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Stability assessment of unlined real horseshoe-shaped tunnels in anisotropic and heterogeneous undrained clay

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Abstract

In the urban underground transportation systems, especially, in case of mechanized tunneling, tunnel boring machine (TBM) of circular shape is mostly used for tunneling advancement. However, circular-shaped TBM particularly of large diameter have large waste of utilization area that is, small space utilization ratio. With the advancement in the machine manufacturing industries, non-circular-shaped TBM is now used, whose cross section allows to use the underground space efficiently to improve space utilization ratio. Despite the significance of this issue, there has not been much prior research reported in the literature for designing and analyzing underground-excavations/tunnels having horseshoe-shaped cross sections in anisotropic–heterogeneous clay. In the present study, peripheral stability analysis of real horseshoe-shaped unlined tunnels in saturated clay with direction reliant and linearly varying undrained shear strength has been performed using lower bound limit analysis coupled with finite elements and second-order cone programming. For a range of material properties and cover depth of tunnel, the stability charts for unlined tunnel have been generated in this study, which will serve as a useful tool for engineering practitioners. It has also been demonstrated that the underground excavations with horseshoe-shaped cross section is more stable as compared to that with equivalent circular-shaped cross section for the same value of utilization area.

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Some data, including the Excel file (input or output data), figures, and references that support the findings of this study, are available from the corresponding author upon reasonable request.

References

  • Bishop AW (1966) The strength of soils as engineering materials. Géotechnique 16:91–130. https://doi.org/10.1680/geot.1966.16.2.91

    Article  Google Scholar 

  • Casagrande A, Carillo N (1944) Shear failure of anisotropic soils. Contrib Soil Mech (BSCE) 1941–1953(4):122–135

    Google Scholar 

  • Davis EH, Christian JT (1971) Bearing capacity of anisotropic cohesive soil. J Soil Mech Found Div 97(5):753–769

    Article  Google Scholar 

  • Davis EH, Gunn MJ, Mair RJ, Seneviratine HN (1980) The stability of shallow tunnels and underground openings in cohesive material. Geotechnique 30(4):397–416

    Article  Google Scholar 

  • Do NA, Dias D (2017) A comparison of 2D and 3D numerical simulations of tunnelling in soft soils. Environ Earth Sci 76(3):1–12

    Article  Google Scholar 

  • Do NA, Dias D, Oreste P (2015) 3D numerical investigation on the interaction between mechanized twin tunnels in soft ground. Environ Earth Sci 73(5):2101–2113

    Article  Google Scholar 

  • Do NA, Dias D, Vu TT, Dang VK (2021) Impact of the shield machine’s performance parameters on the tunnel lining behaviour and settlements. Environ Earth Sci 80(16):1–13

    Article  Google Scholar 

  • Drucker DC (1953) Coulomb friction, plasticity and limit loads. Trans Am Soc Mech Eng 76:71–74

    Google Scholar 

  • Du D, Dias D, Yang X (2018) Analysis of earth pressure for shallow square tunnels in anisotropic and non-homogeneous soils. Comput Geotech 104:226–236

    Article  Google Scholar 

  • Duncan JM, Seed HB (1966) Anisotropy and stress reorientation in clay. J Soil Mech Found Div 92(SM5):21–50

    Article  Google Scholar 

  • Hansen JB, Gibson RE (1949) Undrained shear strengths of anisotropically consolidated clays. Geotechnique 1(3):189–200

    Article  Google Scholar 

  • Hassan SA, Shitote SM, Kiplangat DC (2022) Predictive models to evaluate the interaction effect of soil-tunnel interaction parameters on surface and subsurface settlement. Civ Eng J 8(11):2424–2444

    Article  Google Scholar 

  • Huang M, Tang Z, Zhou W, Yuan J (2018) Upper bound solutions for face stability of circular tunnels in non-homogeneous and anisotropic clays. Comput Geotech 98:189–196

    Article  Google Scholar 

  • Hvorslev MJ (1960) Physical components of shear strength of saturated clays. In: Proceedings, ASCE research conference on shear strength of cohesive soils, Boulder, CO, pp 169–273

  • Jakobson B (1955) Isotropy of clays. Geotechnique 5(1):23–28

    Article  Google Scholar 

  • Kumar B, Sahoo JP (2021a) Stability of unsupported circular tunnels in anisotropic normally and over consolidated saturated clay. Comput Geotech 135:104148. https://doi.org/10.1016/j.compgeo.2021.104148

    Article  Google Scholar 

  • Kumar B, Sahoo JP (2023a) Lining pressure for circular tunnels in two layered clay with anisotropic undrained shear strength. Geomech Geoeng 18(2):91-104. https://doi.org/10.1080/17486025.2021.2012077

  • Kumar B, Sahoo JP (2023b) Support pressure for stability of horseshoe-shaped tunnels in undrained clay using lower-bound finite-element limit analysis. Int J Geomech 23(1):04022264

    Article  Google Scholar 

  • Lee KM, Rowe RK (1989) Effects of undrained strength anisotropy on surface subsidences induced by the construction of shallow tunnels. Can Geotech J 26(2):279–291

    Article  Google Scholar 

  • Lo KY (1965) Stability of slopes in anisotropic soils. J Soil Mech Found Div 91(SM4):85–106

    Article  Google Scholar 

  • Lo KY, Milligan V (1967) Shear strength properties of two stratified clays. J Soil Mech Found Div 93(SM1):1–15

    Article  Google Scholar 

  • Makrodimopoulos A, Martin CM (2006) Lower bound limit analysis of cohesive-frictional materials using second-order cone programming. Int J Numer Methods Eng 66(4):604–634

    Article  Google Scholar 

  • MATLAB (2015b) [Computer software]. MathWorks, Natick, MA

  • MOSEK A (2015) The MOSEK optimization toolbox for MATLAB manual. Version 7.1 (Revision 28). Copenhagen, Denmark

  • Nakase A, Kamei T (1983) Undrained shear strength anisotropy of normally consolidated cohesive soils. Soil Found 23(1):91–101

    Article  Google Scholar 

  • Nguyen TT, Do NA, Kien DV, Karasev MA, Dias D (2021) Influence of tunnel shape on tunnel lining behaviour. Proc Inst Civ Eng Geotech Eng 174(4):355–371

    Google Scholar 

  • Osman AS (2010) Stability of unlined twin tunnels in undrained clay. Tunn Undergr Space Technol 25:290–296. https://doi.org/10.1016/j.tust.2010.01.004

    Article  Google Scholar 

  • Osman AS, Mair RJ, Bolton MD (2006) On the kinematics of 2D tunnel collapse in undrained clay. Geotechnique 56:585–595. https://doi.org/10.1680/geot.2006.56.9.585

    Article  Google Scholar 

  • Pan Q, Dias D (2016) Face stability analysis for a shield-driven tunnel in anisotropic and nonhomogeneous soils by the kinematical approach. Int J Geomech 16(3):04015076

    Article  Google Scholar 

  • Rahaman O, Kumar J (2020) Stability analysis of twin horse-shoe shaped tunnels in rock mass. Tunn Undergr Space Technol 98:103354. https://doi.org/10.1016/j.tust.2020.103354

    Article  Google Scholar 

  • Rowshanzamir MA, Askari AM (2010) An investigation on the strength anisotropy of compacted clays. Appl Clay Sci 50(4):520–524

    Article  Google Scholar 

  • Russo G, Marone G, Di Girolamo L (2021) Hybrid energy piles as a smart and sustainable foundation. J Hum Earth Future 2(3):306–322

    Article  Google Scholar 

  • Saada AS (1972) Discussion on bearing capacity of anisotropic cohesive soil. J Soil Mech Found Div 98:132–135

    Google Scholar 

  • Sahoo JP, Kumar J (2012) Seismic stability of a long unsupported circular tunnel. Comput Geotech 44:109–115. https://doi.org/10.1016/j.compgeo.2012.03.015

    Article  Google Scholar 

  • Sahoo JP, Kumar J (2013a) Stability of a long unsupported circular tunnel in clayey soil by using upper bound finite element limit analysis. Proc Indian Natl Sci Acad 79(64):807–815

    Article  Google Scholar 

  • Sahoo JP, Kumar J (2013b) Stability of long unsupported twin circular tunnels in soils. Tunn Undergr Space Technol 38:326–335. https://doi.org/10.1016/j.tust.2013.07.005

    Article  Google Scholar 

  • Sahoo JP, Kumar B (2021) Peripheral stability of circular tunnels in anisotropic undrained clay. Tunn Undergr Space Technol 114:103898

    Article  Google Scholar 

  • Sloan SW (1988) Lower bound limit analysis using finite elements and linear programming. Int J Numer Anal Methods Geomech 12(1):61–77

    Article  Google Scholar 

  • Sloan SW (2013) Geotechnical stability analysis. Géotechnique 63(7):531–571

    Article  Google Scholar 

  • Sun R, Yang J, Liu S, Yang F (2021) Undrained stability analysis of dual unlined horseshoe-shaped tunnels in non-homogeneous clays using lower bound limit analysis method. Comput Geotech 133:104057

    Article  Google Scholar 

  • Tatiya R (2005) Civil excavations and tunnelling. Thomas Telford, London

    Book  Google Scholar 

  • Topal C, Mahmutoğlu Y (2021) Assessment of surface settlement induced by tunnel excavations for the Esenler-Başakşehir (Istanbul, Turkey) Subway Line. Environ Earth Sci 80(5):1–16

    Article  Google Scholar 

  • Ukritchon B, Keawsawasvong S (2018) Lower bound limit analysis of an anisotropic undrained strength criterion using second-order cone programming. Int J Numer Anal Methods Geomech 42:1016–1033. https://doi.org/10.1002/nag.2781

    Article  Google Scholar 

  • Ukritchon B, Keawsawasvong S (2019) Lower bound solutions for undrained face stability of plane strain tunnel headings in anisotropic and non-homogeneous clays. Comput Geotech 112:204–217

    Article  Google Scholar 

  • Ukritchon B, Keawsawasvong S (2020) Undrained stability of unlined square tunnels in clays with linearly increasing anisotropic shear strength. Geotech Geol Eng 38:897–915. https://doi.org/10.1007/s10706-019-01023-8

    Article  Google Scholar 

  • Ukritchon B, Keawsawasvong S, Yingchaloenkitkhajorn K (2017) Undrained face stability of tunnels in Bangkok subsoils. Int J Geotech Eng 11(3):262–277

    Article  Google Scholar 

  • Van Kien D (2022) Numerical simulation of the stability of rock mass around large underground cavern. Civ Eng J 8(1):81–91

    Article  Google Scholar 

  • Wilson DW, Abbo AJ, Sloan SW, Lyamin AV (2011) Undrained stability of a circular tunnel where the shear strength increases linearly with depth. Can Geotech J 48(9):1328–1342

    Article  Google Scholar 

  • Yamamoto K, Lyamin AV, Wilson DW, Sloan SW, Abbo AJ (2011a) Stability of a circular tunnel in cohesive-frictional soil subjected to surcharge loading. Comput Geotech 38(4):504–514

    Article  Google Scholar 

  • Yamamoto K, Lyamin AV, Wilson DW, Sloan SW, Abbo AJ (2011b) Stability of a single tunnel in cohesive–frictional soil subjected to surcharge loading. Can Geotech J 48(12):1841–1854

    Article  Google Scholar 

  • Zhang J, Feng T, Yang J, Yang F, Gao Y (2018) Upper-bound stability analysis of dual unlined horseshoe-shaped tunnels subjected to gravity. Comput Geotech 97:103–110

    Article  Google Scholar 

  • Zhang C, Li W, Zhu W, Tan Z (2020) Face stability analysis of a shallow horseshoe-shaped shield tunnel in clay with a linearly increasing shear strength with depth. Tunn Undergr Space Technol 97:103291

    Article  Google Scholar 

Download references

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Correspondence to Jagdish Prasad Sahoo.

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Kumar, B., Sahoo, J.P. Stability assessment of unlined real horseshoe-shaped tunnels in anisotropic and heterogeneous undrained clay. Environ Earth Sci 82, 218 (2023). https://doi.org/10.1007/s12665-023-10895-2

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