5.82 3.63 5.02 4.21

Table8. Strain amplitude at different positions of tunnel under El-Centro wave (unit: )

Strain gauge S1 S4 S6 S9 S11 S-E1 Simulation 0.35 4.46 1.85 5.00 2.55 Test 0.75 2.66 1.67 2.50 2.18 S-E2 Simulation 1.02 8.28 4.16 10.5 6.20 Test 1.14 4.09 2.39 4.01 3.05 S-E3 Simulation 0.82 9.38 3.88 10.37 5.55 Test 1.36 4.63 2.92 4.8 3.38

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Table9. Strain amplitude at different positions of tunnel under artificial Nanjing wave (unit: )

Strain gauge S1 S4 S6 S9 S11 S-N1 Simulation 0.61 6.97 2.90 7.77 3.98 Test 0.58 1.92 1.29 1.68 1.67 S-N2 Simulation 0.74 8.76 3.7 9.64 5.06 Test 0.69 3.09 1.75 2.91 2.26 S-N3 Simulation 3.17 16.68 9.77 16.54 14.1 Test 1.08 4.11 2.56 4.11 3.09

5 Conclusion

This paper introduces the comparative analysis between the numerical simulation results and large-size shaking table test records concretely. The results show that simulation results are basically identical with the test records. It also indicates that the calculation model can well simulate the dynamic characteristics of soil, the dynamic interaction between tunnel and soil, the dynamic response of tunnel construction. At the same time, the feasibility of the test and the reliability of the test results is proved as well.

6 References

Liu J B, Li B, Gu Y. Seismic response analysis of shielded subway tunnels. Journal of Tsinghua University(Science and Technology), 2005, 45(6): 757-760. (P. R. China) Hongbin Huo, Antonio Bobet. Seismic design of cut and cover rectangular tunnels-evaluation of observed behavior of Dakai st station during Kobe earthquake, 1995[A]. Proceedings of 1 World Forum of Chinese Scholars in Geotechnical Engineering, August 20-22,2003,Tongji University, Shanghai (P. R. China), 456-466. Yang L D, Yang C, Ji Q Q, Shaking table test and numerical calculation on subway station structure in soft soil. Journal of Tongji University. 2003, 31(10): 1135-1140. (P. R. China) Chen G X, Zhuang H Y, Cheng S G, A Large-scale Shaking Table Test for Dynamic Soil-Metro Tunnel Interaction--Designs of Test. Earthquake Engineering and Engineering Vibration, 2006, 26(6): 178-183. (P. R. China) Chen G X, Zhuang H Y, Du X L, A Large-size Shaking Table Test for Dynamic Soil-Metro Tunnel Interaction--Analysis on the test results. Earthquake Engineering and Engineering Vibration, 2007, 27(1): 164-170. (P. R. China) Zhuang H Y, Chen G X. Zhu D H. Dynamic visco-plastic memorial nested yield surface model of soil and its verification. Chinese Journal of Geotechnical Engineering, 2006, 28(10): 1267-1272. (P. R. China) Jeeho Lee, Gregory L. Fenves. Plastic-damage model for cyclic loading of concrete structures. Journal of engineering mechanics, 1998(4): 892-900. (USA) Zhuang H Y, Chen G X. Analysis of nonlinear earthquake response of metro double-tunnels. Earthquake Engineering and Engineering Vibration, 2006, 26(2):131-137. (P. R. China)

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