An approach for response prediction of a single pile subjected to tension load considering modulus degradation of soil

  • Chun-yu Cui
  • Shu-jian WangEmail author
  • Qiang Liu
  • Yu-long Zhang
Original Paper


Determination on forms of load-transfer curve is a common concern in the response analysis of a single pile subjected to tension load using ‘t–z’ method in practice. Based on ‘t–z’ method, an approach for nonlinear analysis of the load–displacement response of a single pile subjected to tension load is proposed in the present paper. In this paper, based on shear displacement theory, a theoretical load-transfer model is established considering the influence of soil stress on nonlinear deformation of soil, modulus degradation characteristics and shear modulus of soil. The validity of the proposed model is checked using existing theoretical solutions. According to the pile–soil interaction mechanism in different soil types, empirical correlations for limiting unit skin friction of an uplift pile embedded in cohesive and non-cohesive soils are established. To analyze the load–displacement response of a single pile subjected to tension load, a highly effective iterative computer program is developed based on the Runge–Kutta method. Comparisons of the present computed values, the reported centrifuge and field test results are made to verify the reliability of the proposed method.


Single uplift pile Modulus degradation Pile–soil interaction Runge–Kutta method 



  1. Cheng S, Zhang QQ, Li SC, Li LP, Zhang SM, Wang K (2018) Nonlinear analysis of the response of a single pile subjected to tension load using a hyperbolic model. Eur J Environ Civ Eng 22(2):181–191CrossRefGoogle Scholar
  2. Fahey M, Carter JP (1993) A finite element study of the pressure meter test in sand using a nonlinear elastic plastic model. Can Geotech J 30(2):348–362CrossRefGoogle Scholar
  3. Fleming K, Weltman A, Randolph M et al (2009) Piling engineering. Taylor & Francis, LondonGoogle Scholar
  4. Guerra L (2010) Physical modeling of bored piles in sand. Dissertation, Ferrara University, ItalyGoogle Scholar
  5. Hardin BO, Drnevich VP (1972) Shear modulus and damping in soils: design equations and curves. J Soil Mech Found Div 98(7):667–692Google Scholar
  6. He SM (2001) Study on bearing capacity and failure of uplift pile. Rock Soil Mech 22(3):308–310 (in Chinese) Google Scholar
  7. Huang MS, Ren Q, Wang WD et al (2007) Analysis for ultimate uplift capacity of tension piles under deep excavation. Chin J Geotech Eng 29(11):1689–1695 (in Chinese) Google Scholar
  8. Kishida H, Uesugi M (1987) Tests of the interface between sand and steel in the simple shear apparatus. Geotechnique 37(1):45–52CrossRefGoogle Scholar
  9. Kondner RL (1963) Hyperbolic stress–strain response: cohesive soils. J Geotech Eng Div 89(1):115–143Google Scholar
  10. Kraft JL, Ray RP, Kagawa T (1981) Theoretical t–z curves. J Geotech Geoenviron Eng 107(11):1543–1561Google Scholar
  11. Lashkari A (2017) A simple critical state interface model and its application in prediction of shaft resistance of non-displacement piles in sand. Comput Geotech 88:95–110CrossRefGoogle Scholar
  12. Lee J, Salgado R (1999) Determination of pile base resistance in sands. J Geotech Geoenviron Eng 125(8):673–683CrossRefGoogle Scholar
  13. Lehane BM (2005) Scale effects on tension capacity for rough piles buried in dense sand. Geotechnique 55(10):709–719CrossRefGoogle Scholar
  14. Loukidis D, Salgado R (2008) Analysis of the shaft resistance of non-displacement piles in sand. Geotechnique 58(4):283–296CrossRefGoogle Scholar
  15. McCabe BA (2002) Experimental investigations of driven pile group behaviour in Belfast soft clay. Dissertation, Trinity College, IrelandGoogle Scholar
  16. McCabe BA, Lehane BM (2006) Behavior of axially loaded pile groups driven in clayey silt. J Geotech Geoenviron Eng 132(3):401–410CrossRefGoogle Scholar
  17. Randolph MF, Wroth CP (1978) Analysis of deformation of vertically loaded piles. J Geotech Eng 104(12):1465–1488Google Scholar
  18. Seed HB, Reese LC (1957) The action of soft clay along friction piles. Trans ASCE 122:731–754Google Scholar
  19. Sheil BB, McCabe BA (2016) An analytical approach for the prediction of single pile and pile group behaviour in clay. Comput Geotech 75:145–158CrossRefGoogle Scholar
  20. Sheil BB, McCabe BA, Hunt CE, Pestana JM (2015) A practical approach for the consideration of single pile and pile group installation effects in clay: numerical modelling. J Geo-Eng Sci 2(3, 4):119–142Google Scholar
  21. Sun XL, Yang M (2008) Analysis of nonlinear deformation of tension piles by modified method of deformation compatibility. Chin J Rock Mech Eng 27(6):1270–1277 (in Chinese) Google Scholar
  22. Zhang QQ, Zhang ZM (2012) A simplified nonlinear approach for single pile settlement analysis. Can Geotech J 49(11):1256–1266CrossRefGoogle Scholar
  23. Zhang QQ, Li SC, Liang FY, Yang M, Zhang Q (2014) Simplified method for settlement prediction of single pile and pile group using a hyperbolic model. Int J Civ Eng 12(2B):179–192Google Scholar
  24. Zhang QQ, Li SC, Li LP (2015a) Field and theoretical analysis on the response of destructive pile subjected to tension load. Mar Georesour Geotechnol 33(1):12–22CrossRefGoogle Scholar
  25. Zhang QQ, Li SC, Zhang Q, Li LP, Zhang B (2015b) Analysis on response of a single pile subjected to tension load using a softening model and a hyperbolic model. Mar Georesour Geotechnol 33(2):167–176CrossRefGoogle Scholar
  26. Zhang QQ, Liu SW, Zhang SM, Zhang J, Wang K (2016) Simplified non-linear approaches for response of a single pile and pile groups considering progressive deformation of pile–soil system. Soils Found 56(3):473–484CrossRefGoogle Scholar
  27. Zhang QQ, Feng RF, Liu SW, Li XM (2018) Estimation of uplift capacity of a single pile embedded in sand considering arching effect. Int J Geomech 18(9):06018021CrossRefGoogle Scholar
  28. Zhang QQ, Feng RF, Yu YL, Liu SW, Qian JG (2019a) Simplified approach for prediction of nonlinear response of bored pile embedded in sand. Soils Found. CrossRefGoogle Scholar
  29. Zhang QQ, Liu SW, Feng RF, Li XM (2019b) Analytical method for prediction of progressive deformation mechanism of existing piles due to excavation beneath a pile-supported building. Int J Civ Eng 17(6):751–763CrossRefGoogle Scholar
  30. Zhu H, Chang MF (2002) Load transfer curves along bored piles considering modulus degradation. J Geotech Geoenviron Eng 128(9):764–774CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Chun-yu Cui
    • 1
  • Shu-jian Wang
    • 2
    Email author
  • Qiang Liu
    • 3
  • Yu-long Zhang
    • 4
  1. 1.Research Center of Geotechnical and Structural EngineeringShandong UniversityJinanChina
  2. 2.Shandong Luqiao Group Co., Ltd.JinanChina
  3. 3.Tangshi Jianhua Building Material (Shandong) Co., Ltd.ZiboChina
  4. 4.Shandong Academy of Building ResearchJinanChina

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