# Shear Behaviour of Aeolian Sand with Different Density and Confining Pressure
## 3 Results and Discussion
### Critical State  
For the aeolian sand, the \(q\)-\(\epsilon_{1}\) curves and the effective stress paths under undrained loading conditions in triaxial stress space exhibit four types of undrained behaviour, such as flow, limited flow, strain hardening, and strain softening as illustrated in Figure 8. In flow behaviour, the \(q\) reaches a peak value and then strain softens to the critical state (CS) at \(\mathrm{d}q=0\), \(\mathrm{d}p^{\prime}=0\), and \(\mathrm{d}u=0\); where \(p^{\prime}\)= \((\sigma_{1^{\prime}}+2\sigma_{3^{\prime}})/3\). In limited flow, after the initial peak, \(q\) drops to a transient stable value at the quasi-steady state (QSS), and the subsequent shear makes \(q\) increase again approach to the critical state. For strain hardening behaviour, the \(\mathrm{d}q\
eq 0\), \(\mathrm{d}p^{\prime}\
eq 0\), and \(\mathrm{d}u\
eq 0\), indicate that critical state has not been reached. However, the effective stress path has reached the critical state line (CSL). The transformation of the specimen from contraction to dilatancy is called phase transformation (PT). In strain hardening behaviour, the effective stress path turns to the right at phase transformation (PT). For the strain softening behaviour, \(q\) increases to a high transient stable value at the quasi-steady state (QSS), after which shearing causes \(q\) to suddenly decrease to the critical state, which is contrary to limited flow behaviour. In the \(q\)-\(p^{\prime}\) plane, the effective stress path rises from the initial stress point to the original critical state line and moves upward along the original critical state line. After reaching the peak strength, it drops and converges to the new critical state line. The reason for the sudden stress drop is because there should be a shear band during the shearing of the specimen (Figure 4c). The effective stress path curves of aeolian sand specimens under drained and undrained conditions are shown in Figure 9. The points at the end of shearing for aeolian sand specimens are taken as the critical state points to estimate the critical state line in the \(q\)-\(p^{\prime}\) plane, which is represented by a solid symbol in the figure. Under drained conditions, medium-dense sand and dense sand generate strain softening, the hollow symbol is used to represent the peak stress. Some tests do not arrive at critical state, the hollow symbol is also used to represent the peak stress. All tests on aeolian sand yielded CS points in the \(q\)-\(p^{\prime}\) plane that can be fitted with a straight line passing through the origin with a slope of \(M\). Remarkably, for loose sand as shown in Figure 9a, the peak stress does not reach the critical state line, but a smaller stress when the critical state line is reached. For the dense sand, it can be seen from Figure 9d,e that the effective stress path of the specimens drop away from the critical state line after passing through it, which indicates that the specimen has  
Figure 7: \(D_{\mathrm{r}}=50\%\), deviatoric stress-axial strain-excess pore water pressure behaviour of the aeolian sand under undrained condition. (**a**) The deviatoric stress-axial strain curves; (**b**) The excess pore water pressure-axial strain curves. been destroyed and obvious shear band generate at the same time. So there are two critical state lines for dense sand, which are the original critical state line (Original CSL) before the shear band and the new critical state line (New CSL) after the shear band, as shown in Figure 9d,e. It is worth noting that for the loose sand, the peak strength line, the phase transition line, and the critical state line overlap into one line. However, for the dense sand, the peak strength line coincides with the original critical state line, and the phase transition line coincides with the new critical state line. Figure 10 shows the relationship between the \(M\) value and relative density.