Analysis of Foundations on Fluid‐Filled poroelastic stratum
Publication: Journal of Engineering Mechanics
Volume 119, Issue 8
Abstract
A spatially semidiscrete finite‐element technique is developed for the linear analysis of wave propagation in layered, fluid‐filled poroelastic media. The wave motion is expressed as a combination of modes that are discrete in the vertical direction but continuous in any horizontal direction. Algebraic eigenvalue problems are derived for the wave numbers and shapes of these modes. Plane‐strain and antiplane‐shear motions are considered, while arbitrary motions in axisymmetric regions are expanded in Fourier series with respect to the azimuthal coordinate. Consistent transmitting boundaries are constructed for both plane and axisymmetric regions. In problems of dynamics of foundations, these boundaries provide an accurate and convenient representation of the far field and can be coupled directly with conventional finite elements modeling the near field. In the companion paper, results of an application of the present technique to the calculation of the dynamic stiffness of rigid strip and circular foundations are reported and analyzed.
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References
1.
Biot, M. A. (1956). “Theory of propagation of elastic waves in a fluid‐saturated porous solid. I. low‐frequency range.” J. Acoustical Soc. Am., 28(2), 168–178.
2.
Biot, M. A., and Willis, D. G. (1957). “The elastic coefficients of the theory of consolidation.” J. Appl. Mech., 24(4), 594–601.
3.
Bougacha, S. (1990). “Effects of sediments on the response of dams to earthquakes,” PhD dissertation, Univ. of Texas at Austin, Austin, Tex.
4.
Bougacha, S., and Tassoulas, J. L. (1991a). “Seismic analysis of gravity dams. I: modeling of sediments.” J. Engrg. Mech., ASCE, 117(8), 1826–1838.
5.
Bougacha, S., and Tassoulas, J. L. (1991b). “Seismic response of gravity dams. II: effects of sediments.” J. Engrg. Mech., ASCE, 117(8), 1839–1850.
6.
Bougacha, S., Roësset, J. M, and Tassoulas, J. L. (1993). “Dynamic stiffness of foundations on fluid‐filled poroelastic stratum.” J. Engrg. Mech., ASCE, 119(8), 1649–1662.
7.
Deresiewicz, H. (1960). “The effects of boundaries on wave propagation in a liquid‐filled porous solid: non‐dissipative case.” Bull. Seismological Soc. Am., 50, 599–607.
8.
Deresiewicz, H., and Rice, T. J. (1962). “The effects of boundaries on wave propagation in a liquid‐filled porous solid: general case.” Bull. Seismological Soc. Am., 52, 595–625.
9.
Ghaboussi, J., and Wilson, E. L. (1972). “Variational formulation of dynamics of fluid‐saturated porous elastic solids.” J. Engrg. Mech. Div., ASCE, 98(4), 947–963.
10.
Ghaboussi, J., and Wilson, E. L. (1973). “Seismic analysis of earth dam‐reservoir systems.” J. Soil Mech. and Found. Div., ASCE, 99(10), 849–862.
11.
Halpern, M. R., and Christiano, P. (1986a). “Response of poroelastic halfspace to steady‐state harmonic surface tractions.” Int. J. Numer. and Analytical Methods in Geomechanics, 10, 609–632.
12.
Halpern, M. R., and Christiano, P. (1986b). “Steady‐state harmonic response of a rigid plate bearing on a liquid‐saturated poroelastic halfspace.” Earthquake Engrg. and Struct. Dyn., 14, 439–454.
13.
Kausel, E. (1974). “Forced vibrations of circular foundations on layered media.” Res. Rep. R74‐11, Dept. Civ. Engrg., Massachusetts Institute of Technology, Cambridge, Mass.
14.
Kausel, E., and Roësset, J. M. (1975). “Dynamic stiffness of circular foundations.” J. Engrg. Mech. Div., ASCE, 101(6), 771–785.
15.
Kausel, E., Roësset, J. M., and Waas, G. (1975). “Dynamic analysis of footings on layered media.” J. Engrg. Mech. Div., ASCE, 101(5), 679–693.
16.
Kausel, E., and Roësset, J. M. (1977). “Semianalytical hyperelement for layered strata.” J. Engrg. Mech. Div., ASCE, 103(4), 569–588.
17.
Kurtanich, D. G., and Christiano, P. (1983). “Plate on poroelastic halfspace subjected to seismic waves.” Proc., 4th Engrg. Mech. Div. Specialty Conf., ASCE, New York, N.Y. 174–177.
18.
Lysmer, J., and Waas, G. (1972). “Shear waves in plane infinite structures.” J. Engrg. Mech. Div., ASCE, 98(1), 85–105.
19.
Mei, C. C., and Foda, M. A. (1981). “Wave induced responses in a fluid‐filled poroelastic solid with a free surface—a boundary layer theory.” Geophysical Journal of the Royal Astronomical Society, London, England, 66, 597–631.
20.
Paul, S. (1976a). “On the displacements produced in a porous elastic half‐space by an impulsive line load (non‐dissipative case).” Pure and Appl. Geophysics, 114, 605–615.
21.
Paul, S. (1976b). “On the disturbance produced in a semi‐infinite poroelastic medium by a surface load.” Pure and Appl. Geophysics, 114, 615–627.
22.
Tassoulas, J. L., and Kausel, E. (1983). “Elements for numerical analysis of wave motion in layered strata.” Int. J. Numer. Methods in Engrg., 19, 1005–1032.
23.
Waas, G. (1972). “Linear two‐dimensional analysis of soil dynamics problems in semi‐infinite layered media,” PhD dissertation, University of California, Berkeley, Berkeley, Calif.
24.
Zienkiewicz, O. C., and Shiomi, T. (1984). “Dynamic behavior of saturated porous media: the generalized biot formulation and its numerical solution.” Int. J. Numer. and Analytical Methods in Geomechanics, 8, 71–96.
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Copyright © 1993 American Society of Civil Engineers.
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Received: Oct 17, 1990
Published online: Aug 1, 1993
Published in print: Aug 1993
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