## 2 Materials and Methods
### Experimental Methods  
#### 2.2.1 Sample Preparation  
Cylindrical samples were fabricated for triaxial testing, which had a diameter \(D\) of 39.1 mm and a height \(H\) of 80 mm. This dimension was selected aiming to adapt to the testing cell of triaxial apparatus. In addition, the sample diameter \(D\) significantly exceeded the maximum grain size \(d_{\text{max}}\) = 0.01 mm of the clay soils, which was consistent with the ASTM D2850 [23] specification that the \(D/d_{max}\) ratio should be larger than 6 to eliminate the scale effect. The sample preparation began by directly adding the amount of water corresponding to the target water content (optimum water content \(w_{\text{opt}}\) = 27.5% as well as its dry side \(w_{\text{d}}\) = 19% and wet side \(w_{\text{w}}\) = 35%) to the oven-dried clay soils. Then, the moistened soils were sealed in an airtight container for 24 h to achieve moisture homogenization. Subsequently, the homogenized clay soils were compacted in five layers to prepare a sample with \(D\) = 39.1 mm and \(H\) = 80 mm within a cylindrical mold (39.1 mm in diameter and 120 mm in height). The shape and size were selected to ensure the compatibility with the triaxial testing apparatus utilized. A static compaction method was utilized for the compaction procedure. Note that the soil mass used for each layer was carefully controlled to be the same, and to guarantee proper connection between adjacent layers, the surface of each layer was slightly scratched prior to placing the subsequent layer. These standardized protocols ensured that all samples exhibited consistent shape and size. Following compaction, the sample was carefully wrapped in a plastic membrane to prevent moisture loss and stored in a sealed container for 24 h for stabilization. Note that this stabilization period was determined by assessing the water content across the sample diameter. The water contents at the quarter diameter, half diameter and the diameter points were considered, and the results showed that 8 h equilibration duration was sufficient to achieve uniform water distribution. Also note that the compaction degree \(D_{\text{c}}\) of all the samples was controlled at \(D_{\text{c}}\) = 0.80. This level was selected based on the in situ measurement of the \(D_{\text{c}}\) of the subgrade by [PERSON] et al. [24], which reported that \(D_{\text{c}}\) ranged between 0.79 and 0.96. A \(D_{\text{c}}\) value near the lower boundary of this range was chosen, aiming to represent the most unfavorable condition encountered in the field. The prepared samples are presented in Figure 3.  
To ensure accurate measurement and control of water content \(w\) during the experiment, several standardized procedures were implemented. Before wetting the soils to the target water content, the clay soils were oven-dried at 105 \({}^{\circ}\)C for 24 h to remove any residual water. The target water content was then achieved by evenly spraying water onto the dry soils using a high-precision digital scale. The mixtures were sealed and left for 24 h to ensure full moisture homogenization. Prior to compaction, representative soils were taken and oven-dried to verify the actual water content. Any minor deviation from the target value was corrected by adjusting the amount of added water before final compaction. During the compaction stage, the moistened soils were placed into a rigid metal mold, and \begin{table}
\begin{tabular}{c c c} \hline
**Soil Type** & **Index Property** & **Value** \\ \hline \multirow{6}{*}{Clay soils} & Specific gravity, \(G_{\text{s}}\) & 2.6 \\  & Clay content (\textless{2} \(\mu\)m) & 85\% \\  & Liquid limit, \(w_{\text{L}}\) & 63\% \\  & Plastic limit, \(w_{\text{P}}\) & 26\% \\  & USUC a classification & CH \\  & Optimum water content, \(w_{\text{opt}}\) & 27.5\% \\  & Maximum dry density, \(\rho_{\text{dmax}}\) & 1.50 \\ \hline \end{tabular} \({}^{\text{a}}\) Unified Soil Classification System.  
\end{table} 
Table 1: Soil properties. the compaction was achieved through a steel ram.