Effect of longitudinally varying characteristics of soil on metro train-induced ground vibrations based on wave propagation analysis

Soil layers surrounding metro tunnels occasionally have varying characteristics in the longitudinal direction. In the existing vibration prediction model, the soil is usually simplified as a horizontally layered medium, which sometimes conflicts with the practical case mentioned above, thus potentially affecting the prediction accuracy. To address this problem, a novel model based on wave propagation analysis is proposed in this study. First, based on the wave propagation analysis, a tunnel-soil coupled model was presented where the dynamic stiffness matrix for the semi-infinite cell was derived. A useful feature for this matrix was mathematically proven, which can improve the calculation efficiency. Then, the vibration response due to the train operation was obtained by superposing the results under each point load. The accuracy was validated by comparing it with the literature and in-site measurement results. Finally, a case study was conducted to evaluate the effect of longitudinally varying characteristics of soils. In this case study, the inclined soil layers were modelled by two methods: horizontal layers and stepped varying layers. The result demonstrates that the dominant frequency, i.e., at 63 Hz, of the ground vibration is not affected by the variation in the longitudinal soil feature. The values of displacement and acceleration responses calculated by horizontally layered models are either greater or lower than those calculated by the stepped soil model. In addition, the results from the model with more soil layers are closer to those from the stepped soil model. The amplification and reduction of transfer loss due to the variation in longitudinal soil characteristics are observed at specific frequencies. Accordingly, for vibration prediction, more corresponding soil layers should be included in the simplification model. As the soil layer impacts the wave propagation characteristics, it should be modelled in detail to obtain a more accurate transfer loss function.