Mechanical responses of multi-layered ground due to shallow tunneling with arbitrary ground surface load

Abstract

An analytical model based on complex variable theory is proposed to investigate ground responses due to shallow tunneling in multi-layered ground with an arbitrary ground surface load. The ground layers are assumed to be linear-elastic with full-stick contact between them. To solve the proposed multi-boundary problem, a series of analytic functions is introduced to accurately express the stresses and displacements contributed by different boundaries. Based on the principle of linear-elastic superposition, the multi-boundary problem is converted into a superposition of multiple single-boundary problems. The conformal mappings of different boundaries are independent of each other, which allows the stress and displacement fields to be obtained by the sum of components from each boundary. The analytical results are validated based on numerical and in situ monitoring results. The present model is superior to the classical model for analyzing ground responses of shallow tunneling in multi-layered ground; thus, it can be used with assurance to estimate the ground movement and surface building safety of shallow tunnel constructions beneath surface buildings. Moreover, the solution for the ground stress distribution can be used to estimate the safety of a single-layer composite ground.

Graphical abstract

Keywords

analytical model / mechanical response / multi-layered ground / shallow tunneling / ground surface load / complex variable solution

References

[1] Jenck O, Dias D. 3D-finite difference analysis of the interaction between concrete building and shallow tunnelling. Geotechnique, 2004, 54(8): 519–528

[2] Fang Q, Zhang D, Wong L N Y. Shallow tunnelling method (STM) for subway station construction in soft ground. Tunnelling and Underground Space Technology, 2012, 29: 10–30

[3] Zhang D, Fang Q, Hou Y, Li P, Yuen Wong L N. Protection of buildings against damages as a result of adjacent large-span tunneling in shallowly buried soft ground. Journal of Geotechnical and Geoenvironmental Engineering, 2013, 139(6): 903–913

[4] Fang Q, Liu X, Zeng K, Zhang X, Zhou M, Du J. Centrifuge modelling of tunnelling below existing twin tunnels with different types of support. Underground Space, 2022, 7(6): 1125–1138

[5] Shou K J, Napier J A L. A two-dimensional linear variation displacement discontinuity method for three-layered elastic media. International Journal of Rock Mechanics and Mining Sciences, 1999, 36(6): 719–729

[6] Zhang D, Huang H, Hu Q, Jiang F. Influence of multi-layered soil formation on shield tunnel lining behavior. Tunnelling and Underground Space Technology, 2015, 47: 123–135

[7] Yuan Z, Cao Z, Tang H, Xu Y, Wu T. Analytical layer element with a circular cavity and its application in predicting ground vibrations from surface and underground moving sources. Computers and Geotechnics, 2021, 137: 104262

[8] Zhang J, Gao Y, Liu X, Zhang Z, Yuan Y, Mang H. A shield tunneling method for enlarging the diameter of existing tunnels: Experimental investigations. Tunnelling and Underground Space Technology, 2022, 128: 104605

[9] Do N A, Dias D. Tunnel lining design in multi-layered grounds. Tunnelling and Underground Space Technology, 2018, 81: 103–111

[10] Ieronymaki E, Whittle A J, Einstein H H. Comparative study of the effects of three tunneling methods on ground movements in stiff clay. Tunnelling and Underground Space Technology, 2018, 74: 167–177

[11] Chen Z, He C, Xu G, Ma G, Wu D. A case study on the asymmetric deformation characteristics and mechanical behavior of deep-buried tunnel in phyllite. Rock Mechanics and Rock Engineering, 2019, 52(11): 4527–4545

[12] Zheng H, Li P, Ma G, Zhang Q. Experimental investigation of mechanical characteristics for linings of twins tunnels with asymmetric cross-section. Tunnelling and Underground Space Technology, 2022, 119: 104209

[13] Li P, Wang F, Zhang C, Li Z. Face stability analysis of a shallow tunnel in the saturated and multilayered soils in short-term condition. Computers and Geotechnics, 2019, 107: 25–35

[14] Zhang D, Chen S, Wang R, Zhang D, Li B. Behaviour of a large-diameter shield tunnel through multi-layered strata. Tunnelling and Underground Space Technology, 2021, 116: 104062

[15] PeckR B. Deep excavations and tunneling in soft ground. In: Proceedings of 7th International Conference on Soil Mechanics and Foundation Engineering. Mexico City: Sociedad Mexicana de Mecanica de Suelo, 1969, 225–290

[16] Selby A R. Surface movements caused by tunnelling in two-layer soil. Geological Society Engineering Geology Special Publication, 1988, 5(1): 71–77

[17] Sun Z, Zhang D, Li A, Lu S, Tai Q, Chu Z. Model test and numerical analysis for the face failure mechanism of large cross-section tunnels under different ground conditions. Tunnelling and Underground Space Technology, 2022, 130: 104735

[18] Zhang J, Liu X, Ren T, Shi Y, Yuan Y. Numerical analysis of tunnel segments strengthened by steel-concrete composites. Underground Space, 2022, 7(6): 1115–1124

[19] Di Q, Li P, Zhang M, Wu J. Influence of permeability anisotropy of seepage flow on the tunnel face stability. Underground Space, 2022, 8: 1–14

[20] Di Q, Li P, Zhang M, Cui X. Investigation of progressive settlement of sandy cobble strata for shield tunnels with different burial depths. Engineering Failure Analysis, 2022, 141: 106708

[21] Di Q, Li P, Zhang M, Cui X. Influence of relative density on deformation and failure characteristics induced by tunnel face instability in sandy cobble strata. Engineering Failure Analysis, 2022, 141: 106641

[22] Sun Z, Zhang D, Fang Q, Dui G, Tai Q, Sun F. Analysis of the interaction between tunnel support and surrounding rock considering pre-reinforcement. Tunnelling and Underground Space Technology, 2021, 115: 104074

[23] Sun Z, Zhang D, Fang Q, Liu D, Dui G. Displacement process analysis of deep tunnels with grouted rockbolts considering bolt installation time and bolt length. Computers and Geotechnics, 2021, 140: 104437

[24] Sun Z, Zhang D, Fang Q, Dui G, Chu Z. Analytical solutions for deep tunnels in strain-softening rocks modeled by different elastic strain definitions with the unified strength theory. Science China. Technological Sciences, 2022, 65(10): 2503–2519

[25] Zhang Z, Huang M, Zhang M. Theoretical prediction of ground movements induced by tunnelling in multi-layered soils. Tunnelling and Underground Space Technology, 2011, 26(2): 345–355

[26] Zymnis D M, Chatzigiannelis I, Whittle A J. Effect of anisotropy in ground movements caused by tunnelling. Geotechnique, 2013, 63(13): 1083–1102

[27] Cao L, Zhang D, Fang Q. Semi-analytical prediction for tunnelling-induced ground movements in multi-layered clayey soils. Tunnelling and Underground Space Technology, 2020, 102: 103446

[28] Verruijt A, Booker J R. Surface settlements due to deformation of a tunnel in an elastic half plane. Geotechnique, 1996, 46(4): 753–756

[29] Verruijt A. A complex variable solution for a deforming circular tunnel in an elastic half-plane. International Journal for Numerical and Analytical Methods in Geomechanics, 1997, 21(2): 77–89

[30] Fang Q, Song H, Zhang D. Complex variable analysis for stress distribution of an underwater tunnel in an elastic half plane. International Journal for Numerical and Analytical Methods in Geomechanics, 2015, 39(16): 1821–1835

[31] Zhang D, Xu T, Fang H, Fang Q, Cao L, Wen M. Analytical modeling of complex contact behavior between rock mass and lining structure. Journal of Rock Mechanics and Geotechnical Engineering, 2022, 14(3): 813–824

[32] Fang H, Zhang D, Fang Q. A semi-analytical method for frictional contact analysis between rock mass and concrete linings. Applied Mathematical Modelling, 2022, 105: 17–28

[33] ZhangZHuangMPanYLiZMaSZhangY. Time-dependent analyses for ground movement and stress field induced by tunnelling considering rainfall infiltration mechanics. Tunnelling and Underground Space Technology, 2022, 122, 104378

[34] Fang H, Zhang D, Fang Q, Wen M. A generalized complex variable method for multiple tunnels at great depth considering the interaction between linings and surrounding rock. Computers and Geotechnics, 2021, 129: 103891

[35] Katebi H, Rezaei A H, Hajialilue-Bonab M, Tarifard A. Assessment the influence of ground stratification, tunnel and surface buildings specifications on shield tunnel lining loads (by FEM). Tunnelling and Underground Space Technology, 2015, 49: 67–78

[36] Huang H, Zhang D. Resilience analysis of shield tunnel lining under extreme surcharge: Characterization and field application. Tunnelling and Underground Space Technology, 2016, 51: 301–312

[37] Simon H P, Marte G. Effect of surface loading on the hydro-mechanical response of a tunnel in saturated ground. Underground Space, 2016, 1(1): 1–19

[38] Wang H, Chen X, Jiang M, Song F, Wu L. The analytical predictions on displacement and stress around shallow tunnels subjected to surcharge loadings. Tunnelling and Underground Space Technology, 2018, 71: 403–427

[39] Gao X, Wang H, Jiang M. Analytical solutions for the displacement and stress of lined circular tunnel subjected to surcharge loadings in semi-infinite ground. Applied Mathematical Modelling, 2021, 89: 771–791

[40] Zhang Z, Huang M, Pan Y, Jiang K, Li Z, Ma S, Zhang Y. Analytical prediction of time-dependent behavior for tunneling-induced ground movements and stresses subjected to surcharge loading based on rheological mechanics. Computers and Geotechnics, 2021, 129: 103858

[41] Park K H. Analytical solution for tunnelling-induced ground movement in clays. Tunnelling and Underground Space Technology, 2005, 20(3): 249–261

[42] Lee K M, Rowe R K, Lo K Y. Subsidence owing to tunnelling. I. Estimating the gap parameter. Canadian Geotechnical Journal, 1992, 29(6): 929–940

[43] Loganathan N, Poulos H G. Analytical prediction for tunneling-induced ground movements in clays. Journal of Geotechnical and Geoenvironmental Engineering, 1998, 124(9): 846–856

[44] Attewell P B, Farmer I W. Ground deformations resulting from shield tunnelling in London clay. Canadian Geotechnical Journal, 1974, 11(3): 380–395

[45] Rowe R K, Kack G J. Theoretical examination of the settlements induced by tunneling: Four case histories. Canadian Geotechnical Journal, 1983, 20(2): 299–314

[46] PhienwejN. Ground movements in shield tunnelling in Bangkok soils. In: Proceedings of 14th International Conference on Soil Mechanics and Foundation Engineering. Hamburg: International Society for Soil Mechanics and Foundation Engineering, 1997, 1469–1472

[47] ZengBHuangDPengNChenF. Analogous stochastic medium theory method (ASMTM) for predicting soil displacement induced by general and special-section shield tunnel construction. Chinses Journal of Rock Mechanics and Engineering, 2018, 37: 4356–4366 (in Chinese)

[48] SunZZhangDFangQHuangfuNChuZ. Convergenceconfinement analysis for tunnels with combined bolt–cable system considering the effects of intermediate principal stress. Acta Geotechnica, 2022 (in press) https://doi.org/10.1007/s11440-022-01758-4

Acknowledgements

This study was supported by the Fundamental Research Funds for Central Universities (No. 2022JBZY041) and the National Natural Science Foundation of China (Grant Nos. 52208382, 51738002, and 52278387).

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11709-023-0935-4 and is accessible for authorized users.

RIGHTS & PERMISSIONS

2023 Higher Education Press