Torsional vibrations of a cylindrical foundation embedded in a saturated poroelastic half-space

Abstract

Considering the interactions between an embedded foundation and saturated soil, the torsional vibrations of a cylindrical foundation embedded in a saturated poroelastic medium are analyzed in this paper. Both a rigid foundation and an elastic foundation are considered. Assuming both the side surface and the bottom surface of the foundation are perfectly bonded to soil, the reaction torques that the side soil and bottom soil acting on the foundation can be gained from basic dynamic equations of the poroelastic medium. According to the dynamic equilibrium equations of a foundation under harmonic torque, the torsional vibrations of an embedded cylindrical foundation are presented. Besides, the angular amplitude of the foundation, the equivalent stiffness and damping coefficients of the soil are expressed explicitly. Selected examples are presented to investigate the influence of relevant parameters on the torsional vibrations.

Keywords

embedded foundation / saturated soil / rigid foundation / elastic foundation / torsional vibration

References

[1] Pak R Y S, Saphores J D M. Torsion of a rigid disc in a half-space. International Journal of Engineering Science, 1991, 29(1): 1–12

[2] Selvadurai A P S. Rotary osciallations of a rigid disc inclusion embedded in an isotropic elastic infinite space. International Journal of Solids and Structures, 1981, 17(5): 493–498

[3] Pak R Y S, Gobert A T. Forced vertical vibrations of rigid disks with arbitrary embedment. Journal of Engineering Mechanics, 1991, 117(11): 2527–2548

[4] Rahman M. The Reissner-Sagoci problem for a half-space under buried torsional forces. International Journal of Solids and Structures, 2000, 37(8): 1119–1132

[5] Novak M. Vertical vibration of embedded footings. Journal of the Soil Mechanics and Foundation, 1972, 98(SM12): 1291–1310

[6] Novak M, Sachs K. Torsional and coupled vibrations of embedded footings. Earthquake Engineering & Structural Dynamics, 1973, 2(1): 11–33

[7] Sankaran K S, Krishnaswamy N R, Nair P G B. Torsion vibration tests on embedded footings. Journal of Geotechnical Engineering, 1980, 106(GT3): 325–331

[8] Apsel R J, Luco J E. Impedance functions for foundations embedded in a layered medium: an integral equation approach. Earthquake Engineering & Structural Dynamics, 1987, 15(2): 213–231

[9] Spyrakos C C, Xu C J. Dynamic analysis of flexible massive strip-foundations embedded in layered soils by hybrid BEM-FEM. Computers & Structures, 2004, 82(29-30): 2541–2550

[10] Philippacopoulos A J. Buried point source in poroelastic half-space. Journal of Engineering Mechanics, 1997, 123(8): 860–869

[11] Senjuntichai T, Rajapakse R K N D. Dynamic Green’s functions of homogeneous poroelastic half-plane. Journal of Engineering Mechanics, 1994, 120(11): 2381–2404

[12] Zeng X, Rajapakse R K N D. Vertical vibrations of a rigid disk embedded in a poroelastic medium. International Journal for Numerical and Analytical Methods in Geomechanics, 1999, 23(15): 2075–2095

[13] Senjuntichai T, Sapsathiarn Y. Forced vertical vibration of circular plate in multilayered poroelastic medium. Journal of Engineering Mechanics, 2003, 129(11): 1330–1341

[14] Cai Y Q, Hu X Q. Vertical vibrations of a rigid foundation embedded in a poroelastic half space. Journal of Engineering Mechanics, 2010, 136(3): 390–398

[15] Hu X Q, Cai Y Q. Rocking vibrations of rigid cylindrical foundations embedded in saturated soil. Chinese Journal of Geotechnical Engineering, 2009, V31(8): 1200–1207 (in Chinese)

[16] Hu X Q, Cai Y Q. Vertical vibration of rigid embedded foundations in saturated soil overlying bedrock. Rock and Soil Mechanics, 2009, 30(12): 3739–3746 (in Chinese)

[17] Baranov V A. On the calculation of excited vibrations of an embedded foundation. Polytechnical Institute of Riga: Voprosy Dynamiki I Prochnocti, 1967, 195–209(in Russia)

[18] Chen L, Wang G. Torsional oscillations of a rigid disc on saturated poroelastic ground. Engineering Mechanics, 2003, 20: 131–136 (in Chinese)

[19] Bishop R E D, Johnson D C. The mechanics of vibration. Cambridge University Press, 1979: 245–247

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51108421) and the Program for Zhejiang Leading Tearm of S&T Innovation (Grant No. 2011R50020).

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg