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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。
Based on the three-axis axisymmetric unsaturated soil wave equation, considering the influence of soil matrix suction on shear modulus, the coupled pile-soil vibration characteristics of end-supported pile under longitudinal simple harmonic load are studied. The coupling equations are directly decoupled by using the method of operator decomposition and separation. On the basis of obtaining the modal and impedance factor of unsaturated soil, combining with the condition of the interface between pile and soil and the rigid support form of pile tip, The one-dimensional wave equation of the pile is solved. The complex stiffness function of the pile top and the solution of the soil impedance factor in frequency domain are obtained. The influence of the main parameters on the dynamic behavior of pile foundation is also discussed. The calculation results show that as the saturation decreases, the dynamic stiffness of the pile top and the equivalent damping amplitude decrease, but the resonance frequency of pile-soil system is basically unaffected. In the analysis of pile-soil modulus ratio, different responses to soil and pile elastic modulus should be distinguished. The model reveals the complete evolution process of soil dynamic response from single phase to saturated two-phase medium, and provides a complete theoretical framework for describing the dynamic behavior of pile foundation under actual soil environment.