# Numerical Study on Scale Effect of Repetitive Plate-Loading Test
## 1 Introduction  
To control the quality of earthworks in the field, a plate-loading test for roads (KS F 2310, Korea) and a plate-loading test for railways (DIN 18134, Germany) are conducted in Korea. These tests are mainly conducted because they are simpler and less time-intensive than the field-density test with respect to compaction quality-control criteria based on support stiffness [1]. Both tests calculate the elastic modulus (\(E\)) required to assess the stiffness of a material using the bearing-capacity factor whose concept is similar to that of elastic modulus. The tests require considerable cost and time because they are conducted in the field using heavy machinery, and loading plates with diameters larger than 300 mm are specified as a standard [2]. In addition, as the names of the two methods are the same, this study uses the terms \"plate-loading test\" for the plate-loading test for roads (KS F 2310, Korea) and \"repetitive plate-loading test\" for the plate-loading test for railways (DIN 18134, Germany). The plate-loading test uses the subgrade reaction modulus (\(k_{30}\)), and the repetitive plate-loading test uses the strain modulus (\(E_{v2}\)) as the bearing-capacity factor. In the plate-loading test, the scale effect is applied according to the size of the loading plate. In the repetitive plate-loading test, however, the scale effect of the loading plate is not considered. Meanwhile, in the case of the roadbed of a concrete track, whose domestic construction has increased, settlement frequently occurs because of defective natural ground treatment and drainage aswell as insufficient embankment construction, causing problems that relate directly to railway safety [3]. In general, to reinforce the soft ground during the construction of underground structures and tunnels, various injection methods have been researched and applied, including consolidation grouting for sand and weathered soil, and permeation grouting for weathered rocks with developed joints. Their reinforcement effects are assessed in terms of the strength, bearing capacity, and stiffness [4]. For railway roadbeds, however, re-settlement continuously occurs because the roadbed itself cannot be reinforced, although track-restoration methods are being implemented. Cases of direct reinforcement of the railway roadbed and studies on the reinforcement method to prevent re-settlement are also insufficient [5]. To develop reinforcement materials and methods, several small-scale laboratory tests are required to correct numerous errors that may occur in the initial verification stage. In a concrete track roadbed that is sensitive to settlement, assessing the reinforcement effect in terms of the bearing capacity and stiffness, instead of the strength, is reasonable. In current laboratory tests, however, only uniaxial compressive strength tests can be conducted on reinforced subgrade samples. In addition, many difficulties are encountered in assessing the stiffness through laboratory tests because a reaction system that can replace heavy machinery and a large soil tank that considers the influence range of a loading plate with a diameter larger than 300 mm are required. [PERSON] et al. [6] mentioned the necessity for a loading plate with a diameter of less than 300 mm, smaller than those generally used in the laboratory repetitive plate-loading test. To verify the results of the use of a 50-mm-diameter loading plate, the results were compared with those of a 300-mm-diameter loading plate in a field test. The results of the two loading plates showed distinct differences, thereby confirming the need for the loading-plate scale effect. A regression equation was proposed for the scale effect of the loading plate. The study results, however, suffered from limited number of data because of the limitations of field testing, and materials with large particle sizes in the field-embankment roadbed have a greater effect on the 50-mm diameter loading plate than on the 300-mm-diameter one.