# 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 a previous study mentioned earlier, [PERSON] et al. [6] conducted a field test to verify the small loading plate with of 50 mm in diameter and compared the results with those of the 300-mm loading plate. In this section, the repetitive plate-loading tests of the 50-mm and 300-mm loading plates were numerically analyzed by modeling the embankment roadbed where the existing field test was conducted. The results were compared with those of the existing field-verification test. Areas with various strain moduli were simulated similar to those in the field-verification test by varying the value of the elastic modulus among the input properties. All conditions except for the size of the loading plate were the same. Tables 3 and 4 list the results of the field test and numerical analysis, respectively. The primary strain modulus (\(E_{v1}\)), secondary strain modulus (\(E_{v2}\)), and ratio of the secondary to the primary strain moduli (\(E_{v2}\)/\(E_{v1}\)) were summarized. In particular, the difference in E\({}_{v2}\) applied as the subgrade strain modulus is shown as graphs in Figure 3, and the correlation between the two results was analyzed. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Subgrade Type**} & **Unit Weight** & **Friction** & **Dilatancy** & **Cohesion** & **Elastic** & **Loading Plate** \\  & **(kN/m\({}^{\circ}\))** & **Angle (\(\circ\))** & **Angle (\(\circ\))** & **(kPa)** & **Modulus (MPa)** & **Dia. (mm)** \\ \hline \multirow{3}{*}{
\begin{tabular}{c} Embankment \\ roadbed \\ \end{tabular} } & Gravel and fine gravel & 20.0 & 40 & 10 & 1 & \\ \cline{2-6}  & Sand (fine grain) & 20.0 & 35 & 5 & 3 & \\ \cline{2-6}  & Sandy soil & 19.0 & 25 & 0 & 15 & (Spacing: 10) & \(50,150,300\), \\ \cline{2-6}  & Cohesive soil & 18.0 & 15 & 0 & 25 & \\ \hline Field-test embankment roadbed & 18.9 & 35.3 & 5.3 & 4.7 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of the parameters used in the numerical analysis. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Region**} & **Stiffness \(E_{v1}\) (MPa)** & \multicolumn{3}{c}{**Stiffness \(E_{v2}\) (MPa)**} & \multicolumn{3}{c}{\(E_{v2}\)/\(E_{v1}\)} & \multirow{2}{*}{**Difference,**} \\  & **Loading Plate** & **Loading Plate** & **Loading Plate** & **Loading Plate** & **Loading Plate** & **Loading Plate** & **Loading Plate** \\  & **(50 mm)** & **(300 mm)** & **(50 mm)** & **(300 mm)** & **(50 mm)** & **(50 mm)** & **(300 mm)** \\ \hline A & 30.7 & 17.3 & 41.0 & 39.8 & 1.3 & 2.3 & 2.9 \\ B & 31.5 & 12.9 & 47.6 & 43.9 & 1.5 & 3.4 & 8.3 \\ C & 28.9 & 15.7 & 48.0 & 46.4 & 1.7 & 3.0 & 3.4 \\ D & 44.1 & 29.0 & 51.7 & 53.7 & 1.2 & 1.9 & 3.6 \\ E & 51.2 & 30.2 & 57.1 & 59.4 & 1.1 & 2.0 & 3.9 \\ F & 43.6 & 31.1 & 59.4 & 55.1 & 1.4 & 1.8 & 7.7 \\ G & 28.7 & 27.4 & 60.1 & 56.1 & 2.1 & 2.0 & 7.1 \\ H & 47.0 & 32.1 & 63.8 & 61.2 & 1.4 & 1.9 & 4.2 \\ I & 36.2 & 35.3 & 64.9 & 60.0 & 1.8 & 1.7 & 8.2 \\ J & 52.0 & 25.2 & 66.7 & 69.1 & 1.3 & 2.7 & 3.5 \\ K & 30.3 & 27.3 & 69.5 & 70.7 & 2.3 & 2.6 & 1.6 \\ L & 34.5 & 31.2 & 74.9 & 67.4 & 2.2 & 2.2 & 11.2 \\ M & 39.8 & 40.6 & 76.4 & 70.6 & 1.9 & 1.7 & 8.3 \\ N & 68.3 & 47.1 & 111.3 & 96.3 & 1.6 & 2.0 & 15.6 \\ O & 54.2 & 52.3 & 115.4 & 117.9 & 2.1 & 2.3 & 2.1 \\ P & 106.8 & 70.1 & 139.5 & 142.5 & 1.3 & 2.0 & 2.1 \\ Q & 88.5 & 52.2 & 146.9 & 159.6 & 1.7 & 3.1 & 7.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Repetitive plate loading field-test results ([PERSON] et al. [6]). When the degree of compaction was lower, the roadbed exhibited a large plastic strain at the initial load and gradually exhibited an elastic behavior at repetitive loads. In other words, \(E_{v1}\) is a strain modulus expressing the initial settlement, and \(E_{v2}\) is a strain modulus expressing the subsequent elastic settlement. Accordingly, \(E_{v1}\) is more affected by the degree of compaction.