Hybrid Frequency-Time Domain Analysis of Nonlinear Site Response in Inhomogeneous Soils

To accurately represent the nonlinear behavior of soils while maintaining computational simplicity and preserving key frequency-dependent characteristics of soil layers, efficient simulation methods are essential. The nonlinear Hybrid Frequency-Time Domain (HFTD) method, proposed and implemented in this study, efficiently solves the equation of motion in the frequency domain and incorporates soil nonlinearity by transforming the results into the time domain. In the site response, the deviation in soil behavior from linear to nonlinear behavior depends mainly on the severity of the induced ground acceleration to the soil layers. In the innovative approach presented in this study, pseudo linear loads are directly accounted for by pseudo accelerations, which are calculated in the time domain and continuously updated in a repetitive procedure until convergence is reached. In the frequency domain part of the solution, a self-regressed parabolic function is applied to consider a continuous change in shear modulus through the depth of soil profile using a newly developed inhomogeneous transfer function. Such a comprehensive procedure enhances the solution scheme, speeds up the course of calculations, and avoids unfavorable errors while maintaining the accuracy of the method. The utilized functions were numerically formulated in this study and programmed in MATLAB codes of practice, which were next used to carry out case three studies using the published data retrieved the literature. Obtaining comparable results with recorded data as well as to those inferred from the commonly available DEEPSOIL software demonstrated the accuracy and efficiency of the proposed approach of this study.