基于Timoshenko-Pasternak模型的多向受荷桩水平动力响应分析  

Horizontal dynamic response analysis of multi-directional loaded piles based on Timoshenko-Pasternak model

作　　者：江杰[1,2,3] 柴文成 欧孝夺[1,2,3] 付臣志 王顺苇 JIANG Jie;CHAI Wencheng;OU Xiaoduo;FU Chenzhi;WANG Shunwei(College of Civil Engineering and Architecture,Guangxi University,Nanning,Guangxi 530004,China;Key Laboratory ofDisaster Prevention and Structural Safety of Ministry of Education,Guangxi University,Nanning,Guangxi 530004,China;Guangxi Key Laboratory of Disaster Prevention and Engineering Safety,Guangxi University,Nanning,Guangxi 530004,China)

机构地区：[1]广西大学土木建筑工程学院,广西南宁530004 [2]广西大学工程防灾与结构安全教育部重点实验室,广西南宁530004 [3]广西大学广西防灾减灾与工程安全重点实验室,广西南宁530004

出　　处：《岩石力学与工程学报》2022年第1期172-185,共14页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家自然科学基金资助项目(52068004);广西自然科学基金资助项目(2018JJA160134);广西重点研发计划项目(AB19245018)。

摘　　要：为弥补传统动力Winkler地基梁模型在单桩水平动力响应分析中的不足,基于Timoshenko梁理论和Pasternak地基理论,建立同时考虑土体剪切效应和桩身剪切变形的Timoshenko-Pasternak模型。首先,从土体三维波动方程出发,借助微分变换解耦土体方程,利用分离变量法结合桩土边界连续性条件求解桩周土水平阻抗;在此基础上,利用Timoshenko-Pasternak模型推导单桩水平振动控制方程,运用传递矩阵法结合桩底边界条件得到桩顶动力复阻抗频域解析解。通过与已有模型解进行对比,验证该模型的正确性与合理性;最后,对桩身特征、桩周土体性质的参数进行分析。研究结果表明:(1)竖向荷载会对桩顶阻抗产生抑制作用,桩顶水平、摇摆动刚度均随竖向荷载增加而逐渐减小;(2)当单桩达到长径比临界值(L/d=10~15)后,桩底边界条件和桩长对桩顶阻抗几乎没有影响;(3)桩顶阻抗随桩土弹性模量比的减小而增大,且变化趋势愈发明显;同时,表层土的弹性模量对桩顶阻抗的影响要远大于下层土对其的影响。In order to remedy the deficiency of the conventional dynamic Winkler model in horizontal vibration analysis of single pile, a Timoshenko-Pasternak model is established based on the Pasternak foundation theory and Timoshenko beam theory,which considers both the shear effect of soil and the shear deformation of pile. Firstly,the differential transformation from the three-dimensional wave equation of soil is utilized to decouple soil equations,and separation variable method combined with continuity condition of pile-soil boundary is used solve the horizontal impedance of soil around pile. On this basis,the Timoshenko-Pasternak model is applied to derive the governing equation of horizontal vibration,and the analytical solution of dynamic complex impedance of the pile top in frequency domain is obtained by a transfer matrix method combining the boundary conditions at the pile bottom. The model is verified correct and reasonable by comparing with the existing model solutions. In addition,the pile characteristics and the properties of pile periphery soil are analyzed. The research results show that the vertical load can inhibit the impedance of the pile top. Meanwhile,the horizontal dynamic stiffness and the rocking stiffness of the pile top decrease gradually with increasing the vertical load. When the length of piles reaches the critical value of the aspect ratio( L/d = 10-15),the boundary conditions of the pile toe and the pile length have little effect on the impedance of the pile top. The impedance of the pile top would increase with decreasing the pilesoil elastic modulus ratio, and the influence of the elastic modulus of surface soil on the impedance of the pile top is much greater than that of undersoil.

关 键 词：桩基础 多向荷载 水平动力响应 层状地基 Timoshenko-Pasternak模型 桩顶阻抗 

分 类 号：TU473[建筑科学—结构工程]