Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31108
Dynamic Interaction between Two Neighboring Tunnels in a Layered Half-Space

Authors: Chao He, Shunhua Zhou, Peijun Guo


The vast majority of existing underground railway lines consist of twin tunnels. In this paper, the dynamic interaction between two neighboring tunnels in a layered half-space is investigated by an analytical model. The two tunnels are modelled as cylindrical thin shells, while the soil in the form of a layered half-space with two cylindrical cavities is simulated by the elastic continuum theory. The transfer matrix method is first used to derive the relationship between the plane wave vectors in arbitrary layers and the source layer. Thereafter, the wave translation and transformation are introduced to determine the plane and cylindrical wave vectors in the source layer. The solution for the dynamic interaction between twin tunnels in a layered half-space is obtained by means of the compatibility of displacements and equilibrium of stresses on the two tunnel–soil interfaces. By coupling the proposed model with a fully track model, the train-induced vibrations from twin tunnels in a multi-layered half-space are investigated. The numerical results demonstrate that the existence of a neighboring tunnel has a significant effect on ground vibrations.

Keywords: Underground Railway, twin tunnels, transfer matrix method, wave translation and transformation

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 156


[1] D. Clouteau, M. Arnst, T.M. Al-Hussaini, G. Degrande, Freefield vibrations due to dynamic loading on a tunnel embedded in a stratified medium, J. Sound Vib. 283 (1–2) (2005) 173–199.
[2] G. Degrande, D. Clouteau, R. Othman, M. Arnst, H. Chebli, R. Klein, P. Chatterjee, B. Janssens, A numerical model for ground-borne vibrations from underground railway traffic based on a periodic finite element–boundary element formulation, J. Sound Vib. 293(3–5) (2006) 645–666.
[3] S. Gupta, M.F.M. Hussein, G. Degrande, H.E.M. Hunt, D. Clouteau, A comparison of two numerical models for the prediction of vibrations from underground railway traffic, Soil Dynam. Earthq. Eng. 27 (7) (2007) 608–624.
[4] X. Sheng, C.J.C. Jones, D.J. Thompson, Modelling ground vibrations from railways using wavenumber finite- and boundary-element methods, Proc. Royal Soc. 461 (2005) 2043–2070.
[5] S. François, M. Schevenels, P. Galvín, G. Lombaert, G. Degrande, A 2.5D coupled FE–BE methodology for the dynamic interaction between longitudinally invariant structures and a layered halfspace, Comput. Methods Appl. Mech. Eng. 199 (2010) 1536–1548.
[6] A. Romero, P. Galvín, J. António, J. Domínguez, A. Tadeu, Modelling of acoustic and elastic wave propagation from underground structures using a 2.5D BEM-FEM approach, Eng. Anal. Bound. Elem. 76 (2017) 26–39.
[7] C. He, S.H. Zhou, H.G. Di, Y. Shan, A 2.5-D coupled FE–BE model for the dynamic interaction between saturated soil and longitudinally invariant structures, Comput. Geotech. 82 (2017) 211-222.
[8] C. He, S.H. Zhou, P.J. Guo, H.G. Di, X.H. Zhang, Modelling of ground vibration from tunnels in a poroelastic half-space using a 2.5-D FE-BE formulation, Tunn. Underg. Sp. Tech. 82 (2018) 211–221.
[9] Y.B. Yang, H.H. Hung, A 2.5D finite/infinite element approach for modelling viseo-elastic bodies subjected to moving loads, Int. J. Numer. Meth. Eng. 51(11) (2001) 1317-1336.
[10] Y.B. Yang, H.H. Hung, Soil vibrations caused by underground moving trains, J. Geotech. Geoenviron. Eng. 134 (2008) 1633–1644.
[11] J.A. Forrest, H.E.M. Hunt, A three-dimensional tunnel model for calculation of train-induced ground vibration, J. Sound Vib. 294(4–5) (2006) 678–705.
[12] J.A. Forrest, H.E.M. Hunt, Ground vibration generated by trains in underground tunnels, J. Sound Vib. 294(4–5) (2006) 706–736.
[13] M.F.M. Hussein, S. François, M. Schevenels, H.E.M. Hunt, J.P. Talbot, G. Degrande, The fictitious force method for efficient calculation of vibration from a tunnel embedded in a multi-layered half-space, J. Sound Vib. 333 (2014) 6996–7018.
[14] H.G. Di, S.H. Zhou, C. He, X. Zhang, Z. Luo, Three-dimensional multilayer cylindrical tunnel model for calculating train-induced dynamic stress in saturated soils, Comput. Geotech. 80 (2016) 333-345.
[15] S.H. Zhou, C. He, H.G. Di, P.J. Guo, X.H. Zhang, An efficient method for predicting train-induced vibrations from a tunnel in a poroelastic half-space, Eng. Anal. Bound. Elem. 85 (2017) 43–56.
[16] C. He, S.H. Zhou, H.G. Di, P.J. Guo, J.H. Xiao, Analytical method for calculation of ground vibration from a tunnel embedded in a multi-layered half-space, Comput. Geotech. 99 (2018) 149–164.
[17] K.A. Kuo, M.F.M. Hussein, H.E.M. Hunt, The effect of a twin tunnel on the propagation of ground-borne vibration from an underground railway, J. Sound Vib. 330 (2011) 6203–6222.
[18] W. I. Hamad, H. E. M. Hunt, J. P. Talbot, M. F. M. Hussein, D. J. Thompson, The dynamic interaction of twin tunnels embedded in a homogeneous half-space, in Proceedings of the 5th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Crete Island, Greece, May 2015.
[19] C. He, S.H. Zhou, P.J. Guo, H.G. Di, X.H. Zhang, Analytical model for vibration prediction of two parallel tunnels in a full-space, J. Sound Vib. 423 (2018) 306-321.
[20] I. Sneddon, Fourier transforms. New York: McGraw-Hill; 1951.
[21] W.T. Thomson, Transmission of elastic waves through a stratified solid medium, J. Appl. Phys. 21 (1950) 89–93.
[22] N.A. Haskell, The dispersion of surface waves on multi-layered media, Bull. Seismol. Soc. Am. 43 (1953) 17–34.
[23] A. Boström, G. Kristensson, S. Ström, Transformation properties of plane, spherical and cylindrical scalar and vector wave functions, in: Varadan V.V. Lakhtakia A, V.K. Varadan (Eds.), Field Representations and Introduction to Scattering, Elsevier, Amsterdam, 1991, pp. 165–210.
[24] S.K. Bose, A.K. Mal, Longitudinal shear waves in a fiber-reinforced composite, Int. J. Solids. Struct. 9 (1973) 1075–1085.
[25] V.K. Varadan, V.V. Varadan, Y.H. Pao, Multiple scattering of elastic waves by cylinders of arbitrary cross section. I. SH waves, J. Acoust. Soc. Am. 63 (5) (1978) 1310–1319.
[26] A. Leissa, Vibration of Shells, Acoustical Society of America, New York, 1973 (reissued 1993).