# Numerical Study on Scale Effect of Repetitive Plate-Loading Test
## 4 Analysis of the Results
### Examination through Comparison with the Scale Effect of the Existing Plate-Loading Test
Table 7 summarizes these results and the results obtained by replacing the scale-effect calculation factor of the existing plate-loading test, i.e., \(n\), with a.  
Figure 7: Scale effect normalized to the reference loading plate of the repetitive plate-loading test (762 mm): (**a**) gravel and fine gravel; (**b**) sand; (**c**) sandy soil; (**d**) cohesive soil. The list in Table 7 indicates that the scale-effect calculation factor of the plate-loading test was approximately 0.5, on average, for the subgrade condition of sand and zero for cohesive soil, and a median value appeared to have been used in Korean Standard Assocation [11]. On the other hand, the scale-effect calculation factor of the repetitive plate-loading test obtained through the numerical analysis in this study was approximately 0.25, on average, for the subgrade condition of sand and approximately 0.1 for cohesive soil, which were somewhat different from those of the plate-loading test. However, the tendency that the scale-effect calculation factor of sand was higher than that of cohesive soil was the same. The difference in the scale-effect calculation factor between the two tests can be attributed to various causes. First, it could be caused by the assumed or changed conditions in the course of derived Equation (13). The factors were the slope of the stress and amount of settlement under a single loading in the plate-loading test and the slope under the repetitive loading in the repetitive plate-loading test, which may have also caused the difference. Moreover, the results were from the laboratory test and numerical analysis, respectively, and the subgrade condition was not identical despite the condition of the same sand or cohesive soil. The difference appeared to have been caused by these, and further studies by laboratory tests are required for more accurate comparison and analysis. Analysis of the Relationship between the Subgrade Strain Modulus (\(E_{v2}\)) of the Repetitive Plate-Loading Test and Elastic Modulus (\(E\))  
As aforementioned, the subgrade strain modulus of the repetitive plate-loading test is currently used in the field as a quality-control method. However, it represents the solution of the boundary-value problem, and its value varies depending on the condition. Therefore, it cannot be considered as a property of the subgrade material and is different from the elastic modulus, which is a property of the subgrade. [PERSON] et al. [2] proposed a method of estimating the elastic modulus using the subgrade reaction and strain moduli and indirectly estimated the relationship between the strain and elastic moduli using the relationship between the subgrade reaction and strain moduli. In the field or roadbed cases designed for laboratory tests, assessing an accurate elastic modulus of the corresponding subgrade is difficult. On the other hand, in the numerical analysis, the elastic modulus of the subgrade clearly exists as an input property. Therefore, directly analyzing the relationship between the strain modulus, measured from the repetitive plate-loading test simulated through the numerical analysis, and the elastic modulus is possible in the same subgrade. This section presents the comparison of the strain modulus results of the repetitive plate-loading test simulated using numerical analysis with the elastic modulus of the corresponding subgrade according to the subgrade conditions classified in this study. The results are shown in Figure 8. The red solid lines represent the elastic modulus, and the results of the strain modulus according to the loading-plate size are displayed. As shown in Figure 8, the 50-mm loading plate with the smallest diameter exhibited the largest difference in the elastic modulus, and the difference gradually decreased as the loading-plate diameter increased. This phenomenon was also explained by the increase in the