# Qualitative Analysis of Sleeper Supporting Condition for Railway Ballasted Tracks Using Modal Test
###### Abstract
Their findings revealed that an increase in the proportion of tire-derived aggregates in the ballast mixture led to a significant reduction in subgrade stiffness and a corresponding increase in the damping ratio. [PERSON] et al. [18] assessed the vertical vibration and transmission characteristics of railway ballast using impact hammer tests, demonstrating that as depth increased, both the vertical vibration transmission rate and accumulated external force gradually decreased. [PERSON] et al. [19] compared the dynamic response of a ballasted track obtained from discrete element modeling with results from dynamic load tests. [PERSON] and [PERSON] [20] performed numerical analysis to quantitatively assess vibrations induced by high-speed trains on ballasted railway tracks. Their study estimated high vibration magnitudes on railway embarkments and the ground, particularly when the effects of multiple train wheels were superimposed. [PERSON] et al. [21] proposed a method for assessing the condition of railway tracks using GPR. The experimental results were verified through simulations based on RSA-FDTD. [PERSON] et al. [22] reviewed a geometric deterioration prediction model for railway tracks using machine learning and compared and analyzed existing prediction methods. As a result, the machine learning-based method provided high prediction accuracy. However, it showed limitations such as lack of interpretability and difficulty in parameter adjustment, suggesting the need for further research. [PERSON] et al. [23] analyzed the effects of fouling and degradation on the shear strength of the roadbed. As a result, the penetration of fine particles and degradation decreased the shear strength of the roadbed. [PERSON] and [PERSON] [24] utilized impact hammer tests to monitor sleeper vibrations for detecting ballast damage. Their results indicated that ballast degradation led to a reduction in the stiffness supporting the sleeper, altering its vibration characteristics. Additionally, [PERSON] et al. conducted modal tests on various railway track types to analyze the dynamic characteristics of railway bridges. Their findings showed that, despite relatively low experimental excitation loads, damping ratios ranging from 1.0% to 2.0% were consistently observed in most cases [25]. Previous studies have largely focused on the deformation and dynamic characteristics of gravel ballast without accurate track modeling, and they often have not confirmed the precision of the numerical models or the results with comprehensive measurement data. Although research using modal testing to assess concrete sleeper damage has been widely conducted internationally, in South Korea, such damage is predominantly evaluated via visual inspections. This study modeled the rail and the concrete sleeper as three-dimensional elements and configured a spring element, using the spring stiffness of the ballast as a variable, to represent the support condition of the sleeper. Additionally, the natural frequencies measured through modal tests and the analyzed values were compared to validate the numerical analysis modeling and results.