Acta Geotechnica

, Volume 14, Issue 1, pp 193–205 | Cite as

Bearing capacity of pile groups under vertical eccentric load

  • Raffaele Di LaoraEmail author
  • Luca de Sanctis
  • Stefano Aversa
Research Paper


The paper deals with the problem of the bearing capacity of pile groups under vertical eccentric load. Widespread practice is to consider the achievement of the axial capacity on the outermost pile as the ultimate limit state of the pile group. However, this approach neglects the ductility of the foundation system and may be thereby overconservative. With the aim of proposing an alternative and more rational approach, a novel formulation for interaction diagrams based on theorems of limit analysis is presented and discussed. The methodology is applicable to the general case of groups of unevenly distributed, dissimilar piles. Piles’ connections to the pile cap are modeled as either hinges or rigid-plastic internal fixities. An application example to a slender structure is also provided, showing that the proposed approach can lead to significant advantages over the traditional design.


Bearing capacity Eccentric loading Limit analysis Pile groups 

List of symbols


Adhesion factor


Inclination of the applied moment vector


Partial resistance factors for pile base and shaft capacity


Partial factor for shaft capacity in tension


Partial factor for undrained shear strength


Coefficient depending on number of piles


Increment of rotation


Increments of work done by internal forces


Increments of work done by external forces


Efficiency of a pile group


Correlation factor to derive characteristic value


Coordinate of the j-th pile in the reference system (ξ, η)


Total overburden stress at depth L


Base area of the block containing the piles


Side area of the block containing the piles


Distance between two external piles of a row


Abscissa of the center of the row


Pile diameter


Pile length


External moment vector


Moment capacity of the pile group under zero axial loading

Mu,Mui, Muk

Moment capacities of the pile group


Moment capacities along x- and y-axes in the 3D domain


Number of alignments of piles parallel to external moment vector M


Dimensionless yielding bending moments


Yielding bending moments


Bearing capacity factor


Axial capacity of the single pile in compression


Axial capacity in compression of the j-th pile


Number of piles in a row


Number of piles in a group


Unit base resistance


Characteristic value of pile base resistance


External axial capacity


Axial loads on piles i an j


Axial capacity of the pile group

Qu,Qui, Quk

Axial capacity of the pile group


Characteristic value of pile shaft resistance


Axial capacity of the single pile in uplift


Axial capacity in uplift of the j-th pile


Pile spacing


Unit shaft resistance


Soil undrained shear strength


Abscissa of the j-th pile


Ordinate of the j-th pile



This research has been developed under the auspices of research projects ReLUIS 2014-2017, granted by Italian Emergency Management Agency.


  1. 1.
    AASHTO (2012) AASHTO guide specifications for LRFD seismic bridge design, 2nd edn. American Association of State Highway and Transportation Officials, Washington, D.C.Google Scholar
  2. 2.
    Brand EW, Muktabhant C, Taechathummarak A (1972). Load tests on small foundation in soft clay. In: ASCE conference on performance of earth and earth supported structures, Purdue University, Indiana, vol. 1, part 2, pp 903–928Google Scholar
  3. 3.
    Briaud JL, Tucker LM, Ng E (1989) Axially loaded 5 pile group and single pile in sand. Proc XII ICSMFE Rio de Janeiro 2:1121–1124Google Scholar
  4. 4.
    Butterfield R, Gottardi G (1994) A complete three dimensional failure envelope for shallow footings on sand. Géotechnique 44(1):181–184CrossRefGoogle Scholar
  5. 5.
    CEN (2003) (pr)EN 1997-1. Eurocode 7: geotechnical design—part I: general rules. European Committee for Standardization Technical Committee 250, Brussels, BelgiumGoogle Scholar
  6. 6.
    Cooke RW (1986) Piled raft foundations on stiff clays: a contribution to design philosophy. Géotechnique 36(2):169–203CrossRefGoogle Scholar
  7. 7.
    De Mello VFB (1969) Foundations of buildings on clay. State Art Rep Proc VII ICSMFE 1:49–136Google Scholar
  8. 8.
    Dobry R, Gazetas G (1988) Simple method for dynamic stiffness and damping of floating pile groups. Géotechnique 38(4):557–574CrossRefGoogle Scholar
  9. 9.
    de Sanctis L, Mandolini A, Russo G, Viggiani C (2002). Some remarks on the optimum design of piled rafts. In: O’Neill & Townsend (eds) ASCE geotechnical special publication 116, Orlando, pp 405–425Google Scholar
  10. 10.
    Fema 750 (2009) Recommended seismic provisions for new buildings and other structures. Building Seismic Safety Council, National Institute of Building, Washington, D.C.Google Scholar
  11. 11.
    Fleming WGK, Weltman AJ, Randolph MF, Elson WK (1992) Piling engineering, 2nd edn. Blackie Academic and Professional, GlasgowGoogle Scholar
  12. 12.
    Grange S, Kotronis P, Mazars J (2009) A macro-element to simulate dynamic Soil-Structure Interaction. Eng Struct 31(12):3034–3046CrossRefzbMATHGoogle Scholar
  13. 13.
    Houlsby GT, Cassidy MJ (2002) A plasticity model for the behaviour of footings on sand under combined loading. Géotechnique 52(2):117–129CrossRefGoogle Scholar
  14. 14.
    Kezdi A (1957) Bearing capacity of piles and pile groups. In: Proceedings of the IV ICSMFE, London, vol 2Google Scholar
  15. 15.
    Kishida H, Meyerhof GG (1965) Bearing capacity of pile groups under eccentric loads in sand. In: Proceedings of the 6th international conference on soil mechanics, Montreal, Canada, vol 2, pp 270–274Google Scholar
  16. 16.
    Martin CM (2001) Vertical bearing capacity of skirted circular foundations on Tresca soil. In: Proceedings of the 15th ICSMGE, Istanbul, vol 1, pp 743–746Google Scholar
  17. 17.
    Meyerhof GG (1981) The bearing capacity of rigid piles and pile groups under inclined loads in clay. Can Geotech J 18:297–300CrossRefGoogle Scholar
  18. 18.
    Meyerhof GG, Ranjan G (1973) The bearing capacity of rigid piles under inclined loads in sand. III: Pile groups. Can Geotech J 10:428–438CrossRefGoogle Scholar
  19. 19.
    Meyerhof GG, Yalcin S (1984) Pile capacity for eccentric inclined load in clay. Can Geotech J 21:389–396CrossRefGoogle Scholar
  20. 20.
    Meyerhof GG, Yalcin S, Mathur S (1983) Ultimate pile capacity for eccentric inclined load. J Geotech Eng ASCE 109(3):408–423CrossRefGoogle Scholar
  21. 21.
    Nova R, Montrasio L (1991) Settlements of shallow foundations on sand. Géotechnique 41(2):243–256CrossRefGoogle Scholar
  22. 22.
    NTC (2008). D. M. 14 Gennaio 2008. Norme tecniche per le costruzioni’. Gazzetta Ufficiale della Repubblica Italiana no. 29, 4 Feb 2008 (in Italian)Google Scholar
  23. 23.
    O’Neill MW, Hawkins A, Mahar L (1982) Load transfer mechanisms in piles and pile groups. J Geotech Eng Div ASCE 108(GT12):1605–1623Google Scholar
  24. 24.
    Pisanò F, di Prisco C, Lancellotta R (2014) Soil-foundation modelling in laterally loaded historical towers. Géotechnique 64(1):1–15CrossRefGoogle Scholar
  25. 25.
    Randolph MF, Jamiolkowski MB, Zdravkovic L (2004). Load carrying capacity of foundations. In: Thomas T (ed) Keynote lecture, proceedings of the Skempton conference ‘Advances in Geotechnical Engineering’, London, vol 1, pp 207–240Google Scholar
  26. 26.
    Russo G, Viggiani C, de Sanctis L (2004) Piles as settlement reducers: a case history. In: Advances in geotechnical engineering: The Skempton conference: proceedings of a three day conference on advances in geotechnical engineering, organised by the Institution of Civil Engineers and held at the Royal Geographical Society, London, UK, 29–31 March 2004, pp 1143–1154Google Scholar
  27. 27.
    Saffery MR, Tate APK (1961). Model tests on Pile Groups in Clay Soil with particular reference to the behaviour of the group when it is loaded eccentrically. In: Proceedings of the 5th international conference on soil mechanics, Paris, vol 5, pp 129–134Google Scholar
  28. 28.
    Salciarini D, Tamagnini C (2009) A hypoplastic macroelement model for shallow foundations under monotonic and cyclic loads. Acta Geotechnica 4(3):163–176CrossRefGoogle Scholar
  29. 29.
    Skempton AW (1951) The bearing capacity of clays. In: Proceedings of building research congress. ICE, London, pp 180–189Google Scholar
  30. 30.
    St John HD, Randolph MF, McAvoy RP, Gallagher KA (1983) The design of piles for tethered platforms. In: Proceedings of the conference on the design and construction of offshore structures. Institution of Civil Engineers, London, pp 53–64Google Scholar
  31. 31.
    Terzaghi K, Peck RB (1948) Soil mechanics in engineering practice. Wiley, New YorkGoogle Scholar
  32. 32.
    Vesic AS (1969) Experiments with instrumented pile groups in sand. Performance of deep foundations, vol 444. ASTM Special Technical Publication, West Conshohocken, pp 177–222CrossRefGoogle Scholar
  33. 33.
    Viggiani C (1993) Further experience with auger piles in Naples area. In: Inpe WF (ed) Proceedings of the second international geotechnical seminar on deep foundations on bored and auger piles, BAP II. Balkema, Rotterdam, pp 445–458Google Scholar
  34. 34.
    Viggiani C, Mandolini A, Russo G (2011) Piles and piles foundations. Spon Press, LondonCrossRefGoogle Scholar
  35. 35.
    Whitaker T (1957) Experiments with model piles in group. Géotechnique 7(4):147–167CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Università della Campania “Luigi Vanvitelli”AversaItaly
  2. 2.Università di Napoli ParthenopeNapoliItaly

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