# Thermal conductivity of soil

The soil thermal conductivity is the ratio of the magnitude of the conductive heat flux through the soil to the magnitude of the temperature gradient. It is a measure of the soil's ability to conduct heat, just as the hydraulic conductivity is a measure of the soil's ability to 'conduct' water.

Soil thermal conductivity is influenced by a wide range of soil characteristics and it has been found to be a function of dry density, saturation, moisture content, mineralogy, temperature, particle size/shape/arrangement, and the volumetric proportions of solid, liquid, and air phases. A number of empirical relationships have been developed to estimate thermal conductivity based on these parameters.

Among common soil constituents, quartz has by far the highest thermal conductivity and air has by far the lowest thermal conductivity. Often, the majority of the sand-sized fraction in soils is composed primarily of quartz, thus sandy soils have higher thermal conductivity values than other soils, all other things being equal. Since the thermal conductivity of air is so low, air-filled porosity exerts a dominant influence on soil thermal conductivity. The higher the air-filled porosity is, the lower the thermal conductivity is. Soil thermal conductivity increases as water content increases, but not in a purely linear fashion. For dry soil, relatively small increases in the water content can substantially increase the thermal contact between mineral particles because the water adheres to the particles, resulting in a relatively large increase in the thermal conductivity.

For a typical unfrozen silt-clay soil, the Kersten correlation may be used, based on the data for five soils and valid for moisture contents of ≤7 %.The two equations are taken from the paper 'Empirical and theoretical models for prediction of soil thermal conductivity: a review and critical assessment' by A. Różański, 2020.

Although the thermal conductivity of onshore soils has been extensively investigated, until recently there has been little published thermal conductivity data for deepwater soil. Many deepwater offshore sediments are formed with predominantly silt- and clay-sized particles, because sand-sized particles are rarely transported this far from shore. Hence, convective heat loss is limited in these soils, and the majority of heat transfer is due to conduction (see T.A. Newson et al., 2002). Measurements in 1999 of thermal conductivity for deepwater soils from the Gulf of Mexico by MARSCO Inc. have shown values in the range of 0.7 to 1.3 W/(m.K), which is lower than that previously published for general soils and is approaching that of still seawater, 0.65 W/(m.K). This is a reflection of the very high moisture content of many offshore soils, where liquidity indices well in excess of unity can exist and which are rarely found onshore. Although site-specific data are needed for the detailed design most deepwater clay is fairly consistent.

The table lists the thermal conductivities of typical soils surrounding pipelines as given in the Subsea Engineering Handbook by Yong Bai and Qiang Bai, 2012.

Symbol
$k_4$
Unit
W/(m.K)
Formulae
 $\frac{1}{\rho_4}$ inverse of thermal resistivity $0.1442\left(0.9\log\left(\nu_{soil}\right)-0.2\right){\cdot}{10}^{\frac{0.6243\zeta_{soil}}{1000}}$ Kersten correlation for fine-grained soils (silt, clay, etc.) $0.1442\left(0.7\log\left(\nu_{soil}\right)+0.4\right){\cdot}{10}^{\frac{0.6243\zeta_{soil}}{1000}}$ Kersten correlation for coarse-grained soils (sand)
Related
$\nu_{soil}$
$\zeta_{soil}$
Used in
$c_{p,soil}$
$D_{soil}$
$e_{limit}$
$e_{soil}$
$h_{buried}$
$h_{ground}$
$h_{soil}$
Choices
Soil typeminmeanmax
Peat (dry)0.17
Peat (wet)0.54
Peat (icy)1.89
Sand soil (dry)0.430.560.69
Sand soil (moist)0.870.9551.04
Sand soil (soaked)1.92.162.42
Clay soil (dry)0.350.4350.52
Clay soil (moist)0.690.780.87
Clay soil (wet)1.041.31.56
Clay soil (frozen)2.51
Gravel0.91.0751.25
Gravel (sandy)2.51
Limestone1.3
Sandstone1.631.8852.08