Pasternak层状地基中群桩水平动力响应解析解答

Analytical solutions for horizontal dynamic response for pile groups based on Pasternak model

基于Pasternak地基和Euler梁振动理论,提出了一种能考虑轴向荷载影响的单桩水平振动简化分析力学模型,建立了层状地基中桩-土耦合作用下单桩水平振动控制方程;采用微分变换的方法对方程解耦,进一步结合桩-土边界连续条件求出单桩水平位移、转角及内力解析解答。然后,考虑主动桩Ⅰ振动引起被动桩Ⅱ的动态位移,建立被动桩Ⅱ的水平振动控制方程,求解得到被动桩Ⅱ的响应解析解答,依据动力相互作用因子定义进一步求得桩-桩水平动力相互作用因子。最后,利用叠加原理求得群桩水平动力阻抗,并与已有相关解析解进行退化对比验证其合理性。在此基础上,通过参数化分析探讨了地基剪切系数、布桩类型、桩距径比、轴向特征参数对群桩水平阻抗以及桩顶反力分布、桩身内力分布的影响规律,可为实际工程群桩桩基设计提供理论指导和参考作用。

A simplified model for a single pile is established based on the Pasternak foundation and Euler beam models considering the axial second-order effects of pile shaft.The corresponding analytical solutions are derived by utilizing the differential transformation methods and the double-shear theory as well as the pile-soil continuity conditions.Then,considering the dynamic displacement of receiver pile II caused by the vibration of source pile I,the control equation for horizontal vibration of receiver pile II is established,and the analytical solutions for the response of receiver pile II are obtained.According to the definition of dynamic interaction factor,the pile-pile horizontal dynamic interaction factor is further obtained.Finally,the superposition principle is used to solve the horizontal dynamic impedance of pile groups,and its rationality is verified by comparing with the existing analytical solutions.On this basis,the influences of soil shear coefficient,pile type,pile to diameter ratio and axial feature parameters on the horizontal impedance of pile groups are discussed through the parametric analysis,and the distribution of the reaction force at the top of the pile and the distribution of the internal force of the pile body are discussed.It may provide theoretical guidance and reference for the design of pile groups in practical engineering.