Transition zones in railway tracks are locations with a significant variation of track properties (i.e. foundation stiffness) encountered near structures such as bridges and tunnels. Due to strong amplification of the track’s response, transition zones are prone to rapid degradation. To investigate the degradation mechanisms in transition zones, researchers have developed a multitude of models, some of them being very complex. This study compares three solution methods, namely an integral-transform method, a time-domain method, and a hybrid method, with the goal of solving these systems efficiently. The methods are compared in terms of accuracy, computational efficiency, and feasibility of application to more complex systems. The model employed in this paper consists of an infinite, inhomogeneous, and piecewise-linear 1-D structure subjected to a moving constant load. Although the 1-D model is not particularly demanding computationally, it is used to make qualitative observations as to which method is most suitable for the 2-D and 3-D models, which could lead to significant gains. Results show that all three methods can reach similar accuracy levels, and in doing so, the time-domain method is most computationally efficient. The integral-transform method appears to be efficient in dealing with frequency-dependent parameters, while the time-domain and hybrid methods are efficient in dealing with a smooth nonlinearity. For multi-dimensional models, if nonlinearities and inhomogeneities are considered throughout the depth, the time-domain method is likely to be most efficient; however, if nonlinearities and inhomogeneities are limited to the surface layers, the integral-transform and hybrid methods have the potential to be more efficient than the time-domain one. Finally, although the 1-D model presented in this study is mainly used to assess the three methods, it can also be used for preliminary designs of transition zones in railway tracks.

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.