Análise limite recorrendo ao critério de rotura de Matsuoka-Nakai estendido em condições de deformação plana
DOI:
https://doi.org/10.14195/2184-8394_157_2Palavras-chave:
limit analysis, critério de Matsuoka-Nakai estendido, estado plano de deformação, método de direcção alternada de multiplicadores (MDAM)Resumo
Este artigo apresenta a implementação do critério de rotura de Matsuoka-Nakai Estendido numa formulação de Análise Limite, em condições de deformação plana. A abordagem apresentada é baseada num modelo misto de elementos finitos de três campos e no algoritmo de otimização que se designa por Método de Direção Alternada de Multiplicadores. Para esse propósito, é estabelecida e explorada uma equivalência entre o critério clássico de Mohr-Coulomb e o critério de Matsuoka-Nakai estendido. São apresentadas três aplicações
numéricas para testar e ilustrar as capacidades desta abordagem. Os resultados são confrontados com soluções de outros autores ou com dados experimentais.
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Referências
Antão, A., Vicente da Silva, M., Guerra, N., e Delgado, R. (2012). An upper bound-based solution
for the shape factors of bearing capacity of footings under drained conditions using a parallelized mixed f.e. formulation with quadratic velocity fields. Computers and Geotechnics, 41, pp. 23-35. https://doi.org/10.1016/j.compgeo.2011.11.003.
Boyd, S., Parikh, N., Chu, E., Peleato, B., e Eckstein, J. (2011). Distributed optimization and statistical learning via the alternating direction method of multipliers. Foundations and Trends in
Machine Learning, 3(1), pp. 1-122. http://dx.doi.org/10.1561/2200000016.
Caquot, A. e Kerisel, J. (1953). Sur le terme de surface dans le calcul des fondations en milieu pulverulent. Em Proceedings of the 3rd International Conference on Soil Mechanics and Foundation Engineering, vol. 1, pp. 336-337, Zurich.
CEN (2004). EN 1997-1: Eurocode 7: Geotechnical Design “ Part 1: General Rules. European
Committee for Standardization, Brussels, Belgium, 2nd ed. edição.
Green, G. E. e Bishop, A.W. (1969). A note on the drained strength of sand under generalized strain conditions. Géotechnique, 19(1), pp. 144-149. https://doi.org/10.1680/geot.1969.19.1.144.
Griffiths, D. V. e Huang, J. (2009). Observations on the extended matsuoka-nakai failure criterion.
International Journal for Numerical and Analytical Methods in Geomechanics, 33(17), pp.
“1905. https://doi.org/10.1002/nag.810.
Hanna, A. M. (1981a). Experimental study on footings in layered soil. Journal of the Geotechnical
Engineering Division, 107(GT8), pp. 1113-1126. https://doi.org/10.1061/AJGEB6.0001178.
Hanna, A. M. (1981b). Foundations on strong sand overlying weak sand. Journal of the Geotechnical Engineering Division, 107(GT7), pp. 915-927. https://doi.org/10.1061/AJGEB6.0001169.
Hansen, J. B. (1970). A Revised and Extended Formula for Bearing Capacity, vol. 28 de Bulletin of
The Danish Geotechnical Institute, pp. 5-11. Danish Geotechnical Institute.
Hjiaj, M., Lyamin, A., e Sloan, S. (2005). Numerical limit analysis solutions for the bearing capacity
factor Nγ . International Journal of Solids and Structures, 42(5-6), pp. 1681-1704.
https://doi.org/10.1016/j.ijsolstr.2004.08.002.
Kumar, J. e Samui, P. (2006). Stability determination for layered soil slopes using the upper bound
limit analysis. Geotechnical & Geological Engineering, 24(6), pp. 1803-1819.
https://doi.org/10.1007/s10706-006-7172-1.
Lade, P. V. e Duncan, J. M. (1975). Elastoplastic stress-strain theory for cohesionless soil. Journal
of the Geotechnical Engineering Division, 101(10), pp. 1037-1053.
https://doi.org/10.1061/AJGEB6.0000204.
Lade, P. V. e Musante, H. M. (1978). Three-dimensional behavior of remolded clay. Journal of
the Geotechnical Engineering Division, 104(2), pp. 193-209.
https://doi.org/10.1061/AJGEB6.0000581.
Lagioia, R. e Panteghini, A. (2017). Accounting for specific failure criteria in the slip-line method
for plane strain problems. Géotechnique Letters, 7(2), pp. 184-189.
https://doi.org/10.1680/jgele.17.00014.
Martin, C. (2005). Exact bearing capacity calculations using the method of characteristics. Proc.
th Int. Conf. of IACMAG Turin.
Matsuoka, H., Hoshikawa, T., e Ueno, K. (1990). A general failure criterion and stress-strain
relation for granular materials to metals. Soils and Foundations, 30(2), pp. 119-127.
https://doi.org/10.3208/sandf1972.30.2_119.
Matsuoka, H. e Nakai, T. (1974). Stress-deformation and strength characteristics of soil under three different principal stresses. Proc. JSCE, 1974(232), pp. 59-70.
https://doi.org/10.2208/jscej1969.1974.232_59.
Matsuoka, H. e Nakai, T. (1985). Relatioship among Tresca, Mises, Mohr-Coulomb and Matsuoka-
Nakai failure criteria. Soils and Foundations, 25(4), pp. 123-128.
https://doi.org/10.3208/sandf1972.25.4_123.
Meyerhof, G. G. (1963). Some recent research on the bearing capacity of foundations. Canadian
Geotechnical Journal, 1(1), pp. 16-26. https://doi.org/10.1139/t63-003.
Meyerhof, G. G. e Hanna, A. M. (1978). Ultimate bearing capacity of foundations on layered soils
under inclined load. Canadian Geotechnical Journal, 15(4), pp. 565-572.
https://doi.org/10.1139/t78-060.
Potts, D. M. e Gens, A. (1984). The effect of the plastic potential in boundary value problems
involving plane strain deformation. International Journal for Numerical and Analytical Methods
in Geomechanics, 8(3), pp. 259-286. https://doi.org/10.1002/nag.1610080305.
Salgado, R. (2006). The engineering of foundations. McGraw-Hill Education (Europe).
Smith, C. C. (2005). Complete limiting stress solutions for the bearing capacity of strip footings on
a mohr-coulomb soil. Géotechnique, 55(8), pp. 607-612.
https://doi.org/10.1680/geot.2005.55.8.607.
Terzaghi, K. (1943). Theoretical soil mechanics. Wiley, New York.
https://doi.org/10.1002/9780470172766.
Vicente da Silva, M. e Antão, A. (2008). Upper bound limit analysis with a parallel element formulation. International Journal of Solids and Structures, 45(22-23), pp. 5788-5804.
https://doi.org/10.1016/j.ijsolstr.2008.06.012.
Vicente da Silva, M. e Antão, A. N. (2007). A non-linear programming method approach for upper
bound limit analysis. International Journal for Numerical Methods in Engineering, 72(10), pp.
“1218. https://doi.org/10.1002/nme.2061.
Vicente da Silva, M. e Antão, A. N. (2012). A novel augmented lagrangian-based formulation for
upper-bound limit analysis. International Journal For Numerical Methods in Engineering, 89(12),
pp. 1471-1496. https://doi.org/10.1002/nme.3294.
Vicente da Silva, M., Deusdado, N., e Antão, A. (2020). Lower and upper bound limit analysis via
the alternating direction method of multipliers. Computers and Geotechnics, 124, pp. 103571.
