## 3 Results
### Analysis of Conductivity  
Figure 11 shows the changes in the soil conductivity of pollution-free soil. The initial conductivity of the pollution-free soil is \(281\)\(\upmu\)S/cm. For the pollution-free soil, the conductivity of the middle position decreases the least, which is mainly because the anode moisture is transported to the cathode and discharged at the cathode, and after the cathode is blocked, the moisture is gathered in the middle. This is consistent with the law of moisture content, and the vacuum electro-osmosis has the most significant change of \(-103\)\(\upmu\)S/cm, with an attenuation of \(36.7\%\). For pollution-free soil, the conductivity is principally influenced by moisture content. Based on the experimentally measured soil conductivity and moisture content, Figure 12 is drawn. The vertical axis is the conductivity and the horizontal axis is the moisture content, and it can be found that the conductivity is positively correlated with the moisture content. Figure 10: Change ratio of sodium, aluminum, silicon, and calcium before and after the test. content. The relationship can be fitted using a quadratic function, and the fitted expression is as follows:  
\[\sigma_{\rm P}=-0.091\ \omega^{2}+13.9\ \omega-246.7 \tag{5}\]  
where \(\sigma_{\rm P}\) is the soil conductivity without contaminants, and the unit is \(\mu\)S/cm. \(\omega\) is the soil moisture content, and the unit is %. The initial conductivity of the contaminated soil is 1245 \(\mu\)S/cm, which is 4.4 times higher than that of the pollution-free soil, as shown in Figure 13. The presence of copper substantially improves the conductivity of the soil, and for contaminated soils, the change in the amount of soil conductivity is more uniform at the three locations. On the one hand,  
Figure 11: Conductivity difference of pollution-free sediment. Figure 12: Relationship between conductivity and moisture content. the difference in moisture content in the three locations is not significant. On the other hand, the accumulation of copper ions in the middle location also further increases the conductivity of the middle location. Thus, the conductivity of the three places tends to be even. Overall, the attenuation of the vacuum electro-osmosis method is still the largest, with a maximum attenuation of \(-601\) uS/cm, which is nearly 48.3%. It also indicates that the conductivity of the contaminated soil is more attenuated by the migration of copper ions. For the electro-osmosis method, the conductivity attenuates more at the anode and the vacuum method attenuates more at the cathode, which is consistent with the variation pattern of copper content. Consequently, for contaminated soils, the soil conductivity is influenced by both the moisture content and the concentration of copper ions in the soil. Hence, based on the relationship between conductivity and moisture content under pollution-free conditions and the experimentally measured copper concentration, the effect of copper ion concentration is considered and the relationship between conductivity and copper ion concentration is drawn in Figure 14. Obviously, the measured conductivity is approximately linear with copper concentration, and the equation is as follows:  
\[\sigma_{\mathrm{c}}-\sigma_{\mathrm{p}}=0.565\;c_{\mathrm{Cu}}+1.729 \tag{6}\]  
where \(\sigma_{\mathrm{p}}\) and \(\sigma_{\mathrm{c}}\) are the soil conductivity with and without contaminants, respectively, and the unit is uS/cm. \(\omega\) is the soil moisture content, and the unit is %. \(c_{\mathrm{Cu}}\) is the soil copper concentration, and the unit is mg/kg. The above equation establishes the relationship between copper concentration, conductivity, and moisture content. Usually, it is difficult to measure the concentration of copper contaminants inside the soil in real time in practical projects. Based on the above formula, the dynamic prediction of the concentration of contaminants can be calculated based on the changes of real-time conductivity and moisture content inside the soil.