## 3 Results
### Dynamically Induced Porewater Pressure Characteristics  
The observed excess PWP at the lower transducer (PP1) for the clean sand (i.e., ECS00) was the highest throughout the 3-stage shaking for all the studied soil specimens. Figures 8-10 show the results of the evolution of excess dynamic PWP at the lower pore pressure transducer during the three shaking cycles for all the studied soil samples. From the graph legends, PP1 is the name of the pressure transducer installed at the lower end of the SB, F10 signifies the shaking frequency at 10 Hz, and A2, A3, and A4 represent the amplitudes of 2, 3, and 4, respectively. The confirmation of liquefaction in Equation (2) was executed by computing the excess pore pressure ratio \((r_{u})\), obtained by the ratio of the excess pore pressures \((\Delta u)\) to the total effective stresses \((\sigma^{\prime})\). \[r_{u}=\frac{\Delta u}{\sigma^{\prime}} \tag{2}\]  
The liquefaction parameter \((r_{u})\) has been used by several researchers, e.g., [6]. The breakdown of its interpretation is as follows:  
* When \(r_{u}\geq 1\), it implies the occurrence of full liquefaction (FL);
* If \(r_{u}=0.25\) to \(0.70\), the likelihood of partial liquefaction (PL) is reported;
* If \(r_{u}=0\), a no liquefaction case is reported (NL). The number of cycles required for either FL or PL reduces as the kaolinite content decreases correspondingly. Soil samples with more kaolinite (i.e., ECS20 and ECS30) did not liquefy but showed strain-softening behavior and dilative tendencies at higher shaking intensities. The scaling laws, known as the similitude laws, are well-known key factors for consideration while interpreting the physical model results of particulate material, such as soil, in shaking table testing with a finite boundary domain. The key factors that determine similitude per liquefaction physical models have already been discussed in the literature. The relevant and typical applicable scaling laws in the current study adopted those provided by [18] and are summarized in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample/Properties** & \begin{tabular}{c} **Moist Mass** \\ **(kg)** \\ \end{tabular} & \begin{tabular}{c} **Dry Mass** \\ **(kg)** \\ \end{tabular} & \begin{tabular}{c} **Moisture** \\ **Content (\%)** \\ \end{tabular} & \begin{tabular}{c} **Specific** \\ **Gravity (Gs)** \\ \end{tabular} & \begin{tabular}{c} **Wet Unit Wt.** \\ **(kN/m3)** \\ \end{tabular} & \
\begin{tabular}{c} **Estimated** \\ **Void Ratio** \\ \end{tabular} &
\begin{tabular}{c} **Relative** \\ **Density (\%)** \\ \end{tabular} \\ \hline ECS00 & 51.79 & 40.00 & 29.48 & 2.60 & 19.82 & 0.600 & 60 \\ ECS05 & 49.59 & 39.94 & 24.16 & 2.54 & 18.98 & 0.600 & 77 \\ ECS10 & 49.48 & 40.00 & 23.70 & 2.61 & 19.38 & 0.600 & 72 \\ ECS15 & 49.36 & 40.04 & 23.28 & 2.53 & 19.33 & 0.590 & 76 \\ ECS20 & 49.46 & 39.46 & 25.34 & 2.59 & 19.37 & 0.650 & 68 \\ ECS30 & 49.50 & 40.02 & 23.69 & 2.56 & 17.73 & 0.540 & 77 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of experimental shaking table-physical model properties. Figure 8: Excess PWP during the first shaking cycle. Figure 9: Excess PWP during the second shaking cycle. The fundamental physics used for deriving the scaling laws, as explained by [7], are typically governed by the fundamental laws of statics, which simulate the mass and force equilibrium of the soil structure, pore water, and the soil constitutive laws (i.e., the stress-strain characteristics). However, it is out of the scope of the current research to study the soils' deformation characteristics; instead, the main interest herein is the study of the evolution/generation of the soil-fluid/excess (PWP) mechanisms. The soil-fluid similitude is complex, controversial, and poorly understood, as stated in the literature [7; 18]. Overall, the significance of the similitude laws is their requirements