基于格林函数的相邻条形基础摇摆动力相互作用

基于弹性半空间理论,研究两个相邻明置条形基础的摇摆动力相互作用,将各条形基础与地基的接触面分割成若干个子单元,各单元的位移由基础的刚体位移决定。推导了非对称简谐条形均布载荷作用下弹性地基位移的格林函数,通过分段积分及Cauchy主值积分处理多值广义函数的积分问题。运用所得格林函数求解各单元上的接触力,根据叠加原理得到土与相邻明置条形基础的摇摆动力耦合阻抗函数,详细分析了基础和地基参数对摇摆动力相互作用的影响。计算表明,当两明置条形基础距宽比S/L≤4.0时,应考虑其摇摆动力相互作用效应。所提方法具有计算简便和精度高的特点,对全频段阻抗函数的计算均适用,研究结果为结构抗震设计中考虑土体与多基础的动力相互作用提供了理论依据。

Green function analysis of rocking interaction between soil and adjacent strip foundations

The rocking interaction between adjacent strip foundations is studied based on the elastic half-space theory. The interface between the foundations and the supporting medium is divided into a number of strip elements. Asymmetrical Green function of the displacement of elastic soil medium under harmonic uniform excitation is derived. The multi-value improper integral is precisely calculated by the piecewise integration method and Cauchy principal value integral. The coupling rocking impedances between soil and adjacent strip foundations are solved. The bending moments caused by the contact forces of Green function is added on each element. The analysis uses the fact that the displacement of a rigid foundation determines that of each element. Influences of calculating parameters of foundation and soil medium on the rocking interaction between two foundations are discussed in detail. The numerical results show that the rocking interaction between adjacent strip foundations should be taken into consideration when the spacing and width ratio S/L is less than 4.0. This method is simple, has a highly accurate, and can be used for the calculation at a high frequency range. The research results provide a theoretical basis for the study of soil-foundations dynamic interaction, and make it convenient for engineers to consider dynamic interaction between adjacent foundations in the seismic design of structures.