饱和粘弹性土层中空心圆柱桩的轴对称竖向振动

Axisymmetrical Vertical Vibration of Hollow Cylindrical Pile in Saturated Poro-Viscoelastic Soil Layer

考虑桩的径向变形以及饱和土层对桩的径向力作用,分别将空心圆柱桩和饱和土层视为单相弹性介质和饱和粘弹性介质.基于弹性动力理论及不可压饱和多孔介质理论,研究了饱和粘弹性土层中端承弹性空心圆柱桩竖向振动的动力特性.利用Helmholtz分解和变量分离法,在频率域得到了空心圆柱桩竖向稳态振动的轴对称解析解以及桩头复刚度的解析表达式,给出了空心圆柱桩桩头动刚度因子和等效阻尼随激励频率的响应曲线,数值考察了饱和土和桩的材料、几何等参数对桩头动刚度因子和等效阻尼的影响.研究结果表明,虽然空心圆柱桩精确轴对称解析解的桩头静刚度与经典Euler杆模型桩的桩头静刚度几乎相等,但其桩头动刚度因子和等效阻尼存在较大区别,并且空心圆柱桩的内外径比(即桩壁厚比)会对桩头动刚度因子和等效阻尼特性产生显著的影响.因此,经典Euler杆模型桩的适用范围具有一定局限性,应采用轴对称模型进行更加精确的分析.

Considering radial deformation of pile and radial stress of saturated soil layers on the pile profile, and regarding the pile and soil layer as a single phase elastic medium and a saturated poro-viscoelastic medium, respectively, the dynamical behavior of vertical vibration of an end-bearing elastic hollow cylindrical pile in a saturated poro-viscoelastic soil layer is studied. With the Helmholtz decomposition and variable separation, the axisymmetrical analytical solutions for vertical stationary vibrations of hollow cylindrical piles and the analytical expression of complex dynamic stiffness of the pile top are presented in the frequency domain. The responses of dynamic stiffness factor and equivalent damping of pile top with frequency are shown using a numerical method. Effects of material and geometry parameters of the saturated poro-viscoelastic soil and pile on the dynamic stiffness factor and equivalent damping are examined. Although static stiffness of the pile top of a hollow cylindrical pile for the axisymmetrical analytical solution and classical Euler-rod model solution are almost the same, there exist distinct differences for dynamic stiffness factor and equivalent damping between the axisymmetrical analytical solution and classi- cal Euler-rod model solution. Further, the ratio between the inner and outer radii of the hollow cylindrical pile has great influence on dynamic stiffness and equivalent damping of pile top. Therefore, there are limitations for the applicability of the pile with the classical Euler-rod model. A more accurate analysis should be based on the axisymmetrical model.