Correction of thermal resistance of backfill material:

When the cables or ducts are embedded in concrete, the calculation of the thermal resistance $T_{4iii}$ is first of all made assuming a uniform medium having a thermal resistivity equal to the concrete. A correction $T_{4iiidb}$ is then added algebraically to take account of the difference between the thermal resistivity of concrete and soil for that part of the thermal circuit exterior to the duct bank.

When the cables or ducts are not embedded in concrete, $T_{4iiidb}$ is zero.

Reference: M.A. El-Kady and D.J. Horrocks, Ontario Hydro, Toronto, Canada, "Extended Values for Geometric Factor of External Thermal Resistance of Cables in Duct Banks", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No. 8, August 1985.

$T_{\mathrm{4db}}$

K.m/W

$\frac{G_{\mathrm{b}} N_{\mathrm{b}}}{2 \pi} \left(\rho_{\mathrm{4}} - \rho_{\mathrm{b}}\right)$

$N_{\mathrm{b}}$

$\pi$

$\rho_{\mathrm{4}}$

Thermal resistivity of soil [K.m/W]

$\rho_{\mathrm{b}}$

Thermal resistivity backfill [K.m/W]

$T_{\mathrm{4iii}}$

$\theta_{\mathrm{hs}}$

$W_{\mathrm{hs}}$