# Correction of thermal resistance for backfill

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 $\rho_b$. A correction $T_{4db}$ 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 backfill. The backfill is transformed into an equivalent circle with the help of the geometric factor $G_b$.

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

Reference: IEC 60287-2-1 Ed.2.0

Symbol
$T_{4db}$
Unit
K.m/W
Formulae
 $\frac{N_b \left(\rho_4-\rho_b\right)}{2\pi} G_b$ backfill $T_{4pi}+T_{4pii}+T_{4piii}-T_{4iii}$ air-filled pipe with objects
Related
$T_{4iii}$
$T_{4pi}$
$T_{4pii}$
$T_{4piii}$
Used in
$T_{4ss}$
$\theta_{hs}$
$W_{hs}$
Choices
IdMethodInfo
0IEC 60287-2-1When the cables or ducts are embedded in backfill material such as concrete, the calculation of the thermal resistance outside the objects is first of all made assuming a uniform medium outside the ducts having a thermal resistivity equal to the backfill. A correction is then added algebraically to take account of the difference, if any, between the thermal resistivities of backfill and soil for that part of the thermal circuit exterior to the backfill or duct bank. This method is only valid for ratios of width and height ranging from 1/3 to 3 without distinction of the backfills orientation.
1El-Kady/Horrocks (1985)A paper by El-Kady and Horrocks describes an efficient finite-element-based technique for calculating geometric factors for extended ranges of the height/width ratio and presents results for a wide range of values in a direct tabular and graphical format suitable for conventional IEC calculations.This method is valid for ratios of height/width ranging from 0.05 to 5.0 and ratios of depth/height ranging from 0.6 to 20.0 and it differenciates between cases where height > width and cases where height < width.
2Multilayer backfill trenchWith the multi-layer backfill method, it is possible to simulate the filling of a rectangular trench where the cables are buried with one or two superimposed horizontal layers of different materials, stacked above the cable bedding, respectively duct bank. This method is based on fitting the thermal resistances to numerical data from finite element simulations. In two papers by De Lieto Vollaro et.al equations for thermal resistances of different elements in the heat paths were defined with a range of application for the relevant parameters.
3air-filled pipe with objectsThis method allows for calculation of an air-filled pipe with one or many air-filled ducts inside. The thermal resistance of the air inside the pipe is calculated using the same method as for cables in ducts.