## 3 Evaluation of the Stability of a Gravel-Sand-Mixed Embankment Using Finite Element Analysis  
### Effect of Gravel Content on Embankment Behavior  
In order to investigate the effect of gravel content on the embankment behavior, finite element analysis was performed based on the geometry of an actual embankment--the second Tomei Expressway embankment in the Kasesawa area in Japan. The cross-sectional view of the embankment is shown in Figure 8, and its equivalent cross-sectional model used in the finite element analysis is shown in Figure 9. The embankment has a height of 91.9 m and a side slope of 1:1.8. [PERSON] et al. (2001) [PERSON] et al. (2001) clarified that coarse-grained material under loading stress exceeding the preceding compressive stress takes the elastoplastic compressive deformation behavior under the influence of various factors such as particle-size distribution, void ratio, etc. Since the loading stress exceeds the preceding compressive stress, and assuming that the embankment material is the Shimonoseki D-G-S, it is possible to use the elastoplastic model proposed by [PERSON] (1977) [PERSON] (1977) as the material model for the finite element analysis. In the [PERSON] and [PERSON] (1977) [PERSON] (1977) model, the dilatancy coefficient \(D\) is required, which can be obtained from the initial void ratio \(e\), compression index \(\lambda\), and the swelling index \(\kappa\)[PERSON] et al. (2001). A summary of the characteristics of the finite element model is listed in Table 3, and the parameters and calculation formulas used for the finite element analysis are shown in Table 4. Seven simulations were performed by  
Figure 7: Relationship between gravel content and material constant: (**a**) compression index (\(\lambda\)); (**b**) swelling index (\(\kappa\)).  
varying the gravel content (\(P\)) value of the embankment material. [PERSON] et al. (1982, 1983) ([PERSON] et al. (1999) ([PERSON] et al., 1999) ([PERSON] et al., 1999) reported and supported their results that the size of the gravel specimen does not significantly affect the internal friction angle. In this study, the internal friction angle of the material was considered to be equivalent to that of sand, with a size of 2 mm or less.  
Figure 10a-g show the results of the finite element analysis for embankments with gravel contents (\(P\)) of 0, 20, 30, 40, 50, 80, and 100%, respectively, while Figure 11 shows the variation in the vertical displacement at the center of the embankment with the heights for various gravel contents (\(P\)) obtained from the results of Figure 10a-g.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Formula** \\ \hline Marginal state index, \(M\) & \(M=\frac{6\sin\phi^{\prime}}{(3-\sin\phi^{\prime})}\) \\ \hline Dilatancy coefficient, \(D\) & \(D=\frac{(\lambda-\kappa)}{M(1+\epsilon_{o})}\) \\ \hline Poisson’s ratio, \(\
u\) & 0.3 \\ \hline Secondary consolidation coefficient & \(\alpha=\frac{0.4243}{1+\epsilon_{o}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters used for the finite element method.  
Figure 8: Cross-sectional view of the 2 nd Tomei Expressway embankment in the Kasesawa area in Japan.  
Figure 9: Cross-sectional view of the embankment used in the finite element analysis.  
Figure 10: _Cont._  
Figure 11 shows the total settlement at the end of embankment construction. It can be seen that the total settlement amount decreased with the increase in \(P\) from 0% up to 50% of gravel content (\(P\)), and the total settlement increased from a gravel content (\(P\)) of 50% to 100%. This trend is almost the same result as the data showing the relationship between gravel content (\(P\)) and compression index in Figure 7a. The total settlement at the end of construction is related to the material constants (compression index \(\lambda\) and swelling index \(\kappa\)). It means that the material constants are important parameters that greatly influence the result of the simulation via finite element analysis.