Thermodynamic approach to effective stress in partially saturated porous media. (English) Zbl 1034.74019

The authors derive an expression for equilibrium effective stress acting on the solid phase of a porous medium containing two immiscible fluid phases. The derivation makes use of the thermodynamics of the system at a macroscale (a scale of the order of tens of pore diameters, but much smaller than the entire system). This scale in also referred to as the core scale or Darcy scale. At this scale, geometric quantities such as porosity, saturation, and interfacial area per volume can be meaningfully defined and included in the analysis. A macroscale point thus includes a mix of phase interfaces, and the common line where the interfaces are of interest. The analysis leads to an expression for capillary pressure as a function of phase pressures and the disjoining pressure.


74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74A15 Thermodynamics in solid mechanics
74Q15 Effective constitutive equations in solid mechanics
76S05 Flows in porous media; filtration; seepage
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[1] Bailyn, M, A survey of thermodynamics, (1994), AIP Press New York
[2] Bishop, A.W, The principle of effective stress, Teknisk ukeblad, 39, 859-863, (1959)
[3] Bishop, A.W; Blight, G.E, Some aspects of effective stress in saturated and partly saturated soils, Géotechnique, 13, 177-197, (1963)
[4] Bolzon, G; Schrefler, B.A; Zienkiewicz, O.C, Elastoplastic soil constitutive laws generalized to semisaturated state, Géotechnique, 46, 2, 279-289, (1996)
[5] Callen, H.B, Thermodynamics and an introduction to thermostatistics, (1985), Wiley New York · Zbl 0989.80500
[6] Coleman, B.D; Noll, W, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. rational. mech. anal., 13, 168-178, (1963) · Zbl 0113.17802
[7] Coussy, O, Mechanics of porous continua, (1995), Wiley Chichester
[8] Fillunger, P, Versuche ueber die zugfestigkeit bei allseitigem wasserdruck, Oesterr. wochenschrift oeffent. baudienst, 29, 443-448, (1915)
[9] Gaydos, J; Rotenberg, Y; Boruvka, L; Chen, P; Neumann, A.W, The generalized theory of capillarity, (), 1-51
[10] Gray, W.G, Thermodynamics and constitutive theory for multiphase porous-media flow considering internal geometric constraints, Advances in water resources, 22, 5, 521-547, (1999)
[11] Gray, W.G, Macroscale equilibrium conditions for two-phase flow in porous media, International journal of multiphase flow, 26, 467-501, (2000) · Zbl 1137.76596
[12] Hassanizadeh, S.M; Gray, W.G, General conservation equations for multiphase systems: 3 constitutive theory for porous media flow, Advances in water resources, 3, 25-40, (1980)
[13] Hirasaki, G.J, Thermodynamics of thin films and three-phase contact regions, (), 23-75
[14] Hutter, K; Laloui, L; Vulliet, L, Thermodynamically based mixture models of saturated and unsaturated soils, Mech. of cohes. frict. mat., 4, 295-338, (1999)
[15] Kondepudi, D; Prigogine, I, Modern thermodynamics, (1998), Wiley Chichester
[16] Lade, P.V; de Boer, R, The concept of effective stress for soil, concrete and rock, Géotechnique, 47, 61-78, (1997)
[17] Lewis, R.W; Schrefler, B.A, The finite element method in the deformation and consolidation of porous media, (1987), Wiley Chichester
[18] Li, D; Neumann, A.W, Thermodynamic status of contact angles, (), 109-168
[19] Mokni, M; Desrues, J, Strain localization measurements in undrained plane-strain biaxial tests on hostun RF sand, Mech. cohes.-frict. mater., 4, 419-441, (1999)
[20] Schrefler, B.A; Gawin, D, The effective stress principle: incremental or finite form, Int. J. num. anal. meth. geomech., 20, 11, 785-814, (1996)
[21] Schrefler, B.A; Zhang, H.W; Pastor, M; Zienkiewicz, O.C, Strain localisation modelling in saturated sand samples based on a generalised plasticity constitutive model, Computational mechanics, 22, 266-280, (1998) · Zbl 0927.74048
[22] Skempton, A.W, Effective stress in soils, concrete and rock, (), 4-16
[23] Terzaghi, K, The shearing resistance of saturated soils and the angle between the planes of shear, (), 54-56
[24] Zienkiewicz, O.C; Chan, A; Pastor, M; Schrefler, B.A; Shiomi, T, Computational geomechanics with special reference to earthquake engineering, (1999), Wiley Chichester · Zbl 0932.74003
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