Geotechnical and Geological Engineering

, Volume 33, Issue 2, pp 179–192 | Cite as

Pore-Scale Model for Thermal Conductivity of Unsaturated Sand

Original paper


A new framework is proposed for predicting thermal conductivity dry out curves (TCDC) quantifying the relationship between soil thermal conductivity and degree of saturation at non-elevated temperatures. Pore-scale expressions are derived to quantify water retention and corresponding conductive heat transport for an idealized contacting-sphere geometry approximating that of granular (sand-sized) porous media. Measured water retention behavior is used to constrain a simulated soil–water characteristic curve and corresponding TCDC by differentiating pores containing water in the form of inter particle liquid bridges from pores containing water in the form of saturated pockets. Modeled TCDCs compare well with experimental measurements for representative fine-, medium-, and coarse-grained sands. Predicted thermal conductivity is within 5–10 % of the full scale range for saturations greater than 20 %. Model predictions perform as well as or better than predictions made using many existing empirical approaches. Because the model directly incorporates basic soil properties and process variables in its formulation, including grain size, grain size distribution, and wetting direction, it becomes a potentially useful framework to improve understanding of fundamental controls on soil thermal conductivity.


Unsaturated Suction Sand Thermal conductivity Heat transfer Thermal resistivity 



Coefficient of curvature


Coefficient of uniformity


Median grain size by mass


Void ratio


Campbell et al. (1994) TCDC modeling function


Specific gravity of soil solids


Clay content


Porosity; mixing model exponent


Heat flux


Radius in toroidal approximation for liquid bridge


Radius in toroidal approximation for liquid bridge


Spherical particle radius


Minimum particle radius in f(R)


Maximum particle radius in f(R)


Particle radius in f(R) corresponding to snap off


Coefficient of determination


Degree of saturation


Air-water interfacial tension


Volume of air


Volume of soil solids


Volume total


Volume of water


Gravimetric water content


Fractional area of liquid bridge


Fitting parameter in Hu et al. (2001) TCDC model; contact angle


Kersten number


Thermal conductivity


Thermal conductivity of air


Pore-scale thermal conductivity


Thermal conductivity of quartz


Thermal conductivity of mineral solids


Thermal conductivity of water


Thermal conductivity at dry conditions


Thermal conductivity at full saturation


Volumetric water content


Volumetric water content at snap-off


Cut-off water content for liquid return flow, Campbell et al. (1994)


Dry bulk soil density


Density of soil solids


Soil suction


Mean particle radius in f(R)


Standard deviation of particle radius in f(R)


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of Wisconsin-MadisonMadisonUSA

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