Skip to main content
SpringerLink
Log in

Effect of material damping on the impedance functions of an embedded circular foundation under vertical and horizontal excitation

  • Technical paper
  • Published:
Innovative Infrastructure Solutions Aims and scope Submit manuscript

Abstract

Machine foundations are generally affected by the vibratory shocks from different machines. The behavior of these foundations is influenced by the properties of underlying soil and the excitation frequency of the applied dynamic load. The influence of material damping on the dynamic impedance functions of a circular disk embedded in homogeneous elastic half space is analyzed using one-dimensional wave propagation in cones (cone model) and the results are presented in the form of dimensionless plots to observe the more realistic response of machine foundations. Three different types of material damping models viz., Hysteretic, Voigt and Kelvin model are introduced in the above elastic solutions using correspondence principle. The spring and damping coefficients of the embedded foundation are then computed in a wide range of frequency of excitation under vertical and horizontal mode of vibration varying the influencing parameters namely dimensionless frequency (a0), Poisson’s ratio (ν), embedment ratio (e/r0) and damping ratio (ξ). The outcomes from the present analysis suggest that the spring coefficient is nonlinearly affected by the dimensionless frequency and embedment ratio, for both the modes of vibration. The effect of material damping on spring coefficient is only significant for a0> 2, irrespective of the damping model used.

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

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
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

a 0 :

Dimensionless frequency

c :

Appropriate wave velocity

c s :

Shear wave velocity

e :

Embedment of foundation

K Static :

Static stiffness coefficient of disk on homogeneous half space

r 0 :

Radius of foundation

z 0 :

Apex height of the truncated cone

ω :

Excitation frequency

ν :

Poisson’s ratio

ξ :

Damping ratio

S (ω):

Dynamic impedance as a function of excitation frequency

S (a 0):

Dynamic impedance as a function of non-dimensional frequency

S (a 0)damped :

Dynamic impedance, considering material damping

k* (a 0):

Spring coefficient, considering material damping

c* (a 0):

Damping coefficient, considering material damping

References

  1. Luco JE, Wong HL, Trifunac MD (1975) A note on the dynamic response of rigid embedded foundations. Earthq Eng Struct Dyn 4(2):119–127

    Article  Google Scholar 

  2. Gazetas G (1983) Analysis of machine foundation vibrations: state of the art. Int J Soil Dyn Earthq Eng 2(1):2–42

    Article  Google Scholar 

  3. Gazetas G (1991) Formulas and charts for impedances of surface and embedded foundations. J Geotech Eng 117(9):1363–1381

    Article  Google Scholar 

  4. Mita A, Luco JE (1989) Impedance functions and input motions for embedded square foundations. J Geotech Eng 115(4):491–503

    Article  Google Scholar 

  5. Meek JW, Wolf JP (1992) Cone models for homogeneous soil. I. J Geotech Eng 118(5):667–685

    Article  Google Scholar 

  6. Meek JW, Wolf JP (1994) Cone models for embedded foundation. J Geotech Eng 120(1):60–80

    Article  Google Scholar 

  7. Wolf JP (1994) Foundation vibration analysis using simple physical models. Pearson Education, London

    Google Scholar 

  8. Wolf JP (1997) Spring-dashpot-mass models for foundation vibrations. Earthq Eng Struct Dyn 26(9):931–949

    Article  Google Scholar 

  9. Baidya DK, Krishna GM (2001) Investigation of resonant frequency and amplitude of vibrating footing resting on a layered soil system. Geotech Test J 24(4):409–417

    Article  Google Scholar 

  10. Jaya KP, Prasad AM (2002) Embedded foundation in layered soil under dynamic excitations. Soil Dyn Earthq Eng 22(6):485–498

    Article  Google Scholar 

  11. Şafak E (2006) Time-domain representation of frequency-dependent foundation impedance functions. Soil Dyn Earthq Eng 26(1):65–70

    Article  Google Scholar 

  12. Chen SS, Shi JY (2007) Simplified model for torsional foundation vibrations. Soil Dyn Earthq Eng 27(3):250–258

    Article  Google Scholar 

  13. Celebi E, Fırat S, Çankaya I (2006) The evaluation of impedance functions in the analysis of foundations vibrations using boundary element method. Appl Math Comput 173(1):636–667

    Google Scholar 

  14. Pradhan PK, Baidya DK, Ghosh DP (2004) Dynamic response of foundations resting on layered soil by cone model. Soil Dyn Earthq Eng 24(6):425–434

    Article  Google Scholar 

  15. Pradhan PK, Mandal A, Baidya DK, Ghosh DP (2008) Dynamic response of machine foundation on layered soil: cone model versus experiments. Geotech Geol Eng 26(4):453–468

    Article  Google Scholar 

  16. Pradhan PK, Baidya DK, Ghosh DP (2003) Impedance functions of circular foundation resting on layered soil using cone model. Electron J Geotech Eng 8(B):1

    Google Scholar 

  17. Pradhan PK, Baidya DK, Ghosh DP (2003) Horizontal impedance of circular foundation resting on layered soil. Electron J Geotech Eng 8(D):1

    Google Scholar 

  18. Wolf JP, Deeks AJ (2004) Cones to model foundation vibrations: incompressible soil and axi-symmetric embedment of arbitrary shape. Soil Dyn Earthq Eng 24(12):963–978

    Article  Google Scholar 

  19. Wolf JP, Deeks AJ (2004) Foundation vibration analysis: a strength of materials approach. Elsevier, Amsterdam

    Google Scholar 

  20. Baidya DK, Muralikrishna G, Pradhan PK (2006) Investigation of foundation vibrations resting on a layered soil system. J Geotech Geoenviron Eng 132(1):116–123

    Article  Google Scholar 

  21. Liou GS, Chung IL (2009) Impedance matrices for circular foundation embedded in layered medium. Soil Dyn Earthq Eng 29(4):677–692

    Article  Google Scholar 

  22. Mandal A, Baidya DK, Roy D (2012) Dynamic response of the foundations resting on a two-layered soil underlain by a rigid layer. Geotech Geol Eng 30(4):775–786

    Article  Google Scholar 

  23. Han Z, Zhou M, Zhou X, Yang L (2019) Dynamic response of 3D surface/embedded rigid foundations of arbitrary shapes on multi-layered soils in time domain. Int J Struct Stab Dyn 19(9):1950106

    Article  Google Scholar 

  24. Avilés J, Pérez-Rocha LE (1996) A simplified procedure for torsional impedance functions of embedded foundations in a soil layer. Comput Geotech 19(2):97–115

    Article  Google Scholar 

Download references

Funding

Not applicable.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Veer Surendra Sai University of Technology, Burla, India

    Suvendu Kumar Sasmal & Pradip Kumar Pradhan

Authors
  1. Suvendu Kumar Sasmal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pradip Kumar Pradhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suvendu Kumar Sasmal.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sasmal, S.K., Pradhan, P.K. Effect of material damping on the impedance functions of an embedded circular foundation under vertical and horizontal excitation. Innov. Infrastruct. Solut. 6, 4 (2021). https://doi.org/10.1007/s41062-020-00370-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41062-020-00370-3

Keywords

Search

Navigation