Engineering Transactions, 27, 4, pp. 585-594, 1979

The Propagation of Elastic Waves Due to the Action of Fluid Sources in a Consolidating Medium

R. Dzięcielak
Institute of Technical Mechanics, Poznań
Poland

In this study the propagation of elastic waves due to the action of fluid sources in a fluid-saturated porous elastic solid is investigated. The basis of these considerations are the equations of motion formulated by M. A. Biot. In the first part of this work the equations governing the propagation of dilatational waves for the case of the action of fluid sources in such a medium are obtained. In the next section of this paper the action of the point source varying harmonically with time is considered. These considerations are restricted to assumption of the lower radian frequency range where the Poiseuille flow is valid. The fluid source is due to the propagation of two dilatational waves. A detailed discussion of the properties of these waves is presented in the last part of this work.

Full Text: PDF

References

M. A. BIOT. Theory of propagation of clastic waves in a fluid-saturated porous solid, Part I and Part II, J. Acoust, Soc. Am., 28, 168-191, 1956.

C.H. YEW, P.N. JOGI, Study of wave motions in a fluid-saturated porous rocks, J. Acoust. Soc. Am., 60, 2-8, 1976.

W. DERSKI, Equations of the consolidation theory for the case of a source of fluid, Bull. Acad. Polon. Sci., Ser. Sci. Techn., XIII, 37-43, 1965.

R. DZIĘCIELAK, Some applications of the reciprocal theorem for displacements to singular solutions in the theory of consolidation, Acta Mechanica, 6, 147-157, 1968.

R. DZIĘCIELAK, Exciting action of a source of fluid in 0 consolidating medium, Bull. Acad. Polon, Sci., XVII, 519-523, 1969.

R. DZIĘCIELAK, Setting of the surface of a consolidating semi-space due to the action of liquid sources, Arch. Mech., 22, 365-374, 1970.

R. DZIĘCIELAK, The Green function for the settlement of a consolidating semi-space under the action of fluid sources, Studia Geotechnica, II, 13-17, 1971.

M. A. BIOT, D. G. WILLIS, The elastic coefficients of the theory of consolidation, J. Appl. Mech., 24, 594-601, 1957.

H. DERESIEWICZ, J. T. RICE, The effect of boundaries of wave propagation in a liquid-filled porous solid, III Reflection of plane waves at a free plane boundary (General case), Bull. Seism.

Soc. Am., 52, 595-626, 1962.

I. FATT, The Biott-Willis elastic coefficients for a sandstone, J. Appl. Mech., 26, 296-297, 1959.

A.E. SCHEIDEGGER, The physics of flow through porous media, University of Toronto Press, Toronto 1957.




Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland