Linearization of Drucker-Prager Yield Criterion for Axisymmetric Problems: Implementation in Lower-Bound Limit Analysis
Publication: International Journal of Geomechanics
Volume 13, Issue 2
Abstract
The linearization of the Drucker-Prager yield criterion associated with an axisymmetric problem has been achieved by simulating a sphere with the truncated icosahedron with 32 faces and 60 vertices. On this basis, a numerical formulation has been proposed for solving an axisymmetric stability problem with the usage of the lower-bound limit analysis, finite elements, and linear optimization. To compare the results, the linearization of the Mohr-Coulomb yield criterion, by replacing the three cones with interior polyhedron, as proposed earlier by Pastor and Turgeman for an axisymmetric problem, has also been implemented. The two formulations have been applied for determining the collapse loads for a circular footing resting on a cohesive-friction material with nonzero unit weight. The computational results are found to be quite convincing.
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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. Methods Appl. Mech. Eng., 22(1), 131–149.
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., 128(1), 38–43.
Gourvenec, S., Randolph, M., and Kingsnorth, O. (2006). “Undrained bearing capacity of square and rectangular footings.” Int. J. Geomech., 6(3), 147–157.
Hjiaj, M., Lyamin, A. V., and Sloan, S. W. (2005). “Numerical limit analysis solutions for the bearing capacity factor Nγ.” Int. J. Solids Struct., 42(5–6), 1681–1704.
Khatri, V. N., and Kumar, J. (2009). “Vertical uplift resistance of circular plate anchors in clay under undrained condition.” Comput. Geotech., 36(8), 1352–1359.
Khatri, V. N., and Kumar, J. (2010). “Stability of an unsupported vertical circular excavation in clays under undrained condition.” Comput. Geotech., 37(3), 419–424.
Kumar, J. and Ghosh, P. (2005). “Determination of Nγ for rough circular footing using the method of characteristics.” Electr. J. Geotech. Eng., 10(B) 〈http://www.ejge.com/2005/Ppr0540/Ppr0540.htm〉.
Kumar, J., and Ghosh, P. (2007). “Ultimate bearing capacity of two interfering rough strip footings.” Int. J. Geomech., 7(1), 53–62.
Kumar, J., and Khatri, V. N. (2008). “Effect of footing roughness on lower bound Nγ values.” Int. J. Geomech., 8(3), 176–187.
Kumar, J., and Khatri, V. N. (2011). “Bearing capacity factors of circular foundations for a general c-ϕ 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 Nγ.” J. Geotech. Geoenviron. Eng., 133(5), 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. (2002). “Lower bound limit analysis using non-linear programming.” Int. J. Numer. Methods Eng., 55(5), 573–611.
MATLAB 7.9 [Computer software]. Natick, MA, MathWorks.
Martin, C. M. (2004). “ABC—Analysis of bearing capacity.” 〈http://www.eng.ox.ac.uk/civil/people/cmm/software〉 (Oct. 1, 2004).
Martin, C. M. (2005). “Exact bearing capacity calculations using the method of characteristics.” Proc., 11th Int. Association for Computer Methods and Advances in Geomechanics (IACMAG), Vol. 4, Torino, Italy, 441–450.
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.
Schweiger, H. F. (1994). “On the use of Drucker-Prager failure criteria for earth pressure problems.” Comput. Geotech., 16(3), 223–246.
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. Methods Appl. Mech. Eng., 127(1–4), 293–314.
Ukritchon, B., Whittle, A. W., and Klangvijit, C. (2003). “Calculation of bearing capacity factor Nγ using numerical limit analysis.” J. Geotech. Geoenviron. Eng., 129(5), 468–474.
Yamamoto, N., Randolph, M. F., and Einav, I. (2008). “Simple formulas for the response of shallow foundations on compressible sands.” Int. J. Geomech., 8(4), 230–239.
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Information
Published In
International Journal of Geomechanics
Volume 13 • Issue 2 • April 2013
Pages: 153 - 161
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Oct 12, 2010
Accepted: Dec 14, 2011
Published online: Dec 17, 2011
Published in print: Apr 1, 2013
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