Key features of numerical models for the FE-simulation of deep tunnel advance by the NATM

Abstract

In the present work, important aspects of time-dependent nonlinear 3D finite element (FE) models for deep tunnel advance by the New Austrian Tunneling Method(NATM), characterized by repeated sequences of excavation, securing, and idle periods, are discussed on the example of a 3D finite element model of a stretch of the Brenner Base Tunnel, which is currently constructed between Austria and Italy. Nonlinear material models are utilized for representing the surrounding rock mass and the shotcrete shell. Based on the finite element model, strategies for the efficient implementation into a parallel distributed memory numerical code are proposed. They are essential to achieve reasonable computation times for numerical simulations of tunneling based on large 3D FE models. In particular, the implementation of the construction procedure, parallel computing and communication specific details, and efficient linear solvers for the global equation system within the incremental-iterative Newton-Raphson scheme are addressed. Furthermore, possible extensions of the material models for rock mass and shotcrete, used in the 3D FE model, are presented. They concern (i) a gradient-enhanced model for transversely isotropic rock and rock mass, taking into account hardening and softening behavior and (ii) the extension of the shotcrete model to nonlinear creep and damage due to creep. The possible benefits of the model extensions in numerical simulations of tunneling by the NATM are discussed.

Keywords

NATM / Finite element model / Rock / Shotcrete / Damage-plasticity model

References

[1] Abaqus (2015). ABAQUS v6.14 Documentation. RI, USA: Dassault Syste`mes Providence.

[2] Abdollahi M. S., Najafi M., Bafghi A. Y., & Marji M. F. (2019). A 3D numerical model to determine suitable reinforcement strategies for passing TBM through a fault zone, a case study: Safaroud water transmission tunnel, Iran. Tunnelling and Underground Space Technology, 88, 186-199.

[3] ACI Committee 209 (1992). Prediction of creep, shrinkage, and temperature effects in concrete structures. Technical report 209R-92, American Concrete Institute:Farmington Hills, Michigan.

[4] Adams M., Brezina M., Hu J., & Tuminaro R. (2003). Parallel multigrid smoothing: polynomial versus Gauss-Seidel. Journal of Computational Physics, 188, 593-610.

[5] Balay S., Abhyankar S., Adams M.F., Benson S., Brown J., Brune P., Buschelman K., Constantinescu E. M., Dalcin L., Dener A., Eijkhout V., Faibussowitsch J., Gropp W. D., Hapla V., Isaac T., Jolivet P., Karpeev D., Kaushik D., Knepley M. G., Kong F., Kruger S., May D. A., McInnes L. C., Mills R. T., Mitchell L., Munson T., Roman J. E., Rupp K., Sanan P., Sarich J., Smith B. F., Zampini S., Zhang H., Zhang H., & Zhang J. (2022). PETSc Web page.

[6] Bazˇant Z. P., Jira´sek M., Hubler M., & Carol I. (2015). RILEM draft recommendation: TC-242-MDC multi-decade creep and shrinkage of concrete: material model and structural analysis. Model B4 for creep, drying shrinkage and autogenous shrinkage of normal and high- strength concretes with multi-decade applicability. Materials and Structures, 48, 753-770.

[7] Bazˇant Z. P., & Prasannan S. (1989). Solidification theory for concrete creep. I: Formulation. Journal of Engineering Mechanics, 115, 1691-1703.

[8] Blu¨ mel M. (2014). Pru¨ fprotokolle Laborversuche Druckversuche Anfahrtstutzen Ahrntal. Technical report Institut fu¨ r Felsmechanik und Tunnelbau TU Graz, Graz, Austria.

[9] Boehler J. (1970). Equilibre limite des sols anisotropes. Journal de Mecanique, 9, 5-33.

[10] Bryant E. C., & Sun W. (2019). A micromorphically regularized Camclay model for capturing size-dependent anisotropy of geomaterials. Computer Methods in Applied Mechanics and Engineering, 354, 56-95.

[11] Chortis F., & Kavvadas M. (2021a). Three-dimensional numerical analyses of perpendicular tunnel intersections. Geotechnical and Geological Engineering, 39, 1771-1793.

[12] Chortis F., & Kavvadas M. (2021b). Three-dimensional numerical investigation of the interaction between twin tunnels. Geotechnical and Geological Engineering, 39, 5559-5585.

[13] Do N.-A., Dias D., & Oreste P. (2015). 3D numerical investigation on the interaction between mechanized twin tunnels in soft ground. Environmental Earth Sciences, 73, 2101-2113.

[14] Do N.-A., Dias D., & Oreste P. (2016). 3D numerical investigation of mechanized twin tunnels in soft ground-Influence of lagging distance between two tunnel faces. Engineering Structures, 109, 117-125.

[15] Do N.-A., Dias D., Oreste P., & Djeran-Maigre I. (2014). Three- dimensional numerical simulation of a mechanized twin tunnels in soft ground. Tunnelling and Underground Space Technology, 42, 40-51.

[16] Dummer A., Neuner M., & Hofstetter G. (2022). An extended gradient- enhanced damage-plasticity model for concrete considering nonlinear creep and failure due to creep. International Journal of Solids and Structures, 243, 111541.

[17] Dummer A., Smaniotto S., & Hofstetter G. (2023). Experimental and numerical study on nonlinear basic and drying creep of normal strength concrete under uniaxial compression. Construction and Building Materials, 362, 129726.

[18] Gamnitzer P., & Hofstetter G. (2016). Fully coupled multi-phase modelling of pumping induced settlements, airand water flow in multi-layered normally consolidated soils. Computers and Geotechnics, 79, 10-21.

[19] Gee M. W., Siefert C. M., Hu J. J., Tuminaro R. S., & Sala M.G. (2006). ML 5.0 smoothed aggregation user’s guide. Technical report SAND2006-2649, Sandia National Laboratories.

[20] Grassl P., & Jira´sek M. (2006). Damage-plastic model for concrete failure. International Journal of Solids and Structures, 43, 7166-7196.

[21] Heroux M. A., Bartlett R. A., Howle V. E., Hoekstra R. J., Hu J. J., Kolda T. G., Lehoucq R. B., Long K. R., Pawlowski R. P., Phipps E. T., Salinger A. G., Thornquist H. K., Tuminaro R. S., Willenbring J. M., Williams A., & Stanley K. S. (2005). An overview of the Trilinos project. ACM Transactions on Mathematical Software, 31, 397-423.

[22] Hoek E., & Brown E. T. (1980). Empirical strength criterion for rock masses. Journal of the Geotechnical Engineering Division, 106, 1013-1035.

[23] Hoek E., Carranza-Torres C., & Corkum B. (2002). Hoek-Brown failure criterion - 2002 edition. In R.Hammah (Ed.), Proceedings of the 5th North American Rock Mechanics Symposium (pp. 267-273). Toronto, Ontario, Canada: University of Toronto Press.

[24] Janin J., Dias D., Emeriault F., Kastner R., Le Bissonnais H., & Guilloux A. (2015). Numerical back-analysis of the southern Toulon tunnel measurements: A comparison of 3D and 2D approaches. Engineering Geology, 195, 42-52.

[25] Jin Y.-F., Zhu B.-Q., Yin Z.-Y., & Zhang D.-M. (2019). Three-dimensional numerical analysis of the interaction of two crossing tunnels in soft clay. Underground Space, 4, 310-327.

[26] Jira´sek M., & Bazˇant Z. P. (2002). Inelastic Analysis of Structures. John Wiley & Sons Ltd..

[27] Johnson A. A., & Tezduyar T. E. (1994). Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Computer Methods in Applied Mechanics and Engineering, 119, 73-94.

[28] Karakus M. (2007). Appraising the methods accounting for 3D tunnelling effects in 2D plane strain FE analysis. Tunnelling and Underground Space Technology, 22, 47-56.

[29] Karypis G., & Schloegel K. (2011). ParMeTis: Parallel graph partitioning and sparse matrix ordering library. Technical report Version 4.0.

[30] Kavvadas M., Litsas D., Vazaios I., & Fortsakis P. (2017). Development of a 3D finite element model for shield EPB tunnelling. Tunnelling and Underground Space Technology, 65, 22-34.

[31] Liu C., Zhang Z., & Regueiro R. A. (2014). Pile and pile group response to tunnelling using a large diameter slurry shield-Case study in Shanghai. Computers and Geotechnics, 59, 21-43.

[32] Lombardi G. (1971). Zur Bemessung der Tunnelauskleidung mit Beru¨ cksichtigung des Bauvorganges. Schweiz. Bauztg, 89.

[33] Mader T., Schreter M., & Hofstetter G. (2022a). A gradient enhanced transversely isotropic damage plasticity model for rock formulation and comparison of different approaches. International Journal for Numerical and Analytical Methods in Geomechanics, 46, 933-960.

[34] Mader T., Schreter M., & Hofstetter G. (2022b). On the influence of direction-dependent behavior of rock mass in simulations of deep tunneling using a novel gradient-enhanced transversely isotropic damage-plasticity model. Applied Sciences, 12.

[35] Mader T., Schreter M., & Hofstetter G. (2023). An advanced constitutive model for transversely isotropic rock Evaluation of two different regularization approaches. IOP Conference Series: Earth and Environmental Science, 1124, 012115.

[36] Menetrey P., & Willam K. (1995). Triaxial failure criterion for concrete and its generalization. ACI Structural Journal, 92, 311-318.

[37] Meschke G., Ninic´ J., Stascheit J., & Alsahly A. (2013). Parallelized computational modeling of pile-soil interactions in mechanized tunneling. Engineering Structures, 47, 35-44.

[38] Neuner M., Cordes T., Drexel M., & Hofstetter G. (2017a). Time dependent material properties of shotcrete: Experimental and numerical study. Materials, 10, 1067.

[39] Neuner M., Gamnitzer P., & Hofstetter G. (2017b). An extended damage plasticity model for shotcrete: Formulation and comparison with other shotcrete models. Materials, 10, 82.

[40] Neuner M., Gamnitzer P., & Hofstetter G. (2020a). A 3D gradient- enhanced micropolar damage-plasticity approach for modeling quasibrittle failure of cohesive-frictional materials. Computers & Structures, 239, 106332.

[41] Neuner M., Schreter M., Gamnitzer P., & Hofstetter G. (2020b). On discrepancies between time-dependent nonlinear 3D and 2D finite element simulations of deep tunnel advance: A numerical study on the Brenner Base Tunnel. Computers and Geotechnics, 119, 103355.

[42] Neuner M., Schreter M., & Hofstetter G. (2018). Comparative investigation of constitutive models for shotcrete based on numerical simulations of deep tunnel advance. In Numerical Methods in Geotechnical Engineering:9th European Conference on Numerical Methods in Geotechnical Engineering (pp. 103-108). CRC Press Taylor & Francis Group.

[43] Neuner M., Schreter M., Unteregger D., & Hofstetter G. (2017c). Influence of the constitutive model for shotcrete on the predicted structural behavior of the shotcrete shell of a deep tunnel. Materials, 10, 577.

[44] Ninic´ J., Bui H.-G., Koch C., & Meschke G. (2019). Computationally efficient simulation in urban mechanized tunneling based on multilevel BIM models. Journal of Computing in Civil Engineering, 33, 04019007.

[45] Saad Y. (2003). Iterative methods for sparse linear systems. SIAM.

[46] Saad Y., & Schultz M. H. (1986). GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific & Statistical Computing, 7, 856-869.

[47] Schreter M., Neuner M., & Hofstetter G. (2018a). Evaluation of the implicit gradient-enhanced regularization of a damage-plasticity rock model. Applied Sciences, 8, 1004.

[48] Schreter M., Neuner M., Unteregger D., & Hofstetter G. (2018b). On the importance of advanced constitutive models in finite element simulations of deep tunnel advance. Tunnelling and Underground Space Technology, 80, 103-113.

[49] Schweiger H., Schuller H., & Po¨ ttler R. (1997). Some remarks on 2D- models for numerical simulation of underground constructions with complex cross sections. In Proceedings of the 9th International Conference of Computer Methods and Advances in Geomechanics. Wuhan (pp. 103-113).

[50] Shahin H. M., Nakai T., & Okuno T. (2019). Numerical study on 3D effect and practical design in shield tunneling. Underground Space, 4, 201-209.

[51] Simo J. C., Kennedy J. G., & Govindjee S. (1988). Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms. International Journal for Numerical Methods in Engineering, 26, 2161-2185.

[52] Smaniotto S., Neuner M., Cordes T., & Hofstetter G. (2022a). Experimental study of a wet mix shotcrete for primary tunnel linings—Part II: Shrinkage, creep, thermal and hygral behavior of shotcrete. Engineering Fracture Mechanics, 267, 108410.

[53] Smaniotto S., Neuner M., Dummer A., Cordes T., & Hofstetter G. (2022b). Experimental study of a wet mix shotcrete for primary tunnel linings—Part I: Evolution of strength, stiffness and ductility. Engineering Fracture Mechanics, 267, 108409.

[54] Svoboda T., & Masin D. (2011). Comparison of displacement field predicted by 2D and 3D finite element modelling of shallow NATM tunnels in clays. Geotechnik, 34, 115-126.

[55] Tezduyar T. E. (2001). Finite element methods for flow problems with moving boundaries and interfaces. Archives of Computational Methods in Engineering, 8, 83-130.

[56] The Open MPI Project (2022). Open MPI Web page.

[57] Unteregger D., Fuchs B., & Hofstetter G. (2015). A damage plasticity model for different types of intact rock. International Journal of Rock Mechanics and Mining Sciences, 80, 402-411.

[58] Valentini B., & Hofstetter G. (2013). Review and enhancement of 3D concrete models for large-scale numerical simulations of concrete structures. International Journal for Numerical and Analytical Methods in Geomechanics, 37, 221-246.

[59] Vaneˇk P., Mandel J., & Brezina M. (1996). Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. Computing, 56, 179-196.

[60] Vitali O. P., Celestino T. B., & Bobet A. (2018). 3D finite element modelling optimization for deep tunnels with material nonlinearity. Underground Space, 3, 125-139.

[61] Vitali O. P., Celestino T. B., & Bobet A. (2022). Construction strategies for a NATM tunnel in Sa˜o Paulo, Brazil, in residual soil. Underground Space, 7, 1-18.

[62] Volderauer C., Marcher T., & Galler R. (2012). 3-dimensional numerical calculations considering geotechnical measurement data. BHM Bergund Hu¨ ttenma¨ nnische Monatshefte, 12, 451-458.

[63] Wall W. A., Gerstenberger A., Gamnitzer P., Fo¨ rster C., & Ramm E. (2006). Large deformation fluid-structure interaction - advances in ALE methods and new fixed grid approaches. In Fluid-structure Interaction (pp. 195-232). Berlin, Heidelberg: Springer.

[64] Walpole L. (1984). Fourth-rank tensors of the thirty-two crystal classes: multiplication tables. Proceedings of the Royal Society of London. Mathematical and Physical Sciences, 391, 149-179.

[65] Weifner T., & Bergmeister K. (2020). 3D simulations for the Brenner Base Tunnel considering interaction effects. In Tunnels and Underground Cities: Engineering and Innovation meet Archaeology, Architecture and Art (pp. 3355-3364). CRC Press.

[66] Willam K., & Warnke E. (1975). Constitutive model for the triaxial behaviour of concrete. Seminar on Concrete Structure Subjected to Triaxial Stresses. Bergamo, Italy (vol. 19, pp. 1-30)..

[67] Zhao K., Bonini M., Debernardi D., Janutolo M., Barla G., & Chen G. (2015). Computational modelling of the mechanised excavation of deep tunnels in weak rock. Computers and Geotechnics, 66, 158-171.

[68] Zhao K., Janutolo M., & Barla G. (2012). A completely 3D model for the simulation of mechanized tunnel excavation. Rock Mechanics and Rock Engineering, 45, 475-497.

[69] Zhao K., Janutolo M., Barla G., & Chen G. (2014). 3D simulation of TBM excavation in brittle rock associated with fault zones: The Brenner Exploratory Tunnel case. Engineering Geology, 181, 93-111.