基于传递矩阵法的层状土中管桩水平动力阻抗分析

Analysis of horizontal dynamic impedance of pipe pile in layered soils based on transfer-matrix formulation

在考虑土体分层特性的基础上,分别建立了管桩桩周土体和桩芯土体的水平振动控制方程。通过引入势函数并考虑桩周土和桩芯土径向位移和环向位移的边界条件及其奇偶性,求得了管桩-土动力相互作用的刚度系数和阻尼系数。将土体模拟为连续分布的弹簧-阻尼器,并考虑桩芯土和桩周土的作用,建立了层状土中管桩的水平振动方程。借助初参数法和传递矩阵法求解了管桩的水平振动,得到了管桩桩顶的水平动力阻抗。通过数值分析,得到了土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比、土层厚度等对管桩桩顶动力阻抗的影响规律。土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比对层状土中管桩水平振动的影响主要在低频处,土层厚度在较宽的频率范围内对管桩水平振动有影响;管桩壁越厚,桩周土的剪切模量越大时,管桩水平动力阻抗的绝对值越大。

The dynamic equations for the horizontal vibration of outer soil and inner soil of pipe pile are developed with considering the layered characteristics of soil. The stiffness and damping coefficients of pipe pile-soil dynamic interaction are obtained using potential function, boundary conditions and parity of the radial and circumferential displacements of outer soil and inner soil. The soil is simulated as a continuous-distribution spring-damper, and a horizontal vibration equation of the pipe pile is developed under the forces of outer soil and inner soil. The horizontal vibration is solved by the initial parameter method and the transfer-matrix method, and the dynamic horizontal impedance of pipe pile at pile head is obtained. The influences of shear modulus of soil layer, pipe pile wall thickness, outer and inner soil shear modulus ratio and thickness of soil layer on the dynamic impedance of pipe pile are obtained through numerical analysis. It is found that within the range of low frequency, the horizontal vibration of pipe pile in layered soils is mainly affected by the shear modulus of soil layer, pipe pile wall thickness and outer and inner soil shear modulus ratio, while the lateral vibration of pipe pile is influenced by the thickness of soil layer in a wide frequency range. As the thickness of the pipe pile wall and the shear modulus of soil around the pile increase, the absolute value of the lateral dynamic impedance of pipe pile increases.