# Rail Wear Evolution on Small-Radius Curves under Mixed Traffic Conditions, In-Field Investigations
## 2 Materials and Methods
### Rail Wear  
The material loss that the rail profile is subjected to, because of the high temperatures and substantial stress from wheel-rail contact, as a result of the rolling-sliding motion, is called wear [11; 12].  
The wear calculations of the railway wheels can be determined by dividing the phenomenon into two categories: corrugation of the rails and wheels taking into consideration the un-roundness of the wheels and, second, the rail and wheel profiles, which are considered perfectly cylindrical and perfectly round, respectively [13]. The Archard wear law [14]is often used in studies for wear characteristics [15; 16] with the wear rate being expressed as the wear loss per unit sliding distance.  
Rail wear can be categorized into three main types: wear at the top of the rail (vertical wear), wear of the gauge (lateral wear), or a combination of both, which is known as head and side wear. In sharp curves, the most significant form of wear is gauge wear on the lower rail, which escalates with increasing running speeds [17]. In these curves, the wheel flange makes contact with the gauge corner of the rail head, leading to abrasive wear [18]. Understanding the rail's behavior is crucial, focusing on material loss or displacement. The stresses on the rail arise from contact stresses, bending stresses, and thermally induced stresses. Managing contact stresses is essential as they are linked to fatigue and wear. The primary wear mechanisms in wheel-rail sliding or rolling contacts encompass adhesive, abrasive, fatigue-driven, thermal, and oxidative wear processes [18; 19].  
Rail wear is influenced by a multitude of factors, including axle load, rail profile, train speed, material properties of wheels and rails, traffic type, track curvature, line type (straight or curved), surface condition of the contact between the rail and wheel, lubrication, and various other influences. This wear can lead to alterations in the contact surface between the rail and wheel, resulting in surface deterioration, changes in contact geometry, and track instability that may culminate in derailments. Material loss due to wear leads to modifications in the rail cross-section, necessitating maintenance work and replacement activities [12; 20; 21; 22; 23]. Wear is commonly associated with frictional work and is influenced by various factors such as the steel grade of the rail and wheel, the compatibility between the rail and wheel materials, the friction coefficient, normal contact stresses, relative slips, the design, construction, and maintenance of vehicles, tracks, rail and wheel profiles, as well as surface treatments and environmental conditions (e.g., humidity, corrosion) [24; 25; 26; 27]. The distribution of traffic loads on the rail occurs over an approximate surface area of 100 mm\({}^{2}\) with contact stresses significantly high due to loads ranging from 50 to 200 KN/wheel. The rail experiences normal contact pressure, tangential forces, thermal stresses, and residual stresses.  
Given the importance of wear in rail service, it can lead to various track-related issues, including gauge widening, elevated rail-wheel forces, and compromised vehicle dynamics due to rail profile loss and material deterioration in strength and rigidity. The literature categorizes wear as mild, severe, or catastrophic [17]. Research has shown that the wear rate increases linearly with the maximum pressure and friction coefficient. For instance, [PERSON] et al. [28] concluded that the wear rate is directly proportional to the traction coefficient and creepage.