Nomographs to obtain three dimensional (3D) elastic displacements for deep circular tunnels
DOI:
https://doi.org/10.4067/S0718-28132020000200012Keywords:
Nomograph, Finite element method FEM, Circular tunnel, Elastic analysisAbstract
Finite element (FEM) based software is frequently used in practice for tunnel design, alongside the traditional analytical and empirical solutions. Design is not the only challenge in this kind of projects, there are other important factors such as considering what is necessary to develop an efficient construction plan under a schedule and foreseeing possible changes that modify the original design. The use of two-dimensional (2D) FEM is one of the main tools used in the industry. However, 2D results yield not an entirely accurate analysis, since the behaviour of the infrastructure is considered as threedimensional (3D). This paper presents nomographs and a 3D and 2D relationship, to rapidly estimate values of elastic 3D and 2D displacements produced in the periphery of a deep circular tunnel, inside soils of different rigidities. Graphics given correspond to five different radii and for a 100 m excavation length. Nomographs were obtained from RS3© and RS2© FEM simulations and according to the elastic theory. Geotechnical parameters correspond to a constant friction angle, cohesion and soil specific weight. FEM analysis was made using the Mohr-Coulomb model, considering isotropic conditions.
References
Alonso, E., Alejano, L.R., Varas, F., Fdez-Manín, G. and Carranza-Torres, C. (2003). Ground response curves for rock masses exhibiting strain-softening behaviour. International Journal for Numerical and Analytical Methods in Geomechanics 27: 1153–1185. https://doi.org/10.1002/nag.315
Bieniawski, Z.T. (1989). Engineering rock mass classifications: A complete manual for engineers and geologist in mining, civil, and petroleum engineering. John Wiley & Sons, USA.
Broms, B.B. and Bennermark, H. (1967). Stability of clay at vertical openings. Journal of the Soil Mechanics and Foundations 93(1): 71–94. https://doi.org/10.1061/JSFEAQ.0000946
Cording, E.J. (1968). The stability during construction of three large underground openings in rock. Technical Report 1-813, U.S. Army Engineer Waterways Experiment Station, Corps of Engineers, Vicksburg, USA.
Deere, D.U, Peck, R.B., Monsees, J.E. and Schmidt, B. (1969). Design of tunnel liners and support systems. Department of Civil Engineering Final Report, University of Illinois, Urbana for the office of High Speed Transportation, U.S. Department of Transportation. Contract No. 3-0152.
Duncan Fama, M.E. (1993). Numerical modeling of yield zones in weak rock. Comprehensive Rock Engineering: Principles, Practice and Projects. Vol. 2: Analysis and Design Methods. Fairhurst, C. ed., Pergamon Press, Oxford, UK, 49–75. https://doi.org/10.1016/B978-0-08-040615-2.50009-5
Equihua-Anguiano, L.N., Viveros-Viveros, F., Pérez-Cruz, J.R., Chávez-Negrete, C., Arreygue-Rocha, J.E. and OrozcoCalderón, M. (2017). Displacement nomograph from two (2D) to three (3D) dimensions applied to circular tunnels in clay using finite element. 19th International Conference on Soil Mechanics and Geotechnical Engineering, Seoul, South Korea, 733–736.
Farias, M.M., Moraes, A.H. and Assis, A.P. (2004). Displacement control in tunnels excavated by the NATM: 3-D numerical simulation. Tunnelling and Underground Space Technology 19(3): 283–293. https://doi.org/10.1016/j.tust.2003.11.006
Giraldo-Sierra, M.C. (1996). Evaluación de un modelo elastoplástico para predecir el comportamiento de la arcilla de la ciudad de México. Tesis de Maestría, Universidad Nacional Autónoma de México, México.
Hoek, E. (2001). Big tunnels in bad rock. The 36th Karl Terzaghi lecture. Journal of Geotechnical and Geoenviromental Engineering 127(9): 726–740. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:9(726)
Hoek, E. and Brown, E.T. (1980). Empirical strength criterion for rock masses. Journal of Geotechnical Engineerng Division 106(9): 1013–1035. https://doi.org/10.1061/AJGEB6.0001029
Hoek, E. and Brown, E.T. (1997). Practical estimates of rock mass strength. International Journal of Rock Mechanics and Mining Sciences 34(8): 1165-1186. https://doi.org/10.1016/S1365-1609(97)80069-X
Hoek, E. and Marinos, P. (2000). Predicting tunnel squeezing problems in weak heterogeneous rock masses. Tunnels and Tunnelling International 32(11): 45–51.
Hoek, E., Carranza-Torres, C. and Corkum, B. (2002). Hoek-Brown failure criterion—2002 edition. 5th North American Rock Mechanics Symposium and the 17th Tunnelling Association of Canada Conference NARMS-TAC, Toronto, Canada, vol. 1, 267–273.
Kondner, R.L. (1963). Hyperbolic stress-strain response: cohesive soil. Journal of the Soil Mechanics and Foundation Division 89(1): 115–144. https://doi.org/10.1061/JSFEAQ.0000479
Levy, E. (1980). Elementos de mecánica del medio continuo. LIMUSA, México.
Lombardi, G. et Amberg, W.A. (1974). Une méthode de calcul élasto-plastique de l’état de tension et de déformation autour d’une cavité souterraine. 3rd ISMR Congress, Denver, USA, 1049–1060.
Martínez, R., Schroeder, F. and Potts, D. (2015). Numerical study of long-term settlement following twin tunnel construction. Obras y Proyectos 17, 23-29. https://doi.org/10.4067/S0718-28132015000100003
Moreno, A. and Schmmitter, J.J. (1981). Failures of shafts and tunnels in soft soils. Soft-ground tunnelling: failures and displacements. Resendiz and Romo eds. A.A. Balkema, Rotterdam, The Netherlands, 23–32.
Palmstrom, A. and Broch, E. (2006). Use and misuse of rock mass classification systems with particular reference to the Q-system. Tunnelling and Underground Space Technology 21(6): 575–593. https://doi.org/10.1016/j.tust.2005.10.005
Panet, M. (1995). Le calcul des tunnels par la méthode convergence-confinement. Presses de l’École Nationale des Ponts et Chaussées. Paris.
Peck, R.B. (1969). Deep excavations and tunnelling in soft ground. General report. VII International Conference on Soil Mechanics and Foundations Engineering, Mexico, 147–150.
Pérez, M.A. y Auvinet G. (2012). Solución analítica para la determinación de campos de esfuerzos y desplazamientos alrededor de un túnel circular. XXVI Reunión Nacional de Mecánica de Suelos e Ingeniería Geotécnica, Cancún, Quintana Roo, México.
RS2 (2016). 9 Modeler, Version 9.020 64-bit, Copyright ©1990-2016 Rocscience Inc., Toronto, Ontario, Canada.
RS3 (2017). Version 1.022 64-bit, Copyright © 2013-2017 Rocscience Inc., Toronto, Ontario, Canada.
Sánchez, F., Suárez, F. y Maceo, V. (2014). El colapso del túnel Xicotepec I; una investigación sobre sus causas y un estudio para su reconstrucción. IV Congreso Mexicano de Ingeniería de Túneles y Obras Subterráneas. Asociación Mexicana de Ingeniería de Túneles y Obras Subterráneas AMITOS, México, 87–96.
Tamez, E. (1984). Estabilidad de túneles excavados en suelos. Academia Mexicana de Ingeniería, México.
Tamez-González, E., Rangel-Nuñez, J.L. and Holguín, E. (1997). Diseño geotécnico de túneles. Ed. TGC, México.
Terzaghi, K. (1942). Shield tunnels of Chicago Subway. Journal of the Boston Society of Civil Engineers 29(3): 163–210.
Terzaghi, K. (1946). Rock defects and loads on tunnel support. In Proctor, R.V. and White, T.L., eds., Rock Tunneling with Steel Supports, Commercial Shearing and Stamping Co., Youngstown, Ohio, USA.
Timoshenko, S.P. and Goodier, J.N. (1970). Theory of elasticity. Third edition, Mc Graw Hill, New York, USA.
Vlachopoulos, N. and Diederichs, M.S. (2014). Appropriate uses and practical limitations of 2D numerical analysis of tunnels and tunnel support response. Geotechnical and Geological Engineering 32(2): 469-488. https://doi.org/10.1007/s10706-014-9727-x
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