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斜坡基桩水平动力响应解析解

Analytical Solution of Horizontal Dynamic Response of Pile in Sloped Ground
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摘要 随着江河岸边斜坡地段的桩基础日益增多,斜坡基桩桩-土水平耦合振动问题也日益受到重视.本文基于现有平地基桩水平动力响应理论,考虑斜坡效应,提出适用于斜坡基桩水平动力响应解析解.首先借助微分变换、亥姆霍兹分解和分离变量法等手段解耦土体三维波动方程,并引入桩-土边界连续条件,求解了平地基桩的桩周土体水平动抗力;在此基础上,引入折减因子考虑斜坡对临空面一侧土体抗力的弱化效应,并忽略一定深度范围内的浅层土体提供的水平动抗力,推导出斜坡段基桩的桩周土体水平动抗力解析解.此外,利用Euler梁模型推导斜坡段基桩自由段、入土段的水平振动控制方程,获得了基于传递矩阵法的基桩水平动力响应解析解,包括基桩动力阻抗以及桩身内力和变形解析表达式;然后通过与已有平地动力阻抗解析解,斜坡段基桩静力内力变形数值解进行对比,验证了本文解析解的合理性. As the pile foundations in slope areas near rivers are increasingly adopted,the problem of pile-soil horizontal coupling vibration of piles in slope foundations has also received mounting attention.Based on the existing theory of horizontal dynamic response of foundation piles in level ground,this paper proposes an analytical solution for the horizontal vibration response of foundation piles in sloped ground considering the slope effect.Firstly,by means of differential transformation,Helmholtz decomposition and separation of variables method,the three dimensional wave equation of soil is decoupled,and the continuous condition of the pile-soil boundary is introduced to solve the horizontal dynamic resistance of the surrounding soil of the foundation pile in the level ground.On this basis,the horizontal dynamic resistance of the soil around the foundation pile in the sloped ground can then be deduced by introducing a reduction factor to consider the weakening effect of the sloped ground on the soil resistance on the side of the free surface and ignore the horizontal dynamic resistance provided by the shallow soils within a certain depth;in addition,governing equations for the horizontal vibration of the free section and the submerged section of the foundation pile in the sloped ground is deduced based on Euler beam model;the analytical solutions of the horizontal vibration response of the foundation pile can then be obtained by the transfer matrix method,including the dynamic resistance of the foundation pile and the internal force and deformation of the pile shaft.The proposed solutions are verified by comparing with those existing analytical solutions of dynamic cases in the level ground and nu⁃merical simulations for static cases in the sloped ground in terms of internal force and deformation of the foundation pile.
作者 张玲 岳梢 刘亚楠 彭文哲 ZHANG Ling;YUE Shao;LIU Yanan;PENG Wenzhe(College of Civil Engineering,Hunan University,Changsha 410082,China;Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education(Hunan University),Changsha 410082,China;National International Joint Research Center for Building Safety and Environment(Hunan University),Changsha 410082,China)
出处 《湖南大学学报(自然科学版)》 EI CAS CSCD 北大核心 2022年第7期66-74,共9页 Journal of Hunan University:Natural Sciences
基金 国家自然科学基金资助项目(52078205,52108317) 湖南省自然科学基金资助项目(2020JJ3013) 创新平台与人才计划-湖湘高层次人才聚集工程-创新团队项目(2019RS1030)。
关键词 斜坡桩 三维波动效应 水平振动 解析解 pile in sloped ground 3D wave effect horizontal vibration analytical solution
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