## 2 Materials and Methods
### Soil Sample Extraction and Characterization
#### 2.2.1 First borehole  
The first borehole involved extraction of a continuous profile at a depth of 30 m. This process was performed by rotating a barrel into the ground following the recommendations of ASTM D2113 [56]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Borehole** & **Standard** & **Parameter** & **Borehole** & **Standard** & **Parameter** \\ \hline \hline \multirow{6}{*}{1} & ASTM D 2487 [46] & USCS Classification & & ASTM D 2487 [46] & USCS Classification \\  & ASTM D 4318 [47] & LL, PL, PI & & ASTM D 4318 [47] & LL, PL, PI \\  & ASTM D 1140 [48] & & & \\  & ASTM D 7928 [49] & & & \\  & ASTM D 854 [50] & Gs & 2 & ASTM D 854 [50] & Gs \\  & ASTM D 5298 [51] & & & \\  & Unconfined compressive & & & \\  & strength & & & \\  & ASTM D 2974 [54] & Organic Content & & \\  & ASTM D 4972 [55] & pH determination & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Summary of the tests conducted for each borehole. Figure 7: Empirical methodology employed in this study. The test specimens were reconstituted from the soil extracted from this borehole, selecting material from depths between 3 and 7 m as a representative. Soil fractions finer than 2 mm were sieved, homogenized, and used as shown in Figure 8a. The samples were molded using the Harvard Miniature apparatus shown in Figure 8b, following [PERSON]'s STP 479 guidelines [57]. Their characteristics are presented in Table 6. This apparatus was selected to ensure internal homogeneity during sample reconstitution. However, owing to the mold dimensions, the maximum particle size was limited to 2 mm to comply with ASTM D2166. Additionally, Figure 9 and Table 7 show the particle size distribution of the homogenized soil obtained through sieve and sedimentation analyses. According to [PERSON] et al. [15], the distribution of solid particles is related to the distribution of pore sizes and void spaces. The SWCC represents the void ratio distribution, whereas the particle size distribution curve represents the distribution of solid particles. Owing to this relationship, the particle size distribution curves exhibit shapes similar to those of the SWCCs when plotted on a semi-logarithmic scale. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dry Density** & **Gs** & **LL** & **LP [\%]** & **IP [\%]** & **Gravel** & **Sand** & **Fine** & **USCS** \\
**[g/cm\({}^{3}\)]** & **Gs** & **[\%]** & **LP [\%]** & **IP [\%]** & **Fraction [\%]** & **Fraction [\%]** & **Fraction [\%]** & **Classification** \\ \hline \hline
1.5 & 2.52 & 33 & 25 & 9 & 0 & 30 & 70 & ML \\ \hline \end{tabular}
\end{table} 
Table 6: Properties of reconstituted soil samples. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Particles Smaller Than [mm]** & **Soil Fraction** \\ \hline
4.75 & 100.00\% & Gravel & 0.00\% \\
0.425 & 91.74\% & Sand & 30.17\% \\
0.075 & 69.83\% & Silt & 51.55\% \\
0.002 & 18.27\% & Clay & 18.27\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Percent finer and soil particle size distribution. Figure 8: (**a**) Sieving and homogenization process for the reconstituted samples; (**b**) Harvard Miniature Apparatus. Therefore, the particle size distribution acquires additional value for understanding the behavior of unsaturated soils, as a soil with a unimodal particle size distribution will also display a unimodal pore size distribution behavior. This similarity between the SWCC and particle size distribution curve suggests that the Fredholm and Xing equation can be adapted (Equation (7)) to describe the unimodal particle size distribution curve:  
\[\mathrm{P_{P}(d)}\ =\frac{1}{\left\{\ln\left[\exp(1)+\left(\frac{a_{\mathrm{gr}}}{d} \right)^{n_{\mathrm{gr}}}\right]\right\}^{n_{\mathrm{gr}}}}\cdot\left\{1-\left[ \frac{\ln\left(1+\frac{d_{\mathrm{r}}}{d}\right)}{\ln\left(1+\frac{d_{\mathrm{ r}}}{d_{\mathrm{m}}}\right)}\right]^{7}\right\} \tag{7}\]  
where:  
\(\mathrm{P_{P}(d)}\) = percentage of particles passing a particular particle size.