This Letter introduces a seismic metamaterial (SM) composed by a chain of mass-in-mass system able to filter the S-waves of an earthquake. We included the effect of the SM into the mono dimensional model for the soil response analysis. The SM modifies the soil behavior and in presence of an internal damping the amplitude of the soil amplification function is reduced also in a region near the resonance frequency. This SM can be realized by a continuous structure with inside a 3d-matrix of isochronous oscillators based on a sphere rolling over a cycloidal trajectory.
Metamaterials can be engineered to interact with waves in entirely new ways, finding application on the nanoscale in various fields such as optics and acoustics. In addition, acoustic metamaterials can be used in large-scale experiments for filtering and manipulating seismic waves (seismic metamaterials). Here, we propose seismic isolation based on a device that combines some properties of seismic metamaterials (e.g., periodic mass-in-mass systems) with that of a standard foundation positioned right below the building for isolation purposes. The concepts on which this solution is based are the local resonance and a dual-stiffness structure that preserves large (small) rigidity for compression (shear) effects. In other words, this paper introduces a different approach to seismic isolation by using certain principles of seismic metamaterials. The experimental demonstrator tested on the laboratory scale exhibits a spectral bandgap that begins at 4.5 Hz. Within the bandgap, it filters more than 50% of the seismic energy via an internal dissipation process. Our results open a path toward the seismic resilience of buildings and a critical infrastructure to shear seismic waves, achieving higher efficiency compared to traditional seismic insulators and passive energy-dissipation systems.
In this paper the static and seismic values of bearing capacity factors for shallow strip foundations adjacent to slopes have been evaluated using the method of characteristics, accounting, through the pseudo-static approach, for the effect of horizontal and vertical inertia forces arising in the soil and transmitted by the superstructure. Differently from most of the available studies, the effect of the inertia forces in the soil, due to the seismic wave propagation, and the effect of inertia forces acting in the superstructure, due to the structural seismic response, are dealt with independently. It was also demonstrated that the above-mentioned effects can be superimposed without significant error. Original empirical formulas and, in some cases, closed-form solutions, have been provided to calculate bearing capacity factors or suitable corrective coefficients which allow accounting for slope inclination and for horizontal and vertical seismic accelerations in the soil and in the superstructure. The proposed solutions, obtained assuming Hill's and Prandtl's failure mechanisms, have been checked against those obtained through finite-element analyses and compared with results already available in the literature.
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