Abstract
The convergence-confinement method (CCM) is a standard design tool to study the ground-structure interaction. Constitutive model selection is a critical issue in the correct application of the CCM to represent the real behavior of rock mass and plastic zone. In this paper, the post-failure behavior of rock mass is formulated and incorporated by a numerical approach and the results are compared with the experimental observations. Elastic perfectly plastic (EPP) and strain softening (SS) models, are used and compared for a circular tunnel to be applied in the CCM method. The results show that elastic parts of the ground reaction curve and the longitudinal deformation profiles for both models are similar. But when the rock failure occurs and tunnel face exceeds 0.5D, differences in the curves are significant. Based on the results, the maximum displacement in different amount of K (in-situ stress ratios) for the SS model is more than 3 times of the EPP model. Plastic radius in the SS model is about 2 times the radius in the EPP model. In addition to precisely identifying the plastic zone and its distribution, the modified numerical approach in this paper, can determine the critical support pressure within residual and softening regions.
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References
Alejano LR, Rodriguez-Dono A, Alonso E, Fdez-Manin G (2009) 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. https://doi.org/10.1016/j.tust.2009.07.004
Alejano LR, Alonso E, Rodriguez-Dono A, Fdez-Manin G (2010) Application of the convergence-confinement method to tunnels in rock masses exhibiting Hoek-Brown strain-softening behaviour. Int J Rock Mech Min Sci 47:150–160. https://doi.org/10.1016/j.ijrmms.2009.07.008
Alonso E, Alejano LR, Varas F, Fdez-Manin G, Carranza-Torres C (2003) Ground response curves for rock masses exhibiting strain-softening behaviour. Int J Numer Anal Methods Geomech 27:1153–1185. https://doi.org/10.1002/nag.315
Arzúa J, Alejano LR (2013) Dilation in granite during servo-controlled triaxial strength tests. Int J Rock Mech Min Sci 61:43–56. https://doi.org/10.1016/j.ijrmms.2013.02.007
Bour K, Goshtasbi K (2019) Study of convergence confinement method curves considering pore-pressure effect. J Min Environ 10:479–492. https://doi.org/10.22044/jme.2019.7888.1654
Brown ET, Bray JW, Ladanyi B, Hoek E (1983) Ground response curves for rock tunnels. J Geotech Eng 109:15–39. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:1(15)
Cai M, Kaiser PK, Uno H, Tasaka Y, Minami M (2004) Estimation of rock mass deformation modulus and strength of jointed hard rock masses using the GSI system. Int J Rock Mech Min Sci 41:3–19. https://doi.org/10.1016/S1365-1609(03)00025-X
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. https://doi.org/10.1016/S0148-9062(99)00047-9
Carranza-Torres C, Fairhurst C (2000) Application of the convergence-confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criteria. Tunn Undergr Space Technol 15:187–213. https://doi.org/10.1016/S0886-7798(00)00046-8
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 41:1–11. https://doi.org/10.1016/j.ijrmms.2004.03.111
Chern JC, Shiao FY, Yu CW (1998) An empirical safety criterion for tunnel construction. In: Proceedings of the regional symposium on sedimentary rock engineering, Taipei, Taiwan
Med FAMA (1993) Numerical modeling of yield zones in weak rock. Analysis and design methods. Elsevier, pp 49–75
Fahimifar A, Ghadami H, Ahmadvand M (2015) The ground response curve of underwater tunnels, excavated in a strain-softening rock mass. Geomech Eng 8:323–359. https://doi.org/10.12989/gae.2015.8.3.323
Guan Z, Jiang Y, Tanabasi Y (2007) Ground reaction analyses in conventional tunnelling excavation. Tunn Undergr Space Technol 22:230–237. https://doi.org/10.1016/j.tust.2006.06.004
Brown ET, Hoek E (1980) Underground excavations in rock. Institution of Mining and Metallurgy, London
Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34:1165–1186. https://doi.org/10.1016/S1365-1609(97)80069-X
Hoek E (1999) Support for very weak rock associated with faults and shear zones, 1st edn. Routledge, London, pp 19–32. https://doi.org/10.1201/9780203740460-2
Itasca (2013) FLAC 2D Version 8. Minneapolis, Minnesota, USA. http://www.itascacg.com
Itasca (2016) FLAC3D Version 5. Minneapolis, Minnesota, USA. http://www.itascacg.com
Kaiser PK, Diederichs MS, Martin CD, Sharp J, Steiner W (2000) Underground works in hard rock tunnelling and mining. In: ISRM symposium
Klotoé CH, Bourgeois E (2019) Three dimensional finite element analysis of the influence of the umbrella arch on the settlements induced by shallow tunneling. Comput Geotech 110:114–121. https://doi.org/10.1016/j.compgeo.2019.02.017
Lee YK, Pietruszczak S (2008) A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass. Tunn Undergr Space Technol 23:588–599. https://doi.org/10.1016/j.tust.2007.11.002
Ogawa T, Lo KY (1987) Effects of dilatancy and yield criteria on displacements around tunnels. Can Geotech J 24:100–113
Oreste P (2003a) Analysis of structural interaction in tunnels using the convergence–confinement approach. Tunn Undergr Space Technol 18:347–363. https://doi.org/10.1016/S0886-7798(03)00004-X
Oreste P (2003b) A procedure for determining the reaction curve of shotcrete lining considering transient conditions. Rock Mech Rock Eng 36:209–236. https://doi.org/10.1007/s00603-002-0043-z
Oreste P (2008) Distinct analysis of fully grouted bolts around a circular tunnel considering the congruence of displacements between the bar and the rock. Int J Rock Mech Min Sci 45:1052–1067. https://doi.org/10.1016/j.ijrmms.2007.11.003
Panet M, Guenot A (1982) Analysis of convergence behind the face of a tunnel. In: Proceedings of the international symposium tunnelling, IMM, London, UK.
Panet M (1993) Understanding deformations in tunnels. Compr Rock Eng 1:663–690
Panet M (1995) Le calcul des tunnels par la méthode des curves convergence confinement. Presses de l’Êcole Nationale des Ponts et Chaussées, Paris, France
Panet M et al (2001) The convergence–confinement method. AFTES–recommendations des Groupes de Travait
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. https://doi.org/10.1016/j.ijrmms.2005.11.004
Park KH, Tontavanich B, Lee JG (2008) A simple procedure for ground response curve of circular tunnel in elastic-strain softening rock masses. Tunn Undergr Space Technol 23:151–159. https://doi.org/10.1016/j.tust.2007.03.002
Peila D, Oreste P (1995) Axisymmetric analysis of ground reinforcing in tunnelling design. Comput Geotech 17:253–274. https://doi.org/10.1016/0266-352X(95)93871-F
Rooh A, Nejati HR, Goshtasbi K (2018) A new formulation for calculation of longitudinal displacement profile (LDP) on the basis of rock mass quality. Geomech Eng 16:539–545. https://doi.org/10.12989/gae.2018.16.5.539
Sharan SK (2003) Elastic-brittle-plastic analysis of circular openings in Hoek-Brown media. Int J Rock Mech Min Sci 40:817–824. https://doi.org/10.1016/S1365-1609(03)00040-6
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 42:542–549. https://doi.org/10.1016/j.ijrmms.2005.03.019
Unlu T, Gercek H (2003) Effect of Poisson’s ratio on the normalized radial displacements occurring around the face of a circular tunnel. Tunn Undergr Space Technol 18:547–553. https://doi.org/10.1016/S0886-7798(03)00086-5
Vlachopoulos N, Diederichs M (2009) Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels. Rock Mech Rock Eng 42:131–146. https://doi.org/10.1007/s00603-009-0176-4
Wang Y (1996) Ground response of circular tunnel in poorly consolidated rock. J Geotech Eng 122(9):703–708. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:9(703)
Wang S, Yin S (2011) A closed-form solution for a spherical cavity in the elastic–brittle–plastic medium. Tunn Undergr Space Technol 26:236–241. https://doi.org/10.1016/j.tust.2010.06.005
Zhang X et al (2020) Stability analysis model for a tunnel face reinforced with bolts and an umbrella arch in cohesive-frictional soils. Comput Geotech 124:103635. https://doi.org/10.1016/j.compgeo.2020.103635
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Bour, K., Goshtasbi, K. & Bour, M. Effect of Constitutive Model on the Convergence-Confinement Method and Plastic Zone Radius. Geotech Geol Eng 42, 1487–1504 (2024). https://doi.org/10.1007/s10706-023-02630-2
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DOI: https://doi.org/10.1007/s10706-023-02630-2