## 3 Results and Discussion
### Comparison of Shear Strength between Small-Scale Direct Shear and Large-Scale Direct Shear  
A failure envelope of Mohr-Coulomb failure criterion was established through three DS tests that involved three different normal pressures using the linear least squares regression. The coefficient of determination R\({}^{2}\) for the failure envelopes in SSDS varied from 0.914 to 0.999, while in LSDS it varied from 0.906 to 0.999. Shear strength parameters for which the box friction and the possible non-linear nature of the failure envelopes near the origin were omitted are summarised in Table 3. Except the loess specimens with the %PHW equal to 0, the \(\phi^{\prime}\) values were typically 16.3-30.4\({}^{\circ}\) in SSDS and 15.3-29.3\({}^{\circ}\) in LSDS. In most cases the \(\phi^{\prime}\) value was the highest as the %PHW was equal to 0.60 and the effect of the PHW on the improvement of the \(\phi^{\prime}\) value was more significant in SSDS than in LSDS. A comparison of the \(\phi^{\prime}\) values from the SSDS tests and those from the LSDS tests is shown in Figure 9. It was noted that the difference between SSDS and LSDS was typically 0.7-8.8\({}^{\circ}\) except the difference of 17.8\({}^{\circ}\) for which the specimen prepared at \(\omega=22\%\) with the %PHW being equal to 0. The PHW was deemed to be effective in achieving the effect of particle inter-locking and thus impeded the development of shear bands near the shear plane as subjected to shear force. The more PHW added, the greater the effect of particle inter-locking and the lesser the significance of the scale effect. In addition to the \(\phi^{\prime}\) value, the RHD at failure was compared between SSDS and LSDS as well. The RHD varied within the range of 1.9-5.4\(\%\) in SSDS, while it varied within the range of 0.2\(\%\)-6.7\(\%\) in LSDS (Figure 10). The difference in the RHD at failure between SSDS and LSDS averaged 1.6\(\%\), with a maximum of 4.8\(\%\). It is evident that scatter existed in the data although in most cases the difference was generally limited to less than 2.0\(\%\). On the other hand, the difference in the RHD in fact was found to be governed by the added water, not by the added amount of PHW. The effect of particle inter-locking restrained the development of shear bands in the vicinity of the shear plane  
Figure 8: Typical shear stress-horizontal displacement curves. and became distinct when the water content was \(>\)14%. The lesser the amount of water added to loess-PHW mixture specimen, the larger the difference in the RHD and the greater the significance of the scale effect. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{SSDS} & \multicolumn{3}{c}{LSDS} \\ \cline{2-9}
**Specimen** & **c** & \(\phi^{\prime}\) & **R2** & **Specimen no.** & **c** & **(kPa)** & **\(\Phi^{\prime}\)** & **R2** \\ \hline SS14-0 & 79.4 & 22.1 & 0.997 & LS14-0 & 48.5 & 18.4 & 0.965 \\ \hline SS14-0.3 & 73.6 & 21.6 & 0.998 & LS14-0.30 & 59.6 & 24.3 & 0.995 \\ \hline SS14-0.45 & 59.6 & 30.4 & 0.972 & LS14-0.45 & 68.5 & 22.0 & 0.942 \\ \hline SS14-0.6 & 73.2 & 23.9 & 0.914 & LS14-0.60 & 44.8 & 29.3 & 0.999 \\ \hline SS14-0.75 & 60.9 & 16.3 & 0.986 & LS14-0.75 & 65.8 & 20.3 & 0.961 \\ \hline SS18-0 & 66.1 & 11.7 & 0.974 & LS18-0 & 40.7 & 20.1 & 0.977 \\ \hline SS18-0.3 & 46.3 & 23.0 & 0.962 & LS18-0.30 & 54.3 & 23.7 & 0.999 \\ \hline SS18-0.45 & 60.7 & 21.7 & 0.936 & LS18-0.45 & 36.9 & 22.4 & 0.906 \\ \hline SS18-0.6 & 63.0 & 21.0 & 0.968 & LS18-0.60 & 40.3 & 28.1 & 0.966 \\ \hline SS18-0.75 & 60.9 & 16.3 & 0.986 & LS18-0.75 & 28.2 & 22.2 & 0.976 \\ \hline SS22-0 & 79.7 & 4.9 & 0.997 & LS22-0 & 16.4 & 21.4 & 0.987 \\ \hline SS22-0.3 & 41.2 & 15.2 & 0.968 & LS22-0.30 & 39.8 & 21.1 & 0.986 \\ \hline SS22-0.45 & 27.4 & 22.8 & 0.999 & LS22-0.45 & 39.2 & 16.3 & 0.930 \\ \hline SS22-0.6 & 43.4 & 24.1 & 0.997 & LS22-0.60 & 30.2 & 22.2 & 0.999 \\ \hline SS22-0.75 & 60.9 & 16.3 & 0.986 & LS22-0.75 & 31.7 & 15.3 & 0.990 \\ \hline \hline \end{tabular}
\end{table}