# Experiments on the State Boundary Surface of Aeolian Sand for Road Building in the Tengger Desert
## 3 Test Results
### Stress-strain Relationships
Figure 7b shows that the relationships between the axial strain and radial strain change linearly under undrained conditions, which always satisfies the equation \(\varepsilon_{1}=-2\varepsilon_{3}\). The anisotropy characteristic is not obvious, which may be related to the loading rate of the test. Figure 5: Relationships between stress and pore pressure with axial strain under undrained conditions. (**a**) Stress-strain relationships. (**b**) Pore pressure-strain relationships. Figure 6: Relationships between pore pressure coefficient and axial strain. Figures 8a,b and 9a,b show the relationships between generalized stress ratio \(\eta\) and generalized shear strain \(\epsilon_{\text{s}}\) of aeolian sand and the relationships between \(\epsilon_{\text{s}}/\eta\) and \(\epsilon_{\text{s}}\) under drained and undrained conditions, respectively. Comparing Figures 8a and 9a, it can be concluded that the peak stress ratio decreases gradually with the increase of effective confining pressure in both the drained and undrained tests, but the peak stress ratio of the drained condition is slightly higher than that of the undrained condition. The shape of the \(\eta\)-\(\epsilon_{\text{s}}\) relationship for drained and undrained conditions are significantly different. Under undrained conditions, the stress ratio has an obvious peak value, and the peak stress ratio decreases slightly with the increase of \(\epsilon_{\text{s}}\). In Figures 8b and 9b, the \(\epsilon_{\text{s}}/\eta\)-\(\epsilon_{\text{s}}\) relationships are linear under drained and undrained conditions. The slope of the straight line increases with the increase of the effective confining pressure under the drained condition, but the change of the slope is small under an undrained condition. [PERSON] et al. [38] used the peak generalized stress ratio to represent the characteristics of the softening curve and proposed a hyperbolic model characterized by the stress ratio and the shear strain, which reads:  
\[\frac{\eta}{\eta_{\text{max}}}=\frac{\epsilon_{\text{s}}}{B+\epsilon_{\text{s}}} \tag{1}\]  
where \(B\) is the test constant and \(\eta_{\text{max}}\) is the peak value of the generalized stress ratio. The transformation form is as follows. \[\frac{\epsilon_{\text{s}}}{\eta}=\frac{B}{\eta_{\text{max}}}+\frac{\epsilon_{ \text{s}}}{\eta_{\text{max}}} \tag{2}\]  
Our test results are consistent with the hyperbolic model proposed by [PERSON] et al. [38]. The slope of the \(\epsilon_{\text{s}}/\eta\)-\(\epsilon_{\text{s}}\) curve increases gradually with the increase of effective confining pressure under drained conditions, indicating that softening increases gradually. The slope of the \(\epsilon_{\text{s}}/\eta\)-\(\epsilon_{\text{s}}\) curve under undrained conditions is significantly higher than that under drained conditions, indicating that the softening phenomenon is more obvious. Figure 10 shows the variation of peak shear stress and peak friction angle with effective confining pressure under drained and undrained conditions. The black curve in the figure increases linearly, indicating that the generalized peak shear stress increases linearly with the increase of effective confining pressure under both drained and undrained conditions. However, the undrained strength is greater than the drained strength at low effective confining pressure, and the drained and undrained strength becomes the same as the effective confining pressure increases. All the purple curves show a nonlinear decreasing trend, indicating that the peak friction angle decreases nonlinearly with the increase of effective confining pressure. At low effective confining pressure, the peak friction angles of  
Figure 7: Relationships between axial strain and radial strain. (**a**) Drained. (**b**) Undrained.