Metro train-track-tunnel-soil vertical dynamic interactions – semi-analytical approach

An accurate evaluation of the metro train-track-tunnel-soil dynamic interactions is very important in engineering practice. Therefore, an innovative train-track-tunnel-soil vertical coupled model was established to calculate the train-induced dynamic response of the system based on the integration of the substructure method and the semi-analytical approach. The modelling of each subsystem was presented, including the multi-rigid model of the train subsystem, the beam model of the track subsystem and the semi-analytical model of the tunnel-soil subsystem. The wheel-rail contact theory, the fastener force model and the displacement compatibility conditions were used to determine the dynamic interactive relationship between the subsystems. An explicit integral approach was used in the proposed model to analyse the complex system in the time domain which was capable of modelling highly nonlinear loading behaviours of the train-track-tunnel-soil system. The proposed model was validated by comparing with the vehicle-track coupled dynamics software VICT, the Pipe-in-Pipe model and the measured data from the onsite test in the tunnel of Ningbo Metro line 2. An illustrative example of the model was then presented to display the dynamic responses of the tunnel system under the passage of a metro train.