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基于Biot动力控制方程,用解析的方法研究了简谐激振作用下埋置于饱和地基中的刚性圆柱基础的摇摆振动问题。基底以下的土被视为饱和半空间,基础侧面的土视为由若干圆形极薄饱和层组成的独立层,假设土与基础完全黏着接触且接触面完全透水。运用Hankel积分变换对饱和土的动力控制方程进行求解,然后结合基础与地基的混合边值条件求解了相应的动力响应问题,并给出了饱和地基的等效动力刚度表达式。为验证本文结果的正确性,计算了基础位于地基表面时的动力柔度曲线,并与已知文献中的结果进行了相应对比。数值分析结果表明:基础在饱和地基中的动力响应与在弹性地基中有很大的不同,无量纲激振频率、基础埋置深度、渗透系数和泊松比对饱和地基的摇摆动力刚度有很大的影响。
Based on the Biot dynamic governing equations, the oscillation problem of rigid cylindrical foundations embedded in saturated ground under simple harmonic excitation is studied by analytical method. The soil below the basement is considered as a saturated half-space. The base-side soil is considered as a separate layer of several very thin circularly saturated layers, provided that the soil is completely in contact with the foundation and that the contact surface is completely water-permeable. The governing equations of saturated soil are solved by Hankel integral transform. Then the corresponding dynamic response problem is solved by combining the boundary conditions of the foundation and the foundation, and the equivalent dynamic stiffness expression of saturated soil is given. In order to verify the correctness of the results in this paper, the dynamic compliance curves of the foundations on the ground surface are calculated and compared with the results in the known literature. The results of numerical analysis show that the dynamic response of foundation in saturated soil is quite different from that in elastic foundation. The dynamic stiffness of saturated foundation is very large due to the dimensionless excitation frequency, foundation embedment depth, permeability coefficient and Poisson’s ratio Impact.