Geomechanics and Engineering

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Bearing capacity factor Nγ for a rough conical footing

  • Khatri, Vishwas N. (Civil Engineering Department, Indian Institute of Science) ;
  • Kumar, Jyant (Civil Engineering Department, Indian Institute of Science)
  • Received : 2008.11.18
  • Accepted : 2009.07.16
  • Published : 2009.09.25
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Abstract

The bearing capacity factor $N_{\gamma}$ is computed for a rough conical footing placed over horizontal ground surface. The axisymmetric lower bound limit analysis formulation, in combination with finite elements and linear programming, proposed recently by the authors is used in this study. The variation of $N_{\gamma}$ with cone apex angle (${\beta}$), in a range of $30^{\circ}-180^{\circ}$, is obtained for different values of ${\phi}$; where ${\phi}$ is soil friction angle. For ${\phi}<30^{\circ}$, the magnitude of $N_{\gamma}$ is found to decrease continuously with an increase in ${\beta}$ from $30^{\circ}$ to $180^{\circ}$. On the other hand, for ${\phi}>30^{\circ}$, the minimum magnitude of $N_{\gamma}$ is found to occur generally between ${\beta}=120^{\circ}$ and ${\beta}=150^{\circ}$. In all the cases, it is noticed that the magnitude of $N_{\gamma}$ becomes maximum for ${\beta}=30^{\circ}$. For a given diameter of the cone, the area of the plastic zone reduces generally with an increase in ${\beta}$. The obtained values of $N_{\gamma}$ are found to compare quite well with those available in literature.

Keywords

References

  1. Bolton, M.D. and Lau, C.K. (1993), "Vertical bearing capacity factors for circular and strip footings on Mohr-Coulomb soil", Can. Geotech. J., 30(6), 1024-1033. https://doi.org/10.1139/t93-099
  2. Bottero, A., Negre, R., Pastor, J. and Turgeman, S. (1980), "Finite element method and limit analysis theory for soil mechanics problem", Comput. Method. Appl. M., 22(1), 131-149. https://doi.org/10.1016/0045-7825(80)90055-9
  3. Cassidy, M.J. and Houlsby, G.T. (2002), "Vertical bearing capacity factors for conical footings on sand", Geotechnique, 52(9), 687-692. https://doi.org/10.1680/geot.2002.52.9.687
  4. Cox, A.D. (1962), "Axially symmetric plastic deformation in soils-II. Indentation of Ponderable soils", Int. J. Mech. Sci., 4, 371-380. https://doi.org/10.1016/S0020-7403(62)80024-1
  5. Erickson, H.L. and Drescher, A. (2002), "Bearing capacity of circular footings", J. Geotech. Geoenviron., 128(1), 38-43. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:1(38)
  6. Frydman, S. and Burd, H.J. (1997), "Numerical studies of bearing capacity factor $N_{\gamma}$", J. Geotech. Geoenviron., 123(1), 20-29. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:1(20)
  7. Griffiths, D.V. (1982), "Computations of bearing capacity factors using finite elements", Geotechnique, 32(3), 195-202. https://doi.org/10.1680/geot.1982.32.3.195
  8. Hjiaj, M., Lyamin, A.V. and Sloan, S.W. (2005), "Numerical limit analysis solutions for the bearing capacity factor $N_{\gamma}$ ", Int. J. Solids Struct., 42(5-6), 1681-1704. https://doi.org/10.1016/j.ijsolstr.2004.08.002
  9. Krabbenhøft, K., Lyamin, A.V. and Sloan, S.W. (2008), "Three-dimensional Mohr-Coulomb limit analysis using semi-definite programming", Commun. Numer. Meth. En., 24(11), 1107-1119.
  10. Kumar, J. (2003), "$N_{\gamma}$ for rough strip footing using the method of characteristics", Can. Geotech. J., 40(3), 669-674. https://doi.org/10.1139/t03-009
  11. Kumar, J. (2009), "The variation of $N_{\gamma}$ with footing roughness using the method of characteristics", Int. J. Numer. Anal. Met. Geomech., 33(2), 275-284. https://doi.org/10.1002/nag.716
  12. Kumar, J. and Kouzer, K.M. (2007), "Effect of footing roughness on bearing capacity factor $N_{\gamma}$", J. Geotech. Geoenviron., 133(5), 502-511. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:5(502)
  13. Kumar, J. and Khatri, V.N. (2008), "Effect of footing roughness on lower bound $N_{\gamma}$ values", Int. J. Geomech., 8(3), 176-187. https://doi.org/10.1061/(ASCE)1532-3641(2008)8:3(176)
  14. Kumar, J. and Khatri, V.N. (2009), "Bearing capacity factors of circular foundations for a general $c-{\varphi}$ soil using lower bound finite element limit analysis", Int. J. Numer. Anal. Met.
  15. Khatri, V.N. and Kumar, J. (2009), "Bearing capacity factor Nc under ${\varphi}$ = 0 condition for piles in clays", Int. J. Numer. Anal. Met. Geomech., 33(9), 1203-1225. https://doi.org/10.1002/nag.763
  16. Larkin, L.A. (1968), "Theoretical bearing capacity of very shallow footings", J. Soil Mech. Found. Engng. Div., ASCE, 94(6), 1347-1357.
  17. Lyamin, A.V. and Sloan, S.W. (2002), "Lower bound limit analysis using non-linear programming", Int. J. Numer. Meth. Eng., 55, 573-611. https://doi.org/10.1002/nme.511
  18. 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. https://doi.org/10.1680/geot.2007.57.8.647
  19. Martin, C.M. (2004), ABC-Analysis of Bearing Capacity. Available online from www-civil.eng.ox.ac.uk/people/cmm/software/abc 2004.
  20. Martin, C.M. (2005), "Exact bearing capacity calculations using the method of characteristics", Proceedings of the 11th IACMAC, Torino, June, 441-450.
  21. Sloan, S.W. (1988), "Lower bound limit analysis using finite elements and linear programming", Int. J. Numer. Anal. Met., 12, 61-77. https://doi.org/10.1002/nag.1610120105
  22. Sloan, S.W. and Kleeman, P.W. (1995), "Upper bound limit analysis using discontinuous velocity fields", Comput. Method. Appl. M., 127(1), 293-314. https://doi.org/10.1016/0045-7825(95)00868-1
  23. Ukritchon, B. (1996), Evaluation of numerical limit analyses by finite elements and linear programming, M.Sc. thesis, Massachusetts Institute of Technology.
  24. Ukritchon, B., Whittle, A.W. and Klangvijit, C. (2003), "Calculation of bearing capacity factor$N_{\gamma}$ using numerical limit analysis", J. Geotech. Geoenviron., ASCE, 129(7), 468-474. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:6(468)

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