Stability Analyses of Shallow Rectangular Tunnels in Anisotropic and Nonhomogeneous Soils Using a Kinematic Approach
Publication: International Journal of Geomechanics
Volume 24, Issue 7
Abstract
Conducting soil stability assessments around tunnels has always been a concern. However, most existing studies have regarded soil as an isotropic and homogeneous material. To overcome this limitation, within the framework of upper bound theory, this paper proposes a novel rotational–translational failure mechanism where the velocity discontinuity surfaces are derived numerically. This theoretical mechanism includes two cases according to the positions of the velocity discontinuity surfaces. An analytical solution for pore water pressure is obtained using the conformal mapping method, which involves solving the two-dimensional (2D) Laplace equation and considering the soil and shotcrete permeability. Then, upper bound expressions for the limit supporting pressure are derived by computing work equations with and without pore water pressure. Comparisons with previous work and numerical results illustrate that the presented approach offers improvements and could be applicable for stability analyses of shallow rectangular tunnels in anisotropic and nonhomogeneous soils. Finally, this paper discusses the effects of the anisotropy and nonhomogeneity of soil properties on the normalized limit supporting pressure and the collapsing domains of rectangular tunnels with different geometric shapes. In addition, the impact of pore water pressure on the changed water levels is assessed. The results demonstrate that for rectangular tunnels that are excavated in water-bearing zones, the width-to-height ratio plays a significant role in the stability of the surrounding soils.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The financial support from the National Key R&D Program of China (Grant No. 2017YFB1201204) is truly appreciated.
References
Abbo, A. J., D. W. Wilson, S. W. Sloan, and A. V. Lyamin. 2013. “Undrained stability of wide rectangular tunnels.” Comput. Geotech. 53: 46–59. https://doi.org/10.1016/j.compgeo.2013.04.005.
Bhattacharya, P., and P. Dutta. 2020. “Stability of rectangular tunnel in Hoek–Brown rocks under steady-state groundwater flow.” Geotech. Lett. 10 (4): 524–534. https://doi.org/10.1680/jgele.20.00043.
Bhattacharya, P., and P. Dutta. 2023. “Stability of rectangular tunnel in anisotropic cohesionless soil under steady-state groundwater flow.” Eur. J. Environ. Civ. Eng. 27 (4): 1596–1616. https://doi.org/10.1080/19648189.2022.2090444.
Bishop, A. W., and N. Morgenstern. 1960. “Stability coefficients for earth slopes.” Geotechnique 10 (4): 129–153. https://doi.org/10.1680/geot.1960.10.4.129.
Casagrande, A., and N. Carillo. 1944. “Shear failure of anisotropic materials.” J. Boston Soc. Civ. Eng. 31 (4): 74–81.
Chen, G. H., J. F. Zou, Y. M. Sheng, J. Y. Chen, and T. Yang. 2022. “Three-Dimensional seismic bearing capacity assessment of heterogeneous and anisotropic slopes.” Int. J. Geomech. 22 (9): 04022148. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002493.
Chen, G. H., J. F. Zou, X. X. Wei, and F. Q. Guo. 2023a. “Three-dimensional blow-out stability analysis of shield tunnel face in anisotropic and heterogeneous soils.” Tunnelling Underground Space Technol. 131: 104851. https://doi.org/10.1016/j.tust.2022.104851.
Chen, H., H. Zhu, and L. Zhang. 2023b. “Rock slope stability analysis incorporating the effects of intermediate principal stress.” Rock Mech. Rock Eng. 56: 4271–4289. https://doi.org/10.1007/s00603-023-03277-4.
Chen, W. F. 1975. Limit analysis and soil plasticity. Amsterdam: Elsevier.
Chen, W. F., N. Snitbhan, and H. Y. Fang. 1975. “Stability of slopes in anisotropic, nonhomogeneous soils.” Can. Geotech. J. 12 (1): 146–152. https://doi.org/10.1139/t75-014.
Dai, C., H. Sui, and C. Ma. 2020. “Study on the ultimate supporting force of shield excavation face based on anisotropic strength theory.” Appl. Sci. 10 (15): 5222. https://doi.org/10.3390/app10155222.
Davis, E. H., M. J. Gunn, R. J. Mair, and H. N. Seneviratine. 1980. “The stability of shallow tunnels and underground openings in cohesive material.” Geotechnique 30 (4): 397–416. https://doi.org/10.1680/geot.1980.30.4.397.
Du, D., D. Dias, and X. Yang. 2018. “Analysis of earth pressure for shallow square tunnels in anisotropic and non-homogeneous soils.” Comput. Geotech. 104: 226–236. https://doi.org/10.1016/j.compgeo.2018.08.022.
Dutta, P., and P. Bhattacharya. 2022. “Stability of rectangular tunnels in weathered rock subjected to seepage forces.” Arab. J. Geosci. 15: 1–14. https://doi.org/10.1007/s12517-021-08817-2.
EI Tani, M. 2003. “Circular tunnel in a semi-infinite aquifer.” Tunnelling Underground Space Technol. 18 (1): 49–55. https://doi.org/10.1016/S0886-7798(02)00102-5.
He, Z. J., H. Q. Mo, J. F. Zou, and C. Li. 2019. “Approximate analytical solutions for steady seepage into an underwater elliptical tunnel.” [In Chinese.] J. Railway Sci. Eng. 16 (9): 2265–2271.
Huang, F., and X. L. Yang. 2011. “Upper bound limit analysis of collapse shape for circular tunnel subjected to pore pressure based on the hoek–brown failure criterion.” Tunnelling Underground Space Technol. 26 (5): 614–618. https://doi.org/10.1016/j.tust.2011.04.002.
Huang, M., H. Wang, D. Sheng, and Y. Liu. 2013. “Rotational–translational mechanism for the upper bound stability analysis of slopes with weak interlayer.” Comput. Geotech. 53: 133–141. https://doi.org/10.1016/j.compgeo.2013.05.007.
Huang, Q., J. F. Zou, and Z. H. Qian. 2019. “Face stability analysis for a longitudinally inclined tunnel in anisotropic cohesive soils.” J. Cent. South Univ. 26 (7): 1780–1793. https://doi.org/10.1007/s11771-019-4133-4.
Huang, Q., J. F. Zou, and Z. H. Qian. 2020. “Seismic stability analysis of tunnel face in purely cohesive soil by a pseudo-dynamic approach.” Geomech. Eng. 23 (1): 1. https://doi.org/10.12989/gae.2020.23.1.001.
Huangfu, M., M. S. Wang, Z. S. Tan, and X. Y. Wang. 2010. “Analytical solutions for steady seepage into an underwater circular tunnel.” Tunnelling Underground Space Technol. 25 (4): 391–396. https://doi.org/10.1016/j.tust.2010.02.002.
Kolymbas, D., and P. Wagner. 2007. “Groundwater ingress to tunnels–the exact analytical solution.” Tunnelling Underground Space Technol. 22 (1): 23–27. https://doi.org/10.1016/j.tust.2006.02.001.
Lee, I. M., and S. W. Nam. 2001. “The study of seepage forces acting on the tunnel lining and tunnel face in shallow tunnels.” Tunnelling Underground Space Technol. 16 (1): 31–40. https://doi.org/10.1016/j.tust.2006.02.001.
Li, L., H. Chen, and J. Li. 2021. “A semi-analytical solution to steady-state groundwater inflow into a circular tunnel considering anisotropic permeability.” Tunnelling Underground Space Technol. 116: 104115. https://doi.org/10.1016/j.tust.2021.104115.
Lorenzo, S. G. 2019. “Longitudinal beam response of concrete segmental linings simultaneously backfilled with bicomponent grouts.” Tunnelling Underground Space Technol. 90: 277–292. https://doi.org/10.1016/j.tust.2019.05.007.
Lv, A. 1995. “A new method of determination of the mapping function for a non-circle tunnel with full support.” Chin. J. Rock Mech. Eng. 17 (4): 38–44.
Lv, A. Z., and Q. W. Wang. 1995. “New method of determination for the mapping function of tunnel with arbitrary boundary using optimization techniques.” Chin. J. Rock Mech. Eng. 14 (3): 269–274.
Lyamin, A. V., D. L. Jack, and S. W. Sloan. 2001. “Collapse analysis of square tunnels in cohesive–frictional soils.” In Computational mechanics–new frontiers for the new millennium, edited by S. Valliappan and N. Khalili, 405–414. Amsterdam, Netherlands: Elsevier. https://doi.org/10.1016/B978-0-08-043981-5.50063-8.
Michalowski, R. L., and D. Park. 2020. “Stability assessment of slopes in rock governed by the Hoek-Brown strength criterion.” Int. J. Rock Mech. Min. Sci. 127: 104217. https://doi.org/10.1016/j.ijrmms.2020.104217.
Mollon, G., D. Dias, and A. H. Soubra. 2011. “Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield.” Int. J. Numer. Anal. Methods Geomech. 35 (12): 1363–1388. https://doi.org/10.1002/nag.962.
Nian, T. K., G. Q. Chen, M. T. Luan, Q. Yang, and D. F. Zheng. 2008. “Limit analysis of the stability of slopes reinforced with piles against landslide in nonhomogeneous and anisotropic soils.” Can. Geotech. J. 45 (8): 1092–1103. https://doi.org/10.1139/T08-042.
Pan, Q., and D. Dias. 2016. “Face stability analysis for a shield-driven tunnel in anisotropic and nonhomogeneous soils by the kinematical approach.” Int. J. Geomech. 16 (3): 04015076. https://doi.org/10.1061/(ASCE)GM.1943-5622.000056.
Park, K. H., A. Owatsiriwong, and J. G. Lee. 2008. “Analytical solution for steady-state groundwater inflow into a drained circular tunnel in a semi-infinite aquifer: A revisit.” Tunnelling Underground Space Technol. 23 (2): 206–209. https://doi.org/10.1016/j.tust.2007.02.004.
Peng, Z. Z., and Z. H. Qian. 2023. “A New kinematical admissible translational–rotational failure mechanism coupling with the complex variable method for stability analyses of saturated shallow square tunnels.” Buildings 13 (5): 1246. https://doi.org/10.3390/buildings13051246.
Qian, Z. H., J. F. Zou, and Q. J. Pan. 2021. “3D discretized rotational failure mechanism for slope stability analysis.” Int. J. Geomech. 1 (11): 04021210. https://doi.org/10.1061/(ASCE)GM.1943-5622.000216.
Qian, Z. H., J. F. Zou, and Q. J. Pan. 2023. “Blowout analysis of shallow elliptical tunnel faces in frictional-cohesive soils.” Tunnelling Underground Space Technol. 136: 105070. https://doi.org/10.1016/j.tust.2023.105070.
Qian, Z. H., J. F. Zou, Q. J. Pan, G. H. Chen, and S. X. Liu. 2020a. “Discretization-based kinematical analysis of three-dimensional seismic active earth pressures under nonlinear failure criterion.” Comput. Geotech. 126: 103739. https://doi.org/10.1016/j.compgeo.2020.103739.
Qian, Z. H., J. F. Zou, J. Tian, and Q. J. Pan. 2020b. “Estimations of active and passive earth thrusts of non-homogeneous frictional soils using a discretisation technique.” Comput. Geotech. 119: 103366. https://doi.org/10.1016/j.compgeo.2019.103366.
Qin, C., S. C. Chian, X. Yang, and D. Du. 2015. “2D and 3D limit analysis of progressive collapse mechanism for deep-buried tunnels under the condition of varying water table.” Int. J. Rock Mech. Min. Sci. 80: 255–264. https://doi.org/10.1016/j.ijrmms.2015.09.024.
Stockton, E., B. A. Leshchinsky, M. J. Olsen, and T. M. Evans. 2019. “Influence of both anisotropic friction and cohesion on the formation of tension cracks and stability of slopes.” Eng. Geol. 249: 31–44. https://doi.org/10.1016/j.enggeo.2018.12.016.
Sun, Z., J. Li, Q. Pan, D. Dias, S. Li, and C. Hou. 2018. “Discrete kinematic mechanism for nonhomogeneous slopes and its application.” Int. J. Geomech. 18 (12): 04018171. https://doi.org/10.1061/(ASCE)GM.1943-5622.000130.
Tang, Y., D. H. Chan, and D. Z. Zhu. 2018. “Analytical solution for steady-state groundwater inflow into a circular tunnel in anisotropic soils.” J. Eng. Mech. 144 (9): 06018003. https://doi.org/10.1061/(ASCE)EM.1943-7889.000150.
Umeda, T., and A. Ichikawa. 1971. “A modified complex method for optimization.” Ind. Eng. Chem. Process Des. Dev. 10 (2): 229–236. https://doi.org/10.1021/i260038a016.
Verruijt, A. 1997. “A complex variable solution for a deforming circular tunnel in an elastic half-plane.” Int. J. Numer. 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.
Viratjandr, C., and R. L. Michalowski. 2006. “Limit analysis of submerged slopes subjected to water drawdown.” Can. Geotech. J. 43 (8): 802–814. https://doi.org/10.1139/t06-042.
Wang, Z., C. Qiao, C. Song, and J. Xu. 2014. “Upper bound limit analysis of support pressures of shallow tunnels in layered jointed rock strata.” Tunnelling Underground Space Technol. 43: 171–183. https://doi.org/10.1016/j.tust.2014.05.010.
Yang, F., and J. S. Yang. 2008. “Limit analysis method for determination of earth pressure on shallow tunnel.” [In Chinese.] Eng. Mech. 25 (7): 179–184.
Yang, X. L., W. T. Li, and Q. J. Pan. 2015. “Influences of anisotropy and inhomogeneity on supporting pressure of tunnel face with kinematical approach.” J. Cent. South Univ. 22 (9): 3536–3543. https://doi.org/10.1007/s11771-015-2893-z.
Zhang, R., G. Chen, J. Zou, L. Zhao, and C. Jiang. 2019. “Study on roof collapse of deep circular cavities in jointed rock masses using adaptive finite element limit analysis.” Comput. Geotech. 111: 42–55. https://doi.org/10.1016/j.compgeo.2019.03.003.
Zhang, W., X. Liu, Z. Liu, Y. Zhu, Y. Huang, L. Taerwe, and W. De Corte. 2022. “Investigation of the pressure distributions around quasi-rectangular shield tunnels in soft soils with a shallow overburden: A field study.” Tunnelling Underground Space Technol. 130: 104742. https://doi.org/10.1016/j.tust.2022.104742.
Zou, J. F., and Z. H. Qian. 2018. “Face-stability analysis of tunnels excavated below groundwater considering coupled flow deformation.” Int. J. Geomech. 18 (8): 04018089. https://doi.org/10.1061/(ASCE)GM.1943-5622.000119.
Zou, J. F., Z. H. Qian, X. H. Xiang, and G. Chen. 2019. “Face stability of a tunnel excavated in saturated nonhomogeneous soils.” Tunnelling Underground Space Technol. 83: 1–17. https://doi.org/10.1016/j.tust.2018.09.007.
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 8, 2023
Accepted: Jan 13, 2024
Published online: Apr 26, 2024
Published in print: Jul 1, 2024
Discussion open until: Sep 26, 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.