## 3 Application to Resistive Driven-Rod Method: Testing with Some Examples
### Synthetic Examples with Internal Resistance  
To finish the study of synthetic soils, a rod again 9 mm radius with non-zero internal resistance driven into the soil will be considered. Let us consider the synthetic soil \(\rho_{1}\) = 100 \(\Omega\)m, \(\rho_{2}\) = 200 \(\Omega\)m, \(\rho_{3}\) = 40 \(\Omega\)m, h\({}_{1}\) = 3 m, and h\({}_{2}\) = 1 m. In order to get closer to the real data that will be used as a test of the RDR method, suppose that sections 1.5 m long of galvanized-steel low-resistive rod \(\rho\) = 13.8 \(\times\) 10\({}^{-8}\)\(\Omega\)m are assembled as shown in Figure 6. Let also suppose that the imperfect contact between the pieces along the junction, which is 2 cm long, is equivalent to a small branch with an internal resistivity of 1.27 \(\times\) 10\({}^{-6}\)\(\Omega\)m. This value has been estimated after measuring the resistance of a section of 1.5 m rod, 1.02 m\(\Omega\), and of two joined sections, 2.14 m\(\Omega\), which results in a contact resistance of 0.1 m\(\Omega\). This resistance along a 2 cm length with a radius of 0.009 mm is achieved with the assigned junction resistivity. The grounding resistance of a rod composed by N low-resistive rod sections plus N joining sections is measured when N ranges from 1 to 6. Simulated measurements are shown in Table 4.  
The minimization procedure (17) is somewhat more complicated since the calculated resistance profile \(R_{calc}(L_{j};\{\rho_{1},\rho_{2}\ldots,h_{1},h_{2}\ldots\})\) for a given set of soil parameters and for the different rod lengths \(L_{j}\) must be evaluated taking into account the internal resistivity of the different pieces. The minimization procedure applied on data of Table 4 give rise to the best set of estimated soil parameters \(\rho_{1}\) = 99.72 \(\Omega\)m, \(\rho_{2}\) = 159.50 \(\Omega\)m, \(\rho_{3}\) = 37.71 \(\Omega\)m, h\({}_{1}\) = 2.77 m, h\({}_{2}\) = 1.33 m. As in the previous examples, values significantly different from the true ones are estimated for the intermediate layer. As mentioned before, this fact is related to the size of the rods, which results in a coarse sampling of the grounding resistance. Refining the sampling by using low-resistive rods 0.5 m length together with the junction segments, the simulated grounding resistance is shown in Table 5. The estimated soil parameters are \(\rho_{1}\) = 99.99 \(\Omega\)m, \(\rho_{2}\) = 201.32 \(\Omega\)m, \(\rho_{3}\) = 40.01 \(\Omega\)m, h\({}_{1}\) = 2.99 m, and h\({}_{2}\) = 1.02 m which are very close to the real values taken as starting point. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**L (m)** & 1.5 & 3.0 & 4.5 & 6.0 & 7.5 & 9.0 \\ \hline
**R (\(\Omega\))** & 56.85 & 32.17 & 19.65 & 11.81 & 8.65 & 6.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Buried rod length L (m) and the corresponding simulated grounding resistance R (\(\Omega\)) for the considered synthetic soil when a non-zero internal resistance rod is driven into the soil. Figure 6: Detail on the rod sections junction. Figure 7 shows the grounding resistance of the rod as a function of the buried length for data of Table 4 (left panel) and for data of Table 5 (right panel). As it was pointed out in previous Figures, green diamonds correspond to simulated grounding resistance data from the true resistivity profile, whereas the continuous line stands for the calculated grounding resistance profile from the estimated soil parameters obtained from the minimization procedure. Although it is the same synthetic soil, the grounding resistance profile exhibits some different features depending on the performed type of soil sampling. Coarse sampling, such as that shown in Table 4, could hide some of the complexity in the grounding resistance profile. Indeed, this happens between the values 3 m and 4.5 m of depth. A fine sampling as shown in Table 5 reveals a structure that is smoothed in the coarse sampling, which leads to a poor estimate of the soil resistivity profile.