埋置于饱和地基中的刚性圆柱基础的摇摆振动
Rocking vibrations of rigid cylindrical foundations embedded in saturated soil
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摘要: 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。Abstract: Based on the Biot’s poroelastodynamic theory, rocking vibrations of rigid cylindrical foundations embedded in saturated soil subjected to time-harmonic excitation are studied by analytical methods. The soil underlying the foundation base is represented by a saturated half-space while the soil along the side of the foundation is modeled as an independent stratum composed of a series of infinitesimally thin poroelastic layers. The contact surface between the foundation and the soil is assumed to be perfect and fully permeable. General solutions of governing equations for saturated soils are obtained by using the Hankel transform. Based on the mixed boundary value conditions at the contact surface, the rocking integral equations are established by which the dynamic interaction problem is solved. Analytical solutions for the equivalent dynamic impedance of the rigid cylindrical foundation embedded in saturated soil are presented. The accuracy of the present solution is verified by comparisons with exciting solutions of dynamic compliance coefficients for surface foundations. Numerical results indicate that the dynamic response of foundations in a saturated medium is substantially different from that in an ideal elastic medium. The dimensionless frequency of the excitation, the depth ratio of foundation, the permeability coefficient and the Possion’s ratio have significant effects on the rocking dynamic impedance in saturated soil.