Plane-Strain Instability of Saturated Porous Media
Publication: Journal of Engineering Mechanics
Volume 121, Issue 6
Abstract
Herein we investigate the plane-strain instability of rectangular blocks that are made of porous materials saturated with a fluid. We model the material behavior with rate-type constitutive equations, and study instability generated by the interaction of nearly incompressible solid and fluid constituents. Our investigation, although it applies to a broad range of materials, is limited to hypoelastic and elastoplastic models. Elastoplastic models are found to undergo two-phase instability even though the solid phase remains stable. Two-phase instability is more likely to occur in contractant hardening materials than in dilatant materials. Its emergence is triggered by the solid-fluid interaction, and is delayed by the grain-fluid compressibility. Two-phase instability also takes place in dilatant materials, but is less catastrophic than in contractant materials. The present analysis is useful for distinguishing the physical from the artifical origins of instabilities, which is an important issue in the numerical solutions of soil-liquefaction problems.
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References
1.
Bardet, J. P.(1989). “Finite element analysis of surface instability.”J. Comp. Methods in Appl. Mech. and Engrg., 78, 273–296.
2.
Bardet, J. P.(1990). “Finite element analysis of plane strain bifurcation within compressible solids.”Comp. and Struct., 36(6), 993–1007.
3.
Bardet, J. P.(1991a). “Analytical solutions for the plane strain bifurcation of compressible solids.”J. Appl. Mech., 58, 651–657.
4.
Bardet, J. P.(1991b). “Orientation of shear bands in frictional soils.”J. Engrg. Mech., ASCE, 117(7), 1466–1484.
5.
Bardet, J. P.(1992). “A viscoelastic model for the dynamic behavior of saturated poroelastic materials.”J. Appl. Mech., 59, 128–135.
6.
Biot, M.(1941). “General theory of three dimensional consolidation.”J. Appl. Phys., 12, 155–164.
7.
Biot, M. (1965). Mechanics of incremental deformations . John Wiley & Sons, New York, N.Y.
8.
Bowen, R. M.(1982). “Compressible porous media models by use of the theory of mixtures.”Int. J. Engrg. Sci., 20(6), 697–735.
9.
Hill, R. (1950). The mathematical theory of plasticity . Oxford University Press, London, England.
10.
Hill, R.(1959). “Some basic principles in the mechanics of solids without a natural time.”J. Mech. Phys. Solids, 7, 209.
11.
Hill, R., and Hutchinson, J. W.(1975). “Bifurcation phenomena in the plane tension test.”J. Mech. Phys. Solids, 23, 239–264.
12.
Lade, P. V., Nelson, R. B., and Ito, Y. M.(1988). “Instability of granular materials with nonassociated flow.”J. Engrg. Mech., ASCE, 114(12), 2173–2191.
13.
Rice, J. R.(1976). “On the stability of dilatant hardening saturated rock masses.”J. Geophysical Res., 80, 1531–1536.
14.
Rudnicki, J. W., and Rice, J.(1975). “Conditions for the localization of deformation in pressure-sensitive dilatant materials.”J. Mech. and Physics of Solids, 23, 371–394.
15.
Schrefler, B. A., Simoni, L., Xikui, L., and Zienkiewicz, O. C. (1990). “Mechanics of partially saturated porous media.”Numerical methods and constitutive modeling in geomechanics, C. S. Desai and G. Gioda, eds., Springer-Verlag, New York, N.Y., 169–209.
16.
Terzaghi, K. V. (1943). Theoretical soil mechanics . John Wiley and Sons, New York, N.Y.
17.
Truesdell, C., and Noll, W. (1965). Nonlinear field theories of mechanics . Handbuch of Physics III/3, Springer-Verlag, New York, N.Y.
18.
Verdoulakis, I.(1981). “Bifurcation analysis of the plane rectilinear deformation on dry sand samples.”Int. J. Solids & Struct., 17(11), 1085–1101.
19.
Vardoulakis, I.(1985). “Stability and bifurcation of undrained, plane rectilinear deformation on water-saturated granular soils.”Int. J. Numer. and Anal. Methods in Geomech., 9, 399–414.
20.
Vardoulakis, I.(1986). “Dynamic stability analysis of undrained simple shear on water-saturated granular soils.”Int. J. Numer. and Anal. Methods in Geomech., 10, 177–190.
21.
Zienkiewicz, O. C., and Shiomi, T.(1984). “Dynamic behaviour of saturated porous media: the generalized Biot formation and its numerical solutions.”Int. J. Numer. and Anal. Methods in Geomech., 8, 71–96.
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Copyright © 1995 American Society of Civil Engineers.
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Published online: Jun 1, 1995
Published in print: Jun 1995
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