Comparative Analysis of Longitudinal Seismic Responses of Rigid, Flexible, and Semirigid Immersed Tunnels Using the Analytical Method
Publication: International Journal of Geomechanics
Volume 24, Issue 12
Abstract
To adapt to complex underwater geological conditions, immersed tunnel projects have gone through the development from rigid and flexible to semirigid immersed tunnels. The stiffness of segment joints and the element joint could reflect the differences in structural characteristics of the three types of immersed tunnels. This paper presents a theoretical model using segment joints, the element joint, and 16 segments for the longitudinal seismic response analysis of the three types of immersed tunnels. Based on the matrix transfer principle, the end boundary conditions and the continuity conditions for the forces and deformations at the segment joints and element joint were considered. Analytical solutions were validated by verifying the established laws. Results indicate that the semirigid immersed tunnel, in contrast to the rigid immersed tunnel, can reduce shear forces and bending moments along the longitudinal direction by using segment joints and the element joint. In addition, compared with the flexible immersed tunnel, the semirigid immersed tunnel has higher overall stiffness and better continuity of deformation between the adjacent soil regions through the prestressed tendons inside the tube element. The semirigid immersed tunnel is a viable solution for complex geological conditions where the strata change every few tens of meters.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research is supported by the National Key R&D Program of China (Grant No. 2022YFC3080400), the Fundamental Research Funds for the Central Universities (Grant No. 2042023kfyq03), and the National Natural Science Foundation of China (Grant Nos. 52338007, 52078236, and 52078392). The authors gratefully acknowledge the financial supports.
References
Amorosi, A., and D. Boldini. 2009. “Numerical modelling of the transverse dynamic behaviour of circular tunnels in clayey soils.” Soil Dyn. Earthquake Eng. 29 (6): 1059–1072. https://doi.org/10.1016/j.soildyn.2008.12.004.
An, G. F. 2017. Technical guide for construction of immersed tunnel. Beijing: China Architecture and Building Press.
Anastasopoulos, I., N. Gerolymos, V. Drosos, T. Georgarakos, R. Kourkoulis, and G. Gazetas. 2008. “Behaviour of deep immersed tunnel under combined normal fault rupture deformation and subsequent seismic shaking.” Bull. Earthquake Eng. 6 (2): 213–239. https://doi.org/10.1007/s10518-007-9055-0.
Anastasopoulos, I., N. Gerolymos, V. Drosos, R. Kourkoulis, T. Georgarakos, and G. Gazetas. 2007. “Nonlinear response of deep immersed tunnel to strong seismic shaking.” J. Geotech. Geoenviron. Eng. 133 (9): 1067–1090. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:9(1067).
Bobet, A. 2003. “Effect of pore water pressure on tunnel support during static and seismic loading.” Tunnelling Underground Space Technol. 18 (4): 377–393. https://doi.org/10.1016/S0886-7798(03)00008-7.
Cheng, X. J., L. P. Jing, J. Cui, Y. Q. Li, and R. Dong. 2017. “Shaking-table tests for immersed tunnels at different sites.” Shock Vib. 2017: 2546318.
Ding, J. H., X. L. Jin, Y. Z. Guo, and G. G. Li. 2006. “Numerical simulation for large-scale seismic response analysis of immersed tunnel.” Eng. Struct. 28 (10): 1367–1377. https://doi.org/10.1016/j.engstruct.2006.01.005.
Grantz, W. C. 2001. “Immersed tunnel settlements - Part 2: Case histories.” Tunnelling Underground Space Technol. 16 (3): 203–210. https://doi.org/10.1016/S0886-7798(01)00040-2.
Hashash, Y. M. A., J. J. Hook, B. Schmidt, and J. I-Chiang Yao. 2001. “Seismic design and analysis of underground structures.” Tunnelling Underground Space Technol. 16 (4): 247–293. https://doi.org/10.1016/S0886-7798(01)00051-7.
Hashimoto, T., J. Nagaya, and T. Konda. 1999. “Prediction of ground deformation due to shield excavation in clayey soils.” Soils Found. 39 (3): 53–54. https://doi.org/10.3208/sandf.39.3_53.
He, H., Y. Lin, J. Li, and N. Zhang. 2018. “Immersed tunnel foundation on marine clay improved by sand compaction piles.” Mar. Georesour. Geotechnol. 36 (2): 218–226. https://doi.org/10.1080/1064119X.2017.1300615.
Hu, Z. N., Y. L. Xie, and J. Wang. 2015. “Challenges and strategies involved in designing and constructing a 6 km immersed tunnel: A case study of the Hong Kong-Zhuhai-Macao bridge.” Tunnelling Underground Space Technol. 50: 171–177. https://doi.org/10.1016/j.tust.2015.07.011.
Hu, Z. N., Y. L. Xie, G. P. Xu, S. L. Bin, H. Z. Liu, and J. X. Lai. 2018. “Advantages and potential challenges of applying semi-rigid elements in an immersed tunnel: A case study of the Hong Kong-Zhuhai-Macao bridge.” Tunnelling Underground Space Technol. 79: 143–149. https://doi.org/10.1016/j.tust.2018.05.004.
Kattis, S. E., D. E. Beskos, and A. H. D. Cheng. 2003. “2D dynamic response of unlined and lined tunnels in poroelastic soil to harmonic body waves.” Earthquake Eng. Struct. Dyn. 32 (1): 97–110. https://doi.org/10.1002/eqe.216.
Kim, Y. W., and J. Y. Ryu. 2020. “Vibrations of rotationally restrained Timoshenko beam at hinged supports during an earthquake.” Nucl. Eng. Technol. 52 (5): 1066–1078. https://doi.org/10.1016/j.net.2019.10.021.
Li, P. 2013. “Numerical analysis for longitudinal seismic response of tunnels in saturated soils.” Ph.D. Dissertation, School of Civil Engineering, Tsinghua Univ.
Lin, M., W. Lin, Q. Wang, and X. D. Wang. 2018. “The deployable element, a new closure joint construction method for immersed tunnel.” Tunnelling Underground Space Technol. 80: 290–300. https://doi.org/10.1016/j.tust.2018.07.028.
Lin, M., H. Yin, X. Liu, and H. Liang. 2020. Foundation and base of immersed tube tunnel in the Hong Kong-Zhuhai-Macao bridge island tunnel project. Beijing: Science Press.
Lin, W., M. Lin, X. D. Liu, H. Q. Yin, and J. B. Gao. 2022. “Novelties in the islands and tunnel project of the Hong Kong-Zhuhai-Macao bridge.” Tunnelling Underground Space Technol. 120: 104287.
Majkut, L. 2009. “Free and forced vibrations of Timoshenko beams described by single difference equation.” J. Theor. Appl. Mech. 47 (1): 193–210.
Niu, Y. P., Y. L. Xie, H. G. Zhang, X. B. Yue, Y. G. Han, and Z. N. Hu. 2022. “Study on bearing characteristics of marine subsoil for semi-rigid immersed tunnel.” Mar. Georesour. Geotechnol. 40 (10): 1171–1183. https://doi.org/10.1080/1064119X.2021.1974621.
Olsen, T., T. Kasper, and J. de Wit. 2022. “Immersed tunnels in soft soil conditions experience from the last 20 years.” Tunnelling Underground Space Technol. 121: 104315. https://doi.org/10.1016/j.tust.2021.104315.
Ouyang, Z. Y., J. Cui, R. F. Luo, and P. J. Li. 2021. “Shaking table model test of immersed tunnels with different site conditions and seismic wave input directions.” Ships Offshore Struct. 16 (sup2): 20–32. https://doi.org/10.1080/17445302.2020.1829372.
Ouyang, Z. Y., P. J. Li, J. Cui, R. F. Luo, and D. D. Yuan. 2020. “Shaking table test study on flexible and rigid immersed tube tunnel in liquefiable soil layer.” Math. Probl. Eng. 2020: 1–16. https://doi.org/10.1155/2020/4980549.
Song, E. X., P. Li, M. Lin, and X. D. Liu. 2018. “The rationality of semi-rigid immersed tunnel element structure scheme and its first application in Hong Kong Zhuhai Macao bridge project.” Tunnelling Underground Space Technol. 82: 156–169. https://doi.org/10.1016/j.tust.2018.08.040.
St John, C. M., and T. F. Zahrah. 1987. “Aseismic design of underground structures.” Tunnelling Underground Space Technol. 2 (2): 165–197. https://doi.org/10.1016/0886-7798(87)90011-3.
Su, Q. K., Y. L. Zhu, Y. Chen, L. Fang, Y. Yan, Z. X. Su, H. de Wit, and Y. Li. 2022. “Hong Kong Zhuhai Macao bridge-tunnel project immersed tunnel and artificial islands - From an owners” perspective.” Tunnelling Underground Space Technol. 121: 1–18.
Tang, L., L. Yu, M. Wang, Z. Li, X. Zhang, M. Lu, and H. Yang. 2022. “Green’s functions based on the Timoshenko beam model for the longitudinal seismic dynamic response of tunnels crossing soft and hard rock strata.” Tunnelling Underground Space Technol. 128: 104545. https://doi.org/10.1016/j.tust.2022.104545.
Tao, L., Z. Wang, S. Cheng, A. Shao, and J. Zhibo. 2022. “Analytical solution for longitudinal response of pipeline structure under fault dislocation based on Pasternak foundation model.” Chin. J. Geotech. Eng. 44 (9): 1577–1586.
Wang, J. N. 1993. Seismic design of tunnels: A simple state-of-the-art design approach. New York: WIT PressParsons, Brinckerhoff, Quade and Douglas Inc.
Wang, Y. N., H. Z. Zhou, and X. H. Min. 2022. “Modelling the performance of immersed tunnel via considering variation of subsoil property.” Ocean Eng. 266: 1–14.
Wang, Y. N., H. Z. Zhou, and J. Yu. 2023. “Long-term settlement model for immersed tube tunnels under back silting loads during operation and maintenance periods.” Chin. J. Geotech. Eng. 45 (2): 292–300.
Wu, H. N., S. L. Shen, J. Yang, and A. N. Zhou. 2018. “Soil-tunnel interaction modelling for shield tunnels considering shearing dislocation in longitudinal joints.” Tunnelling Underground Space Technol. 78: 168–177. https://doi.org/10.1016/j.tust.2018.04.009.
Xie, X. Y., C. M. Yi, W. P. Li, and Y. G. Fang. 2019. “Safety analysis of settlement monitoring data of joints of yongjiang immersed tube tunnel during operation period.” Chin. J. Geotech. Eng. 41 (12): 2338–2344.
Xu, G. P., Y. Yuan, and Q. K. Su. 2018. Key technology and creation for seismic resistance of immersed tunnels. Beijing: China Communications Press Co., Ltd.
Xu, L. 2005. “Research of longitudinal settlement of soft soil shield tunnel.” Ph.D. Dissertation, College of Civil Engineering, Tongji Univ.
Yang, Y., J. Zhang, Y. Yuan, and H. Yu. 2021. “Dynamic responses of long tunnels in layered viscoelastic ground subjected to inclined SH waves.” Soil Dyn. Earthquake Eng. 141: 106469. https://doi.org/10.1016/j.soildyn.2020.106469.
Yu, H. T., Q. Wang, and T. Liu. 2020. “Analytical solution for longitudinal seismic response of long tunnels in homogeneous stratum.” Hazard Control Tunnelling Underground Eng. 2 (1): 34–41.
Yu, H. T., W. H. Xiao, Y. Yuan, Q. K. Su, and G. P. Xu. 2016. “Experiment on stiffness ratio of immersion joint to immersed tunnel element.” China J Highway Transp. 29 (12): 134–141.
Yu, H. T., Y. Yuan, G. P. Xu, Q. K. Su, X. Yan, and C. Li. 2018a. “Multi-point shaking table test for long tunnels subjected to nonuniform seismic loadings - part II: Application to the HZM immersed tunnel.” Soil Dyn. Earthquake Eng. 108: 187–195. https://doi.org/10.1016/j.soildyn.2016.08.018.
Yu, H. T., Z. W. Zhang, J. T. Chen, A. Bobet, M. Zhao, and Y. Yuan. 2018b. “Analytical solution for longitudinal seismic response of tunnel liners with sharp stiffness transition.” Tunnelling Underground Space Technol. 77: 103–114. https://doi.org/10.1016/j.tust.2018.04.001.
Yu, H. T., Z. W. Zhang, P. Li, W. G. He, and X. Zhao. 2019. “Analytical solution for longitudinal seismic responses of long tunnels crossing soil-rock stratum.” Chin. J. Geotech. Eng. 41 (7): 1244–1250.
Yu, Z., B. Li, W. Qiu, and X. Xu. 2021. “Research on settlement test and numerical calculation of west artificial island foundation of Hong Kong-Zhuhai-Macao bridge.” Ships Offshore Struct. 16 (sup2): 56–65. https://doi.org/10.1080/17445302.2020.1861710.
Zhang, D. M., Z. K. Huang, Z. L. Li, X. Zong, and D. M. Zhang. 2019. “Analytical solution for the response of an existing tunnel to a new tunnel excavation underneath.” Comput. Geotech. 108: 197–211. https://doi.org/10.1016/j.compgeo.2018.12.026.
Zhang, W. W., X. L. Jin, and Z. H. Yang. 2014. “Combined equivalent & multi-scale simulation method for 3-D seismic analysis of large-scale shield tunnel.” Eng. Comput. 31 (3): 584–620. https://doi.org/10.1108/EC-02-2012-0034.
Zhang, X. M., L. L. Song, H. J. Chen, S. C. Chen, Z. A. Hu, and Y. Li. 2022. “Shaking table test investigation on seismic performance of joint model of immersed tunnel.” Shock Vib. 2022: 1095986.
Zhou, H. Z., S. A. Liu, B. Li, W. Y. Chen, L. Su, J. J. Zheng, and Y. W. Zheng. 2023a. “Analytical solution for longitudinal seismic response of immersed tunnel connecting artificial islands crossing different strata.” Comput. Geotech. 164: 105836. https://doi.org/10.1016/j.compgeo.2023.105836.
Zhou, H. Z., Y. N. Wang, W. M. Huang, J. J. Zheng, and Q. X. Wu. 2024. “Deformation pattern of beams rested on different foundation models in nonuniform foundation conditions.” Int. J. Geomech. 24 (1): 04023252. https://doi.org/10.1061/IJGNAI.GMENG-8891.
Zhou, H. Z., Y. Yu, J. F. Hou, J. Yu, and Y. N. Wang. 2023b. “Deformation characteristics of joint of immersed tube tunnel under coupling load of back silting-tidal cycle.” Chin. J. Geotech. Eng. 45 (9): 1926–1933.
Zhou, M., X. Su, Y. Chen, and L. An. 2022. “New technologies and challenges in the construction of the immersed tube tunnel of the Hong Kong-Zhuhai-Macao link.” Struct. Eng. Int. 32 (4): 455–464. https://doi.org/10.1080/10168664.2021.1904487.
Information & Authors
Information
Published In
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jan 22, 2024
Accepted: Jun 14, 2024
Published online: Sep 30, 2024
Published in print: Dec 1, 2024
Discussion open until: Mar 1, 2025
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.