## 3 Results
### Flow Resistance Analysis  
In the Flow Resistance (FR) analysis, FR values of different clay samples are calculated by using Equation (6). The calculated FR values are normalized to the 0-1 range and shown in Figure 4.  
Figure 3: Water content and dry unit weight relation [40].  
In light of the figures above, the time taken to reach 80% FR of the clay samples with and without nanomaterials is given in Table 3. According to the results obtained, we can see that the clay samples with nanomaterials reach the maximum FR much faster than the clay samples without additives and prevent leachate permeation much more quickly. While kaolin clay without additives can reach this value on the 139 th day, the sample with 2% Fe added can reach this value on the 74 th day, the sample with 4% Fe added on the 42 nd day, the sample with 2% Al added on the 39 th day and finally the sample with 4% Al added on the 11 th day. The faster inhibition of leachate permeation after the addition of iron and aluminum nanomaterials to kaolin can be attributed to the fact that nanomaterials fill the pores in the clay soil structure and reduce porosity [47,48].  
According to these results, we can be state that in the selection of the nanomaterial additives to be added to the clay, the Al additives are more successful than the Fe additive in the leachate permeability when compared to the pure kaolin clay sample. The smaller effective pore diameter of aluminum oxide compared to iron oxide means that aluminum oxide has a higher specific surface area. Nanomaterials with higher surface area absorb higher amounts of water and cause a greater increase in the water accumulation capacity of the soil [24,49]. The fact that the maximum FR value is reached in a shorter time in aluminum oxide added to kaolin compared to iron oxide added to kaolin, and that the permeability is lower when the aluminum oxide is added to kaolin, can be explained by the relationship between the surface area of the nanomaterial and its water accumulation capacity.  
Another point is that with the increase in the iron oxide and aluminum oxide concentration added to kaolin, the time to reach the maximum FR is shortened and permeability  
Figure 4: Normalized FR analysis for different types of kaolin clay samples.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Time (Day)** & **Permeability (cm/s)** \\ \hline Kaolin & 139 & 2.350 \(\times\) 10\({}^{-8}\) \\ Kaolin + 2\% Fe & 74 & 3.338 \(\times\) 10\({}^{-9}\) \\ Kaolin + 4\% Fe & 42 & 2.209 \(\times\) 10\({}^{-9}\) \\ Kaolin + 2\% Al & 39 & 1.503 \(\times\) 10\({}^{-9}\) \\ Kaolin + 4\% Al & 11 & 1.430 \(\times\)10\({}^{-9}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Time to reach maximum FR of clay samples with and without nanomaterial additives.  
Figure 5: Graph of actual and regression normalized FR values (kaolin).  
Figure 6: Graph of actual and regression normalized FR values (kaolin 4% Fe).  
According to the results obtained, we can see that the regression performances and similarities decrease from the sample without nanomaterial additive to the sample with 4% Al. This situation is examined with three different regression methods. In the pure kaolin sample with the highest permeability, the regression similarity performance is 0.95. However, when the regression success rate of the 4% Al added clay sample with the lowest permeability is considered, we see that the success has decreased to the range of 78-80% and the similarity value, \(R^{2}\), has decreased to 0.32, away from the safe range. We can say that this result facilitates the predictability of the FR value, as the pollutants in the leachate regularly flow from the pure clay and form a certain flow pattern.