# Experiments on the State Boundary Surface of Aeolian Sand for Road Building in the Tengger Desert
## 3 Test Results
### State Boundary Surface  
Figure 11 plots the critical state line and phase transformation line in the \(p\)-\(q\) space under drained and undrained conditions and gives the slopes of the two-state lines. The green points in Figure 11a are the phase transformation points, which are the inflection points where the void ratio changes from decrease to increase, and it is also the transformation point of volumetric change from contraction to dilation. The phase transformation point is determined according to the corresponding stress state point, as the void ratio increment is 0. Figure 11 shows that the critical state line and phase transformation line determined by the undrained triaxial test are slightly lower than those determined by the drained triaxial test, due to the change of pore pressure and shear rate, and the variation range is less than 5%. The test results show that the aeolian sand has a unified critical state line and phase transformation line. The critical state line and phase transformation line of aeolian sand in the \(p\)-\(q\) space can be expressed linearly by the following equations:  
\[q =M_{\text{CSL1}}p \tag{3}\] \[q =M_{\text{PTL1}}p \tag{4}\]  
where \(M_{\text{CSL1}}\) and \(M_{\text{PTL1}}\) are the slopes of the critical state line and the phase transformation line in \(p\)-\(q\) space, respectively. The information in Figure 12 shows the critical state line, phase transformation line and normal consolidation line under drained conditions, which can be represented by linear relations. At the same effective confining pressure, with the increase of \(\ln\,p\), the void ratio decreases first and then increases rapidly to the critical state (compared to the consolidated void ratio). At different effective confining pressures, with the increase of effective confining pressure and \(\ln\,p\), the decreased degree of void ratio increases gradually compared with the consolidated void ratio. While the effective confining pressure is greater than 800 kPa, the void ratio is always smaller than the consolidation void ratio, and the aeolian sand undergoes only contractive deformation under this condition. The studies of [PERSON] and [PERSON] [39], [PERSON] and [PERSON] [40] show that the critical state characteristics of cohesionless soil are significantly different from those of clay, and the critical state line is no longer unique in the \(\ln\,p\)-\(e\) space, due to the anisotropy of the soil. In this study, the specimen adopts the same specimen preparation method and is sheared under triaxial conditions, so the critical state lines, phase transformation lines and normal consolidation lines of aeolian sand in \(e\)-\(\ln\,p\) space can be expressed by linear equations as expressed by Equations (5)-(7), respectively. Figure 11: Effective stress path for drained and undrained test. (**a**) Effective stress path for drained test. (**b**) Effective stress path for undrained test. \[e_{\rm CSL} =M_{\rm CSL2}\ln p+e_{\rm C} \tag{5}\] \[e_{\rm PTL} =M_{\rm PTL2}\ln p+e_{\rm P}\] (6) \[e_{\rm NCL} =M_{\rm NCL}\ln p+e_{\rm N} \tag{7}\]  
where \(e_{\rm CSL2}\), \(e_{\rm PTL2}\) and \(e_{\rm NCL}\) are the void ratios corresponding to the critical state line, the phase transformation line and the normal consolidation line at any \(p\), respectively. \(M_{\rm CSL2}\), \(M_{\rm PTL2}\) and \(M_{\rm NCL}\) are the slopes of the critical state line, phase transformation line and normal consolidation line in ln \(p\)-\(e\) space, respectively. \(e_{\rm C,\it CP}\) and \(e_{\rm N}\) are the void ratios corresponding to the critical state line, phase transformation line and normal consolidation line at \(p=1\) kPa, respectively. Figure 13 shows the \(e\)-\(q\) relationships of aeolian sand under drained conditions. The shape characteristics of the critical state line and the phase transformation line in the \(e\)-\(q\) space are exponential. Moreover, as \(q\) increases, the void ratio decreases compared with the consolidated void ratio, and the specimen contracts.