Analytical Solution for Segmental-Tunnel Lining Incorporating Interaction between Adjacent Rings
Publication: Journal of Engineering Mechanics
Volume 146, Issue 7
Abstract
The different joint arrangements resulting from different segmental assemblies between adjacent rings may inevitably give rise to the interaction for staggered jointed lining, which is crucial for the structural analysis of segmental-tunnel lining. However, most existing analytical solutions only consider the straight jointed lining and are not applicable to the staggered jointed lining. By using the state-space method, a unified analytical solution is obtained for the circular segmental-tunnel lining irrespective of the layout of segmental assemblies between adjacent rings, and the interaction effect between adjacent rings is explicitly addressed. The segments were treated as curved Euler beams, while the longitudinal joints between the segments were modeled by a set of springs with three-directional resistances, and the circumferential joints between the adjacent rings were modeled by shear springs with both radial and circumferential resistances. A rigorous theoretical proof is implicitly embedded to eliminate the rigid-body displacements of the proposed method as a self-balancing condition of external loads acting on the lining. Finally, the solutions are verified through comparisons with both the experimental and analytical results in the literature. The results show that the present method exhibits high efficiency and suitability for both linings with straight joints and those with staggered joints.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The MATLAB codes for implementing the model and all the data generated in this study are available from the corresponding author upon reasonable request.
Acknowledgments
The research described in this paper was supported by the Natural Science Foundation of China (Grant Nos. 51825803 and 51578499) and the National Key Basic Research Program of China (Grant No. 2015CB057801), which are gratefully acknowledged.
References
Arnau, O., and C. Molins. 2015. “Theoretical and numerical analysis of the three-dimensional response of segmental tunnel linings subjected to localized loads.” Tunnelling Underground Space Technol. 49 (Jun): 384–399. https://doi.org/10.1016/j.tust.2015.05.012.
Blom, C. B. M. 2002. “Design philosophy of concrete linings for tunnels in soft soil.” Ph.D. thesis, Dept. of Civil Engineering, Delft Univ. of Technology.
Bobet, A. 2001. “Analytical solutions for shallow tunnels in saturated ground.” J. Eng. Mech. 127 (12): 1258–1266. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:12(1258).
Croll, J. G. A. 2001. “Buckling of cylindrical tunnel.” J. Eng. Mech. 127 (4): 333–341. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:4(333).
Do, N. A., D. Dias, P. Oreste, and I. Djeran-Maigre. 2014. “A new numerical approach to the hyperstatic reaction method for segmental tunnel linings.” Int. J. Numer. Anal. Methods Geomech. 38 (15): 1617–1632. https://doi.org/10.1002/nag.2277.
EI Naggar, H., and S. D. Hinchberger. 2008. “An analytical solution for jointed tunnel linings in elastic soil or rock.” Can. Geotech. J. 45 (11): 1572–1593. https://doi.org/10.1139/T08-075.
Huang, X., W. Liu, Z. Zhang, Q. Wang, S. Wang, Q. Zhuang, Y. Zhu, and C. Zhang. 2019. “Exploring the three-dimensional response of a water storage and sewage tunnel based on full-scale loading tests.” Tunnelling Underground Space Technol. 88 (Jun): 156–168. https://doi.org/10.1016/j.tust.2019.03.003.
International Tunnelling Association. 2000. “Guidelines for the design of shield tunnel lining.” Tunnelling Underground Space Technol. 15 (3): 303–313. https://doi.org/10.1016/S0886-7798(00)00058-4.
JSCE (Japan Society of Civil Engineers). 2001. Specification of shield tunnelling for design and construction. Tokyo: JSCE.
Klappers, C., F. Grübl, and B. Ostermeier. 2006. “Structural analyses of segmental lining-coupled beam and spring analyses versus 3D-FEM calculations with shell elements.” Tunnelling Underground Space Technol. 21 (3–4): 254–255. https://doi.org/10.1016/j.tust.2005.12.116.
Koyama, Y. 2003. “Present status and technology of shield tunneling method in Japan.” Tunnelling Underground Space Technol. 18 (2): 145–159. https://doi.org/10.1016/S0886-7798(03)00040-3.
Lee, K. M., X. Y. Hou, X. W. Ge, and Y. Tang. 2001. “An analytical solution for a jointed shield-driven tunnel lining.” Int. J. Numer. Anal. Methods Geomech. 25 (4): 365–390. https://doi.org/10.1002/nag.134.
Li, X., Z. Yan, Z. Wang, and H. Zhu. 2015a. “Experimental and analytical study on longitudinal joint opening of concrete segmental lining.” Tunnelling Underground Space Technol. 46 (Feb): 52–63. https://doi.org/10.1016/j.tust.2014.11.002.
Li, X., Z. Yan, Z. Wang, and H. Zhu. 2015b. “A progressive model to simulate the full mechanical behavior of concrete segmental lining longitudinal joints.” Eng. Struct. 93 (Jul): 97–113. https://doi.org/10.1016/j.engstruct.2015.03.011.
Lim, C. W., C. M. Wang, and S. Kitipornchai. 1997. “Timoshenko curved beam bending solutions in terms of Euler-Bernoulli solutions.” Arch. Appl. Mech. 67 (3): 179–190. https://doi.org/10.1007/s004190050110.
Liu, K-Y., and C. W. Bert. 1986. “Stress analysis of thick-walled reinforced tunnel.” J. Eng. Mech. 112 (9): 916–931. https://doi.org/10.1061/(ASCE)0733-9399(1986)112:9(916).
Liu, X., Z. Dong, Y. Bai, and Y. Zhu. 2017. “Investigation of the structural effect induced by stagger joints in segmental tunnel linings: First results from full-scale ring tests.” Tunnelling Underground Space Technol. 66 (Jun): 1–18. https://doi.org/10.1016/j.tust.2017.03.008.
Liu, X., Z. Dong, W. Song, and Y. Bai. 2018. “Investigation of the structural effect induced by stagger joints in segmental tunnel linings: Direct insight from mechanical behaviors of longitudinal and circumferential joints.” Tunnelling Underground Space Technol. 71 (Jan): 271–291. https://doi.org/10.1016/j.tust.2017.08.030.
Mashimo, H., and T. Ishimura. 2003. “Evaluation of the load on shield tunnel lining in gravel.” Tunnelling Underground Space Technol. 18 (2–3): 233–241. https://doi.org/10.1016/S0886-7798(03)00032-4.
MathWorks, Inc. 2019. “Documentation for Matlab R2019b.” Accessed September 16, 2019. https://ww2.mathworks.cn/help/matlab/math/array-indexing.html?lang=en.
Nishikawa, K. 2003. “Development of a prestressed and precast concrete segmental lining.” Tunnelling Underground Space Technol. 18 (2–3): 243–251. https://doi.org/10.1016/S0886-7798(03)00033-6.
Qatu, M. S. 1993. “Theories and analyses of thin and moderately thick laminated composite curved beams.” Int. J. Solids Struct. 30 (20): 2743–2756. https://doi.org/10.1016/0020-7683(93)90152-W.
Tvede-Jensen, B., M. Faurschou, and T. Kasper. 2017. “A modelling approach for joint rotations of segmental concrete tunnel linings.” Tunnelling Underground Space Technol. 67 (Aug): 61–67. https://doi.org/10.1016/j.tust.2017.04.019.
Wang, J. C., W. M. Huang, R. Q. Xu, Z. X. Yang, and R. Q. Xu. 2020. “Analytical approach for circular-jointed shield tunnel lining based on the state space method.” Int. J. Numer. Anal. Methods Geomech. 44 (5): 575–595. https://doi.org/10.1002/nag.3012.
Yang, Y., W. Zhang, J. Wang, and Z. Yang. 2014. “Three-dimensional orthotropic equivalent modelling method of large-scale circular jointed lining.” Tunnelling Underground Space Technol. 44 (Sep): 33–41. https://doi.org/10.1016/j.tust.2014.07.002.
Zhang, J-L., T. Schlappal, Y. Yuan, H. A. Mang, and B. Pichler. 2019. “The influence of interfacial joints on the structural behavior of segmental tunnel rings subjected to ground pressure.” Tunnelling Underground Space Technol. 84 (Feb): 538–556. https://doi.org/10.1016/j.tust.2018.08.025.
Zhang, J-L., C. Vida, Y. Yuan, C. Hellmich, H. A. Mang, and B. Pichler. 2017. “A hybrid analysis method for displacement-monitored segmented circular tunnel rings.” Eng. Struct. 148 ( Oct): 839–856. https://doi.org/10.1016/j.engstruct.2017.06.049.
Zhang, J.-L., H. A. Mang, X. Liu, Y. Yuan, and B. Pichler. 2018. “On a nonlinear hybrid method for multiscale analysis of a bearing-capacity test of a real-scale segmental tunnel ring.” Int. J. Numer. Anal. Methods Geomech. 43 (7): 1343–1372. https://doi.org/10.1002/nag.2894.
Zhao, C., A. A. Lavasan, T. Barciaga, C. Kämper, P. Mark, and T. Schanz. 2017. “Prediction of tunnel lining forces and deformations using analytical and numerical solutions.” Tunnelling Underground Space Technol. 64 (Apr): 164–176. https://doi.org/10.1016/j.tust.2017.01.015.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 146 • Issue 7 • July 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Oct 13, 2019
Accepted: Feb 5, 2020
Published online: May 7, 2020
Published in print: Jul 1, 2020
Discussion open until: Oct 7, 2020
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.