## 3 Materials, Methods, and Equipment
### Specim Preparation and Test Method for Calibration of Relative Densities
While maximum and minimum void ratios followed ASTM D4253 and D4254 standards, the compaction methodology was tailored for laboratory conditions using a wooden box and Proter electro-pneumatic hammer instead of field-scale standards like ASTM D698 or D1557. This equipment selection enabled precise, repeatable energy application in confined settings, with the hammer calibrated empirically through iterative trials to achieve target densities through controlled compaction duration and layer thickness. Moisture content determination adhered strictly to ASTM D2216, maintaining compatibility with standard calculations. This hybrid approach diverged from traditional field compaction practices while ensuring that there were valid relative density calculations through ASTM-compliant void ratio determinations. Though future refinements could align with emerging small-scale modeling standards, the current protocol's repeatability and cross-validation with established measurements provide sufficient rigor for the experimental scope. Then, 15 trials were conducted for direct shear tests (5 relative densities \(\times\) 3 normal stresses) and 30 trials were conducted for interface shear tests (5 relative densities \(\times\) 3 normal stresses \(\times\) 2 pile materials). Each trial represents an independent specimen preparation and testing sequence, ensuring statistical reliability. For direct shear tests, three specimens per relative density (10%, 35%, 50%, 75%, 95%) were tested under distinct normal stresses (54.5 kPa, 109 kPa, 163.5 kPa), while interface shear tests doubled this to accommodate both steel-concrete and timber-concrete interfaces. Replicate testing (3-5 iterations per condition) was performed for critical parameters (e.g., friction angles, unit weights) to ensure consistency, with uncertainties reported in Tables 4-6 (\(\pm 0.5^{\circ}\) for \(\varphi\), \(\pm 1.2\) kN/m\({}^{3}\) for \(\gamma_{\mathrm{d}}\)). \begin{table}
\begin{tabular}{l l l l l l} \hline
**Relative Density, D\({}_{\mathrm{r}}\) (\%)** & **10** & **35** & **50** & **75** & **95** \\ \hline Description & Very Loose & Loose & Medium & Dense & Very Dense \\ \hline Void Ratio, e & 0.886 \(\pm\) 0.015 & 0.771 \(\pm\) 0.012 & 0.682 \(\pm\) 0.010 & 0.565 \(\pm\) 0.008 & 0.476 \(\pm\) 0.006 \\ \hline Dry Unit Weight, \(\gamma_{\mathrm{d}}\) (kN/m\({}^{3}\)) & 14.1 \(\pm\) 0.3 & 15.2 \(\pm\) 0.3 & 15.9 \(\pm\) 0.3 & 17.0 \(\pm\) 0.3 & 18.0 \(\pm\) 0.4 \\ \hline Internal Friction Angle, \(\varphi\) (\({}^{\circ}\)) & 28 \(\pm\) 0.5 & 30.9 \(\pm\) 0.6 & 33.7 \(\pm\) 0.6 & 36.6 \(\pm\) 0.7 & 40 \(\pm\) 0.8 \\ \hline Permeability, k (cm/s) & 1.0 \(\times\) 10\({}^{-2}\)\(\pm\) 8\% & 2.6 \(\times\) 10\({}^{-3}\)\(\pm\) 8\% & 1.1 \(\times\) 10\({}^{-3}\)\(\pm\) 8\% & 3.0 \(\times\) 10\({}^{-4}\)\(\pm\) 12\% & 1.0 \(\times\) 10\({}^{-4}\)\(\pm\) 12\% \\ \hline \end{tabular} Notes: 1. Permeability values derived via constant-head tests (ASTM D2434) for D\({}_{\mathrm{r}}\) = 10–50% and falling-head tests (ASTM D5084) for D\({}_{\mathrm{r}}\) = 75–95%. 2. Uncertainties reflect method-specific precision: \(\pm\)8% for constant-head, \(\pm\)12% for falling-head. 3. Void ratios and unit weights calculated from triplicate trials; uncertainties represent 95% confidence intervals.  
\end{table} 
Table 4: Sand properties with variation in relative density.