Thermal Properties of Soils: Thermal Conductivity
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clay. The range for q is roughly 2 to 6 with coarser materials generally
having lower values, but the pattern is not as clear as for the cutoff water
content.
The complete expression for vapor phase apparent conductivity is
where k, is the thermal conductivity of air.The weighting factors are determined by the shapes, conductivities, and volume fractions of the soil constituents. Campbell et al. (1994) defined a fluid conductivity for the soil as
In dry soil the fluid conductivity is the value for dry air and in saturated
soil it is the value for water. The same f, function used for the liquid
return flow is used in Eq. (8.19). Using Eq. (8.19) the weighting functions
can now be computed:
1
In these equations, kg is from Eq. (8.18), while k, and k, are from Table
8.2. The shape factors, ga and g,, depend on the shape of the soil particles.
One can compute g, from g, = 1 - 2ga. For mineral soils ga has a value
around 0.1. For organic soils it is 0.33.
These equations are most useful as part of a computer program as
they are quite long for hand calculations. They do, however, include all
of the effects of temperature, moisture, density, and soil composition.
The interaction among these factors is complex and sigmficant, and, at
present, no simpler approach is apparent. Figure 8.3 shows thermal conductivity computed using Eq. (8.13) for the soils in Fig. 8.2. The mineral
conductivities of the clay and loam samples are 2.3 and 2 W m-' C-' .
The organic k,,, is 0.3 and the sand k, is 5 W m-I C-' . The sand curve is
meant to represent a sample with high quartz content.
Example 8.2. For the soil in Example 8.1, find the thermal conductivity.
Assume T = 20" C, pa = 101 kPa, k, = 2.5 W m-I C-' , q = 4, and
6 , = 0.15.
Solution. To do the calculation, values are needed for A, A, h,, D,, and
e. From Table A.2, h = 44100 J/mol. From Table A.3, A = 145 PaIC
and e = 2340 Pa. From Table A. 1, D, = 2.42 x
m 2 /s. From Table
8.2, ka = 0.025 W m-I C-I and k, = 0.60 w m-' C-' . There is no easy
way of calculating h,, but a loam soil at 0.2 water content is well above
121
clay. The range for q is roughly 2 to 6 with coarser materials generally
having lower values, but the pattern is not as clear as for the cutoff water
content.
The complete expression for vapor phase apparent conductivity is
where k, is the thermal conductivity of air.The weighting factors are determined by the shapes, conductivities, and volume fractions of the soil constituents. Campbell et al. (1994) defined a fluid conductivity for the soil as
In dry soil the fluid conductivity is the value for dry air and in saturated
soil it is the value for water. The same f, function used for the liquid
return flow is used in Eq. (8.19). Using Eq. (8.19) the weighting functions
can now be computed:
1
In these equations, kg is from Eq. (8.18), while k, and k, are from Table
8.2. The shape factors, ga and g,, depend on the shape of the soil particles.
One can compute g, from g, = 1 - 2ga. For mineral soils ga has a value
around 0.1. For organic soils it is 0.33.
These equations are most useful as part of a computer program as
they are quite long for hand calculations. They do, however, include all
of the effects of temperature, moisture, density, and soil composition.
The interaction among these factors is complex and sigmficant, and, at
present, no simpler approach is apparent. Figure 8.3 shows thermal conductivity computed using Eq. (8.13) for the soils in Fig. 8.2. The mineral
conductivities of the clay and loam samples are 2.3 and 2 W m-' C-' .
The organic k,,, is 0.3 and the sand k, is 5 W m-I C-' . The sand curve is
meant to represent a sample with high quartz content.
Example 8.2. For the soil in Example 8.1, find the thermal conductivity.
Assume T = 20" C, pa = 101 kPa, k, = 2.5 W m-I C-' , q = 4, and
6 , = 0.15.
Solution. To do the calculation, values are needed for A, A, h,, D,, and
e. From Table A.2, h = 44100 J/mol. From Table A.3, A = 145 PaIC
and e = 2340 Pa. From Table A. 1, D, = 2.42 x
m 2 /s. From Table
8.2, ka = 0.025 W m-I C-I and k, = 0.60 w m-' C-' . There is no easy
way of calculating h,, but a loam soil at 0.2 water content is well above