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Nonlinear Analysis of Single Laterally Loaded Piles in Clays Using Modified Strain Wedge Model


This paper proposes a modified strain wedge (MSW) model for nonlinear analysis of laterally loaded single piles in clays. The MSW model is used to calculate the soil resistance under increasing pile deflection. The stress–strain behavior of clays in the MSW, which is needed to calculate the soil resistance, is described in terms of both hyperbolic and bilinear stress–strain relationships. The subgrade reaction modulus of soil below the MSW is assumed to equal the conventional subgrade reaction modulus and to remain constant under the lateral loading of the pile. The applicability of the proposed model was verified by eight case histories. The results indicate that (1) the predicted results are consistent with the measurements for all eight full-scale tested piles; (2) the bilinear stress–strain relationship is not recommended for clays because the clays usually have a large ε 50 and, thus, they exhibit a linear behavior in the MSW during loading; (3) the predicted pile response is less sensitive to the effective friction angle than to the undrained shear strength; and (4) the proposed MSW model applies to normally consolidated clays and to overconsolidated clays until they reach their peak strength.

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  1. 1.

    Reese LC, Cox WR, Koop FD (1975) Field testing and analysis of laterally loaded piles on stiff clay, Proceedings of Offshore Technology Conference, Paper No. OTC 2312, 671–690

  2. 2.

    Sharafi H, Sojoudi Y (2016) Experimental and numerical study of pile-stabilized slopes under surface load conditions. Int J Civil Eng 14(4):221–232. doi:10.1007/s40999-016-0017-2

    Article  Google Scholar 

  3. 3.

    Oyejobi DO, Jameel M, Sulong NR (2016) Nonlinear response of tension leg platform subjected to wave, current and wind forces. Int J Civil Eng. doi:10.1007/s40999-016-0030-5

    Google Scholar 

  4. 4.

    Sato H, Ohya T, Matsushima M (2001) Study on the behavior of full-scaled single piles with rotation-fixed head under large lateral deformation. Proc Jpn Soc Civil Eng 714:95–109 (in Japanese)

    Google Scholar 

  5. 5.

    Kim Y, Jeong S, Lee S (2011) Wedge failure analysis of soil resistance on laterally loaded piles in clay. J Geotech Geoenviron Eng 137(7):678–694

    Article  Google Scholar 

  6. 6.

    Otani J, Pham KD, Sano J (2006) Investigation of failure patterns in sand due to laterally loaded pile using X-ray CT. Soils Found 46(4):529–535

    Article  Google Scholar 

  7. 7.

    Hajialilue-Bonab M, Sojoudi Y, Puppala AJ (2011) Study of strain wedge parameters for laterally loaded piles. Int J Geomech 13(2):143–152

    Article  Google Scholar 

  8. 8.

    Ashour M, Norris G, Pilling P (1998) Lateral loading of a pile in layered soil using the strain wedge model. J Geotech Geoenviron Eng 124(4):303–315

    Article  Google Scholar 

  9. 9.

    Hokmabadi AS, Fakher A, Fatahi B (2012) Full scale lateral behaviour of monopiles in granular marine soils. Mar Struct 29(1):198–210

    Article  Google Scholar 

  10. 10.

    Norris GM (1986) Theoretically based BEF laterally loaded pile analysis, Proceedings of third international conference on numerical methods in offshore piling, Paris. France. 361–386

  11. 11.

    Ashour M, Pilling P, Norris G (2004) Lateral behavior of pile groups in layered soils. J Geotech Geoenviron Eng 130(6):580–592

    Article  Google Scholar 

  12. 12.

    Xu LY, Cai F, Wang GX, Ugai K (2013) Nonlinear analysis of laterally loaded single piles in sand using modified strain wedge model. Comput Geotech 51:60–71

    Article  Google Scholar 

  13. 13.

    Robert DH, William DK (1981) An introduction to geotechnical engineering. Printice-Hall Inc, Englewood Cliffs, New Jersey

    Google Scholar 

  14. 14.

    Das BM (2010) Principles of geotechnical engineering, 7th edn. Cengage Learning, Boston

    Google Scholar 

  15. 15.

    Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice, 3rd edn. John Wiley & SONS INC, Hoboken

    Google Scholar 

  16. 16.

    Nip DCN, Ng CWW (2005) Back-analysis of laterally loaded bored piles. Proc ICE Geotech Eng 158(2):63–73

    Article  Google Scholar 

  17. 17.

    Briaud JL, Smith T, Meyer B (1984) Laterally loaded piles and the pressuremeter: comparison of existing methods. Laterally loaded deep foundations: analysis and performance. ASTM Int 835:97–111

    Google Scholar 

  18. 18.

    De Kuiter J, Beringen FL (1979) Pile foundations for large north Sea structures. Marine Georesour Geotechnol 3:267–314

    Article  Google Scholar 

  19. 19.

    Gowda P (1991) Laterally loaded pile analysis for layered soil based on the strain wedge model, MS thesis, University of Nevada, Reno, Nevada

  20. 20.

    Skempton AW (1954) The pore-pressure coefficients A and B. Geotechnique 4:143–147

    Article  Google Scholar 

  21. 21.

    Wu TH (1976) Soil mechanics. Allyn and Bacon, Boston

    Google Scholar 

  22. 22.

    Sorensen KK, Okkels N (2013) Correlation between drained shear strength and plasticity index of undisturbed overconsolidated clays. Proceedings of 18th international conference on soil mechanics and geotechnical engineering, Paris. pp. 423–428

  23. 23.

    Duncan JM, Chang CY (1970) Nonlinear analysis of stress and strain in soils. J Soil Mech Found Div 96(5):1629–1653

    Google Scholar 

  24. 24.

    Evans LT, Duncan GM (1982) Simplified analysis of laterally loaded piles, Report No. UCB/GT/82-04, University of California, Berkeley, California

  25. 25.

    Carter DP (1984) A non-linear soil model for predicting lateral pile response, Report No. 359, Department of Civil Engineering, University of Auckland, New Zealand

  26. 26.

    Ling LF (1988) Back analysis of lateral load tests on piles. Rep. No. 460, Department of Civil Engineering, University of Auckland, New Zealand

  27. 27.

    Zienkiewicz OZ, Taylor RL (2005) The finite element method for solid and structural mechanics. Butterworth–Heinemann, Amsterdam

    MATH  Google Scholar 

  28. 28.

    Gill HL (1968) Soil behavior around laterally loaded piles, Naval civil engineering laboratory, Report R-571. Port Hueneme, California

    Google Scholar 

  29. 29.

    Rollins KM, Peterson KT, Weaver TJ (1998) Lateral load behavior of full-scale pile group in clay. J Geotech Geoenviron Eng 124(6):468–478

    Article  Google Scholar 

  30. 30.

    Matlock H (1970) Correlations for design of laterally loaded piles in clay. Proceedings of second annual offshore technology conference, Paper No. OTC 1204, 577–594

  31. 31.

    Meyer BJ (1979) Analysis of single piles under lateral loading. University of Texas, Austin

    Google Scholar 

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This research was supported by the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20150958), the National Natural Science Foundation of China (Grant Nos. 51508271, 51121005), and Postdoctoral Science Foundation of both Jiangsu Province, China (Grant No. 1501067B) and China (Grant No. 2015M581782), which are gratefully acknowledged.

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Correspondence to Fei Cai.

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Xu, LY., Cai, F., Wang, GX. et al. Nonlinear Analysis of Single Laterally Loaded Piles in Clays Using Modified Strain Wedge Model. Int J Civ Eng 15, 895–906 (2017).

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  • Strain wedge
  • py method
  • Nonlinear stress–strain relationship
  • Overconsolidated clays
  • Pile–soil interaction