Semi-analytical solution of a coupled tunnel-soil periodic model with a track slab under a moving train load

The prediction of ground-borne vibrations induced by underground trains in tunnels is advantageous for guiding vibration-mitigation designs. The supporting forces of the fastener acting on the track bed that is induced by the train operation are spatially periodic in the tunnel axis direction. Utilising this feature, this paper proposes a novel periodic tunnel-soil model with a track slab to simulate the propagation of train-induced vibrations. The periodic tunnel-soil model based on wave transformations is briefly introduced, and then the slab beam is solved analytically and combined with the tunnel invert using equivalent springs based on the generalised modal function series. The train load and its single component are mathematically decomposed in a generalised modal space for application to the semi-analytical periodic model. Two measures for further improving the calculation efficiency of the semi-analytical model under the moving train load are presented and discussed in detail. The formulation correctness of this model is ensured by literature verification. Furthermore, an in-situ measurement of the vibration on the tunnel wall and ground surface by the train passage in the Hefei metro is conducted to validate this semianalytical model. It is demonstrated that the proposed model is accurate and efficient for predicting ground-borne vibrations generated by train loads, thus it has the potential to predict vibration levels at a large number of receiver points around a newly constructed metro line.