## 2 Materials and Methods
### Test Program and Procedures  
Two types of tests were conducted in this study, including (1) drained and undrained isotropic consolidation triaxial compression tests (ICTTs), and (2) stress path triaxial tests (SPTT). The test program is summarized in Table 3. The objective of the former is to investigate the fundamental mechanical properties for reference. The SPTT is aimed at studying the stress-strain strength behavior of the UGRS under different stress paths and \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Mineral Composition (\%)**} \\ \hline
**Quartz** & **Kaolinite** & **Illite** \\ \hline
70.4 & 27.1 & 2.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mineral composition of the granite residual soil. Figure 3: Position of the granite residual soil in the Casagrande plasticity chart. Figure 2: Particle size distribution curve of the granite residual soil. different patterns of variation of mean effective stress. In order to obtain specimens with high saturation, the specimens were preliminarily saturated using a vacuum pump before being mounted onto the device. In addition, a back pressure of 200 kPa was applied to achieve a minimum B-value of 0.95. In ICTs, the specimens were consolidated isotropically under four different confining pressures (100, 200, 300 and 400 kPa). The consolidation stage was considered complete when the drainage rate of pore water was less than 1 mm\({}^{3}\)/min. Afterwards, the specimens were sheared under strain-controlled condition. The axial strain rates for drained (ICD) and undrained (ICU) tests were 0.005%/min and 0.05%/min, respectively. When the axial strain reached 20%, the tests were terminated. In triaxial tests, soil specimens are under the condition of axisymmetric-loading, so the stress paths can be expressed in the \(p\)-\(q\) space, where \(p\) denotes the mean total stress and \(q\) represents the deviator stress. All stress paths involved in this research are presented in Figure 4. Shearing stress ratio \(\eta\) and loading angle \(\alpha\) were introduced to represent stress paths quantitatively, as shown in Figure 4. It is clear that \(\eta\) is the ratio of the increment of \(q\) to the increment of \(p\), and \(\alpha\) is the angle of rotation from the \(p\)-axis to the shearing stress path. These can be determined according to:  
\[\eta=\frac{dq}{dp}, \tag{1}\]  
\[\alpha=\left\{ \begin{array}{l}\tan^{-1}(\eta),0<\alpha<\frac{\pi}{2}\\ \pi+\tan^{-1}(\eta),\frac{\pi}{2}<\alpha<\frac{3\pi}{2}\end{array} \right.. \tag{2}\]  
Figure 4: Various stress paths for triaxial tests conducted on the granite residual soil. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test Type** & **Series** & \(\boldsymbol{K^{1}}\) & \(\boldsymbol{\sigma^{{}^{\prime}}}_{\boldsymbol{3c}}\) (\(\boldsymbol{kPa}\)) & \(\boldsymbol{\eta^{2}}\) & **Loading angle (\({}^{\circ}\))** & **Loading Rate** \\ \hline \multirow{3}{*}{ICTT 3  } & ICUT 5  & 1 & 100, 200, 300, 400 & 3 & 71.6 & 0.05\%/min \\ \cline{2-8}  & ICD 6  & 0.005\%/min \\ \hline \multirow{3}{*}{SPTT 4  } & BL 7  & & & 1.5 & 56.3 & \\ \cline{2-8}  & increasing-\(p^{\prime}\) & AL 8  & AL 8  & & 3 & 71.6 & \\ \cline{2-8}  & constant-\(p^{\prime}\) & CP 9  & 0.53 & 100, 200, 300, 400 & \(\infty\) & 90 & \\ \cline{2-8}  & decreasing-\(p^{\prime}\) & LU 10  & & \(-1.5\) & 123.7 & \\ \cline{2-8}  & AU 11  & & 3 & 251.6 & \\ \hline \hline \end{tabular}  
* \(K\) denotes the consolidation stress ratio, \(\sigma^{{}^{\prime}}\):\(\chi_{0}\)/\(\
u^{{}^{\prime}}\):\(\chi_{1c}\):2 \(\eta\) denotes the shearing stress ratio, \(dq\)/\(dp\); 3 ICTT (isotropic consolidation triaxial tests);
* \(\mathcal{P}\)T (stress path tests); 5 ICU (isotropic consolidation undrained tests); 6 ICD (isotropic consolidation drained tests);
* \(\mathcal{P}\)BL (loading in both axial and lateral directions); 8 AL (axial-loading); 9 CP (constant \(p\)); 10 LU (lateral-unloading); 11 AU (axial-unloading).  
\end{table} 
Table 3: Summary of triaxial tests.