## 2 Model
### Validity of the Model  
To characterize the dynamics in the frequency range of interest as discussed in the Introduction, corrugation modeling should consider the following issues: static and dynamic contact problems should be validated; structural dynamics should be considered [47]; and coupling between the contact problem and structural dynamics should be validated.  
1. With respect to the contact problems, a method similar to that of [24] is used herein. This method is suitable for resolving dynamic contact problems, and its validity has been demonstrated by the close reproduction of the evolution of squats [7; 48]. Moreover, this method has been verified as suitable for resolving static contact problems based on the established solutions of [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [24; 49].
2. To validate the structural dynamics, (a) the approach used in this paper can reproduce the hammer test [50]; thus, the model can simulate measured track receptance based on identified track parameters. (b) Furthermore, the model can simulate axle-box acceleration (ABA) measurements [30; 51]. Consequently, the model can capture the dynamics of wheels and tracks and the interaction between the vehicle and the track in the relevant frequency range.
3. With respect to assessing the validity of the model for a vehicle-track system with direct coupling between the contact problem and structural dynamics, the model exhibits a good representation of the dynamic response (spatial and frequency) of corrugation induced by squats. As noted in [21], \"the model provides a good explanation for the development of corrugation initiated from isolated railhead irregularities\". Thus, in this paper, the challenge is to extend the model to the study of the more general type of corrugation that does not present clear local irregularities as the source of corrugation initiation.  
Figure 3: Modeled corrugation: (**a**) field measurement of corrugation (27–33 mm bandpass filtering); (**b**) schematic diagram of the corrugation and 4 positions (blue line: P1, red line: P2, green line: P3 and magenta line: P4); and (**c**) illustration of the applied corrugation (Corrugation 2 with P2 at 0.6 m) in the rail surface with 5\(\times\) magnification (only 3 complete waves are plotted).  
As will be discussed in greater detail in Section 4.2 on the prediction of major field observations, the simulated wear in Section 4.2 is in agreement with the field observations shown in Figure 1b,c. Here, the irregular distribution of wear along one sleeper span is clear, and the observations and simulation are in agreement. In the paper, other agreements between the model results and field observations are discussed in greater detail later in the text. For example, the contact solutions that indicate that wear is the more probable damage mechanism at the corrugation trough [1; 11; 52] will be described in Section 3, and the occurrence of squats in agreement with the observation in Figure 1c will be explained in Section 4.2. These summaries comprehensively describe and analyze how the model in this paper was validated.  
For other track and vehicle field data, typical parameters of the Dutch railway are used [29]. For modeling corrugation, a sinusoidal profile is employed based on field measurements (Figure 3a) and observations (Figure 1a).