Resonant Properties of Layered Soil Massif Containing a Layer With Oscillating Inclusions

Abstract

The paper is devoted to modeling of the seismic reaction of an inhomogeneous soil massif consisting of three layers that can incorporate oscillating inclusions. The description of the behavior of soil strata is carried out on the basis of the continual approach, within which the dynamics of the medium is determined by a system of equations of motion and equations of state, where the elastic or visco-elastic properties of the medium are indicated. Classical linear models are quite simple and well verified experimentally, but due to the complex structure of natural geomedia, these models cannot always adequately describe wave processes in them. This requires improvement of models in such a way as to take into account the internal structure of materials. In this paper, to describe the shear dynamics of an inhomogeneous soil massif, the equations of motion for a continuous medium in the form of mutually penetrating continua are used, one of which coincides with the Kelvin-Voigt carrier medium, and the other one is described by a set of noninteracting partial oscillators. Various inclusions, cracks, or cavities filled with gases and/or liquids can act as oscillators. The equations of motion are supplemented by the compatibility conditions at the boundaries of the layers. The set of layers is considered, among which only one contains oscillating inclusions. The one-dimensional boundary value problem with a free surface and the harmonic law of deformation of massif's rigid bedrock is solved. Using the exact solution of the boundary value problem, the amplification factor of strains for massifs with characteristics close to natural is calculated. Moreover, the iterative procedure, which makes it possible to write down the final formula for the amplification factor in the case of a layered medium with layers of more than 3 is developed. It is shown that the incorporation of inclusions in one of the layers leads to the appearance of an additional resonance frequency, a shift of resonances to the low-frequency region, the appearance of zones with significant damping of resonance peaks. The results obtained make it possible to improve the computational methods for determining the quantitative parameters of seismic hazard when work on seismic micro zoning of construction and operational sites in the seismic regions of Ukraine is carried out.