An analytical formulation to model geometric and resonant scattering of buried metabarriers for traffic-induced vibrations mitigation

We propose a metabarrier composed of an array of pipes equipped with resonators and develop an analytical formulation to investigate its mitigation performance on tunnel-induced ground-borne vibrations. The formulation calculates the displacement fields of the half-space by modelling the interaction between the tunnel-radiated waves and metabarrier-scattered waves. Both geometric and resonance scattering effects of the metabarrier are taken into account in the metabarrier-scattered waves. With the aid of the wave function method, multiple geometric scatterings of the pipes are considered by imposing the boundary conditions at the soil-tunnel/pipe interfaces, and multiple resonance scatterings of the resonators are computed by accounting for the interplays between the resonators. We demonstrate that the proposed approach can model the tunnel-radiated waves interacting with single-unit and multiple-unit metabarriers. Our analytical formulation can correctly capture multiple bandgaps provided by a periodically arranged metabarrier, namely the bandgaps induced by Bragg-type scattering due to the spatial periodicity of the pipes and the ones induced by resonance-type scattering due to the barrier resonators. As a result, the proposed barriers can be used to shield the broadband incident waves generated by the trains in a tunnel.