Seismic response of a layered soil deposit with inclusions

It is known that soil massifs can amplify or weaken seismic waves generated by earthquakes. Therefore, the problem of studying the impact of soil deposits on the passage of seismic waves is important in terms of the facilities in operation and the design of new earthquake-resistant objects. Soil deposits, which are allotted for building, are mainly layered. In addition, the materials in these layers are also significantly heterogeneous. To describe the dynamics of inhomogeneous soil massif, the model of an elastic continuum with oscillating non-interacting inclusions is used. Within the framework of this model, the resonant properties of multi-layered soil deposit are analyzed at the conditions of harmonic perturbations applied to the bedrock. On the basis of the solution to the boundary value problem concerning oscillations of the system subjected to the free surface and conjugation conditions on the boundaries between layers, it is derived the transfer function which characterizes the amplification of shear displacements by the layered system. Within the framework of problems on the oscillations of two- and five layered systems, the analytical studies were confirmed by numerical evaluations of transfer functions. In particular, using the built-in functions of the system "Mathematica", it is developed the numerical procedure for evaluating the frequency dependencies of amplification factor for layered Kelvin-Voigt media and media with oscillating inclusions. Moreover, for the two-layered system, it is analyzed the effect on the transfer function for the ratio of layers' shear moduli and the ratio of the inclusions' natural frequencies. It is also shown that the maxima in the transfer function correspond to the eigenfrequencies of the boundary value problem.The obtained results and the proposed approach to the study of the response of the layered inhomogeneous medium to vibrational perturbations can serve as a theoretical basis for earthquake-resistant design and construction.