# Detection of Thermal Strain in Steel Rails with BOTDA
## 1 Introduction  
Rail transportation is one of the most important and efficient forms of transportation. Railway networks are fixed structures that can span many thousands of kilometers. Rail infrastructure typically consist of rail steel anchored onto wooden ties, which sits on a layer of crushed rock ballast over soil foundations. Rail steel is produced in fixed lengths of between 12-120 m. For passenger rail transportation, the preferred method of track construction is to weld sections of rail steel together as a continuously welded rail (CWR). However, CWR does not allow for the expansion or contraction of the rail steel with changes in ambient temperature. This results in thermally induced stresses in the rail (compressive when hot, tensile when cold), which can be extremely large and contribute to rail breaks in cold weather, or rail buckling in hot weather. The long term strain and measurement of rail steel is challenging due to the vastness of most track infrastructure and the harsh climatic operating environment. A high spatial resolution-distributed optical fiber sensor based on Brillouin scattering is a very promising technique for this application. A Brillouin scattering-based optical fiber sensor takes advantage of the optical fiber as the sensing medium to measure both the temperature and strain along the length of the fiber. It has been successfully in many Structural Health Monitoring (SHM) [1; 2] applications. However, distributedBrillouin sensors are commonly used to monitor the strain induced by different loading to the structure [3]. Thermal strain of the steel structure caused by temperature changes is rarely investigated. [PERSON] et al. carried out an outdoor test to measure the strain of the steel beam under external loading force, and used a compensation technique to compensate for the temperature change caused by sun radiation [4]. However, in their test, the temperature change value from sunrise and during the night was limited. For the measurement of rail thermal strain, the optical fiber should be properly chosen to protect the fiber from damage (i.e., with a jacket coating) and to maintain detection sensitivity [5]. In practical applications, the tight-buffered fiber is widely used in distributed fiberoptic sensors. It is important to note that, the coating material influences the measured Brillouin frequency shift variation with temperature [6,7]. [PERSON] et al. [7] performed a theoretical and experimental investigation of the effect of the polymer coating on the Brillouin frequency shift with temperature, however, the work concentrated on the temperature range above zero centigrade. This paper reports the continuous thermal-strain monitoring of the rail steels using a Brillouin optical time-domain analyzer (BOTDA) for the temperature range between \(-40\)\({}^{\circ}\)C and \(+50\)\({}^{\circ}\)C. Three types of optical fiber were glued on the surface of the rail specimen as the distributed sensor; the free fiber between was used as the reference and could be used to investigate the jacket effect as well. Optical fibers are looped five times at different positions on the rail to investigate the position dependence of the thermal strain on the rail. The measurement is also compared to the reference that is obtained by the strain gauge implemented on the middle of the steel rail. This is the first time that optical fiber was used to monitor rail thermal strain in such a broad temperature range, to the best of our knowledge. We found the loose fiber with tight buffer material has a nonlinear relationship with the Brillouin frequency shift and the temperature change due to the temperature-dependent mechanical property of the coating and buffer material. However, when glued onto the rail to detect thermal strain, the measured Brillouin frequency shifts of all fibers exhibited a linear relationship with the temperature change, albeit with lightly different slope coefficients.