Upper-Bound Axisymmetric Limit Analysis Using the Mohr-Coulomb Yield Criterion, Finite Elements, and Linear Optimization
Publication: Journal of Engineering Mechanics
Volume 140, Issue 12
Abstract
An upper-bound limit analysis formulation has been presented for solving an axisymmetric geomechanics stability problem using the Mohr-Coulomb failure criterion in conjunction with finite elements and linear programming. The method is based on the application of the von Karman hypothesis, and it requires only nodal velocities as the basic unknown variables. The computational effort needed to solve the axisymmetric problem becomes almost the same as that required for an equivalent plane strain case. By using the proposed method, bearing capacity factors were obtained for a circular footing placed over a cohesive-frictional soil medium. Nodal velocity patterns were also examined. Necessary comparisons have also been given to examine the usefulness of the proposed formulation.
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References
Bottero, A., Negre, R., Pastor, J., and Turgeman, S. (1980). “Finite element method and limit analysis theory for soil mechanics problem.” Comput. Meth. Appl. Mech. Eng., 22(1), 131–149.
Chakraborty, D., and Kumar, J. (2013). “Solving axisymmetric stability problems by using upper bound finite elements, limit analysis, and linear optimization.” J. Eng. Mech., 06014004.
Drucker, D. C. (1953). “Limit analysis of two and three dimensional soil mechanics problems.” J. Mech. Phys. Solids, 1(4), 217–226.
Erickson, H. L., and Drescher, A. (2002). “Bearing capacity of circular footings.” J. Geotech. Geoenviron. Eng., 38–43.
FLAC 4.0 [Computer software]. Minneapolis, Itasca Consulting Group.
Haar, A., and von Karman, Th. (1909). “Zur theorie der spannungs-zustaende in plastischen und stanartigen medien.” Nachr. Akad. Wiss. Gottingen, Math. Phys. Kl., 204–218 (in German).
Hjiaj, M., Lyamin, A. V., and Sloan, S. W. (2005). “Numerical limit analysis solutions for the bearing capacity factor .” Int. J. Solids Struct., 42(5), 1681–1704.
Krabbenhøft, K., Lyamin, A. V., and Sloan, S. W. (2008). “Three-dimensional Mohr–Coulomb limit analysis using semidefinite programming.” Commun. Numer. Methods Eng., 24(11), 1107–1119.
Kumar, J., and Chakraborty, D. (2013). “Linearization of Drucker-Prager yield criterion for axisymmetric problems: Implementation in lower-bound limit analysis.” Int. J. Geomech., 153–161.
Kumar, J., Chakraborty, M., and Sahoo, J. P. (2014). “Stability of unsupported vertical circular excavations.” J. Geotech. Geoenviron. Eng., 04014028.
Kumar, J., and Khatri, V. N. (2011). “Bearing capacity factors for circular foundations for a general soil using lower bound finite elements limit analysis.” Int. J. Numer. Anal. Methods Geomech., 35(3), 393–405.
Kumar, J., and Kouzer, K. M. (2007). “Effect of footing roughness on bearing capacity factor .” J. Geotech. Geoenviron. Eng., 502–511.
Lyamin, A. V., Salgado, R., Sloan, S. W., and Prezzi, M. (2007). “Two- and three-dimensional bearing capacity of footings in sand.” Geotechnique, 57(8), 647–662.
Lyamin, A. V., and Sloan, S. W. (2002a). “Lower bound limit analysis using non-linear programming.” Int. J. Numer. Methods Eng., 55(5), 573–611.
Lyamin, A. V., and Sloan, S. W. (2002b). “Upper bound limit analysis using linear finite elements and non-linear programming.” Int. J. Numer. Anal. Methods Geomech., 26(2), 181–216.
Martin, C. M. (2004). “ABC—Analysis of bearing capacity.” 〈http://www.eng.ox.ac.uk/civil/people/cmm/software〉.
MATLAB 7.8.0 (R2009a) [Computer software]. Natick, MA, MathWorks.
Pastor, J., and Turgeman, S. (1982). “Limit analysis in axisymmetrical problems: Numerical determination of complete statical solutions.” Int. J. Mech. Sci., 24(2), 95–117.
Salgado, R., Lyamin, A. V., Sloan, S. W., and Yu, H. S. (2004). “Two- and three-dimensional bearing capacity of foundations in clay.” Geotechnique, 54(5), 297–306.
Sloan, S. W. (1988). “Lower bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech., 12(1), 61–77.
Sloan, S. W. (1989). “Upper bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech., 13(3), 263–282.
Sloan, S. W., and Kleeman, P. W. (1995). “Upper bound limit analysis using discontinuous velocity fields.” Comput. Meth. Appl. Mech. Eng., 127(1–4), 293–314.
Turgeman, S., and Pastor, J. (1982). “Limit analysis: A linear formulation of the kinematic approach for axisymmetric mechanic problems.” Int. J. Numer. Anal. Methods Geomech., 6(1), 109–128.
Ukritchon, B., Whittle, A. J., and Klangvijit, C. (2003). “Calculations of bearing capacity factor using numerical limit analyses.” J. Geotech. Geoenviron. Eng., 468–474.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 12 • December 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Mar 12, 2014
Accepted: May 5, 2014
Published online: May 28, 2014
Discussion open until: Oct 28, 2014
Published in print: Dec 1, 2014
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