Skip to main content
SpringerLink
Log in

Dynamic Interaction Between an Embedded Disc and a Nonhomogeneous Saturated Stratum Under Torsional Excitation

  • Original Paper
  • Published:
Geotechnical and Geological Engineering Aims and scope Submit manuscript

Abstract

Assuming the shear modulus of nonhomogeneous soil increased linearly with depth, taking into account the characteristics of torsional vibration, the dynamic motion equations of a nonhomogeneous saturated soil were established. By using Hankel integral transform, the tangential displacement and shear stresses in Hankel transform domain were formulated. The upper surface of the nonhomogeneous saturated stratum underlain by bedrock was free, and there was no shear stress in the upper surface. The lower surface of the stratum was fully bonded to bedrock, and the displacement in the lower surface was zero. In the plane where the foundation was embedded, mixed boundary conditions were considered. Thus, the dual integral equations of a rigid disc embedded in a nonhomogeneous saturated stratum were established. By appropriate transform, the dual integral equations were converted to a Fredholm integral equation of the second kind, which could be solved by numerical method, thus the torsional dynamic response problem was solved. Comparing with the relation between a static torque and angular displacement, the dynamic compliance coefficient and the torsional angular amplitude were given. The problem was reduced to a simplify case and compared with previous research results. Selected numerical studies indicate that both the embedment depth of the foundation and the degree of soil’s nonhomogeneity have an influence on the dynamic compliance coefficient, the torsional angular amplitude and the resultant contact shear stress.

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

Similar content being viewed by others

References

  • Asik MZ (1999) Dynamic response analysis of the machine foundations on a nonhomogeneous soil layer. Comput Geotech 24:141–153

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Awojobi AO (1973) Torsional vibration of a rigid circular body on a non-homogeneous elastic stratum. Quart J Mech Appl Math XXVI:235–247

    Article  Google Scholar 

  • Biot MA (1956a) Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range. J Acoust Soc Am 28:168–178

    Article  Google Scholar 

  • Biot MA (1956b) Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J Acoust Soc Am 28:179–191

    Article  Google Scholar 

  • Biot MA (1962) Mechanics of deformation and acoustic propagation in porous media. J Appl Phys 33:1482–1498

    Article  Google Scholar 

  • Bycroft GN (1956) Forced vibrations of a rigid circular plate on a semi-infinite elastic space and on an elastic stratum. Philos Trans R Soc Lond 248:327–368

    Article  Google Scholar 

  • Cai YQ, Wu DZ, Xu CJ (2005) Torsional vibrations of a rigid circular plate on saturated stratum overlaying bedrock. Acta Mech Solida Sin 18:142–149

    Google Scholar 

  • Cai YQ, Hu XQ, Xu CJ, Hong ZS (2009) Vertical dynamic response of a rigid foundation embedded in a poroelastic soil layer. Int J Numer Anal Meth Geomech 33:1363–1388

    Article  Google Scholar 

  • Chen SL, Zhang JM, Chen LZ (2002) Dynamic response of a rigid circular footing on single-layered saturated soil. Acta Mech Solida Sin 23:325–329

    Google Scholar 

  • Chen G, Cai YQ, Liu FY, Sun HL (2008) Dynamic response of a pile in a transversely isotropic saturated soil to transient torsional loading. Comput Geotech 35:165–172

    Article  Google Scholar 

  • Collins WD (1962) The forced torsional oscillations of an elastic half-space and an elastic stratum. Proc Lond Math Soc 12:226–244

    Article  Google Scholar 

  • Coskun I, Engin H, Erguven ME (1999) Non-linear forced vibrations of an inhomogeneous layer. J Sound Vib 228:91–108

    Article  Google Scholar 

  • Du QW, Zhu XR, Ding BY (2007) Dynamic green’s function for gibson soil subjected to internal excitation. Eng Mech 24:45–49

    Google Scholar 

  • Gibson RE, Brown PT, Andrews KRF (1971) Some results concerning displacements in a non-homogeneous elastic layer. Zeitschrift für angewandte Math und Phys ZAMP 22:855–864

    Article  Google Scholar 

  • Gladwell GML (1969) The forced torsional vibration of an elastic stratum. Int J Eng Sci 7:1011–1024

    Article  Google Scholar 

  • Huang Y, Wang XG (2005) Dynamic interaction between elastic thick circular plate and transversely isotropic saturated soil ground. Appl Math Mech (Engl Ed) 26:1146–1157

    Article  Google Scholar 

  • Nobel B (1963) The solution of Bessel function dual integral equations by a multiplying-factor method. Proc Camb Philos Soc 59:351–362

    Article  Google Scholar 

  • Pak RYS, Abedzadeh F (1993) Forced torsional oscillation from the interior of a half-space. J Sound Vib 160:401–415

    Article  Google Scholar 

  • Pal PC, Mandal D, Sen B (2011) Torsional oscillations of a rigid disc embedded in a transversely isotropic elastic half-space. Adv Theor Appl Mech 4:177–188

    Google Scholar 

  • Pan E (1999) Green’s functions in layered poroelastic half-spaces. Int J Numer Anal Methods Geomech 23:1631–1653

    Article  Google Scholar 

  • Rajapakse RKND, Senjuntichai T (1995) Dynamic response of a multi-layered poroelastic medium. Earthq Eng Struct Dyn 24:703–722

    Article  Google Scholar 

  • Sharfuddin SM (1971) Torsional oscillations of an elastic stratum. Acta Mech 11:1–8

    Article  Google Scholar 

  • Taguchi I, Kurashige M (2002) Fundamental solutions for a fluid-saturated, transversely isotropic, poroelastic solid. Int J Numer Anal Methods Geomech 26:299–321

    Article  Google Scholar 

  • Wang XG (2007) Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground. Appl Math Mech 28:1383–1396. doi:10.1007/s10483-007-1011-3

    Article  Google Scholar 

  • Wang XG (2009) 3D Lamb’s problm in transversely isotropic saturated soils subjected to internal excitation. Chin J Geotech Eng 31:1686–1691

    Google Scholar 

  • Wang K, Zhang Z, Leo CJ, Xie K (2009) Dynamic torsional response of an end bearing pile in transversely isotropic saturated soil. J Sound Vib 327:440–453

    Article  Google Scholar 

  • Wu DZ, Zhang ZY (2014) Torsion of a nonhomogeneous saturated soil. Geotech Spec Publ GSP 240:29–38

    Google Scholar 

  • Wu DZ, Cai YQ, Xu CJ, Chen G (2006a) Torsional vibrations of rigid disk resting on transversely isotropic saturated soil overlaying bedrock. J Zhejiang Univ (Eng Sci) 40:281–284

    Google Scholar 

  • Wu DZ, Cai YQ, Xu CJ, Zhan H (2006b) Torsional vibrations of rigid circular plate on transversely isotropic saturated soil. Appl Math Mech (Engl Ed) 27:1541–1548

    Article  Google Scholar 

  • Xu MJ, Wang C, Meng K (2004) Verticale vibration analysis of Gibson soils and layered saturated soils under cyclic loading. J Zhejiang Univ (Eng Sci) 38:1015–1019

    Google Scholar 

Download references

Acknowledgments

The authors acknowledge the financial support provided by National Natural Science Foundation of China under contract No. 51108421, the Program for Zhejiang Leading Team of S&T Innovation under contract No. 2011R50020, and the 521 Training Program of Zhejiang Sci-Tech University.

Author information

Authors and Affiliations

  1. School of Civil Engineering and Architecture, Zhejiang Sci-Tech University, 928 Second Avenue, Xiasha Higher Education Zone, Hangzhou, 310018, Zhejiang, China

    Dazhi Wu & Zhenying Zhang

Authors
  1. Dazhi Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenying Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dazhi Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, D., Zhang, Z. Dynamic Interaction Between an Embedded Disc and a Nonhomogeneous Saturated Stratum Under Torsional Excitation. Geotech Geol Eng 34, 323–332 (2016). https://doi.org/10.1007/s10706-015-9947-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10706-015-9947-8

Keywords

Search

Navigation