Analytical Solutions for Deep-Buried Lined Tunnels Considering Longitudinal Discontinuous Excavation in Rheological Rock Mass
Publication: Journal of Engineering Mechanics
Volume 146, Issue 6
Abstract
For tunneling in a deep, soft rock mass, rock deformation and lining pressure, which are time-dependent behaviors, are mainly affected by rock rheology and longitudinal excavation processes. In practice, tunneling operations are often suspended due to various reasons, which will result in changes to the time-dependent behaviors of tunnel systems. To investigate the discontinuous advancement of the tunnel face in a soft rheological rock mass, in this study, closed-form analytical solutions are presented to analyze the time dependency of deep-buried circular lined tunnels. In the derivation, four types of viscoelastic models are utilized to consider the different creep behaviors of the host rock. The coupling effect between rock rheology and tunnel face advancement is also taken into account. To realistically simulate the process of tunnel face advancement, five different excavation methods are considered in the solutions that depend on whether the face stops and on the changes of advancing speeds before and after stoppage. The proposed solutions are validated by comparing the calculated results with those predicted by a finite difference simulation. According to the provided solutions, a series of parametric analyses are systematically performed to investigate the influences of the lining installation time, the duration of the tunnel face stoppage, the tunnel face advancing parameters, and the rheological parameters of the rock on rock stresses and displacement, as well as the support pressure. Finally, the proposed solutions are successfully applied to the Rong Jiawan tunnel when an excavation stoppage occurs halfway before tunnel completion, and the theoretical predictions are in good agreement with the field monitoring data. The solutions proposed in this paper provide an efficient analytical approach for predicting and analyzing the discontinuous excavation of rheological tunnels.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data and models generated during the study are available from the corresponding author by request (theoretical results, Flac3D code, and field monitoring data).
Acknowledgments
The research work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51908431 and 41502283), for which the authors are grateful.
References
Alp, M., and A. Apaydin. 2019. “Assessment of the factors affecting the advance rate of the Tunnel Gerede, the longest and one of the most problematic water transmission tunnels of Turkey.” Tunnelling Underground Space Technol. 89 (Jul): 157–169. https://doi.org/10.1016/j.tust.2019.04.001.
Asadollahpour, E., R. Rahmannejad, A. Asghari, and A. Abdollahipour. 2014. “Back analysis of closure parameters of Panet equation and Burger’s model of Babolak water tunnel conveyance.” Int. J. Rock Mech. Min. Sci. 68 (Jun): 159–166. https://doi.org/10.1016/j.ijrmms.2014.02.017.
Birchall, T. J., and A. S. Osman. 2012. “Response of a tunnel deeply embedded in a viscoelastic medium.” Int J Numer Anal Met. 36 (15): 1717–1740. https://doi.org/10.1002/nag.1069.
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).
Boidy, E., A. Bouvard, and F. Pellet. 2002. “Back analysis of time-dependent behaviour of a test gallery in claystone.” Tunnelling Underground Space Technol. 17 (4): 415–424. https://doi.org/10.1016/S0886-7798(02)00066-4.
Bonini, M., and G. Barla. 2012. “The Saint Martin La Porte access adit (Lyon-Turin Base Tunnel) revisited.” Tunnelling Underground Space Technol. 30 (Jul): 38–54. https://doi.org/10.1016/j.tust.2012.02.004.
Bonini, M., D. Debernardi, M. Barla, and G. Barla. 2007. “The mechanical behaviour of clay shales and implications on the design of tunnels.” Rock Mech. Rock Eng. 42 (2): 361–388. https://doi.org/10.1007/s00603-007-0147-6.
Bui, T., H. Wong, F. Deleruyelle, N. Dufour, C. Leo, and D. Sun. 2014. “Analytical modeling of a deep tunnel inside a poro-viscoplastic rock mass accounting for different stages of its life cycle.” Comput. Geotech. 58 (May): 88–100. https://doi.org/10.1016/j.compgeo.2013.11.004.
Carranza-Torres, C., and C. Fairhurst. 1999. “The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek-Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 36 (6): 777–809. https://doi.org/10.1016/S0148-9062(99)00047-9.
Carranza-Torres, C., and C. Fairhurst. 2000. “Application of the convergence-confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criterion.” Tunnelling Underground Space Technol. 15 (2): 187–213. https://doi.org/10.1016/S0886-7798(00)00046-8.
Chen, Z., M. L. Wang, and T. Lu. 1997. “Study of tertiary creep of rock salt.” J. Eng. Mech. 123 (1): 77–82. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:1(77).
Chu, Z., B. Liu, K. Liu, and J. Sun. 2017. “Analytical viscoelastic solutions for lined circular tunnels under two contact conditions in a non-hydrostatic stress field.” Rock Soil Mech. 38 (11): 10. https://doi.org/10.16285/j.rsm.2017.11.017.
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.
Dai, H. L., X. Wang, G. X. Xie, and X. Y. Wang. 2004. “Theoretical model and solution for the rheological problem of anchor-grouting a soft rock tunnel.” Int. J. Pressure Ves. Pip. 81 (9): 739–748. https://doi.org/10.1016/j.ijpvp.2004.05.004.
de la Vaissière, R., G. Armand, and J. Talandier. 2015. “Gas and water flow in an excavation-induced fracture network around an underground drift: A case study for a radioactive waste repository in clay rock.” J. Hydrol. 521 (Feb): 141–156. https://doi.org/10.1016/j.jhydrol.2014.11.067.
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.
Fan, L. F., F. Ren, and G. W. Ma. 2012. “Experimental study on viscoelastic behavior of sedimentary rock under dynamic loading.” Rock Mech. Rock Eng. 45 (3): 433–438. https://doi.org/10.1007/s00603-011-0197-7.
Fei, S., H. Wang, and M. Jiang. 2018. “Analytical solutions for lined circular tunnels in viscoelastic rock considering various interface conditions.” Appl Math Model. 55 (Mar): 109–130. https://doi.org/10.1016/j.apm.2017.10.031.
Feng, X.-T., B.-R. Chen, C. Yang, H. Zhou, and X. Ding. 2006. “Identification of visco-elastic models for rocks using genetic programming coupled with the modified particle swarm optimization algorithm.” Int. J. Rock Mech. Min. Sci. 43 (5): 789–801. https://doi.org/10.1016/j.ijrmms.2005.12.010.
Findley, W. N., J. S. Lai, and K. Onaran. 1977. “Creep and relaxation of nonlinear viscoelastic materials.” J. Appl. Mech. 44 (2): 364. https://doi.org/10.1115/1.3424077.
Fujii, Y., T. Kiyama, Y. Ishijima, and J. Kodama. 1999. “Circumferential strain behavior during creep tests of brittle rocks.” Int. J. Rock Mech. Min. Sci. 36 (3): 323–337. https://doi.org/10.1016/S0148-9062(99)00024-8.
Graziani, A., D. Boldini, and R. Ribacchi. 2005. “Practical estimate of deformations and stress relief factors for deep tunnels supported by shotcrete.” Rock Mech. Rock Eng. 38 (5): 345–372. https://doi.org/10.1007/s00603-005-0059-2.
Guayacán, C., M. Lina, J. Sulem, D. M. Seyedi, S. Ghabezloo, A. Noiret, and G. Armand. 2016. “Analysis of long-term anisotropic convergence in drifts excavated in Callovo-Oxfordian claystone.” Rock Mech. Rock Eng. 49 (1): 97–114. https://doi.org/10.1007/s00603-015-0737-7.
Hasanpour, R., J. Rostami, J. Schmitt, Y. Ozcelik, and B. Sohrabian. 2020. “Prediction of TBM jamming risk in squeezing grounds using Bayesian and artificial neural networks.” J. Rock Mech. Geotech. Eng. 12 (1): 21–31. https://doi.org/10.1016/j.jrmge.2019.04.006.
Heap, M., P. Baud, P. Meredith, A. Bell, and I. Main. 2009. “Time-dependent brittle creep in Darley Dale sandstone.” J. Geophys. Res. Solid Earth 114 (B7). https://doi.org/10.1029/2008JB006212.
Itasca. 2012. Group Inc FLAC3D v.5.0: User’s guide. Minneapolis, MN: Itasca Cons. Group Inc.
Kielbassa, S., and H. Duddeck. 1991. “Stress-strain fields at the tunnelling face—Three-dimensional analysis for two-dimensional technical approach.” Rock Mech. Rock Eng. 24 (3): 115–132. https://doi.org/10.1007/BF01042857.
Ladanyi, B., and D. E. Gill. 1988. “Design of tunnel linings in a creeping rock.” Int. J. Min. Geol. Eng. 6 (2): 113–126. https://doi.org/10.1007/BF00880802.
Lakes, R. S. 1998. Viscoelastic solids. Boca Raton, FL: Taylor & Francis Group.
Li, P., F. Wang, L. Fan, H. Wang, and G. Ma. 2019. “Analytical scrutiny of loosening pressure on deep twin-tunnels in rock formations.” Tunnelling Underground Space Technol. 83 (Jan): 373–380. https://doi.org/10.1016/j.tust.2018.10.007.
Liu, B., and X. Du. 2004. “Visco-elastic analysis on interaction between supporting structure and surrounding rocks of circle tunnel.” Chin. J. Rock Mech. Eng. 23 (4): 561–567.
Lo, K., and C. M. Yuen. 1981. “Design of tunnel lining in rock for long term time effects.” Can. Geotech. J. 18 (1): 24–39. https://doi.org/10.1139/t81-004.
Lu, A., L. Zhang, and N. Zhang. 2011. “Analytic stress solutions for a circular pressure tunnel at pressure and great depth including support delay.” Int. J. Rock Mech. Min. Sci. 48 (3): 514–519. https://doi.org/10.1016/j.ijrmms.2010.09.002.
Ma, K., C. A. Tang, L. X. Wang, D. H. Tang, D. Y. Zhuang, Q. B. Zhang, and J. Zhao. 2016. “Stability analysis of underground oil storage caverns by an integrated numerical and microseismic monitoring approach.” Tunnelling Underground Space Technol. 54 (Apr): 81–91. https://doi.org/10.1016/j.tust.2016.01.024.
Ma, L. J., X. Y. Liu, Q. Fang, H. F. Xu, H. M. Xia, E. B. Li, S. G. Yang, and W.-P. Li. 2013. “A new elasto-viscoplastic damage model combined with the generalized Hoek–Brown failure criterion for bedded rock salt and its application.” Rock Mech. Rock Eng. 46 (1): 53–66. https://doi.org/10.1007/s00603-012-0256-8.
Malan, D. F. 1999. “Time-dependent behaviour of deep level tabular excavations in hard rock.” Rock Mech. Rock Eng. 32 (2): 123–155. https://doi.org/10.1007/s006030050028.
Malan, D. F. 2002. “Manuel rocha medal recipient simulating the time-dependent behaviour of excavations in hard rock.” Rock Mech. Rock Eng. 35 (4): 225–254. https://doi.org/10.1007/s00603-002-0026-0.
Maranini, E., and M. Brignoli. 1999. “Creep behaviour of a weak rock: Experimental characterization.” Int. J. Rock Mech. Min. Sci. 36 (1): 127–138. https://doi.org/10.1016/S0148-9062(98)00171-5.
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.
Nadimi, S., K. Shahriar, M. Sharifzadeh, and P. Moarefvand. 2011. “Triaxial creep tests and back analysis of time-dependent behavior of Siah Bisheh cavern by 3-dimensional distinct element method.” Tunnelling Underground Space Technol. 26 (1): 155–162. https://doi.org/10.1016/j.tust.2010.09.002.
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.
Pan, Y. W., and J. J. Dong. 1991. “Time-dependent tunnel convergence—I. Formulation of the model.” Int. J. Rock Mech. Min. Sci. 28 (6): 469–475. https://doi.org/10.1016/0148-9062(91)91122-8.
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.
Paraskevopoulou, C., M. Perras, M. Diederichs, S. Loew, T. Lam, and M. Jensen. 2018. “Time-dependent behaviour of brittle rocks based on static load laboratory tests.” Geotech. Geol. Eng. 36 (1): 337–376. https://doi.org/10.1007/s10706-017-0331-8.
Pellet, F., M. Roosefid, and F. Deleruyelle. 2009. “On the 3D numerical modelling of the time-dependent development of the damage zone around underground galleries during and after excavation.” Tunnelling Underground Space Technol. 24 (6): 665–674. https://doi.org/10.1016/j.tust.2009.07.002.
Phienwej, N., P. Thakur, and E. Cording. 2007. “Time-dependent response of tunnels considering creep effect.” Int. J. Geomech. 7 (4): 296–306. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:4(296).
Pyatigorets, A. V., S. G. Mogilevskaya, and M. O. Marasteanu. 2008. “Linear viscoelastic analysis of a semi-infinite porous medium.” Int. J. Solids Struct. 45 (5): 1458–1482. https://doi.org/10.1016/j.ijsolstr.2007.10.001.
Re, G. 1989. Introduction to rock mechanics. New York: Wiley.
Roateşi, S. 2014. “Analytical and numerical approach for tunnel face advance in a viscoplastic rock mass.” Int. J. Rock Mech. Min. Sci. 70 (Sep): 123–132. https://doi.org/10.1016/j.ijrmms.2014.04.007.
Sakurai, S. 1978. “Approximate time-dependent analysis of tunnel support structure considering progress of tunnel face.” Int. J. Numer. Anal. Met. 2 (2): 159–175. https://doi.org/10.1002/nag.1610020205.
Shalabi, F. 2005. “FE analysis of time-dependent behavior of tunneling in squeezing ground using two different creep models.” Tunnelling Underground Space Technol. 20 (3): 271–279. https://doi.org/10.1016/j.tust.2004.09.001.
Sharifzadeh, M., A. Tarifard, and M. A. Moridi. 2013. “Time-dependent behavior of tunnel lining in weak rock mass based on displacement back analysis method.” Tunnelling Underground Space Technol. 38 (9): 348–356. https://doi.org/10.1016/j.tust.2013.07.014.
Shi, Z., J. P. Hambleton, and G. Buscarnera. 2019. “Bounding surface elasto-viscoplasticity: A general constitutive framework for rate-dependent geomaterials.” J. Eng. Mech. 145 (3): 04019002. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001578.
Singh, A. K., A. Negi, A. K. Verma, and S. Kumar. 2017. “Analysis of stresses induced due to a moving load on irregular initially stressed heterogeneous viscoelastic rock medium.” J. Eng. Mech. 143 (9): 04017096. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001307.
Song, F., H. Wang, and M. Jiang. 2018. “Analytically-based simplified formulas for circular tunnels with two liners in viscoelastic rock under anisotropic initial stresses.” Constr. Build. Mater. 175 (Jun): 746–767. https://doi.org/10.1016/j.conbuildmat.2018.04.079.
Sterpi, D., and G. Gioda. 2009. “Visco-plastic behaviour around advancing tunnels in squeezing rock.” Rock Mech. Rock Eng. 42 (2): 319–339. https://doi.org/10.1007/s00603-007-0137-8.
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, J., and H. Zhu. 1994. “Mechanical simulation and analysis of behaviour of soft and weak rocks in the construction of a tunnel opening.” Rock Soil Mech. 15 (4): 20–33.
Timoshenko, S., and J. Goodier. 1982. Theory of elasticity. New York: McGraw-Hill.
Tomanovic, Z. 2006. “Rheological model of soft rock creep based on the tests on marl.” Mech. Time-Depend. Mater. 10 (2): 135–154. https://doi.org/10.1007/s11043-006-9005-2.
Tran-Manh, H., J. Sulem, and D. Subrin. 2016. “Progressive degradation of rock properties and time-dependent behavior of deep tunnels.” Acta Geotech. 11 (3): 693–711. https://doi.org/10.1007/s11440-016-0444-x.
Tricomi, F. G. 1985. Integral equations. New York: Courier Corporation.
Wang, H., S. Utili, and M. 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.
Wang, H. N., Y. Li, Q. Ni, S. Utili, M. J. Jiang, and F. Liu. 2013. “Analytical solutions for the construction of deeply buried circular tunnels with two liners in rheological rock.” Rock Mech. Rock Eng. 46 (6): 1481–1498. https://doi.org/10.1007/s00603-012-0362-7.
Wang, H. N., G. S. Zeng, and M. J. Jiang. 2018a. “Analytical stress and displacement around non-circular tunnels in semi-infinite ground.” Appl. Math. Model. 63 (Nov): 303–328. https://doi.org/10.1016/j.apm.2018.06.043.
Wang, Y., B. Liu, and Y. Qi. 2018b. “A risk evaluation method with an improved scale for tunnel engineering.” Arab J. Sci. Eng. 43 (4): 2053–2067. https://doi.org/10.1007/s13369-017-2974-4.
Wazwaz, A. M. 2011. Linear and nonlinear integral equations. New York: Springer.
Weng, L., L. Huang, A. Taheri, and X. Li. 2017. “Rockburst characteristics and numerical simulation based on a strain energy density index: A case study of a roadway in Linglong gold mine, China.” Tunnelling Underground Space Technol. 69 (Feb): 223–232. https://doi.org/10.1016/j.tust.2017.05.011.
Wu, K., and Z. Shao. 2019a. “Study on the effect of flexible layer on support structures of tunnel excavated in viscoelastic rocks.” J. Eng. Mech. 145 (10). https://doi.org/10.1061/(ASCE)EM.1943-7889.0001657.
Wu, K., and Z. Shao. 2019b. “Visco-elastic analysis on the effect of flexible layer on mechanical behavior of tunnels.” Int. J. Appl. Mech. 11 (03): 1950027. https://doi.org/10.1142/S1758825119500273.
Yang, F., C. Zhang, H. Zhou, N. Liu, Y. Zhang, M. U. Azhar, and F. Dai. 2017. “The long-term safety of a deeply buried soft rock tunnel lining under inside-to-outside seepage conditions.” Tunnelling Underground Space Technol. 67 (Aug): 132–146. https://doi.org/10.1016/j.tust.2017.05.004.
Yang, S. Q., H. W. Jing, and L. Cheng. 2014. “Influences of pore pressure on short-term and creep mechanical behavior of red sandstone.” Eng. Geol. 179 (10): 10–23. https://doi.org/10.1016/j.enggeo.2014.06.016.
Zhang, H., Z. Wang, Y. Zheng, P. Duan, and S. Ding. 2012. “Study on tri-axial creep experiment and constitutive relation of different rock salt.” Safety Sci. 50 (4): 801–805. https://doi.org/10.1016/j.ssci.2011.08.030.
Zhang, Q. Y., M. Y. Ren, K. Duan, W. S. Wang, Q. Gao, H. X. Lin, W. Xiang, and Y. Y. Jiao. 2019. “Geo-mechanical model test on the collaborative bearing effect of rock-support system for deep tunnel in complicated rock strata.” Tunnelling Underground Space Technol. 91 (Sep): 103001. https://doi.org/10.1016/j.tust.2019.103001.
Zhao, D., L. Jia, M. Wang, and W. Feng. 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, Y., L. Zhang, W. Wang, W. Wan, and W. Ma. 2018. “Separation of elastoviscoplastic strains of rock and a nonlinear creep model.” Int. J. Geomech. 18 (1): 04017129. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001033.
Zhifa, Y., W. Zhiyin, Z. Luqing, Z. Ruiguang, and X. Nianxing. 2001. “Back-analysis of viscoelastic displacements in a soft rock road tunnel.” Int. J. Rock Mech. Min. Sci. 38 (3): 331–341. https://doi.org/10.1016/S1365-1609(00)00081-2.
Information & Authors
Information
Published In
Copyright
©2020 American Society of Civil Engineers.
History
Received: Oct 13, 2019
Accepted: Jan 7, 2020
Published online: Apr 3, 2020
Published in print: Jun 1, 2020
Discussion open until: Sep 3, 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.