Geomechanics and Engineering

  • 제33권4호
  • /
  • Pages.369-380
  • /
  • 2023
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Static stress analysis of multi-layered soils with twin tunnels by using finite and infinite elements

  • Yusuf Z. Yuksel (Department of Civil Engineering, Bursa Technical University) ;
  • Seref D. Akbas (Department of Civil Engineering, Bursa Technical University)
  • 투고 : 2022.09.13
  • 심사 : 2023.03.21
  • 발행 : 2023.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

The aim of this paper is to investigate stress analysis of semi-infinite soils consisting of two layers with twin rectangular tunnels under static loads. The region close to the ground surface and tunnel modelled within finite elements. In order to use a more realistic model, the far region is modelled within infinite elements. The material model of the layered soil is considered as elastic and isotropic. In the finite element solution of the problem, two dimensional (2D) plane solid elements are used with sixteen-nodes rectangular finite and eight-nodes infinite shapes. Finite and infinite elements are ordered to be suitable for the tunnel and the soils. The governing equations of the problem are obtained by using the virtual work principle. In the numerical process, the five-point Gauss rule is used for the calculation of the integrations. In order to validate using methods, comparison studies are performed. In the numerical results, the stress distributions of the two layered soils containing twin rectangular tunnels presented. In the presented results, effects of the location of the tunnels on the stress distributions along soil depth are obtained and discussed in detail. The obtained results show that the locations of the tunnels are very effective on the stress distribution on the soils.

키워드

과제정보

This work has been supported by Research Fund of the Bursa Technical University. Project Number: 210D004.

참고문헌

  1. Abbo, A.J., Wilson, D.W., Sloan, S.W. and Lyamin, A.V. (2013), "Undrained stability of wide rectangular tunnels", Comput. Geotech., 53, 46-59. https://doi.org/10.1016/j.compgeo.2013.04.005.
  2. Ahn, C.Y., Park, D. and Moon, S.W. (2022), "Analysis of surface settlement troughs induced by twin shield tunnels in sedimentary soils", Geomech. Eng., 30(4), 325-336. https://doi.org/10.12989/gae.2022.30.4.325.
  3. Assadi, A. and Sloan, S.W. (1991), "Undrained stability of shallow square tunnel", J. Geotech. Eng., 117(8), 1152-1173. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:8(1152)
  4. Bettess, P. (1977). "Infinite elements", Int. J. Numer. Method. Eng., 11(1), 53-64. https://doi.org/10.1002/nme.1620110107.
  5. Bettess, P. and Bettess, J.A. (1984), "Infinite elements for static problems", Eng. Comput., 1(1), 4-16. https://doi.org/10.1108/eb023555.
  6. Booker, J.R. and Small, J.C. (1981), "Finite element analysis of problems with infinitely distant boundaries", Int. J. Numer. Anal. Method. Geomech., 5(4), 345-368. https://doi.org/10.1002/nag.1610050403.
  7. Brunotte, X., Meunier, G. and Imhoff, J.F. (1992), "Finite element modeling of unbounded problems using transformations: A rigorous, powerful and easy solution", IEEE T. Magnetics, 28(2), 1663-1666. https://doi.org/10.1109/20.124021.
  8. Curnier, A. (1983), "A static infinite element", Int. J. Numer. Method. Eng., 19(10), 1479-1488. https://doi.org/10.1002/nme.1620191006.
  9. Dasgupta, G. (1982), A finite element formulation for unbounded homogeneous continua. https://doi.org/10.1115/1.3161955.
  10. Demidem, M., Boutemeur, R., Bali, A. and Benyoussef, E.H. (2014), "Analysis of structural and non-structural problems by coupling of finite and infinite elements", Appl. Mech. Mater., 578, 445-455. https://doi.org/10.4028/www.scientific.net/AMM.578-579.445.
  11. El-Esnawy, N.A., Akl A.Y. and Bazaraa A.S. (1995), "A new parametric infinite domain element", Finite Elemen. Anal. Des., 19(1-2), 103-114. https://doi.org/10.1016/0168-874X(94)00060-S.
  12. Erkal, A., Laefer, D.F. and Tezcan, S.S. (2015), "Advantages of infinite elements over prespecified boundary conditions in unbounded problems", J. Comput. Civil Eng., 29(6). https://doi.org/10.1061/(ASCE)CP.1943-5487.0000391.
  13. Fang, Y.S., Kao, C.C. and Shiu, Y.F. (2012), "Double-O-tube shield tunneling for Taoyuan international airport access MRT", Tunn. Undergr. Sp. Tech., 30, 233-245. https://doi.org/10.1016/j.tust.2012.03.001.
  14. Fang, Q., Tai, Q., Zhang, D. and Wong, L.N.Y. (2016), "Ground surface settlements due to construction of closely-spaced twin tunnels with different geometric arrangements", Tunn. Undergr. Sp. Tech., 51, 144-151. https://doi.org/10.1016/j.tust.2015.10.031.
  15. Fu, J., Yang, J., Yan, L. and Abbas, S.M. (2015), "An analytical solution for deforming twin-parallel tunnels in an elastic half plane", Int. J. Numer. Anal. Method. Geomech., 39(5), 524-538. https://doi.org/10.1002/nag.2322.
  16. Haji, T.K., Faramarzi, A., Metje, N., Chapman, D. and Rahimzadeh, F. (2020), "Development of an infinite element boundary to model gravity for subsurface civil engineering applications", Int. J. Numer. Anal. Method. Geomech., 44(3), 418-431. https://doi.org/10.1002/nag.3027.
  17. Hatzigeorgiou, G.D. and Beskos, D.E. (2010). "Soil-structure interaction effects on seismic inelastic analysis of 3-D tunnels", Soil Dynam. Earthq. Eng., 30(9), 851-861. https://doi.org/10.1016/j.soildyn.2010.03.010.
  18. Houmat, A. (2008), "Mapped infinite p-element for two-dimensional problems of unbounded domains", Comput. Geotech., 35(4), 608-615. https://doi.org/10.1016/j.compgeo.2007.09.007.
  19. Hsiao-Hui, H. and Yang, Y.B. (2010), "Analysis of ground vibrations due to underground trains by 2.5 D finite/infinite element approach", Earthq. Eng. Eng. Vib., 9, 327-335. https://doi.org/10.1007/s11803-010-0017-1.
  20. Izra, U. and Neskon, U. (2013), "Application of infinite-element calculations for consolidating a railway foundation of blowing sand reclamation", Mater. Technol., 47(5), 621-626. https://doi.org/519.61/.64:691:620.1.
  21. Kargar, A.R., Rahmannejad, R. and Hajabasi, M.A. (2014), "A semi-analytical elastic solution for stress field of lined non-circular tunnels at great depth using complex variable method", Int. J. Solid. Struct., 51(6), 1475-1482. https://doi.org/10.1016/j.ijsolstr.2013.12.038.
  22. Karpurapu, G.R. (1988), "Composite infinite element analysis of unbounded two-phase media", Adv. Eng. Softw., 10(4), 202-209. https://doi.org/10.1016/0141-1195(88)90039-3.
  23. Karpurapu, G.R. and Bathurst, R.J. (1988). "Comparative analysis of some geomechanics problems using finite and infinite element methods", Comput. Geotech., 5(4), 269-284. https://doi.org/10.1016/0266-352X(88)90007-9.
  24. Kim, H.K., Moon, J.S., An, J.W. and Michael, E.S. (2022), "Development of performance evaluation model for road and railway tunnels in use", Geomech. Eng., 29(3), 369-376. https://doi.org/10.12989/gae.2022.29.3.369.
  25. Kumar, P. (1985), "Static infinite element formulation", J. Struct. Eng., 111(11), 2355-2372. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:11(2355).
  26. Lin, K.C., Hung, H.H., Yang, J.P. and Yang, Y.B. (2016), "Seismic analysis of underground tunnels by the 2.5 D finite/infinite element approach", Soil Dynam. Earthq. Eng., 85, 31-43. https://doi.org/10.1016/j.soildyn.2016.03.005.
  27. Lin, S.Y., Hung, H.H., Yang, J.P. and Yang, Y.B. (2017), "Seismic analysis of twin tunnels by a finite/infinite element approach", Int. J. Geomech., 17(9), 04017060. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000940.
  28. Liou, G.S. (1989), "Analytic solutions for soil-structure interaction in layered media", Earthq. Eng. Struct. D., 18(5), 667-686. https://doi.org/10.1002/eqe.4290180507.
  29. Liu, H. (2012), "Soil-structure interaction and failure of cast-iron subway tunnels subjected to medium internal blast loading", J. Perform. Constr. Fac., 26(5), 691-701. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000292.
  30. Liu, P., Wang, D. and Oeser, M. (2015), "Application of semi-analytical finite element method coupled with infinite element for analysis of asphalt pavement structural response", J. Traffic Transport. Eng. (English Edition), 2(1), 48-58. https://doi.org/10.1016/j.jtte.2015.01.005.
  31. Liu, W. and Novak, M. (1991). "Soil-pile-cap static interaction analysis by finite and infinite elements", Can. Geotech. J., 28(6), 771-783. https://doi.org/10.1139/t91-094.
  32. Liu, X., Suliman, L., Zhou, X. and Abd Elmageed, A. (2022), "Parallel tunnel settlement characteristics: a theoretical calculation approach and adaptation analysis", Geomech. Eng., 28(3), 225-237. https://doi.org/10.12989/gae.2022.28.3.225.
  33. Lokke, A. and Chopra, A.K. (2018). "Direct finite element method for nonlinear earthquake analysis of 3-dimensional semi-unbounded dam-water-foundation rock systems", Earthq. Eng. Struct. D., 47(5), 1309-1328. https://doi.org/10.1002/eqe.3019.
  34. Lokke, A. and Chopra, A.K. (2017), "Direct finite element method for nonlinear analysis of semi-unbounded dam-water-foundation rock systems", Earthq. Eng. Struct. D., 46(8), 1267-1285. https://doi.org/10.1002/eqe.2855.
  35. Lu, A.Z., Chen, H.Y., Qin, Y. and Zhang, N. (2014), "Shape optimisation of the support section of a tunnel at great depths", Comput. Geotech., 61, 190-197. https://doi.org/10.1016/j.compgeo.2014.05.011.
  36. Lynn, P.P. and Hadid, H.A. (1981). "Infinite elements with 1/rn type decay", Int. J. Numer. Method. Eng., 17(3), 347-355. https://doi.org/10.1002/nme.1620170305.
  37. Mori, K. and Abe, Y. (2005), "Large rectangular cross-section tunneling by the multi-micro shield tunneling (MMST) method", Tunn. Undergr. Sp. Tech., 20(2), 129-141. https://doi.org/10.1016/j.tust.2003.11.012.
  38. Nakamura, H., Kubota, T., Furukawa, M. and Nakao, T. (2003), "Unified construction of running track tunnel and crossover tunnel for subway by rectangular shape double track cross-section shield machine", Tunn. Undergr. Sp. Tech., 18(2-3), 253-262. https://doi.org/10.1016/S0886-7798(03)00034-8.
  39. Pissanetzky, S. (1984), "A simple infinite element", COMPEL-The Int. J. Comput. Math. Elec. Electronic Eng., 3(2), 107-114. https://doi.org/10.1108/eb009990.
  40. Rajapakse, R.K.N.D. and Karasudhi, P. (1985), "Elastostatic infinite elements for layered half spaces", J. Eng. Mech., 111(9), 1144-1158. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:9(1144).
  41. Savadatti, S. and Guddati, M.N. (2010), "A finite element alternative to infinite elements", Comput. Method. Appl. Mech. Eng., 199(33-36), 2204-2223. https://doi.org/10.1016/j.cma.2010.03.018.
  42. Selvadurai, A.P.S. and Karpurapu, R. (1989), "Composite infinite element for modeling unbounded saturated-soil media", J. Geotech. Eng., 115(11), 1633-1646. https://doi.org/10.1061/(ASCE)0733-9410(1989)115:11(1633).
  43. Shi, J., Wang, J., Ji, X., Liu H. and Lu, H. (2022), "Three-dimensional numerical parametric study of tunneling effects on existing pipelines", Geomech. Eng., 30(4), 383-392. https://doi.org/10.12989/gae.2022.30.4.383.
  44. Qi, W., Yang, Z., Jiang, Y., Yang, X., Shao, X. and An, H. (2022), "Investigation on ground displacements induced by excavation of overlapping twin shield tunnels", Geomech. Eng., 28(5), 531-546. https://doi.org/10.12989/gae.2022.28.5.531.
  45. Saini, S.S., Bettess, P. and Zienkiewicz, O.C. (1978), "Coupled hydrodynamic response of concrete gravity dams using finite and infinite elements", Earthq. Eng. Struct. D., 6(4), 363-374. https://doi.org/10.1002/eqe.4290060404.
  46. Timoshenko, S. and Goodier, J.N. (1951), "Theory of elasticity" McGraw-Hill Book Company. Inc., New York.
  47. Tzong, T.J. and Penzien, J. (1986), "Hybrid modelling of a single-layer half-space system in SOIL-structure interaction", Earthq. Eng. Struct. D., 14(4), 517-530. https://doi.org/10.1002/eqe.4290140403.
  48. Wang, H.N., Zeng, G.S., Utili, S., Jiang, M.J. and Wu, L. (2017), "Analytical solutions of stresses and displacements for deeply buried twin tunnels in viscoelastic rock", Int. J. Rock Mech. Min. Sci., 93, 13-29. https://doi.org/10.1016/j.ijrmms.2017.01.002.
  49. Wang, H.N., Wu, L., Jiang, M.J. and Song, F. (2018), "Analytical stress and displacement due to twin tunneling in an elastic semi-infinite ground subjected to surcharge loads", Int. J. Numer. Anal. Method. Geomech., 42(6), 809-828. https://doi.org/10.1002/nag.2764.
  50. Wang, H.N., Zeng, G.S. and Jiang, M.J. (2018), "Analytical stress and displacement around non-circular tunnels in semi-infinite ground", Appl. Math. Model., 63, 303-328. https://doi.org/10.1016/j.apm.2018.06.043.
  51. Wen, P.H., Yang, J.J., Huang, T., Zheng, J.L. and Deng, Y.J. (2018). "Infinite element in meshless approaches". Eur. J. Mech.-A/Solids, 72, 175-185. https://doi.org/10.1016/j.euromechsol.2018.05.010.
  52. Wilson, D.W., Abbo, A.J., Sloan, S.W. and Lyamin, A.V. (2013), "Undrained stability of a square tunnel where the shear strength increases linearly with depth", Comput. Geotech., 49, 314-325. https://doi.org/10.1016/j.compgeo.2012.09.005.
  53. Wilson, D.W., Abbo, A.J., Sloan, S.W. and Lyamin, A.V. (2015), "Undrained stability of dual square tunnels", Acta Geotechnica, 10(5), 665-682. https://doi.org/10.1007/s11440-014-0340-1.
  54. Wolf, J.P. and Song, C. (1996). "Finite-element modelling of unbounded media", Chichester: Wiley.
  55. Yang, Y.B., Kuo, S.R. and Hung, H.H. (1996), "Frequency-independent infinite elements for analysing semi-infinite problems", Int. J. Numer. Method. Eng., 39(20), 3553-3569. https://doi.org/10.1002/(SICI)10970207(19961030)39:20<3553::AID-NME16>3.0.CO;2-6.
  56. Yang, Y.B. and Hung, H.H. (2001), "A 2.5 D finite/infinite element approach for modelling visco-elastic bodies subjected to moving loads", Int. J. Numer. Method. Eng., 51(11), 1317-1336. https://doi.org/10.1002/nme.208.
  57. Yang, Y.B., Hung, H.H. and Chang, D.W. (2003), "Train-induced wave propagation in layered soils using finite/infinite element simulation", Soil Dynam. Earthq. Eng., 23(4), 263-278. https://doi.org/10.1016/S0267-7261(03)00003-4.
  58. Yang, Y.B., Zhou, Z., Zhang, X. and Wang, X. (2023), "Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method", Front. Struct. Civil Eng., 1-22. https://doi.org/10.1007/s11709-022-0900-7.
  59. Yerli, H.R., Temel, B. and Kiral, E. (1998). "Transient infinite elements for 2D soil-structure interaction analysis", J. Geotech. Geoenviron. Eng., 124(10), 976-988. https://doi.org/10.1061/(ASCE)1090-0241(1998)124:10(976).
  60. Yun, C.B., Kim, J.M. and Hyun, C.H. (1995), "Axisymmetric elastodynamic infinite elements for multi-layered half-space", Int. J. Numer. Method. Eng., 38(22), 3723-3743. https://doi.org/10.1002/nme.1620382202.
  61. Yuksel, Y.Z. and Akbas, S.D. (2022a), "Stress analysis of multi-layered soil medium by using finite and infinite elements", Proceedings of the 6th International Conference on Computational Mathematics and Engineering Sciences, 2022, Ordu, Turkey, May.
  62. Yuksel, Y.Z. and Akbas, S.D. (2022b), "Static responses of a cavity in a half-space by using finite element method", Proceedings of the 6th International Conference on Computational Mathematics and Engineering Sciences, 2022, Ordu, Turkey, May.
  63. Yuksel, Y.Z. and Akbas, S.D. (2022c), "Stress distribution in two-dimensional semi-infinite medium under the different load types", Proceedings of the 2nd International Conference on Engineering and Applied Natural Sciences, Konya, Turkey, October.
  64. Zienkiewicz, O.C., Emson, C. and Bettess, P. (1983), "A novel boundary infinite element", Int. J. Numer. Method. Eng., 19(3), 393-404. https://doi.org/10.1002/nme.1620190307.