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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。
Based on the theory of elastic half-space, the interaction of rocking forces between two adjacent strip-shaped bars is studied. The contact surface between each strip foundation and the foundation is divided into several sub-units. The displacement of each unit is determined by the basic rigid-body displacement. The Green’s function of elastic foundation displacement under asymmetric simple harmonic strip uniform load is deduced. The integral problem of multi-valued generalized function is solved by means of piecewise integral and Cauchy principal value integral. The obtained Green’s function is used to solve the contact force on each element. According to the principle of superposition, the coupled dynamic impedance function between the soil and the adjacent bright strip foundation is obtained. The influence of the foundation and ground parameters on the dynamic interaction is analyzed in detail. The calculation shows that when the spacing ratio of two strip-shaped strip foundation S / L≤4.0, the swinging dynamic interaction effect should be considered. The proposed method has the advantages of simple calculation and high precision, and is applicable to the calculation of full-range impedance function. The research results provide a theoretical basis for considering the dynamic interaction between soil and multi-foundation in seismic design of structures.