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考虑土体应力-应变的梯度变化及桩土耦合振动,对竖向荷载作用下饱和土中端承桩水平振动问题进行了理论研究。采用Euler模型模拟桩基,建立了竖向荷载作用下桩基水平振动控制方程;通过势函数解耦土体Biot动力固结方程,并利用Laplace变换和分离变量法得到土体应力和位移解析表达式;结合桩土连续性条件得到桩基位移、内力和桩顶水平动力复阻抗解析解。将退化解与已有文献进行对比,验证了解的合理性。通过算例分析,讨论了竖向荷载和长径比对桩基位移和内力的影响,研究结果表明:竖向荷载和长径比均会使桩身位移和内力发生重分布;在进行桩基水平向承载力设计时,有必要考虑竖向荷载的影响。
Considering the gradient of soil stress-strain and the coupling vibration of pile-soil, the horizontal vibration of bearing pile in saturated soil under vertical load is studied theoretically. The Euler model is used to simulate the pile foundation, and the governing equation of pile foundation horizontal vibration under vertical load is established. The Biot dynamic consolidation equation of soil is solved by potential function, and the analytic expression of soil stress and displacement is obtained by Laplace transform and separation variable method The analytic solution of pile foundation displacement, internal force and pile top horizontal complex impedance is obtained by combining the conditions of pile-soil continuity. The degradation solution is compared with the existing literature to verify the rationality of the solution. The influence of vertical load and aspect ratio on the displacement and internal force of pile foundation are discussed. The results show that both the vertical load and the aspect ratio will cause the displacement and internal force of the pile body to redistribute. When the pile foundation Horizontal bearing capacity design, it is necessary to consider the impact of vertical load.