## 3 Experimental Validation
### Case Studies  
The case study was carried out on a mainline, near London, managed by Network Rail. According to their maintenance operations strategy, and in order to quantify the depth of RCF cracks, Eddy Current measurements [45] were carried out every 26 weeks. In this type of inspection, an AC current is conducted through a coil, which produces a magnetic field around it. When the coil is placed near a conducting material, such as a rail, it induces eddy currents on the surface of the material. If a flaw, such as an RCF crack, disturbs the eddy currents, the magnetic coupling with the material is altered and the signal can be read by measuring the change in impedance across the coil. Most of the trains running through this line are passenger vehicles. The vehicle considered in the validation case studies is an Electric Multiple Unit (EMU) with no separate locomotive. The computational vehicle model is composed of one carbody, two bogies and four wheelsets each one having six degrees of freedom (DOF). Additionally, the relationship and link between solids are made by means of suspension elements and/or kinematical restrictions, which represent the real arrangement and characteristics of components in the real vehicle. The methodology has been applied in two different sections of the railway line. Figure 9 shows the track geometry of these two curved sections, whose location is close to one of those used in [PERSON]'s study. Thus, the implemented damage function is valid for this experimental validation. For other locations, the methodology is valid updating the damage function. The characteristics of these sections are suitable to show the influence of the curve radii on the appearance of RCF cracks. This statement is based on recommendations in the Innotrack report [44] regarding the use of standard grade rails, for which the curve radii threshold for RCF is between 700 m and 1000 m on lightly loaded tracks (<10 MTn/year). The loading condition has been set to cover the daily average load. A constant friction coefficient of 0.5 is used in the wheel-rail contact to replicate the dry conditions [46], i.e., without flange lubrication. Traction has been neglected for simplicity, as the train travels at constant speed. The detailed information about the case study parameters is listed in Table 2.  
Two Eddy Current measurements are available, which were taken 220 days one after the other. Within this period of time, an estimated traveled load of 4.752 MTn is considered for these sections. This value is calculated from daily traffic and load per axle detailed in Table 2. The inspection system provides data of rail sections every yard (0.914 m). Crack depth is measured at ten points on each section (see Figure 10) and the maximum value is taken as a reference for our assessment. Figure 8: Crack prediction and associated crack growth rates for different moments. Figure 10: Sketch of Eddy Current measurement system on a rail. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Components** & **Parameters** & **Values** \\ \hline Vehicle & Load condition & 11.25 T / axle \\  & Number of cars per unit & 4 \\  & Primary suspension & Rubber-metallic \\  & Secondary suspension & Air-spring \\  & Maximum speed & 160 km/h \\ \hline Wheels & Type & P8 \\  & Diameter & 860 mm \\  & Back-to-back distance & 1360 mm \\ \hline Rails & Type & BS113a \\  & Inclination & 1/20 \\  & Track gauge & 1435 mm \\ \hline Track Section 1 & Speed & 95 km/h \\  & Mean curve radio & 720 m \\  & Mean curvature & \(138\times 10^{-5}\times 1/\)m \\  & Mean cross-level & 95 mm \\  & Cant deficiency & 53 mm \\ \hline Track Section 2 & Speed & 120 km/h \\  & Mean curve radio & 1100 m \\  & Mean curvature & \(91\times 10^{-5}\times 1/\)m \\  & Mean cross-level & 65 mm \\  & Cant deficiency & 90 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the case studies. Figure 9: Track geometry of the considered sections: (**a**) Section 1; (**b**) Section 2. The difference in crack depth is calculated between these two measurements.