## 3 Results and Discussion  
### Effect of Scaling on Shear Strength of CGS  
Figure 8 presents shear test results for soil samples of varying gradations under normal stresses of 100 kPa, 200 kPa, 400 kPa, and 600 kPa at a moisture content of \(w=0.91\%\). Analysis of Figure 8a reveals that the shear stress of the original gradation CGS sample rises steadily with shear displacement, lacking a distinct peak, and displays characteristic strain-hardening behavior. Figure 8b,c illustrates the shear stress-shear displacement curves for samples scaled by the ESM and SGM at \(w=0.91\%\), respectively. These scaled samples exhibit mild strain-softening, with peak shear stress occurring at displacements of approximately 25-30 mm, followed by a modest decline. Figure 8d depicts the shear strength of specimens across gradations, measured per the \"Standard for Geotechnical Testing Methods\" (GB/T 50123-1999). This standard defines peak shear strength as the maximum value on the shear stress-shear displacement curve or, in the absence of a clear peak, the stress at \(1/10\) to \(1/15\) of the shear displacement range. Results consistently show the original gradation yielding the highest shear strength under all normal stresses, followed by ESM and SGM. At lower stresses, the strength difference among the three is about 40 kPa, rising to roughly 60 kPa at higher stresses, averaging 50 kPa. This suggests that variations in maximum particle size (\(d_{\rm max}\)) and scaling methods exert a limited influence on CGS shear strength at \(w=0.91\%\), with peak strength reductions from the original gradation to ESM and SGM remaining modest. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Gradation Type** & \(d_{\rm max}\) **(mm)** & **Relative Density Dr** & **Moisture Content** & **Normal Stress (kPa)** \\  & & **(\%)** & **(\%)** & **(\%)** \\ \hline Initial gradation & 60 & 85 & 0.91\%, 2.45\%, 7.66\% & 100, 200, 400, 600 \\ Gradation under ESM & 30 & 85 & 0.91\%, 2.45\%, 7.66\% & 100, 200, 400, 600 \\ Gradation under GSM & 30 & 85 & 0.91\%, 2.45\%, 7.66\% & 100, 200, 400, 600 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Direct shear test scheme. Figure 7: Original gradation specimens under different moisture contents. Figure 9 displays shear test outcomes at \(w=2.45\%\). As shown in Figure 9a, the original gradation sample mirrors its \(w=0.91\%\) counterpart, exhibiting strain-hardening behavior. Figure 9b,c indicates that scaled specimens display slight strain-softening at 100 kPa and 200 kPa normal stresses but transition to strain-hardening at 400 kPa and 600 kPa. Figure 9d highlights a marked reduction in shear strength for scaled specimens, particularly at higher stresses: at 600 kPa, ESM and SGM specimens show reductions of 118 kPa and 165 kPa, respectively, compared to the original gradation, while at 100 kPa, reductions are 23 kPa and 34 kPa. Figure 10a illustrates the shear stress-shear displacement curve for the original gradation at \(w=7.66\%\), where shear stress increases gradually, peaks around 36 mm, and then stabilizes, reflecting strain-hardening traits. Figure 10b,c shows ESM and SGM specimens, respectively, with slight strain-softening at low normal stresses and strain-hardening at higher ones, consistent with trends at \(w=2.45\%\). Figure 10d reveals substantial shear strength reductions in scaled specimens under saturated conditions: at 600 kPa, ESM and SGM exhibit drops of 180 kPa and 240 kPa, respectively, relative to the original gradation, with scaling effects more pronounced than at \(w=2.45\%\). Figure 8: Relationship of shear stress and shear displacement under \(w=0.91\%\). Figure 10: Cont. Figure 9: Relationship of shear stress and shear displacement under \(w=2.45\%\). A comprehensive analysis confirms that, under identical conditions, the original gradation consistently achieves the highest shear strength, followed by ESM and SGM. Strength differences are minimal at \(w=0.91\%\) first but grow significantly with increasing moisture content (e.g., \(w=2.45\%\) and \(w=7.66\%\))