## 4 Discussion: Effect of Pattern of Variation of Mean Effective Stress and Their Implications  
It is worth noting that soil properties such as the Mohr-Coulomb strength parameters obtained from conventional triaxial tests are used directly in many geotechnical engineering projects, despite the practical stress paths involved. Therefore, we chose the stress path of conventional triaxial test (\(\alpha=71.6^{\circ}\)) as a benchmark, to investigate the influence of patterns of variation of mean effective stress on shearing strength, ductility and shearing stiffness of the UGRS.  
Compared to the Mohr-Coulomb strength parameters under \(\alpha=71.6^{\circ}\), cohesions under \(\alpha=123.7^{\circ}\) and \(251.6^{\circ}\) decreased by \(58.1\%\) and \(85.7\%\), respectively, while friction angles under \(\alpha=123.7^{\circ}\) and \(251.6^{\circ}\) increased by \(17.3\%\) and \(55.0\%\) respectively. It is shown that under decreasing-\(p^{\prime}\) stress paths, cohesion of the soil is severely weakened while friction angle is strengthened considerably. The findings above signify that patterns of variation of mean effective stress have non-negligible influence on the shearing strength properties of UGRS. Therefore, more attention should be paid to the applicability of the strength parameters used for design to achieve a balance between safety and economy.  
As for ductility, a summary of \((\epsilon_{s})_{50}\) and \((\epsilon_{s})_{90}\) under decreasing-\(p^{\prime}\) stress paths is presented in Table 5. Note that the rate of change of ductility, which is the percentage change in ductility, is also calculated, by choosing the corresponding value under \(\alpha=71.6^{\circ}\) as a benchmark. As can be seen in Table 5, both \((\epsilon_{s})_{50}\) and \((\epsilon_{s})_{90}\) experienced significant decreases under decreasing-\(p^{\prime}\) stress paths, compared to those under \(\alpha=71.6^{\circ}\). In particular, there was a marked decrease of \(62.4\%\)-\(72.6\%\) in \((\epsilon_{s})_{50}\) under \(\alpha=123.7^{\circ}\), while under \(\alpha=251.6^{\circ}\) (\(\epsilon_{s})_{50}\) decreased by \(54.8\%\)-\(65.6\%\). Certainly, the UGRS showed more brittle responses under decreasing-\(p^{\prime}\) stress paths, which indicates that the soil may reach failure state when shear strain is still small. It follows that more efforts must be made in monitoring deformation during excavation in granite residual soils. Monitoring frequency should be raised, and  
Figure 11: Failure lines of the soil under different stress paths.  
Figure 12: Variations of cohesion and friction angle with loading angle.  
if necessary, real-time monitoring systems need to be established to prevent possible soil failure at small strains, especially in the side of foundation pits.  
There was a significant difference between initial secant shear moduli under \(\alpha=123.7^{\circ}\) and \(251.6^{\circ}\), although both of them belonged to decreasing-\(p^{\prime}\) stress paths. The initial secant shear moduli under \(\alpha=123.7^{\circ}\) were about 70%-104% of those under \(\alpha=71.6^{\circ}\), while the initial secant shear moduli under \(\alpha=251.6^{\circ}\) were 2-2.52-fold greater than those under \(\alpha=71.6^{\circ}\). This indicates that the UGRS exhibits quite different shearing stiffness in compression and extension tests. Due to the fact that vertical stresses \(\sigma_{1c}\) are greater than horizontal stresses \(\sigma_{3c}\) after consolidation, soil specimens sheared under \(\alpha=251.6^{\circ}\) (i.e., extension tests) gradually approach a hydrostatic stress state at first. This may explain why soil specimens in extension tests show extraordinarily stiff responses at small strain. Stiffness parameters of soil are essential for numerical simulations of excavation, which are aimed at evaluating deformation near foundation pits. The results above imply that stiffness parameters of granite residual soils should be decided carefully. Specifically, appropriate parameters are assigned to soil elements according to their positions.