在频率域内用解析方法研究分析了简谐轴对称荷载和流体压力作用下分数导数黏弹性准饱和中球空腔的稳态响应问题.将土骨架等效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,通过势函数推导求得了边界部分透水时分数导数粘弹性准饱和土中球空腔的位移、应力和孔压等的解析解.根据界面连续性条件,确定了待定系数的表达式.在此基础上,考察了准饱和土各参数对动力响应的影响,结果表明:轴对称荷载和流体压力两种情况时,相对渗透系数对动力响应的影响有较大的差异.分数导数本构模型更合理地描述了准饱和土中球空腔的振动特性.%By using an analytical method in frequency domain, the steady state responses of a spherical cavity subjected to harmonic axisymmetric load or interior water pressure in nearly saturated fractional-derivative-viscoelastic soil were investigated. The soil skeleton was treated as a viscoelastic medium with fractional derivative constitutive relations. Based on Biot's theory, the analytical solutions to displacement, stress and pore water pressure of the spherical cavity in nearly saturated fractional-derivative-viscoelastic soil under the partial permeable boundary condition were obtained with deduction of potential functions. The expressions of the undetermined coefficients were derived based on the continuity conditions. On these basis, the dynamic responses of the spherical cavity in nearly saturated fractional-derivative-viscoelastic soil were analyzed with different parameters of soil. It was shown that the influences of the relative permeability coefficient on the dynamic responses have obvious differences between the conditions of harmonic axisymmetric load and interior water pressure; the vibration characteristics of the spherical cavity in nearly saturated soil are described more reasonably with the fractional derivative constitutive model.
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