Skip to main content
SpringerLink
Log in

A new dynamic interaction factor for the analysis of pile groups subjected to vertical dynamic loads

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

Τhis paper presents an analytical method for calculating the steady-state impedance factors of pile groups of arbitrary configuration subjected to harmonic vertical loads. The derived solution allows considering the effect of the actual pile geometry on the contribution of pile-soil-pile interaction to the response of the group, via the introduction of a new dynamic interaction factor, defined on the basis of soil resistance instead of pile displacements. The solution is first validated against a published solution for single piles that accounts for the effect of pile geometry on the generated ground vibrations. Accordingly, we show that the derived soil attenuation factor agrees well with existing solutions for pile groups in the high frequency range, but considerable differences are observed in both the stiffness and damping components of the computed impedance when the relative spacing between piles decreases. Numerical results obtained for typical problem parameters suggest that ignoring pile geometry effects while estimating the contribution of pile-soil-pile interaction in the response may lead to inaccurate results, even for relative large pile group spacings.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

r, \(\theta\), z :

Radial, circumferential and vertical directions in the cylindrical coordinate system 1

\(r^{\prime}\), \(\theta^{\prime}\) :

Radial and circumferential directions in the cylindrical coordinate system 2

m :

Number of piles in the group

d :

Pile diameter

R :

Pile radius

H :

Pile length

E p :

Elasticity modulus of pile

A p :

Cross-sectional area of pile

ρ p :

Mass density of pile

C p :

Wave propagation velocity of pile

mFeiωt :

Vertical harmonic force applied on the cap of the pile group

ω :

Circular frequency

λ*, G* :

Lame’s constants of soil

\(\rho\) :

Mass density of soil

\(U_{z}\) :

Soil displacement

n :

The nth mode (n = 1,2,3…)

An, Akn, Atn, Sk1, Sk2 :

Undetermined coefficients

R n :

Soil reaction factor

Z n :

Soil mode

K 0 :

Modified second kind Bessel functions of zero order

q1n, q2n, gn, β1n, β2n, \(\bar{u}_{pk}\), \(\tilde{u}_{pk}\), \(\iota_{n}\), \(\chi_{n}\), γk1, γk2, γk3, γt1, γt2, \(\zeta_{kn}\), \(\zeta_{tn}\), \(\varGamma_{k}\), \(\varGamma_{t}\) :

Temporary variables

\(\tau_{rz}\) :

Soil shear stress

f :

Soil resistance to pile displacement

f a :

Soil resistance relevant to source pile

f p :

Soil resistance relevant to receiver pile

r a :

Radius of source pile

r p :

Radius of receiver pile

r k :

Radius of pile k

r t :

Radius of pile t

r 0 :

Distance between the origins of the two systems

θ 0 :

Angle between the horizontal axis r and the line connecting the two origins of the coordinate systems

~:

Quantities expressed in the cylindrical coordinate system 2

\(\psi\) :

Soil attenuation function

S :

Distance between the centre of two piles

\(\beta_{\text{s}}\) :

Hysteretic damping ratio of soil

v s :

Poisson’s ratio of soil

V s :

Wave propagation velocity in soil

\(H_{0}^{\left( 2 \right)}\) :

Hankel function of zero order and second kind

a 0 :

Dimensionless frequency

\(\alpha\) :

Standard pile interaction factor

\(\kappa\) :

Proposed pile interaction factor

\(\kappa_{kt}\) :

Interaction factor between pile k and pile t

F k :

Total soil resistance relevant to pile k

f k :

Soil resistance relevant to pile k

f t :

Soil resistance relevant to pile t

\(u_{pk}\) :

Vertical displacement of pile k

\(K\) :

Complex impedance of pile group

\(k_{\text{G}}\) :

Real component of the pile group impedance

\(c_{\text{G}}\) :

Imaginary component of the pile group impedance

k :

Real component of single pile impedance

c :

Imaginary component of single pile impedance

References

  1. Ottaviani M (1975) Three-dimensional finite element analysis of vertically loaded pile groups. Géotechnique 25(2):159–174

    Article  Google Scholar 

  2. Pressley JS, Poulos HG (1986) Finite element analysis of mechanisms of pile group behaviour. Int J Numer Anal Meth Geomech 10(2):213–221

    Article  Google Scholar 

  3. Di Laora R, Mandolini A, Mylonakis G (2012) Insight on kinematic bending of flexible piles in layered soil. Soil Dyn Earthq Eng 43:309–322

    Article  Google Scholar 

  4. Di Laora R, Mylonakis G, Mandolini A (2013) Pile-head kinematic bending in layered soil. Earthq Eng Struct Dyn 42(3):319–337

    Article  Google Scholar 

  5. Mucciacciaro M, Sica S (2018) Nonlinear soil and pile behaviour on kinematic bending response of flexible piles. Soil Dyn Earthq Eng 107:195–213

    Article  Google Scholar 

  6. Mamoon SM, Kaynia AM, Banerjee PK (1990) Frequency domain dynamic analysis of piles and pile groups. ASCE J Eng Mech 116(10):2237–2257

    Article  Google Scholar 

  7. Padron LA, Aznárez JJ, Maeso O (2007) BEM-FEM coupling model for the dynamic analysis of piles and pile groups. Eng Anal Bound Elem 31(6):473–484

    Article  Google Scholar 

  8. Ai ZY, Li PC, Shi BK, Hu YD (2018) Influence of a point sink on a pile group in saturated multilayered soils with anisotropic permeability. Int J Numer Anal Methods Geomech 42(6):856–870

    Article  Google Scholar 

  9. Poulos HG (1968) Analysis of the settlement of pile groups. Géotechnique 18(4):449–471

    Article  Google Scholar 

  10. Novak M (1974) Dynamic stiffness and damping of piles. Can Geotech J 11(4):574–598

    Article  Google Scholar 

  11. Luan L, Zheng C, Kouretzis G, Ding X (2020) Dynamic analysis of pile groups subjected to horizontal loads considering coupled pile-to-pile interaction. Comput Geotech 117:103276

    Article  Google Scholar 

  12. Randolph MF, Wroth CP (1979) An analysis of the vertical deformation of pile groups. Géotechnique 29(4):423–439

    Article  Google Scholar 

  13. Nogami T (1983) Dynamic group effect in axial responses of grouped piles. J Geotechn Eng Div ASCE 109:225–243

    Google Scholar 

  14. El Sharnouby B, Novak M (1990) Stiffness constants and interaction factors for vertical response of pilegroups. Can Geotech J 27(6):813–822

    Article  Google Scholar 

  15. Luan L, Zheng C, Kouretzis G, Cao G, Zhou H (2019) Development of a three-dimensional soil model for the dynamic analysis of end-bearing pile groups subjected to vertical loads. Int J Numer Anal Meth Geomech 43(9):1784–1793

    Article  Google Scholar 

  16. Luan L, Ding X, Zheng C, Kouretzis G, Wu Q (2020) Dynamic response of pile groups subjected to horizontal loads. Can Geotech J 57(4):469–481

    Article  Google Scholar 

  17. Zhang S, Cui C, Yang G (2019) Vertical dynamic impedance of pile groups partially embedded in multilayered, transversely isotropic, saturated soils. Soil Dyn Earthq Eng 117:106–115

    Article  Google Scholar 

  18. Kaynia AM, Kausel E (1982) Dynamic stiffness and seismic response of pile groups. Research Report R82-03, Massachusetts Institute of Technology

  19. Dobry R, Gazetas G (1988) Simple method for dynamic stiffness and damping of floating pile groups. Géotechnique 38(4):557–574

    Article  Google Scholar 

  20. Gazetas G, Makris N (1991) Dynamic pile-soil-pile interaction. Part I: analysis of axial vibration. Earthq Eng Struct Dyn 20(2):115–132

    Article  Google Scholar 

  21. Wang AD, Wang WD, Huang MS, Wu JB (2016) Interaction factor for large pile groups. Géotechn Lett 6(1):58–65

    Article  Google Scholar 

  22. Mylonakis G, Gazetas G (1998) Vertical vibration and additional distress of grouped piles in layered soil. Soils Found 38(1):1–14

    Article  Google Scholar 

  23. Sheil BB, McCabe BA (2016) An analytical approach for the prediction of single pile and pile group behaviour in clay. Comput Geotech 75:145–158

    Article  Google Scholar 

  24. Torshizi MF, Saitoh M, Álamo GM, Goit CS, Padrón LA (2018) Influence of pile radius on the pile head kinematic bending strains of end-bearing pile groups. Soil Dyn Earthq Eng 105:184–203

    Article  Google Scholar 

  25. Mylonakis G (2001) Elastodynamic model for large-diameter end-bearing shafts. Soils Found 41(3):31–44

    Article  Google Scholar 

  26. Nogami T, Novak M (1976) Soil-pile interaction in vertical vibration. Earthquake Eng Struct Dyn 4(3):277–293

    Article  Google Scholar 

  27. Zheng C, Ding X, Li P, Fu Q (2015) Vertical impedance of an end-bearing pile in viscoelastic soil. Int J Numer Anal Methods Geomech 39(6):676–684

    Article  Google Scholar 

  28. Sanchez-Salinero I (1983) Dynamic stiffness of pile groups: approximate solutions. Geotechnical Engineering Center, Civil Engineering Department, the University of Texas at Austin

  29. Roesset JM (1984) Dynamic stiffness of pile groups. In: Analysis and design of pile foundations. ASCE, pp 263–286

  30. Zheng C, Liu H, Ding X (2016) Lateral dynamic response of a pipe pile in saturated soil layer. Int J Numer Anal Methods Geomech 40(2):159–184

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Numbers 51622803, 51708064, 51878103).

Author information

Authors and Affiliations

  1. College of Civil Engineering, Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing, People’s Republic of China

    Lubao Luan & Xuanming Ding

  2. School of Civil Engineering, Fujian University of Technology, Fuzhou, People’s Republic of China

    Changjie Zheng

  3. Priority Research Centre for Geotechnical Science and Engineering, Faculty of Engineering and Built Environment, The University of Newcastle, Callaghan, NSW, Australia

    George Kouretzis

  4. Coffey Geotechnics Pty Ltd, Sydney, NSW, Australia

    Harry Poulos

Authors
  1. Lubao Luan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Changjie Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. George Kouretzis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xuanming Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Harry Poulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuanming Ding.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luan, L., Zheng, C., Kouretzis, G. et al. A new dynamic interaction factor for the analysis of pile groups subjected to vertical dynamic loads. Acta Geotech. 15, 3545–3558 (2020). https://doi.org/10.1007/s11440-020-00989-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-020-00989-7

Keywords

Search

Navigation