# Rail Wear Evolution on Small-Radius Curves under Mixed Traffic Conditions, In-Field Investigations
## 2 Materials and Methods
### Data Collection of Rail Wear, Level, Gauge, and Superelevation  
Twice a year, measurements were conducted for a duration of five years on small radii curves subjected to mixed traffic, assessing both vertical and lateral rail wear. The measuring points are highlighted in Figure 7, and all observed curves feature the incorporation of transition curves and a central circle in their construction. Throughout the measurements, maintenance activities were carried out with a focus on monitoring the evolving characteristics of wear and geometric curves over time. The rails employed on the examined curves belong to type 65, featuring a rail inclination of 1:20. Each curve underwent measurement at 35 to 42 points; the quantity was contingent on the length of the specific curve. Here, AT denotes the alignment transition point, and TC designates the transition curve point. Figure 8 showcases the initial rail profile type 65 alongside the maximum wear profile identified during the investigations. Relevant properties for both profiles are detailed in Table 3. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **New Rail** & **Maximum Wear** \\ \hline rail type & 65 & 65 \\ cross sectional area (cm\({}^{2}\)) & 83.7 & 83.0 \\ moment of inertia \(\mathrm{I_{xx}}\) (cm\({}^{4}\)) & 3584 & 3177 \\ moment of inertia \(\mathrm{I_{yy}}\) (cm\({}^{4}\)) & 594 & 618 \\ center of gravity \(\mathrm{y_{c}}\) (cm) & 8.13 & 7.33 \\ center of gravity \(\mathrm{x_{c}}\) (cm) & 7.56 & 7.50 \\ \hline \end{tabular}
\end{table} 
Table 3: New rail and rail most advance wear rate rail properties. Figure 6: Influence line for bending moment calculus. Figure 7: Rail measuring points along the curve’s length. Measurements for R 275 m curve, for time interval 2019-2023, for vertical wear (Vw), are shown in Table 4.  
Measurements for R 275 m curve, for time interval 2019-2023, for lateral wear (Lw), are shown in Table 5.  
Figure 11: Evolution of vertical wear for curve 1, years 2019–2023, over time, for the 18 measured points. Figure 12: Evolution of lateral wear for curve 1, years 2019–2023, over time, for the 18 measured points. Figure 10: Lateral wear for curve 1, years 2019–2023, first and fourth quarter on the curve’s length. Figure 14: Lateral wear for curve 2, years 2019–2023, first and fourth quarter, on the curve’s length. Figure 13: Vertical wear for curve 2, years 2019–2023, first and fourth quarter on the curve’s length. Figure 6:0 Evolution of vertical wear for curve 2, years 2019–2023, over time, for the 22 measured points. The data obtained for the new rail profile and for six points along the curve's length, considering the measured lateral and vertical wear over specific time intervals, are summarized in Figure 6:1  
The stress analysis conducted in this paper focuses on determining bending stresses for the studied curved track, accounting for both lateral and vertical rail wear variations along the lengths of the two curves. The decrease in bending rigidity of the rail due to wear is a key consideration. Given the variations in ballast bed properties from a new line to a track compacted by traffic, the track response differs. To address this, the modulus of