非饱和土半空间中单桩竖向振动特性研究

从三维轴对称的非饱和土波动方程出发，考虑土中基质吸力对剪切模量的影响，对端承桩在纵向简谐荷载作用下桩土耦合振动特性进行了研究。利用算子分解和分离变量法直接对耦合方程进行解耦，在求得非饱和土层振动模态形式和阻抗因子的基础上，结合桩土界面处的衔接条件以及桩端刚性支承形式，对桩的一维波动方程进行求解，得到了桩顶复刚度函数、土层阻抗因子的频域形式解答，并讨论了主要参数对桩基动力行为的影响。计算结果表明：随着饱和度的减小，桩顶动刚度因子和等效阻尼的振幅随之减小，但桩土体系的共振频率则基本不受其影响。在桩土模量比的分析中，应区别对待土和桩弹性模量引起的不同反应。模型揭示了土体动力响应从单相到饱和两相介质条件下的完整演化过程，为描述实际土体环境下桩基动力行为提供了较为完备的理论框架。

Dynamical response of vertically loaded pile in half-space of unsaturated porous media

By virtue of the 3D axisymmetric three-phase elastodynamic theory and considering the effect of matric suction on the dynamic shear modulus, the harmonic dynamic response of end-bearing piles embedded in unsaturated poroelastic medium subjected to vertical loading is investigated. The resistance factor and vibration modes of the soil layer are obtained from the direct decoupling of the governing equations by employing the differential operator splitting and variable separation method. On the basis of the assumptions of perfect contact along the pile-soil and the rigid supported type at the pile tip, the wave equation for the pile treated as a bar and described by the conventional 1-D structure vibration theory is then solved. Ultimately, the functions of complex stiffness at the top of the pile together with the soil impedances in the frequency domain are derived, and the selected numerical solutions are presented to portray the influences of principal parameters on the dynamic behaviors of pile. The results show that as the saturation decreases, the dynamic stiffness factor and the equivalent damping both decrease, while the resonance frequencies of the pile-soil system are almost not affected. It is necessary to differentiate the various responses evoked by the moduli of soil and pile during the analysis of pile-soil modulus ratio. The proposed model reveals an entire evolutional process of dynamic response of soil from single-phase media to two phase saturated media, and provides a comprehensive theoretical framework to describe the dynamic behavior of pile under actual soil environment.