## 3 Evaluation of the Stability of a Gravel-Sand-Mixed Embankment Using Finite Element Analysis
### Engineering Application of the Proposed Equation  
Finite element analysis was performed to evaluate the engineering application of the proposed gravel correction formula for estimating the material constants of gravel  
Figure 11: Total settlement of the embankment after completion using the constants obtained from the one-dimensional compression test.  
Figure 10: Deformation of embankment at various gravel contents using material constants obtained from one-dimensional compression test (displacements scaled up 25 times): (**a**) P = 0%; (**b**) P = 20%; (**c**) P = 30%; (**d**) P = 40%; (**e**) P = 50%; (**f**) P = 80%; (**g**) P = 100%.  
sand mixtures. The proposed method was compared with material constants directly obtained from the one-dimensional compression test, and material constants corrected with the Walker-Holtz method. Figure 12a-c show the results of the analysis when the embankment material was a gravel material with gravel content (\(P\)) = 50%. It can be seen that the deformation behavior in Figure 12c is somewhat identical to the deformation behavior in Figure 12a. Hence, the deformation of the embankment was better represented using the new method rather than the Walker-Holtz method. The analysis result using the material constants corrected with the Walker-Holtz method, as shown in Figure 12b, had a significantly smaller amount of deformation in comparison to the other two sets of material constants.  
A comparison of the vertical displacement distribution with height at the center of the embankment between three different sets of material constants is shown in Figure 13. It can be seen that the results using the material constants corrected with the Walker-Holtz method underestimated the vertical displacement in comparison to the results using the material constants directly obtained from the one-dimensional compression test. In addition, it can be seen that the results of the analysis performed from the material constants corrected with the new method proposed in this study almost accurately reproduced the analysis results using the material constants obtained from the test. From the above results, it can be derived that the material constants obtained from the formula proposed in this study estimated the material constants obtained from the experiment almost accurately, and the same results were found for the total settlement at the end of construction, as shown in  
Figure 12: Deformation of embankment for gravel content (\(P\)) = 50 (displacements scaled up 25 times): (**a**) analysis results using material constants obtained from one-dimensional compression test (experimental result); (**b**) analysis results using material constants corrected using the Walker–Holtz method (Walker–Holtz method); (**c**) analysis results using material constants corrected with the formula proposed in this study (new method).  
Figure 14. At low gravel content (\(P\)) in the range of 0% to 30%, the total settlement at the end of construction using the material constant corrected with the Walker-Holtz method was estimated almost exactly as the analysis result using the material constant directly obtained from the experiment. However, it can be seen that, at a gravel content of more than 30%, the results were significantly different from the analysis results using the directly obtained material constants. The total settlement from the material constant corrected using the new method showed almost the same value as the analysis result using the material constant directly obtained from the experiment for all values of \(P\). From these results, it was revealed that the correction formula proposed in this study could estimate the material constants of the measured values almost accurately and that it could be sufficiently applied for the simulation of settlement in the embankment using the finite element analysis.