具有球形空腔饱和土分数导数 黏弹性土的动力特性

将土骨架视为具有分数阶导数本构关系的黏弹性体，基于Biot两相饱和介质模型，建立具有球形空腔饱和分数导数黏弹性土体稳态振动的控制方程。通过引入势函数，得到球对称情形下具有球形空腔饱和分数导数黏弹性土体的位移、应力和孔隙流体压力等解析表达式。考察分数导数模型参数和饱和土参数等对土体振动特性的影响，结果表明，流体压缩性对饱和土体的动力特性有显著影响，而土骨架压缩性和流-固耦合系数的影响相对较小；分数导数阶数对土体动力特性的影响与材料参数比的取值有关。同时，边界不排水条件下饱和土体的动力响应大于排水条件下饱和土体的动力响应。

Dynamic characteristics of saturated fractional derivative viscoelastic soil with a spherical cavity

Regarding the soil skeleton as a viscoelastic medium with fractional derivative constitutive relation, the governing equations of the steady state vibration of the saturated fractional derivative viscoelastic soil embedded a spherical cavity are established based on the Biot’s theory. The analytical expressions of the displacements, stresses and pore water pressure of the saturated fractional derivative viscoelastic soil with a spherical cavity are obtained with the introduction help of potential functions in case of spherical symmetry. The influences of the parameters of fractional derivative model and saturated soil on the vibration characteristics of the soil are examined; and the numerical results show that the fluid compressibility has a great influence on the dynamic characteristics; while the influences of the soil skeleton compressibility and fluid-solid coupling coefficient are trivial. The influence of the fractional derivative order on the dynamic behavior of the soil depends on the values of material parameter ratio. Furthermore, the dynamic responses of the saturated soil with undrained boundary condition are greater than those with the drained boundary condition.