Broadband and omnidirectional attenuation of bulk waves in transversely isotropic soil by cross-like metamaterials

Metamaterials with bandgap properties have been widely studied and applied in the attenuation of surface and bulk waves propagating in the soil. However, most of the studies consider soil as the isotropic medium and ignore the general anisotropy property from the practical point of view. In this work, we consider the transversely isotropic constitutive model of soil and propose a cross-like metamaterial consisting of concrete inclusion and rubber coating to achieve broadband attenuation for omnidirectional bulk waves. The proposed cross-like metamaterials have more and wider bandgaps compared to circle and square metamaterials, and they have better wave attenuation performance in transversely isotropic soil with higher degrees of anisotropy. The transmission spectra of cross-like metamaterials demonstrate the wave attenuation effect of bandgaps. Furthermore, we build the full-scale transmission model considering the subway tunnel condition and demonstrate the practical wave attenuation performance of cross-like metamaterials in frequency and time domains. We also find that a larger depth of the metamaterial region will enhance wave attenuation in the bandgaps while considering rubber viscosity can enhance wave attenuation in the overall frequency ranges. The variations of omnidirectional bandgaps with rubber thickness, geometric parameters, and hollow concrete sizes are discussed. This study presents an appropriate way to design metamaterials for broadband omnidirectional bulk wave attenuation in transversely isotropic soil, which can be easily extended to other anisotropic media.