轴对称横观各向同性土体中桩的扭转振动响应研究

摘要

基于单相弹性土体的运动方程以及横观各向同性材料的本构关系,研究了轴对称条件下端承桩在横观各向同性土体中的耦合扭转振动响应问题.在柱坐标下推导得到横观各向同性土体受谐和扭转荷载作用的动力控制方程,并采用分离变量法求得了土体扭转振动位移形式解.依据桩土接触面上的衔接条件,求解了桩身的动力平衡方程,并在频域内得到了桩身转角、扭矩和桩顶复刚度的解析解.最后分析了横观各向同性土体的力学参数对动力响应的影响.结果表明,横观各向同性土体的力学参数对桩顶复刚度、桩身转角和扭矩沿深度方向的变化均有着显著影响.%Based on dynamic equation of elastic soil and the stress-strain relationships of transversely isotropic material, the dynamic response of an end bearing pile embedded in a transversely isotropic soil is theoretically investigated. The dynamic governing equation of a linear elastic transversely isotropic soil undergoing axisymmetric torsional deformations is derived in cylindrical coordinates. By utilizing the separation of variables technique, the vibration displacement solution with an undetermined constant of the soil layer is obtained. With the continuity conditions of the interface of pile and soil, the solution is coupled into a one-dimensional governing equation of a pile. Then by using the boundary conditions of the pile-soil system, the twist angle and torque of the pile, and the complex stiffness of the pile head are defined in the frequency domain. Numerical results are obtained to analyze the influence of mechanical parameter of transversely isotropic soil on the response. It is shown that the mechanical parameter has obviously influence on the complex stiffness of the pile head, the variation of the twist angle and torque of the pile body along the depth direction.