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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。
Considering the soil skeleton as a viscoelastic body with fractional derivative constitutive relation, a governing equation of steady state vibration of viscoelastic soil with spherical fractional saturated fractional derivative is established based on Biot two-phase saturated medium model. By introducing the potential function, the analytic expressions of displacements, stresses and pore fluid pressures of spherical viscoelastic soil with spherical fractional saturation fractional derivative under spherical symmetry are obtained. The effects of parameters such as fractional derivative model and saturated soil parameters on the soil vibration are investigated. The results show that the fluid compressibility has a significant effect on the dynamic behavior of saturated soils. However, the effect of soil compressibility and fluid-solid coupling coefficient is relatively The influence of fractional derivative order on the dynamic characteristics of soil is related to the value of material parameter ratio. Meanwhile, the dynamic response of saturated soil under undrained boundary conditions is greater than that of saturated soil under drainage conditions.