## 3 Results and Discussion
### Pore Water Pressure Ratio (\(r_{u}\))  
The observations in Figures 10 and 11 regarding the effect of confinement on the excess pore pressure, on varying the initial shear stress ratios, can be a criterion for liquefaction susceptibility. From Equation (2), it can be observed that the criterion for liquefaction susceptibility pore water pressure ratio (\(r_{u}\)) is the variation of the pore water pressure at failure to the initial effective confining pressure:  
\[r_{u}=\frac{u_{excess\ at\ failure}}{\sigma^{\prime}s_{\rm{c}}} \tag{2}\]  
The susceptibility ranges from 0-1, when \(r_{u}\) approximates unity, and the liquefaction potential increases. [PERSON] et al. [9] had also stated that it is common to have lower \(r_{u}\) within the liquefaction phenomenon, termed as susceptible to liquefaction. Figure 12 presents the liquefaction susceptibility for isotropic and anisotropic specimens; the pore water pressure ratio (\(r_{u}\)) is plotted against the mean effective pressure at failure (Figure 12). It can be seen that most specimens are susceptible to liquefaction, while three of them show a negative value indicating that they have no liquefaction potential. In this study, the \(r_{u}\) values range from \(-\)0.06-0.97. However, 21 out of the 24 tests show a positive value of \(r_{u}\) indicating liquefaction behavior.  
In Figure 12, the scattered pattern of points shows that \(r_{u}\) is related to the relative density (D\({}_{\rm{r}}\)) because on increasing the effective confining pressure from 150 to 350 kPa, the dispersion decreases. The dispersion in tests with \(\sigma_{\rm{3c}}=150\) kPa reveals that except for one of the tests (R-C)\({}_{2}\), which may be an outlier, the outcomes of the other tests fall into two main opposing groups (phases): 1--highly susceptible and 2--completely non-susceptible to liquefaction.  
As observed from the \(r_{u}\) values plotted against the initial relative densities and from the point dispersion comparison shown in Figure 13, specimens with low D\({}_{\rm{r0}}\) exhibit almost the same behavior, whereas for those with high D\({}_{\rm{r0}}\), the tests results differ to a certain extent from each other. For medium D\({}_{\rm{r0}}\), two distinguishable points, (R-A)\({}_{2}\) and (R-B)\({}_{2}\), indicate the commencement of dispersion. It is clear from Figure 13 that the increase in relative density reduces the liquefaction susceptibility. As stated by [PERSON] et al. [37], specimens with high relative density have lower particle failure probability and less extensive failure modes than loose specimens. Additionally, loose specimens exhibit higher  
Figure 11: Comparative curvatures for (R–A)\({}_{6}\), (R–B)\({}_{6}\) and (R–C)\({}_{6}\) in u–\(\epsilon\)% plane. Alpha (\(\alpha\)): the initial shear stress ratio.  
compression due to particle failure leading to more fine generation by the further crushing of existing fragments, and as stated earlier, reach the critical state, resulting in liquefaction.  
The friction angle at the failure point and \(r_{u}\) have a negative correlation, as depicted in Figure 14. The friction angle ranges from \(2^{\circ}\) to \(36^{\circ}\) in this study, and \(\Phi^{\prime}{}_{\text{(deg)}}=2^{\circ}\) and \(\Phi^{\prime}{}_{\text{(deg)}}=36^{\circ}\) are related to specimens with high and low susceptibility to liquefaction, respectively. A low friction angle is  
Figure 12: Pore water pressure ratio versus mean effective stress and effective confining pressure in isotropic and anisotropic stress condition. Alpha (\(\alpha\)): the initial shear stress ratio.  
Figure 13: Pore water pressure ratio versus mean effective stress and effective confining pressure in isotropic and anisotropic stress conditions.  
a result of excess pore water pressure, causing a loss of contact between particles which in turn results in interparticle friction loss.