## 4 Results and Discussion  
### Track Impact Factor According to Measured Dynamic Wheel Load  
In this section, the designed TIF considering the designed speed of the test tracks is compared with the measured TIF for each test section. The wheel load subjected to a passing train includes not only the static load owing to the weight of the train, but also the effect of the dynamic impact load, which is a result of train speed. Therefore, the TIF can be calculated by comparing the dynamic wheel load measured through field measurements [2]. The TIF can be represented by the rate of dynamic wheel load fluctuation, which is obtained by dividing the rate of dynamic wheel load fluctuation subjected to a passing train by the static wheel load, as follows [1; 21; 3; 1]:  
\[\text{Rate of dynamic wheel load fluctuation}=(P_{dyn}-P_{sta})/P_{sta}, \tag{1}\]  
where \(P_{dyn}\) is the dynamic wheel load and \(P_{sta}\) is the static wheel load. TIF was calculated using Equation (2). The equation of the Korean standard for urban transit used for TIF for a train speed of 100 km/h is shown as Equation (2). \[\text{i}=1+0.513\frac{V}{100}, \tag{2}\]  
where \(V\) is maximum train speed. Typically, the TIF is calculated by considering the value \(2\sigma\), where \(\sigma\) is the standard deviation of wheel load fluctuation [2; 19]. The TIF is evaluated based on the dynamic wheel load fluctuation and can be used to determine the dynamic wheel-rail contact force and the track impact. The TIF calculated based on the dynamic wheel load fluctuation is also affected by the track support stiffness and rail surface roughness [2]. The standard TIF used in Korean urban railway track design was applied to that of the American Railway Engineering and Maintenance-of-Way Association (AREMA) [2; 3; 22]. The rates of all wheel load fluctuations calculated using the dynamic wheel load measurements were greater than zero. This value was compared with the measured TIF (i = 1.410) at 80 km/h, considering the design speed of the tested section [1; 2; 3]. To evaluate the TIF considering the range and frequency of the dynamic wheel load fluctuation measured in each test section, a probability statistical analysis was conducted using a Gaussian probability distribution model [2]. The measured TIF converts the static wheel load to an equivalent dynamic wheel load. Moreover, to consider the increase in weight owing to passengers boarding the train, the static wheel load was measured when the trains were in motion. In reality, it is difficult to estimate the static load of a train and the exact number of passengers boarding the train. Therefore, the variations in the total wheel load were measured during peak hours. Figure 6 shows the results of the Gaussian analysis of wheel load fluctuation for each test section. According to the TIF calculation results for each test section, the TIF of rail joints in the ballasted track (Section A) was much higher than that of the direct fixation concrete track CWRs (sections B and C). This suggests that the rail joints amplified the track impact during the train's passage over the discontinuity gaps. The average probability density function was measured as positive, as shown in Figure 6a. The probability of a negative value owing to the normal distribution was negligible because it is close to zero, as shown in Figure 6b,c. Therefore, the track impact along section A was gradually amplified. The TIF calculated for the current track conditions for each test section was compared with the designed TIF, and the results are summarized in Table 3.  
The TIFs calculated for sections A, B, and C were 1.899, 1.207, and 1.220, respectively. These values represent 86% and 87% of the current Korean standard TIF for the slab tracks with CWR (sections B and C). However, for section A, the TIF was approximately 134% higher than the Korean standard for urban railways. Therefore, the measured amplification of the impact load generated on the rail joints exceeded the track impact level considered during railway design.