# Qualitative Prediction Model for Dynamic Behavior of Ballasted Tracks
## 5 Conclusions  
In this study, a QPM was proposed to predict and assess the performance of ballasted tracks as a function of dynamic wheel-rail force and variation in TSS. The results obtained are summarized below.  
Figure 16: Rail bending stress estimated using field measurements, qualitative analysis, measured rail pad stiffness, and predicted ballast stiffness.  
Figure 15: Rail displacement estimated using qualitative analysis, measured rail pad stiffness, and predicted ballast stiffness.  
1. The ballasted track response should be a function of the variations in vertical spring stiffness of the rail pad or ballast. The QPM consists of a 2 DOF dynamic track model and modified track properties, which define the rail pad and ballast stiffness ranges, based on designed and measured values. The proposed QPM is capable of simulating the complex interaction between the properties of track components and dynamic track responses.
2. The parameters and dynamic response of the ballasted track determined through field measurements and qualitative analysis showed that the TSS more strongly affects every parameter and is therefore more affected by ballast stiffness than by rail pad stiffness. A ballast stiffness of 200-300 kN/mm can reduce track deterioration (deflection and deformation) and dynamic response. Furthermore, an appropriate TSS is required to prevent exceeding the dynamic response of the in-service ballasted track, i.e., when the track forces, dynamic contribution, or vibration behavior is over the design specifications. The qualitative analysis results showed good agreement (within 2-5%) with the field measurement results.
3. The proposed QPM presents results as a discrete space of various track responses and parameters, rather than as of single values. The dynamic behavior of in-service ballasted tracks can thus be predicted qualitatively as a function of the rail pad and ballast stiffness using a simple field test and the proposed QPM.
4. Using the proposed QPM, a dynamic response map can be predicted and used to deal with uncertainties and design variables. The results of the qualitative analysis showed good agreement with field measurements and FE analysis results. The proposed QPM can predict the dynamic response of ballasted tracks using field-measured data, such as rail pad stiffness, rail bending stress, or rail displacement.
5. The dynamic track response obtained using qualitative analysis can be used to predict the constraint parameters determined by field measurements and should facilitate practical track maintenance operations. 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. Overall, the study successfully proposed a model to predict track field conditions and suitability for maintaining a ballasted track.  
[PERSON] contributed to conception and acquisition of data; [PERSON] and [PERSON] investigated the data acquisition and formal analysis; [PERSON] and [PERSON] wrote the paper; [PERSON] critically revised the paper. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
This Study was supported by grant from Dong Yang University in 2019.  
The authors declare no conflict of interest regarding the publication of this paper.