Skip to main content
Log in

Longitudinal integral response deformation method for the seismic analysis of a tunnel structure

  • Published:
Earthquake Engineering and Engineering Vibration Aims and scope Submit manuscript

Abstract

for the longitudinal seismic response analysis of a tunnel structure under asynchronous earthquake excitations, a longitudinal integral response deformation method classified as a practical approach is proposed in this paper. The determinations of the structural critical moments when maximal deformations and internal forces in the longitudinal direction occur are deduced as well. When applying the proposed method, the static analysis of the free-field computation model subjected to the least favorable free-field deformation at the tunnel buried depth is performed first to calculate the equivalent input seismic loads. Then, the equivalent input seismic loads are imposed on the integral tunnel-foundation computation model to conduct the static calculation. Afterwards, the critical longitudinal seismic responses of the tunnel are obtained. The applicability of the new method is verified by comparing the seismic responses of a shield tunnel structure in Beijing, determined by the proposed procedure and by a dynamic time-history analysis under a series of obliquely incident out-of-plane and in-plane waves. The results show that the proposed method has a clear concept with high accuracy and simple progress. Meanwhile, this method provides a feasible way to determine the critical moments of the longitudinal seismic responses of a tunnel structure. Therefore, the proposed method can be effectively applied to analyze the seismic response of a long-line underground structure subjected to non-uniform excitations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bardet JP, Ichii K and Lin CH (2000), “EERA: A Computer Program for Equivalent-Linear Earthquake Site Response Analyses of Layered Soil Deposits,” University of Southern California, Los Angeles.

    Google Scholar 

  • Fu Jia, Liang Jianwen and Qin Lin (2016), “Dynamic Soil-Tunnel Interaction in Layered Half-Space for Incident Plane SH Waves,” Earthquake Engineering and Engineering Vibration, 15(4): 715–727.

    Article  Google Scholar 

  • GB 50267-97 (1998), Code for Seismic Design of Nuclear Power Plants, Ministry of Housing and Urban-Rural Development of the People’s Republic of China, China Planning Press, Beijing. (in Chinese)

    Google Scholar 

  • GB 50909–2014 (2014), Code for Seismic Design of Urban Rail Transit Structures, Ministry of Housing and Urban-Rural Development of the People’s Republic of China, China Planning Press, Beijing. (in Chinese)

    Google Scholar 

  • Gu Yin, Chen Kai, Wu Huaiqiang, Zhuo Weidong and Sun Ying (2017), “Shaking Table Tests for a Subway Station Structure Under Spatially Non-Uniform Ground Motion,” Journal of Vibration and Shock, 36(17): 256–261. (in Chinese)

    Google Scholar 

  • He Chuan, Zhang Jing, and Feng Kun (2017), “Research on Structural Analysis Method of Shield Tunnels,” China Journal of Highway and Transport, 30(8): 1–14. (in Chinese)

    Google Scholar 

  • Idriss IM and Sun JI (1992), “User’s Manual for SHAKE91,” Center for Geotechnical Modeling, 388(5–6): 279–360.

    Google Scholar 

  • Jiang Luzhen, Chen Jun and Li Jie (2010), “Seismic Response of Underground Utility Tunnels: Shaking Table Testing and FEM Analysis,” Earthquake Engineering and Engineering Vibration, 9(4): 555–567.

    Article  Google Scholar 

  • John CMS and Zahrah TF (1987), “Aseismic Design of Underground Structures,” Tunnelling & Underground Space Technology Incorporating Trenchless Technology Research, 2(2): 165–197.

    Article  Google Scholar 

  • Knopoff L (1964), “A Matrix Method of Elastic Wave Problems,” Bulletin of the Seismological Society of America, 54(1): 431–438.

    Article  Google Scholar 

  • Li Liyun, Wang Chengbo, Han Junyan, Hou Benwei, Xu Chengshun and Du Xiuli (2015), “Analysis of Site Responses During Shaking Table Test for the Interaction between Pipeline and Soil,” Earthquake Engineering and Engineering Dynamics, 35(3): 166–176. (in Chinese)

    Google Scholar 

  • Li Peng (2013), “Numerical Analysis for Longitudinal Seismic Response of Tunnels in Saturated Soil,” Tsinghua University, Beijing. (in Chinese)

    Google Scholar 

  • Liu Jingbo, Du Yixin, Du Xiuli, Wang Zhenyu and Wu Jun (2006), “3D Viscous-Spring Artificial Boundary in Time Domain,” Earthquake Engineering and Engineering Vibration, 5(1): 93–102.

    Article  Google Scholar 

  • Liu Jingbo and Lv Yandong (1998), “A Direct Method for Analysis of Dynamic Soil-Structure Interaction,” China Civil Engineering Journal, 31(3): 55–64. (in Chinese)

    Google Scholar 

  • Liu Jingbo, Wang Wenhui and Dasgupta Gautam (2014), “Pushover Analysis of Underground Structures: Method and Application,” Science China: Technological Sciences, 57(2): 423–437.

    Article  Google Scholar 

  • Liu Jingbo, Wang Wenhui and Zhao Dongdong (2013a), “Comparison of the Pseudo-Static Methods for Seismic Analysis of the Underground Structures,” Engineering Mechanics, 30(1): 105–111. (in Chinese)

    Article  Google Scholar 

  • Liu Jingbo, Wang Wenhui, Zhao Dongdong and Zhang Xiaobo (2013b), “Integral Response Deformation Method for Seismic Analysis of Underground Structure,” Chinese Journal of Rock Mechanics and Engineering, 32(8): 1618–1624.

    Google Scholar 

  • Liu Jingbo, Wang Wenhui, Zhao Dongdong and Zhang Xiaobo (2014), “Integral Response Deformation Method in Seismic Analysis of Complex Section Underground Structures,” Chinese Civil Engineering Journal, 47(1): 134–142.

    Google Scholar 

  • Liu Jingbo and Wang Yan (2006), “A 1-D Time-Domain Method for 2D Wave Motion in Elastic Half-Spaced by Anti-Plane Wave Oblique Incidence,” China Journal of Theoretical and Applied Mechanics, 38(2): 219–225. (in Chinese)

    Google Scholar 

  • Liu Jingbo and Wang Yan (2007), “A 1-D Time-Domain Method for In-Plane Wave Motion of Free-Field in Layered Media,” Engineering Mechanics, 24(7): 16–22. (in Chinese)

    Google Scholar 

  • Liu Rushan and Shi Hongbin (2006), “An Improved Pseudo-Static Method for Seismic Resistant Design of Underground Structures,” Earthquake Engineering and Engineering Vibration, 5(2): 189–193.

    Article  Google Scholar 

  • Qi Wenhao and Bo Jingshan (2007), “Summarization on Equivalent Linear Method of Seismic Responses for Soil Layers,” World Earthquake Engineering, 23(4): 223–228. (in Chinese)

    Google Scholar 

  • Shao Runmeng and Lei Yang (2013), “Longitudinal Anti-Seismic Analysis of Shield Tunnel Based on Response Deformation Method,” China Civil Engineering Journal, 46(S2): 260–265. (in Chinese)

    Google Scholar 

  • Tateishi A (2005), “A Study on Seismic Analysis Methods in the Cross Section of Underground Structures Using Static Finite Element Method,” Structural Engineering, 22(1): 41–54.

    Article  Google Scholar 

  • Wang Duguo and Zhao Chenggang (2016), “Two-Dimensional Equivalent Linear Seismic Analysis of Free Field in Layered Half-space Due to Oblique Incidence,” Chinese Journal of Geotechnical Engineering, 38(3): 554–561. (in Chinese)

    Google Scholar 

  • Wolf JP and Obernhuber P (1982a), “Free-Field Response from Inclined SH-Waves and Love-Waves,” Earthquake Engineering and Structural Dynamics, 10(6): 823–845.

    Article  Google Scholar 

  • Wolf JP and Obernhuber P (1982b), “Free-Field Response from Inclined SV- and P-Waves and Rayleigh-Waves,” Earthquake Engineering and Structural Dynamics, 10(6): 847–869.

    Article  Google Scholar 

  • Xu Chengshun, Xu Zigang, Du Xiuli and Li Yang (2017), “Comparative Study of Simplified Methods for Seismic Analysis of Underground Structure,” Earthquake Engineering and Engineering Dynamics, 37(2): 65–80.

    Google Scholar 

  • Yu Haitao, Yan Xiao, Antonio Bobet, Yuan Yong, Xu Guoping and Su Quanke (2018), “Multi-Point Shaking Table Test of a Long Tunnel Subjected to Non-Uniform Seismic Loadings,” Bulletin of Earthquake Engineering, 16(2): 1041–1059.

    Article  Google Scholar 

  • Zhao Mi, Du Xiuli, Liu Jingbo and Han Qiang (2013), “Time-Domain Method for Free Field in Layered Half Space under P-SV Waves of Oblique Incidence,” China Earthquake Engineering Journal, 35(1): 84–90. (in Chinese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dongyang Wang.

Additional information

Supported by

National Natural Science Foundation of China under Grant No. 51478247

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, J., Wang, D. & Bao, X. Longitudinal integral response deformation method for the seismic analysis of a tunnel structure. Earthq. Eng. Eng. Vib. 20, 887–904 (2021). https://doi.org/10.1007/s11803-021-2060-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11803-021-2060-5

Keywords

Navigation