## 3 Results and Discussion
Figures 9 and 10 show (as an example) selected temperature distributions for the analyzed calculation cases of a power cable line with a conductor cross-section equal to 120 mm\({}^{2}\). Figure 8: Ampacity (\(I_{\rm A-sb}\)) of the power cable line (240 mm\({}^{2}\)) as a function of the stabilized backfill dimension (\(z\)), its thermal parameters (\(\rho_{\rm z}\)), and native soil thermal parameters (\(\rho_{\rm g}\)). Later in the article, the authors will make an algebraic generalization of the given relationships regarding the determination of the ampacity of power cable lines depending on the thermal and geometric parameters of stabilized backfill and the cross-sectional area of the power cables. For this purpose, a correction factor for the ampacity is introduced:  
\[F_{\text{Ic}}=\frac{I_{\text{A-sb}}}{I_{\text{A}}} \tag{1}\]  
where:  
\(F_{\text{Ic}}\)--correction factor, [-];  
\(I_{\text{A-sb}}\)--ampacity with stabilized backfill, [A];  
\(I_{\text{A}}\)--ampacity without stabilized backfill, [A]. The value of ampacity \(I_{\text{A-sb}}\) for power cable lines with stabilized backfill is included in Table 3. For comparison, the value of ampacity \(I_{\text{A}}\) for power cable lines without stabilized backfill is included in Table 2.  
Figures 13-15 show graphical relationships between correction factor values and stabilized backfill dimensions. The given dependencies have been linearized to a family of straight lines intersecting on the coordinate system at point (0; 1.0)--this point physically means a calculation case for an arrangement without stabilized backfill. In a further stage, the description of the family of straight lines was generalized. Figure 16 shows the relationship between the slope coefficients of the family of lines defined in Figures 13-15 and the ratio (\(r\)) of the thermal resistivity of the ground to the thermal resistivity of stabilized backfill. As can be seen, the relationship for all three types of power cable lines considered is a second-degree polynomial (in general: \(\alpha\)x\({}^{2}\) + \(b\)x + \(c\)). Coefficient \"\(c\)\" is constant for all cases and coefficient \"\(b\)\" changes from 0.0166 to 0.0174, so the relative difference is below 5%. The changes in coefficient \"\(a\)\", for various cross-sections, are definitely more significant, so the strongest dependency is between coefficient \"\(a\)\" and the cross-sectional area. To generalize the first term of the polynomial, the function in Figure 17 has been presented. Figure 14: Value of the correction factor (\(F_{\rm{Ic}}\))as a function of the stabilized backfill dimension (\(z\)) and its thermal parameters for a power cable line with a cross-sectional area of 120 mm\({}^{2}\). Figure 13: Value of the correction factor (\(F_{\rm{Ic}}\)) as a function of the stabilized backfill dimension (\(z\)) and its thermal parameters for a power cable line with a cross-sectional area of 35 mm\({}^{2}\). Figure 15: Value of the correction factor (\(F_{\rm{Ic}}\)) as a function of the stabilized backfill dimension (\(z\)) and its thermal parameters for a power cable line with a cross-sectional area of 240 mm\({}^{2}\). It can be seen that the relationship presented in Figure 17 is approximated by a straight line, which facilitates further considerations.