## 3 Results and Discussion
### Hydraulic Conductivity of Soil--Semi-Technical Scale Test
Figure 12: Difference in height between the initial water level and the level after 60 min (\(\Delta\)H), for: (**a**) column group 1a, b, c supplied with treated wastewater, (**b**) column group 2a, b, c supplied with treated wastewater and brine solution periodically and (**c**) column group 3a, b, c supplied with tap water; terms from 1–8 represent the measurement periods after 1–8 regenerations. of 0.787 \(>\)\(\alpha\) = 0.05 means that, at a significance level of 0.05, there are no grounds to reject the null hypothesis of homogeneity of variance. In order to indicate the significance of differences between the measurement after 1 regeneration and the measurement after 8 regenerations in pairs, [PERSON]'s test was performed. Table 2 presents the differences between the measurement of the change in the height of the liquid in the column at 60 min after 1 regeneration and the same measurement after 8 regenerations, obtained using the [PERSON] test carried out in Statistica 13.3 software (StatSoft Inc., 2013, Tulsa, OK, USA). Based on the results presented in Table 2 at the significance level of \(\alpha\) = 0.01, using [PERSON]'s test, the specific hypotheses were rejected for column pair 1-2 (because \(p\) = 0.009 \(<\)\(\alpha\) = 0.01). At a significance level of 0.01, we found that the true differences between the measurement after one regeneration and the measurement after eight regenerations of the column pairs listed above (treated wastewater dosing option and treated wastewater dosing with brine) were significantly different. In contrast, the differences between the measurement results for column pairs 1-3 and 2-3 (i.e., comparison of the options for water supply alone and the other options) are not significantly different. Figure 14a-c presents the estimated hydraulic conductivity (\(K\)s) according to the Van Hoorn Formula (1) for the individual filter columns. When analysing the effect of the grey water discharged from the water softener into the DWTPs, with reference to the results in Figure 14a-c, no significant effect was found on the deterioration of the hydraulic conductivity of the investigated soil. However, returning to Figure 12b, which shows the height difference between the initial water level and the level after 60 min for column group 2, supplied with treated wastewater and brine, it is important to recall the leading linear trends. This course of the graph, as previously mentioned, is most likely the result of increased salt content in the soil. It cannot, therefore, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Option** & **1** & **2** & **3** \\ \hline
1 & - & 0.008653 & 0.030791 \\ \hline
2 & 0.008653 & - & 0.346422 \\ \hline
3 & 0.030791 & 0.346422 & - \\ \hline \hline \end{tabular} Explanation: Option numbers refer to column groups 1-3.  
\end{table} 
Table 2: Comparison of the difference between the measurement after 1 regeneration and the measurement after 8 regenerations—Fisher’s test. Figure 13: Shapiro–Wilk test for the difference between the measurement after 1 regeneration and the measurement after 8 regenerations (W(\(\alpha\),n)—critical value for fixed \(\alpha\), read from the quantile tables for the Shapiro–Wilk test). be excluded that, recorded at a semi-technical scale, the lack of a significant effect of grey water on changes in the hydraulic conductivity of the soil under investigation was unambiguous with the actual state. In this respect, there is a need to continue research with other parameters, including microbiological and physicochemical research. The brine used in the regeneration process must be disposed of in a proper manner. Conventionally, it is directed to a cesspool, discharged underground into a dry well or routed through building pipes to grade level. Regardless of where it flows, brine has the potential to affect groundwater or surface water. The brine for flushing contains excess chloride, sodium, and potassium ions from regeneration salts and naturally occurring ions removed from tap water that may have been concentrated by the water softener.