Skip to main content
SpringerLink
Log in

Longitudinal vibration of pile in layered soil based on Rayleigh-Love rod theory and fictitious soil-pile model

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

The dynamic response of pile in layered soil is theoretically investigated when considering the transverse inertia effect. Firstly, the fictitious soil-pile model is employed to simulate the dynamic interaction between the pile and the soil layers beneath pile toe. The dynamic interactions of adjacent soil layers along the vertical direction are simplified as distributed Voigt models. Meanwhile, the pile and fictitious soil-pile are assumed to be viscoelastic Rayleigh-Love rods, and both the radial and vertical displacement continuity conditions at the soil-pile interface are taken into consideration. On this basis, the analytical solution for dynamic response at the pile head is derived in the frequency domain and the corresponding quasi-analytical solution in the time domain is then obtained by means of the convolution theorem. Following this, the accuracy and parameter value of the hypothetical boundaries for soil-layer interfaces are discussed. Comparisons with published solution and measured data are carried out to verify the rationality of the present solution. Parametric analyses are further conducted by using the present solution to investigate the relationships between the transverse inertia effects and soil-pile parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. DAVIES R M. A critical study of the Hopkinson pressure bar [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1948, 240(821): 375–457.

    Article  MATH  Google Scholar 

  2. KRAWCZUK M, GRABOWSKA J, PALACZ M. Longitudinal wave propagation. Part I-Comparison of rod theories [J]. Journal of Sound and Vibration, 2006, 295: 461–478.

    Article  Google Scholar 

  3. ANDERSON S P. Higher-order rod approximations for the propagation of longitudinal stress waves in elastic bars [J]. Journal of Sound and Vibration, 2006, 290: 290–308.

    Article  MATH  MathSciNet  Google Scholar 

  4. FEDOTOV I A, POLYANIN A D, SHATALOV M Y. Theory of free and forced vibrations of a rigid rod based on the Rayleigh model [J]. Mechanics, 2007, 52(11): 607–612.

    MATH  Google Scholar 

  5. STEPHEN N G, LAI K F, YOUNG K, CHAN K T. Longitudinal vibrations in circular rods: A systematic approach [J]. Journal of Sound and Vibration, 2012, 331: 107–116.

    Article  Google Scholar 

  6. HAN J B, HONG S Y, SONG J H, KWON H W. Vibrational energy flow models for the Rayleigh-Love and Rayleigh-Bishop rods [J]. Journal of Sound and Vibration, 2014, 333: 520–540.

    Article  Google Scholar 

  7. SHATALOV M, SCHIESSER W, POLYANIN A, FEDOTOV I. Rayleigh-Love model of longitudinal vibrations of conical and exponential rods: Exact solutions and numerical simulation by the method of lines [C]// 18th International Congress on Sound and Vibration. England: Curran Associates, 2011: 1820–1827.

    Google Scholar 

  8. LI Qiang, WANG Kui-hua, XIE Kang-he. Dynamic response for vertical vibration of large diameter pile in saturated soil [J]. Journal of Vibration Engineering, 2005, 18(4): 500–505. (in Chinese)

    Google Scholar 

  9. YANG Xiao, PAN Yuan. Axisymmetrical analytical solution for vertical vibration of end-bearing pile in saturated viscoelastic soil layer [J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(2): 193–204.

    Article  MATH  MathSciNet  Google Scholar 

  10. WU Wen-bing, WANG Kui-hua, WU Deng-hui, MA Bo-ning. Study of dynamic longitudinal impedance of tapered pile considering lateral inertial effect [J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(2): 3618–3625. (in Chinese)

    Google Scholar 

  11. NOGAMI T, REN F Z, CHEN J W, MASON A B. Vertical vibration of pile in vibration in vibration-induced excess pore pressure field [J]. Journal of Geotechnical and Geoenvironmental Engineering, 1997, 123(5): 422–429.

    Article  Google Scholar 

  12. WANG Kui-hua, XIE Kang-he, ZENG Guo-xi. Analytical solution to vibration of finite length pile under exciting force and its application [J]. Chinese Journal of Geotechnical Engineering, 1997, 19(6): 27–35. (in Chinese)

    Google Scholar 

  13. NOVAK M. Dynamic stiffness and damping of piles [J]. Canadian Geotechnical Journal, 1974, 11(4): 574–598.

    Article  Google Scholar 

  14. NOGAMI T, KONAGAI K. Dynamic response of vertically loaded nonlinear pile foundation [J]. Journal of Geotechnical Engineering, 1987, 113(2): 147–160.

    Article  Google Scholar 

  15. SHAHMOHAMADI M, KHOJASTEH A, RAHIMIAN M, PAK R Y S. Seismic response of an embedded pile in a transversely isotropic half-space under incident P-wave excitations [J]. Soil Dynamics and Earthquake Engineering, 2011, 31(3): 361–371.

    Article  Google Scholar 

  16. WU Wen-bing, WANG Kui-hua, ZHANG Zhi-qing, LEO C J. Soil-pile interaction in the pile vertical vibration considering true three-dimensional wave effect of soil [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37: 2860–2876.

    Article  Google Scholar 

  17. LYSMER J, RICHART F E. Dynamic response of footings to vertical load [J]. Journal of Soil Mechanics and Foundations Division, 1966, 92 (SM1): 65–91.

    Google Scholar 

  18. MILITANO G, RAJAPAKSE R K N D. Dynamic response of pile in a multi-layered soil to transient torsional and axial loading [J]. Géotechnique, 1999, 49(1): 91–109.

    Article  Google Scholar 

  19. ZENG X, RAJAPAKSE R K N D. Dynamic axial load transfer from elastic bar to poroelastic medium [J]. Journal of Engineering Mechanics, 1999, 125(9): 1048–1055.

    Article  Google Scholar 

  20. WANG Kui-hua, WU Wen-bing, ZHANG Zhi-qing, LEO C J. Vertical dynamic response of an inhomogeneous viscoelastic pile [J]. Computers and Geotechnics, 2010, 37(4): 536–544.

    Article  Google Scholar 

  21. WU Wen-bing, WANG Kui-hua, MA Shao-jun, LEO C J. Longitudinal dynamic response of pile in layered soil based on virtual soil pile model [J]. Journal of Central South University, 2012, 19: 1999–2007.

    Article  Google Scholar 

  22. WANG Ning, WANG Kui-hua, WU Wen-bing. Analytical model of vertical vibrations in piles for different tip boundary conditions: parametric study and applications [J]. Journal of Zhejiang University-Science A, 2013, 14(2): 79–93.

    Article  Google Scholar 

  23. YU Jin, CAI Yan-yan, WU Wen-bing. Effect of sediment on vertical dynamic impedance of rock-socketed pile with large diameter [J]. Journal of Central South University, 2013, 20: 2856–2862.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Soft Soils and Geoenvironmental Engineering of Ministry of Education (Zhejiang University), Hangzhou, 310058, China

    Shu-hui Lü  (吕述晖) & Kui-hua Wang  (王奎华)

  2. Engineering Faculty, China University of Geosciences, Wuhan, 430074, China

    Wen-bing Wu  (吴文兵)

  3. School of Computing, Engineering and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith, Sydney, NSW, 2751, Australia

    C. J. Leo

Authors
  1. Shu-hui Lü  (吕述晖)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kui-hua Wang  (王奎华)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wen-bing Wu  (吴文兵)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. J. Leo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kui-hua Wang  (王奎华).

Additional information

Foundation item: Projects(51378464, 51309207) supported by the National Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lü, Sh., Wang, Kh., Wu, Wb. et al. Longitudinal vibration of pile in layered soil based on Rayleigh-Love rod theory and fictitious soil-pile model. J. Cent. South Univ. 22, 1909–1918 (2015). https://doi.org/10.1007/s11771-015-2710-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-015-2710-8

Key words

Search

Navigation