## 4 Modeling the Hydro-Mechanical Coupling Behavior of Unsaturated Geotechnical Materials
### Bentonite/Kaolin Mixture (Highly Expansive Doil)  
The mixture include about 10% Wyoming sodium bentonite and 90% Speswhite kaolin [41], and the model parameters are also listed in Table 1. The data of Tests 8/9/10 were used to verify the efficiency of the model, and these behaviors were well simulated by the proposed model. The stress paths are as follows:  
* [leftmargin=0.5 cm]
* Wetting-drying at constant mean met stress \(\overline{p}\) = 10 kPa; Suction s(kPa) = 300(a)\(\rightarrow\)20(b)\(\rightarrow\)300(c)
* Isotropic loading-unloading at constant suction \(s\) = 200 kPa; Mean met stress \(\overline{p}\) (kPa) = 10(a)\(\rightarrow\)100(b)\(\rightarrow\)10(c)\(\rightarrow\)250(d)\(\rightarrow\)100(e)
* [leftmargin=0.5 cm]
* (1) Isotropic loading-unloading at constant suction \(s\) = 200 kPa; Mean met stress \(\overline{p}\) (kPa) = 10(a)\(\rightarrow\)100(b)\(\rightarrow\)10(c) (2) Wetting-drying at constant mean met stress \(\overline{p}\) = 10 kPa; Suction \(s\)(kPa) = 200(c)\(\rightarrow\)20(d)\(\rightarrow\)200(e) (3) Isotropic loading-unloading at constant suction \(s\) = 200 kPa Mean met stress \(\overline{p}\) (kPa) = 10(e)\(\rightarrow\)250(f)\(\rightarrow\)10(g)  
Figure 4: Comparison between predicted results and measured test data for Speswhite kaolin during the wetting and drying cycle: (**a**) specific volume; (**b**) degree of saturation.  
Figure 3: Comparison between modeling results and measured test data for Speswhite kaolin under isotropic loading and unloading: (**a**) specific volume; (**b**) degree of saturation.  
Figure 5a shows that no collapse compression occurred in wetting path a\(\rightarrow\)b and the irreversible shrinkage occurred in drying path b\(\rightarrow\)c due to a greater change in saturation degree (about 0.27), i.e., a larger effective stress than the previous. Figure 5b provides the clear evidence for the hydraulic hysteresis behavior of the material.  
Figure 6 shows the compressive and rebound characteristics of the material under isotropic loading-unloading cycles. The saturation degree increased with the increase of mean net stress during the loading process, while it changed a little during the unloading process, as shown in Figure 6b. In addition, the small mechanical hysteresis behavior could be seen during the unloading-reloading loop, and the yield point occurred near \(\overline{p}\) = 100 kPa, corresponding to the maximum mean net stress previously applied (Figure 6a).  
Test 10 differed from Test 9, only in that the wetting and drying cycle was added between the two loading-unloading cycles. The results show that there was no net shrinkage during the wetting-drying cycle (points c and e in Figure 7a), while in the second loading, e\(\rightarrow\)f, the material yielded at a lower value of about 80 kPa due to the wetting-drying cycle. Additionally, the degree of saturation increased with the increasing value of mean net stress, as shown in Figure 7b. Although there is no net volume change, the points c and e were different due to the increase of saturation after the wetting-drying cycle. The model can well describe this phenomenon.  
Figure 5: Comparison between modeling results and Test 8 measured data for bentonite/kaolin mixture material during the wetting–drying cycle: (**a**) specific volume; (**b**) degree of saturation.  
Figure 6: Comparison between modeling results and Test 9 measured data for bentonite/kaolin mixture under isotropic loading–unloading cycles: (**a**) specific volume; (**b**) saturation degree.