不同经验公式对地基阻抗函数影响的对比分析

Comparison Analysis of the Influence of Different Empirical Formulas on Soil Impedance Functions

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 for soil-structure dynamic interaction analysis is to obtain the dynamic stiffness matrix of soil,which is also called soil impedance. Lots of empirical formulas are deduced and proposed by many scholars during the golden age for the study of soil impedance in 1970s and 1980s,which enrich the soil impedance functions greatly. Nowadays,the importance of soil-structure dynamic interaction has attracted extensive attention. It should be clear that how to use these empirical formulas rationally,and this is the aim of this paper. The basic formulas for soil impedance will be deduced based on the simplest single degree of freedom. And then,two kinds of representative formulas are introduced:( 1) the system in which the natural frequency characteristics are considered and represented by Veletsos formula;( 2) the system in which the natural frequency characteristics are not considered and represented by Richart formula. Lastly,taking a three-layered frame structure as an example,the soil impedances are calculated by above two formulas,and modal analysis and transient analysis are conducted. The computation results show that the differences of soil impedances come from three empirical formulas are small,which have little influence on structure dynamic response. And the Richart formula is recommended by the authors based on comparison of three formulas. The suggested formulas and the computation method and procedure for soil impedance calculation will provide references for the design of practical engineering structures.