###### Abstract  
The maximum permissible load of underground power cables (known in U.S. engineering as \"ampacity\") is a function of many parameters, in particular, the thermal resistivity of the native soil. If this resistivity is relatively high, thermal/stabilized backfill is applied, i.e., another material is placed around the cables, providing favourable conditions for heat transfer to the environment. It has a positive impact on the reliability of the power supply and favours the operational durability of the cables. In design practice, however, there is a difficult task--correct determination of the ampacity of the cable line depending on the thermal parameters and the geometry of the backfill. Therefore, this article presents the results of a numerical analysis to determine the ampacity of cable lines in which stabilized backfill is used. A new mathematical relationship is proposed that allows the correction of the ampacity of cable lines depending on their cross-section as well as the thermal and geometric parameters of the cable surroundings.  
ampacity; numerical modelling; power cables; reliability; thermal analysis +
Footnote †: journal: Applied sciences  
0000-0002-4000-0000-0000-0000-0000-0000-0000-0000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-000000-000000-00000-  
lines laid in the ground. In order to improve the conditions of heat exchange between the cable and the ground (increasing the ampacity), the surrounding soil is most often replaced by stabilized backfill with a lower thermal resistivity. Because the resistivity of the native soil depends on several factors, including grain composition, grain size and moisture content [10,11], the use of stabilized backfill allows for uniform heat exchange conditions between the power cables and the surroundings. Uniform and good heat exchange conditions help to avoid local thermal exposure of cables in places where the thermal resistivity of the native soil is high [3,12]. Local overheating of cables leads to the rapid aging of their insulation, and it reduces the operational durability of cables [12, 13, 14]. Stabilized backfill is also beneficial to avoid mechanical stress on the cables. The native soil may contain stones and other sharp elements, whereas the backfill is homogeneous and free from damaging fractions [10]. The use of stabilized backfill also makes it possible to avoid the occurrence of so-called dry zones in underground installations. Dry zones occur as a result of local moisture migration due to the heating of power cables' surroundings by Joule heat. As a consequence, the thermal resistance of the surrounding soil increases and the long-term permissible temperature for a power cable's insulation may be exceeded [15]. Therefore, both designers and power system operators are concerned about maintaining stable and optimal thermal conditions around the installed power cable lines [11,16,17]. In addition to the technical arguments indicated, economic issues are also important for the use of stabilized backfill [8,18]. Taking into account the above information, the main issue when designing a cable line is determining its long-term ampacity correctly in order to avoid thermal damage to the cables. If no stabilized backfill is used, this is not a major problem. In this respect, the use of common standards [19, 20, 21, 22] is sufficient, and their provisions can be used to verify numerical calculations [3,23,24,25,26]. As noted by the authors of article [26], the ampacity determined based on standards [20, 21, 22] is overestimated when compared to numerical models.