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The paper deals with the problem of shape optimization of underground tunnel excavation. In the pioneering work of Sałustowicz, the elliptic shape was assumed a priori to be an optimal one and then a determination of suitable semi-axes ratio was only the question. Two cases were distinguished there: self-supporting excavation and excavation with the structural support. An evolutionary structural optimization (ESO) procedure, employed in 2005 to optimize shape of underground excavation, confirms the assumptions concerning the case of self-supporting excavations. The case of supported excavation is considered in the present work. Optimization procedure of the simulated annealing (SA) is incorporated in the study. An energetic optimality condition, formulated in the authors’ previous papers is also adopted. Itasca FLAC software is utilized in numerical examples. Four different in situ stress ratios are investigated. The numerical results obtained confirm that the optimal shape tends to be an ellipse. The semi-axes ratio demonstrates compliance with the assumptions already existing in literature.

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

[2] KAWA M., RÓŻAŃSKI A., SOBÓTKA M., A verification of shape optimization procedures of tunnel underground excavations, (in Polish), Górnictwo i Geoinżynieria, Book 2, 2011, 535-541.

[3] KIRKPATRICK S., GELATT C., VECCHI M., Optimization by simulated annealing, Science, 1983, Vol. 220, No. 4598, 1983, 671-680.

[4] METROPOLIS N. et al., Equation of state calculation by fast computing machines, The Journal of Chemical Physics, Vol. 21, No. 6, 1953, 1087-1092.

[5] REN G., SMITH J.V., TANG J.W., XIE Y.M., Underground excavation shape optimization using an evolutionary procedure, Computers and Geotechnics, No. 32, 2005, 122-132.

[6] RÓŻAŃSKI A., SOBÓTKA M., A procedure of underground excavations shape optimization, (in Polish), Górnictwo i Geoinżynieria, Book 1, 2009, 519-529.

[7] SAŁUSTOWICZ A., Zarys mechaniki górotworu, Wydawnictwo Śląsk, Katowice, 1968.

[8] XIE Y.M., STEVEN G.P., A simple evolutionary procedure for structural optimization, Comput. Struct., No. 49(5), 1993, 885-896.

[9] XIE Y.M., STEVEN G.P., Evolutionary structural optimization, Springer, Berlin, 1997.

Studia Geotechnica et Mechanica

The Journal of Wrocław University of Science and Technology and AGH University of Science and Technology

Journal Information

CiteScore 2017: 0.14

SCImago Journal Rank (SJR) 2017: 0.131
Source Normalized Impact per Paper (SNIP) 2017: 0.448

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