Viscoelastic ground responses around shallow tunnels considering surcharge loadings and effect of supporting

References

• Bilotta, E., Paolillo, A., Russo, G., & Aversa, S. (2017). Displacements induced by tunnelling under a historical building. Tunnelling and Underground Space Technology, 61, 221–232.
   Web of Science ®Google Scholar
• Carranza-Torres, C., Rysdahl, B., & Kasim, M. (2013). On the elastic analysis of a circular lined tunnel considering the delayed installation of the support. International Journal of Rock Mechanics and Mining Sciences, 61, 57–85.
   Web of Science ®Google Scholar
• Dindarloo, S. R., & Siami-Irdemoosa, E. (2015). Maximum surface settlement based classification of shallow tunnels in soft ground. Tunnelling and Underground Space Technology, 49, 320–327.
   Web of Science ®Google Scholar
• Fahimifar, A., Tehrani, F. M., Hedayat, A., & Vakilzadeh, A. (2010). Analytical solution for the excavation of circular tunnels in a visco-elastic Burger’s material under hydrostatic stress field. Tunnelling and Underground Space Technology, 25(4), 297–304.
   Web of Science ®Google Scholar
• Feng, X. T., Chen, B. R., Yang, C., Zhou, H., & Ding, X. (2006). Identification of visco-elastic models for rocks using genetic programming coupled with the modified particle swarm optimization algorithm. International Journal of Rock Mechanics and Mining Sciences, 43(5), 789–801.
   Web of Science ®Google Scholar
• Flamant, A. (1892). Sur la répartition des pressions dans un solide rectangulaire chargé transversalement. CR Académie des Sciences Paris, 114, 1465–1468.
   Google Scholar
• Fu, J., Yang, J., Yan, L., & Abbas, S. M. (2014). An analytical solution for deforming twin-parallel tunnels in an elastic half plane. International Journal for Numerical and Analytical Methods in Geomechanics, 39(5), 524–538.
   Web of Science ®Google Scholar
• Huang, H. W., & Zhang, D. M. (2016). Resilience analysis of shield tunnel lining under extreme surcharge: Characteriztion and field application. Tunnelling and Underground Space Technology, 51, 301–312.
   Web of Science ®Google Scholar
• Jeffery, G. B. (1921). Plane stress and plane strain in bipolar co-ordinates. Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences, 221(582–593), 265–293.
   Google Scholar
• Jiang, M., Chen, H., & Crosta, G. B. (2015). Numerical modeling of rock mechanical behavior and fracture propagation by a new bond contact model. International Journal of Rock Mechanics and Mining Sciences, 78, 175–189.
   Web of Science ®Google Scholar
• Jiang, M., & Yin, Z. Y. (2012). Analysis of stress redistribution in soil and earth pressure on tunnel lining using the discrete element method. Tunnelling and Underground Space Technology, 32(6), 251–259.
   Google Scholar
• Jiang, M., & Yin, Z. Y. (2014). Influence of soil conditioning on ground deformation during longitudinal tunneling. Comptes Rendus Mécanique, 342(3), 189–197.
   Web of Science ®Google Scholar
• Jiang, M. J., Yan, H. B., Zhu, H. H., & Utili, S. (2011). Modeling shear behavior and strain localization in cemented sands by two-dimensional distinct element method analyses. Computers and Geotechnics, 38(1), 14–29.
   Web of Science ®Google Scholar
• Jiang, M. J., Yu, H. S., & Harris, D. (2005). A novel discrete model for granular material incorporating rolling resistance. Computers and Geotechnics, 32(5), 340–357.
   Web of Science ®Google Scholar
• Lee, E. H. (1955). Stress analysis in visco-elastic bodies. Quarterly of Applied Mathematics, 13, 183–190.
   Google Scholar
• Liu, X. R., Chen, H. J., Liu, K., & He, C. M. (2017). Model test and stress distribution law of unsymmetrical loading tunnel in bedding rock mass. Arabian Journal of Geosciences, 10(7), 184.
   Web of Science ®Google Scholar
• Loganathan, N., & Poulos, H. G. (1998). Analytical prediction for tunneling-induced ground movements in clays. Journal of Geotechnical and Geoenvironmental Engineering, 124(9), 846–856.
   Web of Science ®Google Scholar
• Lu, A., Zeng, X., & Xu, Z. (2016). Solution for a circular cavity in an elastic half plane under gravity and arbitrary lateral stress. International Journal of Rock Mechanics and Mining Sciences, 89, 34–42.
   Web of Science ®Google Scholar
• Massinas, S., & Sakellariou, M. G. (2009). Closed form solution for plastic zone formation around a circular tunnel in half-space obeying Mohr-Coulomb criterion. Géotechnique, 60(7), 691–701.
   Web of Science ®Google Scholar
• Mindlin, R. D. (1940). Stress distribution around a tunnel. Transactions of the American Society of Civil Engineers, 195, 1117–1140.
   Google Scholar
• Mindlin, R. D. (1948). Stress distribution around a hole near the edge of a plate under tension. Proceedings of the Society for Experimental Stress Analysis, 5, 56–68.
   Google Scholar
• Nomikos, P., Rahmannejad, R., & Sofianos, A. (2011). Supported axisymmetric tunnels within linear viscoelastic burgers rocks. Rock Mechanics and Rock Engineering, 44(5), 553–564.
   Web of Science ®Google Scholar
• Muskhelishvili, N. I. (1955). Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff International Publishing.
   Google Scholar
• Osman, A. S., Bolton, M. D., & Mair, R. (2006). Predicting 2D ground movements around tunnels in undrained clay. Géotechnique, 56(9), 597–604.
   Web of Science ®Google Scholar
• Osman, A. S., Mair, R., & Bolton, M. D. (2006). On the kinematics of 2D tunnel collapse in undrained clay. Géotechnique, 56(9), 585–595.
   Web of Science ®Google Scholar
• Panet, M. (1995). Le calcul des tunnels par la méthode convergence-confinement. Presses ENPC.
   Google Scholar
• Panji, M., Koohsari, H., Adampira, M., Alielahi, H., & Marnani, J. A. (2016). Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method. Journal of Rock Mechanics and Geotechnical Engineering, 8(4), 480–488.
   Web of Science ®Google Scholar
• Park, K. H. (2005). Analytical solution for tunnelling-induced ground movement in clays. Tunnelling and Underground Space Technology, 20(3), 249–261.
   Web of Science ®Google Scholar
• Peck, R. B. (1969). Deep excavations and tunnelling in soft ground. Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering, Mexico (pp. 225–290).
   Google Scholar
• Prassetyo, S. H., & Gutierrez, M. (2016). Effect of surface loading on the hydro-mechanical response of a tunnel in saturated ground. Underground Space 1(1), 1–19.
   Web of Science ®Google Scholar
• Sagaseta, C. (1988). Analysis of undrained soil deformation due to ground loss. Géotechnique, 37(3), 301–320.
   Web of Science ®Google Scholar
• Sokolnikoff, I. S., & Specht, R. D. (1956). Mathematical theory of elasticity. McGraw-Hill.
   Google Scholar
• Song, F., Wang, H., & Jiang, M. (2018). Analytically-based simplified formulas for circular tunnels with two liners in viscoelastic rock under anisotropic initial stresses. Construction and Building Materials. 175, 746–767.
   Web of Science ®Google Scholar
• Strack, O. E., & Verruijt, A. (2002). A complex variable solution for a deforming buoyant tunnel in a heavy elastic half-plane. International Journal for Numerical and Analytical Methods in Geomechanics, 26(12), 1235–1252.
   Web of Science ®Google Scholar
• Sulem, J., Panet, M., & Guenot, A. (1987a). Closure analysis in deep tunnels. International Journal of Rock Mechanics and Mining Sciences and Geomechanics Abstracts, 24(3), 145–154.
   Web of Science ®Google Scholar
• Sulem, J., Panet, M., & Guenot, A. (1987b). An analytical solution for time-dependent displacements in a circular tunnel. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, 24(3), 155–164.
   Web of Science ®Google Scholar
• Suwansawat, S., & Einstein, H. H. (2006). Artificial neural networks for predicting the maximum surface settlement caused by EPB shield tunneling. Tunnelling and Underground Space Technology, 21, 133–150.
   Web of Science ®Google Scholar
• Unlu, T., & Gercek, H. (2003). Effect of Poisson's ratio on the normalized radial displacements occurring around the face of a circular tunnel. Tunnelling and Underground Space Technology, 18(5), 547–553.
   Web of Science ®Google Scholar
• Verruijt, A. (1997). A complex variable solution for a deforming circular tunnel in an elastic half-plane. International Journal for Numerical and Analytical Methods in Geomechanics 21, 77–89.
   Web of Science ®Google Scholar
• Verruijt, A. (1998). Deformations of an elastic half plane with a circular cavity. International Journal of Solids and Structures, 35(21), 2795–2804.
   Web of Science ®Google Scholar
• Verruijt, A., & Booker, J. (1996). Surface settlements due to deformation of a tunnel in an elastic half plane. Géotechnique, 46(4), 753–756.
   Web of Science ®Google Scholar
• Vlachopoulos, N., & Diederichs, M. S. (2009). Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels. Rock Mechanics and Rock Engineering, 42(42), 131–146.
   Google Scholar
• Wang, G., Liu, C., Jiang, Y., Wu, X., & Wang, S. (2015). Rheological model of DMFC rockbolt and rockmass in a circular tunnel. Rock Mechanics and Rock Engineering, 48(6), 2319–2357.
   Web of Science ®Google Scholar
• Wang, H. N., Chen, X. P., Jiang, M. J., Song, F., & Wu, L. (2018). The analytical predictions on displacement and stress around shallow tunnels subjected to surcharge loadings. Tunnelling and Underground Space Technology, 71, 403–427.
   Web of Science ®Google Scholar
• Wang, H. N., Li, Y., Ni, Q., Utili, S., Jiang, M. J., & Liu, F. (2013). Analytical solutions for the construction of deeply buried circular tunnels with two liners in rheological rock. Rock Mechanics and Rock Engineering, 46(6), 1481–1498.
   Web of Science ®Google Scholar
• Wang, H. N., Utili, S., Jiang, M. J., & He, P. (2015). Analytical solutions for tunnels of elliptical cross-section in rheological rock accounting for sequential excavation. Rock Mechanics and Rock Engineering, 48(5), 1997–2029.
   Web of Science ®Google Scholar
• Wang, L. Z., Li, L. L., & Lv, X. J. (2009). Complex variable solutions for tunneling-induced ground movement. International Journal of Geomechanics, 9(2), 63–72.
   Google Scholar
• Yang, X. L., & Wang, J. M. (2008). Stress dilatancy analysis of shallow tunnels subjected to unsymmetrical pressure. Journal of Central South University of Technology, 15(s2), 28–33.
   Google Scholar
• Yu, L. Y., Jing, H. W., & Wang, Y. C. (2014). Elastic analysis for subaqueous tunnel surrounding rock via the complex variable method. Mathematical Problems in Engineering, 2014(1), 6.
   Google Scholar
• Zymnis, D. M., Whittle, A. J., & Chatzigiannelis, I. (2013). Effect of anisotropy in ground movements caused by tunnelling. Géotechnique, 63(13), 1083–1102.
   Web of Science ®Google Scholar