# Shear Behaviour of Aeolian Sand with Different Density and Confining Pressure
## 4 Conclusions  
In this paper, the experiment was performed on aeolian sand, subjected to shear properties with triaxial apparatus. A study of numerous typical influencing factors on aeolian sand was also performed, such as the compactness state, effective confining pressure, and drainage condition. The main findings are as follows:  
Figure 14: Variation of effective internal friction angle with confining pressure in aeolian sand under undrained condition. Figure 15: Variation of peak deviatoric stress with relative density of aeolian sand under drained condition. (1) The results of the drained test show that the stress and volumetric strain of all the specimens reached a constant value at the end of the tests, indicating that all the specimens reached the critical state and the residual stress in the final state tends to be the same. Under undrained conditions, the \(q\)-\(e_{1}\) curves and the effective stress paths show four types of undrained behaviour, such as flow, limited flow, strain hardening, and strain softening. Meanwhile all the specimens exhibit three types of failure, such as flow slip, bulging failure, and shear band. (2) The results of the same initial relative density but different confining pressures indicate that analogous drained and undrained stress paths are followed by the test pairs in the \(q\)-\(p^{\prime}\) plane. For dense sand (\(D_{\rm r}=70\%\) and \(90\%\)), there are two critical state lines, which are the original critical state line before the shear bands and the new critical state line after the shear bands, and the generation of shear band has great influence on its strength. (3) The critical state line in the \(e\)-\(\mathsf{ln}p^{\prime}\) plane can be described with linear function. The critical state lines of the aeolian sand in \(e\)-\(\mathsf{ln}p^{\prime}\) plane decrease with increasing initial relative density \(D_{\rm r}\), that is, the material constant \(e_{\rm T}\) decreases with increasing \(D_{\rm r}\), and the \(\lambda\) is also not constant but decreases with the increase in \(D_{\rm r}\). (4) Based on the results, the internal friction angles of aeolian sand are obtained by Mohr stress circle envelope. As the relative density increases, the internal friction angles increase linearly, and the effective internal friction angle increases by \(0.859^{\circ}\) for every \(10\%\) increase in \(D_{\rm r}\). The results show that the strength of aeolian sand is linearly related to its relative density and confining pressure. An empirical formula for the drained strength considering density and confining pressure is established. This study only conducts triaxial tests under the condition of limited void ratio and confining pressure, and it is necessary to supplement triaxial static and dynamic tests with more stress paths, so as to make up for the lack of aeolian sand test results. At the same time, the influence of the sample preparation method and the microfabric of aeolian sand on its mechanical properties still needs to be tested. Conceptualization, X.L. and W.X. ; methodology, W.X. ; software, X.L. and W.X. ; validation, W.Y. ; formal analysis, L.C. ; investigation, W.Y. ; resources, L.C. ; data curation, W.X. ; writing--original draft preparation, W.X. ; writing--review and editing, X.L. and W.X. ; visualization, W.X. ; supervision, X.L. ; project administration, X.L. ; funding acquisition, X.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No. 12162028), the Projects for Leading Talents of Science and Technology Innovation of Ningxia (No. KJT2019001), the Technology Innovation Team of Ningxia Hui Autonomous Region for multi-scale mechanics and its engineering applications (2021) and the Key R&D Program of Ningxia Hui Autonomous Region Projects of International Cooperation and Exchanges (No. 2018 DWHZ0084), and these supports are gratefully acknowledged. Not applicable.