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The results of modern studies of the earthquakes impact indicate that the soil layers located under buildings and structures can significantly transform the seismic wave passing through their thickness and have a catastrophic effect on these objects. Hence, the study of wave processes in soil massifs is extremely important and relevant. It is known that soils are characterized by significant heterogeneity, which affects the spectral characteristics of seismic waves, so this should be taken into account when analyzing wave fields in the soil layers. In this paper, it is proposed to describe the dynamics of an inhomogeneous soil massif within the model of an elastic continuum with oscillating non-interacting dissipative inclusions. To examine vibrations in the layer of finite thickness with a free surface and harmonic perturbation applied to its lower edge, it is formulated the boundary value problem for the equations of medium’s motion. Based on the solution of this problem, the influence of inclusions on the characteristics of waves is analyzed. It is found out that the natural frequency of inclusions significantly affects the transfer function, which characterizes the amplification of the displacements on the free surface relative to the displacements at the lower boundary of the layer, i. e. when the natural frequency of inclusions increases, near the leading resonant peak additional resonant frequency appears, while for high frequencies a degeneration of resonant frequencies is observed. In the case when the natural frequencies of the inclusions have a non-discrete distribution with two separate frequencies, the effect of the inclusions is manifested at low-frequency oscillations, and in the high-frequency region only the resonant amplitude decreases. The approach, which uses the model with oscillating inclusions to the analysis of layer response to seismic disturbances, is promising for seismic design and construction.

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.

Experiments on deformation structured model medium formed by elements in the form of balls of the same diameter under the impulse loading are performed. It is found that the stress-strain diagram of such medium depends on the size of structure elements and the nature of their interaction. The character of deformation of the structured medium by multiple loads is investigated.