Modeling of seismic response of soil layer within the framework of nonlocal model of continuous medium
Keywords:amplitude-frequency characteristics, resonant phenomena, nonlocal models, methods of modeling of medium response to seismic effects
According to modern research, the seismic risks of the destruction of buildings and constructions depend not only on the proximity of their location to the earthquake epicenters, but also on the reaction of soil massifs lying beneath them. Particularly important is the proportionality of the set of resonant frequencies of the soil massif and the natural frequencies of the objects located on it. It is well known that soils are rheologically complex media that cannot be described in terms of simple mathematical models. This stimulates to develop new or to modify already known models. To describe the dynamics of a heterogeneous soil massif, the model, which is a spatially nonlocal generalization of the linear Kelvin-Voigt model, is used. The work purpose is to estimate the response of the soil layer to shear strain when the soil massif is characterized by significant heterogeneity. Based on the boundary value problem solution describing standing waves in a soil layer, the dependence of the amplification of wave amplitude at the layer surface on the harmonic disturbance frequency applied to the underlying bedrock is derived. It is shown that the model describes the damping of oscillations at high frequencies and the shift of resonant frequencies towards lower frequencies. To evaluate these effects, the length of the frequency interval containing the main of the spectrum is investigated on the basis of asymptotic analysis methods. Conclusions about the influence of soil heterogeneity on its resonance properties are formulated by means of comparative analysis of the results obtained in the framework of the classical Kelvin-Voigt model and its nonlocal generalization. The proposed approach of soil layer response analysis is promising for practical use in seismic microzoning.
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