Seismic wave amplification in a weakly nonlinear two-layered soil deposit

Based on numerous observations, local soil site conditions can significantly affect the formation of seismic responses. In this paper, we examine seismic responses caused by shear waves propagating through a twolayered soil deposit. The aim of the research is to study the phenomenon of amplification of shear waves due to the resonant properties of the soil deposit and the nonlinear characteristics of partial layers, which are assumed to be the cubically nonlinear continuous media. The target problem relates to a nonlinear boundary value problem, the solution of which is carried out using a semi-analytical approach. According to the approach, the problem's solution is sought using the method of separation of variables, while the solution to the corresponding spectral problem is derived in the form of a power series. Additionally, good agreement is shown between theoretical studies and numerical simulations. The developed approach allows one to evaluate the amplification factor for a nonlinear two-layered soil deposit and to detect changes in the shape of amplification factor profiles when the frequency of an incident wave on a rigid bedrock is varied.