Stress waves in half-space due to moving train loads by 2.5D finite/infinite element approach

In this paper, the 2.5D finite/infinite element approach is extended to the stress waves analysis of the half-space under moving train loads. Firstly, the 2.5D approach for calculating the frequency response functions (FRFs) of the displacements and stresses due to the moving loads is briefed with the key parameters highlighted. Then, closed-form solutions are summarized based on Eason's work. Each moving load is modeled as a point load acting on an elastically supported infinite beam. The validity of the numerical solutions is verified against the theoretical ones. Based on the results for the sub-, trans-, and super-critical cases, it is found that the responses of stresses are more complicated than those of displacements due to involvement of differentiations on displacements. Typical phenomena, such as the Doppler effect, are much clearer in time domain than in frequency domain. Unlike the previous studies that focus mainly on the vertical displacement response, all the six stress components contain equally rich information for waves propagation and attenuation. Finally, the propagation of stress waves relates strongly to the load-moving direction. As for the ground waves, some stresses can be observed at a farther place than the others for the trans-critical case.