中文摘要：

将土骨架视为具有分数阶导数本构关系的粘弹性体,采用Biot动力固结方程,在频率域内研究了饱和分数导数粘弹性土层的土骨架粘性、土层厚度等对竖向振动放大系数的影响。通过动力控制方程解耦和边界条件束缚,给出了经典弹性饱和土、分数导数型粘弹性饱和土和经典粘弹性饱和土三种情况下饱和土层的位移、应力和孔压解析表达式。考察了饱和土各物理和几何参数对竖向振动放大系数的影响,结果表明：在不同土层厚度时,经典弹性饱和土、分数导数型粘弹性饱和土及经典粘弹性饱和土的竖向振动放大系数各不相同;分数导数模型的材料参数对振动放大系数有较大影响。

英文摘要：

The soil skeleton is treated as a viscoelastic medium with a fractional derivative constitutive relation.By utilizing the Biot’s theory,the influences of the viscosity of soil skeleton and the thickness of soil layer for a saturated soil layer on the vertical vibration amplification coefficient are investigated in the frequency domain.By decoupling dynamic control equations and bounding the boundary conditions,the analytical expressions of the displacement,stress and pore water pressure for the saturated classic elastic,saturated fractional derivative viscoelastic soil and saturated classic viscoelastic soil are obtained.On the basis,the vertical vibration amplification of the soil layer is analyzed for different physical and geometrical parameters of the soil.It is shown that the vertical vibration amplification of the saturated classic elastic,fractional derivative viscoelastic saturated soil and saturated classic viscoelastic soil are different for the different thickness of soil layers;the material parameters of the fractional derivative model have great influences on the vertical vibration amplification coefficient.