To accurately analyze structures, soil-structure interaction effects must be taken into account. One approach is to create a complete finite element model of the full system wherein the soil is represented as a semi-infinite domain. This direct method is frequently adopted in research studies, but it is typically avoided in engineering practice due to the labor-intensive model development, and the high computational cost. In practice, soil-structure interaction analysis is mostly carried out through a substructure approach where the superstructure is modeled through a detailed model and is placed on a soil-foundation substructure which is represented by a system called impedance function. Then, the entire system is analyzed under foundation input motions. While the method is theoretically designed for linear-elastic behavior, it can be partially applied to nonlinear systems too. Although impedance functions for various soil and foundation configurations can be obtained from analytical, numerical, or experimental analyses, their implementation in the time-domain is not trivial because they are frequency-dependent. A simple solution for this problem has been to convert them to some physical models with frequency-independent components, but there is no straightforward way to connect these components. More importantly, the coefficients of these components could be non-physical parameters that cannot be modeled in software like OpenSEES. To resolve these problems, various alternative approaches have been proposed in the literature. In this project, we review some of the existing solutions and verify them through numerical examples. After extensive review and evaluation, the Hybrid Time Frequency Domain method seems a more practical solution with fewer stability issues. This method is implemented in Opensees to be used by researchers and practitioners.

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