Bending moments in raft of a piled raft system using Winkler analysis

  • Jamil, Irfan (Department of Civil Engineering, University of Engineering & Technology) ;
  • Ahmad, Irshad (Department of Civil Engineering, University of Engineering & Technology)
  • Received : 2019.01.28
  • Accepted : 2019.04.16
  • Published : 2019.05.20


Bending moments in the raft of a pile raft system is affected by pile-pile interaction and pile-raft interaction, amongst other factors. Three-Dimensional finite element program has to be used to evaluate these bending moments. Winkler type analysis is easy to use but it however ignores these interactions. This paper proposes a very simplified and novel method for finding bending moments in raft of a piled raft based on Winkler type where raft is supported on bed of springs considering pile-pile and pile-raft interaction entitled as "Winkler model for piled raft (WMPR)" The pile and raft spring stiffness are based on load share between pile and raft and average pile raft settlement proposed by Randolph (1994). To verify the results of WMPR, raft bending moments are compared with those obtained from PLAXIS 3D software. A total of sixty analysis have Performed varying different parameters. It is found that raft bending moments obtained from WMPR closely match with bending moments obtained from PLAXIS 3D. A comparison of bending moments ignoring any interaction in Winkler model is also made with PLAXIS-3D, which results in large difference of bending moments. Finally, bending moment results from eight different methods are compared with WMPR for a case study. The WMPR, though, a simple method yielded comparable raft bending moments with the most accurate analysis.



  1. Ahmed, M., Mohamed, M.H., Mallick, J. and Hasan, M.A. (2014), "3D-analysis of soil-foundation-structure interaction in layered soil", Open J. Civ. Eng., 4(4), 373.
  2. Brinkgreve, R.B.J., Engin, E., Swolfs, W.M., Waterman, D., Chesaru, A., Bonnier, P.G. and Galavi, V. (2012), Plaxis 3D 2012, Plaxis bv.
  3. Burland, J.B. (1995), "Piles as settlement reducers", Proceedings of the 18th Italian Congress on Soil Mechanics, Pavia, Italy.
  4. Burland, J.B. and Kalra, J.C. (1986), "Queen Elizabeth II conference centre: Geotechnical aspects", Proc. Inst. Civ. Eng., 80(6), 1479-1503.
  5. Chang, D.W., Lien, H.W. and Wang, T. (2018), "Finite difference analysis of vertically loaded raft foundation based on the plate theory with boundary concern", J. GeoEng., 13(3), 135-147.
  6. Clancy, P. and Randolph, M. F. (1993), "An approximate analysis procedure for piled raft foundations", Int. J. Numer. Anal. Meth. Geomech., 17(12), 849-869.
  7. Davis, E.H. and Poulos, H.G. (1972), "The analysis of piled raft systems", Aust. Geomech. J., G2, 21-27.
  8. Fattah, M.Y., Al-Mosawi, M.J. and Al-Zayadi, A.A. (2013), "Time dependent behavior of piled raft foundation in clayey soil" Geomech. Eng., 5(1), 17-36.
  9. FLAC3D, I. (2002), Fast Lagrangian Analysis of Continua in 3 Dimensions.
  10. Fleming, W.G.K., Weltman, A.J, Randolph, M.F. and Elson, W.K. (1992), Piling Engineering, Surrey Univ. Press
  11. Ghiasi, V. and Moradi, M. (2018), "Assessment the effect of pile intervals on settlement and bending moment raft analysis of piled raft foundations", Geomech. Eng., 16(2), 187-194.
  12. Ko, J., Cho, J. and Jeong, S. (2018), "Analysis of load sharing characteristics for a piled raft foundation", Geomech. Eng., 16(4), 449-461.
  13. Mandolini, A., Di Laora, R. and Mascarucci, Y. (2013), "Rational design of piled raft", Proc. Eng., 57, 45-52.
  14. Mayne, P.W. and Poulos, H.G. (1999), "Approximate displacement influence factors for elastic shallow foundations", J. Geotech. Geoenviron. Eng., 125(6), 453-460.
  15. Nguyen, D.D.C., Jo, S.B. and Kim, D.S. (2013), "Design method of piled-raft foundations under vertical load considering interaction effects", Comput. Geotech., 47, 16-27.
  16. Poulos, H.G. (2001), "Methods of analysis of piled raft foundations", A Report Prepared on Behalf of Technical Committee TC18 on Piled Foundations, International Society of Soil Mechanics and Geotechniscal Engineering.
  17. Poulos, H.G. (2001), "Piled raft foundations: Design and applications", Geotechnique, 51(2), 95-113.
  18. Poulos, H.G. and Davis, E.H. (1974). Elastic Solutions for Soil and Rock Mechanics, John Wiley.
  19. Poulos, H.G. and Davis, E.H. (1980), Pile Foundation Analysis and Design (No. Monograph).
  20. Poulos, H.G., Small, J.C. and Chow, H. (2011), "Piled raft foundations for tall buildings", Geotech. Eng. J. SEAGS AGSSEA, 42(2), 78-84.
  21. Randolph, M.F. (1994), "Design methods for pile groups and Piled rafts", Proceedings of the 13th International Conference on Soil Mechanics and Foundation Engineering, New Delhi, India, January.

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