# Rail Wear Evolution on Small-Radius Curves under Mixed Traffic Conditions, In-Field Investigations
## 2 Materials and Methods
### Rail Measurements  
The investigation into the progression of rail wear involved conducting measurements on sharp curved tracks, specifically focusing on the outer rail of rail type 65 with the Romanian Vignole profile. The rail wear assessment utilized a dedicated rail wear measuring device, as depicted in Figure 2. This device is positioned on the rail base and employs contact needles to measure both vertical and lateral rail wear. The obtained values from measurements on the rail head and gauge corner are documented on a rail wear measuring form. Rail type 65 is characterized by a weight of 65 kg/m, a height of 17.2 cm, and additional properties that are detailed in Table 1.  
The chemical composition of Romanian rail type 65, in addition to iron, includes the following elements: C 0.60%, Mn 1.20%, Si 0.35%, P 0.03%, 5.0.03%. According to Romanian regulations I314 [7], which govern wear measurements, specific procedures are mandated based on time and traffic loads, particularly at characteristic points of curves and locations where the gauge and level are assessed for the outer rail:  
For curves with a radius exceeding 300 m, an annual wear measurement is required irrespective of traffic loads.  
For curves with a radius less than or equal to 300 m and annual loads up to 15 million tons, biannual measurements are mandatory in the March-April and September-October intervals.  
For curves with a radius less than or equal to 300 m and annual loads exceeding 15 million tons, three measurements per year are stipulated in March, July, and October.  
On alignment sections, an annual wear measurement is mandated.  
Figure 1: Spatial railway curve.  
In compliance with Romanian standards, the vertical wear limit for rail type 65 is 9 mm for speeds over 100 km/h, 11 mm for speeds below 100 km/h, and the horizontal wear limit is set at 13 mm. If wear values exceed these limits, the worn rail section should be replaced. Figure 3 illustrates the specific points where wear measurements were conducted.  
For this research, a comprehensive dataset comprising 800 points was collected over a five-year period: from 2019 to 2023. Measurements were conducted semi-annually, focusing on all designated points along curves. A cord length of 20 m was utilized, as illustrated in Figure 4. The curves studied had a radii of 275 m and 280 m.  
Utilizing the data acquired from rail measurements, tables were generated to document wear information, including:  
* Track section;
* Kilometer of the measured section;
* Nature of the section (alignment or curve) with the radius value and curve orientation (left/right);  
\begin{table}
\begin{tabular}{c c c c} \hline
**Type of Rail** & **Young’s Modulus (Gpa)** & **Poisson’s Ratio** & **Ultimate Strength (MPa)** \\ \hline
65 & 210 & 0.3 & 7 \\ carbon-steel & & & \\ \hline \end{tabular}
\end{table}
Table 1: Rail properties.  
Figure 3: Rail wear measuring points.  
Figure 2: Rail wear mechanical measuring device.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Curve 1** & **Curve 2** \\ \hline R = 275 m & R = 280 m \\ timber sleepers & concrete sleepers \\ rail type 65 & rail type 65 \\ gradient 4\% & gradient 6\% \\ mixed traffic & mixed traffic \\ total: 12.4 million tones/year: & total: 9.4 million tones/year: \\ passengers 5.9 million tones/year & passengers 4.5 million tones/year \\ freight: 6.5 million tones/year & freight: 4.9 million tones/year \\ gauge 1435 mm & gauge 1435 mm \\ gauge widening 15 mm & gauge widening 10 mm \\ superelevation 100 mm & superelevation 110 mm \\ superelevation deficiency for Vmax & superelevation deficiency for Vmax \\ Imax = 174 mm & Imax = 159 mm \\ superelevation deficiency for V & superelevation deficiency for V \\ I = 81 mm & I = 68 mm \\ maximum speed Vmax = 80 km/h & maximum speed Vmax = 80 km/h \\ limited speed V = 65 km/h & limited speed V = 65 km/h \\ \hline \hline \end{tabular}
\end{table}
Table 2: Studied curve’s characteristics.  
Figure 4: Fictive beam considered for rigidity length L calculus.