黏弹性地基中基于虚土桩模型的桩顶纵向振动阻抗研究

基于虚土桩模型,对均质黏弹性地基中桩土纵向耦合振动问题进行了研究。首先,假定桩侧土为各向同性的线性黏弹性材料,并考虑土体的竖向波动效应,结合Euler-Bernoulli杆件理论,建立了桩土纵向耦合振动的定解问题;其次,采用分离变量法求解桩侧土纵向振动的控制方程,得到了桩侧土与桩身接触面上的剪切动刚度,将所得的剪切动刚度代入到桩身振动控制方程,采用Laplace变换技术,进一步求得了任意荷载作用下桩顶纵向振动阻抗的解析解。基于所得解,详细讨论了不同桩身设计参数时桩端土厚度对桩顶纵向振动阻抗的影响。最后,将虚土桩模型与其他桩端土支承模型进行了对比研究,结果表明,对虚土桩模型选用合适的材料参数和桩端土厚度,其得到的桩端支承复刚度值介于现有多种模型的计算值之间。

Study on the vertical dynamic impedance of pile embedded in viscoelastic soil based on fictitious soil pile model

Based on fictitious soil pile model, the vertical dynamic response of pile embedded in homogeneous viscoelastic soil is investigated. Firstly, assuming the surrounding soil of pile to be isotropic viscoelastic material and considering its vertical wave effect, the definite problem of soil-pile system subjected to arbitrary dynamic force is established based on the Euler-Bernoulli rod theory. Secondly, the shear dynamic stiffness at the interface of soil and pile is derived by means of separation of variables to solve the governing equation of surrounding soil. Substituting the shear dynamic stiffness into governing equation of pile, the analytical solution of vertical dynamic impedance is derived by virtue of Laplace transform technique. Based on the obtained solution, the influence of depth of pile end soil on the vertical dynamic impedance is studied in detail for different designing parameters of pile. Lastly, fictitious soil pile model and other pile end soil supporting models are compared. It is shown that complex supporting stiffness calculated by fictitious soil pile model is among the supporting stiffness calculated by other existing models if there are appropriate material parameters and depth of pile end soil for the fictitious soil pile model.