Theoretical basis for modeling porous geomaterials under frost actions: A review

Soil Science Society of America Journal

Volumn 76, Issue 2, 2012, Pages 313-330

  Liu, Zhen ^a   Sun, Ye ^a   Yu, Xiong Bill ^a  

^a Case Western Reserve University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EARTH SCIENCES; SOILS;

COUPLED PROCESS; COUPLING ACTIONS; ENGINEERING MECHANICS; EXPLICIT AND IMPLICIT RELATIONSHIPS; FROST ACTION; GEOMATERIALS; PHYSICAL MECHANISM; SOIL SCIENCE;

POROUS MATERIALS;

CIVIL ENGINEERING; FROST; HOLISTIC APPROACH; LITERATURE REVIEW; NUMERICAL MODEL; POROUS MEDIUM; SOIL MECHANICS; SOIL SCIENCE; TERMINOLOGY; THEORETICAL STUDY;

EID: 84863276667     PISSN: 03615995     EISSN: 14350661     Source Type: Journal    
DOI: 10.2136/sssaj2010.0370     Document Type: Review

References (179)

1. Ahuja, L.R., and D. Swartzendruber. 1972. An improved form of soil-water dif usivity function. Soil Sci. Soc. Am. J. 36:9-14. doi:10.2136/sssaj1972. 03615995003600010002x
2. Alonso, E.E., A. Gens, and A. Josa. 1990. A constitutive model for partially saturated soils. Geotechnique 40:405-430. doi:10.1680/geot.1990.40.3. 405
3. Anderson, D.M., and N.R. Morgenstern. 1973. Physics, chemistry and mechanics of frozen ground: A review. p. 257-288. In Proc. Int. Conf. Permafrost, 2nd, Yakutsk, Siberia. 13-28 July 1973. Natl. Acad. Sci., Washington, DC.
4. Anderson, D.M., A.R. Tice, and H.L. McKim. 1973. T e unfrozen water and the apparent specif c heat capacity of frozen soils. p. 289-295. In Proc. Int. Conf. Permafrost, 2nd, Yakutsk, Siberia. 13-28 July 1973. Natl. Acad. Sci., Washington, DC.
5. Arvidson, W.D., and N.R. Morgenstern. 1977. Water f ow induced by soil freezing. Can. Geotech. J. 14:237-245. doi:10.1139/t77-024
6. Averjanov, S.F. 1950. About permeability of subsurface soils in case of incomplete saturation. Engl. Collect. 7:19-21.
7. Bachmann, J., M. Deurer, and G. Arye. 2007. Modeling water movement in heterogeneous water-repellent soil: 1. Development of a contact angle-dependent water-retention model. Vadose Zone J. 6:436-445.doi:10.2136/vzj2006.0060 (Pubitemid 47360481)
8. Bachmann, J., R. Horton, S.A. Grant, and R.R. van der Ploeg. 2002. Temperature dependence of water retention curves for wettable and water-repellent soils. Soil Sci. Soc. Am. J. 66:44-52. doi:10.2136/sssaj2002. 0044 (Pubitemid 34108485)
9. Bachmann, J., R. Horton, T. Ren, and R.R. van der Ploeg. 2001. Comparison of the thermal properties of four wettable and four water-repellent soils. Soil Sci. Soc. Am. J. 65:1675-1679. doi:10.2136/sssaj2001.1675 (Pubitemid 34003968)
10. Bachmann, J., and R.R. van der Ploeg. 2002. A review on recent developments in soil water retention theory: Interfacial tension and temperature ef ects. J. Plant Nutr. Soil Sci. 165:468-478. doi:10.1002/1522-2624(200208) 165:43.0.CO;2-G (Pubitemid 37240566)
11. Bai, M., and D. Elsworth. 2000. Coupled processes in subsurface deformation, f ow, and transport. Am. Soc. Civ. Eng., Reston, VA .
12. Banin, J.M., and D.M. Anderson. 1974. Effects of salt concentration changes during freezing on the unfrozen water content of porous materials. Water Resour. Res. 10:124-128. doi:10.1029/WR010i001p00124
13. Baron, J. 1982. Les retraits de la pate de ciment. p. 485-501. In J. Baron and R. Sauterey (ed.) Le béton hydraulique. Presses de l'ENPC, Paris.
14. Benson, C.H., and M.A. Othman. 1993. Hydraulic conductivity of compacted clay frozen and thawed in situ. J. Geotech. Eng. 119:276-294. doi:10.1061/(ASCE)0733-9410(1993)119:2(276) (Pubitemid 23383464)
15. Biot, M.A. 1941. General theory of three-dimensional consolidation. J. Appl. Phys. 12:155-164. doi:10.1063/1.1712886
16. Biot, M.A., and D.G. Willis. 1957. T e elastic coef cients of the theory of consolidation. J. Appl. Mech. 24:594-601.
17. Bittelli, M., M. Flury, and G.S. Campbell. 2003. A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media. Water Resour. Res. 39(2):1041. doi:10.1029/2001WR000930
18. Bond, F.W., C.R. Cole, and P.J. Gutknecht. 1984. Unsaturated groundwater f ow model (UNSAT1D) computer code manual. CS-2434-CCM. Electric Power Res. Inst., Palo Alto, CA.
19. Briggs, L.J. 1897. T e mechanics of soil moisture. Bull. 10. USDA Bureau of Soils, Washington, DC.
20. Brooks, R.H., and A.T. Corey. 1964. Hydraulic properties of porous media. Hydrol. Pap. no. 3. Colorado State Univ., Fort Collins.
21. Brutsaert, W. 1967. Some methods of calculating unsaturated permeability. Trans. ASAE 10:400-404.
22. Buckingham, E. 1907. Studies on the movement of soil moisture. Bull. 38. USDA Bureau of Soils, Washington, DC.
23. Bumb, A.C. 1987. Unsteady-state f ow of methane and water in coalbeds. Ph.D. diss. Univ. of Wyoming, Laramie (Diss. Abstr. AAT DP15253).
24. Burdine, N.T. 1953. Relative permeability calculations from pore-size distribution data. Pet. Trans. Am. Inst. Min. Metall. Eng. 198:71-78.
25. Burger, H.C. 1915. Das lertvermogen verdummter mischristallfreier lonsungen. Phys. Z. 20:73-76.
26. Campbell, G.S. 1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Sci. 117:311-314. doi:10.1097/00010694-197406000-00001
27. Campbell, G.S. 1985. Soil physics with BASIC: Transport models for soil-plant systems. Elsevier Sci. BV, Amsterdam.
28. Cary, J.W. 1965. Water f ux in moist soil: T ermal versus suction gradients. Soil Sci. 100:168-175. doi:10.1097/00010694-196509000-00004
29. Cary, J.W. 1966. Soil moisture transport due to thermal gradients: Practical aspects. Soil Sci. Soc. Am. Proc. 30:428-433. doi:10.2136/sssaj1966. 03615995003000040011x
30. Cass, A.G., G.S. Campbell, and T.L. Jones. 1981. Hydraulic and thermal properties of soil samples from the buried waster test facility. PNL-4015. Pacific Northwest Natl. Lab., Richland, WA .
31. Celia, M.A., and P. Binning. 1992. A mass conservative numerical solution for two-phase f ow in porous media with application to unsaturated fow. Water Resour. Res. 28:2819-2828. doi:10.1029/92WR01488 (Pubitemid 23377399)
32. Celia, M.A., E.F. Bouloutas, and R.L. Zarba. 1990. A general mass-conservative numerical solution for the unsaturated f ow equation. Water Resour. Res. 26:1483-1496. doi:10.1029/WR026i007p01483
33. Childs, E.C., and G. Collis-George. 1950. T e permeability of porous materials. Proc. R. Soc. London A 201:392-405. doi:10.1098/rspa.1950.0068
34. Cooling, L.F. 1961. Discussion on Session 3: Roads and runways and agriculture. p. 143-151. In Proc. Conf. on Pore Pressure and Suction in Soil, London. 30-31 Mar. 1960. Butterworths, London.
35. Cooper, A.I. 2003. Porous materials and supercritical fluids. Adv. Mater. 15:1049-1059. doi:10.1002/adma.200300380
36. Côté, J., and J.M. Konrad. 2005. A generalized thermal conductivity model for soils and construction materials. Can. Geotech. J. 42:443-458. doi:10.1139/t04-106 (Pubitemid 41213860)
37. Coussy, O. (ed.). 2004. Poromechanics. John Wiley & Sons, Chichester, UK.
38. Coussy, O. 2005. Poromechanics of freezing materials. J. Mech. Phys. Solids 53:1689-1718. doi:10.1016/j.jmps.2005.04.001 (Pubitemid 40822334)
39. Coussy, O., and P. Monteiro. 2007. Unsaturated poroelasticity for crystallization in pores. Comput. Geotech. 34:279-290. doi:10.1016/j.compgeo. 2007.02.007 (Pubitemid 47243567)
40. Coussy, O., and P.J.M. Monteiro. 2008. Poroelastic model for concrete exposed to freezing temperatures. Cement Concr. Res. 38:40-48. doi:10.1016/j.cemconres.2007.06.006 (Pubitemid 350087000)
41. Croney, D., and J.D. Coleman. 1961. Pore pressure and suction in soil. p. 31-37. In Proc. Conf. on Pore Pressure and Suction in Soil, London. 30-31 Mar. 1960. Butterworths, London.
42. Dash, J.G. 1989. T ermomolecular pressure in surface melting: Motivation for frost heave. Science 246:1591-1593. doi:10.1126/science.246.4937.1591
43. Davidson, J.M., L.R. Stone, D.R. Nielsen, and M.E. Larue. 1969. Field measurement and use of soil-water properties. Water Resour. Res. 5:1312-1321. doi:10.1029/WR005i006p01312
44. Davis, M.E. 2002. Ordered porous materials for emerging applications. Nature 417:813-821. doi:10.1038/nature00785 (Pubitemid 34685481)
45. de Groot, S.R., and P. Mazur. 1984. Non-equilibrium thermodynamics. Dover Publ., Mineola, NY.
46. de Vries, D.A. 1963. T ermal properties of soils. p. 210-235. In W.R. van Wijk (ed.) Physics of plant environment. North-Holland Publ. Co., Amsterdam.
47. Dirksen, C., and R.D. Miller. 1966. Closed-system freezing of unsaturated soil. Soil Sci. Soc. Am. Proc. 30:168-173. doi:10.2136/sssaj1966. 03615995003000020010x
48. Dormieux, L., A. Molinari, and D. Kondo. 2002. Micromechanical approach to the behavior of poroelastic materials. J. Mech. Phys. Solids 50:2203-2231. doi:10.1016/S0022-5096(02)00008-X (Pubitemid 34803083)
49. Duquennoi, C., M. Fremond, and M. Levy. 1989. Modelling of thermal soil behavior. p. 895-915. In H. Rathmayer (ed.) Frost in geotechnical engineering, Int. Symp., Saariselk, Finland. 13-15 Mar. 1989. VTT Symp. 94. Valtion Teknillinen Tutkimuskeskus, Espoo, Finland.
50. Edlefsen, N.E., and A.B.C. Anderson. 1943. T ermodynamics of soil moisture. Hilgardia 15:31-298.
51. Endelman, F.J., G.E.P. Box, J.R. Royle, R.R. Hughes, D.R. Keeney, M.L. Northrup, and P.G. Safigna. 1974. T e mathematical modeling of soil-water-nitrogen phenomena. Rep. EDFB-IBP-74-8. Oak Ridge Natl. Lab., Oak Ridge, TN.
52. Farouki, O.T. 1981. T ermal properties of soils. CRREL Monogr. 81-1. U.S. Army Corps Eng., Cold Reg. Res. Eng. Lab., Hanover, NH.
53. Farouki, O.T. 1982. Evaluation of methods for calculating soil thermal conductivity. CRREL Rep. 82-8. U.S. Army Corps Eng., Cold Reg. Res. Eng. Lab., Hanover, NH.
54. Fayer, M.J. 2000. UNSAT-H version 3.0: Unsaturated soil water and heat flow model, theory, user manual, and examples. Rep. 13249. Pacific Northwest Natl. Lab., Richland, WA .
55. Fayer, M.J., and C.S. Simmons. 1995. Modif ed soil water retention functions for all matric suctions. Water Resour. Res. 31:1233-1238. doi:10.1029/95WR00173 (Pubitemid 26437818)
56. Fen-Chong, T., A. Fabbri, and A. Azouni. 2006. Transient freezing-thawing phenomena in water-filled cohesive porous materials. Cold Reg. Sci. Technol. 46:12-26. doi:10.1016/j.coldregions.2006.04.001 (Pubitemid 44276195)
57. Flerchinger, G.N. 2000. T e simultaneous heat and water (SHAW) model: Technical documentation. Tech. Rep. NWRC 2000-09. USDA-ARS Northwest Watershed Res. Ctr., Boise, ID.
58. Flerchinger, G.N., and F.B. Pierson. 1991. Modeling plant canopy Effects on variability of soil temperature and water. Agric. For. Meteorol. 56:227-246. doi:10.1016/0168-1923(91)90093-6
59. Fredlund, D.G., and A. Xing. 1994. Equations for the soil-water characteristic curve. Can. Geotech. J. 31:521-532. doi:10.1139/t94-061
60. Fredlund, D.G., A. Xing, and S. Huang. 1994. Predicting the permeability function for unsaturated soils using the soil-water characteristic curve. Can. Geotech. J. 31:533-546. doi:10.1139/t94-062
61. Fremond, M., and M. Mikkola. 1991. T ermomechanical modeling of freezing soil. p. 17-24. In X. Yu and C. Wang (ed.) Ground freezing '91: Proc. Int. Symposium on Ground Freezing, 6th, Beijing. 10-12 Sept. 1991.
62. A.A. Balkema, Rotterdam, the Netherlands.
63. Gardner, W.R. 1958. Some steady-state solutions of the unsaturated moisture f ow equation with application to evaporation from a water table. Soil Sci. 85:228-232. doi:10.1097/00010694-195804000-00006
64. Gilpin, R.R. 1980. A model for the prediction of ice lensing and frost heave in soils. Water Resour. Res. 16:918-930. doi:10.1029/WR016i005p00918
65. Grant, S.A., and J. Bachmann. 2002. Effect of temperature on capillary pressure. p. 199-212. In P.A.C. Raats et al. (ed.) Environmental mechanics: Water, mass and energy transfer in the biosphere. Geophys. Monogr.129. Am. Geophys. Union, Washington, DC.
66. Grant, S.A., and A. Salehzadeh. 1996. Calculation of temperature Effects on wetting coef cients of porous solids and their capillary pressure functions. Water Resour. Res. 32:261-270. doi:10.1029/95WR02915 (Pubitemid 26309854)
67. Groenevelt, P.H., and B.D. Kay. 1974. On the interaction of water and heat transport in frozen and unfrozen soils: II. T e liquid phase. Soil Sci. Soc. Am. Proc. 38:400-404. doi:10.2136/sssaj1974.03615995003800030012x
68. Guymon, G.L., and J.N. Luthin. 1974. A coupled heat and moisture transport model for arctic soils. Water Resour. Res. 10:995-1001. doi:10.1029/WR010i005p00995
69. Hansson, K. 2005. Water and heat transport in road structures; Development of mechanical models. Compr. Summ. Uppsala Diss. Sci. Technol., Uppsala Univ., Uppsala, Sweden.
70. Hansson, K., J. Šim?nek, M. Mizoguchi, L.C. Lundin, and M.T. van Genuchten. 2004. Water flow and heat transport in frozen soil: Numerical solution and freeze-thaw applications. Vadose Zone J. 3:693-704.
71. Harlan, R.L. 1973. Analysis of coupled heat-f uid transport in partially frozen soil. Water Resour. Res. 9:1314-1323. doi:10.1029/WR009i005p01314
72. Hassanizadeh, S.M., and W.G. Gary. 1993. T ermodynamic basics of capillary pressure in porous media. Water Resour. Res. 29:3389-3405. doi:10.1029/93WR01495 (Pubitemid 24401191)
73. Haverkamp, R., M. Vauclin, J. Touma, P.J. Wierenga, and G. Vachaud. 1977. A comparison of numerical simulation models for one-dimensional inf ltration. Soil Sci. Soc. Am. J. 41:285-294. doi:10.2136/sssaj1977.03615995004100020024x
74. Horiguchi, K., and R.D. Miller. 1980. Experimental studies with frozen soil in an "ice sandwich" permeameter. Cold Reg. Sci. Technol. 3:177-183. doi:10.1016/0165-232X(80)90023-3 (Pubitemid 11421828)
75. Horton, R., and P.J. Wierenga. 1984. The effect of column wetting on soil thermal conductivity. Soil Sci. 138:102-108. doi:10.1097/00010694-198408000- 00002 (Pubitemid 16264636)
76. Hromadka, T.V., and C. Yen. 1986. A dif usion hydrodynamic model (DHM). Adv. Water Resour. 9:118-170. doi:10.1016/0309-1708(86)90031-X
77. Hua, C., P. Acker, and A. Ehrlacher. 1995. Analyses and models of the autogenous shrinkage of hardening cement paste: I. Modelling at macroscopic scale. Cement Concr. Res. 25:1457-1468. doi:10.1016/0008-8846(95)00140-8
78. Hudson, C.S. 1906. T e freezing of pure liquids and solutions under various kinds of positive and negative pressure and the similarity between osmotic and negative pressure. Physiol. Rev. 22:257-264.
79. Jame, Y.W., and D.I. Norum. 1980. Heat and mass transfer in a freezing unsaturated porous medium. Water Resour. Res. 16:811-819. doi:10.1029/ WR016i004p00811 (Pubitemid 11266433)
80. Jansson, P.E., and L. Karlberg (ed.). 2001. Coupled heat and mass transfer model for soil-plant-atmosphere systems. R. Inst. Technol., Dep. Civ. Environ. Eng., Stockholm, Sweden.
81. Johansen, O. 1975. T ermal conductivity of soils. Ph.D. diss. (CRREL Draf Transl. 637, 1977.) Norwegian Univ. of Sci. and Technol., Trondheim.
82. Kay, B.D., and P.H. Groenevelt. 1974. On the interaction of water and heat transport in frozen and unfrozen soils: I. Basic theory: T e vapor phase. Soil Sci. Soc. Am. J. 38:395-400. doi:10.2136/sssaj1974.03615995003800030011x
83. Kersten, M.S. 1949. Laboratory research for the determination of the thermal properties of soils. ACFEL Tech. Rep. 23. Univ. of Minnesota, Minneapolis.
84. Khlosi, M., W.M. Cornelis, D. Gabriels, and G. Sin. 2006. Simple modif cation to describe the soil water retention curve between saturation and oven dryness. Water Resour. Res. 42:W11501. doi:10.1029/2005WR004699 (Pubitemid 46134894)
85. Konrad, J.M., and N.R. Morgenstern. 1980. A mechanistic theory office lens formation in f ne-grained soils. Can. Geotech. J. 17:473-486. doi:10.1139/t80-056
86. Konrad, J.M., and N.R. Morgenstern. 1981. T e segregation potential of a freezing soil. Can. Geotech. J. 18:482-491. doi:10.1139/t81-059
87. Konrad, J.M., and N.R. Morgenstern. 1982a. Prediction of frost heave in the laboratory during transient freezing. Can. Geotech. J. 19:250-259. doi:10.1139/t82-032
88. Konrad, J.M., and N.R. Morgenstern. 1982b. Effects of applied pressure of freezing soils. Can. Geotech. J. 19:494-505. doi:10.1139/t82-053 (Pubitemid 13490795)
89. Koopmans, R .W.R., and R.D. Miller. 1966. Soil freezing and soil water characteristic curves. Soil Sci. Soc. Am. Proc. 30:680-685. doi:10.2136/ sssaj1966.03615995003000060011x
90. Krahn, J., and D.G. Fredlund. 1972. On total, matric and osmotic suction. Soil Sci. 114:339-348. doi:10.1097/00010694-197211000-00003
91. Kujala, K. 1997. Estimation of frost heave and thaw weakening by statistical analyses. p. 31-41. In S. Knutsson (ed.) Proc. Int. Symp. on Ground Freezing and Frost Action in Soils, 7th, Lulea, Sweden. 15-17 Apr. 1997.
92. A.A. Balkema, Rotterdam, the Netherlands.
93. Kunze, R.J., G. Uehara, and K. Graham. 1968. Factors important in the calculation of hydraulic conductivity. Soil Sci. Soc. Am. Proc. 32:760-765. doi:10.2136/sssaj1968.03615995003200060020x
94. Li, N., B. Chen, and F. Chen. 2000. T e coupled heat-moisture-mechanic model of the frozen soil. Cold Reg. Sci. Technol. 31:199-205. doi:10.1016/S0165-232X(00)00013-6 (Pubitemid 32007472)
95. Li, N., F. Chen, B. Su, and G. Cheng. 2002. T eoretical frame of the saturated freezing soil. Cold Reg. Sci. Technol. 35:73-80. doi:10.1016/S0165- 232X(02)00029-0
96. Lu, N., and W.J. Likos. 2006. Suction stress characteristic curve for unsaturated soil. J. Geotech. Geoenviron. Eng. 132:131-142. doi:10.1061/(ASCE) 1090-0241(2006)132:2(131) (Pubitemid 43118990)
97. Lu, S., T. Ren, Y. Gong, and R. Horton. 2007. An improved model for predicting soil thermal conductivity from water content at room temperature. Soil Sci. Soc. Am. J. 71:8-14. doi:10.2136/sssaj2006.0041 (Pubitemid 46203477)
98. Lundin, L.C. 1989. Water and heat flows in frozen soils: Basic theory and operational modeling. Ph.D. diss. Uppsala Univ., Uppsala, Sweden.
99. Lundin, L.C. 1990. Hydraulic properties in an operational model of frozen soil. J. Hydrol. 118:289-310. doi:10.1016/0022-1694(90)90264-X
100. Lura, P., O.M. Jensen, and K. van Breugel. 2003. Autogenous shrinkage in high-performance cement paste: An evaluation of basic mechanisms. Cement Concr. Res. 33:223-232. doi:10.1016/S0008-8846(02)00890-6
101. Marshall, T.J. 1958. A relation between permeability and size distribution of pores. J. Soil Sci. 9:1-8. doi:10.1111/j.1365-2389.1958.tb01892. x
102. McInnes, K.J. 1981. T ermal conductivities of soils from dryland wheat regions of eastern Washington. M.S. thesis. Washington State Univ., Pullman.
103. McKee, C.R., and A.C. Bumb. 1984. T e importance of unsaturated flow parameters in designing a monitoring system for hazardous wastes and environmental emergencies. p. 50-58. In Proc. Hazardous Materials Control Research Institute Natl. Conf., Houston, TX. Mar. 1984. Hazardous Mat. Control Res. Inst., Silver Spring, MD.
104. Miller, E.E., and R.D. Miller. 1955. T eory of capillary flow: I. Practical implications. Soil Sci. Soc. Am. Proc. 19:267-275. doi:10.2136/sssaj1955.03615995001900030005x
105. Miller, R .D. 1973. Soil freezing in relation to pore water pressure and temperature. p. 344-452. In Proc. Int. Conf. Permafrost, 2nd, Yakutsk, Siberia. 13-28 July 1973. Natl. Acad. Sci., Washington, DC.
106. Miller, R.D. 1978. Frost heaving in non-colloidal soils. p. 708-713. In Proc. Int. Conf. on Permafrost, 3rd, Edmonton, AB, Canada. 10-13 July 1978. Natl. Res. Counc. of Canada, Ottawa, ON.
107. Miller, R.D. 1980. Freezing phenomena in soil. p. 254-299. In D. Hillel (ed.) Applications of soil physics. Academic Press, New York.
108. Miller, R.D., and N.R. Morgenstern. 1973. Physics, chemistry, and mechanics of frozen ground: A review. p. 257-288. In Proc. Int. Conf. Permafrost, 2nd, Yakutsk, Siberia. 13-28 July 1973. Natl. Acad. Sci., Washington, DC.
109. Milly, P.C.D. 1982. Moisture and heat transport in hysteretic, inhomogeneous porous media: A matric head-based formulation and a numerical model. Water Resour. Res. 18:489-498. doi:10.1029/WR018i003p00489 (Pubitemid 13261139)
110. Mizoguchi, M. 1990. Water heat and salt transport in freezing soil. Ph.D. diss. Univ. of Tokyo, Tokyo.
111. Mizoguchi, M. 1993. A derivation of matric potential in frozen soil. Bull. Fac. Bioresour. Mie Univ. 10:175-182.
112. Morrow, N.R. 1970. Physics and thermodynamics of capillary action in porous media. Ind. Eng. Chem. 62:32-56.
113. Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12:513-522. doi:10.1029/ WR012i003p00513
114. Mualem, Y. 1986. Hydraulic conductivity of unsaturated soils: Prediction and formulas. p. 799-823. In A. Klute (ed.) Methods of soil analysis. Part 1. 2nd ed. Agron. Monogr. 9. ASA and SSSA, Madison, WI.
115. Murton, J.B., R. Peterson, and J.C. Ozouf. 2006. Bedrock fracture by ice segregation in cold regions. Science 314:1127-1129. doi:10.1126/science.1132127 (Pubitemid 44789039)
116. Nakano, Y., and J. Brown. 1971. Effect of a freezing zone of f nite width on the thermal regime of soils. Water Resour. Res. 7:1226-1233. doi:10.1029/WR007i005p01226
117. Nassar, I.N., and R. Horton. 1992. Simultaneous transfer of heat, water, and solute in porous media: I. T eoretical development. Soil Sci. Soc. Am. J. 56:1350-1356. doi:10.2136/sssaj1992.03615995005600050004x
118. Nassar, I.N., and R. Horton. 1997. Heat, water, and solute transfer in unsaturated porous media: I. T eory development and transport coef cient evaluation. Transp. Porous Media 27:17-38. doi:10.1023/A:1006583918576 (Pubitemid 27388312)
119. Newman, G.P., and G.W. Wilson. 1997. Heat and mass transfer in unsaturated soils during freezing. Can. Geotech. J. 34:63-70.
120. Nimmo, J.R., and E.E. Miller. 1986. T e temperature dependence of isothermal moisture vs. potential characteristics of soils. Soil Sci. Soc. Am. J. 50:1105-1113. doi:10.2136/sssaj1986.03615995005000050004x
121. Nishimura, S., A. Gens, S. Olivella, and R.J. Jardine. 2009. THM-coupled f nite element analysis of frozen soil: Formulation and application. Geotechnique 59:159-171. doi:10.1680/geot.2009.59.3.159
122. Nixon, J.F. 1991. Discrete ice lens theory for frost heave in soils. Can. Geotech. J. 28:843-859. doi:10.1139/t91-102
123. Noborio, K., K.J. McInnes, and J.L. Heilman. 1996a. Two-dimensional model for water, heat and solute transport in furrow-irrigated soil: I. T eory. Soil Sci. Soc. Am. J. 60:1001-1009. doi:10.2136/sssaj1996.03615995006000040007x
124. Noborio, K., K.J. McInnes, and J.L. Heilman. 1996b. Two-dimensional model for water, heat, and solute transport in furrow-irrigated soil: II. Field evaluation. Soil Sci. Soc. Am. J. 60:1010-1021. doi:10.2136/sssaj1996. 03615995006000040008x
125. Noorishad, J., and C.F. Tsang. 1996. Coupled thermo-hydro-elasticity phenomena in variably saturated fractured porous rocks: Formulation and numerical solution. p. 93-134. In O. Stephansson et al. (ed.) Coupled thermo-hydro-mechanical processes of fractured media: Mathematical and experimental studies. Dev. Geotech. Eng. 79. Elsevier Sci. B V, Amsterdam. (Pubitemid 127035227)
126. Noorishad, J., C.F. Tsang, and P.A. Witherspoon. 1992. T eoretical and f eld studies of coupled hydromechanical behaviour of fractured rocks: 1. Development and verif cation of a numerical simulator. Int. J. Rock Mech. Min. Sci. 29:401-409.
127. Ochsner, T.E., R. Horton, and T. Ren. 2001. A new perspective on soil thermal properties. Soil Sci. Soc. Am. J. 65:1141-1147.
128. O'Neill, K. 1983. T e physics of mathematical frost heave models: A review. Cold Reg. Sci. Technol. 6:275-291. doi:10.1016/0165-232X(83)90048-4 (Pubitemid 13505189)
129. O'Neill, K., and R.D. Miller. 1982. Numerical solutions for a rigid-ice model of secondary frost heave. CRREL Rep.82-13. U.S. Army Corps Eng., Cold Reg. Res. Eng. Lab., Hanover, NH.
130. O'Neill, K., and R.D. Miller. 1985. Exploration of a rigid ice model of frost heave. Water Resour. Res. 21:281-296. doi:10.1029/WR021i003p00281
131. Or, D., and M. Tuller. 1999. Liquid retention and interfacial area in variably saturated porous media: Upscaling from single-pore to sample-scale model. Water Resour. Res. 35:3591-3605. doi:10.1029/1999WR900262
132. Othman, M.A., and C.H. Benson. 1993. Effect of freeze-thaw on the hydraulic conductivity and morphology of compacted clay. Can. Geotech. J. 30:236-246. doi:10.1139/t93-020 (Pubitemid 24393328)
133. Penner, E. 1970. T ermal conductivity of frozen soils. Can. J. Earth Sci. 7:982-987. doi:10.1139/e70-091
134. Philip, J.R., and D.A. de Vries. 1957. Moisture movement in porous materials under temperature gradients. Eos Trans. AGU 38:222-232.
135. Powers, T.C. 1949. T e air requirement of frost-resistant concrete. Highw. Res. Board Proc. 29:184-211.
136. Powers, T.C. 1958. Structure and physical properties of hardened Portland cement paste. J. Am. Ceram. Soc. 41:1-6. doi:10.1111/j.1151-2916.1958.tb13494.x
137. Reeves, P.C., and M.A. Celia. 1996. Functional relationships between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model. Water Resour. Res. 32:2345-2358. doi:10.1029/96WR01105 (Pubitemid 26312050)
138. Richards, L.A. 1931. Capillary conduction of liquids in porous mediums. Physics 1:318-333. doi:10.1063/1.1745010
139. Rijtema, P.E. 1965. An analysis of actual evapotranspiration. Ph.D. diss. Agric. Univ. Rep. 659. Pudoc, Wageningen, the Netherlands.
140. Russell, H.W. 1935. Principles of heat flow in porous insulators. J. Am. Ceram. Soc. 18:1-5. doi:10.1111/j.1151-2916.1935.tb19340.x
141. Rutqvist, J., L. Börgesson, M. Chijimatsu, A. Kobayashi, L. Jing, T.S. Nguyen, J. Noorishad, and C.-F. Tsang. 2001a. T ermo-hydro-mechanics of partially saturated geological media: Governing equations and formulation of four f nite element models. Int. J. Rock Mech. Min. Sci. 38:105-127. doi:10.1016/S1365-1609(00)00068-X (Pubitemid 32196737)
142. Rutqvist, J., L. Börgesson, M. Chijimatsu, T.S. Nguyen, L. Jing, J. Noorishad, and C.-F. Tsang. 2001b. Coupled thermo-hydro-mechanical analysis of a heater test in fractured rock and bentonite at Kamaishi Mine: Comparison of f eld results to predictions of four f nite element codes. Int. J. Rock Mech. Min. Sci. 38:129-142. doi:10.1016/S1365-1609(00)00069-1 (Pubitemid 32196738)
143. Sahimi, M. 1995. Flow and transport in porous media and fractured rock: From classical methods to modern approaches. VCH Verlag, Weinheim, Germany.
144. Sawada, S. 1977. Temperature dependence of thermal conductivity of frozen soil. Res. Rep. Kitami Inst. of Technol., Kitami, Japan.
145. Scanlon, B.R., and P.C.D. Milly. 1994. Water and heat f uxes in desert soils: 2. Numerical simulations. Water Resour. Res. 30:721-733. doi:10.1029/93WR03252 (Pubitemid 24405765)
146. Scanlon, B.R., S.W. Tyler, and P.J. Wierenga. 1997. Hydrologic issues in arid, unsaturated systems and implications for contaminant transport. Rev. Geophys. 35:461-490. doi:10.1029/97RG01172 (Pubitemid 127659334)
147. Scherer, G.W. 1999. Crystallization in pores. Cement Concr. Res. 29:1347-1358. doi:10.1016/S0008-8846(99)00002-2
148. Schofield, R.K. 1935. T e pF of the water in soil. p. 37-48. In Trans. World Congr. Soil Sci., 3rd, Oxford, UK. July-Aug. 1935. Vol. 2.
149. Schofield, R.K., and J.V.B. da Costa. 1938. T e measurement of pF in soil by freezing-point. J. Agric. Sci. 28:644-653. doi:10.1017/S0021859600051042
150. Seeton, C.J. 2006. Viscosity-temperature correlation for liquids. Tribol. Lett. 22:67-78. doi:10.1007/s11249-006-9071-2 (Pubitemid 44018836)
151. Sheng, D., K. Axelsson, and S. Knutsson. 1995. Frost heave due to ice lens formation in freezing soils: 1. T eory and verif cation. Nord. Hydrol. 26:125-146. (Pubitemid 26437549)
152. Šim?nek, J., M. Sejna, and M.T van Genuchten. 1998. T e Hydrus-1D sof ware package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media: User's manual, version 2.0. U.S. Salinity Lab., Riverside, CA.
153. Sliwinska-Bartkowiak, M., G. Dudziak, R. Sikorski, R. Gras, K.E. Gubbins, R. Radhakrishnan, and K. Kaneko. 2001. Freezing behavior in porous materials: T eory and experiment. Pol. J. Chem. 75:547-555. (Pubitemid 33393008)
154. Slowik, V., T. Hubner, M. Schmidt, and B. Villmann. 2009. Simulation of capillary shrinkage cracking in cement-like materials. Cement Concr. Compos. 31:461-469. doi:10.1016/j.cemconcomp.2009.05.004
155. Sophocleous, M. 1979. Analysis of water and heat in unsaturated-saturated porous media. Water Resour. Res. 15:1195-1206. doi:10.1029/WR015i005p01195
156. Spaans, E.J.A., and J.M. Baker. 1996. T e soil freezing characteristic: Its measurement and similarity to the soil moisture characteristic. Soil Sci. Soc. Am. J. 60:13-19. doi:10.2136/sssaj1996.03615995006000010005x
157. Stähli, M., P.E. Janson, and L.C. Lundin. 1999. Soil moisture redistribution and inf ltration in frozen sandy soils. Water Resour. Res. 35:95-103. doi:10.1029/1998WR900045 (Pubitemid 29054151)
158. Stephansson, O., L. Jing, and C.-F. Tsang (ed.). 1997. Coupled thermo-hydro-mechanical processes of fractured media: Mathematical and experimental studies. Dev. Geotech. Eng. 79. Elsevier Sci. BV, Amsterdam.
159. Sutherland, H.B., and P.H. Gaskin. 1973. Pore water and heaving pressures developed in partially frozen soils. p. 409-419. In Proc. Int. Conf. Permafrost, 2nd, Yakutsk, Siberia. 13-28 July 1973. Natl. Acad. Sci., Washington, DC.
160. Tarnawski, V.R., and B. Wagner. 1992. A new computerized approach to estimating the thermal properties of unfrozen soils. Can. Geotech. J. 29:714-720. doi:10.1139/t92-079 (Pubitemid 23378205)
161. Taylor, G.S., and J.N. Luthin. 1978. A model for coupled heat and moisture transfer during soil freezing. Can. Geotech. J. 15:548-555. doi:10.1139/t78-058
162. Taylor, S.A., and J.W. Cary. 1964. Linear equations for the simultaneous flow of matter and energy in a continuous soil system. Soil Sci. Soc. Am. Proc. 28:167-172. doi:10.2136/sssaj1964.03615995002800020013x
163. Thomas, H.R. 1985. Modelling two-dimensional heat and moisture transfer in unsaturated soils including gravity Effects. Int. J. Num. Anal. Methods Geomech. 9:573-588. doi:10.1002/nag.1610090606 (Pubitemid 15605810)
164. T omas, H.R., P. Cleall, Y.C. Li, C. Harris, and M. Kern-Luetschg. 2009. Modelling of cryogenic processes in permafrost and seasonally frozen soils. Geotechnique 59:173-184. doi:10.1680/geot.2009.59.3.173
165. Thomas, H.R., and Y. He. 1995. Analysis of coupled heat, moisture and air transfer in a deformable unsaturated soil. Geotechnique 45:677-689. doi:10.1680/geot.1995.45.4.677 (Pubitemid 26443836)
166. Thomas, H.R., and Y. He. 1997. A coupled heat-moisture transfer theory for deformable unsaturated soil and its algorithmic implementation. Int. J. Num. Methods Eng. 40:3421-3441. doi:10.1002/(SICI)1097-0207(19970930)40:183.0.CO;2-C
167. Thomas, H.R., and S.D. King. 1991. Coupled temperature/capillary potential variations in unsaturated soil. J. Eng. Mech. 117:2475-2491. doi:10.1061/(ASCE)0733-9399(1991)117:11(2475)
168. van Genuchten, M.T 1980. A close-form equation for predicting the hydraulic conductivity of unsaturated soil. Soil Sci. Soc. Am. J. 44:892-898. doi:10.2136/sssaj1980.03615995004400050002x
169. Vogel, T., M.T van Genuchten, and M. Cislerova. 2000. Effect of the shape of the soil hydraulic functions near saturation on variably saturated flow predictions. Adv. Water Resour. 24:133-144. doi:10.1016/S0309-1708(00)00037-3 (Pubitemid 32145495)
170. Wang, W., G. Kosakowski, and O. Kolditz. 2009. A parallel f nite element scheme for thermo-hydro-mechanical (THM) coupled problems in porous media. Comput. Geosci. 35:1631-1641. doi:10.1016/j.cageo.2008.07.007
171. Watanabe, K., and T. Wake. 2008. Capillary bundle model of hydraulic conductivity for frozen soil. Water Resour. Res. 44:1927-1932.
172. Webb, S.W. 2000. A simple extension of two-phase characteristic curves to include the dry region. Water Resour. Res. 36:1425-1430. doi:10.1029/ 2000WR900057 (Pubitemid 30334243)
173. Williams, J., R.E. Prebble, W.T. Williams, and C.T. Hignett. 1983. The inf uence of texture, structure and clay mineralogy on the soil moisture characteristic. Aust. J. Soil Res. 21:15-32. doi:10.1071/SR9830015 (Pubitemid 14250414)
174. Williams, P.J. 1964. Specif c heat and apparent specif c heat of frozen soils. p. 225-229. In Proc. Int. Conf. Permafrost, West Lafayette, IN. 11-15 Nov. 1963. Natl. Acad. Sci., Washington, DC.
175. Williams, P.J. 1967. Pore pressures at a penetrating frost line and their prediction. Geotechnique 16:187-208.
176. Williams, P.J., and M.W. Smith. 1989. The frozen earth: Fundamentals of geocryology. Cambridge Univ. Press, Cambridge, UK.
177. Wind, G.P. 1955. A field experiment concerning capillary rise of moisture in a heavy clay soil. Neth. J. Agric. Sci. 3:60-69.
178. Woodside, W. 1958. Calculation of the thermal conductivity of porous media. Can. J. Phys. 36:815-822. doi:10.1139/p58-087
179. Zapata, C.E., W.N. Houston, S.L. Houston, and K.D. Walsh. 2000. Soil water characteristic curve variability. p. 84-123. In C.D. Shackelford et al. (ed.) Advances in unsaturated geotechnics, Proc. Geo-Denver 2000, Denver, CO. 5-8 Aug. 2000. Geotech. Inst. Spec. Publ. 99. Am. Soc. Civ. Eng., Reston, VA.