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Numerical check of the Meyerhof bearing capacity equation for shallow foundations

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Abstract

Most geotechnical design codes and books use the equations of Meyerhof or Terzaghi to calculate shallow foundations. These equations are based on the failure mechanism published by Prandtl for shallow strip foundations. The common idea is that failure of a footing occurs in all cases according to a Prandtl-wedge failure mechanism. To check the failure mechanism and the equations of the currently used bearing capacity factors and correction factors, a large number of finite-element calculations of strip and circular footings have been made. The finite-element calculations show that in cases of soils with high friction angles, soils without cohesion or a surcharge, footings with inclined loading or circular footings, not the Prandtl-wedge failure mechanism, but other failure mechanisms occur. In addition, the currently used equations for the bearing capacity factors and correction factors are too high. Therefore, new equations have been presented in this article. For some correction factors, for example, the inclination factors and the cohesion slope factor, an analytical solution is found.

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References

  1. Bolton MD (1979) Guide to soil mechanics. Macmillian Press, London, p 330

    Google Scholar 

  2. Brinch Hansen JA (1970) Revised and extended formula for bearing capacity. Bulletin No 28, Danish Geotechnical Institute Copenhagen, pp 5–11

  3. Caquot A, and Kerisel J (1953) Sur le terme de surface dans le calcul des fondations en milieu pulverulent. Proceeding Third International Conference on Soil Mechanics and Foundation Engineering, Zurich, Switzerland, 1:336–337

  4. Caquot A, Kerisel J (1966) Traité de Méchanique des sols, vol 349. Gauthier-Villars, Paris, p 353

    Google Scholar 

  5. Chen WF (1975) Limit analysis and soil plasticity. Elsevier, Amsterdam

    Google Scholar 

  6. Das BM (1999) Shallow foundations, bearing capacity and settlement. CRC Press, New York, p 89

    Book  Google Scholar 

  7. De Beer EE (1967) Proefondervindelijke bijdrage tot de studie van het grensdraagvermogen van zand onder funderingen op staal; Bepaling van de vormfactor sb. Annales des Travaux Publics de Belgique 68(6):481–506; 69(1):41–88; 4:321–360; 5:395–442; 6:495–522

  8. De Beer EE, Ladany B (1961) Etude expérimentale de la capacité portante du sable sous des fondations circulaire établies en surface. Proc 5th Intern Conf Soil Mech Found EngParis 1:577–581

    Google Scholar 

  9. De Beer EE (1970) Experimental determination of the shape factors and the bearing capacity factors of sand. Géotechnique 20(4):387–411

    Article  Google Scholar 

  10. Eurocode 7 (2004) Geotechnical design—part 1: general rules, EN 1997-1, 159

  11. Hertz H (1881) Ueber die Berührung fester elastischer Körper. J für die reine und angewandte Mathematik 92(1956):156–171

    Google Scholar 

  12. Ip KW (2005) Bearing capacity for foundation near slope, Master-thesis. Concordia University, Montreal, pp 61–64

    Google Scholar 

  13. Jumikis AR (1956) Rupture surfaces in sand under oblique loads. J Soil Mech Found Des ASCE 82(SM 1)

  14. Keverling Buisman AS (1940) Grondmechanica. Waltman, Delft, p 243

    Google Scholar 

  15. Knudsen BS and Mortensen N (2016) Bearing capacity comparison of results from FEM and DS/EN 1997-1 DK NA 2013, Northern Geotechnical Meeting 2016, Reykjavik, pp 577–586

  16. Lambe TW, Whitman RV (1969) Soil mechanics. John Wiley and Sons Inc., New York

    Google Scholar 

  17. Loukidis D, Chakraborty T, Salgado R (2008) Bearing capacity of strip footings on purely frictional soil under eccentric and inclined loads. Can Geotech J 45:768–787

    Article  Google Scholar 

  18. Meyerhof GG (1951) The ultimate bearing capacity of foundations. Géotechnique 2:301–332

    Article  Google Scholar 

  19. Meyerhof GG (1953) The bearing capacity of foundations under eccentric and inclined loads. In: Proceeding III Intl. Conf. on soil mechanics found. Eng, Zürich, 1, pp 440–445

  20. Meyerhof GG (1957) The ultimate bearing capacity of foundations on slopes. In: Proceeding of the 4th Int. Conf. on soil mechanics and foundation engineering, London, pp 384–386

  21. Meyerhof GG (1963) Some recent research on the bearing capacity of foundations. Can Geotech J 1(1):16–26

    Article  Google Scholar 

  22. Meyerhof GG (1965) Shallow foundations. J Soil Mech Found Div ASCE 91(2):21–32

    Google Scholar 

  23. Muhs H, Weiß K (1972) Versuche über die Standsicheheit flach gegründeter Einzelfundamente in nichtbindigem Boden, Mitteilungen der Deutschen Forschungsgesellschaft für Bodenmechanik (Degebo) an der Technischen Universität Berlin. Heft 28:122

    Google Scholar 

  24. Prandtl L (1920) Über die Härte plastischer Körper. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. Dieterichschen Buchhandlung, Göttingen, pp 74–85

    Google Scholar 

  25. Selig ET and McKee KE (1961) Static behavior of small footings. J Soil Mech Found Design ASCE 87(6):29–50

  26. Reissner H (1924) Zum Erddruckproblem. In: Biezeno CB, Burgers JM (eds) Proceeding 1st Int Congress for applied mechanics. Delft, The Netherlands, pp 295–311

    Google Scholar 

  27. Sokolovski VV (1960) Statics of soil media. Butterworths Scientific Publications, New York

    Google Scholar 

  28. Tapper L, Martin CM, Byrne BW, Lehane BM (2015) Undrained vertical bearing capacity of perforated shallow foundations. Front Offshore Geotech Fig 7:816

    Google Scholar 

  29. Terzaghi K (1943) Theoretical soil mechanics. John Wiley & Sons Inc, New York

    Book  Google Scholar 

  30. Van Baars S (2014) The inclination and shape factors for the bearing capacity of footings. Soils Found 54(5):985–992

    Article  Google Scholar 

  31. Van Baars S (2015) The bearing capacity of footings on cohesionless soils. Electron J Geotech Eng 20:12945–12955 (ISSN 1089-3032)

    Google Scholar 

  32. Van Baars S (2016) Failure mechanisms and corresponding shape factors of shallow foundations. 4th Int. Conf. on New Development in Soil Mech. and Geotechn. Eng., Nicosia, pp 551–558

  33. Van Baars S (2016) The influence of superposition and eccentric loading on the bearing capacity of shallow foundations. J Comput Mater Civil Engineering 1(3):121–131 (ISSN 2371-2325)

    Google Scholar 

  34. Vesic AS (1973) Analysis of ultimate loads of shallow foundations. J Soil Mech Found Div 99(1):45–76

    Google Scholar 

  35. Vesic AS (1975) Bearing capacity of shallow foundations. In: Winterkorn HF, Fang HY (eds) Foundation engineering handbook. Van Nostrand Reinhold, New York, pp 121–147

    Google Scholar 

  36. Zhu M, Michalowski RL (2005) Shape factors for limit loads on square and rectangular footings. J Geotech Geoenviron Eng ASCE 131:223–231

    Article  Google Scholar 

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  1. Research Unit Engineering Science, Faculty of Science and Technology, University of Luxembourg, Campus Kirchberg, 6, rue R. Coudenhove-Kalergi, 1359, Luxembourg, Grand Duchy of Luxembourg

    Stefan Van Baars

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  1. Stefan Van Baars
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Correspondence to Stefan Van Baars.

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This paper was selected from GeoMEast 2017—sustainable civil infrastructures: innovative infrastructure geotechnology

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Van Baars, S. Numerical check of the Meyerhof bearing capacity equation for shallow foundations. Innov. Infrastruct. Solut. 3, 9 (2018). https://doi.org/10.1007/s41062-017-0116-1

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