Bearing Capacity of Shallow Circular and Strip Foundation Resting on Two Layered Clays

  • Prateek Kumar
  • Manash ChakrabortyEmail author
Conference paper
Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 55)


By using the lower and upper bound limit analysis in conjunction with finite elements and nonlinear optimization undrained bearing capacity of rough circular and strip foundation resting on two layered clayey soil is computed. The circular and the strip foundation are analyzed by assuming the axisymmetric and the plane strain condition, respectively. The clay is assumed to follow Mohr–Coulomb yield criteria and an associated flow rule. Results are provided for different (i) t/b ratio and (ii) cu1/cu2 ratio; where, t = top layer thickness, b = diameter/width of the foundation, and cu1 and cu2 refers to the undrained cohesion of the top and bottom layers, respectively. The results indicate that there is an optimum t/b ratio beyond which the bearing capacity remains the same. The magnitude of the optimum t/b ratio depends on cu1/cu2 ratio and the type of the foundation. For the same cu1/cu2 ratio, the optimum t/b ratio for the circular foundation is less in comparison to the strip foundation. The obtained numerical solutions are in good agreement with the previously available literatures. Failure patterns and nodal velocity contour are provided for a few cases.


Bearing capacity Circular foundation Limit analysis Layered clay Strip foundation 



The corresponding author acknowledges the support of “Department of Science and Technology (DST), Government of India” under grant number DST/INSPIRE/04/2016/001692.


  1. 1.
    Reddy AS, Srinivasan RJ (1967) Bearing capacity of footings on layered clays. J. Soil Mech. Found. Div., ASCE 93, SM2, 83-99Google Scholar
  2. 2.
    Brown JD, Meyerhof GG (1969) An experimental study of ultimate bearing capacity of layered clay foundations. In: Proceedings of 7th international conference on soil mechanics and foundation engineering, Sociedad Mexicana de Mecanica de Suelos, Mexico City, 45–51Google Scholar
  3. 3.
    Chen WF (1975) Limit analysis and soil plasticity. Elsevier, AmsterdamzbMATHGoogle Scholar
  4. 4.
    Meyerhof GG, Hanna AM (1978) Ultimate bearing capacity of foundations on layered soils under inclined load. Can Geotech J 15:565–572CrossRefGoogle Scholar
  5. 5.
    Georgiadis M, Michalopoulos AP (1985) Bearing capacity of gravity bases on layered soil. J. Geotech. Eng. 111:712–729CrossRefGoogle Scholar
  6. 6.
    Merifield R, Sloan SW, Yu HS (1999) Rigorous solutions for the bearing capacity of two-layered clay soils. Geotechnique 49:471–490CrossRefGoogle Scholar
  7. 7.
    Michalowski R (2002) Collapse loads over two-layer clay foundation soils. Soils Found 42:1–7CrossRefGoogle Scholar
  8. 8.
    Kuo YL, Jaksa M, Lyamin A, Kaggwa WS (2008) ANN-based model for predicting the bearing capacity of strip footing on multi-layered cohesive soil. Computers and Geotechnics. 36. Scholar
  9. 9.
    Benmebarek S, Benmoussa S, Belounar L, Benmebarek N (2012) Bearing capacity of shallow foundation on two clay layers by numerical approach. Geotech Geol Eng 30. Scholar
  10. 10.
    Ahmadi MM, Kouchaki BM (2016) New and simple equations for ultimate bearing capacity of strip footings on two-layered clays: numerical study. Int J Geomech 16(4):06015014CrossRefGoogle Scholar
  11. 11.
    Sloan SW (1988) Lower bound limit analysis using finite elements and linear programming. Int. J. Numer. Anal. Methods Geomech. 12:61–77CrossRefGoogle Scholar
  12. 12.
    Sloan SW, Kleeman PW (1995) Upper bound limit analysis using discontinuous velocity fields. Comp. Methods Applied Mech. Eng. 127(1):293–314CrossRefGoogle Scholar
  13. 13.
    Makrodimopoulos A, Martin CM (2006) Lower bound limit analysis of cohesive frictional materials using second-order cone programming. Int J Numer Meth Eng 66:604–634CrossRefGoogle Scholar
  14. 14.
    Makrodimopoulos A, Martin CM (2007) Upper bound limit analysis using simplex strain elements and second-order cone programming. Int J Numer Anal Meth Geomech 31:835–865CrossRefGoogle Scholar
  15. 15.
    Chakraborty M, Kumar J (2014) Lower bound axisymmetric formulation for geomechanics problems using nonlinear optimization. Int J Geomech 15:06014024CrossRefGoogle Scholar
  16. 16.
    Kumar J, Khatri VN (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):393–405CrossRefGoogle Scholar
  17. 17.
    Kumar J, Chakraborty M (2014) Upper-bound axisymmetric limit analysis using the Mohr-Coulomb yield criterion, finite elements, and linear optimization. J Eng Mech 140(12):06014012CrossRefGoogle Scholar
  18. 18.
    Optum G2, Version: 2018.06.08 (academic license) Optum Computational Engineering, Copenhagen, DenmarkGoogle Scholar
  19. 19.
    Kumar J, Chakraborty M (2015) Bearing capacity of a circular foundation on layered sand–clay media. Soils and Found. 55(5):1058–1068CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Indian Institute of Technology (Banaras Hindu University)VaranasiIndia

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