# Characterization of Soil Enhancement Mixtures at Low-Magnitude Currents
## 3 Results
### Characterization of Dry Mixtures Under AC  
These EMs have been recommended for use with water content to provide good conduction to ground electrodes. In this work, the effect of dry low-resistivity mixtures, which may be used in real installation processes, was also considered. This also provides information on the effect of water content when it is added later, as discussed in Section 3.2. The frequency was varied from 50 Hz to 20 kHz at a specific maximum voltage of 10 V. It can be seen that in all the dry mixtures (dry sand, sand + 5%EM1, sand + 5%EM2 and sand + EM3), at low frequencies (below 100 Hz), there was a small phase angle difference between the voltage and the current, while at higher frequencies (above 100 Hz), the current waveforms were seen to be more significantly ahead of the voltage waveforms, as shown in Figures 5 and 6, respectively, at 100 Hz and 10 kHz for sand + 5%EM1. From these observations, the equivalent circuit for dry mixtures can be represented as a non-linear resistive component connected in parallel to a non-linear capacitive component, where at low frequencies, \(R\) becomes dominant, while at high frequencies, \(C\) becomes dominant. Both the \(R\) and \(C\) components can be calculated using (2) and (3), respectively. From the measured resistance and capacitance values, the resistive and relative permittivity values were calculated, respectively, from (4) and (1). Figures 7 and 8 show, respectively, the resistivity and relative permittivity of all the dry mixtures. As can be seen in both figures, both the resistivity and relative permittivity of all the mixtures decrease with increasing frequencies, with the same degree of reduction for all dry test media, indicating that when  
Figure 4: (**a**) Example of sand mixed with 5%WC and 5%EM1: inside view within the parallel plate setup. (**b**) Example of sand mixed with dry 5%EM1 within the parallel plate setup.  
subjected to a high-frequency impulse current, the rate of reduction in impulse impedance and the ground potential rise may be similar. The highest resistivity was found in sand with 5%EM1 and the lowest was observed in sand with 5%EM2 for frequencies below 1 kHz, while the resistivity values were similar for all dry test media at higher frequencies. This could be due to several factors, such as the production of space charges, dipoles and ions at various frequencies when the materials are mixed, as discussed in [6]. This shows that the addition of some EMs may cause more adverse effects when the soil mixture is dry, in which case the resistivity value might be higher than that of the original soil, which was dry sand in this study. This shows that an extra precaution must be considered when using EM1, particularly in dry soil and in hot weather, as the resistivity becomes higher than the resistivity of the original soil.  
On the other hand, the soil permittivity was found to be highest in dry sand and lowest in sand with 5%EM2 for frequencies below 5 kHz. This is in agreement with several other studies [4; 10; 11], where, generally, an inverse proportional relationship between the resistivity and permittivity parameters of soil is observed such that when the resistivity of the test medium is higher than that of the other material, the permittivity of the test medium becomes lower than that of the other material, and vice versa. At higher frequencies, the permittivity values for all the test media were found to be similar and independent of frequency, indicating that the test media have similar dielectric strengths.  
The results show that it is important to consider soil parameters at different frequencies, as this provides accurate information when grounding systems are subjected to an impulse current.  
\[\frac{1}{R}=\left|\frac{1}{Z}\right|\cos\theta \tag{2}\]  
\[C\omega=\left|\frac{1}{Z}\right|\sin\theta \tag{3}\]  
\[R=\left(\frac{\rho}{S}\right)d \tag{4}\]  
Figure 5: Voltage and current traces of dry sand mixed with 5%EM1 at 100 Hz.