Theoretical Basis for Modeling Porous Geomaterials under Frost Actions: A Review
2012; Wiley; Volume: 76; Issue: 2 Linguagem: Inglês
10.2136/sssaj2010.0370
ISSN1435-0661
Autores Tópico(s)Landslides and related hazards
ResumoSoil Science Society of America JournalVolume 76, Issue 2 p. 313-330 Review & Analysis–Soil Physics Theoretical Basis for Modeling Porous Geomaterials under Frost Actions: A Review Zhen Liu, Zhen Liu Dep. of Civil Engineering, Case Western Reserve Univ., 2104 Adelbert Rd., Bingham 256, Cleveland, OH, 44106Search for more papers by this authorYe Sun, Ye Sun Dep. of Electrical Engineering and Computer Science, Case Western Reserve Univ., 2104 Adelbert Rd., Bingham 203C, Cleveland, OH, 44106Search for more papers by this authorXiong (Bill) Yu, Corresponding Author Xiong (Bill) Yu [email protected] Dep. of Civil Engineering, Case Western Reserve Univ., 2104 Adelbert Rd., Bingham 206, Cleveland, OH, 44106Corresponding author ([email protected])Search for more papers by this author Zhen Liu, Zhen Liu Dep. of Civil Engineering, Case Western Reserve Univ., 2104 Adelbert Rd., Bingham 256, Cleveland, OH, 44106Search for more papers by this authorYe Sun, Ye Sun Dep. of Electrical Engineering and Computer Science, Case Western Reserve Univ., 2104 Adelbert Rd., Bingham 203C, Cleveland, OH, 44106Search for more papers by this authorXiong (Bill) Yu, Corresponding Author Xiong (Bill) Yu [email protected] Dep. of Civil Engineering, Case Western Reserve Univ., 2104 Adelbert Rd., Bingham 206, Cleveland, OH, 44106Corresponding author ([email protected])Search for more papers by this author First published: 01 March 2012 https://doi.org/10.2136/sssaj2010.0370Citations: 19 All rights reserved. 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Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract We review the theoretical basis for modeling the behaviors of porous materials under frost actions. An attempt is made to categorize the previous research to understand the frost-induced coupled processes. The importance of the coupled processes between the thermal, hydraulic. and mechanical fields in porous materials is emphasized. Methods to describe such coupling actions are classified into basic governing mechanisms as well as the explicit and implicit relationships among individual parameters. Analytical models developed from soil science, civil engineering, and engineering mechanics are summarized. Various terminologies and expressions from different disciplines are discussed in relationship to the general physical mechanisms. From this, models can be selected for implementing holistic simulations of porous geomaterials under frost actions. We also discuss problems deserving further investigation. REFERENCES 1Ahuja, L.R., and Swartzendruber, D.. 1972. An improved form of soil-water diffusivity function. Soil Sci. Soc. Am. J. 36: 9–14. https://doi.org/10.2136/sssaj1972.03615995003600010002x http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1972L813200002&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 2Alonso, E.E., Gens, A., and Josa, A.. 1990. A constitutive model for partially saturated soils. Geotechnique 40: 405–430. https://doi.org/10.1680/geot.1990.40.3.405 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1990EK75800005&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 3Anderson, D.M., and Morgenstern, N.R.. 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. 4Anderson, D.M., Tice, A.R., and McKim, H.L.. 1973. The unfrozen water and the apparent specific 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. 5Arvidson, W.D., and Morgenstern, N.R.. 1977. Water flow induced by soil freezing. Can. Geotech. J. 14: 237–245. https://doi.org/10.1139/t77-024 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1977DG24600007&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 6Averjanov, S.F.. 1950. About permeability of subsurface soils in case of incomplete saturation. Engl. Collect. 7: 19–21. 7Bachmann, J., Deurer, M., and Arye, G.. 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. https://doi.org/10.2136/vzj2006.0060 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000249015500002&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 8Bachmann, J., Horton, R., Grant, S.A., and van der Ploeg, R.R.. 2002. Temperature dependence of water retention curves for wettable and water-repellent soils. Soil Sci. Soc. Am. J. 66: 44–52. https://doi.org/10.2136/sssaj2002.0044 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000173219300006&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 9Bachmann, J., Horton, R., Ren, T., and van der Ploeg, R.R.. 2001. Comparison of the thermal properties of four wettable and four water-repellent soils. Soil Sci. Soc. Am. J. 65: 1675–1679. https://doi.org/10.2136/sssaj2001.1675 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000172918600013&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 10Bachmann, J., and van der Ploeg, R.R.. 2002. A review on recent developments in soil water retention theory: Interfacial tension and temperature effects. J. Plant Nutr. Soil Sci. 165: 468–478. https://doi.org/10.1002/1522-2624(200208)165:4 3.0.CO;2-G http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000177660800012&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 11Bai, M., and Elsworth, D.. 2000. Coupled processes in subsurface deformation, flow, and transport. Am. Soc. Civ. Eng., Reston, VA. 12Banin, J.M., and Anderson, D.M.. 1974. Effects of salt concentration changes during freezing on the unfrozen water content of porous materials. Water Resour. Res. 10: 124–128. https://doi.org/10.1029/WR010i001p00124 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1974S411600020&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 13Baron, 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. 14Benson, C.H., and Othman, M.A.. 1993. Hydraulic conductivity of compacted clay frozen and thawed in situ. J. Geotech. Eng. 119: 276–294. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:2(276) http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1993KK25400006&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 15Biot, M.A.. 1941. General theory of three-dimensional consolidation. J. Appl. Phys. 12: 155–164. https://doi.org/10.1063/1.1712886 16Biot, M.A., and Willis, D.G.. 1957. The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24: 594–601. 17Bittelli, M., Flury, M., and Campbell, G.S.. 2003. A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media. Water Resour. Res. 39 (2): 1041. https://doi.org/10.1029/2001WR000930 18Bond, F.W., Cole, C.R., and Gutknecht, P.J.. 1984. Unsaturated groundwater flow model (UNSAT1D) computer code manual. CS-2434-CCM. Electric Power Res. Inst., Palo Alto, CA. 19Briggs, L.J.. 1897. The mechanics of soil moisture. Bull. 10. USDA Bureau of Soils, Washington, DC. 20Brooks, R.H., and Corey, A.T.. 1964. Hydraulic properties of porous media. Hydrol. Pap. no. 3. Colorado State Univ., Fort Collins. 21Brutsaert, W.. 1967. Some methods of calculating unsaturated permeability. Trans. ASAE 10: 400–404. 22Buckingham, E.. 1907. Studies on the movement of soil moisture. Bull. 38. USDA Bureau of Soils, Washington, DC. 23Bumb, A.C. 1987. Unsteady-state flow of methane and water in coalbeds. Ph.D. diss. Univ. of Wyoming, Laramie (Diss. Abstr. AAT DP15253). 24Burdine, N.T.. 1953. Relative permeability calculations from pore-size distribution data. Pet. Trans. Am. Inst. Min. Metall. Eng. 198: 71–78. 25Burger, H.C.. 1915. Das lertvermogen verdummter mischristallfreier lonsungen. Phys. Z. 20: 73–76. 26Campbell, G.S.. 1974. A simple method for determining unsaturated conductivity from moisture retention data. Soil Sci. 117: 311–314. https://doi.org/10.1097/00010694-197406000-00001 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1974T337700001&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 27Campbell, G.S.. 1985. Soil physics with BASIC: Transport models for soil–plant systems. Elsevier Sci. BV, Amsterdam. 28Cary, J.W.. 1965. Water flux in moist soil: Thermal versus suction gradients. Soil Sci. 100: 168–175. https://doi.org/10.1097/00010694-196509000-00004 29Cary, J.W.. 1966. Soil moisture transport due to thermal gradients: Practical aspects. Soil Sci. Soc. Am. Proc. 30: 428–433. https://doi.org/10.2136/sssaj1966.03615995003000040011x http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A19668228200009&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 30Cass, A.G., Campbell, G.S., and Jones, T.L.. 1981. Hydraulic and thermal properties of soil samples from the buried waster test facility. PNL-4015. Pacific Northwest Natl. Lab., Richland, WA. 31Celia, M.A., and Binning, P.. 1992. A mass conservative numerical solution for two-phase flow in porous media with application to unsaturated flow. Water Resour. Res. 28: 2819–2828. https://doi.org/10.1029/92WR01488 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1992JR40900025&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 32Celia, M.A., Bouloutas, E.F., and Zarba, R.L.. 1990. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resour. Res. 26: 1483–1496. https://doi.org/10.1029/WR026i007p01483 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1990DN50500015&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 33Childs, E.C., and Collis-George, G.. 1950. The permeability of porous materials. Proc. R. Soc. London A 201: 392–405. https://doi.org/10.1098/rspa.1950.0068 34Cooling, 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. 35Cooper, A.I.. 2003. Porous materials and supercritical fluids. Adv. Mater. 15: 1049–1059. https://doi.org/10.1002/adma.200300380 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000184135900002&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 36Côté, J., and Konrad, J.M.. 2005. A generalized thermal conductivity model for soils and construction materials. Can. Geotech. J. 42: 443–458. https://doi.org/10.1139/t04-106 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000229415500009&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 37 O. Coussy (ed.). 2004. Poromechanics. John Wiley & Sons, Chichester, UK. 38Coussy, O.. 2005. Poromechanics of freezing materials. J. Mech. Phys. Solids 53: 1689–1718. https://doi.org/10.1016/j.jmps.2005.04.001 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000230614200001&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 39Coussy, O., and Monteiro, P.. 2007. Unsaturated poroelasticity for crystallization in pores. Comput. Geotech. 34: 279–290. https://doi.org/10.1016/j.compgeo.2007.02.007 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000249548600008&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 40Coussy, O., and Monteiro, P.J.M.. 2008. Poroelastic model for concrete exposed to freezing temperatures. Cement Concr. Res. 38: 40–48. https://doi.org/10.1016/j.cemconres.2007.06.006 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000251917300004&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 41Croney, D., and Coleman, J.D.. 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. 42Dash, J.G.. 1989. Thermomolecular pressure in surface melting: Motivation for frost heave. Science 246: 1591–1593. https://doi.org/10.1126/science.246.4937.1591 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1989CE81500042&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 43Davidson, J.M., Stone, L.R., Nielsen, D.R., and Larue, M.E.. 1969. Field measurement and use of soil-water properties. Water Resour. Res. 5: 1312–1321. https://doi.org/10.1029/WR005i006p01312 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1969F423200016&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 44Davis, M.E.. 2002. Ordered porous materials for emerging applications. Nature 417: 813–821. https://doi.org/10.1038/nature00785 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000176285600038&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 45De Groot, S.R., and Mazur, P.. 1984. Non-equilibrium thermodynamics. Dover Publ., Mineola, NY. 46De Vries, D.A.. 1963. Thermal properties of soils. p. 210–235. In W.R. Wijk (ed.) Physics of plant environment. North-Holland Publ. Co., Amsterdam. 47Dirksen, C., and Miller, R.D.. 1966. Closed-system freezing of unsaturated soil. Soil Sci. Soc. Am. Proc. 30: 168–173. https://doi.org/10.2136/sssaj1966.03615995003000020010x http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A19667848000007&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 48Dormieux, L., Molinari, A., and Kondo, D.. 2002. Micromechanical approach to the behavior of poroelastic materials. J. Mech. Phys. Solids 50: 2203–2231. https://doi.org/10.1016/S0022-5096(02)00008-X http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000177560400007&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 49Duquennoi, C., Fremond, M., and Levy, M.. 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. 50Edlefsen, N.E., and Anderson, A.B.C.. 1943. Thermodynamics of soil moisture. Hilgardia 15: 31–298. 51Endelman, F.J., Box, G.E.P., Royle, J.R., Hughes, R.R., Keeney, D.R., Northrup, M.L., and Saffigna, P.G.. 1974. The mathematical modeling of soil–water–nitrogen phenomena. Rep. EDFB-IBP-74-8. Oak Ridge Natl. Lab., Oak Ridge, TN. 52Farouki, O.T.. 1981. Thermal properties of soils. CRREL Monogr. 81-1. U.S. Army Corps Eng., Cold Reg. Res. Eng. Lab., Hanover, NH. 53Farouki, 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. 54Fayer, 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. 55Fayer, M.J., and Simmons, C.S.. 1995. Modified soil water retention functions for all matric suctions. Water Resour. Res. 31: 1233–1238. https://doi.org/10.1029/95WR00173 56Fen-Chong, T., Fabbri, A., and Azouni, A.. 2006. Transient freezing–thawing phenomena in water-filled cohesive porous materials. Cold Reg. Sci. Technol. 46: 12–26. https://doi.org/10.1016/j.coldregions.2006.04.001 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000241350100002&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 57Flerchinger, G.N.. 2000. The simultaneous heat and water (SHAW) model: Technical documentation. Tech. Rep. NWRC 2000-09. USDA-ARS Northwest Watershed Res. Ctr., Boise, ID. 58Flerchinger, G.N., and Pierson, F.B.. 1991. Modeling plant canopy effects on variability of soil temperature and water. Agric. For. Meteorol. 56: 227–246. https://doi.org/10.1016/0168-1923(91)90093-6 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1991GG84200004&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 59Fredlund, D.G., and Xing, A.. 1994. Equations for the soil-water characteristic curve. Can. Geotech. J. 31: 521–532. https://doi.org/10.1139/t94-061 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1994PK00300006&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 60Fredlund, D.G., Xing, A., and Huang, S.. 1994. Predicting the permeability function for unsaturated soils using the soil-water characteristic curve. Can. Geotech. J. 31: 533–546. https://doi.org/10.1139/t94-062 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1994PK00300007&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 61Fremond, M., and Mikkola, M.. 1991. Thermomechanical 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. A.A. Balkema, Rotterdam, the Netherlands. 62Gardner, W.R.. 1958. Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table. Soil Sci. 85: 228–232. https://doi.org/10.1097/00010694-195804000-00006 63Gilpin, R.R.. 1980. A model for the prediction of ice lensing and frost heave in soils. Water Resour. Res. 16: 918–930. https://doi.org/10.1029/WR016i005p00918 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1980KN50500012&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 64Grant, S.A., and Bachmann, J.. 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. 65Grant, S.A., and Salehzadeh, A.. 1996. Calculation of temperature effects on wetting coefficients of porous solids and their capillary pressure functions. Water Resour. Res. 32: 261–270. https://doi.org/10.1029/95WR02915 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1996TT02500003&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 66Groenevelt, P.H., and Kay, B.D.. 1974. On the interaction of water and heat transport in frozen and unfrozen soils: II. The liquid phase. Soil Sci. Soc. Am. Proc. 38: 400–404. https://doi.org/10.2136/sssaj1974.03615995003800030012x http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1974T609400006&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 67Guymon, G.L., and Luthin, J.N.. 1974. A coupled heat and moisture transport model for arctic soils. Water Resour. Res. 10: 995–1001. https://doi.org/10.1029/WR010i005p00995 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1974U463100015&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 68Hansson, K.. 2005. Water and heat transport in road structures; Development of mechanical models. Compr. Summ. Uppsala Diss. Sci. Technol., Uppsala Univ., Uppsala, Sweden. 69Hansson, K., Šimůnek, J., Mizoguchi, M., Lundin, L.C., and van Genuchten, M.Th.. 2004. Water flow and heat transport in frozen soil: Numerical solution and freeze–thaw applications. Vadose Zone J. 3: 693–704.https://doi.org/10.2136/vzj2004.0693 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=000227468800035&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 70Harlan, R.L.. 1973. Analysis of coupled heat–fluid transport in partially frozen soil. Water Resour. Res. 9: 1314–1323. https://doi.org/10.1029/WR009i005p01314 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1973Q978600020&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 71Hassanizadeh, S.M., and Gary, W.G.. 1993. Thermodynamic basics of capillary pressure in porous media. Water Resour. Res. 29: 3389–3405. https://doi.org/10.1029/93WR01495 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1993MA36800009&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 72Haverkamp, R., Vauclin, M., Touma, J., Wierenga, P.J., and Vachaud, G.. 1977. A comparison of numerical simulation models for one-dimensional infiltration. Soil Sci. Soc. Am. J. 41: 285–294. https://doi.org/10.2136/sssaj1977.03615995004100020024x http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1977DL12900011&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 73Horiguchi, K., and Miller, R.D.. 1980. Experimental studies with frozen soil in an "ice sandwich" permeameter. Cold Reg. Sci. Technol. 3: 177–183. https://doi.org/10.1016/0165-232X(80)90023-3 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1980KA30900010&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 74Horton, R., and Wierenga, P.J.. 1984. The effect of column wetting on soil thermal conductivity. Soil Sci. 138: 102–108. https://doi.org/10.1097/00010694-198408000-00002 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1984TJ39600002&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 75Hromadka, T.V., and Yen, C.. 1986. A diffusion hydrodynamic model (DHM). Adv. Water Resour. 9: 118–170. https://doi.org/10.1016/0309-1708(86)90031-X http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1986E917300001&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 76Hua, C., Acker, P., and Ehrlacher, A.. 1995. Analyses and models of the autogenous shrinkage of hardening cement paste: I. Modelling at macroscopic scale. Cement Concr. Res. 25: 1457–1468. https://doi.org/10.1016/0008-8846(95)00140-8 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1995RV43000011&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 77Hudson, C.S.. 1906. The 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. 78Jame, Y.W., and Norum, D.I.. 1980. Heat and mass transfer in a freezing unsaturated porous medium. Water Resour. Res. 16: 811–819. https://doi.org/10.1029/WR016i004p00811 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1980KG45700025&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 79 P.E. Jansson, 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. 80Johansen, O. 1975. Thermal conductivity of soils. Ph.D. diss. (CRREL Draft Transl. 637, 1977.) Norwegian Univ. of Sci. and Technol., Trondheim. 81Kay, B.D., and Groenevelt, P.H.. 1974. On the interaction of water and heat transport in frozen and unfrozen soils: I. Basic theory: The vapor phase. Soil Sci. Soc. Am. J. 38: 395–400. https://doi.org/10.2136/sssaj1974.03615995003800030011x http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1974T609400005&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 82Kersten, M.S.. 1949. Laboratory research for the determination of the thermal properties of soils. ACFEL Tech. Rep. 23. Univ. of Minnesota, Minneapolis. 83Khlosi, M., Cornelis, W.M., Gabriels, D., and Sin, G.. 2006. Simple modification to describe the soil water retention curve between saturation and oven dryness. Water Resour. Res. 42: W11501. https://doi.org/10.1029/2005WR004699 84Konrad, J.M., and Morgenstern, N.R.. 1980. A mechanistic theory of ice lens formation in fine-grained soils. Can. Geotech. J. 17: 473–486. https://doi.org/10.1139/t80-056 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1980KW40100002&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 85Konrad, J.M., and Morgenstern, N.R.. 1981. The segregation potential of a freezing soil. Can. Geotech. J. 18: 482–491. https://doi.org/10.1139/t81-059 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1981MV92200002&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 86Konrad, J.M., and Morgenstern, N.R.. 1982a. Prediction of frost heave in the laboratory during transient freezing. Can. Geotech. J. 19: 250–259. https://doi.org/10.1139/t82-032 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1982PC99000005&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 87Konrad, J.M., and Morgenstern, N.R.. 1982b. Effects of applied pressure of freezing soils. Can. Geotech. J. 19: 494–505. https://doi.org/10.1139/t82-053 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1982PV89500009&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 88Koopmans, R.W.R., and Miller, R.D.. 1966. Soil freezing and soil water characteristic curves. Soil Sci. Soc. Am. Proc. 30: 680–685. https://doi.org/10.2136/sssaj1966.03615995003000060011x http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A19668818800009&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCustomerID=523bbf5d2a868de7bbaeea0bc70ec0e4 89Krahn, J., and Fredlund, D.G.. 1972. On total, matric and osmotic suction. Soil Sci. 114: 339–348. https://doi.org/10.1097/00010694-197211000-00003 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=agrocropsoil&KeyUT=A1972O291000002&DestLinkType=FullRecord&DestApp=WOS_CPL&UsrCusto
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