## 2 Theoretical Background
### Relationship between Void Ratio and Dry Density in Gravel-Sand Mixtures
#### 2.2.3 Compression Characteristics of D-G-S  
To estimate the compression characteristics of gravel-sand mixtures considering various gravel contents \(P\), the compression curves for sand (\(P\) = 0%) and gravel (\(P\) = 100%) were utilized, as shown in Figure 5. The individual void ratios \(e_{\rm g}\) and \(e_{\rm g}\) at a specified vertical stress \(\sigma_{\rm v}\) were obtained based on Figure 5 and then substituted into Equation (5) while utilizing the values of \(R_{\rm m}\) shown in Figure 5. The overall void ratio of the gravel-sand mixture corresponding to each gravel content (\(P\)) value was then obtained for specified values \(\sigma_{\rm v}\). The \(e\) log \(\sigma_{\rm v}\) curve was then estimated and plotted for any gravel content value \(P\), and the values of the compression index (\(\lambda\)) and swelling index (\(\kappa\)) were predicted as well.  
Using the method presented in this study, the predicted compression curves for \(P\) = 20%, 40%, and 80% using an \(R_{\rm m}\) of 0.85 was compared with the measured data, as shown in Figure 6, and it can be seen that the predicted curves fairly agreed with the measured data. Therefore, \(R_{\rm m}\) obtained from the compaction test could be utilized to reasonably predict the compression curves of the gravel-sand mixture. As a summary, and for comparison, Figure 7a,b show the comparison of the predicted and measured compression index and swelling index for various values of \(R_{\rm m}\). As shown, the swelling  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specimen** & \(G_{e}\)**(\(P\))** & \(e\)**(\(P\))** & \(\rho_{d}\)**(\(P\) /cm\({}^{3}\))** \\ \hline \(P\)(0\%) & 2.650 & 0.661 & 1.616 \\ \(P\)(20\%) & 2.682 & 0.588 & 1.686 \\ \(P\)(30\%) & 2.678 & 0.570 & 1.703 \\ \(P\)(40\%) & 2.674 & 0.554 index varied with gravel content with the values ranging between 0.005 and 0.015, in which the predicted curves using \(R_{\rm m}\) of 0.85 and 1.0 showed closer agreement with the measured curve. Similarly, for the compression index, the predicted curves with \(R_{\rm m}\) of 0.85 and 1.0 showed good agreement with the measured curve. These results showed that parameters at various gravel contents could be predicted by using the mixing degree \(R_{\rm m}\) of the gravel material and the data of the one-dimensional compression test of sand only (\(P=0\%\)) and gravel only (\(P=100\%\)). Hence, the method can be used to quantitatively assess the influence of the gravel ratio on the compression characteristics of mixed materials. It should be noted, however, that the test results presented herein are valid only for the indicated conditions of D-G-S (in terms of grain-size distributions, initial water content, and compaction energy), and other conditions may lead to different values of \(R_{\rm m}\). Furthermore, the degree of weathering of the D-G-S can also affect the compressibility of the mixture.  
Figure 5: Compression characteristics of sand and gravel components of D-G-S.  
Figure 6: Comparison between measured and predicted compression curves for \(P=20\%\), 40%, and 80% using an \(R_{\rm m}\) of 0.85.