# Plate Size Effects in Gravelly Soil Based on In Situ Plate Load Tests and Finite Element Analysis
## 1 Introduction  
The bearing capacity of soil refers to the maximum load intensity that the soil can withstand under external forces without experiencing excessive deformation, failure, or settlement. Both the bearing capacity and deformation behavior under the load of soil are critical in geotechnical engineering design [1, 2]. With the advancement of numerical computation technologies and sophisticated computational tools, researchers have increasingly utilized more efficient numerical methods to model the actual site conditions and failure mechanisms of foundation soils [3, 4, 5, 6]. However, the plate load test (PLT) remains recognized as a direct, rapid, and reliable field test, useful for investigating soil deformation and estimating the ultimate bearing capacity of the on-site soil [7, 8].  
The plate load test (PLT) is a significant in situ test in geotechnical engineering, providing essential information for foundation design. The stress-displacement trends observed from the in situ PLT can be used to determine the load-settlement relationship, failure mechanisms, subgrade modulus, and bearing capacity of the foundation [8]. However, in many instances, the dimensions of the test plate used in the test are generally smaller than those of the actual foundation. Since the dimensions of the foundation differ significantly from those of the load plate used in the plate load test (PLT), it is necessary to extrapolate the load-displacement relationship determined from the load plate test to the foundation prototype in the foundation design [9].  
Compression bearing tests on square and circular foundations in non-cohesive soils show that the bearing capacity increases as the foundation size increases [10,11]. This conclusion is further confirmed by PLT tests in reinforced soft soils [3].  
PLT tests in non-cohesive soils indicate that, for both square and circular foundations, the settlement increases with larger foundation sizes under identical loading conditions, with the settlement increasing as the foundation diameter grows [12,13].  
Analyzing the test results in conjunction with existing literature reveals that the bearing capacity of the foundation and the settlement displacement under identical loads are closely related to the size of the foundation [9]. Specifically, under identical pressure conditions, the magnitude of the settlement differs with variations in foundation size, leading to discrepancies in the pressure-settlement curves for foundations of varying sizes. Therefore, the proportional limit and ultimate bearing capacity obtained from the stress-settlement curve will also change. Simultaneously, based on [PERSON]'s theory [14], the determined coefficient of subgrade reaction and the secant modulus established from the semi-infinite elastic space theory will also vary with changes in foundation size.  
In this study, horizontal plate load tests were conducted on gravel soil foundations in a flat tunnel environment, and finite element analysis software was used for supplementary analysis to investigate the relationship between the foundation stiffness coefficient, loading response, and plate size.