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弹性半空间理论的研究表明,基底地基的弹性系数和阻尼系数随振动的频率而变化,其变化的规律视地基介质的性质、基础的几何特性以及振动类型而不同。T.K.Hsieh经过对前人研究成果的分析指出,为工程上能应用,在一定的相对频率范围内,可以认为基底的弹性系数随振动频率的平方而减小,而基底的阻尼系数则随频率而线性增大。文献[4]还给出了基础竖向、水平、摇摆、扭转四种单向振动情形弹性系数与阻尼系数随振动频率变化的具体定量关系。根据这些关系,刚度系数和阻尼系数可统一表示成如下的形式:
The study of the elastic half-space theory shows that the elastic coefficient and the damping coefficient of the foundation vary with the frequency of the vibration, and the law of its variation depends on the nature of the foundation, the basic geometric characteristics, and the type of vibration. TKHsieh analyzed the results of previous studies and pointed out that for applications in engineering, in a certain relative frequency range, it can be considered that the elastic coefficient of the substrate decreases with the square of the vibration frequency, while the damping coefficient of the substrate follows the frequency. Increased linearly. The literature [4] also gives the specific quantitative relationship between the elasticity coefficient and the damping coefficient with the change of the vibration frequency in the four vertical one-way vibration situations of vertical, horizontal, swaying and torsion. According to these relationships, the stiffness coefficient and the damping coefficient can be expressed collectively as follows: