基于虚土桩模型的三维饱和介质中浮承桩纵向振动特性分析

Longitudinal vibration characteristics of floating pile in threedimensional saturated soils based on virtual soil pile model

基于Biot波动理论提出了一种桩底饱和虚土桩模型,同时考虑桩周、桩底土体三维波动效应及饱和特性,建立了三维饱和黏弹性土、虚土桩和实体桩完全耦合振动定解问题。采用势函数求解得出饱和土体位移解,并利用饱和土-桩界面耦合条件,求解得出桩顶纵向振动动力阻抗解析解答。将所得解退化到已有解析解进行对比验证,并在此基础上对浮承桩纵向振动特性进行参数化分析,计算结果表明:桩底饱和土层厚度越大,桩顶动刚度和动阻尼曲线振幅及共振频率越小,且当桩底饱和土层厚度增大到一定程度后,振幅呈现大、小峰值交替现象;桩周饱和土体孔隙率仅对桩顶动力阻抗曲线振幅产生明显影响,而桩底饱和土体孔隙率对桩顶动力阻抗曲线共振幅值和共振频率均影响显著;随桩周、桩底饱和土体剪切模量的增加,桩顶动力阻抗曲线共振幅值水平均明显降低,且受桩周饱和土体剪切模量影响更为突出。

Based on the Biot’s theory of wave propagation, a saturated virtual soil pile model is proposed. Considering the three-dimensional wave effect and saturation characteristics of surrounding soil and beneath the pile toe, a three-dimensional system including saturated viscoelastic soil, virtual soil pile and solid pile is established. The analytical solution for displacement of saturated soil is also derived by potential function method. The vertical dynamic impedance at the pile head is obtained using the pile-soil compatibility conditions. Finally, the obtained solution is reduced to verify its validity with existing solutions. Furthermore, extensive parametric analysis is performed to investigate the effects of saturated soil parameters on the vibration characteristics at the pile head. The computational results show that the amplitude and resonance frequency of dynamic impedance at the pile head in saturated soil decrease with increase of saturated soil thickness beneath the pile toe. When the thickness of saturated soil beneath the pile toe increases to a certain extent, the pattern of staggering peak become evident. The porosity of saturated soil beneath the pile toe has significant effects on both the resonance amplitude and resonance frequency of the dynamic impedance at the pile head, while the porosity of saturated surrounding soil only influence the resonance amplitude. With increasing shear modulus of surrounding soil and soil beneath the pile toe, the amplitude of the dynamic impedance at the pile head is significantly reduced, and it is more affected by the shear modulus of surrounding soil.