基于分数导数理论的横观各向同性饱和黏弹性地基中大直径嵌岩桩的竖向振动  

Vertical vibration of a large-diameter rock-socketed pile in a transversely isotropic saturated viscoelastic soil based on fractional derivative theory

作　　者：李兴毓 陈曦菲 LI Xingyu;CHEN Xifei(Anhui Transportation Holding Group Co.,Ltd.,Hefei 230088,China;School of Traffic and Transportation Engineering,Changsha University of Science and Technology,Changsha 410114,China)

机构地区：[1]安徽省交通控股集团有限公司,安徽合肥230088 [2]长沙理工大学交通运输工程学院,湖南长沙410114

出　　处：《世界地震工程》2023年第3期227-238,共12页World Earthquake Engineering

基　　金：安徽省交通控股集团有限公司科技项目(JKKJ-2020-16)。

摘　　要：为探究各横观向同性饱和黏弹性土中大直径嵌岩桩的纵向耦合振动特性,基于Boer饱和多孔介质理论、分数导数黏弹性模型以及横观各向同性本构方程建立了u-p形式的横观各向同性饱和黏弹性土体动力控制方程组,并使用分离变量法求解得到桩侧土反力基本解。继而结合Rayleigh-Love杆模型建立了大直径黏弹性桩在横观各向同性饱和黏弹性土中的竖向振动方程,基于桩土相容条件和边界条件求解得到了桩顶竖向动力阻抗解析表达式,进一步通过Fourier逆变换得到了激振荷载为半正弦脉冲时桩顶的速度时域半解析解。通过将本文解与数值模拟和已有研究结果进行对比验证了本文推导的合理性。最后,通过数值算例分析了横观各向同性和黏性对桩基振动特性的影响。研究结果表明:土骨架的横观各向同性和黏性特性对桩基的振动特性具有显著影响。桩顶动力阻抗共振幅度以及速度响应反射波信号幅值随着土骨架横观各向同性比δ的增大而减小,而随着土体黏性参数比τ_(ε)/τ_(σ)以及分数导数阶数α的增大而增大。并且当δ较大或τ_(ε)/τ_(σ)及α较小时,不利于速度响应反射波信号的观测。从整体来看:土体横观各向同性及黏性特性对桩顶动力阻抗共振频率的影响较小。Vibration characteristics of a large-diameter rock-socketed viscoelastic pile embedded in a transversely isotropic saturated viscoelastic soil and subjected to a vertically harmonic-time load were investigated in present study.Upon the Boer′s balance equations of momentum and mass of porous medium,and introducing transversely isotropic constitutive relationship,and fraction derivative viscoelastic model for stress and strain to describe the anisotropy and viscous properties of the soil skeleton,respectively,the u-p type dynamic governing equations for the soil were obtained.By using the separation of variable method to solve the equations,the soil reaction on the pile side was gained.Then,treating the pile as a Rayleigh-Love rod,and combining the soil reaction,the vibration equation of the pile in the soil was established.The analytical solution for dynamic impedance at the pile head was deduced by solving the equation for the pile and according to the continuity and boundary conditions of the pile and the soil.The semi-analytical solution of velocity response of pile top subjected to half-sine exciting force was obtained by employing inverse Fourier transformation for the dynamic impedance.The validity of the solution was verified by comparing special case of our model with existing study.Effects of transversely isotropic and viscous properties of the soil on the pile vibration were discussed by parametric comparative analyses.The results show that the transverse isotropy and viscosity of the soil skeleton have significant influence on the vibration characteristics of the pile.The dynamic impedance resonance amplitude and velocity response of the reflected wave signal decrease with the increase of the transverse isotropy ratioδof the soil skeleton,but increase with the increase of the soil viscosity parameter ratioτ_(ε)/τ_(σ)and the fractional derivative orderα.Whenδis larger orτ_(ε)/τ_(σ)andαare smaller,it is not conducive to observe the reflected wave signal of the velocity response.On the whole,

关 键 词：桩 饱和土 振动 横观各向同性 分数导数黏弹性模型 Boer多孔介质模型 

分 类 号：TU435[建筑科学—岩土工程]