考虑竖向荷载的Timoshenko模型桩水平振动响应解析解  

Analytical Solution for Horizontal Dynamic Response of a Timoshenko Pile Considering Vertical Loads

作　　者：余涛 王有昌[2] 

机构地区：[1]云南堃路道路桥梁工程咨询有限公司,昆明650200 [2]国家林业局昆明勘察设计院工程勘察所,昆明650216

出　　处：《科学技术与工程》2016年第26期103-114,共12页Science Technology and Engineering

摘　　要：考虑饱和土应力和位移沿深度的变化,将桩基等效为Timoshenko模型,对饱和土中竖向荷载作用下的端承桩水平振动响应进行了理论研究。基于Biot动力固结理论,通过引入势函数解耦土体方程。利用Laplace变换和分离变量法求得桩周土体频域响应解析解。考虑桩基的剪切变形和转动惯性效应,结合桩土接触连续性条件,得到桩体位移和桩顶动力复阻抗频域解析解。通过数值算例,比较了竖向荷载作用下Euler-Bernoulli模型与Timoshenko模型桩顶振动特性;并研究了长径比和竖向荷载对桩顶动力复阻抗的影响。结果表明:采用Euler-Bernoulli模型计算桩顶动力复阻抗偏于危险;长径比增大到临界值后,长径比对桩顶动力复阻抗影响较小;竖向荷载导致桩顶动力复阻抗突然降低,对桩基承载能力有不可忽视的影响。The horizontal dynamic response of an end bearing pile in saturated soil was investigated based on the Timoshenko Model. Variations of the soil stress and displacement along depth were taken into account in the derivation of soil equation solving. Potential functions were applied to decouple the equations of the soil based on Biot’ s consolidation theory. The analytical solutions of the soil in frequency domain were obtained by the Laplace transform technique and the separation of variables method. Displacements and complex impedances of the pile which consider the shear deformation and rotational inertial effect were derived based on the continuous conditions between the pile and the soil in frequency domain. Comparisons of vibrating characteristics were made between the EulerBernoulli Model and Timoshenko Model. Numerical examples were presented to analyze the influences of slenderness ratios and vertical loads on the complex impedances. The results showed that it is an insecure method to calculate the complex impedances based on the Euler-Bernoulli Model; the complex impedances show little variations when slenderness ratio reaches a critical value; the complex impedances would be decreased dramatically by vertical loads,which has a great influence on the pile capacity.

关 键 词：饱和土 Timoshenko模型 水平振动 动力复阻抗 解析解 

分 类 号：TU473.1[建筑科学—结构工程]