The calculation of the response stratified soil deposits subjected to earthquake excitations is a very important problem in earthquake engineering. The problem becomes complicated when one wants to consider simultaneously the nonlinear behavior of the soils and to use the hysteretic or complex modulus damping. The use of the Equivalent Linear method and the Frequency Response method allows one to handle the problem in an approximate way. The Equivalent Linear method is an iterative procedure in which the approximate solution is obtained by solving linear problems with equivalent properties. A new methodology to obtain the nonlinear response of horizontally stratified soil deposits is presented in this paper. The proposed method is based on the application of the Volterra series in the frequency domain. The method uses Higher Order Frequency Response functions, which are generalizations of the well known Frequency Response Function. Up to Third Order Frequency Response functions or kernels are developed in this study. Since depending on the analytical model of the soil deposit the determination of these functions can become quite intricate, a shear model of the system is used. The use of these functions in some numerical examples and a comparison with the Equivalent Linear method are presented. Also, a sensitivity analysis is done to study how the series is affected by the numbers of terms used. It is shown that for low or medium shear strains, three terms in the series are enough to obtain acceptable results.
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