## 4 Modeling the Hydro-Mechanical Coupling Behavior of Unsaturated Geotechnical Materials
### Speswhite Kaolin (Non-Expansive Clay)  
[PERSON] [40] carried out a series of experiments to study the hydro-mechanical coupling behavior through various stress path tests, including wetting, drying, isotropic loading, and unloading. Here, using the data of Test A9 for comparison, the stress paths are shown in Table 2. The mean net stress loading rate was 0.033 kPa/min, while the suction change rate was 0.0167 kPa/min in wetting or drying stages. The values of the slope of compression curve and unloading curve were 0.177 and 0.024, respectively.  
Figure 3 shows the comparison of modeling results and test data for isotropic loading and unloading stages. The isotropic loading-unloading cycle, A-B-C, performed at constant suction 300 kPa, is followed by a wetting-drying cycle, C-D-E, and then subsequent isotropic reloading, E-F, at the same suction 300 kPa. Due to the effect of hydraulic hysteresis, the saturation degree increases, while the specific volume is almost unchanged during the wetting-drying cycle (see points C and E). Additionally, the results show the degree of saturation changes irreversibly during the mechanical loading and unloading process, A-B-C. In addition, it can be seen that, during the second isotropic loading stage, E-F, yield occurs before the first loading, which can be interpreted as the increase of degree of saturation during the preceding wetting-drying cycle [5]. The modeling results are in good agreement with the test data.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Thermodynamics Parameters**} \\ \hline \multirow{2}{*}{**Speswhite Kaolin**} & \multicolumn{2}{c}{**Bentonite/Kaolin**} & \multirow{2}{*}{**Speswhite Kaolin**} & \multirow{2}{*}{**Bentonite/Kaolin**} \\  & & **Mixture** & & & **Mixture** \\ \hline \(B_{0}\) & \(2.192\times 10^{7}\) kPa & \(4.545\times 10^{6}\) kPa & \(c_{2}\) & 6701.2 & 8536.4 \\ \(\xi\) & 0.6 & 0.6 & \(c_{3}\) & 15,000 & 10,000 \\ \(c\) & 0.0022 & 0.0028 & \(c_{4}\) & 0.15 & 0.17 \\ \(c_{1}\) & 0.11 & 0.05 & \(c_{5}\) & 37.3 & 20.6 \\ \hline \multicolumn{4}{c}{**SWCC Parameters**} \\ \hline \multicolumn{4}{c}{**Drying**} & \multicolumn{4}{c}{**Wetting**} \\ \hline \multirow{2}{*}{**Speswhite Kaolin**} & \multicolumn{2}{c}{**Bentonite/Kaolin**} & \multirow{2}{*}{**Speswhite Kaolin**} & \multirow{2}{*}{**Bentonite/Kaolin**} \\  & & **Mixture** & & **Mixture** \\ \hline \(a_{1}\) & 631 & 1.46 & \(a_{1}\) & 368 & 0.716 \\ \(b_{1}\) & 0.963 & 0.243 & \(b_{1}\) & 0.922 & 0.175 \\ \(n\) & 14.8 & 2.56 & \(n\) & 3.87 & 2.88 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geotechnical materials types and model parameters. Soil-water characteristic curves (SWCC).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{4}{c}{**Stage**} \\ \hline \multirow{2}{*}{**From**} & \multirow{2}{*}{**To**} & \multirow{2}{*}{**Description**} & \multirow{2}{*}{**\(\overline{p}\) (kPa)**} & \multirow{2}{*}{**\(\boldsymbol{s}\) (kPa)**} \\ \hline A & B & Isotropic loading & 10\(\rightarrow\)200 & 300 \\ B & C & Isotropic unloading & 200\(\rightarrow\)10 & 300 \\ C & D & Wetting & 10 & 300\(\rightarrow\)10 \\ D & E & Drying & 10 & 10\(\rightarrow\)300 \\ E & F & Isotropic loading & 10\(\rightarrow\)375 & 300 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Stress paths of Test A9.  
Figure 4 shows the modeling results and test data under the wetting-drying cycle, while the mean net stress remains constant during the process. It can be seen that the change of specific volume was almost the same during the wetting and drying process and changed little after a wetting-drying cycle due to a slight variation in the saturation degree (about 0.05). The modeling results were consistent with the test data.