考虑桩体剪切变形的分数导数黏弹性土层中单桩水平振动

Lateral Vibration of Single Pile in Viscoelastic Soil Described by Fractional Derivative Model Considering Shear Deformation

建立了分数导数黏弹性(FDV)土层的水平振动控制方程,在Novak平面应变假定的基础上,求得FDV土体的水平动力等效刚度和阻尼.利用等效Winkler动力弹簧-阻尼器模型描述桩基和土体之间的动力相互作用,将桩体简化为Timoshenko梁模型,在同时考虑桩体弯曲和剪切变形的情况下建立了单桩水平振动的控制方程,求得了考虑桩体剪切变形的FDV土层中单桩的水平动力阻抗,讨论了分数导数的阶数、土体本构模型参数和桩体剪力形状系数对桩顶水平动力阻抗的影响.研究表明:对FDV土层中单桩的水平动力阻抗,采用Euler梁模型和Timoshenko梁模型得到的结果存在较大差异;分数导数的阶数主要对桩顶水平动力阻抗随频率变化曲线的峰值有的影响;FDV土体本构模型参数Tσ/Tε越小,桩顶的水平动力阻抗越大.桩体剪力变形系数对桩顶水平动力阻抗有较大影响.

The lateral vibration equations of the soil described by fractional derivative viscoelastic model are established.The lateral dynamic equivalent stiffness and damping of viscoelastic soil described by fractional derivative viscoelastic model are obtained on the basis of assumed surface strain of Novak.The dynamic interaction between pile and soil is described by equivalent Winkler dynamic spring-damping model,and the pile is simplified as Timoshenko model.The formula of lateral vibration of single pile is established by considering bending and shear deformation.The lateral dynamic impedance of single pile in soil is obtained by considering shear deformation.The influences of fractional derivative order,soil constitutive model parameters and shear shape factor of pile on lateral dynamic impedance are then investigated.It is indicated through the research that the results of Euler beam model and Timoshenko beam model have great difference for the pile in viscoelastic soil.The fractional derivative order has influence on the peaks of curves of dynamic impedance versus frequency.The dynamic impedance of pile increases with the decrease of constitutive model parameters of the soil.The shear shape factor of pile has great effect on the dynamic impedance.