# Numerical Study on Scale Effect of Repetitive Plate-Loading Test
## 5 Conclusions  
In this study, the limitations of the field-verification test conducted for the verification of small loading plates in the laboratory repetitive plate-loading test were mitigated, and a numerical analysis was conducted to propose the scale effect of the loading plate. The results are summarized as follows. 1. From the comparison of the field verification tests of the 50-mm and 300-mm loading plates using numerical analysis, first, in the field-test results, \(E_{\mathrm{v2}}\) did not show any trend with irregular differences with an average of 6.0% and a standard deviation of 10.0. On the other hand, in the numerical-analysis results, the results of the 50-mm loading plate exhibited a smaller trend in all areas with differences at an average of 19.0% and a standard deviation of 0.6. 2. The strain modulus was analyzed according to the loading-plate diameter under the condition of field-test embankment roadbed. The result showed that the strain modulus decreased as the loading-plate size decreased. From this result, scale effects of 1.44 (50 mm), 1.22 (150 mm), 1.17 (300 mm), 1.09 (400 mm), and 1.08 (600 mm) were proposed according to the diameter of the used loading plate. 3. The subgrade was classified into four types, and a numerical analysis was conducted using the abovementioned applied six loading-plate diameters. The result confirmed that the scale effect  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Subgrade Condition**} \\ \cline{2-7} \multicolumn{1}{c}{\(E\) (MPa)} & \multicolumn{1}{c}{**Gravel and Fine Gravel**} & \multicolumn{1}{c}{**Sand**} & \multicolumn{1}{c}{**Sandy Soil**} \\ \cline{2-7} \multicolumn{1}{c}{} & \(E_{\mathrm{v2}}\) (MPa) & \(E/E_{\mathrm{v2},782 mm}\) & \(E_{\mathrm{v2}}\) (MPa) & \(E/E_{\mathrm{v2},782 mm}\) \\ \hline
20 & 17.56 & 1.14 & 16.32 & 1.23 & 20.77 & 0.96 \\
40 & 35.36 & 1.13 & 32.82 & 1.22 & 41.68 & 0.96 \\
60 & 54.55 & 1.10 & 49.40 & 1.21 & 62.79 & 0.96 \\
80 & 70.82 & 1.13 & 66.00 & 1.21 & 83.69 & 0.96 \\
100 & 87.85 & 1.14 & 82.41 & 1.21 & 104.78 & 0.95 \\
120 & 105.56 & 1.14 & 99.03 & 1.21 & 125.64 & 0.96 \\
140 & 123.69 & 1.13 & 115.53 & 1.21 & 146.74 & 0.95 \\
160 & 141.41 & 1.13 & 131.97 & 1.21 & 167.56 & 0.95 \\
180 & 159.18 & 1.13 & 148.44 & 1.21 & 188.90 & 0.95 \\
200 & 176.73 & 1.13 & 165.02 & 1.21 & 209.74 & 0.95 \\ \hline  & Mean (standard deviation) & 1.13 (0.00) & Mean (standard deviation) & 1.21 (0.00) & Mean (standard deviation) & 0.96 (0.01) \\ \hline  & \multicolumn{6}{c}{**Subgrade Condition**} \\ \cline{2-7} \multicolumn{1}{c}{\(E\) (MPa)} & \multicolumn{1}{c}{**Cohesive Soil**} & \multicolumn{1}{c}{**Field-Test Roaded**} \\ \cline{2-7} \multicolumn{1}{c}{} & \(E_{\mathrm{v2}}\) (MPa) & \(E/E_{\mathrm{v2},782 mm}\) & \(E_{\mathrm{v2}}\) (MPa) & \(E/E_{\mathrm{v2},782 mm}\) \\ \hline
20 & 20.54 & 0.97 & 18.15 & 1.10 \\
40 & 41.01 & 0.98 & 36.38 & 1.10 \\
60 & 61.47 & 0.98 & 54.5  
varied depending on the subgrade condition. Thus, scale effects applicable to each subgrade condition were proposed. We expect that the trend equation derived using the trend curves can be used to roughly estimate the scale effect that can be applied when a loading plate with a diameter that is not used in this study is used. 4. The result of the comparison of the scale effect obtained through the numerical analysis in this study with that of the existing plate-loading test revealed that the values were somewhat different, but the same trend in which the subgrade condition of sand exhibited a higher scale-effect calculation factor than that of cohesive soil was confirmed. 5. The strain modulus of the repetitive plate-loading test obtained through the numerical analysis was compared with the elastic modulus of the corresponding subgrade according to the subgrade condition. The result showed that the calculated strain modulus approached closer to the elastic modulus as the loading-plate size increased.