Long-Term Analysis of Tunnels in Rheological Rock Masses Considering the Excavation-Damaged Zone
Publication: International Journal of Geomechanics
Volume 23, Issue 1
Abstract
According to the excavation methods of tunneling, a damaged zone may be developed in the rock mass around the tunnel, the mechanical properties of which can be significantly altered. This issue is of great importance in the analyses of both the short-term and the long-term performance of tunnels. In this paper, a closed-form solution is presented to find the long-term-induced stresses and the convergence of the tunnel considering the altered zone development. To account for the time-dependency effect, the Burgers viscoelastic rheological model is assigned to altered and unaltered zones. The proposed method is applicable for the case in which the tunnel excavation is halted or for the case in which the tunnel is continuously excavated. The predictions made by the proposed analytical method are compared with those made by using FLAC3D software. Then, a parametric study is performed to investigate the effects of different key parameters associated with the research aim. Finally, the numerical simulation is extended so that the combining Burgers substance and the Mohr–Coulomb failure criterion (CVISC) model, i.e., a viscoplastic rheological model, is adopted to the medium. The results indicate a remarkable difference between the predictions of tunnel convergence by the Burgers and the CVISC models, in very severe and extreme squeezing conditions.
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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, specifically the FLAC3D code.
References
Alonso, E., L. R. Alejano, F. Varas, G. Fdez-Manin, and C. Carranza-Torres. 2003. “Ground response curves for rock masses exhibiting strain-softening behaviour.” Int. J. Numer. Anal. Methods Geomech. 27 (13): 1153–1185. https://doi.org/10.1002/nag.315.
Bäckblom, G., and C. D. Martin. 1999. “Recent experiments in hard rocks to study the excavation response: Implications for the performance of a nuclear waste geological repository.” Tunnelling Underground Space Technol. 14 (3): 377–394. https://doi.org/10.1016/S0886-7798(99)00053-X.
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.
Bobet, A., and H. Einstein. 2011. “Tunnel reinforcement with rockbolts.” Tunnelling Underground Space Technol. 26 (1): 100–123. https://doi.org/10.1016/j.tust.2010.06.006.
Brown, E. T., J. W. Bray, B. Ladanyi, and E. Hoek. 1983. “Ground response curves for rock tunnels.” J. Geotech. Eng. 109 (1): 15–39. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(15).
Chen, R., and F. Tonon. 2011. “Closed-form solutions for a circular tunnel in elastic–brittle–plastic ground with the original and generalized Hoek–Brown failure criteria.” Rock Mech. Rock Eng. 44 (2): 169–178. https://doi.org/10.1007/s00603-010-0122-5.
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: 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. 2021. “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.
Cui, L., Q. Sheng, Y.-k. Dong, C.-x. Miao, J.-h. Huang, and A. Zhang. 2022a. “Two-stage analysis of interaction between strain-softening rock mass and liner for circular tunnels considering delayed installation of liner.” Eur. J. Environ. Civ. Eng. 26 (4): 1492–1517. https://doi.org/10.1080/19648189.2020.1715849.
Cui, L., Q. Sheng, Y.-k. Dong, and M.-x. Xie. 2022b. “Unified elasto-plastic analysis of rock mass supported with fully grouted bolts for deep tunnels.” Int. J. Numer. Anal. Methods Geomech. 46 (2): 247–271. https://doi.org/10.1002/nag.3298.
Cui, L., Q. Sheng, J.-j. Zheng, Z. Cui, A. Wang, and Q. Shen. 2019. “Regression model for predicting tunnel strain in strain-softening rock mass for underground openings.” Int. J. Rock Mech. Min. Sci. 119: 81–97. https://doi.org/10.1016/j.ijrmms.2019.04.014.
Do, D.-P., N.-H. Tran, H.-L. Dang, and D. Hoxha. 2019. “Closed-form solution of stress state and stability analysis of wellbore in anisotropic permeable rocks.” Int. J. Rock Mech. Min. Sci. 113: 11–23. https://doi.org/10.1016/j.ijrmms.2018.11.002.
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.
Dong, X., A. Karrech, C. Qi, M. Elchalakani, and H. Basarir. 2019. “Analytical solution for stress distribution around deep lined pressure tunnels under the water table.” Int. J. Rock Mech. Min. Sci. 123: 104124. https://doi.org/10.1016/j.ijrmms.2019.104124.
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.
Fang, Q., D. Zhang, P. Zhou, and L. N. Y. Wong. 2013. “Ground reaction curves for deep circular tunnels considering the effect of ground reinforcement.” Int. J. Rock Mech. Min. Sci. 60: 401–412. https://doi.org/10.1016/j.ijrmms.2013.01.003.
Findley, W. N., J. S. Lai, K. Onaran, and R. Christensen. 1977. Creep and relaxation of nonlinear viscoelastic materials with an introduction to linear viscoelasticity. Amsterdam, Netherlands: Elsevier.
Giordanella, M., M. Ranjbarnia, P. Oreste, and M. Zaheri. 2022. “Study of the systematic fully grouted rock bolts performance in tunnels considering installation condition of bolt head.” Geomech. Geoeng. 17 (4): 1151–1167. https://doi.org/10.1080/17486025.2021.1928761.
Guan, K., W. Zhu, J. Wei, X. Liu, L. Niu, and X. Wang. 2018. “A finite strain numerical procedure for a circular tunnel in strain-softening rock mass with large deformation.” Int. J. Rock Mech. Min. Sci. 112: 266–280. https://doi.org/10.1016/j.ijrmms.2018.10.016.
Hedayat, A. 2016. “Stability of circular tunnels excavated in rock masses under gravity loading.” In Vol. 9 of 50th U.S. Rock Mechanics/Geomechanics Symp. Houston: American Rock Mechanics Association.
Hedayat, A., and J. Weems. 2019. “The elasto-plastic response of deep tunnels with damaged zone and gravity effects.” Rock Mech. Rock Eng. 52: 5123–5135. https://doi.org/10.1007/s00603-019-01834-4.
Hoek, E. 2006. “Practical rock engineering.” www.rocscience.com.
Hoek, E., and E. T. Brown. 2019. “The Hoek–Brown failure criterion and GSI—2018 edition.” J. Rock Mech. Geotech. Eng. 11 (3): 445–463. https://doi.org/10.1016/j.jrmge.2018.08.001.
Hoek, E., C. Carranza-Torres, and B. Corkum. 2002. “Hoek–Brown failure criterion—2002 edition.” Proc. NARMS-Tac 1: 267–273.
Hoek, E., and P. Marinos. 2000. “Predicting tunnel squeezing problems in weak heterogeneous rock masses.” Tunnels Tunnelling Int. 32 (11): 45–51.
Huang, L., J. Liang, J. Ma, H. Yang, and Y. Gui. 2021. “Spherical cavity expansion in porous rock considering plasticity and damage.” Int. J. Numer. Anal. Methods Geomech. 45 (15): 2235–2259. https://doi.org/10.1002/nag.3264.
Huang, M., J. W. Zhan, C. S. Xu, and S. Jiang. 2020. “New creep constitutive model for soft rocks and Its application in the prediction of time-dependent deformation in tunnels.” Int. J. Geomech. 20 (7): 04020096. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001663.
Itasca. 2012. Fast Lagrangian analysis of continua. Minneapolis: Itasca Consulting Group.
Kabwe, E., M. Karakus, and E. Chanda. 2018. “Assessment of analytical solutions for time-dependent behavior of unlined tunnels.” In Proc., 4th Int. Symp. on Underground Excavation, 1–9. Istanbul, Turkey: Chamber of Mining Engineers of Turkey.
Kabwe, E., M. Karakus, and E. K. Chanda. 2020. “Isotropic damage constitutive model for time-dependent behaviour of tunnels in squeezing ground.” Comput. Geotech. 127: 103738. https://doi.org/10.1016/j.compgeo.2020.103738.
Kanji, M., M. He, and L. R. e Sousa. 2019. Soft rock mechanics and engineering. Dordrecht, Netherlands: Springer.
Kargar, A. R. 2019. “An analytical solution for circular tunnels excavated in rock masses exhibiting viscous elastic–plastic behavior.” Int. J. Rock Mech. Min. Sci. 124: 104128. https://doi.org/10.1016/j.ijrmms.2019.104128.
Katebian, E., and H. Molladavoodi. 2017. “Practical ground response curve considering post-peak rock mass behaviour.” Eur. J. Environ. Civ. Eng. 21 (1): 1–23. https://doi.org/10.1080/19648189.2015.1090928.
Liu, Y., J. Sulem, D. Subrin, and H. Tran-Manh. 2020. “Long-term behavior of lined tunnels excavated in squeezing ground.” In Applied numerical modeling in geomechanics, edited by J. H. Daniel Billaux, M. Nelson, and M. Schöpfer. Minneapolis: Itasca Consulting Group.
Lu, A.-z., G.-s. Zeng, and N. Zhang. 2021. “A complex variable solution for a non-circular tunnel in an elastic half-plane.” Int. J. Numer. Anal. Methods Geomech. 45 (12): 1833–1853. https://doi.org/10.1002/nag.3244.
Ma, Y., A. Lu, X. Zeng, and H. Cai. 2020. “Analytical solution for determining the plastic zones around twin circular tunnels excavated at great depth.” Int. J. Rock Mech. Min. Sci. 136: 104475. https://doi.org/10.1016/j.ijrmms.2020.104475.
Martin, C. D., P. K. Kaiser, and D. R. McCreath. 1999. “Hoek–Brown parameters for predicting the depth of brittle failure around tunnels.” Can. Geotech. J. 36 (1): 136–151. https://doi.org/10.1139/t98-072.
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., A. Hedayat, and G. Spagnoli. 2019. “Effect of gravity of the plastic zones on the behavior of supports in very deep tunnels excavated in rock masses.” Int. J. Geomech. 19 (9): 04019107. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001490.
Panet, M. 1995. Le calcul des tunnels par la méthode Convergence-Confinement. Paris: Presses des Ponts et Chaussées.
Paraskevopoulou, C., J. Oke, and N. Vlachopoulos. 2012. “Practical modelling approaches to determine the long term behaviour of tunnel construction.” In Proc., Canadian Tunnelling Symposium TAC on Tunnels and Underground Spaces: Sustainability and Innovations. Toronto, ON: Tunnelling Association of Canada (TAC).
Park, K.-H., and Y.-J. Kim. 2006. “Analytical solution for a circular opening in an elastic–brittle–plastic rock.” Int. J. Rock Mech. Min. Sci. 43 (4): 616–622. https://doi.org/10.1016/j.ijrmms.2005.11.004.
Park, K.-H., B. Tontavanich, and J.-G. Lee. 2008. “A simple procedure for ground response curve of circular tunnel in elastic-strain softening rock masses.” Tunnelling Underground Space Technol. 23 (2): 151–159. https://doi.org/10.1016/j.tust.2007.03.002.
Pellet, F.-L. 2009. “Contact between a tunnel lining and a damage-susceptible viscoplastic medium.” Comput. Model. Eng. Sci. 52 (3): 279–296. https://doi.org/10.3970/cmes.2009.052.279.
Polyanin, A. D., and A. V. Manzhirov. 2008. Handbook of integral equations. New York: Chapman and Hall/CRC.
Quevedo, F. P. d. M., D. Bernaud, and A. C. Filho. 2022. “Numerical analysis of deep tunnels in viscoplastic rock mass considering the creep and shrinkage of the concrete lining.” Int. J. Geomech. 22 (4): 04022005. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002282.
Ranjbarnia, M., A. Fahimifar, and P. Oreste. 2015. “Analysis of non-linear strain-softening behaviour around tunnels.” Proc. Inst. Civ. Eng. Geotech. Eng. 168 (1): 16–30. https://doi.org/10.1680/geng.13.00144.
Ranjbarnia, M., M. Zaheri, and D. Dias. 2020. “Three-dimensional finite difference analysis of shallow sprayed concrete tunnels crossing a reverse fault or a normal fault: A parametric study.” Front. Struct. Civ. Eng. 14 (4): 998–1011. https://doi.org/10.1007/s11709-020-0621-8.
Rocscience. 2007. “Roclab version 1.031—Rock mass strength analysis using the Hoek–Brown failure criterion.” Toronto: Rocscience.
Sakurai, S. 1978. “Approximate time-dependent analysis of tunnel support structure considering progress of tunnel face.” Int. J. Numer. Anal. Methods Geomech. 2 (2): 159–175. https://doi.org/10.1002/nag.1610020205.
Song, F., A. Rodriguez-Dono, S. Olivella, and A. Gens. 2021. “Coupled solid–fluid response of deep tunnels excavated in saturated rock masses with a time-dependent plastic behaviour.” Appl. Math. Modell. 100: 508–535. https://doi.org/10.1016/j.apm.2021.07.030.
Song, F., A. Rodriguez-Dono, S. Olivella, and Z. Zhong. 2020. “Analysis and modelling of longitudinal deformation profiles of tunnels excavated in strain-softening time-dependent rock masses.” Comput. Geotech. 125: 103643. https://doi.org/10.1016/j.compgeo.2020.103643.
Song, X.-G., H. Yang, H.-Y. Yue, X. Guo, H.-S. Yu, and P.-Z. Zhuang. 2022. “Closed-form solutions for large strain analysis of cavity contraction in a bounded Mohr–Coulomb medium.” Eur. J. Environ. Civ. Eng. 26 (10): 4548–4575. https://doi.org/10.1080/19648189.2020.1857309.
Wang, H., F. Song, T. Zhao, and M. Jiang. 2022. “Solutions for lined circular tunnels sequentially constructed in rheological rock subjected to non-hydrostatic initial stresses.” Eur. J. Environ. Civ. Eng. 26 (5): 1834–1866. https://doi.org/10.1080/19648189.2020.1737576.
Wang, H., L. Wu, and M. Jiang. 2020. “Viscoelastic ground responses around shallow tunnels considering surcharge loadings and effect of supporting.” Eur. J. Environ. Civ. Eng. 24 (13): 2306–2328. https://doi.org/10.1080/19648189.2018.1505662.
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., and G. H. Nie. 2010. “Analytical expressions for stress and displacement fields in viscoelastic axisymmetric plane problem involving time-dependent boundary regions.” Acta Mech. 210 (3): 315–330. https://doi.org/10.1007/s00707-009-0208-x.
Wang, H. N., L. Wu, M. J. Jiang, and F. Song. 2018. “Analytical stress and displacement due to twin tunneling in an elastic semi-infinite ground subjected to surcharge loads.” Int. J. Numer. Anal. Methods Geomech. 42 (6): 809–828. https://doi.org/10.1002/nag.2764.
Wang, X.-f., B.-s. Jiang, F. Lin, Y.-q. Liu, and Y. Bai. 2021. “Elastic–viscoplastic solution of a circular tunnel in Hoek–Brown rock mass.” Lat. Am. J. Solids Struct. 18 (1): 1–25. https://doi.org/10.1590/1679-78256328.
Wang, X.-F., B.-S. Jiang, Q. Zhang, M.-M. Lu, and M. Chen. 2019. “Analytical solution of circular tunnel in elastic-viscoplastic rock mass.” Lat. Am. J. Solids Struct. 16 (6): 1–19. https://doi.org/10.1590/1679-78255701.
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): 04019077. 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 (3): 1950027. https://doi.org/10.1142/S1758825119500273.
Wu, K., Z. Shao, and S. Qin. 2020a. “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, N. Zhao, and H. Hu. 2020b. “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.
Xu, C., and C. Xia. 2021. “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: 104786. https://doi.org/10.1016/j.ijrmms.2021.104786.
Yang, F., H. Zhou, C. Zhang, D. Hu, J. Lu, and F. Meng. 2018. “An elastoplastic coupling mechanical model for hard and brittle marble with consideration of the first stress invariant effect.” Eur. J. Environ. Civ. Eng. 22 (4): 405–428. https://doi.org/10.1080/19648189.2016.1197160.
Zaheri, M., and M. Ranjbarnia. 2021. “A new procedure for calculation of ground response curve of a circular tunnel considering the influence of Young’s modulus variation and the plastic weight loading.” Geotech. Geol. Eng. 39: 1079–1099. https://doi.org/10.1007/s10706-020-01546-5.
Zaheri, M., and M. Ranjbarnia. 2022a. “Ground reaction curve of a circular tunnel considering the effects of the altered zone and the self-weight of the plastic zones.” Eur. J. Environ. Civ. Eng. 26 (11): 4973–4997. https://doi.org/10.1080/19648189.2021.1877829.
Zaheri, M., and M. Ranjbarnia. 2022b. “Theoretical and numerical analyses of squeezing rock mass around a spherical opening considering the existence of a damaged zone.” Amirkabir J. Civil Eng. https://doi.org/10.22060/CEEJ.2022.20529.7452.
Zaheri, M., M. Ranjbarnia, and D. Dias. 2020a. “3D numerical investigation of segmental tunnels performance crossing a dip-slip fault.” Geomech. Eng. 23 (4): 351–364. https://doi.org/10.12989/gae.2020.23.4.351.
Zaheri, M., M. Ranjbarnia, D. Dias, and P. Oreste. 2020b. “Performance of segmental and shotcrete linings in shallow tunnels crossing a transverse strike-slip faulting.” Transp. Geotech. 23: 100333. https://doi.org/10.1016/j.trgeo.2020.100333.
Zaheri, M., M. Ranjbarnia, and M. Goudarzy. 2022. “Analytical and numerical simulations to predict the long-term behavior of lined tunnels considering excavation-induced damaged zone.” Rock Mech. Rock Eng. 55: 5879–5904. https://doi.org/10.1007/s00603-022-02962-0.
Zaheri, M., M. Ranjbarnia, and P. Oreste. 2021. “Performance of systematic fully grouted rockbolts and shotcreted layer in circular tunnel under the hydrostatic conditions using 3D finite difference approach.” Geomech. Geoeng. 16 (3): 198–211. https://doi.org/10.1080/17486025.2019.1648885.
Zareifard, M. R. 2020a. “A new semi-numerical method for elastoplastic analysis of a circular tunnel excavated in a Hoek–Brown strain-softening rock mass considering the blast-induced damaged zone.” Comput. Geotech. 122: 103476. https://doi.org/10.1016/j.compgeo.2020.103476.
Zareifard, M. R. 2020b. “A simple closed-form solution for analysis of tunnels in Mohr–Coulomb grounds considering gravity loading.” Geotech. Geol. Eng. 38: 3751–3760. https://doi.org/10.1007/s10706-020-01255-z.
Zareifard, M. R. 2021. “Ground response curve of deep circular tunnel in rock mass exhibiting Hoek–Brown strain-softening behaviour considering the dead weight loading.” Eur. J. Environ. Civ. Eng. 25 (14): 2509–2539. https://doi.org/10.1080/19648189.2019.1632745.
Zareifard, M. R., and A. Fahimifar. 2012. “A new solution for shallow and deep tunnels by considering the gravitational loads.” Acta Geotech. Slov. 2: 37–49.
Zareifard, M. R., and A. Fahimifar. 2014. “Effect of seepage forces on circular openings excavated in Hoek–Brown rock mass based on a generalised effective stress principle.” Eur. J. Environ. Civ. Eng. 18 (5): 584–600. https://doi.org/10.1080/19648189.2014.891470.
Zareifard, M. R., and A. Fahimifar. 2015. “Elastic–brittle–plastic analysis of circular deep underwater cavities in a Mohr–Coulomb rock mass considering seepage forces.” Int. J. Geomech. 15 (5): 04014077. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000400.
Zareifard, M. R., and A. Fahimifar. 2016. “Analytical solutions for the stresses and deformations of deep tunnels in an elastic–brittle–plastic rock mass considering the damaged zone.” Tunnelling Underground Space Technol. 58: 186–196. https://doi.org/10.1016/j.tust.2016.05.007.
Zeng, G., H. Wang, and M. Jiang. 2019. “Analytical study of ground responses induced by the excavation of quasirectangular tunnels at shallow depths.” Int. J. Numer. Anal. Methods Geomech. 43 (13): 2200–2223. https://doi.org/10.1002/nag.2980.
Zhang, B.-q., F.-q. Chen, and Q.-y. Wang. 2019. “Elastoplastic solutions for surrounding rock masses of deep-buried circular tunnels with non-Darcian flow.” Int. J. Geomech. 19 (7): 04019065. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001442.
Zhang, Q., C. Shao, H. Su, H. Wang, Y. Jiang, and B. Jiang. 2022. “A closed-form hydraulic–mechanical coupling solution of a circular tunnel in elastic–brittle–plastic rock mass.” Eur. J. Environ. Civ. Eng. 26 (8): 3594–3611. https://doi.org/10.1080/19648189.2020.1806933.
Zhang, Q., C. Zhang, B. Jiang, N. Li, and Y. Wang. 2018. “Elastoplastic coupling solution of circular openings in strain-softening rock mass considering pressure-dependent effect.” Int. J. Geomech. 18 (1): 04017132. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001043.
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.
Zhou, J., X.-A. Yang, M.-J. Ma, and L.-H. Li. 2021. “The support load analysis of deep-buried composite lining tunnel in rheological rock mass.” Comput. Geotech. 130: 103934. https://doi.org/10.1016/j.compgeo.2020.103934.
Zou, J., and Y. Su. 2016. “Theoretical solutions of a circular tunnel with the influence of the out-of-plane stress based on the generalized Hoek–Brown failure criterion.” Int. J. Geomech. 16 (3): 06015006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000547.
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International Journal of Geomechanics
Volume 23 • Issue 1 • January 2023
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© 2022 American Society of Civil Engineers.
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Received: Mar 22, 2022
Accepted: Aug 20, 2022
Published online: Nov 4, 2022
Published in print: Jan 1, 2023
Discussion open until: Apr 4, 2023
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