分数导数模型描述的粘弹性土层中桩基水平振动研究

LATERAL VIBRATION OF SINGLE PILE IN VISCOELASTIC SOIL DESCRIBED BY FRACTIONAL DERIVATIVE MODEL

借助分数导数理论、粘弹性理论和土动力学理论建立了三维轴对称条件下分数导数粘弹性土层的水平振动控制方程,采用势函数和分离变量法求解了分数导数粘弹性土层的水平振动,得到了土层的水平动力阻抗。并借助于桩-土界面的连续条件和三角函数的正交性得到了分数导数粘弹性土层中单桩的水平动力阻抗。通过数值算例研究了桩土参数对分数导数粘弹性土层水平动力阻抗因子和土层中单桩水平动力阻抗的影响。研究表明:分数导数粘弹性土层的水平动力阻抗因子和分数导数粘弹性土层中桩顶水平动力阻抗可以退化为经典粘弹性和弹性土层的情况;桩土模量比对分数导数粘弹性土层中桩顶水平动力阻抗的影响与弹性情况存在较大差异。

The axisymmetric lateral vibration equations of the soil described by fractional derivative viscoelastic model are established by the theory of fractional derivative as well as viscoelastic and soil dynamics,and the lateral vibration of the soil described by a fractional derivative viscoelastic model is analyzed and obtained the lateral resistance of the soil by potential functions and separation of variables.The horizontal vibration equations of a single pile in soil are established,and the lateral dynamic impedance of the pile is obtained by considering the continuous conditions at the soil-pile and the orthogonality of trigonometric functions.The lateral resistance factor of the soil described by a fractional derivative viscoelastic model and the horizontal dynamic impedance of a single pile in soil are investigated with the numerical examples.The result indicated that the lateral resistance factor of the soil and the horizontal dynamic impedance of a single pile in soil described by a fractional derivative viscoelastic model can reduced to the cases of classic viscoelasticity and elasticity,the influence of the modulus ratio on the lateral dynamic impedance of the pile has great difference between fractional derivative viscoelastic and elastic soil.