## 4 Results and Discussion
### Unloaded Swelling Deformation
#### 4.1.2 Unloaded Swelling Deformation of MB  
The unloaded swelling strain is an important indicator of the waterproofing performance of bentonite, which can reflect the capacity of it to fill cracks. The unloading swelling deformation tests on MB specimens with five different initial dry densities and the same initial moisture content were conducted under saline water conditions. The relationships between the unloaded swelling strains of MB specimens and swelling times were obtained (Figure 6). The swelling strain of different MB specimens exhibited similar changes with increasing swelling time. At the beginning of the test, the swelling strain in the MB specimen increased rapidly over time. After that, the swelling strain increased slowly and reached a stable final value, which indicated that the swelling deformation was complete. This occurred because montmorillonite is the main component of bentonite: in the initial stage of the swelling process, due to the small thickness of water film around the montmorillonite, a large amount of space was available for swollen minerals to adsorb water and swell [40]. With increasing water absorption, the arrangement of montmorillonite wafers gradually developed from the initial anisotropic arrangement into an aligned arrangement. The thickness of the water film between the montmorillonite wafers increased stepwise, thus the speed of the water absorption process decreased and the rate of change in the swelling strain decreased. The thickness of the water film finally reached its maximum value, and swelling strain remained unchanged thereafter. Furthermore, curves of swelling strain to swelling time always follow a rectangular hyperbolic relationship [41]. Linear relationships between the ratio of time to swelling strain and swelling time for the MB specimens under five different dry densities (Figure 7) can be fitted by Equation (3):  
\[\frac{t}{\epsilon}=a+bt \tag{3}\]  
where \(\epsilon\) is the unloading swelling strain of an MB specimen; \(t\) represents the swelling time (h); and \(a\) and \(b\) are fitting parameters. Figure 5: Relationships between the unloading swelling strain and swelling time for NB (Natural sodium bentonite) and MB (Modified bentonite). Since \(a\) and \(b\) are related to the initial dry density, their values under each corresponding initial dry density of MB specimen were discussed and fitting equations for the linear relationships between \(a\) and \(b\), and dry density were obtained (Equations (4) and (5)). The correlation coefficient values (R\({}^{2}\)) are 0.97 for \(a\) and 0.95 for \(b\). \[a=0.016\rho_{d}-0.015 \tag{4}\]  
\[b=-0.014\rho_{d}+0.03 \tag{5}\]  
where \(a\) and \(b\) refer to fitting parameters; and \(\rho_{d}\) is the initial dry density of the MB specimen (g/cm\({}^{3}\)). Figure 6: Relationships between unloaded swelling strain and swelling time for MB specimens with different initial dry densities under saline water conditions. Figure 7: Fitting relationships between ratio of time to swelling strain and swelling time for MB specimens with different dry densities. Based on Equations (3)-(5), relationship between the ratio of time to unloaded swelling strain and swelling time for MB specimens can be further fitted by Equation (6), which was related to the initial dry density of MB specimen and swelling time:  
\[\frac{t}{\varepsilon}=0.016\rho_{d}-0.014\rho_{d}t+0.03t-0.015 \tag{6}\]  
where \(\varepsilon\) is the unload swelling strain of an MB specimen; \(\rho_{d}\) denotes the initial dry density (g/cm\({}^{3}\)); and \(t\) is the swelling time (h). The initial dry density is the main control index in the engineering application of bentonite. The relationship between the final swelling strain and initial dry density was obtained through the swelling strain testing of MB specimens with different initial dry densities under saline water conditions (Figure 8). The relationship between final swelling strain and initial dry density can be fitted by Equation (7).