# Effect of Non-Homogeneous Soil Characteristics on Substation Grounding-Grid Performances: A Review
## 3 Effect of Horizontal Three-Layer Soil Characteristics on Grounding System Performances  
### Apparent Soil Resistivity and Reflection Factor (K)  
Grounding performance analysis in horizontal three-layer soil structure is not as common as horizontal two-layer soil structure due to its complexity in computation. Since the computations and analysis of grounding systems which deal with the multilayer, soil structure are usually complex; the equations and the derivations of three-layered soils' apparent soil resistivity were explained in [49; 58; 59], and are discussed in this section. Figure 7a,b below represent the three-layer soil structure. According to IEEE 80 [42], the initial apparent soil resistivity between the first and second layers is calculated using Equations (5) and (6) and is represented by \(\rho_{12}\) where \(\rho_{1}\) and \(\rho_{2}\) are the resistivities of the first and second layers, respectively, and \(H^{\prime}\) is the thickness of the first layer, as shown in Figure 7a. The apparent soil resistivity of the three layers is then calculated using the following IEEE 80 equation, with the first- and second layers having soil resistivity of \(\rho_{12}\) as one layer and the third layer resistivities having a resistivity of \(\rho_{3}\) as another layer. In this example, \(K^{\prime}\) is the reflection factor defined in Equation (7). \[\rho_{12}=\frac{\text{l}_{2}(\rho_{1}\rho_{2})}{(\rho_{2}(H^{\prime}-\text{h} )+\text{ }\rho_{1}(\text{l}_{2}+\text{h}-H^{\prime}))} \tag{5}\]  
\[\rho_{\text{a}}=\frac{\text{l}_{2}(\rho_{12}\rho_{3})}{(\rho_{3}(H^{\prime}- \text{h})+\rho_{12}(\text{l}_{2}+\text{h}-H^{\prime}))} \tag{6}\]  
\[K^{\prime}=\frac{\rho_{3}-\text{ }\rho_{12}}{\rho_{3}+\text{ }\rho_{12}} \tag{7}\]  
Figure 7b depicts the calculations in Equations (8)-(10) and is presented according to IEEE 80 [42]. The apparent soil resistivity of the second and third layers is \(\rho_{23}\); the resistivity values of the second and third soil layers are \(\rho_{2}\) and \(\rho_{3}\), respectively. As illustrated in Figure 7b, H stands for the height of first layer soil, H\({}_{1}\) for the second layer's height, l\({}_{2}\) for the length of grounding rods, and h for the grounding laying depth. The reflection factor, \(K^{\prime\prime}\) is defined in Equation (10). \[\rho_{23}=\frac{\text{l}_{2}(\rho_{2}\rho_{3})}{(\rho_{3}(\text{H}_{1}-\text{ h})+\text{ }\rho_{2}(\text{l}_{2}+\text{h}-\text{H}_{1}))} \tag{8}\]  
\[\rho_{\text{a}}=\frac{\text{l}_{2}(\rho_{1}\rho_{23})}{(\rho_{23}(\text{H}- \text{h})+\rho_{1}(\text{l}_{2}+\text{h}-\text{H}))} \tag{9}\]  
Figure 7: Horizontal three-layer soil structure (**a**) The first and second layers are represented as \(\rho_{\text{a}0}\), (**b**) The second and third layers are represented as \(\rho_{\text{a}0}\)[50]. \[K^{\prime\prime}=\frac{\rho_{23}-\ \rho_{1}}{\rho_{23}+\ \rho_{1}} \tag{10}\]  
The performance of the grounding grid is investigated using two three-layered soil structures with different soil resistivities and reflection factors, as shown in Table 6. The apparent resistivity of the soil is calculated using Equations (5)-(10). Figure 8a indicates that a rise in the positive reflection factors (+K) reduces the apparent soil resistivity when \(\rho_{12}>\rho_{3}\) and increases the apparent soil resistivity when \(\rho_{3}>\rho_{12}\) for negative reflection factors (\(-\)K) in structure A. The same Figure 8a also indicates that a vice versa trend of the apparent soil resistivity in case of \(\rho_{1}>\rho_{23}\) or \(\rho_{3}>\rho_{12}\). Similar measurements are conducted using structure (B), where the apparent soil resistivity increases with positive reflection factor in both cases of (\(\rho_{23}>\rho_{1}\)) and (\(\rho_{3}>\rho_{12}\)) and reduces for negative reflection factors when (\(\rho_{12}>\rho_{3}\) or when \(\rho_{1}>\rho_{23}\)) given in Figure 8b [49]. A similar pattern on apparent resistivity behavior can also be seen in [58].