Geomechanics and Engineering

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Elastic solutions for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface

  • Wang, Ling (School of Civil Engineering, Central South University, Central South University Railway Campus) ;
  • Zou, Jin-Feng (School of Civil Engineering, Central South University, Central South University Railway Campus) ;
  • Yang, Tao (School of Civil Engineering, Central South University, Central South University Railway Campus) ;
  • Wang, Feng (School of Civil Engineering, Central South University, Central South University Railway Campus)
  • Received : 2019.01.16
  • Accepted : 2019.10.11
  • Published : 2019.10.30
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Abstract

A new approach of analyzing the displacements and stress of the surrounding rock for shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface is investigated in this study. In the proposed approach, by using a virtual image technique, the shear stress of the vertical ground surface is revised to be zero, and elastic solutions of the surrounding rock are obtained before stress revision. To revise the vertical normal stress and shear stress of horizontal ground surface generated by the combined action of the actual and image sinks, the harmonic functions and corresponding stress function solutions were adopted. Based on the Boussinesq's solutions and integral method, the horizontal normal stress of the vertical ground surface is revised to be zero. Based on the linear superposition principle, the final solution of the displacements and stress were proposed by superimposing the solutions obtained by the virtual image technique and the stress revision on the horizontal and vertical ground surfaces. Furthermore, the ground settlements and lateral displacements of the horizontal and vertical ground surfaces are derived by the proposed approach. The proposed approach was well verified by comparing with the numerical method. The discussion based on the proposed approach in the manuscript shows that smaller horizontal ground settlements will be induced by lower tunnel buried depths and smaller limb distances. The proposed approach for the displacement and stress of the surrounding rocks can provide some practical information about the surrounding rock stability analysis of shallow tunnels excavated under non-axisymmetric displacement boundary conditions on a vertical surface.

Keywords

References

  1. Alonso, E., Alejano, L.R., Varas, F., Fdez-Manin, G. and Carranza-Torres, C. (2003), "Ground response curves for rock masses exhibiting strainsoftening behavior", Int. J. Numer. Anal. Meth. Geomech., 27(13), 1153-1185. https://doi.org/10.1002/nag.315.
  2. Boussinesq, J. (1885), Application des Potentiels a L'Equilibre et des Mouvements des Solides Elastiques, Gauthier-Villars, Paris, France.
  3. Broere, W. and Van T.A.F. (2000), Influence of Infiltration and Groundwater Flow on Tunnel Face Stability, in Geotechnical Aspects of Underground Construction in Soft Ground, 339-344.
  4. Brown, E.T., Bray, J.W., Ladanyi, B. and Hoek, E. (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).
  5. Chen, G.H., Zou, J.F. and Qian, Z.H. (2019a), "An improved collapse analysis mechanism for the face stability of shield tunnel in layered soils", Geomech. Eng., 17(1), 97-107. https://doi.org/10.12989/gae.2019.17.1.097.
  6. Chen, G.H., Zou, J., Min, Q., Guo, W.J. and Zhang, T.Z. (2019b), "Face stability analysis of a shallow square tunnel in nonhomogeneous soils", Comput. Geotech., 114, 103-112. https://doi.org/10.1016/j.compgeo.2019.103112.
  7. Daraei, A. and Zare, S. (2018), "A new strain-based criterion for evaluating tunnel stability", Geomech. Eng., 16(2), 205-215. https://doi.org/10.12989/gae.2018.16.2.205.
  8. Farmer, I.W. and Glossop, N.H. (1979), "Settlement associated with removal of compressed air pressure during tunnelling in alluvial clay", Geotechnique, 29(1), 67-72. https://doi.org/10.1680/geot.1979.29.1.67.
  9. Fahimifar, A.; Ghadami, H. and Ahmadvand, M. (2015), "The ground response curve of underwater tunnels, excavated in a strain-softening rock mass", Geomech. Eng., 8(3), 323-359. http://dx.doi.org/10.12989/gae.2015.8.3.323.
  10. Han, K.H., Zhang, C.P. and Zhang, D.L. (2016), "Upper-bound solutions for the face stability of a shield tunnel in multilayered cohesive-frictional soils", Comput. Geotech., 79, 1-9. https://doi.org/10.1016/j.compgeo.2016.05.018.
  11. Huang M.S., Li, S., Zhou, W.X. and Yu, J.Y. (2018), "Continuous field based upper bound analysis for three-dimensional tunnel face stability in undrained clay", Comput. Geotech., 94, 207-213. https://doi.org/10.1016/j.compgeo.2017.09.014.
  12. Kassir, M.K. and Sih, G.C. (1975), Three-Dimensional Crack Problems, Noordhoff International Publishing, Dordrecht, The Netherlands.
  13. Lee, Y.K. and Pietruszczak, S. (2008), "A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass", Tunn. Undergr. Sp. Technol., 23(5), 588-599. https://doi.org/10.1016/j.tust.2007.11.002.
  14. Li, C., Zou, J.F. and A, S.G. (2019a), "Closed-Form solution for undrained cavity expansion in anisotropic soil mass based on spatially mobilized plane failure criterion", Int. J. Geomech., 19(7), 04019075. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001458.
  15. Li, C., Zou, J.F. and Zhou, H. (2019b), "Cavity expansion in k0 consolidated clay", Eur. J. Environ. Civ. Eng., 2019, 1-19. DOI: 10.1080/19648189.2019.1605937.
  16. Loganathan, N. and Poulos, H.G. (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).
  17. Li, J.P., Zhang, Y.G., Chen, H.B. and Liang, F.Y. (2013), "Analytical solutions of spherical cavity expansion near a slope due to pile installation", J. Appl. Math., 1-11. http://dx.doi.org/10.1155/2013/306849.
  18. Li, T.Z. and Yang, X.L. (2019), "Three-dimensional face stability of shallow-buried tunnels with tensile strength cut-off", Comput. Geotech., 110, 82-93. https://doi.org/10.1016/j.compgeo.2019.02.014.
  19. Mollon, G., Dias, D. and Soubra, A.H. (2011), "Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield", Int. J. Numer. Anal. Meth. Geomech., 35(12), 1363-1388. https://doi.org/10.1002/nag.962.
  20. Mollon, G., Dias, D. and Soubra, A.H. (2013), "Continuous velocity fields for collapse and blowout of a pressurized tunnel face in purely cohesive soil", Int. J. Numer. Anal. Meth. Geomech., 37(13), 2061-2083. https://doi.org/10.1002/nag.2121.
  21. Oreste, P.P. and Dias, D. (2012), "Stabilisation of the excavation face in shallow tunnels using fibreglass dowels", Rock Mech. Rock Eng., 45(4), 499-517. https://doi.org/10.1007/s00603-012-0234-1.
  22. Peck, R.B. (1969), "Deep excavations and tunneling in soft ground", Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering, Mexico City, Mexico.
  23. Park, K.H. (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).
  24. Pan, Q.J. and Dias, D. (2017), "Upper-bound analysis on the face stability of a non-circular tunnel", Tunn. Undergr. Sp. Technol., 62, 96-102. https://doi.org/10.1016/j.tust.2016.11.010.
  25. Pan, Q.J. and Dias, D. (2018), "Three dimensional face stability of a rock tunnel subjected to seepage forces" Tunn. Undergr. Sp. Technol., 71, 555-566. https://doi.org/10.1016/j.tust.2017.11.003.
  26. Timoshenko, S.P. and Goodier, J.N. (1970), Theory of Elasticity, McGraw Hill, New York, U.S.A.
  27. Verruijt, A. (1997), "A complex variable solution for a deforming circular tunnel in an elastic half plane", Int. J. Numer. Anal. Meth. Geomech., 21(2), 77-89. https://doi.org/10.1002/(SICI)1096-9853(199702)21:2%3C77::AID-NAG857%3E3.0.CO;2-M.
  28. Verruijt, A. (1998), "Deformations of an elastic half plane with circular cavity", Int. J. Solid. Struct., 35(21), 2795-2804. https://doi.org/10.1016/S0020-7683(97)00194-7.
  29. Wood, A.M.M. (1975), "Circular tunnel in elastic ground", Geotechnique, 25(1), 115-127. https://doi.org/10.1680/geot.1975.25.1.115.
  30. Wang, S., Yin, K., Tang, Y.H. and Ge, X. (2010), "A new approach for analyzing circular tunnel in strain-softening rock masses", Int. J. Rock Mech. Min. Sci., 47(1), 170-178. http://dx.doi.org/10.1016%2Fj.ijrmms.2009.02.011. https://doi.org/10.1016/j.ijrmms.2009.02.011
  31. Wang, L., Zou, J.F. and Sheng, Y.M. (2019), "An improved stress and strain increment approaches for circular tunnel in strainsoftening surrounding rock considering seepage force", Adv. Mater. Sci. Eng. https://doi.org/10.1155/2019/2075240.
  32. Xiao, Y., Sun, Y., Yin, F., Liu, H. and Xiang, J. (2017a), "Stressstrain-strength response and ductility of gravels improved by polyurethane foam adhesive", J. Geotech. Geoenviron. Eng., 144(2), 04017108. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001812.
  33. Xiao, Y., Sun, Y., Yin, F., Liu, H. and Xiang, J. (2017b), "Constitutive modeling for transparent granular soils", Int. J. Geomech., 17(7), 04016150. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000857.
  34. Yu, H.S. and Houlsby, G.T. (1995), "Large strain analytical solution for cavity contraction in dilatant soils", Int. J. Numer. Anal. Meth. Geomech., 19(11), 793-811. https://doi.org/10.1002/nag.1610191104.
  35. Yu, H.S. and Rowe, R.K. (1999), "Plasticity solutions for soil behavior around contracting cavities and tunnels", Int. J. Numer. Anal. Meth. Geomech., 23(12), 1245-1279. https://doi.org/10.1002/(SICI)1096-9853(199910)23:12%3C1245::AID-NAG30%3E3.0.CO;2-W.
  36. Yu, H.S. and Carter, J.P. (2002), "Rigorous similarity solutions for cavity expansion in cohesive-frictional soils", Int. J. Geomech., 2(2), 233-258. https://doi.org/10.1061/(ASCE)1532-3641(2002)2:2(233).
  37. Zhang, C., Han, K. and Zhang, D. (2015), "Face stability analysis of shallow circular tunnels in cohesive-frictional soils", Tunn. Undergr. Sp. Technol., 50, 345-357. https://doi.org/10.1016/j.tust.2015.08.007.
  38. Zhang, F., Gao, Y.F., Wu, Y.X. and Zhang, N. (2018), "Upperbound solutions for face stability of circular tunnels in undrained clays", Geotechnique, 68(1), 1-13. https://doi.org/10.1680/jgeot.16.T.028.
  39. Zou, J.F. and Zuo, S.Q. (2017), "Similarity solution for the synchronous grouting of shield tunnels under the nonaxisymmetric displacement boundary on vertical surface", Adv. Appl. Math. Mech., 9(1), 205-232. https://doi.org/10.4208/aamm.2016.m1479.
  40. Zou, J.F., Liu, S.X., Li, J.B. and Qian, Z H. (2019a), "Face stability analysis for a shield-driven tunnel with non-linear yield criterion", Proc. Inst. Civ. Eng. Geotech. Eng., 172(3), 243-254. https://doi.org/10.1680/jgeen.17.00222.
  41. Zou, J.F., Qian, Z.H., Xiang, X.H. and Chen, G.H. (2019b), "Face stability of a tunnel excavated in saturated nonhomogeneous soils", Tunn. Undergr. Sp. Technol., 83(1), 1-17. https://doi.org/10.1016/j.tust.2018.09.007.
  42. Zou J.F., Wang, F. and Wei, A. (2019c), "A semi-analytical solution for shallow tunnels with radius-iterative-approach in semi-infinite space", Appl. Math. Modell., 73(9), 285-302. https://doi.org/10.1016/j.apm.2019.04.007.
  43. Zou, J.F., Yang, T., Wang, L., Guo, W.J. and Huang, F.L. (2019d), "A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass", Geomech. Eng., 18(3), 225-234. https://doi.org/10.12989/gae.2019.18.3.225.