分数导数黏弹性模型描述的土中部分埋入单桩的扭转振动

TORSIONAL VIBRATION OF PARTIALLY EMBEDDED SINGLE PILE SOIL DESCRIBED BY FRACTIONAL DERIVATIVE VISCOELASTIC MODEL

桩周土体的本构关系利用分数导数黏弹性模型来描述,桩土扭转动力相互作用采用等效扭转Winkler弹簧-阻尼器来模拟,利用分离变量法得到了分数导数黏弹性土层的扭转等效Winkler弹簧-阻尼器模型的刚度系数和阻尼系数。利用传递矩阵法并考虑埋入部分及外露部分的边界条件求得了分数导数黏弹性土中部分埋入单桩的桩顶复刚度。以数值算例的形式讨论了分数阶黏弹性本构模型的模型参数和桩土参数等对桩顶扭转复刚度的影响。研究表明:分数导数的阶数对桩顶复刚度随频率变化曲线的峰值附近有一定的影响,桩的埋入深度和桩土模量比对桩顶复刚度有较大的影响,且埋入深度对桩顶复刚度的影响与外露部分的长度有一定的关系,本构模型参数对桩顶复刚度的影响较为复杂,本构模型的黏性项Tε较大时可能导致等效阻尼为负值。

The constitutive relationship of soil aroud pile was described by fractional derivative viscoelastic model, and the pile-soil dynamic torsional interaction was modeled by equivalent torsional Winkler spring-damper, and the stiffness and damping coefficients of equivalent torsional Winkler spring-damper model of fractional derivative viscoelastic soil were obtained with the method of separation of variables. By considering the boundary conditions, the torsional complex stiffness at pile head was also got by the transfer matrix method. It was investigated the influence of model parameters of fractional derivative viscoelastic model and the parameters of pile and soil on the torsional complex stiffness at pile head by means of numerical example. The result indicated that the order of fractional derivative had a certain effect on torsional complex stiffness, while, the influence of embedded depth of the pile and the modulus ratio on torsional complex stiffness was great, and the influence of embedded depth of the pile on torsional complex stiffness has a certain relationship of the length of the exposed part of the pile. The effect of constitutive model parameters on the pile stiffness was more complex, the equivalent damping would be negative when the viscous terms of constitutive model was large.