# Effect of Non-Homogeneous Soil Characteristics on Substation Grounding-Grid Performances: A Review
## 2 Effect of Horizontal Two-Layer Soil Characteristics on Grounding System Performances
### The Resistivity and Depth of Top Layer Soil  
A grounding system for a substation in a two-layer soil structure must be carefully designed for safety purposes. The IEEE 81-2012 standard [43] explains how a grid buried in a non-homogeneous soil layer with a different soil resistivity affects its performance. The soil resistivity in each layer, as well as the height of the soil's top layer, influence the grid's behavior. This study is crucial because it allows the designer to anticipate the grid impedance pattern and determine the length of additional vertical rods if needed to enhance the grounding safety, depending on the top soil layer height. A sudden transformation in resistivity that occurs at the borders of the soil layer is denoted in Equation (2) as a reflection coefficient (K). Equations (1) and (2) [18] are used to calculate the two-layer soil's parameters where K signifies the reflection coefficient, \(\rho_{\mathbf{a}}\) is the soil's apparent resistivity, h shows the finite height of soil top layer, n, represents the total sum of measurements and a, is the distance of the probe in [PERSON]'s test [26; 38; 44; 45; 46; 47]. The effect of the reflection factor (K) on current dispersal into the soil layer has been addressed in [48; 49; 50; 24; 40]. \[\rho_{\mathbf{a}}=\rho_{1}\cdot\left\{1+4\sum_{n=1}^{\infty}\mathrm{K}^{n} \left[\frac{1}{\sqrt{1+\left(\frac{2.n\,\mathrm{h}}{\mathrm{a}}\right)^{2}}}- \frac{1}{\sqrt{4+\left(\frac{2.n\,\mathrm{h}}{\mathrm{a}}\right)^{2}}}\right] \right\} \tag{1}\]  
\[\mathrm{K}=\frac{\rho_{2}-\ \rho_{1}}{\rho_{2}+\ \rho_{1}} \tag{2}\]  
The effect of the upper layer's soil resistivity of a two-layer soil in terms of GPR is explained in [40]. Based on the results presented in [40], K \(<\) 0 is denoting that the top layer's soil resistivity is greater than the bottom layer, where the GPR of the grounding grid reduces significantly. That is because the current density is high at the center, and the conductor ends. The fault current discharges directly into the lower resistivity bottom layer. In contrast, there will be a slight reduction in GPR value for K \(>\) 0, in which the top layer's soil resistivity is lower than the bottom layer's resistivity. Since the fault current stays inside the top layer and expands as it disperses into the soil, the density of the current is higher only at the conductor's ends. Apart from the top soil layer's soil resistivity, the top soil layer's height also affects the grounding performance. Figure 2 displays the grid resistance for 30 m \(\times\) 30 m with four meshes placed 0.5 m within the soil. The bottom layer resistivity differs to obtain different reflection factors (K), while the top layer's soil resistivity is kept constant. From Figure 2, it can be seen that a homogeneous soil structure exerts no response from the on-grid resistance (K = 0). Increasing the depth of the top soil layer for K > 0, the grid resistance reduces as the top layer's soil depth increases. On the other hand, the grid \begin{table}
\begin{tabular}{c c} \hline \hline
**Case** & **GPR** \\ \hline
**A** & Reduces until it reaches the border of the top layer and increases after the grid enters the bottom layer with high resistivity. \\ \hline
**B** & The same trend as case A, but the GPR values are higher than case A. \\ \hline
**C** & Reduces significantly as the depth of the grid buried rises, particularly after the border of the top layer. \\ \hline
**D** & The same pattern as in case C but higher GPR values than case C. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: GPR performances for each case. resistance increases as the top layer's soil depth increase when K < 0. The grid resistance values converge with a homogeneous soil structure as the top layer's soil depth approaches infinity [19; 50]. When the top layer's soil depth is 0.5 m, which is equivalent to the grid burial depth, a substantial change in grid resistance can be seen. The grounding resistance value is impacted by the bottom layer's soil resistivity when the top layer's is small in height.