# Ballasted Track Status Evaluation Based on Apparent Track Stiffness Index
## 1 Introduction  
Ballasted track has the advantages of low initial construction cost, low noise and vibration, and flexible handling of ground settlement. However, differential settlement can occur in ballasted track because this type of track is prone to plastic deformation, which leads to track irregularity and requires periodic maintenance. The first stage of Gyeongbu high-speed railway, i.e., the Gwangmyeong-Dongdaegu section, was constructed with ballasted tracks. Fifteen years have passed since Korea Train eXpress (KTX) opened, and with the increase in the train passing tonnage following the opening of the Super Rapid Train (SRT), the maintenance cycle of the ballasted track has become shorter and the associated costs have increased. The maintenance of high-speed rail ballasted tracks in South Korea is performed based on the amplitude of track irregularities. The Railway Track Maintenance Guidelines [1] prescribe obtaining monthly measurements of track irregularities such as vertical track irregularity, cross level irregularity, twist, and gauge irregularity using a track inspection vehicle with versine method for a chord of a certain length. In high-speed rail, the control standard is set by measuring versine for 10 m and 30 m chords. In addition to the track irregularity amplitude, the Track Quality Index (TQI) is used as a measure to evaluate the quality of the overall track geometry. TQI is the standard deviation calculated over a 200 m long section of the track irregularities. It can be regarded as a statistical expression of the differential settlement of the track over a certain section. TQI is not a fundamental countermeasure against the cause of ballasted track deterioration, only a follow-up measure to the final differential settlement. When maintenance work is performed on a section with a significant TQI, although the TQI value of the section decreases, the abrasion of the ballast increases. Abraded ballast aggregates expedite track irregularity; thus, maintenance work is performed to reduce it, and the abrasion of the ballast increases further. As this phenomenon isrepeated, a problem occurs in that the maintenance cycle for a specific section becomes increasingly short. In this context, the train may even derail in serious cases when timely maintenance work cannot be performed. Vertical track irregularities occur owing to the differential settlement of ballasted tracks. The irregularity can be predicted well in time if the settlement of ballasted tracks can be predicted. It is known that determinants including ballast condition, track stiffness, and external load affect the settlement of ballasted tracks. Ballast fouling affects the railroad effectiveness and structural capacity [2; 3]. Ballast particle size distribution and the number of load cycles cause ballast deformations [4]. Axle loads and train speed lead to ballast track deformation. The conditions of all layers under the sleepers (i.e., ballast thickness, ballast fouling, sub-ballast properties, etc.) affect the quality of ballast railway tracks [5]. Track stiffness directly influences the ballast settlement [6]. Of these, the stiffness of the ballasted track is directly related to the behavior of the track. This aspect has been researched actively. [PERSON] [7] suggested that the settlement progress rate is inversely proportional to the square of the vertical track rigidity, and that the standard deviation of the longitudinal level of track irregularity is inversely proportional to the track stiffness. [PERSON] [8] compared and reviewed track irregularity prediction models and concluded that vertical track stiffness has a direct effect on track irregularity. [PERSON] et al. [9] reported through a literature review that track stiffness is dominant in track behavior, and that maintenance by tamping, etc., without a cause analysis for track irregularity is only a short-term solution and induces an increase in maintenance costs in the long run.