基于群桩振动方程组的群桩基础阻抗函数求解及比较

Solution and Comparison of Impedance Function Based upon Piles Group Vibration Equations

本文首先在位移场叠加的基础上,对经典的单桩振动方程进行了修正得到群桩振动方程组;然后根据群桩振动方程组的近似求解,导出了群桩阻抗函数求解的常用方法一群桩阻抗方程方法。本文中给出的群桩阻抗方程方法在具体的表达形式上与常见的阻抗方程计算方法略有差别;而后根据振动方程组系数矩阵在复空间为正规阵的性质,提出了该四阶耦合微分方程组解耦求解的详细步骤,在直接求解微分方程组的基础上给出了群桩基础阻抗计算的一种新方法。与阻抗方程方法相比较,新方法未采用柔度因子来考虑桩与桩之间的相互影响,而是通过耦合的运动方程组对桩与桩之间的相互作用作了新的表述,并且近似地考虑了屏蔽效应。本文最后给出了上述两种计算方法的数值算例。

Based upon the displacement response superposition, the classical vibration equation of single pile was revised, and the piles group vibration equations were further proposed. The piles group impedance was obtained in accordance with the simultaneous equations. There are two aspects of this research having to be addressed. The first question involves that one approximate solution method, which leads to the impedance equations and the correspondent impedance solutions. In essence, the approximate solutions are the same as those of traditional approach but of different form. The second aspect relates to that a new solution approach was provided in accordance with the normal matrix characteristics relating to the coefficient matrix of the simultaneous equations. In this presentation, the uncoupling procedure on the simultaneous equations was deduced, in which the piles interaction was taken into account with the simultaneous equations instead of flexibility factor. Finally, the numerical examples were illustrated.