Honggui Di

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

ABSTRACT 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.

A semi-analytical model of the train-floating slab track–tunnel–soil system considering the non-linear wheel/rail contact

This paper presents a three-dimensional model for the calculation of train-induced vibration of a floating slab track in an underground tunnel based on the integration of a semi-analytical approach and a dynamic substructure method. The methodology for the train-floating slab track–tunnel–soil coupled model is described and validated by comparing the vibration response of the system with that of the Pipe-in-Pipe model. The innovations of the proposed model include the following: (1) it considers all components of the metro train-induced vibration problem including the train, the floating slab track, the tunnel, the soil and the interactions of the subsystems; and (2) it operates in the time domain and thus is capable of modelling the highly non-linear loading behaviours (i.e. the wheel/rail contact relationship). A hypothetical example is presented to illustrate the vibration isolation effect of the floating slab track using the developed model, and the following conclusions can be drawn. Excellent vibration isolation performance is observed for the floating slab track system, especially for vibrations at a high frequency (above 12.5 Hz), whereas the vibration is amplified near the natural frequency of the floating slab (i.e. 8 Hz in this study) because of the resonance effect. The amplitudes of the soil stresses are reduced due to the floating slab track system, especially for the high-frequency soil stresses.