横观各向同性地基中管桩扭转振动响应解析解

Analytical solution for torsional dynamic response of a pipe pile in transversely isotropic soil

考虑地基沉积过程中产生的竖向和水平向力学性质的差异,对横观各向同性地基中管桩扭转振动频域响应进行了理论研究。基于横观各向同性材料的本构关系以及桩-土耦合扭转振动,建立了桩土系统定解问题,通过Laplace变换和分离变量法求得了桩周土和桩芯土扭转振动位移形式解。通过桩-土接触面的连续条件,求得了管桩扭转频域响应解析解,并得到了桩顶复动刚度和速度导纳的表达式。将所得解退化到横观各向同性地基中实心桩解以及均匀地基中管桩解,并与已有文献进行了对比,验证了解的合理性。通过数值算例,分析了桩周土和桩芯土的横观各向同性力学参数对桩顶扭转复刚度及速度导纳的影响。

With considering the difference between the horizontal and vertical mechanical properties of ground base, the torsional dynamic response of a pipe pile in transversely isotropic soil is investigated. Based on the stress-strain relationships of transversely isotropic material and soil-pile coupled vibration, differential equations and boundary conditions of the pile and soil are established. The solutions for the displacements of the outer and inner soil are obtained by Laplace transform and the variable separation method. The torsional response of the pipe pile is obtained based on the continuity conditions between the pile and both the outer and inner soil. The expressions of the complex impedance and velocity admittance at the pile head are obtained. The solution proposed in this paper is then compared with existing solutions to verify the validity. A parametric study is conducted to investigate the influence of the anisotropy of the outer and inner soil on the torsional vibration characteristics of the pipe pile.