Harnessing multi-layered soil to design seismic metamaterials with ultralow frequency band gaps

Phononic metamaterials are capable ofmanipulatingmechanicalwave propagation in applications ranging from nanoscale heat transfer to noise and vibration mitigation. The design of phononic metamaterials to control lowfrequency vibrations, such as those induced by ground transportation and low-amplitude seismic waves, however, remains a challenge. Here we propose a new design methodology to generate seismic metamaterials that can attenuate surface waves below 10 Hz. Our design concept evolves around the engineering of the multilayered soil, the use of conventional construction materials, and operational construction constraints. The proposed seismic metamaterials are constructed by periodically varying concrete piles in the host multi-layered soil. We first validate the design concept and the numerical models by performing a lab-scale experiment on the low-amplitude surface wave propagation in a finite-size seismic metamaterial. To the best of the Authors' knowledge, this is one of the few attempts made to date to experimentally understand the vibration mitigation capability of seismic metamaterials.We then numerically demonstrate that the multi-layered seismic metamaterials can attenuate surface waves over a wide frequency range, with the incident wave energy being confined within the softest layer of the shallow layered seismic metamaterials. In addition to the localized wave energy distribution, deep layered seismic metamaterials exhibit broadband cut-off band gaps up to 7.2 Hz due to the strongly imposed constraint between piles and surrounding soil. Furthermore, these cut-off band gaps strongly depend on the constraint between the piles and the bottomlayer of the soil and hence can be tuned by tailoring the foundation stiffness.We also evidence the possibility to create constant wave band gaps by introducing hollow concrete piles with pile volume fraction b10% in the deep layered seismic metamaterials. The findings reported here open new avenues to protect engineering structures from low-frequency seismic vibrations.