Formulation of capillary hysteresis with internal state variables

Water Resources Research

Volumn 42, Issue 7, 2006, Pages

  Wei, Changfu ^a,b   Dewoolkar, Mandar M ^b  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b University of Vermont   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH THEORY; HYSTERESIS; MATHEMATICAL MODELS; VOLUME FRACTION; WETTING;

BOUNDARY LOOPS; CAPILLARY HYSTERESIS; PORE FLUIDS;

POROUS MATERIALS;

GRAPH THEORY; HYSTERESIS; MATHEMATICAL MODELS; POROUS MATERIALS; VOLUME FRACTION; WETTING;

CAPILLARITY; DISSIPATION; HYDROLOGICAL MODELING; HYSTERESIS; MATHEMATICAL ANALYSIS; MOISTURE CONTENT; POREWATER; POROUS MEDIUM; THERMODYNAMICS; WETTING-DRYING CYCLE;

EID: 33748207266     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2005WR004594     Document Type: Article

References (54)

1. Bagagiolo, F., and A. Visintin (2000), Hysteresis in filtration through porous media, Z Anal. Anwendungen, 19, 977-997.
2. Braddock, R. D., J.-Y. Parlange, and H. Lee (2001), Application of a soil water hysteresis model to simple water retention curves, Transp. Porous Media, 44, 407-420.
3. Brokate, M., and J. Sprekels (1996), Hysteresis and Phase Transitions, Springer, New York.
4. Brooks, R. H., and C. T. Corey (1964), Hydraulic properties of porous media, Hydrol Pap. 3, Colo. State Univ., Fort Collins.
5. Dafalias, Y. F. (1986), Bounding surface plasticity. I: Mathematical foundation and hypoplasticity, J. Eng. Mech., 112, 967-987.
6. Dafalias, Y. F., and E. P. Popov (1976), Plastic internal variables formulism of cyclic plasticity, J. Appl. Mech., 43, 645-651.
7. Dane, J. H., and S. Hruska (1983), In-situ determination of soil hydraulic properties during drainage, Soil Sci. Soc. Am. J., 4, 619-624.
8. Feng, M., and D. G. Fredlund (1999), Hysteretic influence associated with thermal conductivity sensor measurements, in Proceeding From Theory to the Practice of Unsaturated Soil Mechanics, pp. 14:2:14-14:2:20, 52nd Can. Geotech. Conf. and Unsaturated Soil Group, Regina.
9. Flynn, D., H. McNamara, P. O'Kane, and A. Pokrovskii (2006), Application of the Preisach Model in soil-moisture hysteresis, in the Science of Hysteresis, edited by I. Mayergoyz and G. Bertotti, Elsevier, New York.
10. Gray, W. G. (1999), Thermodynamics and constitutive theory for multiphase porous-media flow considering internal geometric constraints, Adv. Water Resour., 22, 521-547.
11. Gray, W. G., and S. M. Hassanizadeh (1991), Unsaturated flow theory including interfacial phenomena, Water Resour. Res., 27, 1855-1863.
12. Gray, W. G., A. F. B. Tompson, and W. E. Soil (2002), Closure conditions for two-fluid flow in porous media, Transp. Porous Media, 47, 29-65.
13. Hassanizadeh, S. M., and W. G. Gray (1990), Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries, Adv. Water Resour., 13(4), 169-186.
14. Hassanizadeh, S. M., and W. G. Gray (1993), Thermodynamic basis of capillary pressure in porous media, Water Resour. Res., 29, 3389-3405.
15. Haverkamp, R., J. L. Arrue, and M. Soet (1997), Soil physical properties within the root zone of the vine area of Tomelloso. Local and spatial standpoint, in Final Integrated Report of EFEDA II (European Field Experiment in a Desertification Area) Spain, edited by J. F. Santa Olalla, chap. 3, CEE Proj. CT920090, Brussels.
16. Haverkamp, R., P. Reggiani, P. J. Ross, and J.-Y. Parlange (2002), Soil water hysteresis prediction model based on theory and geometric scaling, in Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere, Geophys. Monogr. Ser., vol. 129, pp. 213-246, AGU, Washington, D. C.
17. Heinen, M., and P. A. Raats (1997), Hysteretic hydraulic properties of a coarse sand and horticultural substrate, in Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media 1, edited by M. T. van Genuchten, F. J. Leij, and L. Wu, pp. 467-476, Dep. of Environ. Sci., Univ. of Calif, Riverside.
18. Held, R. J., and M. A. Celia (2001), Modeling support of functional relationships between capillary pressure, saturation, interfacial areas and common lines, Adv. Water Resour., 24, 325-343.
19. Hopmans, J. W., and J. H. Dane (1986), Temperature dependence of soil water retention curves, Soil Sci. Soc. Am. J., 50, 562-567.
20. Kool, J. B., and J. C. Parker (1987), Development and evaluation of closed-form expressions for hysteretic soil hydraulic properties, Water Resour. Res., 23(1), 105-114.
21. Krasnoselskii, M., and A. Pokrovskii (1983), Systems With Hysteresis, Nauka, Moscow.
22. Lemaitre, J., and J.-L. Chaboche (1990), Mechanics of Materials, Cambridge Univ. Press, New York.
23. Li, X. S. (2005), Modeling of hysteresis response for arbitrary wetting/drying paths, Comput. Geotech., 32, 133-137.
24. Lubliner, J. (1974), A simple theory of plasticity, Int. J. Soilds Struct., 10, 313-317.
25. Lubliner, J. (1990), Plasticity Theory, Macmillan, New York.
26. Maugin, G. A. (1992), The Thermomechanics of Plasticity and Fracture, Cambridge Univ. Press, New York.
27. Maugin, G. A. (1999), The Thermomechanics of Nonlinear Irreversible Behaviors: An Introduction, World Sci., Hackensack, N. J.
28. Mayergoyz, I. D. (1991), Mathematical Models of Hysteresis, Springer, New York.
29. Mitchell, R. J., and A. S. Mayer (1998), The significance of hysteresis in modeling solute transport in unsaturated porous media, Soil Sci. Soc. Am. J., 62, 1506-1512.
30. Mualem, Y. (1973), Modified approach to capillary hysteresis based on a similarity hypothesis, Water Resour. Res., 9, 1324-1331.
31. Mualem, Y. (1974), A conceptual model of hysteresis, Water Resour. Res., 10, 514-520.
32. Muraleetharan, K. K., and C. Wei (1999), Dynamic behavior of unsaturated porous media: Governing equations using the theory of mixtures with interfaces (TMI), Int. J. Numer. Anal. Methods Geomech., 23, 1579-1608.
33. Parker, J. C., and R. J. Lenhard (1987), A model of hysteretic constitutive relations governing multiphase flow: 1. Saturation-pressure relationship, Water Resour. Res., 23, 2187-2196.
34. Parlange, J.-Y. (1976), Capillary hysteresis and relationship between drying and wetting curves, Water Resour. Res., 12, 224-228.
35. Passman, S. L., J. W. Nunziato, and E. K. Walsh (1984), A theory of multi-phase mixtures, in Rational Thermodynamics, edited by C. Truesdell, pp. 286-325, McGraw-Hill, New York.
36. Pham, H. Q., D. G. Fredlund, and S. L. Barbour (2003), A practical hysteresis model for the soil-water characteristic curve for soils with negligible volume change, Géotechnique, 53, 293-298.
37. Poulovassilis, A. (1962), Hysteresis of pore water: An application of the concept of independent domains, Soil Sci., 93, 405-412.
38. Poulovassilis, A. (1970a), Hysteresis of pore water in granular porous bodies, Soil Sci., 109(1), 5-12.
39. Poulovassilis, A. (1970b), The effect of the entrapped air on the hysteresis curve of a porous body and on its hydraulic conductivity, Soil Sci., 109(3), 154-162.
40. Pride, S. R., and E. G. Flekkøy (1999), Two-phase flow through porous media in the fixed-contact-line regime, Phys. Rev. E; 60(4), 4285-4299.
41. Reeves, P. C., and M. A. Celia (1996), A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model, Water Resour. Res., 32, 2345-2358.
42. Rice, J. R. (1971), Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity, J. Mech. Phys. Solids, 19, 433-455.
43. Russo, D., W. A. Jury, and G. L. Butters (1989), Numerical analysis of solute transport during transient irrigation: 1. The effect of hysteresis and profile heterogeneity, Water Resour. Res., 25, 2109-2118.
44. Scott, P. S., G. J. Farquhar, and N. Kouwen (1983), Hysteretic effects on net infiltration, Advances in infiltration, Am. Soc. Agric. Eng., Publ. 11-83, 163-170.
45. Si, B. C., and R. G. Kachanoski (2000), Unified solution for infiltration and drainage with hysteresis: Theory and field test, Soil Sci. Soc. Am. J., 64, 30-36.
46. Topp, G. C. (1969), Soil-water hysteresis measured in a sandy loam and compared with the hysteretic domain model, Soil. Sci. Soc. Am. Proc., 33, 643-651.
47. Topp, G. C. (1971a), Soil-water hysteresis: the domain theory extended to pore interaction conditions, Soil Sd. Soc. Am. J., 35, 219-225.
48. Topp, G. C. (1971b), Soil water hysteresis in silt loam and clay loam soils, Water Resour. Res., 7(4), 914-920.
49. van Genuchten, M. T. (1980), A closed form equation for predicting hydraulic conductivity of unsaturated soils, Soil Sd. Soc. Am. J., 44, 892-898.
50. Viaene, P., H. Vereecken, J. Diels, and J. Feyen (1994), A statistical analysis of six hysteresis models for the moisture retention characteristic, Soil Sci., 157, 345-355.
51. Visintin, A. (1994), Differential Models of Hysteresis, Springer, New York.
52. Wei, C., and K. K. Muraleetharan (2002a), A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity, Int. J. Eng. Sci., 40, 1807-1833.
53. Wei, C., and K. K. Muraleetharan (2002b), A continuum theory of porous media saturated by multiple immiscible fluids: II. Lagrangian description and variational structure, Int. J. Eng. Sci., 40, 1835-1854.
54. Wei, C., and K. K, Muraleetharan (2006), Acoustical characterization of fluid-saturated porous media with local heterogeneities: Theory and application, Int. J. Solids Struct., 43, 982-1008.