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Evaluation of Tunnel Elastic and Elasto-Plastic Deformations with Approximations Obtained from 3D-FEM Simulations
Evaluación de las deformaciones elásticas y elastoplásticas en túneles usando aproximaciones obtenidas de simulaciones 3D-FEM
DOI:
https://doi.org/10.15446/ing.investig.96880Keywords:
tunnels, finite element method, Mohr-Coulomb, elastic-elastoplastic (en)túneles, método de elementos finitos, Mohr-Coulomb, elástico-elastoplástico (es)
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Nowadays, there are computer tools designed to simulate engineering problems. Numerical simulations in three dimensions (3D) are the closest to reality, but they require a significant amount of time and experience. In this paper, the aim is to present formulae and graphs obtained from numerical simulations using the finite element method (FEM). Their application decreases the time required to obtain deformations in the periphery of different tunnel sections and further serves to evaluate them for different excavation lengths in the face of unexpected geotechnical changes during drilling. Using the RS2 and RS3 software, 3D analyses were carried out according to the Mohr-Coulomb (MC) model, considering elastic and elasto-plastic perfect behaviors as well as isotropic and anisotropic conditions. The graphs presented herein allow obtaining displacements from an axisymmetric model to infer the 3D displacements horseshoe tunnels, and the polynomial expressions aid in determining the displacements of an established excavation length. Finally, comparisons between the displacements reported by other authors and those obtained with the polynomial expressions are presented as a means of validation for this research.
En la actualidad existen herramientas computacionales diseñadas para simular problemas de ingeniería. Las simulaciones numéricas tridimensionales (3D) son las más cercanas a la realidad, pero requieren una cantidad importante de tiempo y experiencia. En este artículo, el objetivo es presentar fórmulas y gráficos obtenidos de simulaciones realizadas utilizando el método de elementos finitos (FEM). La aplicación de estos disminuye el tiempo requerido para obtener deformaciones en la periferia de distintas secciones de túnel, e incluso funciona para evaluarlas con respecto a distintas longitudes de excavación cuando se encuentren cambios geotécnicos inesperados durante la perforación. Mediante el software RS2 y RS3, se realizaron análisis 3D de acuerdo con el modelo Mohr-Coulomb, teniendo en cuenta comportamientos elásticos y elastoplásticos perfectos, así como condiciones isotrópicas y anisotrópicas. Los gráficos aquí presentados permiten obtener los desplazamientos a partir de un modelo axisimétrico para a su vez inferir los desplazamientos 3D de túneles con forma de herradura, y las expresiones polinómicas ayudan a determinar los desplazamientos de una longitud de excavación establecida. Por último, se presentan comparaciones entre los desplazamientos reportados por otros autores y aquellos obtenidos con las expresiones polinómicas como medio para la validación de esta investigación.
References
American Association of State Highway and Transportation Officials (AASHTO). (2012). AASHTO LRFD bridge design specifications (6th ed). AASHTO.
Arnau, O., and Molins, C. (2012). Three-dimensional structural response of segmental tunnel linings. Engineering Structures, 44, 210-221. https://doi.org/10.1016/j.engstruct.2012.06.001 DOI: https://doi.org/10.1016/j.engstruct.2012.06.001
Azimi, M., Mirjavadi, S. S., and Asli, S. A. (2016). Investigation of mesh sensitivity influence to determine crack characteristics by finite element methods. Journal of Failure Analysis and Prevention, 16(3), 506-512. https://doi.org/10.1007/s11668-016-0117-y DOI: https://doi.org/10.1007/s11668-016-0117-y
Bjureland, W., Spross, J., Johansson, F., Prästings, A., and Larson, S. (2017). Reliability aspects of rock tunnel design with the observational method. International Journal of Rock Mechanics and Mining Sciences, 98, 102-110. https://doi.org/10.1016/j.ijrmms.2017.07.004 DOI: https://doi.org/10.1016/j.ijrmms.2017.07.004
Celestino, T. B., Aoki, N., Silva, R. M., Gornes, R. A. M. P., Borto-lucci, A. A., and Ferreira, D. A. (2006). Evaluation of tunnel support structure reliability. Tunneling and Underground Space Technology, 21(3-4), 311. https://doi.org/10.1016/j.tust.2005.12.028 DOI: https://doi.org/10.1016/j.tust.2005.12.028
European Committee for Standardization (CEN). (2004). Geotechnical design – Part 1: General rules, Eurocode 7. CEN.
Chen, F., Wang, L., and Zhang, W. (2019). Reliability assessment on stability of tunnelling perpendicularly beneath an existing tunnel considering spatial variabilities of rock mass properties. Tunnelling and Underground Space Technology, 88, 276-289. https://doi.org/10.1016/j.tust.2019.03.013 DOI: https://doi.org/10.1016/j.tust.2019.03.013
Conte, S. D., and De Boor C. (1972). Elementary numerical analysis (2nd ed.). McGraw-Hill Inc.
Deere, D. U., Peck, R. B., Monsees, J. E., and Schmidt, B. (1969). Design of tunnel liners and support systems. US Department of Transportation.
Du, M., Wang, X., Zhang, Y., Li, L., and Zhang, P. (2020). In-situ monitoring and analysis of tunnel floor heave process. Engineering Failure Analysis, 109, 104323. https://doi.org/10.1016/j.engfailanal.2019.104323 DOI: https://doi.org/10.1016/j.engfailanal.2019.104323
Equihua-Anguiano, L. N., Rubio-Saldaña, I., Orozco-Calderón, M., Arreygue-Rocha, J. E., and Chávez-Negrete, C. (2018). Equivalent FEM meshes from Axisymmetric (AXID) to three (3D) dimensions applied to tunnels in clay. In S. Shu, L. He, and Y. Kai (Eds.), New Developments in Materials for Infrastructure Sustainability and the Contemporary Issues in Geo-environmental Engineering (pp. 11-22). Springer. https://doi.org/10.1007/978-3-319-95774-6_2 DOI: https://doi.org/10.1007/978-3-319-95774-6_2
Equihua-Anguiano, L. N., Viveros-Viveros, F., Pérez-Cruz, J. R., Chávez-Negrete, C., Arreygue-Rocha, J. E., Orozco-Calderón, M. (2017). Displacement nomograph from two (2D) to three (3D) dimensions applied to circular tunnels in clay using finite element [Conference paper]. International Conference on Soil Mechanics and Geotechnical Engineering, Seoul, Korea.
Forsat, M., Taghipoor, M., and Palassi, M. (2022). 3D FEM model on the parameters’ influence of EPB-TBM on settlements of single and twin metro tunnels during construction. International Journal of Pavement Research and Technology, 15(3), 525-538. https://doi.org/10.1007/s42947-021-00034-0 DOI: https://doi.org/10.1007/s42947-021-00034-0
Hamming R. W. (1987). Numerical methods for scientists and engineers (2nd ed.). Dover Publications.
Hanumanthappa, M., and Maji, V. B. (2017). Empirical and numerical analyses of tunnel closure in squeezing rock. International Journal of Geosynthetics and Ground Engineering, 3, 38. https://doi.org/10.1007/s40891-017-0118-2 DOI: https://doi.org/10.1007/s40891-017-0118-2
Hao, W. U., and Zhao, G. Y. (2022). Failure behavior of horse-shoe-shaped tunnel in hard rock under high stress: Phenome-non and mechanisms. Transactions of Nonferrous Metals Society of China, 32(2), 639-656. https://doi.org/10.1016/S1003-6326(22)65822-9 DOI: https://doi.org/10.1016/S1003-6326(22)65822-9
Hejazi, Y., Dias, D., and Kastner, R. (2008). Impact of constitutive models on the numerical analysis of underground constructions. Acta Geotechnica, 3(4), 251-258. https://doi.org/10.1007/s11440-008-0056-1 DOI: https://doi.org/10.1007/s11440-008-0056-1
Holmberg, M., and Stille, H. (2007). The application of the observational method for design of underground excavations. SveBeFo.
Huang, M., Zhan, J. W., Xu, C. S., and Jiang, S. (2020). New creep constitutive model for soft rocks and its application in the prediction of time-dependent deformation in tunnels. International Journal of Geomechanics, 20(7), 04020096. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001663 DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001663
Johansson, F., Bjureland, W., and Spross, J. (2016). Application of reliability-based design methods to underground excavation in rock. BeFo.
Katebi, H., Rezaei, A. H., Hajialilue-Bonab, M., and Tarifard, A. (2015). Assessment the influence of ground stratification, tunnel and surface buildings specifications on shield tunnel lining loads (by FEM). Tunnelling and Underground Space Technology, 49, 67-78. https://doi.org/10.1016/j.tust.2015.04.004 DOI: https://doi.org/10.1016/j.tust.2015.04.004
Kaya, A., and Bulut, F. (2019). Geotechnical studies and primary support design for a highway tunnel: A case study in Turkey. Bulletin of Engineering Geology and the Environment, 78(8), 6311-6334. https://doi.org/10.1007/s10064-019-01529-8 DOI: https://doi.org/10.1007/s10064-019-01529-8
Khan, B., Jamil, S. M., Jafri, T. H., and Akhtar, K. (2019). Effects of different empirical tunnel design approaches on rock mass behaviour during tunnel widening. Heliyon, 5(12), e02944. https://doi.org/10.1016/j.heliyon.2019.e02944 DOI: https://doi.org/10.1016/j.heliyon.2019.e02944
Khan, M. A., Sadique, M., Harahap, I. H., Zaid, M., and Alam, M. M. (2022). Static and dynamic analysis of the shielded tunnel in alluvium soil with 2D FEM model. Transportation Infrastructure Geotechnology, 9(1), 73-100. https://doi.org/10.1007/s40515-021-00160-z DOI: https://doi.org/10.1007/s40515-021-00160-z
Kong, F., Lu, D., Du, X., and Shen, C. (2019). Elastic analytical solution of shallow tunnel owing to twin tunnelling based on a unified displacement function. Applied Mathematical Modeling, 68, 422-442. https://doi.org/10.1016/j.apm.2018.11.038 DOI: https://doi.org/10.1016/j.apm.2018.11.038
Langford, J. C., and Diederichs, M. S. (2013). Evaluating uncertainty in intact and rock mass parameters for the purpose of reliability assessment [Conference paper]. 7th US Rock Mechanics/Geomechanics Symposium, ARMA, San Francisco, California, United States.
Li, B., Fu, Y., Hong, Y., and Cao, Z. (2021). Deterministic and probabilistic analysis of tunnel face stability using support vec-tor machine. Geomechanics and Engineering, 25(1), 17-30. https://doi.org/10.3208/jgssp.v08.c13
Lombardi, G., and Amberg, W. (1974). Une méthode de calcul élasto-plastique de l'état de tension et de déformazion autour d'une cavité souterraine [Conference paper]. Con-gresso Internazionale, ISRM, Denver, Colorado, United States.
Lu, D., Shen, C., Kong, F., and Du, X. (2020). Viscoelastic analytical solution for shallow tunnel considering time-dependent displacement boundary. Japanese Geotechnical Society Special Publication, 8(11), 430-435. DOI: https://doi.org/10.3208/jgssp.v08.c13
Lunardi, P. (2008). Design and construction of tunnels. Analysis of controlled deformation in rocks and soils (ADECO-RS). Springer. https://doi.org/10.1007/978-3-540-73875-6 DOI: https://doi.org/10.1007/978-3-540-73875-6
Ma, K., Zhang, J., Zhang, J., Dai, Y., and Zhou, P. (2022). Floor heave failure mechanism of large-section tunnels in sand-stone with shale stratum after construction: A case study. Engineering Failure Analysis, 140, 106497. https://doi.org/10.1016/j.engfailanal.2022.106497 DOI: https://doi.org/10.1016/j.engfailanal.2022.106497
Miro, S., Hartmann, D., and Schanz, T. (2014). Global sensitivity analysis for subsoil parameter estimation in mechanized tunneling. Computers and Geotechnics, 56, 80-88. https://doi.org/10.1016/j.compgeo.2013.11.003 DOI: https://doi.org/10.1016/j.compgeo.2013.11.003
Mishra, S., Zaid, M., Rao, K. S., and Gupta, N. K. (2022). FEA of urban rock tunnels under impact loading at targeted velocity. Geotechnical and Geological Engineering, 40(4), 1693-1711. https://doi.org/10.1007/s10706-021-01987-6 DOI: https://doi.org/10.1007/s10706-021-01987-6
National Concrete Masonry Association (NCMA). (2010). Design manual for segmental retaining walls (3rd ed.). NCMA.
Naqvi, M. W., Akhtar, M. F., Zaid, M., and Sadique, M. R. (2021). Effect of superstructure on the stability of underground tunnels. Transportation Infrastructure Geotechnology, 8(1), 142-161. https://doi.org/10.1007/s40515-020-00119-6 DOI: https://doi.org/10.1007/s40515-020-00119-6
Ngueyep Mambou, L. L., Ndop, J., and Ndjaka, J. (2015). Numerical investigations of stresses and strains redistribution around the tunnel: Influence of transverse isotropic behavior of granitic rock, in situ stress and shape of tunnel. Journal of Mining Science, 51(3), 497-505. https://doi.org/10.1134/S1062739115030102 DOI: https://doi.org/10.1134/S1062739115030102
Qiu, L., Wang, E., Song, D., Liu, Z., Shen, R., Lv, G., and Xu, Z. (2017). Measurement of the stress field of a tunnel through its rock EMR. Journal of Geophysics and Engineering, 14(4), 949-959. https://doi.org/10.1088/1742-2140/aa6dde DOI: https://doi.org/10.1088/1742-2140/aa6dde
Rehman, H., Ali, W., Naji, A. M., Kim, J. J., Abdullah, R. A., and Yoo, H. K. (2018). Review of rock-mass rating and tunneling quality index systems for tunnel design: Development, refinement, application and limitation. Applied sciences, 8(8), 1250. https://doi.org/10.3390/app8081250 DOI: https://doi.org/10.3390/app8081250
Rocscience Inc. (n.d.). RS2, 2D Geotechnical Finite Element Analysis, version 9.0 64 bits [Computer software]. Rocscience Inc.
Rocscience Inc. (n.d.). RS3, 3D Geotechnical Finite Element Analysis, version 2.0 64 bits [Computer software]. Rocscience Inc.
Sadique, M., Ali, A., Zaid, M., and Masroor Alam, M. (2021). Experimental and numerical modeling of tunneling-induced ground settlement in clayey soil. In S. Kumar Shukla, S. N. Ra-man, B. Bhattacharjee, and J. Bhattacharjee (Eds.), Advances in Geotechnics and Structural Engineering (pp. 23-33). Springer. https://doi.org/10.1007/978-981-33-6969-6_3 DOI: https://doi.org/10.1007/978-981-33-6969-6_3
Sadique, M., Zaid, M., and Alam, M. (2022). Rock tunnel performance under blast loading through finite element analysis. Geotechnical and Geological Engineering, 40(1), 35-56. https://doi.org/10.1007/s10706-021-01879-9 DOI: https://doi.org/10.1007/s10706-021-01879-9
Soldo, L., Vendramini, M., and Eusebio, A. (2019). Tunnels design and geological studies. Tunnelling and Underground Space Technology, 84, 82-98. https://doi.org/10.1016/j.tust.2018.10.013 DOI: https://doi.org/10.1016/j.tust.2018.10.013
Spross, J. (2016). Toward a reliability framework for the observational method [Doctoral thesis, KTH Royal Institute of Technology.
Spross J., and Johansson, F. (2017). When is the observational method in geotechnical engineering favourable. Structural Safety, 66, 17-26. https://doi.org/10.1016/j.strusafe.2017.01.006 DOI: https://doi.org/10.1016/j.strusafe.2017.01.006
Stoer, J., and Bulirsch, R. (1993). Introduction to numerical analysis (2nd ed.). Springer-Verlag. https://doi.org/10.1007/978-1-4757-2272-7 DOI: https://doi.org/10.1007/978-1-4757-2272-7
Tamez-González, E., Rangel-Núñez, J. L., and Holguín, E. (1997). Diseño geotécnico de túneles. TGC Geotecnia S.A. de C.V.
Teodorescu, P., Stanescu N-D., and Pandrea N. (2013). Numerical analysis with applications in mechanics and engineering (1st ed.). Wiley, IEEE Press. https://doi.org/10.1002/9781118614563 DOI: https://doi.org/10.1002/9781118614563
Terzaghi, K. (1942). Liner-plate tunnels on the Chicago (IL) subway. Proceedings of the American Society of Civil Engineers, 68(6), 862-899.
Vitali, O. P., Celestino, T. B., and Bobet, A. (2020). Analytical solution for a deep circular tunnel in anisotropic ground and anisotropic geostatic stresses. Rock Mechanics and Rock Engineering, 53(9), 3859-3884. https://doi.org/10.1007/s00603-020-02157-5 DOI: https://doi.org/10.1007/s00603-020-02157-5
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 DOI: https://doi.org/10.1007/s10706-014-9727-x
Wolfram Research Inc. (2020). Mathematica [Computer software]. https://www.wolfram.com/mathematica
Xing-Tao, L., Ren-Peng, C., Huai-Na, W., and Hong-Zhan C. (2019). Three-dimensional stress-transfer mechanism and soil arching evolution induced by shield tunneling in sandy ground. Tunnelling and Underground Space Technology, 93, 103104. https://doi.org/10.1016/j.tust.2019.103104 DOI: https://doi.org/10.1016/j.tust.2019.103104
Zaid, M. (2021). Preliminary study to understand the effect of impact loading and rock weathering in tunnel constructed in quartzite. Geotechnical and Geological Engineering, 2021, s10706-021-01948-z. https://doi.org/10.1007/s10706-021-01948-z DOI: https://doi.org/10.1007/s10706-021-01948-z
Zaid, M., and Mishra, S. (2021). Numerical analysis of shallow tunnels under static loading: a finite element approach. Geotechnical and Geological Engineering, 39(3), 2581-2607. https://doi.org/10.1007/s10706-020-01647-1 DOI: https://doi.org/10.1007/s10706-020-01647-1
Zaid, M., and Rehan Sadique, M. (2021). A simple approximate simulation using coupled Eulerian–Lagrangian (CEL) simulation in investigating effects of internal blast in rock tunnel. Indian Geotechnical Journal, 51(5), 1038-1055. https://doi.org/10.1007/s10706-021-01927-4 DOI: https://doi.org/10.1007/s40098-021-00511-0
Zaid, M., Sadique, M., and Alam, M. (2022). Blast resistant analysis of rock tunnel using Abaqus: Effect of weathering. Geotechnical and Geological Engineering, 40(2), 809-832. https://doi.org/10.1007/s10706-021-01927-4 DOI: https://doi.org/10.1007/s10706-021-01927-4
Zaid, M., and Sadique, M. R. (2021). Blast-resistant behavior of tunnels in sedimentary rocks. International Journal of Protective Structures, 12(2), 153-173. https://doi.org/10.1177/2041419620951211 DOI: https://doi.org/10.1177/2041419620951211
Zaid, M., and Shah, I. A. (2021). Numerical analysis of Himalayan rock tunnels under static and blast loading. Geotechnical and Geological Engineering, 39(7), 5063-5083. https://doi.org/10.1007/s10706-021-01813-z DOI: https://doi.org/10.1007/s10706-021-01813-z
Zhang, L., and Lin, P. (2021). Multi-objective optimization for limiting tunnel-induced damages considering uncertainties. Reliability Engineering & System Safety, 216, 107945. https://doi.org/10.1016/j.ress.2021.107945 DOI: https://doi.org/10.1016/j.ress.2021.107945
Zhang, M., Li, S., and Li, P. (2020). Numerical analysis of ground displacement and segmental stress and influence of yaw excavation loadings for a curved shield tunnel. Computers and Geotechnics, 118, 103325. https://doi.org/10.1016/j.compgeo.2019.103325 DOI: https://doi.org/10.1016/j.compgeo.2019.103325
Zhao, H., Liu, C., Huang, G., Yu, B., Liu, Y., and Song, Z. (2020). Experimental investigation on rockburst process and failure characteristics in trapezoidal tunnel under different lateral stresses. Construction and Building Materials, 259, 119530. https://doi.org/10.1016/j.conbuildmat.2020.119530 DOI: https://doi.org/10.1016/j.conbuildmat.2020.119530
Zhiming, L., Jian, C., Mitsutaka, S., and Hongyan, G. (2019). Numerical simulation model of artificial ground freezing for tunneling under seepage flow conditions. Tunneling and Underground Space Technology, 92, 103035. https://doi.org/10.1016/j.tust.2019.103035 DOI: https://doi.org/10.1016/j.tust.2019.103035
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