Closed-Form Equation for Thermal Conductivity of Unsaturated Soils at Room Temperature
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 141, Issue 6
Abstract
Thermal conductivity is a fundamental physical property governing heat transfer in soil. It depends on soil types, pore structure, temperature, and moisture content, and can vary over an order of magnitude. Some theories have been established to address the effect of temperature on thermal conductivity. Other theoretical works focus on the effect of moisture content on thermal conductivity of different sandy and loamy soils. This work addresses the effect of all soil types and moisture content on thermal conductivity for ambient temperatures from 20 to 25°C. Thermal conductivity varies little within the hydration and capillary regimes, varies moderately within the funicular regime, and varies greatly within the pendular regime. A closed-form equation is proposed and validated by explicitly considering the soil-water retention regimes. Results taken from the literature for 25 soils and from the current study for two clay soils show that the closed-form equation can accurately predict thermal conductivity of all types of unsaturated soil.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research is supported by a grant from the National Science Foundation (NSF CMMI-1230544) to N. L. The authors would like to thank Brian Ebel and John S. McCartney for providing insightful comments on the work.
References
Adam, D., and Markiewicz, R. (2009). “Energy from earth-coupled structures, foundations, tunnels and sewers.” Géotechnique, 59(3), 229–236.
ASTM. (2010). “Standard tests for unified soil classification system.” D 2487, West Conshohocken, PA.
Brandl, H. (2006). “Energy foundations and other thermo-active ground structures.” Géotechnique, 56(2), 81–122.
Brettmann, T., and Amis, T. (2011). “Thermal conductivity evaluation of a pile group using geothermal energy piles.” Geo-Frontiers 2011, ASCE, Reston, VA, 499–508.
Campbell, G., Jungbauer, J., Jr., Bidlake, W., and Hungerford, R. (1994). “Predicting the effect of temperature on soil thermal conductivity.” Soil Sci., 158(5), 307–313.
Carslaw, H. S., and Jaeger, J. C. (1959). Conduction of heat in solids, 2nd Ed., Oxford University Press, London.
Cortes, D. D., Martin, A. I., Yun, T. S., Francisca, F. M., Santamarina, J. C., and Ruppel, C. (2009). “Thermal conductivity of hydrate-bearing sediments.” J. Geophys. Res., 114(B11), B11103.
Côté, J., and Konrad, J.-M. (2005). “A generalized thermal conductivity model for soils and construction materials.” Can. Geotech. J., 42(2), 443–458.
De Vries, D. A. (1963). “Thermal properties of soils.” Physics of plant environment, W. R. Van Wijk, ed., Wiley, New York, 210–235.
De Vries, D. A. (1987). “The theory of heat and moisture transfer in porous media revisited.” Int. J. Heat Mass Transf., 30(7), 1343–1350.
Dong, Y., Lu, N., Wayllane, A., and Smits, K. (2014). “Measurement of thermal conductivity function of unsaturated soil by using a transient water release and imbibition method.” Geotech. Test. J., 37(6), 980–990.
Dong, Y., McCartney, J. S., and Lu, N. (2015). “Critical review of thermal conductivity models for unsaturated soils.” Geotech. Geol. Eng., 1–15.
Ebigbo, A. (2005). “Thermal effects of carbon dioxide sequestration in the subsurface.” Doctoral dissertation, Institut für Wasserbau, Universität at Stuttgart, Stuttgart, Germany.
Johansen, O. (1975). “Thermal conductivity of soils.” Ph.D. thesis, Univ. of Trondheim, Trondheim, Norway.
Likos, W., Olson, H., and Jaafar, R. (2012). “Comparison of laboratory methods for measuring thermal conductivity of unsaturated soils.” GeoCongress 2012, ASCE, Reston, VA, 4366–4375.
Likos, W. J. (2014a). “Modeling thermal conductivity dryout curves from soil-water characteristic curves.” J. Geotech. Geoenviron. Eng., 140(5), 04013056.
Likos, W. J. (2014b). “Pore-scale model for thermal conductivity of unsaturated sand.” J. Geotech. Geol. Eng., 1–14.
Lipiec, J., Usowicz, B., and Ferrero, A. (2007). “Impact of soil compaction and wetness on thermal properties of sloping vineyard soil.” Int. J. Heat Mass Transf., 50(19–20), 3837–3847.
Lu, N., and Ge, S. (1996). “Effect of horizontal heat and fluid flow on the vertical temperature distribution in a semiconfining layer.” Water Resour. Res., 32(5), 1449–1453.
Lu, N., and Likos, J. W. (2004). Unsaturated soil mechanics, Wiley, Hoboken, NJ.
Lu, N., Zeidman, B. D., Lusk, M. T., Willson, C. S., and Wu, D. T. (2010). “A Monte Carlo paradigm for capillarity in porous media.” Geophys. Res. Lett., 37(23), L23402.
Lu, S., Ren, T., Gong, Y., and Horton, R. (2007). “An improved model for predicting soil thermal conductivity from water content at room temperature.” Soil Sci. Soc. Am. J., 71(1), 8–14.
McCartney, J. S., Ge, S., Reed, A., Lu, N., and Smits, K. (2013). “Soil-borehole thermal energy storage systems for district heating.” European Geothermal Congress 2013, European Geothermal Energy Council, Brussels, Belgium.
McInnes, K. (1981). “Thermal conductivities of soils from dryland wheat regions in eastern Washington.” Ph.D. dissertation, Washington State Univ., Pullman, WA.
Mickley, A. S. (1951). “The thermal conductivity of moist soil.” Trans. Am. Inst. Electr. Eng., 70(2), 1789–1797.
Mitchell, J. K., and Soga, K. (2005). Fundamentals of soil behavior, Wiley, Hoboken, NJ.
Murphy, K. D., Henry, K., and McCartney, J. S. (2014). “Impact of horizontal run-out length on the thermal response of full-scale energy foundations.” GeoCongress 2014, ASCE, Reston, VA.
Noborio, K., Mcinnes, K., and Heilman, J. (1996). “Two-dimensional model for water, heat, and solute transport in furrow-irrigated soil: I. Theory.” Soil Sci. Soc. Am. J., 60(4), 1001–1009.
Olgun, C. G., Martin, J. R., and Bowers, G. A. (2012). “Energy piles: Using deep foundations as heat exchangers.” Geo-Strata, 13(2), 46–51.
Preene, M., and Powrie, W. (2009). “Ground energy system: From analysis to geotechnical design.” Géotechnique, 59(3), 261–271.
Revil, A., and Lu, N. (2013). “Unified water isotherms for clayey porous materials.” Water Resour. Res., 49(9), 5685–5699.
Sepaskhah, A. R., and Boersma, L. (1979). “Thermal conductivity of soils as a function of temperature and water content.” J. Soil Sci. Soc. Am., 43(3), 439–444.
Smits, K. M., Sakaki, T., Limsuwat, A., and Illangasekare, T. H. (2010). “Thermal conductivity of sands under varying moisture and porosity in drainage-wetting cycles.” Vadose Zone J., 9(1), 172–180.
Tarnawski, V. R., and Gori, F. (2002). “Enhancement of the cubic cell soil thermal conductivity model.” Int. J. Energy Res., 26(2), 143–157.
van Genuchten, M. T. (1980). “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J., 44(5), 892–898.
Wayllace, A., and Lu, N. (2012). “A transient water release and imbibitions method for rapidly measuring wetting and drying soil water retention and hydraulic conductivity functions.” Geotech. Test. J., 35(1), 103–117.
Wu, R., Tinjum, J. M., and Likos, W. J. (2014). “Coupling thermal conductivity dryout curves with unsaturated modeling of shallow horizontal geothermal exchange loops.” Proc., ASCE Geo-Congress 2014, ASCE, Reston, VA.
Zhang, R., Lu, N., and Wu, Y.-S. (2012). “Efficiency of a community-scale borehole thermal energy storage technique for solar thermal energy.” Proc., GeoCongress 2012, ASCE, Reston, VA, 4386–4395.
Zhang, Y. Q., Lu, N., and Ross, B. (1994). “Convective instability of moist gas in a porous medium.” Int. J. Heat Mass Transf., 37(1), 129–138.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 141 • Issue 6 • June 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Apr 13, 2014
Accepted: Dec 22, 2014
Published online: Feb 6, 2015
Published in print: Jun 1, 2015
Discussion open until: Jul 6, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.