考虑土体真三维波动效应时桩的振动理论及对近似理论的校核

从三维轴对称土体模型出发,同时考虑土体径向和竖向位移,对完整端承桩在垂直谐和激振力作用下与土的耦合振动特性进行了分析。假定桩为竖直弹性等截面体,土为线性粘弹性体,其材料阻尼为滞回阻尼。首先通过引入势函数对土体位移进行分解,将土体动力平衡方程解耦并求解,得到土层的振动模态形式和阻抗因子;然后利用该解以小应变条件下桩土接触面上力平衡和位移连续条件来考虑桩土耦合作用,求解桩的动力平衡方程,得到桩的频域响应解析解,进而得到土层局部复刚度和桩顶复刚度。从土层阻抗因子、土层局部复刚度和桩顶复刚度3方面,将所得解与平面应变解和其他忽略土体径向位移的简化解在主要影响参数变化情况下进行比较,研究表明,不同解在硬土、细长桩并处于低频时有较大差别,随激振频率的提高,它们将趋于一致。

THEORY OF PILE VIBRATION CONSIDERING TRUE THREE-DIMENSIONAL WAVE EFFECT OF SOIL AND ITS CHECK ON THE APPROXIMATE THEORIES

By modeling soil as a three-dimensional axisymmetric continuum and taking its radial and vertical displacement into account,the interaction between a soil layer and an integral end bearing pile undergoing vertical harmonic load is theoretically investigated. The pile is assumed to be vertical,elastic and of uniform cross-section, and the soil is considered as a linear visco-elastic layer with hysteretic type damping. With the aid of two potentials,the displacement of soil layer is decomposed and then its dynamic equilibrium equation is uncoupled and solved first. Thus the resistance factor and vibration modes of the soil layer are obtained and used to analyze the pile response. By considering the interaction between the soil layer and the pile with boundary condition of displacement continuity and force equilibrium at the interface of them,the dynamic equilibrium equation of pile is solved and an analytical solution for the pile response in frequency domain is yielded,which is used to define complex stiffness of the pile head and the soil local complex stiffness. When governing parameters are varying,a comparison is made with simplified solutions obtained at the condition of plane strain hypothesis or neglecting radial displacement. The comparison involves the soil resistance factor,the soil local complex stiffness and the complex stiffness of the pile head. It proves that in the case of low frequency,stiff soil and slender pile,there can be significant discrepancies between them,but with frequency increasing,the simplified solutions converge to the same.