Modelação 2.5D MEF-PML de vibrações induzidas em túneis
DOI:
https://doi.org/10.24849/j.geot.2018.144.08Palavras-chave:
Modelação numérica, 2.5D MEF-PML, propagação de ondas, interacção túnel-maciçoResumo
A simulação e o estudo da problemática das vibrações induzidas pelo tráfego ferroviário em túneis é uma tarefa difícil e complexa. O carácter semi-indefinido do domínio circundante do túnel associado às características tridimensionais do problema são os principais responsáveis pela complexidade do problema. Uma solução eficiente e precisa para a simulação do comportamento dinâmico de estruturas muito longas, como por exemplo, vias férreas ou túneis, é proposta utilizando técnicas 2.5D no contexto do método dos elementos finitos, e adoptando PML’s para o tratamento das fronteiras devido à truncatura do domínio. Dado o recurso a uma abordagem 2.5D MEF-PML não ser usual, as equações do 2.5D PML são derivadas, salientando-se a compatibilidade com o 2.5D MEF. Após essa breve descrição do modelo, exemplos de validação são apresentados, demonstrando a precisão do modelo. Por último, um estudo paramétrico é desenvolvido por forma a avaliar a influência de algumas propriedades do túnel e do solo, nas vibrações induzidas à superfície do maciço.
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Referências
Alves Costa, P., et al., A 2.5D finite element model for simulation of unbounded domains under dynamic loading, in 7th European Conference on Numerical Methods in Geotechnical Engineering, T. Benz and S. Nordal, Editors. 2010: Trondheim. p. 782-790.
Alves Costa, P., et al., Influence of soil non-linearity on the dynamic response of high-speed railway tracks. Soil Dynamics and Earthquake Engineering, 2010. 30(4): p. 221-235.
Alves Costa, P., Moving loads on the ground: a 2.5D transformed finite element code for train- track-soil interaction, in (Relatório interno). 2008, FEUP: Porto.
Alves Costa, P., R. Calçada, and A. Cardoso, Track–ground vibrations induced by railway traffic: In-situ measurements and validation of a 2.5D FEM-BEM model. Soil Dynamics and Earthquake Engineering, 2012a. 32: p. 111-128.
Alves Costa, P., R. Calçada, and A. Silva Cardoso, Ballast mats for the reduction of railway traffic vibrations. Numerical study. Soil Dynamics and Earthquake Engineering, 2012b. 42(0): p. 137-150.
Alves Costa, P., R. Calçada, and A. Silva Cardoso, Track-ground vibrations induced by railway traffic, in Applications of Computational Mechanics in Geotechnical Engineering,, L. Sousa, et al., Editors. 2012c, Balkema. p. 125-159.
Amado Mendes, P., L. Godinho, and P. Alves Costa, 2.5D modeling of soil-structure interaction using a coupled MFS-FEM formulation, in 11th World Congress on Computational Mechanics (WCCM XI), E. Oñate, J. Oliver, and Huerta, Editors. 2014: Barcelona.
Barbosa, J.M.d.O., J. Park, and E. Kausel, Perfectly matched layers in the thin layer method. Computer Methods in Applied Mechanics and Engineering, 2012. 217–220(0): p. 262-274.
Basu, U. and A.K. Chopra, Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation. Computer Methods in Applied Mechanics and Engineering, 2003. 192: p. 1337-1375.
Basu, U., Explicit finite element perfectly matched layer for transient three-dimensional elastic waves. International Journal for Numerical Methods in Engineering, 2009. 77: p. 151-176.
Berenger, J., A perfectly matched layer for absorption of electromagnetic waves. Journal of computational physics, 1994. 114: p. 185-200.
Bian, X., E. Zeng, and Y. Chen, Ground motions generated by harmonic loads moving in subway tunnel, in Proceedings of the Third International Symposium on Environmental Vibrations: Prediction, Monitoring, Mitigation and Evaluation. ISEV 2007. 2007: Taipei, Taiwan.
Bian, X., W. Jin, and H. Jiang, Ground-borne vibrations due to dynamic loading from moving trains in subway tunnels. Journal of Zhejiang University - Science A (Applied Physics & Engineering), 2012. 13(11): p. 870-876.
Chew, W. and Q. Liu, Perfectly matched layers for elastodynamics: a new absorbing boundary condition. Journal of Computational Acoustics, 1996. 4: p. 341-359.
Clouteau, D., et al., Free field vibrations due to dynamic loading on a tunnel embedded in a stratified medium. Journal of Sound and Vibration, 2005. 283(1-2): p. 173-199.
Domínguez, J., Boundary Elements in Dynamics. 1993: Elsevier Applied Science.
Forrest, J. and H. Hunt, A three-dimensional tunnel model for calculation of train-induced ground vibration. Journal of Sound and Vibration, 2006. 294: p. 678-705.
François, S., et al., A 2.5D coupled FE–BE methodology for the dynamic interaction between longitudinally invariant structures and a layered halfspace. Computer Methods in Applied Mechanics and Engineering, 2010. 199(23-24): p. 1536-1548.
François, S., et al., A 2.5D displacement-based PML for elastodynamic wave propagation, in IV European Conference on Computational Mechanics 2010: Paris, France.
François, S., Nonlinear modelling of the response of structures due to ground vibrations, in Departement Burgerlijke Bouwkunde. 2008, Katholieke Universiteit Leuven: Leuven.
Galvín, P. and J. Domínguez, Experimental and numerical analyses of vibrations induced by high- speed trains on Córdoba-Málaga line. Soil Dynamics and Earthquake Engineering, 2009. 29(4): p. 641-657.
Galvín, P., et al., A 2.5D coupled FE-BE model for the prediction of railway induced vibrations. Soil Dynamics and Earthquake Engineering, 2010. 30(12): p. 1500-1512.
Godinho, L., et al., A coupled MFS–FEM model for 2-D dynamic soil–structure interaction in the frequency domain. Computers & Structures, 2013. 129(0): p. 74-85.
Grundmann, H. and J. Dinkel, Moving oscillating loads acting on a dam over a layered half space, in Wave 2000, C. Schmid, Editor. 2000, Balkema: Bochum. p. 53-70.
Gupta, S., et al., A comparison of two numerical models for the prediction of vibrations from underground railway traffic. Soil Dynamics and Earthquake Engineering, 2007. 27(7): p. 608-624.
Gupta, S., et al., Influence of tunnel and soil parameters on vibrations from underground railways. Journal of Sound and Vibration, 2009. 327: p. 70-91.
Gupta, S., et al., Numerical modelling of vibrations from a Thalys high speed train in the Groene Hart tunnel Soil Dynamics and Earthquake Engineering, 2010. 30(3): p. 82-97.
Hussein, M. and H. Hunt, A computationally efficient software application for calculating vibration from underground railways. Journal of Physics Conference Series, 2009. 181(1): p. 1-6.
Hussein, M. and H. Hunt, A numerical model for calculating vibration from a railway tunnel embedded in a full-space. Journal of Sound and Vibration, 2007. 305(3): p. 401-431.
Hwang, R. and J. Lysmer, Response of buried structures to travelling waves. Journal of Geotechnical Engineering Division, 1981. 107(2): p. 183-200.
Johnson, S., Notes on Perfectly Matched Layers (PMLs), L. notes, Editor. 2010, Massachusetts Institute of Technology.
Jones, S. and H. Hunt, Predicting surface vibration from underground railways through inhomogeneous soil. Journal of Sound and Vibration, 2012. 331: p. 2055-2069.
Jones, S. and H. Hunt, Voids at the tunnel–soil interface for calculation of ground vibration from underground railways. Journal of Sound and Vibration, 2011. 330: p. 245-270.
Kausel, E. and J.M. de Oliveira Barbosa, PMLs: A direct approach. International Journal for Numerical Methods in Engineering, 2012. 90(3): p. 343-352.
Khani, M., Dynamic Soil-Structure Interaction Analysis Using the Scaled Boundary Finite Elements Method in School of Civil and Environmental Engineering. 2007, University of New South-Wales: Sidney.
Kuo, K.A., H. Hunt, and M. Hussein, The effect of a twin tunnel on the propagation of ground vibration from an underground railway. Journal of Sound and Vibration, 2011. 330: p. 6203-6222.
Liu, G. and S. Jerry, A non-reflecting boundary for analyzing wave propagation using the finite element method. Finite Elements in Analysis and Design, 2003. 39(5-6): p. 403-417.
Lombaert, G. and G. Degrande, Ground-borne vibration due to static and dynamic axle loads of InterCity and high-speed trains. Journal of Sound and Vibration, 2009. 319(3-5): p. 1036-1066.
Lopes, P., et al., Análise numérica de vibrações induzidas por tráfego ferroviário em túneis baseada em modelos 2.5D, in 12o Congresso Nacional de Geotecnia, G. Correia, Editor. 2010: Guimarães. p. CD-ROM publication.
Lopes, P., et al., Modeling of infinite structures by 2.5D FEM-PML. Application to the simulation of vibrations induced in tunnels, in Railways 2012. The First International Conference o Railway Technology: Research, Development and Maintenance, J. Pombo, Editor. 2012: Tenerife, Canarias.
Lopes, P., et al., Numerical Modeling of Vibrations Induced in Tunnels: A 2.5D FEM-PML Approach, in Traffic Induced Environmental Vibrations and Controls: Theory and
Application, H. Xia and R. Calçada, Editors. 2013, Nova. p. 133-166.
Lysmer, J. and R.L. Kuhlemeyer, Finite dynamic model for infinite media. Journal of Engineering Mechanics Division, 1969. 95: p. 859-877.
Muller, K., Dreidimensionale dynamische Tunnel-Halbraum-Interaktion, in Lehrstuhl fur Baumechanik. 2007, Technische Universitat Munchen: Munchen.
Rieckh, G., et al., A 2.5D-Fourier-BEM model for vibrations in a tunnel running through layered anisotropic soil. Engineering Analysis With Boundary Elements, 2012. 36: p. 960-967.
Sheng, X., C. Jones, and D. Thompson, Prediction of ground vibration from trains using wavenumber finite and boundary element method. Journal of Sound and Vibration, 2006. 293: p. 575-586.
Sommerfeld, A., Partial Differential Equations in Physics. 1949, New York: Academic Press. Tadeu, A. and E. Kausel, Green’s functions for two-and-a-half-dimensional elastodynamic problems. Journal of Engineering Mechanics, 2000. 126(10): p. 1093–1096.
Wolf, J.P., The Scaled Boundary Finite Element Method. 2003: Wiley. Yang, Y. and H. Hung, Soil Vibrations Caused by Underground Moving Trains. Journal of
Geotechnical and Geoenvironmental Engineering, 2008. 134(11): p. 1633-1644.
Yang, Y., S. Kuo, and H. Hung, Frequency independent infinite elements for analyzing semi-infinite problems. International Journal for Numerical Methods in Engineering, 1996. 39: p. 3553-3569.
Yang, Y.B. and H.H. Hung, A 2.5D finite/infinite element approach for modelling visco-elastic body subjected to moving loads. International Journal for Numerical Methods in Engineering, 2001. 51: p. 1317-1336.
Yaseri, A., M.H. Bazyar, and N. Hataf, 3D coupled scaled boundary finite-element/finite-element analysis of ground vibrations induced by underground train movement. Computers and eotechnics, 2014. 60(0): p. 1-8.
