## 4 Model Validation and Discussion
### Discussion  
(1) Damage variable \(D\)  
The variation pattern of damage variable \(D\) under the effect of matrix suction and confining pressure obtained from experiments and model analysis is shown in Figure 7.  
According to Figure 7: (i) As the strain increased, the damage variable \(D\) first increased rapidly at a larger rate. Although the rate of increase gradually declined, the overall increasing trend remained. However, \(D\) was below 1 throughout the test, i.e., the unsaturated soil exhibited incomplete damage. This occurred because, on the one ha  
Figure 6: Comparison between the proposed model and experimental data. Figure 7: Variation pattern of the damage variable in the moistening and stress fields. (**a**) \(s\) = 50 kPa; (**b**) s = 100 kPa; (**c**) \(s\) = 200 kPa. prone to strain hardening, and its stress-strain under triaxial test conditions does not reach the limit state. On the other hand, unsaturated soil is frictional material, and the damaged part of the soil still has residual strength instead of completely losing its bearing capacity. Since this part of the bearing capacity is manifested in an undamaged form, the damage variable of unsaturated soil rarely reaches 1. (ii) In the moistening and stress fields, the damage variable increased with the increase in matrix suction. As the confining pressure increased, the damage variable decreased. This occurred because the soil always exerts cohesive strength first, followed by frictional strength in the unsaturated soil structure. Therefore, under the same strain conditions and constant total damage of unsaturated soil, the damage of the cohesive strength increases with the increase in matrix suction. However, the frictional strength increases with the increase in confining pressure, and the damage decreases accordingly. (iii) There is an initial damage threshold for unsaturated soil at the initial stage of damage, which decreases with the increase in matrix suction and increases with the increase in confining pressure. This occurs because, as the matrix suction increases, the viscoelasticity of the soil increases, and the hardening index \(\alpha\) and the initial damage threshold of the soil decrease accordingly. The soil structural strength increases with the increase in confining pressure, and the initial damage threshold increases accordingly. 2. Laplace distribution parameters \(m_{0}\) and \(K_{0}\)  
The variation pattern of \(m_{0}\) and \(K_{0}\) under different matrix suction and confining pressure can be obtained from Table 2, as shown in Figures 8 and 9. As shown in Figures 8a and 9a, \(m_{0}\) and \(K_{0}\) increase nonlinearly with the increase in matrix suction, indicating that the micro-unit strength decreases in the moistening field as the soil saturation increases. As shown in Figures 8b and 9b, \(m_{0}\) and \(K_{0}\) increase nonlinearly in the stress field with the increase of confining pressure, indicating that the micro-unit strength increases in the stress field as the confining pressure increases. Therefore, \(m_{0}\) and \(K_{0}\) performed well in reflecting the variation pattern of micro-unit strength in the moistening and stress fields. 3. Strain hardening parameter \(\alpha\)  
The variation pattern of \(\alpha\) under different matrix suctions and confining pressures is shown in Figure 10.  
According to the definition of the hardening parameter \(\alpha\) of unsaturated loess and Equation (32), the actual hardening capacity of unsaturated loess can be expressed as \((1-\alpha)\)  
Figure 8: Variation pattern of \(m_{0}\) in the moistening and stress fields. (**a**) \(m_{0}-s\); (**b**) \(m_{0}-\sigma_{3}\). As shown in Figure 10a, \((1-\alpha)\) increases with the increase in matrix suction, indicating that the hardening capacity increases in the moistening field as the soil saturation increases. As shown in Figure 10b, \((1-\alpha)\) increases with the increase in confining pressure, indicating that the hardening capacity increases in the stress field as the confining pressure increases.