Acta Geotechnica

, Volume 14, Issue 1, pp 101–110 | Cite as

Kinematic bending of single piles in layered soil

  • Wenhai Ke
  • Qijian LiuEmail author
  • 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.


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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

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