Technical Papers
May 3, 2018

Complex Variable Solutions for Soil and Liner Deformation due to Tunneling in Clays

Publication: International Journal of Geomechanics
Volume 18, Issue 7

Abstract

Current research to predict the soil deformation due to tunneling pays little attention to the impact of soil–liner interaction. Moreover, the conventional solution for the stress function method has an inherent physical defect that leads to a nonzero ground displacement at infinity. To overcome these disadvantages, an analytical solution by the complex variable method is presented for problems in evaluating the liner and disturbed surrounding soil deformation due to tunneling in clays. The interaction mechanism between tunnel liners and surrounding soils is considered in this study, and the deterministic nonuniform convergence boundary model is composed as the displacement controlled condition on tunnel opening. The applicability of the proposed method is observed based on the existing analytical solutions and a series of field cases. It has been demonstrated that the proposed complex variable solution for the estimation of soil displacements considering the soil–liner interaction and nonuniform convergence model agrees well with the observation data. The impacts of key parameters on the tunneling-induced soil deformation are also assessed, including the tunneling gap, the soil and liner physical characteristics, and the buried depth liner thickness for the tunnel. In addition, the effects of the liner thickness and buried depth on the circular expression of liner deformation, including the radial and tangential displacements, are investigated by the parametric analyses considering the soil–liner interaction mechanism. To consider the liner stiffness influence and the nonuniform convergence boundary condition, the complex variable solution in this study can be regarded as an effective approach to conservatively predict the soil and liner deformation.

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Acknowledgments

The authors acknowledge the financial support provided by the National Key Research and Development Program of China (2016YFC0800200); the Natural Science Foundation of China (41772331); and the Open Project Program of the State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology (SKLGDUEK1707).

References

Almeida e Sousa, J., A. Negro, M. Fernandes, and A. Cardoso. 2011. “Three-dimensional nonlinear analyses of a metro tunnel in São Paulo Porous Clay, Brazil.” J. Geotech. Geoenviron. Eng. 137 (4): 376–384.https://doi.org/10.1061/(ASCE)GT.1943-5606.0000433.
Amorosi, A., D. Boldini, G. D. Felice, M. Malena, and M. Sebastianelli. 2014. “Tunnelling-induced deformation and damage on historical masonry structures.” Géotechnique 64 (2): 118–130. https://doi.org/10.1680/geot.13.P.032.
Avgerinos, V., D. M. Potts, and J. R. Standing. 2016. “The use of kinematic hardening models for predicting tunnelling-induced ground movements in London clay.” Géotechnique 66 (2): 106–120. https://doi.org/10.1680/jgeot.15.P.035.
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),
Bobet, A. 2010. “Drained and undrained response of deep tunnels subjected to far-field shear loading.” Tunnelling Underground Space Technol. 25 (1): 21–31. https://doi.org/10.1016/j.tust.2009.08.001.
Boonyarak, T., and C. W. W. Ng. 2015. “Effects of construction sequence and cover depth on crossing-tunnel interaction.” Can. Geotech. J. 52 (7): 851–867. https://doi.org/10.1139/cgj-2014-0235.
Celestino, T. B., R. A. M. P. Gomes, and A. A. Bortolucci. 2000. “Errors in ground distortions due to settlement trough adjustment.” Tunnelling Underground Space Technol. 15 (1): 97–100. https://doi.org/10.1016/S0886-7798(99)00054-1.
Chehade, F. H., and I. Shahrour. 2008. “Numerical analysis of the interaction between twin-tunnels: Influence of the relative position and construction procedure.” Tunnelling Underground Space Technol. 23 (2), 210–214. https://doi.org/10.1016/j.tust.2007.03.004.
Cheng, C. Y., G. R. Dasari, Y. K. Chow, and C. F. Leung. 2007. “Finite element analysis of tunnel-soil-pile interaction using displacement controlled model.” Tunnelling Underground Space Technol. 22 (4): 450–466. https://doi.org/10.1016/j.tust.2006.08.002.
Chou, W. I., and A. Bobet. 2002. “Predictions of ground deformations in shallow tunnels in clay.” Tunnelling Underground Space Technol. 17 (1): 3–19. https://doi.org/10.1016/S0886-7798(01)00068-2.
Ding, L. Y., L. Ma, H. B. Luo, M. H. Yu, and X. G. Wu. 2011. “Wavelet analysis for tunneling-induced ground settlement based on a stochastic model.” Tunnelling Underground Space Technol. 26 (5): 619–628. https://doi.org/10.1016/j.tust.2011.03.005.
Fang, Q., Q. Tai, D. Zhang, and L. N. Y. Wong. 2016. “Ground surface settlements due to construction of closely-spaced twin tunnels with different geometric arrangements.” Tunnelling Underground Space Technol. 51 (1): 144–151. https://doi.org/10.1016/j.tust.2015.10.031.
Flügge, W. 1966. Stresses in shells. New York: Springer-Verlag.
Franza, A., A. M. Marshall, T. Haji, A. O. Abdelatif, S. Carbonari, and M. Morici. 2017. “A simplified elastic analysis of tunnel-piled structure interaction.” Tunnelling Underground Space Technol. 61 (1): 104–121. https://doi.org/10.1016/j.tust.2016.09.008.
Fu, J., J. Yang, H. Klapperich, and S. Wang. 2016. “Analytical prediction of ground movements due to a nonuniform deforming tunnel.” Int. J. Geomech. 04015089. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000580,
Fu, J., J. Yang, L. Yan, and S. M. Abbas. 2015. “An analytical solution for deforming twin-parallel tunnels in an elastic half plane.” Int. J. Numer. Anal. Methods Geomech. 39 (5): 524–538. https://doi.org/10.1002/nag.2322.
Gioda, G., and G. Swoboda. 1999. “Developments and applications of the numerical analysis of tunnels in continuous media.” Int. J. Numer. Anal. Methods Geomech. 23 (13): 1393–1405. https://doi.org/10.1002/(SICI)1096-9853(199911)23:13%3C1393::AID-NAG933%3E3.0.CO;2-Z.
González, C., and C. Sagaseta. 2001. “Patterns of soil deformations around tunnels. Application to the extension of Madrid Metro.” Comput. Geotech. 28 (6–7): 445–468. https://doi.org/10.1016/S0266-352X(01)00007-6.
Haji, T. K., A. M. Marshall, and W. Tizani. 2018. “A cantilever approach to estimate bending stiffness of buildings affected by tunnelling.” Tunnelling Underground Space Technol. 71 (Jan): 47–61. https://doi.org/10.1016/j.tust.2017.08.005.
Hasanpour, R. 2014. “Advance numerical simulation of tunneling by using a double shield TBM.” Comput. Geotech. 57 (Apr): 37–52. https://doi.org/10.1016/j.compgeo.2014.01.002.
Ieronymaki, E., A. Whittle, and D. Sureda. 2017. “Interpretation of free-field ground movements caused by mechanized tunnel construction.” J. Geotech. Geoenviron. Eng.143 (4): 04016114. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001632.
Jeffery, G. B. 1921. “Plane stress and plane strain in bipolar co-ordinates.” Philos. Trans. R. Soc. London, Ser. A 221 (582–593): 265–293. https://doi.org/10.1098/rsta.1921.0009.
Klar, A., I. Elkayam, and A. Marshall. 2016. “Design oriented linear-equivalent approach for evaluating the effect of tunneling on pipelines.” J. Geotech. Geoenviron. Eng. 142 (1): 04015062. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001376.
Klar, A., and A. M. Marshall. 2015. “Linear elastic tunnel pipeline interaction: The existence and consequence of volume loss equality.” Géotechnique 65 (9): 788–792. https://doi.org/10.1680/geot.14.P.173.
Kooi, C. B., and A. Verruijt. 2001. “Interaction of circular holes in an infinite elastic medium.” Tunnelling Underground Space Technol. 16 (1): 59–62. https://doi.org/10.1016/S0886-7798(01)00027-X.
Lee, K. M., R. K. Rowe, and K. Y. Lo. 1992. “Subsidence owing to tunnelling. I. Estimating the gap parameter.” Can. Geotech. J. 29 (6): 929–940. https://doi.org/10.1139/t92-104.
Liang, R. Z., T. D. Xia, M. S. Huang, and C. G. Lin. 2017. “Simplified analytical method for evaluating the effects of adjacent excavation on shield tunnel considering the shearing effect.” Comput. Geotech. 81 (1): 167–187. https://doi.org/10.1016/j.compgeo.2016.08.017.
Loganathan, N., and H. Poulos. 1998. “Analytical prediction for tunneling-induced ground movements in clays.” J. Geotech. Geoenviron. Eng. 124 (9): 846–856. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:9(846).
Ma, L., L. Ding, and H. Luo. 2014. “Non-linear description of ground settlement over twin tunnels in soil.” Tunnelling Underground Space Technol. 42 (May): 144–151. https://doi.org/10.1016/j.tust.2014.02.006.
Mair, R. J., and R. N. Taylor, 1997. “Theme lecture: Bored tunnelling in the urban environment.” In Vol. 5 of Proc., 14th Int. Conf. Soil Mechanics and Foundation Engineering, 2353–2385. Rotterdam, Netherlands: Balkema.
Mair, R. J., R. N. Taylor, and A. Bracegirdle. 1993. “Subsurface settlement profiles above tunnels in clays.” Géotechnique 43 (2): 315–320. https://doi.org/10.1680/geot.1993.43.2.315.
Marshall, A. 2012. “Tunnel-pile interaction analysis using cavity expansion methods.” J. Geotech. Geoenviron. Eng. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000709, 138 (10): 1237–1246.
Marshall, A. M., R. Farrell, A. Klar, and R. Mair. 2012. “Tunnels in sands: The effect of size, depth, and volume loss on greenfield displacements.” Géotechnique 62 (5): 385–399. https://doi.org/10.1680/geot.10.P.047.
Mindlin, R. D. 1940. “Stress distribution around a tunnel.” Trans. Am. Soc. Civ. Eng. 105, 1117–1140.
Mindlin, R. D. 1948. “Stress distribution around a hole near the edge of a plate under tension.” Proc. Soc. Exp. Stress Anal. 5 (2): 56–68.
Neaupane, K. M., and N. R. Adhikari. 2006. “Prediction of tunneling-induced ground movement with the multi-layer perceptron.” Tunnelling Underground Space Technol. 21 (2): 151–159. https://doi.org/10.1016/j.tust.2005.07.001.
Ng, C., T. Boonyarak, and D. Mašín. 2015. “Effects of pillar depth and shielding on the interaction of crossing multitunnels.” J. Geotech. Geoenviron. Eng. 141 (6): 04015021. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001293.
Park, K. 2004. “Elastic solution for tunneling-induced ground movements in clays.” Int. J. Geomech. 4 (4): 310–318. https://doi.org/10.1061/(ASCE)1532-3641(2004)4:4(310).
Park, K. H. 2005. “Analytical solution for tunnelling-induced ground movement in clays.” Tunnelling Underground Space Technol. 20 (3): 249–261. https://doi.org/10.1016/j.tust.2004.08.009.
Peck, R. B. 1969. “Deep excavations and tunneling in soft ground.” In Proc., 7th Int. Conf. on Soil Mechanics and Foundation Eng., 225–290. Rotterdam, Netherlands: Balkema.
Pinto, F., and A. J. Whittle. 2006. “Discussion of ‘elastic solution for tunneling-induced ground movements in clays by K. H. Park.” Int. J. Geomech. 6 (1): 72–73. https://doi.org/10.1061/(ASCE)1532-3641(2006)6:1(72),
Pinto, F., and A. Whittle. 2014. “Ground movements due to shallow tunnels in soft ground. I: Analytical solutions.” J. Geotech. Geoenviron. Eng. 140 (4): 04013040. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000948.
Pinto, F., D. Zymnis, and A. Whittle. 2014. “Ground movements due to shallow tunnels in soft ground. II: Analytical interpretation and prediction.” J. Geotech. Geoenviron. Eng. 140 (4): 04013041. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000947.
Sagaseta, C. 1987. “Analysis of undrained soil deformation due to ground loss.” Géotechnique 37 (3): 301–320. https://doi.org/10.1680/geot.1987.37.3.301.
Sokolnikoff, I. S. 1956. Mathematical theory of elasticity. New York: McGraw-Hill.
Strack, O. E., and A. Verruijt. 2000. “A complex variable solution for the ovalization of a circular tunnel in an elastic half-plane.” In Proc., GeoEng 2000, Int. Conf. on Geotechnical and Geological Eng., Melbourne, Australia. Lisbon, Portugal: International Society for Rock Mechanics and Rock Engineering.
Strack, O. E., and A. Verruijt. 2002. “A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane.” Int. J. Numer. Anal. Methods Geomech. 26 (12): 1235–1252. https://doi.org/10.1002/nag.246.
Tsinidis, G. 2017. “Response characteristics of rectangular tunnels in soft soil subjected to transversal ground shaking.” Tunnelling Underground Space Technol. 62 (1): 1–22. https://doi.org/10.1016/j.tust.2016.11.003.
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.
Verruijt, A. 1998. “Deformations of an elastic half plane with a circular cavity.” Int. J. Solids. Struct. 35 (21): 2795–2804. https://doi.org/10.1016/S0020-7683(97)00194-7.
Verruijt, A., and J. R. Booker. 1996. “Surface settlements due to deformation of a tunnel in an elastic half plane.” Géotechnique 46 (4): 753–756. https://doi.org/10.1680/geot.1996.46.4.753.
Verruijt, A., and J. R. Booker, 2000. “Complex variable analysis of Mindlin’s tunnel problem.” In Proc., Booker Memorial Symp., Developments in Theoretical Geomechanics, 3–22. Rotterdam, Netherlands: Balkema.
Verruijt, A., and O. E. Strack. 2008. “Buoyancy of tunnels in soft soils.” Géotechnique 58 (6): 513–515. https://doi.org/10.1680/geot.2008.58.6.513.
Wang, M. B., and S. C. Li. 2009. “A complex variable solution for stress and displacement field around a lined circular tunnel at great depth.” Int. J. Numer. Anal. Methods Geomech. 33 (7): 939–951. https://doi.org/10.1002/nag.749.
Wang, L., L. Li, and X. Lv. 2009. “Complex variable solutions for tunneling-induced ground movement.” Int. J. Geomech. 9 (2): 63–72. https://doi.org/10.1061/(ASCE)1532-3641(2009)9:2(63).
Yang, J. S., B. C. Liu, and M. C. Wang. 2004. “Modeling of tunneling induced ground surface movements using stochastic medium theory.” Tunnelling Underground Space Technol. 19 (2): 113–123. https://doi.org/10.1016/j.tust.2003.07.002.
Yang, X. L., and J. M. Wang. 2011. “Ground movement prediction for tunnels using simplified procedure.” Tunnelling Underground Space Technol. 26 (3): 462–471. https://doi.org/10.1016/j.tust.2011.01.002.
Zhang, Z. G., and M. S. Huang. 2014. “Geotechnical influence on existing subway tunnels induced by multiline tunneling in Shanghai soft soil.” Comput. Geotech. 56 (Mar): 121–132. https://doi.org/10.1016/j.compgeo.2013.11.008.
Zhang, Z. G., M. S. Huang, and M. X. Zhang. 2011. “Theoretical prediction of ground movements induced by tunnelling in multi-layered soils.” Tunnelling Underground Space Technol. 26 (2): 345–355. https://doi.org/10.1016/j.tust.2010.11.005.
Zhang, Z. G., M. S. Huang, and M. X. Zhang. 2012. “Deformation analysis of tunnel excavation below existing pipelines in multi-layered soils based on displacement controlled coupling numerical method.” Int. J. Numer. Anal. Methods Geomech. 36 (11): 1440–1460. https://doi.org/10.1002/nag.2098.
Zhang, Z. G., and M. X. Zhang. 2013. “Mechanical effects of tunneling on adjacent pipelines based on Galerkin solution and layered transfer matrix solution.” Soils Found.53 (4): 557–568. https://doi.org/10.1016/j.sandf.2013.06.007.
Zhang, Z. G., M. X. Zhang, Y. J. Jiang, Q. M. Bai, and Q. H. Zhao. 2017. “Analytical prediction for ground movements and liner internal forces induced by shallow tunnels considering non-uniform convergence pattern and ground-liner interaction mechanism.” Soils Found. 57 (2): 211–226. https://doi.org/10.1016/j.sandf.2017.03.004.
Zhang, Z. G., Q. H. Zhao, and M. X. Zhang. 2016. “Deformation analyses during subway shield excavation considering stiffness influences of underground structures.” Geomech. Eng. 11 (1): 117–139. https://doi.org/10.12989/gae.2016.11.1.117.
Zheng, G., T. Cui, X. Cheng, Y. Diao, T. Zhang, J. Sun, and L. Ge. 2017. “Study of the collapse mechanism of shield tunnels due to the failure of segments in sandy ground.” Eng. Fail. Anal. 79 (Sep): 464–490. https://doi.org/10.1016/j.engfailanal.2017.04.030.
Zheng, G., P. Lu, and Y. Diao. 2015a. “Advance speed-based parametric study of greenfield deformation induced by EPBM tunneling in soft ground.” Comput. Geotech. 65 (Apr): 220–232. https://doi.org/10.1016/j.compgeo.2014.12.013.
Zheng, G., T. Zhang, and Y. Diao. 2015b. “Mechanism and countermeasures of preceding tunnel distortion induced by succeeding EPBS tunnelling in close proximity.” Comput. Geotech. 66 (May): 53–65. https://doi.org/10.1016/j.compgeo.2015.01.008.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 18Issue 7July 2018

History

Received: Sep 18, 2017
Accepted: Jan 26, 2018
Published online: May 3, 2018
Published in print: Jul 1, 2018
Discussion open until: Oct 3, 2018

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Zhiguo Zhang, Ph.D. [email protected]
Associate Professor, School of Environment and Architecture, Univ. of Shanghai for Science and Technology, 516 Jungong Rd., Shanghai 200093, China; Dept. of Geotechnical Engineering, Tongji Univ., Shanghai 200092, China; State Key Laboratory for Geomechanics and Deep Underground Engineering, China Univ. of Mining and Technology, Xuzhou 221116, China (corresponding author). Email: [email protected]
Maosong Huang
Professor, Dept. of Geotechnical Engineering, Tongji Univ., Shanghai 200092, China.
Xiaoguang Xi
Postgraduate, School of Environment and Architecture, Univ. of Shanghai for Science and Technology, 516 Jungong Rd., Shanghai 200093, China.
Xuan Yang
Postgraduate, School of Environment and Architecture, Univ. of Shanghai for Science and Technology, 516 Jungong Rd., Shanghai 200093, China.

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