## 5 Conclusions  
In the present study, the isotropic consolidation conventional triaxial tests and anisotropic consolidation stress path triaxial tests were conducted on a typical undisturbed granite residual soil. Based on the test results, the influence of stress path, which was quantified by loading angle, on the stress-strain strength behavior of the soil was investigated. Many aspects including the Mohr-Coulomb strength parameters, failure strain, volume change behavior, ductility, as well as shearing stiffness were involved. The main conclusions are summarized as follows.  
1. For compression tests, friction angle of the UGRS continues to increase while cohesion decreases monotonically as the loading angle increases. Compared with compression tests, soil specimens in extension tests show a lower cohesion but a higher friction angle. Both cohesion and friction angles of the soil in AL tests are slightly smaller than those in ICD tests, indicating the influence of consolidation stress states on the strength properties of the UGRS.
2. Both consolidation pressure and loading angle impose impacts on the deformation behavior of the soil. The failure strain increases gradually as consolidation pressure increases or loading angle decreases. The increase in consolidation pressure leads to more volume contraction, while the increase in loading angle diminishes the contractive behavior of the soil.
3. In this paper, \((\varepsilon_{s})_{50}\) and \((\varepsilon_{s})_{90}\) were employed to formulate the ductility of soil. The UGRS shows larger \((\varepsilon_{s})_{50}\) and \((\varepsilon_{s})_{90}\) (i.e., more ductile) under higher consolidation pressure, and the effect of consolidation pressure is enhanced as loading angle decreases. Due to the stronger confining effect imposed by stress path with smaller loading angle, the UGRS shows a less brittle response during shearing.
4. The initial secant shear modulus \(E_{0}\) was defined to evaluate the shearing stiffness of the soil. It is found that the shearing stiffness of the UGRS is path-dependent. \(E_{0}\) first  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(\sigma^{{}^{\prime}}_{\mathbf{3c}}\) & \multicolumn{2}{c}{\(\alpha=71.6^{\circ}\) (Benchmark)} & \multicolumn{3}{c}{\(\alpha=123.7^{\circ}\)} & \multicolumn{3}{c}{\(\alpha=251.6^{\circ}\)} \\ \cline{2-10} (kPa) & \((\varepsilon_{s})_{50}\) (\%) & \((\varepsilon_{s})_{90}\) (\%) & \((\varepsilon_{s})_{50}\) (\%) & \(RC^{\ 1}\) & \((\varepsilon_{s})_{90}\) (\%) & \(RC\) & \((\varepsilon_{s})_{50}\) (\%) & \(RC\) & \((\varepsilon_{s})_{90}\) (\%) & \(RC\) \\ \hline
100 & 1.050 & 3.095 & 0.288 & 72.6\% & 2.092 & 32.4\% & 0.361 & 65.6\% & 2.840 & 8.2\% \\
200 & 1.125 & 3.569 & 0.423 & 62.4\% & 2.219 & 37.8\% & 0.499 & 55.6\% & 3.145 & 11.9\% \\
300 & 1.211 & 4.010 & 0.440 & 63.7\% & 2.393 & 40.3\% & 0.547 & 54.8\% & 3.266 & 18.5\% \\
400 & 1.362 & 4.338 & 0.442 & 67.6\% & 2.561 & 41.0\% & / & / & / & / \\ \hline \hline \end{tabular} \({}^{1}RC\) denotes the rate of change.  
\end{table}
Table 5: Summary of \((\varepsilon_{s})_{50}\) and \((\varepsilon_{s})_{90}\) under decreasing-\(p^{\prime}\) stress paths.  
decreases and then increases as loading angle increases. There is a certain value of loading angle lying between \(90^{\circ}\) and \(123.7^{\circ}\), under which the lowest \(E_{0}\) occurs.  
[PERSON] and [PERSON] proposed the research method and designed the test plan; [PERSON], [PERSON] and [PERSON] performed the laboratory tests; [PERSON] analyzed the data and wrote the paper under the guidance of [PERSON]. 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 (Grant No. 11672320).  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.