Journal of Ocean University of China

, Volume 18, Issue 1, pp 123–132 | Cite as

Theoretical Analysis of Bearing Capacity of Shallowly Embeded Rectangular Footing of Marine Structures

  • Qiyi ZhangEmail author
  • Shaoxuan Wu
  • Liangpeng Wu
  • Zhijie Liu


In this paper, the finite element analysis software ABAQUS is used to analyze the ultimate bearing capacity of three-dimensional rectangular footing of marine structures. The deformation law and the failure mode of homogeneous seabed soil beneath the rectangular footing are analyzed in detail. According to the equivalent plastic strain of soil under rectangular footing, an allowable velocity field of homogeneous seabed soil is reasonably constructed. Based on the plastic limit analysis theory of soil mass and by using the Mohr-Coulomb yield criterion, an upper bound solution of the ultimate bearing capacity of three- dimensional rectangular footing on general homogeneous seabed soil is derived, and a correction factor of ultimate bearing capacity of three-dimensional rectangular footing is given. To verify the rationality and applicability of this theoretical solution, some numerical solutions are achieved using the general-purpose FEM analysis package ABAQUS, and comparisons are made among the derived upper bound solution, the solution of Vesic, and the solution of Salgado et al. The results indicate that the upper bound solution of the three-dimensional shallowly embedded rectangular footing proposed in this paper is accurate in calculating the bearing capacity of homogeneous seabed soil. For undrained saturated clay foundation and sandy foundation with smaller internal friction angle, this upper bound solution can evaluate the ultimate bearing capacity of rectangular footing; with the gradual increase of the internal friction angle of the soil, the ultimate bearing capacity of the proposed upper bound solution is slightly higher than that of the rectangular footing.

Key words

upper bound analysis velocity field ultimate bearing capacity rectangular footing ABAQUS 


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This paper is supported by the Project of National Science and Technology Ministry (No. 2014BAB16B03), and the National Natural Science Foundation of China (No. 51679224).


  1. Benmebarek, S., Saifi, I., and Benmebarek, N., 2017. Depth factors for undrained bearing capacity of circular footing by numerical approach. Journal of Rock Mechanics and Geotechnical Engineering, 9 (4): 761–766.CrossRefGoogle Scholar
  2. Chakraborty, M. and Kumar, J., 2016. The size effect of a conical footing on N?. Computers and Geotechnics, 76: 212–221.CrossRefGoogle Scholar
  3. De Beer, E. E., 1970. Experimental determination of the shape factor and the bearing capacity factors for sand. Geotechnique, 20 (4): 387–411.CrossRefGoogle Scholar
  4. Gourvenec, S., Randolph, M., and Kingsnorth, O., 2006. Undrained bearing capacity of square and rectangular footings. International Journal of Geomechanics, 6 (3): 147–157.CrossRefGoogle Scholar
  5. Gupta, A., Dutta, R. K., and Shrivastava, R., 2017. Ultimate bearing capacity of square/rectangular footing on layered soil. Indian Geotechnical Journal, 47 (3): 303–313.CrossRefGoogle Scholar
  6. Hansen, B. J., 1970. A revised and extended formula for bearing capability. Bulletin 28. Danish Geotechnical Institute Copenhagen, Denmark, 55–62.Google Scholar
  7. Lavasan, A. A., and Ghazavi, M., 2012. Behavior of closely spaced square and circular footings on reinforced sand. Soils and Foundations, 52 (1): 160–167.CrossRefGoogle Scholar
  8. Levin, E., 1955. Indentation pressure of a smooth circular punch. Applied Mathematics Quarterly, 13 (2): 133–137.CrossRefGoogle Scholar
  9. Liu, J., Li, M. Z., Hu, Y. X., and Han, C. C., 2017. Bearing capacity of rectangular footings in uniform clay with deep embedment. Computers and Geotechnics, 86: 209–218.CrossRefGoogle Scholar
  10. Micahlowski, R. L., and Dawson, E. M., 2002. Three–dimensional analysis of limit loads on Mohr–Coulomb soil. In: Foundations of Civil and Environmental Engineering Vol. 1. Poznan University of Technology Press, Poland, 37–147.Google Scholar
  11. Michalowski, R. L., 2001. Upper bound load estimates on square and rectangular footings. Geotechnique, 51 (9): 787–798.CrossRefGoogle Scholar
  12. Salgado, R., Lyamin, A. V., Sloan, S. W., and Yu, H. S., 2004. Twoand three–dimensional bearing capacity of foundations in clay. Geotechnique, 54 (5): 297–306.CrossRefGoogle Scholar
  13. Shen, Z., Bie, S., and Guo, L., 2017. Undrained capacity of a surface circular foundation under fully three–dimensional loading. Computers and Geotechnics, 92: 57–67.CrossRefGoogle Scholar
  14. Shen, Z., Feng, X., and Gourvenec, S., 2016. Undrained capacity of surface foundations with zero–tension interface under planar V–H–M loading. Computers and Geotechnics, 73: 47–57.CrossRefGoogle Scholar
  15. Shield, R. T., and Drucker, D. C., 1953. The application of limit analysis to punch indentation problems. Journal of Applied Mechanics, 20: 453–460.Google Scholar
  16. Skempton, A. W., 1951. The bearing capacity of clays. In: Proceedings of Building and Research Congress. London, 1: 180–189.Google Scholar
  17. Soubra, A. H., 1999. Upper bound solutions for bearing capacity of foundations. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 125 (1): 59–68.CrossRefGoogle Scholar
  18. Terzaghi, K., 1943. Theoretical Soil Mechanics. Wiley, New York, 525pp.CrossRefGoogle Scholar
  19. Vesic, A. S., 1973 Analysis of ultimate loads of shallow foundations. Journal of Soil Mechanics and Foundations Division, ASCE, 99 (SM1): 45–73.Google Scholar
  20. Yu, J., Huang, M. S., Leung, C. F., and Li, S. Y., 2017. Upper bound solution of a laterally loaded rigid monopile in normally consolidated clay. Computers and Geotechnics, 91: 131–145.CrossRefGoogle Scholar

Copyright information

© Science Press, Ocean University of China and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Qiyi Zhang
    • 1
    • 2
    Email author
  • Shaoxuan Wu
    • 1
    • 2
  • Liangpeng Wu
    • 1
    • 2
  • Zhijie Liu
    • 1
    • 2
  1. 1.Department of Ocean Engineering, College of EngineeringOcean University of ChinaQingdaoChina
  2. 2.Key Laboratory of Ocean Engineering of Shandong ProvinceQingdaoChina

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