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

Transcription

1 The 12 th International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1-6 October, 28 Goa, India Comparative Analysis on Earthquake Response of Subway Tunnels between Numerical Simulation and Shaking Table 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 ; shaking table ABSTRACT: Based on the shaking table 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 conditions, all the instances are simulated. Compared with the record, it is proved that both the finite element model and the shaking table 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(25) 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(23) compared the destruction of Dakai subway station and the finite element numerical results, taking ABAQUS as 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(23) designed the model box and conducted shaking table model on subway station. Then, the numerical of model is performed based on the Lagrangian difference algorithm. Due to lack of measured data and record, numerical 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 results, the comparison research between numerical results and model is very necessary. In this paper, the numerical 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 results are compared with the results. 2 Brief introduction about large-size shaking table model of liquefiable soil-subway tunnels The is conducted on the large-size shaking table(6m 6m,8t) in China Construction Science Research Institute. In the, 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.24m, 1.2m and.16m 171

2 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.8m. 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, 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 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 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 elastic modulus is 4.13MPa, the poisson ratio is.7 and the density is 15kg/m 3. Rigid material is used to simulate the model box, whose elastic modulus of material is 2Gpa and the poisson ratio is.3. Fig.2 Meshes of soil- subway station structure system in two dimensional finite element analysis 172

3 Table.1 Physical and mechanical parameters of model soils Soil layer Thickness Density Velocity of shear wave Friction angle ( ) (m) (g/cm 3 Poisson s ratio ) (m/s) Clay Slit fine sand Slit fine sand Slit fine sand Slit fine sand Slit fine sand Clay Comparative analysis between numerical results and shaking table 4.1 Acceleration response The and numerical results of accelerometers A1, A9 and A12 are compared under S-K2, S-N2 and S-E2 condition, and the acceleration timehistory and Fourier spectra are shown as Figure.3, Figure.4 and Figure.5. The second letter K, E, N denote the action of Kobe wave, El-Centro wave, Nanjing artificial wave respectively, the number 1, 2, 3 denote the load levels. It is shown from the figures that waveform change of acceleration time-history from the is in accordance with the numerical results, so is the characteristic of Fourier spectrum obtained from acceleration time-history. The result shows that the numerical method can well simulate the seismic response of subway station structure in liquefiable soil. The variation law for positive peak Table.2 Dynamic Plastic-damage model parameters of microconcrete for subway tunnels Model parameters Parameter values Elastic modulus E (MPa) Poisson s ratioν.18 Density ρ (kg/m 3 ) 25 Expansion angleψ ( ) 32.4 Initial yield compressive stress σ c (MPa) 3.91 Ultimate compressive stress σ cu (MPa) 5.69 Initial yield tensile stress σ t (MPa).68 ω t Ω 1 d c ξ.1 acceleration and negative peak acceleration is showed as Figure.6. The peak acceleration of for accelerometers A1 and A12 under different load conditions is listed in Table.3 and Table.4. In general, the numerical results are in accordance with the under Kobe wave and Nanjing artificial wave, and the similarity of numerical results and the is a little weaker under El-Centro wave. Fouri er spect rum(m/s) Time(sec) Fouri er spect rum(m/s) A12 Numerical simul at i on Fouri er spect rum(m/s) Fig.3 Time-history and Fourier spectra of acceleration with different depth in model site in S-K2 condition 173

4 A1 Numerical simul at i on A9 r ecor ds Four i er spect r um(m/s) Fig.4 Time-history and Fourier spectra of acceleration with different depth in model site in S-N2 condition A9 r ecor ds A12 Numerical simul at i on Fig.5 Time-history and Fourier spectra of acceleration with different depth in model site in S-E2 condition Soil depth(m) (a) S-K2 (b) S-N2 (c) S-E2 Fig.6 at different points Soil depth(m). 8 Soi l dept h(m) Table.3 of point A1 on ground surface Table.4 of point A12 under tunnel S-K % S-K % S-N % S-N % S-E % S-E % The and numerical results of accelerometers A1, A9 and A12 are compared under condition S-K1, S-K2 and S-K3, and the acceleration time-history and Fourier spectra are showed as Figure.7 174

5 and Figure.8. The variation law for positive peak acceleration and negative peak acceleration is showed as Figure.9. The peak acceleration of for accelerometers A1 and A12 under 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 results and shaking table is increasing with the peak acceleration increasing of inputting seismic waves. The result under condition S-K1 is best, and the result under condition S-K2 is worse than that under condition S-K1. But under the condition S-K3, the difference between results and is great. This is because that the subway tunnels are floating, and the interface between soil and structure is separating under 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 and. So, how to simulate the interface exactly needs further research A1 Numerical simul at i on Four i er spect r um(m/s) Fig.7 Time-history and Fourier spectra of acceleration with different depth in model site in S-K1 condition Four i er spect r um(m/s) Fig.8 Time-history and Fourier spectra of acceleration with different depth in model site in S-K3 condition r ecor ds Soil depth(m). 8 (a) S-K1 (b) S-K2 (c) S-K3 Fig.9 of different points when Kobe wave input Soi l dept h(m). 8 Soi l dept h(m) 175

6 Table.5 of point A1 on ground surface Table.6 of point A12 under tunnel S- K1 S- K2 S- K % 12.3% 29.5% S- K1 S- K2 S- K % 25.7% 36.3% 4.2 Strain response The arrangement plan of sensors at section is shown as Figure.1. 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 results of strain gauges S4, S9 and S11 are higher than (The amplitudes of strain gauges S6 are approximately the same under condition S-K1, S-K2 and S-K3.). The numerical results are lower than the on the position S1 under condition S-K1, S-K2, S-K3 and S- E1, S-E2, S-E3. The numerical results are higher than the under condition S-N1, S- N2 and S-N3. It can also be found that there is some difference between numerical results and. 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 results and, 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 results. S2 S1 S2 S19 S3 S18 S4 S17 S5 S16 A1-1 P1-1 S6 S15 S7 S14 S8S9 S12 S13 S1 S11 Fig.1 Arrangement plan of sensors at section of tunnel Table7. Strain amplitude at different positions of tunnel under Kobe wave(unit: με) Strain S-K1 S-K2 S-K3 gauge Simulation Simulation Simulation S S S S S Table8. Strain amplitude at different positions of tunnel under El-Centro wave (unit: με) Strain S-E1 S-E2 S-E3 gauge Simulation Simulation Simulation S S S S S

7 Table9. Strain amplitude at different positions of tunnel under artificial Nanjing wave (unit: με) Strain S-N1 S-N2 S-N3 gauge Simulation Simulation Simulation S S S S S Conclusion This paper introduces the comparative analysis between the numerical results and large-size shaking table concretely. The results show that results are basically identical with the. 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 and the reliability of the 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), 25, 45(6): (P. R. China) Hongbin Huo, Antonio Bobet. Seismic design of cut and cover rectangular tunnels-evaluation of observed behavior of Dakai station during Kobe earthquake, 1995[A]. Proceedings of 1 st World Forum of Chinese Scholars in Geotechnical Engineering, August 2-22,23,Tongji University, Shanghai (P. R. China), Yang L D, Yang C, Ji Q Q, Shaking table and numerical calculation on subway station structure in soft soil. Journal of Tongji University. 23, 31(1): (P. R. China) Chen G X, Zhuang H Y, Cheng S G, A Large-scale Shaking Table for Dynamic Soil-Metro Tunnel Interaction Designs of. Earthquake Engineering and Engineering Vibration, 26, 26(6): (P. R. China) Chen G X, Zhuang H Y, Du X L, A Large-size Shaking Table for Dynamic Soil-Metro Tunnel Interaction Analysis on the results. Earthquake Engineering and Engineering Vibration, 27, 27(1): (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, 26, 28(1): (P. R. China) Jeeho Lee, Gregory L. Fenves. Plastic-damage model for cyclic loading of concrete structures. Journal of engineering mechanics, 1998(4): (USA) Zhuang H Y, Chen G X. Analysis of nonlinear earthquake response of metro double-tunnels. Earthquake Engineering and Engineering Vibration, 26, 26(2): (P. R. China) 177