Geotechnical and Geological Engineering

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

Pore-Scale Model for Thermal Conductivity of Unsaturated Sand

Original paper

Abstract

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.

Keywords

Unsaturated Suction Sand Thermal conductivity Heat transfer Thermal resistivity 

Notation

Cc

Coefficient of curvature

Cu

Coefficient of uniformity

d50

Median grain size by mass

e

Void ratio

g

Campbell et al. (1994) TCDC modeling function

Gs

Specific gravity of soil solids

mc

Clay content

n

Porosity; mixing model exponent

qt

Heat flux

r1

Radius in toroidal approximation for liquid bridge

r2

Radius in toroidal approximation for liquid bridge

R

Spherical particle radius

Rmin

Minimum particle radius in f(R)

Rmax

Maximum particle radius in f(R)

Rfill

Particle radius in f(R) corresponding to snap off

R2

Coefficient of determination

S

Degree of saturation

Ts

Air-water interfacial tension

Va

Volume of air

Vs

Volume of soil solids

Vt

Volume total

Vw

Volume of water

w

Gravimetric water content

xf

Fractional area of liquid bridge

α

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

κ

Kersten number

λ

Thermal conductivity

λa

Thermal conductivity of air

λp

Pore-scale thermal conductivity

λq

Thermal conductivity of quartz

λs

Thermal conductivity of mineral solids

λw

Thermal conductivity of water

λdry

Thermal conductivity at dry conditions

λsat

Thermal conductivity at full saturation

θ

Volumetric water content

θcrit

Volumetric water content at snap-off

θo

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

ρb

Dry bulk soil density

ρs

Density of soil solids

ψ

Soil suction

μ

Mean particle radius in f(R)

σ

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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