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考虑竖向荷载对桩基水平承载力的影响,采用能量法对地基土中端承桩的水平振动问题进行理论研究。根据分析动力学建立在水平动荷载作用下桩土系统的拉格朗日方程,通过复变函数和广义变分原理分别建立桩基和土体控制方程,采用分离变量法推导出土体位移表达式,结合桩土耦合振动条件和迭代程序得到桩基位移、内力和桩顶水平动力复阻抗解析表达式。通过算例分析,研究竖向荷载对桩顶动力复阻抗的影响以及桩周土剪切模量和桩长对桩身位移分布规律的影响。研究结果表明:动力复阻抗随竖向荷载增大而逐渐降低,桩身水平位移和转角随桩周土剪切模量增加而注浆降低;桩长达到有效桩长时,桩土系统有效耦合振动长度不发生变化。
Considering the influence of vertical load on the horizontal bearing capacity of pile foundation, the energy method is used to study the horizontal vibration problem of end bearing pile in foundation soil. The Lagrange equation of pile-soil system under the action of horizontal dynamic load is established based on analytical dynamics. The governing equations of pile foundation and soil mass are established respectively by complex variable function and generalized variational principle, and the displacement expression , The analytic expressions of pile foundation displacement, internal force and pile top horizontal complex impedance are obtained by coupling pile-soil vibration condition and iterative program. The influence of vertical load on dynamic impedance of pile top and the influence of pile shear modulus and pile length on the displacement distribution of pile body are studied. The results show that the dynamic complex impedance decreases with the increase of vertical load, and the horizontal displacement and rotation angle of the pile decrease with the increase of the shear modulus of the soil around the pile. When the pile length reaches the effective pile length, the pile-soil system is effectively coupled Vibration length does not change.