Simplified Method for Predicting the Shield Tunnel Longitudinal Responses to Over-Crossing Tunneling Considering Circumferential Joint Effect
Publication: International Journal of Geomechanics
Volume 24, Issue 7
Abstract
A simplified theoretical approach for predicting the longitudinal behaviors of the existing shield tunnel related to over-crossing tunneling is developed by considering the circumferential joint effect. A simplified beam–spring model (SBSM) is established to describe the shield tunnel longitudinal behaviors, in which the segmental linings are simplified into Euler–Bernoulli short beams, and the circumferential joints are represented using the linear rotation and shearing springs. The SBSM can reflect the opening and dislocation of shield tunnels simultaneously. The existing shield tunnel is then regarded as the SBSM lying on the Pasternak foundation, and the displacement and joint deformations of the existing tunnel are obtained by the finite-difference method (FDM). By virtue of the FDM, the complex tunnel–soil interaction and ring-to-ring interaction can be easily transformed into the numerical solutions. The feasibility of the present approach is examined by two published cases and comparison with previous solutions. Parametric analyses are also conducted to explore the impacts of several dominant variables. The findings showed that the predicted tunnel displacements from the present solution are almost the same as those from the Timoshenko beam model and the measurements, but the present method predicts a slightly higher joint opening and lower dislocation between rings than the Timoshenko beam model. In addition, the present method takes the stiffness reduction at circumferential joints into consideration, which leads to the obtained tunnel displacement curves being neither smooth nor continuous. The rigid motion primarily appears at the lining rings, whereas the rotation and dislocation appear at the circumferential joints. The existing solutions always give continuous tunnel heave curves, which fails to truly reflect the discontinuous deformations at circumferential joints.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work had been supported by the Wuhan Municipal Construction Group Research Program (Grant No. wszky 202013), the Science and Technology Plan Program of MOHURD (Grant No. 2021-K-074), and the Hubei Province of Construction Science and Technology Plan (Grant No. 2020-22).
References
Avgerinos, V., D. M. Potts, and J. R. Standing. 2017. “Numerical investigation of the effects of tunnelling on existing tunnels.” Géotechnique 67 (9): 808–822. https://doi.org/10.1680/jgeot.SiP17.P.103.
Chen, Q. J., J. C. Wang, W. M. Huang, Z. X. Yang, and R. Q. Xu. 2020. “Analytical solution for a jointed shield tunnel lining reinforced by secondary linings.” Int. J. Mech. Sci. 185: 105813. https://doi.org/10.1016/j.ijmecsci.2020.105813.
Fang, Q., D. Zhang, Q. Li, and L. N. Y. Wong. 2015. “Effects of twin tunnels construction beneath existing shield-driven twin tunnels.” Tunnelling Underground Space Technol. 45: 128–137. https://doi.org/10.1016/j.tust.2014.10.001.
Franza, A., A. M. Marshall, T. Haji, A. O. Abdelatif, S. Carbonari, and M. Morici. 2017. “A simplified elastic analysis of tunnel-piled structure interaction.” Tunnelling Underground Space Technol. 61: 104–121. https://doi.org/10.1016/j.tust.2016.09.008.
Hu, X., J. Wang, W. Fu, J. W. Ju, C. He, and Y. Fang. 2021. “Laboratory test of EPB shield tunneling in mixed-face conditions.” Int. J. Geomech. 21 (9): 04021161. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002098.
Huang, S., Z. Chen, Y. Xie, and Z. Lin. 2022a. “A variational approach to the analysis of excavation-induced vertical deformation in a segmental tunnel.” Tunnelling Underground Space Technol. 122: 104342. https://doi.org/10.1016/j.tust.2021.104342.
Huang, W. M., J. C. Wang, Z. X. Yang, and R. Q. Xu. 2022b. “Analytical analysis of the longitudinal response of shield tunnel lining considering ring-to-ring interaction.” Comput. Geotech. 146: 104705. https://doi.org/10.1016/j.compgeo.2022.104705.
Jin, D., D. Yuan, X. Li, and H. Zheng. 2018. “An in-tunnel grouting protection method for excavating twin tunnels beneath an existing tunnel.” Tunnelling Underground Space Technol. 71: 27–35. https://doi.org/10.1016/j.tust.2017.08.002.
Koizumi, J., H. Murakami, and K. Saino. 1988. “Modelling of longitudinal structure of shield tunnel.” [In Japanese.] J. Jpn. Soc. Civ. Eng. 394: 79–88.
Li, P., S.-J. Du, X.-F. Ma, Z.-Y. Yin, and S.-L. Shen. 2014. “Centrifuge investigation into the effect of new shield tunnelling on an existing underlying large-diameter tunnel.” Tunnelling Underground Space Technol. 42: 59–66. https://doi.org/10.1016/j.tust.2014.02.004.
Liang, R. 2019. “Simplified analytical method for evaluating the effects of over-crossing tunnelling on existing shield tunnels using the nonlinear Pasternak foundation model.” Soils Found. 59 (6): 1711–1727. https://doi.org/10.1016/j.sandf.2019.07.009.
Liang, R., C. Kang, L. Xiang, Z. Li, C. Lin, K. Gao, and Y. Guo. 2021. “Responses of in-service shield tunnel to overcrossing tunnelling in soft ground.” Environ. Earth Sci. 80 (5): 1–15. https://doi.org/10.1007/s12665-021-09374-3.
Liang, R., W. Wu, F. Yu, G. Jiang, and J. Liu. 2018. “Simplified method for evaluating shield tunnel deformation due to adjacent excavation.” Tunnelling Underground Space Technol. 71: 94–105. https://doi.org/10.1016/j.tust.2017.08.010.
Liang, R., T. Xia, Y. Hong, and F. Yu. 2016. “Effects of above-crossing tunnelling on the existing shield tunnels.” Tunnelling Underground Space Technol. 58: 159–176. https://doi.org/10.1016/j.tust.2016.05.002.
Lin, D., J. D. Nelson, M. Beecroft, and J. Cui. 2021. “An overview of recent developments in China’s metro systems.” Tunnelling Underground Space Technol. 111: 103783. https://doi.org/10.1016/j.tust.2020.103783.
Liu, B., Z. Yu, Y. Han, Z. Wang, R. Zhang, and S. Wang. 2020. “Analytical solution for the response of an existing tunnel induced by above-crossing shield tunneling.” Comput. Geotech. 124: 103624. https://doi.org/10.1016/j.compgeo.2020.103624.
Liu, B., Z. Yu, R. Zhang, Y. Han, Z. Wang, and S. Wang. 2021. “Effects of undercrossing tunneling on existing shield tunnels.” Int. J. Geomech. 21 (8): 04021131. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002102.
Liu, H., P. Li, and J. Liu. 2011. “Numerical investigation of underlying tunnel heave during a new tunnel construction.” Tunnelling Underground Space Technol. 26 (2): 276–283. https://doi.org/10.1016/j.tust.2010.10.002.
Liu, W. Z., X. Y. Dai, K. Sun, G. P. Ai, and T. Lei. 2022a. “Calculation method of longitudinal deformation of metro shield tunnel overpassing existing line at short distance.” [In Chinese.] Rock Soil Mech. 43 (03): 831–842. https://doi.org/10.16285/j.rsm.2021.0864.
Liu, X., Q. Fang, A. Jiang, and J. Li. 2022b. “Deformation analysis of existing tunnels with shearing and bending stiffness reduction at movement joints.” Tunnelling Underground Space Technol. 123: 104408. https://doi.org/10.1016/j.tust.2022.104408.
Liu, X., L. Wang, X. Zhou, J. Wang, Z. Zhong, P. Liu, F. Xiong, and C. He. 2022c. “EM calculation model and its application of calculating deformation in a new tunnel orthogonally undercrossing an existing tunnel.” Tunnelling Underground Space Technol. 123: 104418. https://doi.org/10.1016/j.tust.2022.104418.
Liu, X.-X., S.-L. Shen, Y.-S. Xu, and Z.-Y. Yin. 2018. “Analytical approach for time-dependent groundwater inflow into shield tunnel face in confined aquifer.” Int. J. Numer. Anal. Methods Geomech. 42 (4): 655–673. https://doi.org/10.1002/nag.2760.
Mindlin, R. D. 1936. “Force at a point in the interior of a semi-infinite solid.” Physics 7 (5): 195–202. https://doi.org/10.1063/1.1745385.
MOHURD (Ministry of Housing and Urban-Rural Development of the People’s Republic of China). 2013. Technical code for protection structures of urban rail transit. CJJ/T 202-2013. Beijing: MOHURD.
Pasternak, P. L. 1954. On a new method of analysis of an elastic foundation by means of two foundation constants. [In Russian.] Moscow: Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture.
Shen, S.-L., Q.-L. Cui, E.-C. Ho, and Y.-S. Xu. 2016. “Ground response to multiple parallel microtunneling operations in cemented silty clay and sand.” J. Geotech. Geoenviron. Eng. 142 (5): 04016001. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001441.
Shi, J., Y. Wang, and C. W. W. Ng. 2016. “Three-dimensional centrifuge modeling of ground and pipeline response to tunnel excavation.” J. Geotech. Geoenviron. Eng. 142 (11): 04016054. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001529.
Shiba, Y., K. Kawashima, M. Ohikata, and M. Kana. 1989. “Calculation method on sectional forces of longitudinal structure of shield tunnel under earthquake force based on response deformation method.” [In Japanese.] J. Jpn. Soc. Civ. Eng. 1989: 385–394. https://doi.org/10.2208/jscej.1989.404_385.
Tanahashi, H. 2004. “Formulas for an infinitely long Bernoulli-Euler beam on the Pasternak model.” Soils Found. 44 (5): 109–118. https://doi.org/10.3208/sandf.44.5_109.
Wu, B., W. Liu, P. Shi, X. Xu, and Y. Liu. 2022. “A case study of newly tunnels over-crossing the existing subway tunnels.” Int. J. Distrib. Sens. Netw. 18 (3): 155013292210871. https://doi.org/10.1177/15501329221087183.
Wu, H.-N., S.-L. Shen, S.-M. Liao, and Z.-Y. Yin. 2015. “Longitudinal structural modelling of shield tunnels considering shearing dislocation between segmental rings.” Tunnelling Underground Space Technol. 50: 317–323. https://doi.org/10.1016/j.tust.2015.08.001.
Wu, H.-N., S.-L. Shen, J. Yang, and A. 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.
Xu, L. 2005. Study on the longitudinal settlement of shield tunnel in soft soil. [In Chinese.] Shanghai, China: Tongji Univ.
Yang, M., and X. Zhao. 1992. “An approach for a single pile in layered soil.” [In Chinese.] J. Tongji Univ. (Nat. Sci.) 20 (4): 421–428.
Zhang, D., B. Liu, and Y. Qin. 2016. “Construction of a large-section long pedestrian underpass using pipe jacking in muddy silty clay: A case study.” Tunnelling Underground Space Technol. 60: 151–164. https://doi.org/10.1016/j.tust.2016.08.009.
Zhang, Z., M. Huang, C. Zhang, K. Jiang, and M. Lu. 2019. “Time-domain analyses for pile deformation induced by adjacent excavation considering influences of viscoelastic mechanism.” Tunnelling Underground Space Technol. 85: 392–405. https://doi.org/10.1016/j.tust.2018.12.020.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 24 • Issue 7 • July 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Mar 9, 2023
Accepted: Jan 31, 2024
Published online: May 9, 2024
Published in print: Jul 1, 2024
Discussion open until: Oct 9, 2024
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.