## 3 Model Validation for Sand-Fines Mixtures
### Evaluating the Cohesive Packing Parameter \"\(p\)\"  
The current model [Equations (1)-(6)] was applied to various sand-silt and sand-clay mixtures (Table 1), to find the suitable parameter \(p\) that reproduces the experimental results. All mixtures used consists of binary mixed soils containing large particles (i.e., sand) and fine particles (i.e., fine silt or clay), where \(R\) is very small (R \(\leq\) 0.1) and \(d_{f}\) is smaller than 0.15 mm. All mixtures in Table 1 were prepared under dry conditions. The compaction condition (loose/poured versus dense/tapped) is shown in Table 1. The median particle size (\(d_{50}\)) was used to represent the particle size when the particle size distribution is available while the average of the upper and lower sieve size was used otherwise. The best fitting value of \(p\) for each mixture is shown in Table 1. The analysis shows that \(p\) values for mixtures M1 to M10 are very close to each other (Table 1). Using an average value of \(p\) = 0.15, the experimental data can be reproduced reasonably well for all mixtures as demonstrated in Figure 3. When compared with the prediction of the ideal packing model, the use of the current model significantly improved the porosity and void ratio prediction (Figure 3). \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Sand-Fines** & **Data** & \multirow{2}{*}{**Source**} & \multirow{2}{*}{**Packing**} & \multirow{2}{*}{**\(d_{l}\) (mm)**} & \multirow{2}{*}{\(d_{f}\) (mm)**} & \multirow{2}{*}{\(R\)=\(d_{f}\)/\(d_{l}\)} & \multirow{2}{*}{\(n_{l}\) or \(e_{l}\)} & \multirow{2}{*}{\(n_{f}\) or \(e_{f}\)} & \multirow{2}{*}{\(p\)} \\
**Mixture** & & & & & & & & \\ \hline M1: & \multirow{4}{*}{[20]} & \multirow{4}{*}{P} & 0.280 & 0.0025 & 0.009 & 0.389 & 0.624 & 0.13 \\ Ottawa-Kaolinite & & & & & & & & \\ M2: Hokksund & \multirow{4}{*}{[60]} & \multirow{4}{*}{P} & 0.440 & 0.032 & 0.073 & 0.949 & 1.48 & 0.13 \\ sand-silt & & & & & & & & \\ M3: Crushed & \multirow{4}{*}{[61]} & \multirow{4}{*}{T} & 0.250 & 0.025 & 0.1 & 0.33 & 0.42 & 0.17 \\ sand-Kolinite & & & & & & & & \\ M4: Monterey & \multirow{4}{*}{[62]} & \multirow{4}{*}{T} & 0.430 & 0.030 & 0.07 & 0.82 & 1.73 & 0.14 \\ sand-silt & & & & & & & & \\ M6: Toyoura & \multirow{4}{*}{[63]} & \multirow{4}{*}{T} & 0.170 & 0.010 & 0.059 & 0.591 & 0.609 & 0.15 \\ sand-silt & & & & & & & & \\ M7: Foundry & \multirow{4}{*}{[64]} & \multirow{4}{*}{T} & 0.250 & 0.010 & 0.04 & 0.8 & 2.1 & 0.15 \\ sand-silt & & & & & & & & \\ M8:Asysros & \multirow{4}{*}{[62]} & \multirow{4}{*}{T} & 0.300 & 0.020 & 0.067 & 0.802 & 0.77 & 0.17 \\ sand-silt & & & & & & & & \\ M9: Fujian & \multirow{4}{*}{[56]} & \multirow{4}{*}{P} & 0.427 & 0.061 & 0.1 & 0.855 & 1.385 & 0.15 \\ sand-crushed silica & & & & & & & & & \\ M10: Large-fine & \multirow{4}{*}{[28]} & \multirow{4}{*}{P} & 4.470 & 0.090 & 0.02 & 0.605 & 0.739 & [0:1] \\ washed sand & & & & & & & & & \\ M11: Sand-Kaolinite & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Materials properties of selected published experimental results for sand-fines mixtures used in the model evaluation. P and T in the third column refers to the poured and tapped packing conditions respectively. For the remaining mixtures (M10 and M11), the analysis shows that \(p\) can take any value between 0 and 0.5 or 1 (Table 1) without significantly affecting the prediction. For those mixtures, packing seems to almost follow an ideal packing condition, which is also predicted by the current model as demonstrated in Figure 4. In the following section, a discussion about the packing of sand-fines mixtures in light of the recent findings is provided along with an explanation of why some mixtures deviates significantly from ideal packing while others seem to closely follow it. After that, the implications for minimum porosity (maximum dry packing density) and permeability prediction are discussed. Figure 4: Porosity, \(n\), (or void ratio, \(e\)) as function of fines fraction for mixtures (**a**) M10 and (**b**) M11.