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进行土-结构动力相互作用分析的第一步便是获得地基的动力刚度矩阵,即地基阻抗。在上世纪七八十年代关于阻抗函数理论研究的黄金时期期间,众多学者建立了诸多的经验公式,极大地丰富了阻抗函数理论。在土-结构动力相互作用的重要性得到普遍重视的当今,该如何合理使用这些经验公式,是一个必须澄清的问题,这便是本文工作的目的。本文拟先基于最简单的单自由度情形,推导阻抗函数的基本公式,然后介绍目前有代表性的两类常用经验公式,第一类是以Veletsos经验公式为代表的考虑体系频率相关性的阻抗函数,第二类是以Richart经验公式为代表的不考虑体系频率相关性的阻抗函数。然后以一个简单的三层框架结构为例,利用上述两类经验公式分别计算地基的阻抗值,并以此为基础对框架结构进行模态分析和瞬态分析。计算分析表明各经验公式得到的不同阻抗值对体系频率特性和动力响应影响不大,并在对比分析的基础上推荐优先使用不考虑体系频率相关性的Richart经验公式。论文所建议的经验公式以及阻抗函数计算方法和步骤均可为实际工程结构的抗震设计提供依据。
The first step in carrying out the soil-structure dynamic interaction analysis is to obtain the foundation dynamic stiffness matrix, that is, the foundation resistance. During the golden age of the theory of impedance function in the seventies and eighties of last century, many scholars established many empirical formulas, which greatly enriched the impedance function theory. Nowadays, how to reasonably use these empirical formulas is a problem that must be clarified in the current situation where the importance of soil-structure dynamic interaction is universal. This is the purpose of this paper. In this paper, we first derive the basic formula of the impedance function based on the simplest single-degree-of-freedom case. Then, we introduce two commonly used empirical formulas, the first one is the impedance considering the frequency dependence of the system represented by Veletsos empirical formula Function, and the second type is the impedance function that does not consider the frequency dependence of the system, which is represented by Richart empirical formula. Taking a simple three-story frame structure as an example, the impedance values of the foundation are calculated respectively by using the above two types of empirical formulas, and the modal analysis and the transient analysis of the frame structure are carried out based on the results. Computational analysis shows that the different impedance values obtained by empirical formulas have little effect on the frequency characteristics and dynamic response of the system. Based on the comparative analysis, it is recommended to use the Richart empirical formula that does not consider the frequency dependence of the system. The empirical formulas proposed in this paper and the calculation methods and steps of the impedance function can all provide the basis for the aseismic design of the actual engineering structure.