La réponse dynamique d’un train roulant sur une voie réelle dépend de plusieurs paramètres. Certains d’entre eux ne peuvent pas être correctement identifiés et doivent être considérés comme incertains. L’objectif de cette thèse est la construction d’un modèle probabiliste de la fatigue du rail, en considérant la géométrie de la voie et l’usure des rails comme champs aléatoires modélisés en utilisant le développement de Karhunen-Loève. Ce dernier requiert le calcul des fonctions et des valeurs propres de l’opérateur de covariance pour la représentation modale du champ. Cette étape peut devenir très coûteuse si le domaine est beaucoup plus grand que la longueur de corrélation. Pour résoudre ce problème, une adaptation de la technique est proposée. Les distributions multivariées des coefficients de projection sont identifiées à l’aide d’un développement en Chaos Polynomiaux, qui est calibré sur des données de mesures. Le rayon de courbure, l’âge du rail et la vitesse opérationnelle du train induisent des effets non stationnaires qui doivent être pris en compte dans le modèle. La validation du modèle probabiliste des quantités d’entrée est faite en comparant des données de mesure des efforts de contact roue-rail avec les résultats des simulations. Une analyse de sensibilité globale est menée sur des quantités d’intérêts dynamiques pour quantifier l’impact des irrégularités aléatoires sur la dynamique du véhicule et l’initiation à fatigue du rail. / The dynamical response of a train rolling on a real track depends on several parameters. Most of them cannot be accurately identified and have to be considered as uncertain. The aim of this thesis is the construction of a probabilistic model of the rail fatigue life considering the track geometry and the rail wear as random fields modelled with the Karhunen-Loève expansion. This latter requires the modal decomposition of the covariance operator. This step can be very expensive if the domain if much larger than the correlation length. To deal with this issue, an adaptation of the KLE, consisting in splitting the domain in sub-domains where this modal decomposition and the sample generation can be comfortably computed, is proposed. A correlation between the KLE coefficients of each sub-domain is imposed to ensure the desired correlation structure. The multivariate distributions of the random projection coefficients are characterized using a Polynomial Chaos Expansion (PCE) calibrated on measurements data of the track irregularities. The curve radius, the rail age and the train operational velocity introduce nonstationary effects that have to be taken into account to model the track. A validation of the random models is therefore performed using a set of measurements of the wheel-rail contact forces.A global sensitivity analysis is performed on some dynamical quantities of interest in order to quantify the impact of the random fields on the vehicle dynamics and the rail fatigue initiation. Since this step is computationally expensive, a PCE-based meta-modelling technique is employed to estimate the fatigue index.

As rails are vital parts of a track system, it is essential to ensure their safe and reliable operation. The present verification approaches and limit values regarding the permissible additional stresses of the rail under compression and tension considering track-bridge-interaction (TBI) were developed in the 1980s. However, with the rapid development of the railway industry and the increasing of train speeds, rail infrastructures are subjected to ever more frequent, greater loads and more complicated loading conditions, especially in the area of bridges. Moreover, the manufacturing technologies of railway components have been further developed. Taking all the aforementioned variations into account, the current verification approaches and limit values do not apply properly today and shall be updated. For this purpose, new investigations are carried out in this dissertation. As major parts of this cumulative dissertation, the published investigations are divided into three main blocks. The first block is the state of the art. In this block, a detailed background knowledge and a state of the art description of the permissible additional stresses in railway tracks due to TBI are given. Furthermore, the motivation for the studies within the scope of this dissertation is addressed. The second block deals with the rail resistance under compressive forces in ballastless track systems. Accordingly, numerical investigations on the behaviour of rails in ballastless track systems under compressive axial forces in the vicinity of bridge joints were performed. Experimental tests were also carried out on two 8.17 m long rails fixed with BSPFF-B-1 and SBS300-1 fasteners on the ÖBB-Porr slab track system. It was found that the rail resistance under longitudinal compressive loads can be largely increased. The third block focuses on the rail resistance under tension. First, extensive experiments were conducted on rail behaviour for up to five million cyclic loads in both vertical and transverse directions under different minimum stress levels. Subsequently, the sectioning method and the X-Ray diffraction method were applied to determine the residual stress distribution in the rail. Afterwards, the determined residual stress results and the fatigue test results are analysed together. As a result, a new comprehensive Smith-diagram, which took into account the actual rail residual stresses, up to five million load cycles in both vertical and transverse directions of the rail, was achieved. In addition, two studies are supplemented. One deals with the fatigue behaviour of rails for up to 50 million load cycles and the other concerns the fatigue behaviour of rails from a different batch for up to five million load cycles. Based on all these aforementioned investigations, it is concluded that the current limit values and approaches regarding the rail resistance in ballastless track systems under compression and tension considering TBI are too conservative. In the end, new verification approaches and limit values are proposed.