An analytical solution for the transient response of saturated porous elastic solids. (English) Zbl 0539.73128

The general forms for the field equations governing the transient response of poroelastic media given by Biot and by Zienkiewicz are compared and relations between the material constants are obtained. A one-dimensional analytical solution is presented for the situation where the solid and fluid materials satisfy Biot’s dynamic compatibility relation.


74L10 Soil and rock mechanics
76S05 Flows in porous media; filtration; seepage
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[1] Biot, J. Applied Physics 33 pp 1482– (1962)
[2] Levy, Int. J. Eng. Sci. 17 pp 1005– (1979)
[3] Auriault, Int. J. Eng. Sci. 18 pp 775– (1980)
[4] Prevost, Int. J. Eng. Sci. 8 pp 787– (1980)
[5] and , ’Variational formulation of dynamics of fluid-saturated porous elastic solids’, J. Engr. Mech. Div., ASCE, (EM4), 947-963 (1972).
[6] and , ’Seismic analysis of earth dam-reservoir systems’, J. Soil Mech. and Found. Div., ASCE, (SM10), 849-862 (1973).
[7] and , ’Liquefaction analysis of horizontally layered sands’, J. Geotech. Div, ASCE, (GT3), 341-356 (1978).
[8] ’Nonlinear transient phenomena in saturated porous media’, Comp. Mech. Appl. Mech. Engr. (1982). · Zbl 0489.73114
[9] and , ’A unified approach to soil mechanics problems’ in Finite Elements in Geomechanics, Wiley, New York, 1977, Chap. 4, pp. 151-178.
[10] ’Nonlinear problems of soil statics and dynamics’, Proc. Europe-U. S. Symposium on Nonlinear Finite Element analysis in Structural Mechanics, Ruhr-Universitat, Bochum, Springer-Verlag, 1980.
[11] Biot, J. Appl. Physics 12 pp 155– (1941)
[12] Zienkiewicz, Géotechnique 30 pp 385– (1980)
[13] and , Handbook of Mathematical Functions, National Bureau of Standards, Washington, D. C., 1965.
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