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An Analytical Model to Study the Behavior of Non-connected Piled Rafts with Granular Cushion Subjected to Vertical Load


Understanding the load transfer mechanism and the load settlement behavior of non-connected piled raft foundations with cushion is so complicated. In the present research, based on the assumption of an axisymmetric cylindrical unit cell including pile, subsoil, cushion, and raft, an analytical model is developed and introduced. This model is capable of estimating the transferred vertical stress from raft to piles head and subsoil, compression of cushion, and differential settlement between pile head and subsoil. Also, an experimental test program has been introduced to investigate the behavior of non-connected piled raft foundations and to validate the proposed model. To represent the effectiveness of using non-connected piled raft with different cushion thickness, number, and length of piles measure with the unpiled raft, the load improvement ratio and the settlement efficiency ratio are used. According to the results, the minimum increase in the bearing capacity and the reduction in the settlement of non-connected piled raft to the unpiled raft are 42% and 38% respectively. Also, increasing the cushion thickness increases the differential settlement at the pile head elevation, and for a given number and length of pile, reduced the bearing capacity of the piled raft by 30%. The good agreement of model predictions with the experimental results is verified. The difference between the experimental and analytical values of the cushion compression above the pile head is within an acceptable range.

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  1. 1.

    Nguyen DDC, Jo S-B, Kim D-S (2013) Design method of piled-raft foundations under vertical load considering interaction effects. ComputGeotech 47:16–27.

    Article  Google Scholar 

  2. 2.

    Poulos HG (2001) Piled raft foundations: design and applications. Géotechnique 51(2):95–113.

    Article  Google Scholar 

  3. 3.

    Sawada K, Takemura J (2014) Centrifuge model tests on piled raft foundation in sand subjected to lateral and moment loads. Soils Found 54(2):126–140.

    Article  Google Scholar 

  4. 4.

    Sinha A, Hanna AM (2017) 3D numerical model for piled raft foundation. Int J Geomech 17(2):04016055.

    Article  Google Scholar 

  5. 5.

    El Sawwaf M (2010) Experimental study of eccentrically loaded raft with connected and unconnected short piles. J GeotechGeoenvironEng 136(10):1394–1402.

    Article  Google Scholar 

  6. 6.

    Fioravante V (2011) Load transfer from a raft to a pile with an interposed layer. Géotechnique 61(2):121–132.

    Article  Google Scholar 

  7. 7.

    Cao XD, Wong IH, Chang M-F (2004) Behavior of model rafts resting on pile-reinforced sand. J GeotechGeoenvironEng 130(2):129–138.

    Article  Google Scholar 

  8. 8.

    Ko K-W, Park H-J, Ha J-G, Jin S, Song Y-H, Song M-J, Kim D-S (2019) Evaluation of dynamic bending moment of disconnected piled raft via centrifuge tests. Can Geotech J 56(12):1917–1928.

    Article  Google Scholar 

  9. 9.

    SaeediAzizkandi A, Rasouli H, Baziar MH (2018) Load sharing and carrying mechanism of piles in non-connected pile rafts using a numerical approach. Int J CivEng 17(6):793–808.

    Article  Google Scholar 

  10. 10.

    Chen RP, Xu ZZ, Chen YM, Ling DS, Zhu B (2010) Field tests on pile-supported embankments over soft ground. J GeotechGeoenvironEng 136(6):777–785.

    Article  Google Scholar 

  11. 11.

    Ghalesari AT, Rasouli H (2014) Effect of gravel layer on the behavior of piled raft foundations. Adv Soil Dyn Found Eng.

    Article  Google Scholar 

  12. 12.

    Choi J-I, Min K-H, Kim S-H, Kwon OS, Kim MM (2009) Behavior of disconnected pile foundation system. Contemp Top Ground ModifProbl Soils Geo-Support.

    Article  Google Scholar 

  13. 13.

    SaeediAzizkandi A, Taherkhani R (2020) Experimental study on connected and non-connected piled raft foundations subjected to eccentric loading. Int J CivEng 18(7):743–761.

    Article  Google Scholar 

  14. 14.

    Tradigo F, Pisanò F, di Prisco C, Mussi A (2015) Non-linear soil–structure interaction in disconnected piled raft foundations. ComputGeotech 63:121–134.

    Article  Google Scholar 

  15. 15.

    Fioravante V, Giretti D (2010) Contact versus noncontact piled raft foundations. Can Geotech J 47(11):1271–1287.

    Article  Google Scholar 

  16. 16.

    Liang F-Y, Chen L-Z, Shi X-G (2003) Numerical analysis of composite piled raft with cushion subjected to vertical load. ComputGeotech 30(6):443–453.

    Article  Google Scholar 

  17. 17.

    Hamidi B, Masse F, Racinais J, Varaksin S (2016) The boundary between deep foundations and ground improvement. ProcInstCivEngGeotechEng 169(2):201–213.

    Article  Google Scholar 

  18. 18.

    Zhang H, Shi ML (2011) Mechanical performance of settlement-reducing pile foundation with cushion. Adv Mater Res 368:2545–2549.

    Article  Google Scholar 

  19. 19.

    Chen RP, Chen YM, Han J, Xu ZZ (2008) A theoretical solution for pile-supported embankments on soft soils under one-dimensional compression. Can Geotech J 45(5):611–623.

    Article  Google Scholar 

  20. 20.

    Zhao L-S, Zhou W-H, Geng X, Yuen K-V, Fatahi B (2019) A closed-form solution for column-supported embankments with geosynthetic reinforcement. GeotextGeomembr 47(3):389–401.

    Article  Google Scholar 

  21. 21.

    Rui R, Han J, Ye Y, Chen C, Zhai Y (2020) Load transfer mechanisms of granular cushion between column foundation and rigid raft. Int J Geomech 20(1):04019139.

    Article  Google Scholar 

  22. 22.

    Yun-min C, Wei-ping C, Ren-peng C (2008) An experimental investigation of soil arching within basal reinforced and unreinforced piled embankments. GeotextGeomembr 26(2):164–174.

    Article  Google Scholar 

  23. 23

    Abdollahi M, BolouriBazaz J (2017) Reconstitution of sand specimens using a rainer system. Int J Eng.

    Article  Google Scholar 

  24. 24.

    Han J, Gabr MA (2002) Numerical analysis of geosynthetic-reinforced and pile-supported earth platforms over soft soil. J GeotechGeoenvironEng 128(1):44–53.

    Article  Google Scholar 

  25. 25.

    Lade PV (1977) Elasto-plastic stress–strain theory for cohesionless soil with curved yield surfaces. Int J Solids Struct 13(11):1019–1035.

    Article  MATH  Google Scholar 

  26. 26.

    Bolton MD, Gui MW, Garnier J, Corte JF, Bagge G, Laue J, Renzi R (1999) Centrifuge cone penetration tests in sand. Géotechnique 49(4):543–552.

    Article  Google Scholar 

  27. 27.

    Lee S-H, Chung C-K (2005) An experimental study of the interaction of vertically loaded pile groups in sand. Can Geotech J 42(5):1485–1493.

    Article  Google Scholar 

  28. 28.

    El-Garhy B, Galil AA, Youssef A-F, Raia MA (2013) Behavior of raft on settlement reducing piles: experimental model study. J Rock MechGeotechEng 5(5):389–399.

    Article  Google Scholar 

  29. 29.

    Patil JD, Vasanvala SA, Solanki CH (2015) An experimental study on behaviour of piled raft foundation. Indian Geotech J 46(1):16–24.

    Article  Google Scholar 

  30. 30.

    Deb K, Samadhiya NK, Namdeo JB (2011) Laboratory model studies on unreinforced and geogrid-reinforced sand bed over stone column-improved soft clay. GeotextGeomembr 29(2):190–196.

    Article  Google Scholar 

  31. 31.

    Deschamps RJ (1995) Discussion of “Load settlement curve method for spread footings on sand” by Jean-Louis Briaud and Philippe Jeanjean. J GeotechEng 121(9):684–685.

    Article  Google Scholar 

  32. 32.

    Vesic AS (1974) Analysis of ultimate loads of shallow foundations. Int J Rock Mech Min SciGeomechAbstr 11(11):A230.

    Article  Google Scholar 

  33. 33

    Kumar V, Kumar A (2018) An experimental study to analyse the behaviour of piled-raft foundation model under the application of vertical load. InnovInfrastructSolut.

    Article  Google Scholar 

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The authors are grateful to Dr. Ahmad Aftabi Sani of the Ferdowsi University of Mashhad for his favor, kindness, and precious guidance. The performed tests were financially supported by the “Vice President for Research and Technology” of the Ferdowsi University of Mashhad which is acknowledged.


All the Ph.D. research programs in Ferdowsi University of Mashhad are supported by the “Vice President for Research and Technology” of the Ferdowsi University of Mashhad.

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Correspondence to Jafar Bolouri Bazaz.

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Malekkhani, M.J., Bazaz, J.B. An Analytical Model to Study the Behavior of Non-connected Piled Rafts with Granular Cushion Subjected to Vertical Load. Int J Civ Eng 19, 941–956 (2021).

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  • Non-connected piled raft
  • Analytical analysis
  • Cushion
  • Negative friction
  • Pile settlement