Analytical Approach to Estimating the Influence of Shotcrete Hardening Property on Tunnel Response
Publication: Journal of Engineering Mechanics
Volume 148, Issue 1
Abstract
Ignoring the shotcrete hardening property in tunnel design may lead to an overestimation of the bearing capacity of shotcrete liners and underestimation of tunnel convergence. However, accounting for this nonlinear hardening behavior of shotcrete in the tunnel analytical model is difficult because of the complexity of the mathematical derivation. This study aims to establish an analytical model to estimate the influence of the shotcrete hardening property on tunnel response. To overcome this challenge, the shotcrete hardening age was divided into several linear stages, and the corresponding equivalent Young’s modulus in each stage was calculated. A unified time-dependent solution was then proposed for predicting tunnel displacement and shotcrete liner pressure, with the tunnel face advancing effect and the installation delay of the shotcrete liner taken into consideration. The proposed analytical solution was applied to the Rong Jiawan tunnel in China, and the general trend of the analytical results agreed with that of the field data. Finally, a comprehensive parametric investigation including the sensitivity of the division of shotcrete age, geostress, and shotcrete hardening model was conducted based on the analytical model, and some useful recommendations for tunnel design are presented. The outcomes of this research can support tunnel design in similar projects.
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 work has been supported by the National Natural Science Foundation of China (Nos. 11872287 and 51908431), and the Fund of Shaanxi Key Research and Development Program (No. 2019ZDLGY01-10).
References
Aldrian, W. 1991. Beitrag zum materialverhalten von fruh belastetem spritzbeton. Leoben, Austria: Institut fur Geomechanik.
Barla, G., D. Debernardi, and D. Sterpi. 2012. “Time-dependent modeling of tunnels in squeezing conditions.” Int. J. Geomech. 12 (6): 697–710. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000163.
Birchall, T. J., and A. S. Osman. 2012. “Response of a tunnel deeply embedded in a viscoelastic medium.” Int. J. Num. Anal. Methods Geomech. 36 (15): 1717–1740. https://doi.org/10.1002/nag.1069.
Carranza-Torres, C., B. Rysdahl, and M. Kasim. 2013. “On the elastic analysis of a circular lined tunnel considering the delayed installation of the support.” Int. J. Rock Mech. Min. Sci. 61 (Jul): 57–85. https://doi.org/10.1016/j.ijrmms.2013.01.010.
Chang, Y. 1994. “Tunnel support with shotcrete in weak rock: A rock mechanics study.” Ph.D. thesis, Division of Soil and Rock Mechanics, Royal Institute of Technology.
Chu, Z., Z. Wu, B. Liu, and Q. Liu. 2019. “Coupled analytical solutions for deep-buried circular lined tunnels considering tunnel face advancement and soft rock rheology effects.” Tunnelling Underground Space Technol. 94 (Dec): 103111. https://doi.org/10.1016/j.tust.2019.103111.
Chu, Z., Z. Wu, Q. Liu, and B. Liu. 2020. “Analytical solutions for deep-buried lined tunnels considering longitudinal discontinuous excavation in rheological rock mass.” J. Eng. Mech. 146 (6): 04020047. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001784.
Chu, Z., Z. Wu, Q. Liu, B. Liu, and J. Sun. 2021a. “Analytical solution for lined circular tunnels in deep viscoelastic burgers rock considering the longitudinal discontinuous excavation and sequential installation of liners.” J. Eng. Mech. 147 (4): 04021009. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001912.
Chu, Z., Z. Wu, Q. Liu, L. Weng, Z. Wang, and Y. Zhou. 2021b. “Evaluating the microstructure evolution behaviors of saturated sandstone using NMR testing under uniaxial short-term and creep compression.” Rock Mech. Rock Eng. 54 (Jun): 4905–4927. https://doi.org/10.1007/s00603-021-02538-4.
Do, D. P., N. T. Tran, V. T. Mai, D. Hoxha, and M. N. Vu. 2020. “Time-dependent reliability analysis of deep tunnel in the viscoelastic Burger rock with sequential installation of liners.” Rock Mech. Rock Eng. 53 (3): 1259–1285. https://doi.org/10.1007/s00603-019-01975-6.
Exadaktylos, G. E., and M. C. Stavropoulou. 2002. “A closed-form elastic solution for stresses and displacements around tunnels.” Int. J. Rock Mech. Min. Sci. 39 (7): 905–916. https://doi.org/10.1016/S1365-1609(02)00079-5.
Fahimifar, A., F. M. Tehrani, A. Hedayat, and A. Vakilzadeh. 2010. “Analytical solution for the excavation of circular tunnels in a visco-elastic Burger’s material under hydrostatic stress field.” Tunnelling Underground Space Technol. 25 (4): 297–304. https://doi.org/10.1016/j.tust.2010.01.002.
Fahimifar, A., and A. R. Hedayat. 2008. “Determination of ground response curve of the supported tunnel considering progressive hardening of shotcrete lining.” In Proc., ISRM Int. Symp., 5th Asian Rock Mechanics Symp. Tehran, Iran: International Society for Rock Mechanics and Rock Engineering.
Fan, S., Z. Song, T. Xu, K. Wang, and Y. Zhang. 2021. “Tunnel deformation and stress response under the bilateral foundation pit construction-a case study.” Arch. Civ. Mech. Eng. 21 (3): 109. https://doi.org/10.1007/s43452-021-00259-7.
Gschwandtner, G. G., and R. Galler. 2012. “Input to the application of the convergence confinement method with time-dependent material behaviour of the support.” Tunnelling Underground Space Technol. 27 (1): 13–22. https://doi.org/10.1016/j.tust.2011.06.003.
Kargar, A. R., R. Rahmannejad, and M. A. Hajabasi. 2014. “A semi-analytical elastic solution for stress field of lined non-circular tunnels at great depth using complex variable method.” Int. J. Solids Struct. 51 (6): 1475–1482. https://doi.org/10.1016/j.ijsolstr.2013.12.038.
Kontogianni, V., P. Psimoulis, and S. Stiros. 2006. “What is the contribution of time-dependent deformation in tunnel convergence?” Eng. Geol. 82 (4): 264–267. https://doi.org/10.1016/j.enggeo.2005.11.001.
Li, S. C., and M. B. Wang. 2008. “An elastic stress-displacement solution for a lined tunnel at great depth.” Int. J. Rock Mech. Min. Sci. 45 (4): 486–494. https://doi.org/10.1016/j.ijrmms.2007.07.011.
Malan, D. F. 2002. “Simulating the time-dependent behavior of excavations in hard rock.” Rock Mech. Rock Eng. 35 (4): 225–254. https://doi.org/10.1007/s00603-002-0026-0.
Meschke, G., C. Kropik, and H. A. Mang. 1996. “Numerical analyses of tunnel linings by means of a viscoplastic material model for shotcrete.” Int. J. Num. Methods Eng. 39 (18): 3145–3162. https://doi.org/10.1002/(SICI)1097-0207(19960930)39:18%3C3145::AID-NME992%3E3.0.CO;2-M.
Mogilevskaya, S. G., and B. Lecampion. 2018. “A lined hole in a viscoelastic rock under biaxial far-field stress.” Int. J. Rock Mech. Min. Sci. 106 (Jun): 350–363. https://doi.org/10.1016/j.ijrmms.2018.02.019.
Neuner, M., M. Schreter, D. Unteregger, and G. Hofstetter. 2017. “Influence of the constitutive model for shotcrete on the predicted structural behavior of the shotcrete shell of a deep tunnel.” Materials (Basel) 10 (6): 577. https://doi.org/10.3390/ma10060577.
Nomikos, P., R. Rahmannejad, and A. Sofianos. 2011. “Supported axisymmetric tunnels within linear viscoelastic Burgers rocks.” Rock Mech. Rock Eng. 44 (5): 553–564. https://doi.org/10.1007/s00603-011-0159-0.
Oreste, P. P. 2003. “A procedure for determining the reaction curve of shotcrete lining considering transient conditions.” Rock Mech. Rock Eng. 36 (3): 209–236. https://doi.org/10.1007/s00603-002-0043-z.
Oreste, P. P., and D. Pella. 1997. “Modelling progressive hardening of shotcrete in convergence-confinement approach to tunnel design.” Tunnelling Underground Space Technol. 12 (3): 425–431. https://doi.org/10.1016/S0886-7798(97)00033-3.
Pan, Y. W., and Z. L. Huang. 1994. “A model of the time-dependent interaction between rock and shotcrete support in a tunnel.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 31 (3): 213–219. https://doi.org/10.1016/0148-9062(94)90465-0.
Panet, M. 1995. Calcul des tunnels par la Me’thode de convergence-confinement. Paris: Presses de l’Ecole Nationale des Ponts et Chaussées.
Panet, M., and A. Guenot. 1982. “Analysis of convergence behind the face of a tunnel.” In Proc., Int. Symp. Tunnelling, 197–204. London: IMM. https://doi.org/10.1016/0148-9062(83)91744-8.
Paraskevopoulou, C., and M. Diederichs. 2018. “Analysis of time-dependent deformation in tunnels using the convergence-confinement method.” Tunnelling Underground Space Technol. 71 (Jan): 62–80. https://doi.org/10.1016/j.tust.2017.07.001.
Pöttler, R. 1990. “Time-dependent rock-Shotcrete interaction a numerical shortcut.” Comput. Geotech. 9 (3): 149–169. https://doi.org/10.1016/0266-352X(90)90011-J.
Sakurai, S. 1978. “Approximate time-dependent analysis of tunnel support structure considering progress of tunnel face.” Int. J. Num. Anal. Methods Geomech. 2 (2): 159–175. https://doi.org/10.1002/nag.1610020205.
Schädlich, B., H. F. Schweiger, T. Marcher, and E. Saurer. 2014. “Application of a novel constitutive shotcrete model to tunneling.” In Proc., ISRM Regional Symp.-EUROCK 2014. Int. Society for Rock Mechanics and Rock Engineering. Leiden, Netherlands: CRC Press.
Schweiger, H. F., T. Marcher, and B. Schädlich. 2014. “Application of a new shotcrete constitutive model to the numerical analysis of a tunnel excavation.” In Tunneling and underground construction, 890–899. Reston, VA: ASCE.
Sulem, J., M. Panet, and A. Guenot. 1987. “An analytical solution for time-dependent displacements in a circular tunnel.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 24 (3): 155–164. https://doi.org/10.1016/0148-9062(87)90523-7.
Sun, Y., G. Li, J. Zhang, and D. Qian. 2020. “Experimental and numerical investigation on a novel support system for controlling roadway deformation in underground coal mines.” Energy Sci. Eng. 8 (2): 490–500. https://doi.org/10.1002/ese3.530.
Sun, Y., G. Li, N. Zhang, Q. Chang, J. Xu, and J. Zhang. 2021. “Development of ensemble learning models to evaluate the strength of coal-grout materials.” Int. J. Min. Sci. Tech. 31 (2): 153–162. https://doi.org/10.1016/j.ijmst.2020.09.002.
Unlu, T. 2003. “Gercek H. Effect of Poisson’s ratio on the normalized radial displacements occurring around the face of a circular tunnel.” Tunnelling Underground Space Technol. 18 (5): 547–553. https://doi.org/10.1016/S0886-7798(03)00086-5.
Verruijt, A. 1997. “A complex variable solution for a deforming circular tunnel in an elastic half-plane.” Int. J. Num. Anal. Methods Geomech. 21 (2): 77–89. https://doi.org/10.1002/(SICI)1096-9853(199702)21:2%3C77::AID-NAG857%3E3.0.CO;2-M.
Vlachopoulos, N., and M. S. Diederichs. 2009. “Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels.” Rock Mech. Rock Eng. 42 (2): 131–146. https://doi.org/10.1007/s00603-009-0176-4.
Wang, H. N., S. Utili, and M. J. Jiang. 2014. “An analytical approach for the sequential excavation of axisymmetric lined tunnels in viscoelastic rock.” Int. J. Rock Mech. Min. Sci. 68 (Jun): 85–106. https://doi.org/10.1016/j.ijrmms.2014.02.002.
Wu, K., and Z. Shao. 2019. “Study on the effect of flexible layer on support structures of tunnel excavated in viscoelastic rocks.” J. Eng. Mech. 145 (10): 04019077. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001657.
Wu, K., Z. Shao, S. Hong, and S. Qin. 2020a. “Analytical solutions for mechanical response of circular tunnels with double primary linings in squeezing grounds.” Geomech. Eng. 22 (6): 509–518. https://doi.org/10.12989/gae.2020.22.6.509.
Wu, K., Z. Shao, and S. Qin. 2020b. “An analytical design method for ductile support structures in squeezing tunnels.” Arch. Civ. Mech. Eng. 20 (3): 91. https://doi.org/10.1007/s43452-020-00096-0.
Wu, K., Z. Shao, S. Qin, and B. Li. 2020c. “Determination of deformation mechanism and countermeasures in silty clay tunnel.” J. Perform. Constr. Facil. 34 (1): 04019095. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001381.
Wu, K., Z. Shao, S. Qin, W. Wei, and Z. Chu. 2021a. “A critical review on the performance of yielding supports in squeezing tunnels.” Tunnelling Underground Space Technol. 115 (9): 103815. https://doi.org/10.1016/j.tust.2021.103815.
Wu, K., Z. Shao, S. Qin, N. Zhao, and H. Hu. 2020d. “Analytical-based assessment of effect of highly deformable elements on tunnel lining within viscoelastic rocks.” Int. J. Appl. Mech. 12 (3): 2050030. https://doi.org/10.1142/S1758825120500301.
Wu, K., Z. Shao, M. Sharifzadeh, S. Hong, and S. Qin. 2021b. “Analytical computation of support characteristic curve for circumferential yielding lining in tunnel design.” J. Rock Mech. Geotech. Eng. 13 (1): 22–45. https://doi.org/10.1016/j.jrmge.2020.11.003.
Xu, C., C. Cai, and S. Du. 2021a. “Simplified solution for viscoelastic-plastic interaction between tunnel support and surrounding rock based on MC and GZZ strength criteria.” Comput. Geotech. 139 (Nov): 104393. https://doi.org/10.1016/j.compgeo.2021.104393.
Xu, C., and C. Xia. 2021b. “A new large strain approach for predicting tunnel deformation in strain-softening rock mass based on the generalized Zhang-Zhu strength criterion.” Int. J. Rock Mech. Min. Sci. 143 (5): 104786. https://doi.org/10.1016/j.ijrmms.2021.104786.
Yan, Y., J. Qiu, Q. Huang, Z. Wang, Y. Xie, and T. Liu. 2021. “Ground fissures geology in Xi’an and failure mitigation measures for utility tunnel system due to geohazard.” Arabian J. Geosci. 14 (13): 1207. https://doi.org/10.1007/s12517-021-07189-x.
Zhao, D., L. Jia, M. Wang, and F. Wang. 2016. “Displacement prediction of tunnels based on a generalised Kelvin constitutive model and its application in a subsea tunnel.” Tunnelling Underground Space Technol. 54 (Apr): 29–36. https://doi.org/10.1016/j.tust.2016.01.030.
Zhao, N., Z. Shao, K. Wu, Z. Chu, and S. Qin. 2021. “Time-dependent solutions for lined circular tunnels considering rockbolts reinforcement and face advancement effects.” Int. J. Geomech. 21 (10): 04021179. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002130.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 148 • Issue 1 • January 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Apr 7, 2021
Accepted: Sep 23, 2021
Published online: Oct 28, 2021
Published in print: Jan 1, 2022
Discussion open until: Mar 28, 2022
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.
Cited by
- Li-Zhuang Cui, Jian Liu, Hongzheng Luo, Jianhong Wang, Xiao Zhang, Gaohang Lv, Quanyi Xie, Deformation Measurement of Tunnel Shotcrete Liner Using the Multiepoch LiDAR Point Clouds, Journal of Construction Engineering and Management, 10.1061/JCEMD4.COENG-14518, 150, 6, (2024).
- Chi Liu, Yuhang Liu, Yuhua Chen, Chujun Zhao, Junling Qiu, Dingyi Wu, Tong Liu, Haobo Fan, Yiwen Qin, Kunjie Tang, A State-of-the-Practice Review of Three-Dimensional Laser Scanning Technology for Tunnel Distress Monitoring, Journal of Performance of Constructed Facilities, 10.1061/JPCFEV.CFENG-4205, 37, 2, (2023).
- Nannan Zhao, Zhushan Shao, Kui Wu, Analytical Approach to Evaluating the Influence of the Compressible Layer on the Time-Dependent Response of Deep Soft-Rock Tunnels, International Journal of Geomechanics, 10.1061/IJGNAI.GMENG-8099, 23, 6, (2023).
- Quansen Wu, Fengjun Han, Shengjian Liang, Fanxing Sun, Daqing Wan, Huairui Su, Fuwu Ma, Quanlin Wu, Development Law of Mining Fracture and Disaster Control Technology under Hard and Thick Magmatic Rock, Sustainability, 10.3390/su141811140, 14, 18, (11140), (2022).
- Sisi Tian, Yanjun Shen, Shuguang Li, Wen Ma, You Lv, Xueting Li, Study on Splitting Damage Characteristics of a Rock–Shotcrete Interface Subjected to Corrosive Water, Sustainability, 10.3390/su14094987, 14, 9, (4987), (2022).
- Jiaxu Jin, Shihao Yuan, Hongzhi Cui, Xiaochun Xiao, Baoxin Jia, A Threshold Model of Tailings Sand Liquefaction Based on PSO-SVM, Sustainability, 10.3390/su14052720, 14, 5, (2720), (2022).
- Qing Chai, Huimin Li, Wei Tian, Yang Zhang, Critical Success Factors for Safety Program Implementation of Regeneration of Abandoned Industrial Building Projects in China: A Fuzzy DEMATEL Approach, Sustainability, 10.3390/su14031550, 14, 3, (1550), (2022).
- Xiaomeng Zheng, Zhushan Shao, Nannan Zhao, Chenglong Li, Kui Wu, Performance Evaluation of Tunnel-Slag-Improved High Liquid Limit Soil in Subgrade: A Case Study, Materials, 10.3390/ma15051976, 15, 5, (1976), (2022).
- Xiaomeng Zheng, Kui Wu, Zhushan Shao, Bo Yuan, Nannan Zhao, Tunnel Squeezing Deformation Control and the Use of Yielding Elements in Shotcrete Linings: A Review, Materials, 10.3390/ma15010391, 15, 1, (391), (2022).
- Zhixiong Zhang, Yun Cheng, Zhanping Song, Xueyun Ye, Anisotropy and Directivity Effects on Uniaxial Compression of Carbonaceous Slate Form Jinman Mine, Applied Sciences, 10.3390/app12199811, 12, 19, (9811), (2022).
- See more