An analytical solution for the dynamic tunnel-soil-shallow foundation interaction under a harmonic point load

Elastic waves excited by railway tunnels can induce excessive vibration in nearby buildings. The dynamic interaction between the tunnel, soils, and the shallow foundations of buildings can significantly affect wave transmission from the vibration source to buildings. In this study, a three-dimensional theoretical model involving structure-soil-structure interaction (SSSI) is proposed and the analytical solution is obtained. The foundation is assumed to be seated on the ground surface, and the full coupling between the soil and structures is considered through the perfect contact at the tunnel-soil and soil-foundation interfaces. The response of the foundation to an incident wave field generated by a harmonic point load in a tunnel is calculated, and the impact of the tunnel-soil-foundation interaction is evaluated. The numerical results show that the SSSI needs to be considered when the relative distance between the tunnel and the foundation is within twice the shear wave-length. The vertical compliance coefficient at the center of the foundation features a significant peak due to the existence of a tunnel at the resonance frequency of the soil-tunnel system. The existence of the foundation re-strains the displacement response of the ground surface within the foundation area, while causing significant amplification of the surface displacement outside the foundation area.