Dynamic Response of Rigid Foundations of Arbitrary Shape Using Half-Space Green’s Function
Publication: International Journal of Geomechanics
Volume 11, Issue 5
Abstract
This paper deals with the dynamic steady-state force-displacement relationships (impedance) for rigid foundations of arbitrary shape resting on a semi-infinite medium consisting of homogeneous, isotropic, linear elastic materials using the boundary element method (BEM). An elaborate numerical technique is used to calculate Green’s function, yielding a highly accurate numeric approximation in an explicit form. By using a BEM formulation for triangular elements (linear and infinite shape function) compliance of rigid massless surface foundations was obtained. The use of triangular elements causes stress continuity between elements to be satisfied. Meanwhile, the tendency for foundation edge stresses toward infinity can be modeled by using these triangular infinite stress elements. As a result of this, computations are more accurate but less time-consuming. This procedure is used to evaluate the vertical rocking compliance functions for rigid rectangular, circular, and square foundations with internal holes. Finally, comparisons are made between the results obtained from the proposed approach and those from other methods.
Get full access to this article
View all available purchase options and get full access to this article.
References
Dominguez, J., and Abascal, R. (1987). “Dynamic of foundations.” Chapter 2, Topics in boundary element research, C. A. Brebbia, ed., Vol. 4, Springer-Verlag, Berlin, 27–75.
Karabalis, D. L., and Beskos, D. E. (1987). “Three-dimensional soil-structure interaction by boundary element methods.” Chapter 1, Topics in boundary element research, C. A. Brebbia, ed., Vol. 4, Springer-Verlag, Berlin, 1–26.
Karasudhi, P., Ker, L. M., and Lee, S. (1968). “Vibratory motion of a body on an elastic half-plane.” J. Appl. Mech., 35, 697–705.
Kitamura, Y., and Sakurai, S. (1979). “Dynamic stiffness for rectangular rigid foundation on a semi-infinite elastic medium.” Int. J. Numer. Anal. Methods Geomech., 3, 159–171.
Kobori, T., Minai, R., and Suzuki, T. (1966a). “Dynamic ground compliance of rectangular foundation on an elastic stratum.” Proc. 2nd Japan Natl. Symp. Earthd. Engng., 261–266.
Kobori, T., Minai, R., and Suzuki, T. (1971). “The dynamical ground compliance of a rectangular foundation on a viscoelastic stratum.” Bull. Divas. Prey. Res. Inst., Kyoto Univ., 20, 289–329.
Kobori, T., Minai, R., Suzuki, T., and Kusakabe, K. (1966b). “Dynamical ground compliance of rectangular foundations.” Proc. 16th Japan Natl. Congress Appl. Mech.
Kobori, T., Minai, R., Suzuki, T., and Kusakabe, K. (1968). “Dynamic ground compliance of rectangular foundation on a semi-infinite viscoelastic medium.” Annual Report, Disaster prevention Research Institute of Kyoto Univ., 11, 349–367.
Lamb, H. (1904). “On the propagation of tremors over the surface of an elastic solid.” Philos. Trans. R. Soc. A, 203, 1–42.
Luco, J. E., and Westmann, R. A. (1971). “Dynamic response of circular footing.” J. Eng. Mech., 97(5), 1381–1395.
Luco, J. E., and Westmann, R. A. (1972). “Dynamic response of a rigid footing bonded to an elastic half-space.” J. Engrg. Mech. Div., 39, 527–534.
Shahi, R. (1996). “An efficient method to calculate dynamics stiffness of rigid surface foundations with arbitrary shape.” M.S. thesis, Faculty of Eng., Tehran Univ.
Tajimi, H. (1968). “Interaction of building and ground.” Chapter 2, Earthquake Engineering, (Jishin-Kogaku) et al., eds., Shokoku Co. Ltd., Japan, 55–105 (in Japanese).
Thomson, W. T., and Kobori, T. (1963). “Dynamical compliance of rectangular foundation on an elastic half-space.” J. Appl. Mech., 30, 579–584.
Veletsos, A. S., and Wei, Y. T. (1971). “Lateral and rocking vibrations of footings.” J. Soil Mech. and Found. Div., 97(9), 1227–1248.
Wei, Y. T. (1971). “Steady state of certain foundation systems.” Ph.D. thesis, Rice Univ.
Wong, H. L., and Luco, J. E. (1976). “Dynamic response of rigid foundations of arbitrary shape.” Earthquake Eng. Struct. Dyn., 4, 579–587.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 11 • Issue 5 • October 2011
Pages: 391 - 398
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Mar 8, 2010
Accepted: Oct 21, 2010
Published online: Oct 26, 2010
Published in print: Oct 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.