Thermal Conductivity of Sand–Silt Mixtures
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 147, Issue 2
Abstract
Heat flow controls the design and operation of a wide range of engineered geosystems. This study uses transient thermal probe measurements to determine the evolution of the thermal conductivity of air-dry and water-saturated sand–silt mixtures as a function of effective stress. Results confirm that the thermal conductivity of soils varies with state of stress, dry mass density, mineralogy, and pore fluid properties and highlight the effect of thermal contact resistance on the thermal conductivity of granular materials. Thermal conductivity follows a linear relationship with the logarithm of effective stress as a consequence of fabric compaction, increased coordination number, contact deformation, and reduced thermal contact resistance. The bulk thermal conductivity of water-saturated soils is more than seven times that of air-dry soils for the same fines content (FC) and effective stress. Pore-filling fines contribute conduction paths and interparticle coordination; the peak in thermal conductivity takes place at ; this mixture range corresponds to the transition from fines-controlled to coarse-controlled mechanical response (i.e., both fines and coarse grains are load bearing), in agreement with the revised soil classification system.
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Data Availability Statement
Data generated during the study are available from the corresponding author upon request.
Acknowledgments
Support for this research was provided by the Goizueta Foundation at the Georgia Institute of Technology and the KAUST endowment at King Abdullah University of Science and Technology. The authors’ gratitude extends to Gabrielle E. Abelskamp, who edited the manuscript.
References
Abdulagatova, Z., I. M. Abdulagatov, and V. N. Emirov. 2009. “Effect of temperature and pressure on the thermal conductivity of sandstone.” Int. J. Rock Mech. Min. Sci. 46 (6): 1055–1071. https://doi.org/10.1016/j.ijrmms.2009.04.011.
ASTM. 2008. Standard test method for determination of thermal conductivity of soil and soft rock by thermal needle probe procedure. ASTM D5334. West Conshohocken, PA: ASTM.
Bajpai, P., and V. Dash. 2012. “Hybrid renewable energy systems for power generation in stand-alone applications: A review.” Renewable Sustainable Energy Rev. 16 (5): 2926–2939. https://doi.org/10.1016/j.rser.2012.02.009.
Beck, A. E. 1976. “An improved method of computing the thermal conductivity of fluid-filled sedimentary rocks.” Geophysics 41 (1): 133–144. https://doi.org/10.1190/1.1440596.
Bergman, T. L., F. P. Incropera, D. P. DeWitt, and A. S. Lavine. 2011. Fundamentals of heat and mass transfer, 114–119. Hoboken, NJ: Wiley.
Beziat, A., M. Dardaine, and V. Gabis. 1988. “Effect of compaction pressure and water content on the thermal conductivity of some natural clays.” Clays Clay Miner. 36 (5): 462–466. https://doi.org/10.1346/CCMN.1988.0360512.
Bidarmaghz, A., and G. A. Narsilio. 2018. “Heat exchange mechanisms in energy tunnel systems.” Geomech. Energy Environ. 16 (Dec): 83–95. https://doi.org/10.1016/j.gete.2018.07.004.
Bresme, F., and F. Römer. 2013. “Heat transport in liquid water at extreme pressures: A non-equilibrium molecular dynamics study.” J. Mol. Liq. 185 (Sep): 1–7. https://doi.org/10.1016/j.molliq.2012.09.013.
Broniarz-Press, L., and K. Pralat. 2009. “Thermal conductivity of Newtonian and non-Newtonian liquids.” Int. J. Heat Mass Transfer 52 (21–22): 4701–4710. https://doi.org/10.1016/j.ijheatmasstransfer.2009.06.019.
Brosseau, D., J. W. Kelton, D. Ray, M. Edgar, K. Chisman, and B. Emms. 2005. “Testing of thermocline filler materials and molten-salt heat transfer fluids for thermal energy storage systems in parabolic trough power plants.” J. Sol. Energy Eng. 127 (1): 109–116. https://doi.org/10.1115/1.1824107.
Chen, S. X. 2008. “Thermal conductivity of sands.” Heat Mass Transfer 44 (10): 1241. https://doi.org/10.1007/s00231-007-0357-1.
Cho, G. C., J. Dodds, and J. C. Santamarina. 2006. “Particle shape effects on packing density, stiffness, and strength: Natural and crushed sands.” J. Geotech. Geoenviron. Eng. 132 (5): 591–602. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:5(591).
Cho, G. C., and J. C. Santamarina. 2001. “Unsaturated particulate materials—Particle-level studies.” J. Geotech. Geoenviron. Eng. 127 (1): 84–96. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:1(84).
Choo, J., J. H. Lee, J. Lee, Y. Kim, and T. S. Yun. 2012. “Stress-dependent thermal conductivity evolution of granular materials.” In GeoCongress 2012: State of the art and practice in geotechnical engineering, 4486–4494. Reston, VA: ASCE.
Cortes, D. D., A. I. Martin, T. S. Yun, F. M. Francisca, J. C. Santamarina, and C. Ruppel. 2009. “Thermal conductivity of hydrate-bearing sediments.” J. Geophys. Res. 114 (11): 1–10. https://doi.org/10.1029/2008JB006235.
Dagan, G. 1989. Flow and transport in porous formations. Berlin: Springer.
Deresiewicz, H. 1958. “Mechanics of granular matter.” In Advances in applied mechanics, 233–306. Amsterdam, Netherlands: Elsevier.
Ewen, J., and H. R. Thomas. 1987. “The thermal probe—A new method and its use on an unsaturated sand.” Géotechnique 37 (1): 91–105. https://doi.org/10.1680/geot.1987.37.1.91.
Farouki, O. T. 1981. Thermal properties of soils. Hanover, NH: USACE.
Freedman, J. P., J. H. Leach, E. A. Preble, Z. Sitar, R. F. Davis, and J. A. Malen. 2013. “Universal phonon mean free path spectra in crystalline semiconductors at high temperature.” Sci. Rep. 3 (1): 2963. https://doi.org/10.1038/srep02963.
Garrett, D., and H. Ban. 2011. “Compressive pressure dependent anisotropic effective thermal conductivity of granular beds.” Granular Matter 13 (5): 685–696. https://doi.org/10.1007/s10035-011-0273-4.
Gens, A. 2010. “Soil-environment interactions in geotechnical engineering.” Géotechnique 60 (1): 3–74. https://doi.org/10.1680/geot.9.P.109.
Gori, F., C. Marino, and M. Pietrafesa. 2001. “Experimental measurements and theoretical predictions of the thermal conductivity of two phases glass beads.” Int. Commun. Heat Mass Transfer 28 (8): 1091–1102. https://doi.org/10.1016/S0735-1933(01)00312-8.
Greenwood, J. A., and J. P. Williamson. 1966. “Contact of nominally flat surfaces.” In Vol. 295 of Proc., Royal Society of London. Series A. Mathematical and Physical Sciences, 300–319. London: Royal Society.
Haigh, S. K. 2012. “Thermal conductivity of sands.” Géotechnique 62 (7): 617–625. https://doi.org/10.1680/geot.11.P.043.
Hashin, Z., and S. Shtrikman. 1962. “A variational approach to the theory of the effective magnetic permeability of multiphase materials.” J. Appl. Phys. 33 (10): 3125–3131. https://doi.org/10.1063/1.1728579.
Hooper, F. C., and F. R. Lepper. 1950. “Transient heat flow apparatus for the determination of thermal conductivities.” Trans. Am. Soc. Heating Ventilating Eng. 56: 309–324.
Johansen, O. 1977. Thermal conductivity of soils. Hanover, NH: Cold Regions Research and Engineering Lab.
Kell, G. S. 1972. “Thermodynamic and transport properties of fluid water.” In The physics and physical chemistry of water, 363–412. Boston: Springer.
Lade, P. V., J. A. Yamamuro, and P. A. Bopp. 1996. “Significance of particle crushing in granular materials.” J. Geotech. Eng. 122 (4): 309–316. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:4(309).
Laloui, L., M. Nuth, and L. Vulliet. 2006. “Experimental and numerical investigations of the behaviour of a heat exchanger pile.” Int. J. Numer. Anal. Methods Geomech. 30 (8): 763–781. https://doi.org/10.1002/nag.499.
Lenz, A., and L. Ojamäe. 2009. “A theoretical study of water equilibria: The cluster distribution versus temperature and pressure for (H2O)n, n = 1–60, and ice.” J. Chem. Phys. 131 (13): 134302. https://doi.org/10.1063/1.3239474.
Lide, D. R. 2010. CRC handbook of chemistry and physics, 1199–2306. Boca Raton, FL: CRC Press.
Lovisa, J., and N. Sivakugan. 2015. “Tall oedometer testing: Method to account for wall friction.” Int. J. Geomech. 15 (2): 04014045. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000359.
Madsen, F. T. 1998. “Clay mineralogical investigations related to nuclear waste disposal.” Clay Miner. 33 (1): 109–129. https://doi.org/10.1180/000985598545318.
Maxwell, J. C. 1873. Treatise on electricity and magnetism, 365. London: Oxford University Press.
McGeary, R. K. 1961. “Mechanical packing of spherical particles.” J. Am. Ceram. Soc. 44 (10): 513–522. https://doi.org/10.1111/j.1151-2916.1961.tb13716.x.
Mikić, B. B. 1974. “Thermal contact conductance: Theoretical considerations.” Int. J. Heat Mass Transfer 17 (2): 205–214. https://doi.org/10.1016/0017-9310(74)90082-9.
Mizutani, U. 2001. Introduction to the electron theory of metals. Cambridge, UK: Cambridge University Press.
Ould-Lahoucine, C., H. Sakashita, and T. Kumada. 2002. “Measurement of thermal conductivity of buffer materials and evaluation of existing correlations predicting it.” Nucl. Eng. Des. 216 (1–3): 1–11. https://doi.org/10.1016/S0029-5493(02)00033-X.
Pang, X. F. 2014. Water: Molecular structure and properties. Singapore: World Scientific.
Park, J., and J. C. Santamarina. 2017. “Revised soil classification system for coarse-fine mixtures.” J. Geotech. Geoenviron. Eng. 143 (8): 04017039. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001705.
Pinson, D., R. P. Zou, A. B. Yu, P. Zulli, and M. J. McCarthy. 1998. “Coordination number of binary mixtures of spheres.” J. Phys. D: Appl. Phys. 31 (4): 457–462. https://doi.org/10.1088/0022-3727/31/4/016.
Prasher, R., T. Tong, and A. Majumdar. 2007. “Diffraction-limited phonon thermal conductance of nanoconstrictions.” Appl. Phys. Lett. 91 (14): 1–3. https://doi.org/10.1063/1.2794428.
Prasher, R. S., and P. E. Phelan. 2006. “Microscopic and macroscopic thermal contact resistances of pressed mechanical contacts.” J. Appl. Phys. 100 (6): 1–8. https://doi.org/10.1063/1.2353704.
Progelhof, R. C., J. L. Throne, and R. R. Ruetsch. 1976. “Methods for predicting the thermal conductivity of composite systems: A review.” Polym. Eng. Sci. 16 (9): 615–625. https://doi.org/10.1002/pen.760160905.
Regner, K. T., D. P. Sellan, Z. Su, C. H. Amon, A. J. McGaughey, and J. A. Malen. 2013. “Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance.” Nat. Commun. 4 (1): 1640. https://doi.org/10.1038/ncomms2630.
Richard, P., L. Oger, J. Lemaître, L. Samson, and N. N. Medvedev. 1999. “Application of the Voronoï tessellation to study transport and segregation of grains inside 2D and 3D packings of spheres.” Granular Matter 1 (4): 203–211. https://doi.org/10.1007/s100350050026.
Roshankhah, S., and J. C. Santamarina. 2014. “Engineered granular materials for heat conduction and load transfer in energy geotechnology” Géotech. Lett. 4 (2): 145–150. https://doi.org/10.1680/geolett.14.00001.
Salomone, L. A., and W. D. Kovacs. 1984. “Thermal resistivity of soils.” J. Geotech. Eng. 110 (3): 375–389. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:3(375).
Sperl, M. 2006. “Experiments on corn pressure in silo cells–translation and comment of Janssen’s paper from 1895.” Granular Matter 8 (2): 59–65. https://doi.org/10.1007/s10035-005-0224-z.
Stovall, T., F. De Larrard, and M. Buil. 1986. “Linear packing density model of grain mixtures.” Powder Technol. 48 (1): 1–12. https://doi.org/10.1016/0032-5910(86)80058-4.
Tang, A. M., Y. J. Cui, and N. Barnel. 2008. “Thermo-mechanical behavior of a compacted swelling clay.” Géotechnique 58 (1): 45–54. https://doi.org/10.1680/geot.2008.58.1.45.
Tavman, I. H. 1996. “Effective thermal conductivity of granular porous materials.” Int. Commun. Heat Mass Transfer 23 (2): 169–176. https://doi.org/10.1016/0735-1933(96)00003-6.
Valdes, J. R., and T. M. Evans. 2008. “Sand–rubber mixtures: Experiments and numerical simulations.” Can. Geotech. J. 45 (4): 588–595. https://doi.org/10.1139/T08-002.
Vincenti, W. G., and C. H. Kruger. 1965. Introduction to physical gas dynamics. Hoboken, NJ: Wiley.
Wallen, B. M., K. M. Smits, T. Sakaki, S. E. Howington, and T. K. K. Deepagoda. 2016. “Thermal conductivity of binary sand mixtures evaluated through full water content range.” Soil Sci. Soc. Am. J. 80 (3): 592–603. https://doi.org/10.2136/sssaj2015.11.0408.
Wang, Y., and M. B. Dusseault. 2003. “A coupled conductive–convective thermo-poroelastic solution and implications for wellbore stability.” J. Pet. Sci. Eng. 38 (3–4): 187–198. https://doi.org/10.1016/S0920-4105(03)00032-9.
Weidenfeld, G., Y. Weiss, and H. Kalman. 2004. “A theoretical model for effective thermal conductivity (ETC) of particulate beds under compression.” Granular Matter 6 (2–3): 121–129. https://doi.org/10.1007/s10035-004-0170-1.
Woodside, W. M. J. H., and J. H. Messmer. 1961. “Thermal conductivity of porous media. I. Unconsolidated sands.” J. Appl. Phys. 32 (9): 1688–1699. https://doi.org/10.1063/1.1728419.
Yagi, S., and D. Kunii. 1957. “Studies on effective thermal conductivities in packed beds.” Am. Inst. Chem. Eng. J. 3 (3): 373–381. https://doi.org/10.1002/aic.690030317.
Yamamuro, J. A., P. A. Bopp, and P. V. Lade. 1996. “One-dimensional compression of sands at high pressures.” J. Geotech. Eng. 122 (2): 147–154. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:2(147).
Youd, T. L. 1973. “Factors controlling maximum and minimum densities of sands.” In Evaluation of relative density and its role in geotechnical projects involving cohesionless soils, 98–112. West Conshohocken, PA: ASTM.
Yovanovich, M. M. 2005. “Four decades of research on thermal contact, gap, and joint resistance in microelectronics.” IEEE Trans. Compon. Packag. Technol. 28 (2): 182–206. https://doi.org/10.1109/TCAPT.2005.848483.
Yun, T. S., and J. C. Santamarina. 2008. “Fundamental study of thermal conduction in dry soils.” Granular Matter 10 (3): 197–207. https://doi.org/10.1007/s10035-007-0051-5.
Zhang, N., and Z. Wang. 2017. “Review of soil thermal conductivity and predictive models.” Int. J. Therm. Sci. 117 (Jul): 172–183. https://doi.org/10.1016/j.ijthermalsci.2017.03.013.
Zou, J., and A. Balandin. 2001. “Phonon heat conduction in a semiconductor nanowire.” J. Appl. Phys. 89 (5): 2932–2938. https://doi.org/10.1063/1.1345515.
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Received: Dec 28, 2019
Accepted: Aug 12, 2020
Published online: Dec 12, 2020
Published in print: Feb 1, 2021
Discussion open until: May 12, 2021
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