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Soil thermal diffusivity

The soil thermal diffusivity is the ratio of the thermal conductivity to the volumetric heat capacity. It is an indicator of the rate of at which a temperature change will be transmitted through the soil by conduction. When the thermal diffusivity is high, temperature changes are transmitted rapidly through the soil. Logically, soil thermal diffusivity is influenced by all the factors which influence thermal conductivity and heat capacity. Thermal diffusivity is somewhat less sensitive to soil water content than are thermal conductivity and volumetric heat capacity. The thermal diffusivity is a particularly useful parameter to aid in understanding and modeling soil temperatures.

For calculation of cyclic rating factors it is not necessary to accurately know the value of thermal diffusivity and it is generally satisfactory to use the tabulated functions given in the standard IEC 60853 which are based on the value of 5*10-7 m$^2$/s, and correspond roughly to a soil having a thermal resistivity of 1 K.m/W, and a moisture content of around 7% of dry weight.

There are currently five options to choose from to define the thermal diffusivity:

  1. If no data are available on the soil the IEC 60853-2 recommends the value 5*10-7 m$^2$/s.
  2. If only the thermal resistivity is known the IEC 60853-2 provides values in table D1 from which we have created a best fit power function.
  3. If dry density, moisture content in % of dry weight and thermal resistivity are measured the IEC 60853-2 provides equation D-1.
  4. Difusivity is related to density, heat capacity and thermal conductivity of the material.
  5. The paper 'Estimation of soil thermal parameters from surface temperature of underground cables and prediction of cable rating' by H.J. Li, 2005 provides an empirical formula based on the publication 'The Transient Temperature Rise of Buried Cable Systems' by J.H. Neher, 1964.
  6. The value can also be entered manually. Only the positive real number of the scientific notation shall be entered and the exponent 10-7 is added automatically.

Symbol
$\delta_{soil}$
Unit
m$^2$/s
Formulae
$\frac{{10}^{-3}}{\rho_4 \zeta_{soil} \left(0.82+0.042\nu_{soil}\right)}$IEC 60853-2 eq. D-1
$4.68{\cdot}{10}^{-7} \left(\frac{1}{\rho_4}\right)^{-0.8}$Li2005 / Neher1964
$4.7717{\cdot}{10}^{-7} {\rho_4}^{-0.785}$IEC 60853-2 Table D1 optimal fit
$\frac{k_4}{\zeta_{soil} c_{p,soil}}$Related to density, heat capacity and conductivity
Related
$c_{p,soil}$
Specific volumetric heat capacity of soil material [J/(kg.K)]
$k_4$
Thermal conductivity of soil [W/(m.K)]
$\nu_{soil}$
Soil moisture content [$\%$]
$\rho_4$
Thermal resistivity of soil [K.m/W]
$\zeta_{soil}$
Density of soil material [kg/m$^3$]
Used in
$\beta_6$
Factor $|1-\beta(6)|$
$\beta_t$
Attainment factor cable surface to ambient
$D_x$
Characteristic diameter [mm]
$\Delta \theta_{e,t}$
Transient temperature rise of outer surface [K]
$\Delta \theta_{kp,t}$
Transient temperature rise of outer surface by object k [K]
$\gamma_t$
Attainment factor for groups of cables
$L_{deep}$
Equivalent depth for deep burial [m]
$q_x$
Factor for characteristic diameter
$\tau$
Transient load period [s]
Choices
Valuediffusivityresistivityconductivity
8e-078.0e-7 m²/s0.5 K.m/W2.00 W/(K.m)
7e-077.0e-7 m²/s0.6 K.m/W1.67 W/(K.m)
6.5e-076.5e-7 m²/s0.7 K.m/W1.43 W/(K.m)
6e-076.0e-7 m²/s0.8 K.m/W1.25 W/(K.m)
5.5e-075.5e-7 m²/s0.9 K.m/W1.11 W/(K.m)
5e-075.0e-7 m²/s1.0 K.m/W1.00 W/(K.m)
4.5e-074.5e-7 m²/s1.2 K.m/W0.83 W/(K.m)
4e-074.0e-7 m²/s1.5 K.m/W0.67 W/(K.m)
3e-073.0e-7 m²/s2.0 K.m/W0.50 W/(K.m)
2.5e-072.5e-7 m²/s2.5 K.m/W0.40 W/(K.m)
2e-072.0e-7 m²/s3.0 K.m/W0.33 W/(K.m)
Image
IEC standard 60853-2-1 Ed. 1.0 (1989) created from Table D1