## 1 Introduction  
The real-time information about the presence of a train in a specific track section is realized by a \"track circuit\" system and is paramount to avoid hazardous situations. It ensures the accurate localization of the train on the railway and hence the track safety as shown in Figure 1. When the train is absent, the signal sent by the transmitter reaches the receiver via the transmission line. In this situation, the residual is generally close to the circuit's supply voltage. On the contrary, the presence of a train axle on the track creates a low resistance, known as a shunt, which \"short-circuits\" the two rails, causing the residual voltage to drop \"to zero\". This is referred to as \"shunting\". When the residual voltage falls below a certain threshold, indicating the occupancy of the zone, the signaling systems are activated accordingly. A high-quality electrical contact must be maintained for ensuring the reliability of the track circuit system. A high impedance of the contact spot leads to a critical safety issue, known as \"deshunting\", in which, for a certain period, the train is no longer detected. As already pointed out in the very recent study focusing on wheel-rail contact in static conditions [1], it is well known that among several sources of pollution that can modify the contact resistance, thin oxide layers can play a major role, especially on tracks with low frequentation. Even though various devices to prevent [2; 3] or reduce the occurrence of deshunting have been implemented, many instances are still detected every year. Consequently, there is a need to better understand the behavior of the wheel rail electrical contact of a rolling stock to design fault resistant railway management strategies intending to avoid potentially dangerous situations (level crossing failures, rail accidents, etc.). Wheel-rail contact is a complex, multi-physical subject since it involves both mechanical and electrical aspects. In [4; 5; 6], the detection and impact of the mechanical degradation of the wheel and the rail were studied. Parameters related to the surface, such as roughness [7; 8], local temperature, and physical chemistry [9], were shown to have a strong influence on the wheel-rail contact resistance. In certain instances, arcing has been observed to occur between the wheel and the rail, resulting in microstructural modifications of the surfaces [7; 10]. The state of the surfaces and the inherent complexities of its multi-physical character are not exclusive to the two solids in contact, but also extend to a layer referred to as a \"third body\" present at their interface. This third body has been found to contain a wide variety of components, including wear particles from wheels and rails, external contaminants, such as dead leaves, frost, sand, and oil, as well as rust formed naturally on the surfaces [11]. Such components can potentially affect the friction at the interface [12; 13]. In [14], the tribological, morphological, and microscopic properties of third body samples were examined and their electrical conductivity, heterogeneity, and compactness were compared between good and bad shunting conditions. Railway maintenance is significantly impacted by rust, particularly in coastal or humid regions where corrosion is known to be more severe. Rainwater can deposit salts or atmospheric contaminants, resulting in the formation of acidic rain which accelerates the corrosion process [15]. [PERSON] et al. studied the rust composition by using in situ X-ray diffraction [16]. On the railhead, they mainly found FeO(OH) oxyhydroxides in various forms and Fe\({}_{3}\)O\({}_{4}\) magnetite. Taking a step back from these considerations, [PERSON]  
Figure 1: Operating principle of a track circuit and the ideal residual voltage profile. (**Top**): No train present on the track. (**Bottom**): Track occupied by an axle, indicating a prohibited passage. et al. [17] examined how the type of track environment and how often trains pass affect the rust thickness on rails and the wheels roughness.