## 3 Results and Discussion  
### Definition of Failure  
Due to limited space, only some of the SSDS and LSDS results are presented. The HD in DS tests was normalized to specimen diameter, termed the relative horizontal displacement (RHD) hereafter, for the sake of easy comparison. Figure 6 shows the relationships between the shear stress and the RHD for the SSDS tests, while Figure 7 shows the relationships between the shear stress and the RHD for the LSDS tests. Generally, the shear stress versus the RHD relationships for the SSDS tests can be categorised into strain-softening curve (Type 1) and strain-hardening curve (Types 2 and 3) (Figure 8). Shear stress increasing to a peak value and then gradually decreasing with increasing horizontal displacement was categorised into Type 1 (Figure 6a). In the case shear stress increasing to an ultimate value and then remaining essentially constant with increasing horizontal displacement was categorised into Type 2 (Figure 6b). Type 3 comprised two sub-types. Type 3a can be described as shear stress increasing to the curve inflection point where some factor starts to have influence on the shearing behaviour and then gradually increasing at a constant rate with additional horizontal displacement. Type 3b was similar to Type 3a, but followed by a gradual increase in shear stress at another constant rate with larger horizontal displacement. The gradual increases in shear stress observed in Type 3 were most likely attributed to the effect of particle-box interaction, as discussed subsequently. It is evident that Type 1, Type 2 and Type 3a were characterised by two distinguished curve slopes, initial slope and additional-displacement slope and that Type 3b was characterised by three distinguished slopes; that are, initial slope, additional-displacement slope and larger-displacement slope. In Type 3a and Type 3b for which no distinct peak stress was available, a suggested criterion of 4 mm HD (i.e., 6.5% RHD) [44] to determine the failure stress still had some distance from the onset of the tangent line, which also indicated an inappropriate criterion for determining the failure stress. Thus, the failure stress for Type 1 and Type 2 was defined using the peak stress and the horizontal tangent line, respectively, and from the onset of the tangent line, resulting from the additional-displacement slope, for Type 3a and Type 3b.  
Figure 6: Shear stress-relative horizontal displacement relationships from SSDS tests on the loess-PHW specimens at \(\omega\) = 14%: (**a**) %PHW = 0 and (**b**) %PHW = 0.3.  
Figure 7: Shear stress-relative horizontal displacement relationships from LSDS tests on the loess-PHW specimens at \(\omega\)=14%: (**a**) %PHW = 0 and (**b**) %PHW = 0.45.  
The shear stress versus the RHD curves from the LSDS tests exhibited two out of the four relationships observed from the SSDS tests, which are Type 2 (not shown) and Type 3a. The gradual increase in shear stress observed in Type 3a was believed to be related to the effect of particle-box interaction. Similarly, the failure stress for Type 2 and Type 3a was defined using the horizontal tangent line and the onset of the tangent line, respectively. Additionally, the suggested criterion of 4 mm HD was redefined by regarding the specimen size and applied to the shear stress versus the RHD curves for evaluation of its applicability. It was also found that the redefined criterion of 19.4 mm HD (i.e., \(6.5\%\times 300\) mm) differed considerably from the onset of the tangent line, indicating that the 19.4 mm horizontal displacement might not be appropriate for determining the failure stress.