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Explicit Procedure and Analytical Solution for the Ground Reaction Due to Advance Excavation of a Circular Tunnel in an Anisotropic Stress Field

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Abstract

The convergence–confinement method applied in boring a circular tunnel through a rock-mass assumed to be subject to a non-hydrostatic stress is investigated. The closed-form analytical solutions of the stresses/displacements in the elastic region and plastic region for the ground reaction due to excavation of the tunnel in an anisotropic stress state field are presented in a theoretically consistent way. The explicit procedure realized the analytical solution to an executable computation that can be estimated using a simple spreadsheet. The validity of the procedure for the analytical solution was examined by numerical analysis to investigate the influence of in situ stress ratio on the ground reaction curve, the stress path at the intrados of the tunnel, and the distribution of stresses/displacements on the cross-sections of a circular tunnel. The agreement between the finite element results and the proposed closed-form solutions with the explicit procedure was found to be excellent.

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References

  • AFTES (1983) Recommandations pour l’emploi de la méthode convergence–confinement. Tunnels et Ouvrages Souterrains 59:119–138

    Google Scholar 

  • AFTES, Panet M et al (2001) Recommendations on the convergence–confinement method. Association Française des Tunnels et de l’Espace Souterrain, pp 1–11

  • Alejano LR, Rodriguez-Dono A, Alonso E, Fdez.-Manín G (2011) Ground reaction curves for tunnels excavated in different quality rock masses showing several types of post-failure behaviour. Tunn Undergr Space Technol 24:689–705

    Article  Google Scholar 

  • Bernaud D, Rosset G (1992) La nouvelle méthode implicite pour l’étude du dimensionnement des tunnels. Rev Fr Géotech 60:5–26

    Article  Google Scholar 

  • Bernaud D, Rosset G (1996) The new implicit method for tunnel analysis. Int J Numer Anal Meth Geomech 20(9):673–690

    Article  Google Scholar 

  • Brady BHG, Brown ET (1993) Rock mechanics for underground mining. Chapman & Hall, London

    Google Scholar 

  • Brown ET, Bray JW, Ladanyi B, Hoek E (1983) Ground response curves for rock tunnels. J Geotech Eng ASCE 109:15–39

    Article  Google Scholar 

  • Carranza-Torres C (2004) Elasto-plastic solution of tunnel problems using the generalized form of the Hoek–Brown failure criterion. Int J Rock Mech Min Sci 41(3):480–491

    Article  Google Scholar 

  • Carranza-Torres C, Fairhurst C (1999) The elasto-plastic response of underground excavations in rock masses that satisfy the Hoek–Brown failure criterion. Int J Rock Mech Min Sci 36:777–809

    Article  Google Scholar 

  • Carranza-Torres C, Fairhurst C (2000) Application of the convergence–confinement method of tunnel design to rock masses that satisfy the Hoek–Brown failure criterion. Tunn Undergr Space Technol 15(2):187–213

    Article  Google Scholar 

  • Detournay E, St. John CM (1988) Design charts for a deep circular tunnel under non-uniform loading. Rock Mech Rock Eng 21:119–137

    Article  Google Scholar 

  • González-Nicieza C, Álvarez-Vigil AE, Menéndez-Díaz A, González-Palacio C (2008) Influence of the depth and shape of a tunnel in the application of the convergence–confinement method. Tunn Undergr Space Technol 23(1):25–37

    Article  Google Scholar 

  • Guan Z, Jiang Y, Tanabasi Y (2007) Ground reaction analyses in conventional tunnelling excavation. Tunn Undergr Space Technol 22:230–237

    Article  Google Scholar 

  • Hoek E, Brown ET (1980) Underground excavations in rock. The Institution of Mining and Metallurgy, London

    Google Scholar 

  • Kirsch G (1898) Die theorie der Elastizität und die bedürfnisse der festigkeitslehre. Zeit Ver Deut Ing J 42:797–807

    Google Scholar 

  • LCPC-ITECH (2003) CESAR-LCPC software package, CLEO2D Reference Manual, pp 114–117

  • Lee YL (1994) Prise en compte des non-linéarité de comportement des sols et des roches dans la modélisation du creusement d’un tunnel. Thèse, École Nationale des Ponts et Chaussées

  • Lee YL, Lin MY, Hsu WK (2008) Study of relationship between the confinement loss and the longitudinal deformation curve by using three-dimensional finite element analysis. Chin J Rock Mechan Eng 27(2):258–265

    Google Scholar 

  • Lee YL, Hsu WK, Lin MY (2009) Analysis of the advancing effect and the confinement loss by using deformation measurement in tunneling. Chin J Rock Mechan Eng 28(1):39–46

    Google Scholar 

  • Nguyen MD, Corbette F (1991) New calculation methods for lined tunnels including the effect of the front face. In: Proceedings of the international congress on rock mechanics, Aachen, vol 1, pp 1335–1338

  • Nguyen MD, Guo C (1993) A ground support interaction principle for constant rate advancing tunnels. In: Proceedings of the Eurock, Lisbon, Portugal, vol 1, pp 171–177

  • Oreste PP (2003) Analysis of structural interaction in tunnels using the convergence–confinement approach. Tunn Undergr Space Technol 18:347–363

    Article  Google Scholar 

  • Oreste P (2009) The convergence–confinement method: roles and limits in modern geomechanical tunnel design”. Am J Appl Sci 6(4):755–771

    Article  Google Scholar 

  • Pacher F (1964) Deformationsmessungen in Versuchsstollen als Mittel zur Erforschung des Gebirgsverhaltens und zur Bemessung des Ausbaues. Felsmechanik und Ingenieursgeologie Supplementum IV, pp 149–161

  • Panet M (1986) Calcul du souténement des tunnels à section circulaire par la method convergence–confinement avec un champ de contraintes initiales anisotrope. Tunnels et Ouvrages Souterrains 77:228–232

    Google Scholar 

  • Panet M (1995) Le Calcul des Tunnels par la Méthode de Convergence–Confinement. Presses de l’Ecole Nationale des Ponts et Chaussées, Paris

    Google Scholar 

  • Panet M, Guellec P (1974) Contribution a l’étude du sousténement derrière le front de taille. In: Proceedings of 3rd congress of the international society rock mechanics, part B, Denver, vol 2, pp 1130–1134

  • Panet M, Guenot A (1982) Analysis of convergence behind the face of a tunnel. In: Proceedings of international symposium tunelling’82, IMM, London, pp 197–204

  • Park KH, Kim YJ (2006) Analytical solution for a circular opening in an elastic–brittle–plastic rock. Int J Rock Mech Min Sci 43:616–622

    Article  Google Scholar 

  • Ravandi EG, Rahmannejad R (2013) Wall displacement prediction of circular, D shaped and modified horseshoe tunnels in anisotropic stress fields. Tunn Undergr Space Technol 34:54–60

    Article  Google Scholar 

  • Serrano A, Olalla C, Reig I (2011) Convergence of circular tunnels in elastoplastic rock masses with non-linear failure criteria and non-associated flow laws. Int J Rock Mech Min Sci 48:878–887

    Article  Google Scholar 

  • Sharan SK (2003) Elastic–brittle–plastic analysis of circular openings in Heok-Brown media. Int J Rock Mech Min Sci 40:817–824

    Article  Google Scholar 

  • Sharan SK (2005) Exact and approximate solutions for displacements around circular openings in elastic-brittle plastic Hoek-Brown rock. Int J Rock Mech Min Sci 42:42–549

    Article  Google Scholar 

  • Shen B, Barton N (1997) The disturbed zone around tunnels in jointed rock masses. Int J Rock Mech Min Sci 34(1):117–125

    Article  Google Scholar 

  • Wang Y (1996) Ground response of a circular tunnel in poorly consolidated rock. J Geotech Eng ASCE 122(9):703–708

    Article  Google Scholar 

  • Wong RCK, Kaiser PK (1991) Performance assessment of tunnels in cohesionless soils. J Geotech Eng ASCE 117(12):1880–1901

    Article  Google Scholar 

Download references

Acknowledgements

The author appreciates the financial support of the National Science Council of Taiwan (Project Nos.: NSC 96-2221-E-216-020-MY2 and NSC 97-2221-E-216-020-MY2).

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  1. Department of Civil Engineering, Chung-Hua University, 707, Sec. 2, Wufu Rd., Hsinchu, 30012, Taiwan, ROC

    Yu-Lin Lee

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  1. Yu-Lin Lee
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Correspondence to Yu-Lin Lee.

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Lee, YL. Explicit Procedure and Analytical Solution for the Ground Reaction Due to Advance Excavation of a Circular Tunnel in an Anisotropic Stress Field. Geotech Geol Eng 36, 3281–3309 (2018). https://doi.org/10.1007/s10706-018-0537-4

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  • DOI: https://doi.org/10.1007/s10706-018-0537-4

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