# Numerical Study on Scale Effect of Repetitive Plate-Loading Test
## 4 Analysis of the Results
### Comparison with the Results of the Existing Field-Verification Test
In South Korea, among the measurements of a repetitive plate-loading test, \(E_{v2}\) is conventionally used as the strain modulus to manage the quality of the roadbed, whereas \(E_{v1}\) is not adopted for roadbed management. However, the ratio between \(E_{v2}\) and \(E_{v1}\) (\(E_{v2}\)/\(E_{v1}\)) is used to manage the degree of compaction of the roadbed. Accordingly, \(E_{v2}\) is the strain modulus of the roadbed, and \(E_{v2}\)/\(E_{v1}\) indicates the compaction degree of the roadbed. In the field test, the difference in the measurements between \(E_{v1}\) and \(E_{v2}\) was irregular both for the 50 mm and 300 mm loading plates. The results of either loading plate did not show a tendency to be smaller or larger. In every area, both the 50 mm and 300 mm loading plates exhibited a variety of distribution in the values of \(E_{v2}\)/\(E_{v1}\), and the difference between \(E_{v1}\) and \(E_{v2}\) was also irregular. On the other hand, in the numerical analysis, the results of the 50 mm loading plate were smaller than those of the 300 mm loading plate, and the deviation was not large for both \(E_{v1}\) and \(E_{v2}\). The value of \(E_{v2}\)/\(E_{v1}\) was also 2.0 for both the loading plates in every range, and the difference between \(E_{v2}\) and \(E_{v1}\) tended to be constant. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline  & \multicolumn{2}{c}{**Stiffness \(E_{v1}\) (MPa)**} & \multicolumn{2}{c}{**Stiffness \(E_{v2}\) (MPa)**} & \multicolumn{2}{c}{\(E_{v2}\)/\(E_{v1}\)} & \multicolumn{2}{c}{**Difference, Difference,**} \\ \cline{2-9} \multicolumn{1}{c}{_E_ **(MPa)**} & \multicolumn{1}{c}{**Loading Plate**} & \multicolumn{1}{c}{**Loading Plate**} & \multicolumn{1}{c}{**Loading Plate**} & \multicolumn{1}{c}{**Loading Plate**} & \multicolumn{1}{c}{**Loading Plate**} & \multicolumn{1}{c}{**Loading Plate**} & \multicolumn{1}{c}{**\(E_{v1}\)(\%)**} & \multicolumn{1}{c}{\(E_{v2}\) (\%)**} \\  & \multicolumn{1}{c}{**Plate (60 mm)**} & \multicolumn{1}{c}{**(300 mm)**} & \multicolumn{1}{c}{**Plate (50 mm)**} & \multicolumn{1}{c}{**(60 mm)**} & \multicolumn{1}{c}{**Plate (50 mm)**} & \multicolumn{1}{c}{**(600 mm)**} & \multicolumn{1}{c}{**(600 mm)**} & \multicolumn{1}{c}{**(600 mm)**} \\ \hline  
\hline \multicolumn{9}{l}{Average difference} & & & & & & 18.23 & 19.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical analysis results of the field-test embankment roadbed. Figure 3: Correlation analysis comparison between the field-test and numerical-analysis results: (a) field-test results ([PERSON] et al. [6]); (b) numerical-analysis results. As for the result of the field test, [PERSON] et al. (2018) found that the 50-mm loading plate was more affected by solid materials with large particle sizes, which are often included in rough embankment roadbeds, than the 300-mm loading plate, and thus, the strain modulus was excessively measured. As the elasto-plastic model used in this numerical analysis assumed homogeneous areas and excluded the effect of roadbed materials with large particle sizes, the strain modulus for the 50 mm loading plate was not excessively measured and the values of \(E_{\
u 2}/E_{\
u 1}\) were constant. Consequently, the numerical analysis could improve the limitations of the field test, and the sole effect of the loading plates could be identified. Figure 4 shows the linear regression analysis of the field test and numerical analysis results of the 50-mm and 300-mm loading plates. Equation (5) represents the regression equation of the field test, and Equation (6) represents the regression equation of the numerical analysis results derived from the analysis. The coefficient of determination of the field-test regression equation was 0.974, and the standard error was approximately 3.7. The average difference from the actual data was approximately 5.5%. For the regression equation of the numerical analysis results, the coefficient of determination was 0.999, and the standard error was approximately 0.7. The average difference from the actual data was approximately 1.8%.