Abstract Summary
Transition zones are critical in high-speed railways because of the concentrated occurrence of track and substructure degradations. Even if the rail geometry irregularity has been well controlled by intensive maintenances, amplification of dynamic responses can be commonly found at the various substructures interfaces and their vicinity. These phenomena could be explained by the abrupt change of the subgrade stiffness. Combining with a typical transition zone configuration of high-speed railways involving wedge-shaped backfills, this study is expected to explain the reason why components of transition zone easily deteriorate from the perspective of energy concentration. In addition, considering the background of constant increase of train speed, the elastic field state and the energy distribution when the load speed is close to the critical velocity will be focused on. In this study, the two-dimensional plane-stress model, in which two elastic layers with different physical properties are coupled by an inclined interface, is established. Both layers have a free surface and rigid bottom. The vehicle is simply regarded as a constant load moving along the free surface with a constant velocity. The elastic field of the model is composed of an eigenfield and a free field. The eigenfield describes the steady-state response part of the elastic layers subjected to the moving load. The free field, composed of guided waves that are excited when the load moves over the inclined interface, is the key to reveal transition radiation of such a physical model. The model is divided into a finite-difference region containing the inclined interface and continuous media regions on both sides. Based on hybrid method, the semi-analytical solution of guided wave modal coefficients and elastic field are solved in turn. The investigation of energy distribution in the space–frequency domain is realized by assessing the energy flux through enclosing surfaces. This study carries out a single factor analysis, in which a series of models with different model parameter values (e.g., inclination angle, stiffness ratio of two elastic layers and load speed) are compared. The results indicate that the power of transition radiation and the energy distribution around the interface change when the inclination angle changes. Stronger energy radiation is brought by larger stiffness ratio and such energy is in general accumulating in the softer layer. Analogies can be drawn between the abovementioned conclusions about energy and viewpoints obtained from existing research on transition zones of high-speed railways, which proves that the model is meaningful for revealing some physical phenomena in transition zones. When the load speed approaches the critical velocity, the magnitudes of the spectral density of transition radiation energy in the whole frequency range are significantly magnified. It provides explanation for the restriction of train speed increase
