分数阶三维积分型黏弹性土体中单桩的水平动力阻抗研究  

Horizontal dynamic impedance of single pile in viscoelastic soil described by Three-Dimensional Integral Constitutive Model

作　　者：姚庆钊[1] 刘林超[1] 闫启方[1] 

机构地区：[1]信阳师范学院土木工程学院,河南信阳464000

出　　处：《水利学报》2013年第7期835-841,847,共8页Journal of Hydraulic Engineering

基　　金：河南省科技发展计划项目(122300410309);河南省科技发展计划项目(112300410105);河南省教育厅自然科学研究计划项目(2011A1301001);信阳师范学院青年骨干教师资助计划(2012007)

摘　　要：基于土动力学、黏弹性理论和分数阶导数理论建立了分数阶三维积分型黏弹性土体水平振动控制方程。利用势函数对分数阶三维积分型黏弹性土体的水平振动方程进行解耦,借助分离变量法在频率内求解了分数阶三维积分型黏弹性土体的水平振动,得到了土体对单桩的水平作用,进而建立了分数阶三维积分型黏弹性土体中单桩的水平振动方程。考虑单桩的边界条件和桩顶水平动力阻抗的定义,求解了单桩的水平振动,并对桩顶水平动力阻抗进行了数值分析和讨论。研究表明:高频时,分数导数的阶数对水平动力阻抗有影响,土体黏性系数较小时水平动力阻抗实部和虚部随频率的变化曲线存在波动现象;长径比越大,水平动力阻抗越小,长径比达到一定程度时其对水平动力阻抗几乎没有影响。The lateral dynamic equations of viscoelastic soil described by fractional derivative threedimen sional integral constitutive relationship has been established based on soil dynamics, viscoelastic theory and theory of fractional derivative. The horizontal dynamic equations of the viscoelastic soil are decoupled by us ing potential functions, the lateral vibration of the viscoelastic soil is solved and obtained the horizontal force of the soil acting on the pile with the method of separation of variables, and the horizontal dynamic equation of the single pile in the viscoelastic soil is described by fractional derivative threedimensional in tegral constitutive relationship. The lateral vibration of the single is solved by considering the boundary con ditions and the definition of dynamic impedance of the pile at pile head, and the numerical analysis and discussion of the dynamic impedance of the pile is also investigated. The research indicates that the order of fractional derivative has effect on the dynamic impedance of the pile at pile head for higher frequency, and the curves of the real part and image part of lateral dynamic impedance varying with frequency have fluctuations when the soil viscosity coefficient is smaller; the larger the ratio of length to diameter, the smaller lateral dynamic impedance will be, and the ratio of length to diameter has almost no effect on the lateral dynamic impedance when it increases to a certain extent.

关 键 词：积分型本构方程 黏弹性 水平振动 动力阻抗 黏性系数 

分 类 号：TU573.12[建筑科学—建筑技术科学]