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.

翻译：为准确分析结构，必须考虑土-结构相互作用效应。一种方法是对整个系统建立完整的有限元模型，其中土体被表示为半无限域。这种直接方法在研究工作中被广泛采用，但由于建模工作量大且计算成本高，在工程实践中通常被避免。在实践中，土-结构相互作用分析大多通过子结构方法进行，其中上部结构采用详细模型建模，并置于由称为阻抗函数的系统表示的土-基础子结构上。然后，在基础输入运动下对整个系统进行分析。虽然该方法理论上针对线弹性行为设计，但也可部分应用于非线性系统。尽管可以通过解析、数值或实验分析获得各种土和基础构型的阻抗函数，但由于它们是频率依赖的，其在时域中的实现并非易事。该问题的一个简单解决方案是将它们转换为具有频率无关组件的某些物理模型，但没有直接的方法来连接这些组件。更重要的是，这些组件的系数可能是非物理参数，无法在像 OpenSEES 这样的软件中建模。为解决这些问题，文献中提出了各种替代方法。在本项目中，我们回顾了一些现有解决方案，并通过数值算例对其进行了验证。经过广泛审查和评估，混合时频域方法似乎是更实用且稳定性问题更少的解决方案。该方法已在 Opensees 中实现，供研究人员和工程师使用。