Decorated membrane resonators as underground seismic wave barriers against high magnitude earthquakes

Abstract

We report a framework of underground barriers against seismic waves from high-magnitude earthquakes, which consist of the deep subwavelength decorated membrane resonators (DMR's) modeled as a type of artificial soil, the meta-soil, which is buried in the host soil. The meta-soil has the same elastic properties as the host soil but with a dynamic effective mass density that mimics the functionality of the DMR's mixed with the host soil. Metallic membrane DMR's with multiple working frequencies down to 7 Hz are experimentally demonstrated. Transmission attenuation exceeding 20 dB and absorption above 98% are numerically demonstrated for the 1 Hz Rayleigh waves using about 12 rows of underground meta-soil columns. The findings obtained from the meta-soil are validated by using discrete generic tuned mass dampers buried in the soil. A scaling law similar to the mass density law for acoustic waves that relates the meta-soil mass density to the wave frequency for a given transmission attenuation has been analytically derived and numerically verified. The main mechanism for the wave attenuation is the resonant enhancement of scattering and dissipation by the resonators in the meta-soil. The findings for attenuating the 1 Hz seismic waves serve as a benchmark and design platform for the broadband seismic wave barriers due to the following findings. (1) It is a representative frequency for high magnitude earthquakes. The practical lower frequency limit is about 0.5 Hz, so the dimension and weight of the dampers for 0.5 Hz will be comparable to that for 1 Hz, while the dampers for higher frequencies will be smaller in size and lighter in weight. (2) The length of the wells will be comparable to that of the 1 Hz ones and proportionally shorter for higher frequency waves. Our findings provide a viable solution that could fill the gap between the maximum earthquake resistance capability of most modern buildings and infrastructures (∼seventh magnitude) and the need to resist the highest (∼eighth) magnitude earthquakes recorded in human history, and remedy one of the main shortcomings in the literature on the local resonators for underground seismic wave barriers, which is the gross over-estimation of the seismic wave blocking power of the barriers due to the omission or unrealistic under-estimation of the intrinsic dissipation of the elastic components of the local resonators.