# Role of Bimodal Water Retention Curve on the Unsaturated Shear Strength
## 4 Results of Laboratory Testing  
Figure 2 shows both 70S30K and 50S50K specimens are in the dry optimum of their corresponding compaction curves. The maximum dry densities for specimens 70S30K and 50S50K are 1.95 Mg/m\({}^{3}\) and 1.845 Mg/m\({}^{3}\), respectively. The optimum water content for specimens 70S30K and 50S50K are 9.5% and 14%, respectively. The compaction curve for 70S30K illustrates that a higher maximum dry density is observed at a lower optimum water content as compared to 50S50K. Dry optimum of water content was selected to improve the possibility of producing compacted sand-kaolin bimodal soils, as suggested by [PERSON] and [PERSON] [46]. Figure 3 shows a double-humped grain size distribution for both specimens. It can be observed that the main constituents for both specimens are medium-sized sand and silt-sized kaolin. The soil properties of the specimens are listed in Table 2.  
Figure 3: Grain size distribution curve. Figure 2: Compaction curve. Figures 4 and 5 depict volumes of water for different matric sutions that were calculated from mass of water divided by unit weight of water. The volume of water should reach equilibrium before increasing matric suction to a higher value during WRC testing. Moreover, Figures 3 and 4 show that a significant drop in volume of water does not necessarily mean that the corresponding suction is the \(AEV\) of the specimen. For example, there is a significant decrease in the volume of water between matric suction 95 and 200 kPa, but none of them is \(AEV\). Figure 6 exhibits WRC measurements that are fitted using Equation (1). The comprehensive fitting parameters of the equation are listed in Table 3. Table 3 shows that 70S30K has a higher \(AEV\) in the first and second sub-curves of WRC than the respective air-entry values of 50S50K. This can be explained by the fact that the percentage of coarse particles for 70S30K is higher than that for 50S50K, resulting in a faster water flow out of 70S30K than that of 50S50K. Table 3 also indicates that the [PERSON] et al. [16] equation performed very well, as shown by R\({}^{2}\) close to 1. \begin{table}
\begin{tabular}{c c c} \hline
**Soil Properties** & **70S30K** & **50S50K** \\ \hline Dry Density, \(\gamma_{d}\) (Mg/m\({}^{3}\)) & 1.85 & 1.65 \\ Water Content, \(w\) (\%) & 7.50 & 13.50 \\ Saturated Water Content, \(w_{sat}\) (\%) & 17.7 & 20.5 \\ Void Ratio, \(e\) & 0.43 & 0.64 \\ Liquid Limit, \(LL\) (\%) & 27.50 & 38.00 \\ Plastic Limit, \(PL\) (\%) & 14.76 & 19.72 \\ Plasticity Index, \(l_{p}\) (\%) & 12.74 & 18.28 \\ Specific Gravity, \(G_{s}\) & 2.61 & 2.59 \\ GSD–Sand (\%) & 73.3 & 50.0 \\ GSD–Silt (\%) & 19.2 & 36.0 \\ GSD–Clay (\%) & 7.5 & 14.0 \\ Unified Soil Classification System & SC & CL \\ (USCS) & (Clayey Sand) & (Sandy Clay with Low Plasticity) \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of Soil Properties. Figure 4: Equalization time of soil specimen 70S30K. Figure 5: Equalization time of soil specimen 50S50K. Figure 6: WRC of 70S30K and 50S50K. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **70S30K** & **50S50K** \\ \hline \(\theta_{\delta 1}\) & 0.310 & 0.341 \\ \(\theta_{\delta 2}\) & 0.248 & 0.269 \\ \(\psi_{\alpha 1}\) or \(AEV_{1}\) (kPa) & 6 & 20 \\ \(\psi_{m1}\) (kPa) & 10 & 25 \\ \(s_{1}\) & 1.50 & 1.17 \\ \(\theta_{\mu 2}\) & 0.000 & 0.000 \\ \(\psi_{\mu 2}\) or \(AEV_{2}\) (kPa) & 50 & 75 \\ \(\psi_{m2}\) (kPa) & 152 & 225 \\ \(\psi_{r2}\) (kPa) & 1175 & 1500 \\ \(s_{2}\) & 1.92 & 1.00 \\ R\({}^{2}\) & 0.9989 & 0.9985 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: WRC fitting parameters based on bimodal equation proposed by [PERSON] et al. [17]. Figure 7 shows that 70S30K has two dominant pore sizes at radius 0.015 mm and 0.001 mm with frequency 0.017 and 0.057, respectively. Figure 6 also indicates that the dual porosity structure of 50S50K is observed at pore radius 0.004 mm and 0.001 mm, having frequencies of 0.014 and 0.111, correspondingly.