## 4 Model Validation and Discussion  
### Model Parameters and Validation  
Triaxial series tests for unsaturated soils on Xi'an loess, performed by [PERSON] et al. [35], were selected to verify the ability of the proposed model to describe the mechanical behavior of unsaturated soil loess. The details of the soils and tests can be found in [PERSON] et al. [35]. The values of model parameters identified for Xi'an loess are given in Table 1. The test apparatus used in this study was the unsaturated soil triaxial test equipment developed by Professor [PERSON], which was calibrated before the test. The initial matrix suction of the samples was adjusted to 50 kPa, 100 kPa, and 200 kPa, and the confining pressure was adjusted to 100 kPa, 200 kPa, and 300 kPa, respectively. The consolidation stability standard of unsaturated soil is 0.005 mL/h, and the average consolidation time of each sample is greater than 40 h. The shear rate was set to 0.0072 mm/min, and it took about 30 h to reach an axial strain of 15%. The results of the triaxial shearing test for unsaturated soil are shown in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline
**Dry Density** & **Relative Density** & **Plastic Limit** & **Liquid Limit** \\ \(\rho_{\text{d}}\)/g\(\cdot\)cm\({}^{-3}\) & \(d_{\text{s}}\) & \(w_{\text{p}}\)/\% & \(w_{\text{L}}\)/\% \\ \hline
1.51 & 2.71 & 17.3 & 31.1 \\ \end{tabular}
\end{table} 
Table 1: Basic physical properties of Xi’an loess collected from Yan’an New District (Data from [PERSON] et al. [35]). According to the triaxial shearing test results of unsaturated loess from Yan'an New District, shown in Figure 4, the stress-strain relationships are all strain-hardening, which increases with the increase of matrix suction and confining pressure. The increased shear strength and slope of the stress-strain curve of unsaturated loess indicates enhanced viscoelasticity and strain-hardening of unsaturated loess. As shown in Table 2, each parameter in the proposed model is solved according to the test results of unsaturated loess, and parameters \(m_{0}\) and \(K_{0}\) are solved as shown in Figure 5.  
As shown in Figure 6, based on the calculated parameters, the results of the proposed model were compared with the experimental data for validation. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Basic Physical Parameters**} & \multicolumn{2}{c}{**Saturated Soil**} & \multicolumn{2}{c}{**Laplace Distribution**} & \multicolumn{2}{c}{**Strain**} \\ \cline{3-10} \(\mathbf{s}\) & \(\sigma_{\mathbf{3}}\) & & & & **Strength Parameters** & **Parameters** & **Hardening** \\ \cline{3-10} /\(\mathbf{kPa}\) & /\(\mathbf{kPa}\) & \(E_{\mathbf{0}}\) & \(\mu\) & \(v_{\mathbf{0}}\) & \(c^{\prime}\) & \(\phi^{{}^{\prime}}\) & \(m_{\mathbf{0}}\) & \(K_{\mathbf{0}}\) & \(\alpha\) \\  & & /\(\mathbf{kPa}\) & \(\mu\) & /\(\mathbf{mm\cdot h^{-1}}\) & /\(\mathbf{kPa}\) & \(f^{{}^{\prime}}\) & \(m_{\mathbf{0}}\) & \(K_{\mathbf{0}}\) & \(\alpha\) \\ \hline  & 100 & 19.7 & & & & & 122.03 & 273.50 & 0.452 \\
50 & 200 & 20.5 & & & & 168.20 & 227.05 & 0.330 \\  & 300 & 20.9 & & & & 246.61 & 361.40 & 0.270 \\ \hline  & 100 & 25.7 & & & & 128.11 & 310.78 & 0.435 \\
100 & 200 & 27.1 & 0.38 & 0.432 & 12.26 & 30.65 & 174.51 & 317.17 & 0.325 \\  & 300 & 28.0 & & & & 220.66 & 470.55 & 0.251 \\ \hline  & 100 & 31.0 & & & & & 227.36 & 396.41 & 0.255 \\
200 & 200 & 31.8 & & & & 283.92 & 441.97 & 0.219 \\  & 300 & 32.6 & & & & 332.64 & 493.81 & 0.170 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the proposed model. Figure 4: Triaxial test curve of unsaturated loess from Yan’an New District ([PERSON] et al. [35]). (**a**) \(s=50\) kPa; (**b**) \(s=100\) kPa; (**c**) \(s=200\) kPa. Figure 5: Fitting lines for parameters \(m_{0}\) and \(K_{0}\). (**a**) \(s=50\) kPa; (**b**) \(s=100\) kPa; (**c**) \(s=200\) kPa.