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Studia Geotechnica et Mechanica

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Shape optimization of road tunnel cross-section by simulated annealing

Maciej Sobótka
  • Faculty of Civil Engineering, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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/ Michał Pachnicz
  • Faculty of Civil Engineering, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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Published Online: 2016-07-15 | DOI: https://doi.org/10.1515/sgem-2016-0018


The paper concerns shape optimization of a tunnel excavation cross-section. The study incorporates optimization procedure of the simulated annealing (SA). The form of a cost function derives from the energetic optimality condition, formulated in the authors’ previous papers. The utilized algorithm takes advantage of the optimization procedure already published by the authors. Unlike other approaches presented in literature, the one introduced in this paper takes into consideration a practical requirement of preserving fixed clearance gauge. Itasca Flac software is utilized in numerical examples. The optimal excavation shapes are determined for five different in situ stress ratios. This factor significantly affects the optimal topology of excavation. The resulting shapes are elongated in the direction of a principal stress greater value. Moreover, the obtained optimal shapes have smooth contours circumscribing the gauge.

Keywords: simulated annealing; underground excavation; shape optimization; linear elasticity; energy of volumetric strain


  • [1] Kawa M., Różański A., Sobótka M., A verification of shape optimization procedures of tunnel underground excavations, Górnictwo i Geoinżynieria, 2011, Book 2, 535–541, (in Polish).Google Scholar

  • [2] Ren G., Smith J.V., Tang J.W., Xie Y.M., Underground excavation shape optimization using an evolutionary procedure, Computers and Geotechnics, 2005, No. 32, 122–132.CrossrefGoogle Scholar

  • [3] Różański A., Sobótka M., A procedure of underground excavations shape optimization, Górnictwo i Geoinżynieria, 2009, Book 1, 519–529, (in Polish).Google Scholar

  • [4] Sobótka M., Łydżba D., Różański A., Shape optimization of underground excavation by simulated annealing, Studia Geotechnica et Mechanica, 2013, 35(1), 209–218.Google Scholar

  • [5] Nguyen T., Ghabraie K., Tran-Cong T., Simultaneous pattern and size optimisation of rock bolts for underground excavations, Computers and Geotechnics, 2015, 66, 264–277.Web of ScienceGoogle Scholar

  • [6] Sałustowicz A., Zarys mechaniki górotworu, Wydawnictwo Śląsk, Katowice, 1968.Google Scholar

  • [7] Xie Y.M., Steven G.P., A simple evolutionary procedure for structural optimization, Comput. Struct., 1993, No. 49(5), 885–896.CrossrefGoogle Scholar

  • [8] Xie Y.M., Steven G.P., Evolutionary structural optimization, Springer, Berlin, 1997.Google Scholar

  • [9] Kirkpatrick S., Gelatt C., Vecchi M., Optimization by simulated annealing, Science, 1983, Vol. 220, No. 4598, 671–680.Google Scholar

  • [10] Sonmez F.O., Shape optimization of 2D structures using simulated annealing, Computer Methods in Applied Mechanics and Engineering, 2007, 196, 35, 3279–3299.Google Scholar

  • [11] Sobótka M., Łydżba D., Shape Optimization of Soil-steel Structure by Simulated Annealing, Procedia Engineering, 91, 304–309.Google Scholar

  • [12] Różański A., Łydżba D., Jabłoński P., Numerical study of the size of representative volume element for linear elasticity problem, Studia Geotechnica et Mechanica, 2013, 35(2), 67–81.Google Scholar

  • [13] Różański A., Łydżba D., From digital image of microstructure to the size of representative volume element: B4C/Al composite, Studia Geotechnica et Mechanica, 2011, 33(1), 55–68.Google Scholar

  • [14] Chapman D., Metje N., Stärk A., Introduction to tunnel construction. 2010, Vol. 3. CRC Press.Google Scholar

  • [15] Rabcewicz L.V., Bemessung von Hohlraumbauten, die “Neue Österreichische Bauweise” und ihr Einfluß auf Gebirgsdruckwirkungen und Dimensionierung, Felsmechanik und Ingenieurgeologie, 1963, 1, 3–4.Google Scholar

  • [16] Shim P.Y., Manoochehri S., Generating optimal configurations in structural design using simulated annealing, International Journal for Numerical Methods in Engineering, 1997, 40(6), 1053–1069.Google Scholar

  • [17] Metropolis N. et.al., Equation of state calculation by fast computing machines, The Journal of Chemical Physics, 1953, Vol. 21, No. 6, 1087–1092.Google Scholar

  • [18] FLAC Fast Lagrangian Analysis of Continua, User’s Guide, Itasca Consulting Group Inc. Minneapolis, 2011.Google Scholar

  • [19] Majcherczyk T., Niedbalski Z., Kowalski M., 3D numerical modeling of road tunnel stabilityThe Laliki project, Archives of Mining Sciences, 2012, 57(1), 61–78.Google Scholar

About the article

Published Online: 2016-07-15

Published in Print: 2016-06-01

Citation Information: Studia Geotechnica et Mechanica, Volume 38, Issue 2, Pages 47–52, ISSN (Online) 2083-831X, DOI: https://doi.org/10.1515/sgem-2016-0018.

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© 2016 Maciej Sobótka et al., published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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