Transition zones in railway tracks are areas with considerable variation of track properties (e.g., foundation stiffness) which may cause strong amplification of the response, leading to rapid degradation of the track geometry. Two possible indicators of degradation in the supporting structure are identified, namely the wheel-rail contact force and the power/energy input by the vehicle. This paper analyses the influence of accounting for the interaction between the vehicle and the supporting structure on the contact force and on the power/energy input. To this end, a one-dimensional model is formulated, consisting of an infinite Euler-Bernoulli beam resting on a locally inhomogeneous Kelvin foundation, interacting with a moving loaded oscillator that has a nonlinear Hertzian spring. The solution is obtained using the Green's-function method. To obtain the Green's function of the inhomogeneous and infinite beam-foundation sub-system, the finite difference method is used for the spatial discretization and non-reflective boundary conditions are applied. Accounting for the interaction between the moving oscillator and the supporting structure generally leads to stronger wave radiation, caused by the variation of the vertical momentum of the moving mass. Results show that for relatively high velocity and small transition length, the maximum contact force as well as the energy input exhibit a significant increase compared to the moving constant load case. Furthermore, for relatively high velocities, the maximum contact force also increases significantly with increasing stiffness dissimilarity, findings which supplement the existing literature. Finally, the two degradation indicators can be used in the preliminary stages of design to assess the performance of railway track transition zones.

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Transition zones in railway lines are areas between different track structures such as the transition from conventional track (ballasted track) to slab track, to a tunnel or a viaduct. The main feature of a transition zone is that it exhibits a dramatic change in structural behaviour to bridge the difference in the adjacent track parts. This change causes high dynamic loads which contribute to quality deterioration of the track. Two main factors influence the magnitude of the interaction forces between trains and track in transition zones. Firstly, the abrupt change in track stiffness. This stiffness is determined by the mechanical features of the entire track structure; the conventional track is a compliant structure, while slab track, tunnels and viaducts are relatively stiff. A train passing a stiffness change induces a variation of track deflection under the moving dead loads and, consequently, also a variation in the wheelset’s vertical momentum leading to higher (dynamic) loads. Secondly, settlements of the backfill and its foundation are typically larger than those of stiff structures, leading to unevenness of the track. This abstract deals with the issue of the dynamic analysis of an infinite Euler-Bernoulli beam on elastic foundation with transition in foundation stiffness, subjected to a moving oscillator. This model is one of the simplest ones for a vehicle passing a transition zone. The equations of motion are solved by means of the time-domain Green’s function method using convolution integrals in terms of the unknown contact force. Considering the track as an aperiodic structure, the Green’s functions (receptances) are calculated in a stationary reference frame (i.e., non-moving sources). Two methods of solution are investigated. The first one is based on the Laplace Transform, where the response consists of a contribution from the initial conditions and one from the moving contact force. By choosing the initial conditions in accordance with the response of a beam with homogenous foundation subjected to a moving load, the free vibrations and waves due to oscillator entrance are suppressed and steady-state behaviour is achieved before the oscillator reaches the transition zone. The second method is based on the Fourier Transform, which automatically ensures this steady-state behaviour. Both methods are exemplified in the paper. The influence of the length of the transition zone and the speed of the moving oscillator on the contact force are analysed; both sub-critical and super-critical speeds are considered.@en

Transition zones are locations of discontinuity in the support, such as stiffness transition zones in the ballasted track (close to bridges, culverts and tunnels). These zones necessitate special attention, mainly because they: - Require frequent and expensive maintenance activities. - Cause delays due to unexpected maintenance.@en

Transition zones in railway tracks require a high maintenance frequency which leads to high costs and delays. To better understand the underlying mechanisms, a one-dimensional model is used, consisting of an infinite Euler-Bernoulli beam resting on locally inhomogeneous viscoelastic Winkler foundation subjected to a moving oscillator. The governing equation is solved by means of the time-domain Green’s function method using convolution integrals in terms of the unknown contact force. To this end, the Green’s functions of the beam-foundation sub-system and of the oscillator are computed independently. They are combined through the nonlinear contact relation. The sources of nonlinearity are: the Hertzian contact relation and the possibility of contact loss between the oscillator and the beam. Results show that the contact force in the transition zone can reach 3-6 times the steady-state one. In some cases, the contact loss occurs at the oscillator velocity of around 75% of the critical velocity in the structure. The model can be used for preliminary design of transition zones in railway tracks, for preliminary predictions of a structure’s remaining life time and for fatigue predictions of a train’s wheelset. @en