Axisymmetric Vibration of Disk Resting on Saturated Layered Half‐Space
Publication: Journal of Engineering Mechanics
Volume 115, Issue 10
Abstract
The force‐displacement relationship associated with the vertical vibration of a circular rigid disk resting on a saturated layered half‐space is derived using Biot's two‐phased linear theory. The analysis relies on the use of integral transform techniques in conjunction with axisymmetric potential theory by means of which Green's functions are derived. Using the latter, the determination of the force‐displacement relationship of the disk is reduced to the evaluation of a stress function that satisfies a Fredholm integral equation of the second kind similar to that obtained in relative studies involving uniform or layered dry media. Plots of vertical stiffness and damping coefficients in terms of frequency and saturation depth‐to‐disk radius ratio are given. Comparisons are also presented with results from the corresponding dry case. Numerical results obtained from a representative range of parameters show that the effect due to the saturation on the impedence functions is generally not significant. Specifically, at low dimensionless frequencies (i.e., less than 3), this effect is practically negligible, while at higher dimensionless frequencies (i.e., between 3 and 6), the departure from the dry case was about 30%.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Achenbach, J. D. (1973). Wave propagation in elastic solids. North‐Holland Publishing Co.
2.
Anderson, W. L. (1984). “Computation of Green's tensor integrals for three‐dimensional electromagnetic problems using Hankel transforms.” Geophysics, 49(10), 1754–1759.
3.
Apsel, R. J., and Luco, E. J. (1983). “On the Green's functions for layered half‐space. Part II.” Bull. Seismol. Soc. Am., 73(4), 931–951.
4.
Biot, M. A. (1956). “The theory of propagation of elastic waves in a fluid‐saturated porous solid.” J. Acoust. Soc. Am., 28, 168–191.
5.
Brekhovskikh, L. M. (1960). Waves in layered media. Academic Press, New York, N.Y.
6.
Ewing, W. M., Jardetzky, W. S., and Press, F. (1956). Elastic waves in layered media. McGraw‐Hill Co., New York, N.Y.
7.
Frazer, N. L., and Gettrust, F. (1984). “On a generalization of Fillon's method and the computation of oscillatory integrals of seismology.” Geophys. J. Royal Astr. Soc., 76, 461–468.
8.
Halpern, M. R., and Christiano, P. (1986). “Steady‐state response of a rigid plate bearing on a liquid‐saturated poroelastic halfspace.” Int. J. Earthquake Engrg. Struct. Dyn., 14, 439–454.
9.
Kashio, J. (1970). “Steady‐state response of a circular disk resting on a layered medium,” thesis presented to Rice University, at Houston, Tex., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
10.
Luco, E. J. (1969). “Application of singular integral equations to the problem of forced vibrations of a rigid foundation,” thesis presented to the University of California, at Los Angeles, Calif., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
11.
Luco, J. E., and Westmann, R. A. (1971). “Dynamic response of circular footings.” J. Engrg. Mech., ASCE, 97(5), 1381–1395.
12.
Lung, R. H. (1980). “Seismic analysis of structures embedded in saturated soils,” thesis presented to City University of New York, at New York, N.Y., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
13.
Maslenikov, O., et al. (1985). “SMACS—A system of computer programs for probabilistic seismic analysis of structures and subsystems.” Report UCID‐20413, Lawrence Livermore Lab.
14.
Philippacopoulos, A. J. (1988a). “Lamb's problem for fluid‐saturated porous media.” Bull. Seismol. Soc. Am., 78(2), 908–923.
15.
Philippacopoulos, A. J. (1988b). “Waves in a partially saturated medium due to surface loads.” J. Engrg. Mech., ASCE, 114(10), 1740–1759.
16.
Sneddon, I. N. (1966). Mixed boundary value problems in potential theory. North‐Holland Publishing Co., New York, N.Y.
17.
Watson, G. N. (1958). A treatise on the theory of Bessel functions. 2nd Ed., Cambridge University Press, Cambridge, England.
18.
Xu, J. (1988). “Influence functions of stractures bonded to saturated elastic half‐space,” thesis presented to the City University of New York, at New York, N.Y., in partial filfillment of the requirements for the degree of Doctor of Philosophy.
Information & Authors
Information
Published In
Copyright
Copyright © 1989 ASCE.
History
Published online: Oct 1, 1989
Published in print: Oct 1989
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.