Kinematic bending of single piles in layered soil

  • Wenhai Ke
  • Qijian Liu
  • Chao Zhang
Research Paper


A continuum solution is proposed for the kinematic bending of single piles embedded in a layered soil deposit. A displacement model is proposed to represent the displacement of the model of interest incorporating soil–pile interaction. The displacement functions and the attenuation function are obtained in the coupled form by means of Hamilton’s principle. Then an iterative procedure is applied to solve the coupled functions. The contributions of the proposed model are threefold: (1) The continuity of the Winkler springs is considered. (2) The effects of the inertial force of the surrounding soil on the kinematic response of the piles are taken into account. (3) An improved formula is proposed for the kinematic pile bending strain at the interface of two-layer soil deposit. A parametric study is performed to investigate the influence of the soil inhomogeneity on the kinematic bending of single piles. The results highlight that the stiffness discontinuity significantly influences the kinematic bending of single piles. There is a critical depth considering the effect of the pile head estimated as a non-dimensional length of the pile.


Kinematic bending Layered soil Single piles Soil–pile interaction 



The study was supported by the Technology Project of Department of Transportation of China under Grant No. 2013 318 798 320 and the Technology Project of Transportation of Hunan Province under Grant No. 2012 19. The second author appreciates the Funding by Open Research Fund Program of Hunan Provincial Key Laboratory of Geotechnical Engineering for Stability Control and Health Monitoring of Hunan University of Science and Technology.


  1. 1.
    Blaney GW, Kausel E, Roesset JM (1976) Dynamic stiffness of piles. In: Proceedings in 2nd international conference on numerical methods in geomechanics, Blacksburg, VA, ASCE, pp 1010–1012Google Scholar
  2. 2.
    Chidichimo A, Cairo R, Dente G, Taylor CA, Mylonakis G (2014) 1-g experimental investigation of bi-layer soil response and kinematic pile bending. Soil Dyn Earthq Eng 67:219–232CrossRefGoogle Scholar
  3. 3.
    de Sanctis L, Maiorano RMS, Aversa S (2010) A method for assessing kinematic bending moments at the pile head. Earthq Eng Struct D 39(10):1133–1154Google Scholar
  4. 4.
    Dezi F, Poulos H (2017) Kinematic bending moments in square pile groups. Int J Geomech 17(3):04016066CrossRefGoogle Scholar
  5. 5.
    Dezi F, Carbonari S, Leoni G (2009) A model for the 3D kinematic interaction analysis of pile groups in layered soils. Earthq Eng Struct D 38(11):1281–1305CrossRefGoogle Scholar
  6. 6.
    Dezi F, Carbonari S, Leoni G (2010) Kinematic bending moments in pile foundations. Soil Dyn Earthq Eng 30(3):119–132CrossRefGoogle Scholar
  7. 7.
    Dezi F, Carbonari S, Morici M (2016) A numerical model for the dynamic analysis of inclined pile groups. Earthq Eng Struct D 45(1):45–68CrossRefGoogle Scholar
  8. 8.
    Di Laora R, Mandolini A, Mylonakis G (2012) Insight on kinematic bending of flexible piles in layered soil. Soil Dyn Earthq Eng 43(12):309–322CrossRefGoogle Scholar
  9. 9.
    Di Laora R, Mylonakis G, Mandolini A (2013) Pile-head kinematic bending in layered soil. Earthq Eng Struct D 42(2):319–337CrossRefGoogle Scholar
  10. 10.
    Dobry R, O’Rourke M (1983) Discussion on seismic response of end bearing piles. J Geotech Eng ASCE 109(5):778–781CrossRefGoogle Scholar
  11. 11.
    Dobry R, Oweis I, Urzua A (1976) Simplified procedures for estimating the fundamental period of a soil profile. Bull Seismol Soc Am 66(4):1293–1321Google Scholar
  12. 12.
    Fan K, Gazetas G, Kaynia A, Kausel E, Ahmad S (1991) Kinematic seismic response of single piles and pile groups. J Geotech Eng ASCE 117(12):1860–1879CrossRefGoogle Scholar
  13. 13.
    Gazetas G (1984) Seismic response of end-bearing piles. Soil Dyn Earthq Eng 3(2):82–93Google Scholar
  14. 14.
    Gazetas G, Fan K, Tazoh T, Shimizu K, Kawadas M, Makris N (1992) Seismic pile group structure interaction. In: Prakash S (ed) Piles under dynamic loads. Special Publication, London, pp 56–93Google Scholar
  15. 15.
    Kavvads M, Gazetas G (1993) Kinematic seismic response and bending of free-head piles in layered soil. Géotechnique 43(2):207–222CrossRefGoogle Scholar
  16. 16.
    Kaynia A, Kausel E (1991) Dynamics of piles and pile groups in layered soil media. Soil Dyn Earthq Eng 10(8):386–401CrossRefGoogle Scholar
  17. 17.
    Liu Q, Deng F, He Y (2014) Transverse seismic kinematics of single piles by a modified Vlasov mode. Int J Numer Anal Methods 38(18):1953–1968CrossRefGoogle Scholar
  18. 18.
    Maiorano RMS, de Sanctis L, Aversa S, Mandolini A (2009) Kinematic response analysis of piled foundations under seismic excitation. Can Geotech J 46(5):571–584CrossRefGoogle Scholar
  19. 19.
    Margason E (1975) Pile bending during earthquakes. ASCE-UC/Berkeley seminar on design construction and performance of deep foundationsGoogle Scholar
  20. 20.
    Martinelli M, Burghignoli A, Callisto L (2016) Dynamic response of a pile embedded into a layered soil. Soil Dyn Earthq Eng 87:16–28CrossRefGoogle Scholar
  21. 21.
    Mylonakis G (2001) Simplified model for seismic pile bending at soil-layer interfaces. Soils Found 41(4):47–58CrossRefGoogle Scholar
  22. 22.
    Naggar EI, Ali Shayanfar M, Kimiaei M (2005) Simplified BDWF model for nonlinear seismic response analysis of offshore piles with nonlinear input ground motion analysis. Can Geotech J 42(2):365–380CrossRefGoogle Scholar
  23. 23.
    Nikolaou S, Mylonakis G, Gazetas G, Tazoh T (2001) Kinematic pile bending during earthquakes: analysis and field measurements. Géotechnique 51(5):425–440CrossRefGoogle Scholar
  24. 24.
    Papazoglou A, Elnashai A (1996) Analytical and field evidence of the damaging effect of vertical earthquake ground motion. Earthq Eng Struct D 25(10):1109–1137CrossRefGoogle Scholar
  25. 25.
    Roesset J, Whitman R, Dobry R (1973) Modal analysis for structures with foundation interaction. J Struct Div 99(3):399–416Google Scholar
  26. 26.
    Rovithis E, Mylonakis G, Pitilakis K (2013) Dynamic stiffness and kinematic response of single piles in inhomogeneous soil. Bull Earthq Eng 11(6):1949–1972CrossRefGoogle Scholar
  27. 27.
    Saitoh M (2010) Effect of local nonlinearity in cohesionless soil on optimal radius minimizing fixed-head pile bending by inertial and kinematic interactions. Acta Geotech 5(4):273–286CrossRefGoogle Scholar
  28. 28.
    Sica S, Mylonakis G, Simonelli AL (2011) Transient kinematic pile bending in two-layer soil. Soil Dyn Earthq Eng 31(7):891–905CrossRefGoogle Scholar
  29. 29.
    Sun K (1994) Laterally loaded piles in elastic media. J Geotech Eng ASCE 120(8):1324–1344CrossRefGoogle Scholar
  30. 30.
    Vallabhan CVG, Das YC (1988) Parametric study of beams on elastic foundations. J Eng Mech ASCE 114(12):2072–2082CrossRefGoogle Scholar
  31. 31.
    Wang R, Liu X, Zhang J (2017) Numerical analysis of the seismic inertial and kinematic effects on pile bending moment in liquefiable soils. Acta Geotech 12(4):773–791CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.College of Civil EngineeringHunan UniversityChangshaPeople’s Republic of China
  2. 2.Department of Civil and Environmental EngineeringMichigan Technological UniversityHoughtonUSA

Personalised recommendations