A multiple scattering formulation to design meta-trenches for mitigating low-frequency ground-borne vibrations induced by surface railways and subways

We propose a multiple scattering formulation to investigate the performance of meta-trenches. The meta-trench is a novel device, composed of an array of resonant units buried in the ground in a proper arrangement, aimed at reducing the railway and/or subway induced ground motion by exploiting its scattering and resonant properties. Compared to classical open trenches, the resonators contribute to improving the wave mitigation performance of the trench in the low-frequency regime.The proposed formulation allows to consider the wave source anywhere in the half-space and a generic distribution of resonators in terms of number and position. The incident wave field generated by the source, such as a train or subway, along with the scattered wave fields produced by the resonant units that constitute the meta-trench, are modeled via Green's functions. The multiple scattering formulation enables the solution of coupled wave problems by determining the amplitudes of scattered wave fields at various frequencies. Through comparison with finite element simulations, we demonstrate that in both buried source (i.e., subway) and surface-located source (i.e., ground railway) scenarios, our analytical formulation is able to properly model the dynamics of the coupled problems with a noticeable computational cost saving. Opening to fast and reliable parametric simulations, our formulation allows for a deeper knowledge of the wave interaction processes, resulting thus in a reliable tool for predicting the coupled wave field under both bulk and Rayleigh waves.