## 3 Results and Discussion  
A computational model was developed to determine the ampacity of power cable lines using stabilized backfill, according to Figure 5.  
The model presented in Figure 5 assumes, similarly to the verification of the previous model in Figure 2, a flat formation of the power cable line with a cross-sectional area of 35 mm\({}^{2}\), 120 mm\({}^{2}\) and 240 mm\({}^{2}\). Unlike the original model (see Figure 2), a stabilized backfill was used. Stabilized backfill is contained in the area limited by dimension \"\(\mathrm{\SIUnitSymbolDegree}\)\". The value of this parameter varied accordingly: \(z=10\) cm, 20 cm, and 30 cm. The thermal resistivity of stabilized backfill \(\rho_{\mathrm{z}}\) varied (two values): 0.75 and 1.0 (K\(\cdot\)m)/W. The stabilized backfill parameters presented above are often used in practice. Table 3 contains the results of calculations of the ampacity for the analyzed power cable lines and the parameters of stabilized backfill. Graphical interpretations of the results obtained in Table 3 are presented in Figures 6-8. In order to better present the obtained results, further considerations cover calculation cases for which the thermal resistivity of the ground (native soil) is equal to \(\rho_{\mathrm{g}}=1.0\) and 2.0 (K\(\cdot\)m)/W. For practical reasons, further analyses do not present results for native soil resistivity \(\rho_{\mathrm{g}}=0.5\) (K\(\cdot\)m)/W (soil would be better than stabilized backfill). Figure 5: A simplified graphical model presenting the method of the ampacity testing using stabilized backfill. Figure 6: Ampacity (\(I_{\rm A-sb}\)) of the power cable line (35 mm\({}^{2}\)) as a function of the stabilized backfill dimension (\(z\)), its thermal parameters (\(\rho_{\rm z}\)), and native soil thermal parameters (\(\rho_{\rm g}\)). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(z_{\rm s}\) & \(\rho_{\rm g^{\prime}}\) & \(\rho_{\rm zv}\) & \(I_{\rm A-sb}\)**A** & \(I_{\rm A-sb}\)**A** & \(I_{\rm A-sb^{\prime}}\)**A** \\
**cm** & **(K-m)/W** & **(K-m)/W** & **(for 35 mm\({}^{2}\)** & **(for 120 mm\({}^{2}\))** & **(for 240 mm\({}^{2}\))** \\ \hline
10 & 0.5 & 0.75 & 200.3 & 395.6 & 575.3 \\
10 & 1.0 & 0.75 & 179.7 & 351.6 & 508.8 \\
10 & 2.0 & 0.75 & 152.8 & 293.6 & 428.4 \\
10 & 0.5 & 1.0 & 187.6 & 365.8 & 537.0 \\
10 & 2.0 & 1.0 & 146.7 & 281.8 & 410.4 \\
20 & 0.5 & 0.75 & 197.6 & 386.9 & 566.7 \\
20 & 1.0 & 0.75 & 183.2 & 356.4 & 515.2 \\
20 & 2.0 & 0.75 & 161.5 & 312.3 & 450.8 \\
20 & 0.5 & 1.0 & 181.2 & 354.8 & 518.4 \\
20 & 2.0 & 1.0 & 152.8 & 293.6 & 424.6 \\
30 & 0.5 & 0.75 & 195.7 & 384.0 & 560.9 \\
30 & 1.0 & 0.75 & 184.7 & 359.6 & 521.6 \\
30 & 2.0 & 0.75 & 166.5 & 323.0 & 468.6 \\
30 & 0.5 & 1.0 & 178.2 & 348.3 & 508.8 \\
30 & 2.0 & 1.0 & 156.3 & 301.2 & 436.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Ampacity (\(I_{\rm A-sb}\)) for the cable system with stabilized backfill (\(z\) = 10 cm, 20 cm, 30 cm)—summary of the results of numerical calculation. Figure 7: Ampacity (\(I_{\rm A-sb}\)) of the power cable line (120 mm\({}^{2}\)) as a function of the stabilized backfill dimension (\(z\)), its thermal parameters (\(\rho_{\rm z}\)), and native soil thermal parameters (\(\rho_{\rm g}\)). The contents of Figures 6-8 present approximate characteristics of the variability ampacity depending on the characteristic dimension (\(z\)) of stabilized backfill and the thermal resistivity parameters of the ground and stabilized backfill, respectively, for cable lines of 35 mm\({}^{2}\) (see Figure 6), 120 mm\({}^{2}\) (see Figure 7), 240 mm\({}^{2}\) (see Figure 8). According to the presented relationships, which show the same trends for each of the three lines laid in the ground (native soil) with the following thermal resistivities: \(\rho_{\rm g}\) = 1.0 and 2.0 (K\(\cdot\)m)/W, the use of stabilized backfill is justified--as the stabilized backfill volume increases, the permissible load/ampacity of the line increases.