Abstract
In the framework of the volume fraction theories, the governing equations of problems of mechanics of partially saturated porous media are derived. The use of general averaging principles provides the definition of averaged field variables, which allow the connection with experimental data. A finite element discretization of the governing equations is subsequently presented.
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References
Bedford, A. and Drumheller, D.S.: Theories of immiscible and structured mixtures, Int. J. Engng. Sci., 21(1983), 863–960.
Lewis, R.W. and Schrefler, B.A.: The finite element method in the deformation and consolidation of porous media, Wiley, Chichester 1987.
Simoni, L. and Schrefler, B.A.: F.E. solution of a vertically averaged model for regional land subsidence. Int. J. Num. Meth. Eng., 27(1989), 215–230.
Bear, J. and Bachmat, Y.: Transport phenomena in porous media — Basic equations, in: Fundamentals of transport phenomena in porous media (Bear, J. and Corapcioglu, M.Y. eds.), Nato ASI Series, Nijhoff, Dordrecht 1984, 5–61.
Lemaitre, J. and Chaboche J.L.: Mecanique des materiaux solides, Dunod, Paris 1988.
Skempton, A.W.: Effective stress in soils, concrete and rocks, in Pore pressure and suction in soils, Butterworths London 1961, 4–16.
Bishop, A.W. and Blight, G.E.: Some aspects of effective stress in saturated and partly saturated soils, Geotechnique, 13(1963), 177–197.
Aitchison, G.D. and Donald, I.B.: Effective stress in unsaturated soils, Proc. 2nd Australia-New Zealand Conf. Soil Mech., 1956, 192–199.
Morland, L.W.: A simple constitutive theory for a fluid saturated porous solid, Journal Geophys. Res. 77(1972), 890–900.
Lloret, A., Alonso, E.E. and Gens, a A.: Undrained loading and consolidation analysis for unsaturated soils, Proc. Eur. Conf. Num. Meth. Geomech., 2, Stuttgart, 1986.
Zienkiewicz, O.C. and Shiomi, T.: Dynamic behaviour of saturated porous media: the general Biot’s formulation and its numerical solution, Int. J. Num. Anal. Meth. Geom., 8(1985), 71–96.
Hassanizadeh, M. and Gray W.G.: General conservation equations for multiphase systems: 1. Averaging procedure, Adv. Water Resources, 2(1979), 131–144.
Hassanizadeh, M. and Gray W.G.: General conservation equations for multiphase systems: 2. Mass, momenta, energy and entropy equations, Adv. Water Resources, 2(1979), 191–203.
Hassanizadeh, M. and Gray W.G.: General conservation equations for multiphase systems: 3. Constitutive theory for porous media flow, Adv. Water Resources, 3(1980), 25–40.
Marsden J.E. and Hughes, T.J.R.: Mathematical foundations of elasticity, Prentice-Hall, Englewood Cliffs, 1983.
Li, X., Ding, D., Chan, A.H.C. and Zienkiewicz, O.C.: A coupled finite element method for the soil-pore fluid interaction problems with immiscible two-phase fluid flow, Proc. V-th Int. Symposium on Num. Meth. Eng., Lausanne, 1989.
Zienkiewicz, O.C. and Taylor, R.L.: Coupled problems — A simple time stepping procedure, Comm. Appl. Num. Meth., 1(1985), 233–239.
Zienkiewicz, O.C., Paul, D.K. and Chan, A.H.C.: Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems, Int. J. Num. Meth. Eng., 25(1988), 1093–1055.
Narasimhan, T.N. and Witherspoon, P.A.: Numerical model for saturated-unsaturated flow in deformable porous media. 3 Applications, Water Resour. Res., 14(1978), 1017–1034.
Schrefler, B.A. and Simoni, L.: A unified approach to the analysis of saturated-unsaturated elastoplastic porous media, in Numerical Methods in Geomechanics. Innsbruck 1988. (ed. G. Swoboda), Balkema, Rotterdam 1988.
Suquet, P.M.: Elements of homogenization for inelastic solid mechanics, in: Homogenization techniques for composite media (eds. E. Sanchez-Palencia and A. Zaoui), Springer-Verlag, Berlin 1987.
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Schrefler, B.A., Simoni, L., Xikui, L., Zienkiewicz, O.C. (1990). Mechanics of Partially Saturated Porous Media. In: Desai, C.S., Gioda, G. (eds) Numerical Methods and Constitutive Modelling in Geomechanics. International Centre for Mechanical Sciences, vol 311. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2832-9_2
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DOI: https://doi.org/10.1007/978-3-7091-2832-9_2
Publisher Name: Springer, Vienna
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