Three-dimensional train-periodic slab track-subgrade dynamics model based on the iterative solution and Green’s function method

This paper develops an iterative solution model for the efficient and accurate simulation of the dynamics of a three-dimensional (3D) train-periodic slab track-subgrade (TPSTS) system. The entire system is divided into the train-rail subsystem and the periodic slab-subgrade subsystem. An ordinary differential equation (ODE) model of the train-rail system is established, and a step-moving strategy is employed to enhance the computational efficiency. A frequency-domain Green's function method (GFM) model is employed for modelling the periodic slab-subgrade. Considering the periodicity, symmetry, and attenuation characteristics of the track structure, the Green's function of the slab-subgrade structure is obtained by conducting harmonic response analysis on a finite element model (FEM) of a quarter slab-subgrade structure. The proposed model is utilized to investigate the vibration characteristics of the high-speed train-track-subgrade system. The results indicate that the model exhibits good convergence, accuracy, and efficiency. The periodicity of the track structure has a significant impact on the statistical values of subgrade displacement and stress amplitudes along the track's longitudinal direction. At the subgrade surface, the amplitudes of displacement, stress, and acceleration exhibit fluctuations in the lateral direction of the track. However, with increasing depth, these amplitudes generally attenuate, leading to a more uniform distribution.