# Qualitative Prediction Model for Dynamic Behavior of Ballasted Tracks
## 4 Results and Discussion
### Validation of Proposed QPM  
A qualitative dynamic behavior prediction model was proposed to predict and assess ballasted track performance as a function of dynamic vehicle loading and track support stiffness. To validate the proposed model, which consists of a 2 DOF dynamic track model and modified track properties that define the rail pad and ballast stiffness ranges based on designed and measured values, field rail pad stiffness measurements were performed using a test track. A pandrol rail pad used in conventional Korean ballasted tracks was adopted according to the Korean standard (KS F2310). Seven rail pad specimens used for conventional ballasted tracks in South Korea were selected to measure the dynamic rail pad stiffness. Each specimen was in relatively good condition, and the dynamic rail pad stiffness was approximately 480-520 kN/mm. The proposed QPM is summarized in Figure 13. Using the assumed and measured data, including the measured rail pad stiffness, track support stiffness, and predicted ballast stiffness, the dynamic response of an in-service ballasted track can be predicted through the following four-step process. * Step 1: Draw the measured data block (the rail pad stiffness, Figure 13 ()) in horizontal direction on the qualitative analysis map (track support stiffness (TSS) map). * Step 2: Plot the measured TSS data (circles in Figure 13 ()) in the TSS map and check the intersection region of a duplicated zone (Figure 13 ()) in vertical direction between the measured data block and TSS data. * Step 3: Draw the blocks in both the vertical and horizontal directions on the qualitative analysis map (track response map). Then, check that the intersection region of a duplicated zone between the vertical and horizontal direction; this represents the predicted response of the in-service ballasted track. * Step 4: Verify the range of the predicted results (value in white box) using the real response data obtained from the target track (circles in Figure 13 ()) from the intersection region of the proposed qualitative analysis map. The TSS, rail displacement, and rail bending stress were then analyzed as dependent variables of the proposed qualitative analysis method. The measured rail pad stiffness and vehicle speed were 480-520 kN/mm and 120 km/h, respectively, and the measured TSS and rail displacement were defined as reference or guide data. The resulting TSS variation with the rail pad and ballast stiffness is summarized in Figure 14. The TSS of the in-service ballasted track was predicted from the intersection region of the duplicated zone between the vertical and horizontal direction, which represented the predicted response of the in-service ballasted track. The predicted rail displacement and rail bending stress maps using the proposed qualitative analysis method are compared with the measured rail pad stiffness from chapter 3 in Figures 15 and 16,  
Figure 14: Track support stiffness (TSS) map of ballasted track using field measurements (circles) qualitative analysis, measured rail pad stiffness, and predicted ballast stiffness. Figure 13: Process for using the qualitative prediction model (QPM) to predict a dynamic track response. respectively. The proposed model predicted the rail displacement and rail bending stress within approximately 2-5% of the obtained field measurement, thus validating the proposed method. The results obtained using the proposed QPM thus verified the model and demonstrated that the obtained measured data, such as rail pad stiffness and dynamic TSS, are suitable for predicting the dynamic responses acting on a ballasted track and should thus be employed in track maintenance. The proposed model thus allows for the use of measured track responses to predict the responses and parameters of the ballasted track using a solution space. This study presents a statistical analysis of the measured results and provides a good understanding about the responses and response variation of a ballasted track.