# The Effect of Cu (II) on Swelling and Shrinkage Characteristics of Sodium Bentonite in Landfills
## 3 Results
### Non-Load Suell Rate  
The bentonite liner is fabricated by compressed clay. Thus, the non-load swell rate is used to evaluate the performance of the clay structure. The non-load swelling curve of bentonite with different concentrations of CuSO4 solution was shown in Figure 4. The comparison of FSR and the final swelling rate was illustrated in Figure 4b. The overall  
Figure 3: Relation between free swelling ratio and the solution concentration(c represents the concentration of solution).  
trend between them agrees well with each other. The deflection point happened in the concentration of 2.5 g/L.  
As shown in Figure 4, the testing time of non-load swell rate experiments with different concentrations of CuSO4 were 580 h, 360 h, 440 h, and 420 h, respectively. With the increase of the concentration of Cu, less testing time is required. As mentioned in Section 3.1, Cu can reduce the FSR. Similar trends can be observed in the non-load swell ratio. It was proved that Cu (II) could significantly weaken the swelling performance of bentonite. The swelling curve of bentonite can be divided into uniform velocity stage, accelerating stage, and steady stage. The gradient of the swelling curve represented the swelling speed of the samples. The swelling speed of the four samples shows slightly different within 300 h because of the large swelling potential. However, after 300 h, the swelling rate in the low Cu (II) concentration group is getting larger. Finally, it entered the stable stage. It confirmed that the increase of concentration of salt solution could inhibit the swelling deformation of clay [33].  
The dose-response logarithmic model is adapted as shown in Equation (1), which was usually used to describe the swelling process of the clay. In this case, the model was adapted to fit the non-load swelling curve:  
\[\delta_{2}=\frac{A_{1}-A_{2}}{1+\left(t/t_{0}\right)^{p}}+A_{2} \tag{1}\]  
where, \(A_{1}\) and \(A_{2}\) were undetermined parameters, respectively; \(P\) represented the index, \(t_{0}\) corresponds to the time of \(\delta_{2}\). The coefficients in Equation (1) were derided based on Figure 4 and summarized in Table 3.  
Based on the Dose-Response model, when t is approaching infinity or zero, the corresponding \(\delta\) converges towards \(A_{2}\) or \(A_{1}\), respectively. Consequently, the curve-based model can be described as S-type (see Equation (1)). However, in reality, the profile of  
Figure 4: (**a**) The non-load swelling curve of bentonite (**b**) the comparison between free swell rate and final swell rate.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Coefficient**} & \multicolumn{4}{c}{**c(g/L)**} \\ \cline{2-5}  & **0** & **2.5** & **5** & **10** \\ \hline \(A_{1}\) & 0.955 & 0.731 & 0.034 & \(-\)0.012 \\ \(A_{2}\) & 34.410 & 70.740 & 254.133 & 11.700 \\ \(t_{0}\) & 907.511 & 3008.984 & 55,932.723 & 530.176 \\ \(P\) & 1.845 & 1.161 & 0.758 & 0.893 \\ \(R^{2}\) & 0.986 & 0.987 & 0.996 & 0.997 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The undetermined parameters and correlation coefficient.  
obtained curve is not obvious S-type because the swell process of bentonite itself is very fast. To this end, does the response logarithmic model is not applicable to characterize the swelling behavior of bentonite. However, with the increase of concentration of Cu, the swell performance has been impaired significantly. Then the S-type of the non-load swelling curve can be observed again, especially in the case of 10 g/L. Therefore, the dose-response logarithmic model was only suitable for the curve at a high concentration of Cu (II).