Abstract
A three-scale theory of swelling clay soils is developed which incorporates physico-chemical effects and delayed adsorbed water flow during secondary consolidation. Following earlier work, at the microscale the clay platelets and adsorbed water (water between the platelets) are considered as distinct nonoverlaying continua. At the intermediate (meso) scale the clay platelets and the adsorbed water are homogenized in the spirit of hybrid mixture theory, so that, at the mesoscale they may be thought of as two overlaying continua, each having a well defined mass density. Within this framework the swelling pressure is defined thermodynamically and it is shown to govern the effect of physico-chemical forces in a modified Terzaghi's effective stress principle. A homogenization procedure is used to upscale the mesoscale mixture of clay particles and bulk water (water next to the swelling mesoscale particles) to the macroscale. The resultant model is of dual porosity type where the clay particles act as sources/sinks of water to the macroscale bulk phase flow. The dual porosity model can be reduced to a single porosity model with long term memory by using Green's functions. The resultant theory provides a rational basis for some viscoelastic models of secondary consolidation.
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Achanta, S. and Cushman, J. H.: 1994, Non-equilibrium swelling and capillary pressure relations for colloidal systems, J. Collord Interface Sci. 168, 266–268.
Achanta, S. and Cushman, J. H. and Okos, M.R.: 1994, On multicomponent, multiphase thermomechanics with interfaces, Int. J. Engrg. Sci. 32(11): 1717–1738.
Arbogast, T.: 1992, A simplified dual-porosity model for two-phase flow, in: T. F. Russel, R. E. Ewing, C. A. Brebbia, W. G. Gray, and G. F. Pindar, (eds), Computational Methods in Water Resources, Computational Mechanics Publication, Southampton, U.K., pp. 419–426.
Arbogast, T.: 1993, Gravitational forces in dual-porosity systems, Transport in Porous Media, 13, 179–220.
Arbogast, T. and Douglas Jr., J. and Hornung, U.: 1991, Modeling of naturally fractured reservoirs by formal homogenization techniques, in: R. Dautray (ed.), Frontiers in Pure and Applied Mathematics, Elsevier, Amsterdam, pp. 1–19
Auriault, J. L.: 1990, Behavior of porous saturated deformable media, in F. Darve (ed.), Geomaterials: Constitutive Equations and Modelling, Elsevier, New York, pp. 311–328.
Auriault, J. L.: 1991, Heterogeneous media: Is an equivalent macroscopic description possible? Int. J. Eng. Sci. 29, 785–795.
Auriault, J. L. and Boutin, C.: 1992, Deformable porous mediawith double porosity. Quasi-Statics I: Coupling effects, Transport in Porous Media 7, 63–82.
arbour, S. L. and Fredlund, D. G.: 1989, Mechanisms of osmotic flow and volume changes in clay soils, Can. Geotech J. 26, 551–562.
Barden, L.: 1965, Consolidation of clay with nonlinear viscosity, Geotechnique 15, 345–361.
Bedford, A. and Drumheller, D. S.: 1983, Theories of immiscible and structured mixtures, Int. J. Eng. Sci. 21(8), 863–960.
Bennethum, L. S. and Cushman, J. H.: 1996, Multiscale hybrid mixture theory for swelling systems: Part II: Constitutive theory, Int. J. Eng. Sci. 34(2), 147–169.
Bennethum, L. S. and Cushman, J. H.: 1996, Multiscale hybrid mixture theory for swelling systems: Part I: Balance laws, Int. J. Eng. Sci. 34(2), 125–145.
Bennethum, L. S., Murad, M. M. and Cushman, J. H.: 1996, Macroscale thermodynamics and the chemical potential for swelling porousmedia, Center for Computational Mathematics, University of Colorado at Denver.
Bensoussan, A., Lions, J. L. and Papanicolaou G.: 1978, A Symptotic Analysis for Periodic Structures, North-Holland, Amsterdam.
Biot, M.: 1941, General theory of three-dimensional consolidation, J. Appl. Phys. 12, 155–164.
Biot, M.: 1955, Theory of elasticity and consolidation for a porous anisotropic solid, J. Appl. Phys. 26, 182–185.
Bowen, R. M.: 1976, Theory of mixtures, in: A. C. Eringen (ed.), Continuum Physics, 3. Academic Press, New York.
Budkowska, B. and Fu, Q.: 1988, Some aspects of numerical analysis of creep in layered granular medium, Comput. Geotech. 5, 285–306.
Allen, H.: 1980, Thermodynamics, Wiley, New York.
Coleman, B. D. and Noll, W.: 1963, The thermodynamics of elastic materialswith heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178.
Cushman, J. H.: 1990, Molecular-scale lubrication, Nature 347, 227–228.
Derjaguin, B. V. and Churaev, N.V.: 1978, On the question of determining the concept of disjoining pressure and its role in the equilibrium and flow of thin films, J. Colloid Interface Sci. 66(3), 389–398.
Derjaguin, B. V. and Churaev, N.V.: 1989, The current state of the theory of long-range surface forces. Colloids and Surfaces 41, 223–237.
Derjaguin, B. V., Churaev, N. V. and Muller, V. M.: 1987, Surface Forces, Plenum Press, New York.
Douglas, J., Peszynska, M. and Showalter, R. E.: Single phase flow in partially fissured media, Transport in Porous Media, in press.
Douglas, Jr., J. and Arbogast, T.: 1990, Dual porosity models for flow in naturally fractured reservoirs, in: J. H. Cushman (ed.), Dynamics of Fluid in Hierarchical Porous Media, Academic Press, New York, pp. 177–222.
Eringen, A. C.: 1967, Mechanics of Continua. Wiley, New York.
Gee, M. L., Mcguiggan, P. M. and Israelachvili, J.: 1895- 1906, 1990, Liquid to solidlike transitions of molecularly thin films under shear, J. Chem. Phys. 93(3).
Gibson, R. E. and Lo, K. Y.: 1961, A theory of consolidation for soils exhibiting secondary compression. Norweg. Geotech. Inst. Publ. 41, 1–16.
Graham, J., Oswell, J. M. and Gray, M. N.: 1992, The effective stress concept in a saturated sand-clay buffer. Canad. Geotech. J. 29, 1033–1043.
Grim, R. E.: 1968, Clay Mineralogy, McGraw-Hill, New York.
Hassanizadeh, S. M. and Gray, W. G.: 1979, General conservation equations for multiphase systems: 1. Averaging procedure, Adv. Water Resour. 2, 131–144.
Hassanizadeh, S. M. and Gray, W. G.: 1979, General conservation equations for multiphase systems: 2. Mass, momenta, energy, and entropy equations, Adv. Water Resour. 2, 191–208.
Hassanizadeh, S. M. and Gray, W. G.: 1980, General conservation equations for multiphase systems: 3. Constitutive theory for porous media, Adv. Water Resour. 3, 25–40.
Hassanizadeh, S. M. and Gray, W. G.: 1993, Thermodynamic basis of capillary pressure in porous media, Water Resour. Res. 29(10), 3389–3405.
Hassanizadeh, S. M. and Gray, W. G.: 1993, Toward an improved description of the physics of two-phase flow, Adv. Water Resour. 16, 53–67.
Hornung, U. and Showalter, R. E.: 1990, Diffusion models for fractured medis, J. Math. Anal. Appl. 147, 69–80.
Hueckel, T.: 1992, On effective stress concepts and deformation in clays subjected to environmental loads, Canad. Geotech. J. 29, 1120–1125.
Hueckel, T.: 1992, Water mineral interaction in hygromechanics of clays exposed to environmental loads: a mixture theory approach, Canad. Geotech. J. 29, 1071–1086.
Israelachvili, J.: 1991, Intermolecular and Surface Forces, Academic Press, New York.
Israelachvili, J., Mcguiggan, P. M. and Homola, A. M.: 1988, Dynamic properties of molecularly thin liquid films, Science 240, 189–191.
Ivanov, I. B. and Kralchevsky, P. A.: 1988, Mechanics and thermodynamics of curved thin films, in: I. B. Ivanov (ed.), Surfactant Science Series 29, Dekker, New York, pp. 49–129.
Feda, J.: 1992, Creep of Soils and Related Phenomena, Developments in Geotechnical Engineering 68, Elsevier, New York.
Karabomi, S., Urai B. Smith, J., Heidug, W. and Oort, E.: 1996, The swelling of clays:Molecular simulations of the hydration of montmorillonite, Science 271, 1102–1104.
Keedwell, M. J.: 1984, Rheology and Soil Mechanics, Elsevier, New York.
Kralchevsky, P. A. and Ivanov, I. B.: 1990, Micromechanical description of curved interfaces: II Film surface tensions, disjoining pressure and interfacial stress balances, J. Colloid Interface Sci. 137(1), 235–252.
Lambe, T. W.: 1960, A mechanistic picture of shear strength in clay, in Proc. ASCE Research Conference on Shear Strength of Cohesive Soils, Boulder, Colorado, pp. 503–532.
Levy, T. and Palencia, S.: 1975, On boundary conditions for flow in porous media, Int. J. Engrg. Sci. 13, 923–940.
Lewis, R. W. and Tran, D. V.: 1989, Numerical simulation of secondary consolidation of soil: Finite element formulation, Int. J. Anal. Methods Geomech. 13, 1–18.
Li, D.: 1993, Thermodynamics of thin liquid films, in Thermodynamics and the Design, Analysis, and Improvement of Energy Systems, Amer. Soc. Mech. Eng., Advanced Energy Systems Division (Publication) AES, New York.
Li, D. and Neumann, A. W.: 1991, Thermodynamics of contact angle phenomena in the presence of a thin film, Advances in Colloid and Interface Sci. 36, 125–151.
Liu, I. S.: 1972, Method of Lagrange multipliers for exploitation of the entropy principle, Arch. Rational. Mech. Anal. 46, 131–148.
Low, P. F.: 1976, Viscosity of interlayer water in montmorillonites, Soil Sci. Soc. Am. J. 40, 500–505.
55 Low, P. F.: 1976, Viscosity of interlayer water in montmorillonites, Soil Sci. Soc Am. J. 40, 500–505.
Low, P. F.: 1980, The swelling of clay: II. Montmorillonite-water systems, Soils Sci. Soc. Am. J. 44(4), 667–676.
Low, P. F.: 1987, Structural component of the swelling pressure of clays, Langmuir 3, 18–25.
Low, P. F.: 1994, The clay/water interface and its role in the environment, in: Progress in Colloid and Polymer Science 95, 98–107.
Ma, C. and Hueckel, T.: 1992, Effects of inter-phase mass transfer in heated clays: A mixture theory, Int. J. Eng. Sci. 30(11), 1567–1582.
Morgensten, N. M. and Balasubramonian, B. I.: 1980, Effects of pore fluid on the swelling of clay-shale, in Proceedings of the 4th International Conference on Expansive Soils, Denver Colo, pp. 190–205.
Murad, M. A., Bennethum, L. S. and Cushman, J. H.: 1995, A Multiscale theory of swelling porous media: I Application to one-dimensional consolidation, Transport in Porous Media 19, 93–122.
Murad, M. A. and Cushman, J. H.: 1996, Multiscale flow and deformation in hydrophilic swelling porous media, Int. J. Eng. Sci. 34(3), 313–336.
Peszenska, M.: 1992, Mathematical analysis and numerical approach to flow through fissured media, PhD thesis, Univ. Augsburg.
Sanchez-Palencia, E.: 1980, Non-homogeneous media and vibration theory, in J. Ehler (ed.), Lecture Notes in Physics 127. Springer-Verlag, New York.
Schoen, M., Diestler, D. J. and Cushman, J. H.: 1987, Fluids in micropores. I. Structure of a simple classical fluid in a slit-pore, J. Chem. Phys. 87(9), 5464–5476.
Showalter, R. E.: 1991, Diffusion models with microstructure, Transport in Porous Media 6, 567–580.
Showalter, R. E.: 1992, Distributed Microstructure Models of Porous Media, Int. Series Numer. Math. Birkhäuser, Verlag, Basel, 1993, pp. 155–164; J. Douglas, Jr. and U. Hornung (eds), Proc. Oberwolfach Conference, 1992.
Sridharan, A.: 1991, Engineering behaviour of fine grained soils:Afundamental approach, Indian Geotech. J. 21(1), 1–136.
Sridharan, A.: 1991, Role of clay minerals in controlling the engineering properties of soils, Clay Res. 10(2), 39–47.
Sridharan, A. and Rao, G. V.: 1973, Mechanisms controlling volume change of saturated clays and the role of the effective stress concept, Geotechnique 23(3), 359–382.
Sridharan, A. and Rao, G. V.: 1982, Mechanisms controlling the secondary compression of clays, Geotechnique 32(3), 249–260.
Terzaghi, K.: 1942, Theoretical Soil Mechanics, Wiley, New York, 1942.
Truesdell, C. and Toupin, R.: 1960, The classical field theories, in Flugge (ed.), Handbuchder Physik, volume III. Springer-Verlag, New York.
Wang, Y. C., Murti, V. and Valliappan, S.: 1992, A transient finite element analysis of linear viscoelastic material model, Int. J. Num. Anal. Methods Geomech. 16, 265–294.
Wilcox, R. D.: 1990, Surface area approach key to borehole stability, Oil and Gas J. Feb. 26, 66–80.
Wray, W.: 1995, So Your Home is Built on Expansive Soils, Amer. Soc. Civil Eng., New York.
Zeevart, L.: 1986, Consolidation in the intergranular viscosity of highly compressible soils, in N. Yong and F. C. Townsend (ed.), Consolidation of Soils: Testing and Evaluation. Amer. Soc. for Testing and Materials ASTM 892, Philadelphia.
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Murad, M.a., Cushman, J.H. A Multiscale Theory of Swelling Porous Media: II. Dual Porosity Models for Consolidation of Clays Incorporating Physicochemical Effects. Transport in Porous Media 28, 69–108 (1997). https://doi.org/10.1023/A:1006539928751
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DOI: https://doi.org/10.1023/A:1006539928751