Design of an underground metamaterial for attenuation of seismic shear waves

In the recent decade, some effort is expended in deviating and attenuating seismic waves, following the sophisticated electromagnetic-wave (photon) control by a well-known synthetic-material technology: metamaterial. There are many reports in the literature on successful control of mechanical waves (phonons) in acoustic and thermal frequency ranges by phononic crystals and metamaterials; however, they fail to efficiently control waves over low-frequency ranges, like seismic and earthquake waves. The bottleneck is the very long wavelengths of the earthquake waves which inevitably necessitates large-scale structures for seismic metamaterials. This research intends to dampen destructive shear waves before reaching the target structures by designing metamaterials with small dimensions and easy portability and execution. The rationale of this study is that in earthquakes, a significant part of the damage to the building is caused by the excitation of the first vibrational mode, and if the waves with frequencies near to the frequency of the first vibration of the building are filtered out or damped from the frequency content of the input excitation, the resonance phenomenon may not occur, and damage to the building is expected to be significantly reduced. In this study, with the aim of protecting typical two- to six-story buildings, the frequency range of the first vibrating mode is determined based on the experimental relationships presented in Section 6 of the Iran National Building Code. Then, utilizing the proposed dispersion relation for the one-dimensional metamaterial, the geometry and material of the metamaterial base resonator are designed so that the metamaterial stop-band corresponds to the target frequency range which is supposed to be filtered out. In order to facilitate the implementation, efforts have been made so that the dimensions of the base resonator are not large. The metamaterial designed for placement in medium clay, is a cylinder with a diameter and a length of 0.5 m of lightweight and high-strength concrete in which the interior lead cylinders are located in an intermediate filling fluid. Using the simplified continuous model of the proposed metamaterial, its performance against the shear wave with the frequency located in the target stop-band has been investigated. Based on this study, the proposed metamaterial is able to quickly reduce the amplitude of shear waves of an earthquake. This metamaterial can be used to protect urban buildings built near faults. It might also be used for cases where earthquake-resistant systems cannot be installed in the body of structures or foundations (e.g. historical and sensitive buildings, rural or old urban areas, etc.).